Advances in Catalysis and Related Subjects, Volume 12

ADVANCES IN CATALYSIS AND RELATED SUBJECTS

VOLUME XI1

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ADVANCES IN CATALYSIS AND RELATED SUBJECTS VOLUME XI1

EDITED BY

D. D. ELEY

P. W. SELWOOD

Nottingham, England

Evanston, Illinois

PAULB. WEISZ Paulsboro, New Jersey

ADVISORY BOARD

PETER J. DEBYE Ithaca, New York

P. H. EMMETT Baltimore, Maryland

E. K. RIDEAL

W. JOST Gottingen, Germany

H. S. TAYLOR

London, England

Princeton, New Jersey

1960

ACADEMIC PRESS, NEW YORK AND LONDON

COPYRWHTQ 1960, ACADEMIC PRESSINC. ALL RIaHTS RESERVED NO PART OF THIS BOOK MAY BE REPRODUCED I N ANY FORM, BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.

ACADEMIC PRESS INC. 111 FIFTH AVENUE NEWYORK3, N. Y.

United Kingdom Edition Published by ACADEMIC PRESS I N C . (LONDON) LTD. 17 OLDQUEENSTREET, LONDON S.W. 1

Library of Congress Catalog Card Number: 49-7766

PRINTED I N THE UNITED STATES OF AMERICA

Contributors T. B. GRIMLEY,Department of Inorganic and Physical Chemistry, University of Liverpool, Liverpool, England D. E. O'REILLY, Gulf Research & Development Company, Pittsburgh, Pennsylvania HERMAN PINES,The Ipatiefl High Pressure and Catalytic Laboratoqi, Department of Chemistry, Northwestern University, Evanston, Illinois

LUKEA. SCHAAP, Research and Development Department, Standard Oil Company (Indiana), Whiting, Indiana ROBERT A. VANNORDSTRAND, Sinclair Research Laboratories, Inc., Harvey, Illinois

TH.WOLKENSTEIN, Institute of Physical Chemistry, Academy of Sciences U.S.S.R., University of MOSCOW, MOSCOW, U.S.S.R.

D.J. C.YATES,Department of Colloid Science, University of Cambridge, Cambridge, England

* Now at the School of

Mines, Columbia University, New York, New York.

V

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Preface This volume will appear in print a t about the same time as numerous scientists from many countries meet together a t the Second International Congress of Catalysis, July 3 to July 9, in Paris, France. Both this meeting and the appearance of another volume of the Advances in Catalysis cause us to reflect on the unique nature of our field of interest. With colleagues from nearly all disciplines of the physical and life sciences, from nearly all nations and races, we find ourselves engaged in a common effort and quest for knowledge. We stand reminded that knowledge is the basic ingredient for creation of the things we may need or desire. How closely related the phenomenon of catalysis is to the rate at which we can create these things! As we give and exchange that knowledge which is the capacity for creation of what each of us may need or desire, perhaps we give and exchange the basic ingredient to peace on our planet itself. P. B. W. June, 1960

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Contents CONTRIBUTORS ........................................................ PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v vii

.

1 The Wave Mechanics of the Surface Bond in Chemisorption

BY T. B . GRIMLEY I . Introduction ......................................................... 1 I1. A Solid with a Free Surface ........................................... 3 I11. The Molecular Orbital Theory of the Surface Bond . . . . . . . . . . . . . . . . . . . 7 IV . Types of Surface Bonds ............................................... 19 V . Chemisorption on Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 VI . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 References ............................................................ 30

.

2 Magnetic Resonance Techniques in Catalytic Research

BY D . E . O’REILLY I . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

I1. Nuclear Magnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11. Electron Paramagnetic Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34 76 111 111

.

3 Base-Catalyzed Reactions of Hydrocarbons BY HERMAN PINESAND

LUKEA . SCHMP

I . Introduction .......................................................... I1. Isomerization ............................ I11. Side-Chain Alkylation of Arylalkanes . . . . ..................... IV . Nuclear Alkylation of Aromatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V . Alkylation of Alkylpyridines . . . . . . . . . . . . . . . . . . . . . . . . . . ........... VI . Reactions of Olefins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII . Conclusion ............................. ................. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117 126 139 140 141 146 147

.

4 The Use of X-Ray K-Absorption Edges in the Study of Catalytically Active Solids

BY ROBERTA . VAN NORDSTRAND I. Introduction .......................................................... I1. Origin of Fine Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I11. Experimental ......................................................... ix

149 150 154

CONTENTS

X

IV . Spectra of Known Compounds ........................................ V . Spectra of Catalysts .................................................. VI . Summary ............................................................. References ............................................................

156 180 185 187

.

5 The Electron Theory of Catalysis on Semiconductors BY TH. WOLKENSTEIN

I . Introduction .......................................................... 189 I1. Types of Chemisorption Bonds ............................. . . . 191 I11. Radical and Valence-Saturated Forms of Chemisorption . . . . . . . . . . . . . . . . 198 IV . Electron Transitions in Chemisorption .................................. 207 V . Catalytic Activity of a Semiconductor ................................. 215 VI . Interaction of the Surface with the Bulk of the Semiconductor . . . . . . . . . . 224 VII . Promoters and Poisons in Catalysis ............................... VIII . Factors Affecting the Adsorptivity and Catalytic Activity of a Semiconductor ........................................................ 241 I X . Chemisorption and Catalysis on a Real Surface . . . . . . . . . . . . .. 249 X . Conclusions .......................................................... 259 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

.

6 Molecular Specificity in Physical Adsorption

BY D . J . C. YATES 1. Introduction ......................... ...................... I1. The Perturbation of Solids by Adsorbed Molecules ..................... I11. Perturbation of Adsorbed Gases ....................................... IV . Over-all Changes a t the Solid-Gas Interface ............................

...................................... ..... ...................................... SUBJECT INDEX .............................................................. References ............................

265 266 284 290 307 308 313 321

The Wave Mechanics of the Surface Bond in Chemisorption T. B. GRIMLEY Department of Inorganic and Physical Chemistq, University of Liverpool, Liverpool, England

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. A Solid with a Free Surface.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111. The Molecular Orbital Theory of the Surface Bond.. . . . . . . . . . . . . . . . . . . A. The One-Dimensional Model.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Three-Dimensional Crystal. C. Bonding and Antibonding States.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page 1 3

12

14 19 . . . . . . . . . . . . . . . . . . 19 B. Bonds with Ionic Character.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 C. Metallic-Like Bonds. ................................. 22 V. Chemisorption on Semiconductors.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 A. Anionic Chemisorption on p-Type Semiconductors. . . . . . . . . . ..........l...............

IV. Types of Surface

................................................

...

B. Cationic Chemisorption on p-Type Semiconductors. . . . . . . . . . C. Anionic Chemisorption on n-Type Semiconductors. D. Cationic Chemisorption on n-Type Semiconductors.. . . . . . VI. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction An important problem in surface chemistry concerns the nature of the bond formed when an atom or molecule is adsorbed onto the surface of a solid. The magnitude of the heat of adsorption provides a rough guide to the sort of interaction to be expected. If the heat is low, say -5 kcal. mole-', we speak of physical adsorption and imply that the electronic structures of the solid and the adsorbate are not seriously modified when the two are in mutual interaction. If the heat is high, say, -50 kcal. mole-', we speak of chemisorption and imply that a change in the electronic structures does occur. This change may be drastic, as with H) and the transition metals where the gas is chemisorbed as atoms, or less obvious 1

2

T. B. QRIMLEY

as with CO on Pt and Pd, where the molecule is undissociated but only the order of the carbon-oxygen bond changes in going from the free to the chemisorbed state ( I ) . This article is concerned with chemisorption, and our main problemis t o discover how strong bonds might be formed between a solid and an adsorbate. This is a very difficult task. From the viewpoint of conventional valency theory, the solid is a giant molecule with free valence a t its surface. This free valence is taken up by the adsorbate in forming the chemisorbed species, and the activity of the surface is thereby extinguished. This is, of course, an oversimplification. The surface may still have a residual activity, perhaps towards a different adsorbate, because the original free valence a t the solid surface is partly transferred to the new surface composed of the chemisorbed species. If we are to attempt a discussion of the surface bond using these concepts, we require a detailed knowledge of the electronic structures of both the chemisorbed species and the solid with a free surface. Granted this knowledge, we might expect to understand the surface bond in terms of the shapes and manners of occupation of the orbitals of the solid and the adsorbate. We know, however, from our experience in similar discussions of the binding of an atom in a molecule, that the concept of the valence state of the atom in the molecule is very important. The valence states of an atom are certain hypothetical excited states formed by linear superposition of the ground state and one or more excited states. Now in the solid metals the excited states are quasi-continuous from the ground state upwards. Hence, the possible valence states of the metal for chemisorption are also quasi-continuous, and this method of approach to the problem is not, therefore, very useful. It might be used for insulators, and even for semiconductors, but in general it seems better to adopt the molecular orbital approach. In this method we look at the outset for the one-electron wave functions and energies of the system-solid plus adsorbed species as a whole. In this way, the existence of quasi-continuous bands of energy levels in the solid is fed into the problem a t the beginning and does not have to be faced explicitly later on. There exists a powerful mathematical technique for handling this and similar problems (2, S),by which the solution is made to depend upon a knowledge of the electronic structures of the adsorbed species and of the solid with a free surface when interactions between them are ignored. It appears, therefore, that it will be impossible t o develop a general theory of chemisorption without first treating the problem of the electronic structure of a solid with a free surface. Normally, when we speak of the electronic structure of a solid, we mean only those features which are independent of the conditions existing a t any free surfaces or interfaces. In the next section we illustrate in the

THEl SWFAm BOND

3

simplest manner possible the new features which arise when a free surface is introduced.

II. A Solid with a Free Surface Little theoretical work has been done on the electronic structure of a solid with a free surface. The main contributions are those of Tamm (4), Shockley (6),Goodwin (6),Artmann (7)) and Kouteckg (8))and the main conclusion is that, in certain circumstances, surface states may exist in the gaps between the normal bands of crystal states. In this section we investigate the problem in the simplest way. The solid is represented by a straight chain of similar atoms, and its two ends represent the free surfaces. This onedimensional model exhibits the essential features of the problem, and the results are easily generalized to three dimensions. Starting from one end, let the atoms in the chain be numbered 0, 1, . . . , N . Associated with each atom m we introduce a n atomic orbital +(r,m), and assume that any wave function $(r) for the chain can be written as

W )=

c

40.) m>c(m).

(1)

m

If X is the effective one-electron Hamiltonian operator for the chain, $(r) satisfies the equation X# = E$. (2) Substituting Equation (19 into Equation (2) and neglecting overlap between the atomic orbitals, we arrive at the usual system of linear equations

n

for the wave-function coefficients c(m) and the energies E. I n Equation (3) we have H(m, n) = J+*(r, m ) x + ( r , n) dr. Now put H ( m , m ) = a, m # 0, H ( 0 , 0 ) = a’, H(m, m f 1) = 8,

and neglect all other matrix elements of X. Thus, we include only the resonance integral between nearest neighbors and take account of the existence of the free surface at m = 0 by changing the Coulomb integral from a to a’ on this atom. These are the usual approximations of the “tight binding” method. Equation (3) now gives

4

T. B. GRIMLEY

+ 1) + c(m - l)],m # 0,

( E - a)c(m) = B[c(m

(4)

with the boundary condition

( E - LY’)c(O) = @(l).

(5)

We still have to apply a boundary condition at the other end of the chain (m = N ) . If N is large, this boundary condition cannot affect the conditions near m = 0 in any important way, and we shall assume that c(N) = 0. This defines the problem as that of the electronic structure of a chain with one free end a t m = 0. The solution is

c(m) = sin ( N

- m)e,m = 0, 1, . . . N .

(6)

This satisfies the boundary condition a t m = N . It satisfies Equation (4) if

E

=a

+ 28 cos e,

(7)

and the boundary condition, Equation (5), if 0 is one of the N roots of the equation z cos 0 sin 0 cot NO = 0, (8) with

+

+

2

= (a

- a’)//%

(9)

Equation (8) has a t least N - 1 real roots. According to Equation (6), the corresponding wave functions are periodic, and if we write E’ = (E - a)/2B, then, according to Equation (7), the energy levels lie in the range

< E’ < 1.

-1

(10)

These are nonlocalixed states, and Equation (10) defines the familiar band of levels (width 4lBl) arising from the single state $ ( T ) of the isolated atoms. The remaining root of Equation (8) may also be real, in which case the energy also lies in the band, and the chain has only nonlocalized states. On the other hand, if IzI > 1 N-1, the remaining root has 6 of the form it or a it, with [ real and positive. The corresponding wave functions are damped in the c h i n as we move away from the end atom. These are localized states associated with the free end at m = 0. Their energies lie outside the normal band of levels defined by Equation (lo), and we shall refer to them as end states. A state with 0 = it has E’ positive and will be denoted by 6 ;a state with 0 = a it has E’ negative and will be denoted by 3t. From Equation (S), a 6 state exists if

+

+

+

- z = cosh t

+ sinh

coth N&,

and since N is large, we may take this condition as - z = exp

t

(5: > 0 ) ,

6

THE SURFACE BOND

so that a 6 state exists if z < - 1. [The exact condition is z The wave function and the energy are given by

44 E

< - (1 + N-I)].

= 4 0 ) exp ( - m O , = a! 2/3 cosh t.

+

For an X state, z = exp [ if N is large, so that such a state exists if z The wave function and the energy are given by

> 1.

c(m) = c(0)(- 1)" exp (-mE), E = a - 2/3 cash [.

The situation may now be summarized, assuming for definiteness that + ( T ) had the symmetry of atomic s-states.] When z = 0, the chain has N nonlocalized states with a band width 41/31.As z decreases (chain end electron attracting), the energies of all these states decrease (but only by small amounts, the maximum decrease being proportional to N-I), until at z = - 1 an end state of type 6 separates below the band. There are now only N - 1 nonlocalized states in the band. As z decreases further, the 6 level falls further below the bottom of the band, and its wave function becomes more and more concentrated on the end atom. As z 3 - co , the wave function for the 6 state degenerates to the atomic orbital $(r, 0) centered on the end atom, and the wave functions for the nonlocalized states are zero on the end atom. As z increases above zero (chain end electron repelling), the energies of all the states in the band increase slightly, until a t z = 1 an end state of typo 92 separates above the band. Its energy increases steadily with z , and its wave function becomes more concentrated on the end atom. Again, the wave function for the end state degenerates to +(r, 0 ) ,and the amplitudes of the N - 1 nonlocalized states on the end atom fall to zeio as z + a. The three-dimensional crystal can be treated by a straightforward generalization of the method outlined above (6). A simple cubic lattice is defined by three integers (ml, m2, m3),which take the values 0, 1, . . . , N . A free (100) surface is defined by the plane ml = 0, and the Coulomb integral is changed from a to a' for all atoms in this plane. The wave functions are assumed to vanish on the other five surfaces of a cube. The wave function coefficients are given by

B < 0. [This would be the case if the orbitals

c(mlm2m3)= sin (N

- ml)& sin m202sin m&,

with e2 = k2r/N, k2 = 1, 2, . . . , N , and O3 = k3r/N, k, = 1 , 2 , . . . , N , while el is one of the N roots of Equation (8).The energy levels are given by

E

=a

+

el + cos e2 + cos e,).

~ ~ ( C O S

The essential features of the onedimensional problem are therefore re-

6

T. B. GRIMLEY

tained. The only difference is that the discrete end state which exists in the onedimensional case when IzI > 1 now appears as a band of surjace states of width SIP1 and containing N 2levels. N 2 levels are, of course, missing from the normal band of crystal states. If IzI is not too large, the surface band overlaps the normal crystal band, but when Iz[is large, the two bands are quite separate, and the amplitudes of the normal crystal states become vanishingly small on the surface atoms. This situation is interesting because i t means that as far as its external interactions are concerned, the crystal behaves like a twodimensional array of atoms whose electronic structure is described by the band of surface states. So far we have assumed that the electronic structure of the crystal consists of one band derived, in our approximation, from a single atomic state. In general, this will not be a realistic picture. The metals, for example, have a complicated system of overlapping bands derived, in our approximation, from several atomic states. This means that more than one atomic orbital has to be associated with each crystal atom. When this is done, it turns out that even the equations for the onedimensional crystal cannot be solved directly. However, the mathematical technique developed by Baldock (8) and Koster and Slater (3)can be applied (8) and a formal solution obtained. Even so, the question of the existence of otherwise of surface states in real crystals is difficult to answer from theoretical considerations. For the simplet3t metals, i.e., the alkali metals, for which a oneband model is a fair approximation, the problem is still difficult. The nature of the difficulty can be seen within the framework of our simple model. I n the first place, the effective one-electron Hamiltonian operator is really different for each electron. If we overlook this complication and use some sort of mean value for this operator, the operator still contains terms representing the interaction of the considered electron with all other electrons in the crystal. The Coulomb part of this interaction acts in such a way as to reduce the effect of the perturbation introduced by the existence of a free surface. A self-consistent calculation is therefore essential, and the various parameters in our theory would have t o be chosen in conformity with the results of such a calculation. With ionic crystals, there are some rather interesting possibilities. A large part of the perturbation which a free surface introduces is associated with the change in the electrostatic environment of an ion in going from the interior to the surface. If the normally filled valence band is associated with the anions (as is the case with the alkali halides and with certain n-type semiconducting oxides), the surface perturbation acts in the direction of producing a band of surface states with its center lying above the center of the normal anion band. This anion surface band will normally be completely filled. Conversely, for the normally empty cation band (the

7

THE SURFACE BOND

conduction band) the surface perturbation acts in the direction of producing a surface cation band with its center lying below the normal cation band. Thus, the surface electronic structure shows a narrower gap between filled and vacant bands than that characteristic of the bulk structure. It is possible, therefore, that there is an intrinsic surface semiconductivity or even a metallic-like surface conductivity if the surface anion and cation bands overlap each other. Correspondingly, homopolar binding will be more important in the surface region. Effects of this sort are obviously important in the theory of chemisorption; we note, however, that this simple anioncation band picture is not adequate for the transition metal oxides.

111. The Molecular Orbital Theory of the Surface Bond The basic problem in the molecular orbital theory of chemisorption is to find the one-electron wave functions (molecular orbitals) and energy levels for the whole system-solid plus adsorbed species. Knowing these, we could then calculate the energy of chemisorption. So far, the theory has not been taken to the stage of an energy calculation for even the simplest case of practical interest. Enough is now known, however, about the general problem to enable a review to be given of the types of surface bonds which can arise, although little is known about the nature of the surface bond in individual cases. We begin by considering a onedimensional model in which the crystal is represented by n straight chain of similar atoms and a foreign atom is in interaction with one end of the chain. This is the simplest model of the chemisorption process which may be expected to yield useful results (9). If the normal electronic structure of the chain consists of just one band, this onedimensional model is easily treated in the “tight-binding” approximation. A. THEONE-DIMENSIONAL MODEL Let the atoms in the chain be numbered 0, 1, . . . , N , and let the foreign atom be denoted by X (Fig. 1).Associated with each atom we introduce an atomic orbital +(r, m).These orbitals are divided into two sets. One set (m = X) contains only one member, which is the orbital on the foreign atom; the other set (m = 0, 1, . . , N ) consists of the orbitals on the “crystal” atoms. Thus, we have the problem of the interaction of a hydrogen-like atom with a crystal whose normal electronic structure consists of just one band of states.

.

a A

o

o

o

*

*

0 I i Fro. 1. One-dimensional model for chemisorption.

o N

8

T. B. GRIMLEY

Any wave function for the system is expressed as $(T)

=

144.)

m>c(m>,

m

and neglecting overlap between the atomic orbitals, we arrive a t a system of linear equations like those in Equation (3), except that X is now the oneelectron Hamiltonian operator for the whole system, chain plus foreign atom. We make the same assumptions about the matrix elements of X that we made in Sec. 11, and in addition we put H(X,A) = a”, H ( 0 , A) = H(X, 0 ) = 8’.

Thus, the foreign atom is characterized by having a different Coulomb integral a)’from the crystal atoms, and we take account of its presence a t the end of the chain by changing a to a’ on the end crystal atom (m = O ) , and by changing j3 to 8’ between the foreign atom and the end crystal atom. We now have Equation (4) to solve with the boundary conditions

+

( E - a’)c(O) = 8 c ( l ) B’c(A), (E - a”)c(X) = B‘c(0).

As in Sec. 11, we assume that the wave functions vanish a t the end of the chain (m = N ) remote from the foreign atom. If N is large, this boundary condition cannot affect the conditions near m = 0 in any important way. Introducing the dimensionless quantities z = (a - a’)//3, Z’ = (a - a’’)/j3, 9 = @’/a, E’ = (E - c~)/28

gives the solution c(m) = sin ( N - m)O, m # A, c ( X ) = 7 sin Ne/(.d 2 cos 0).

+

1

(11)

The energy levels are given by

EI = cos e,

+ 1 roots of the equation (z + cos e + sin e cot N e ) ( d + 2 cos 0)

and 0 is one of the N

= q2.

(12)

Equation (12) has at least N - 1 real roots. The corresponding wave functions are nonlocalized, and the energies lie in the range defined by Equation (10). This is the normal band of crystal states. The remaining two roots may both be real, and in this case they also lie in the normal crystal band, and the system has only nonlocalized states. On the other hand, one or both of the remaining roots may have values of 0 of the form i# or r it with # real and positive. The corresponding wave functions

+

9

THE SURFACE BOND

are damped in the crystal. These are localized states associated with the foreign atom and the crystal atoms near the “surface.” Their energies lie outside the normal band of crystal states, and their existence allows for the formation of localized covalent bonds between the foreign atom and the crystal. Again we denote localized states by 6 or 37. according to whether E‘ is positive or negative. When N is large, the eigenvalue condition, Equation (12) for 6 states is (z

+ exp t)(z’ + 2 cosh l ) = q2,

(13)

and the wave-function coefficients are given by c(m) = exp c(X) = q/(z’

(-mi), m # A, 2 cosh E),

+

and the energy by E’ = cosh [. For 37. states, the corresponding equations are ( z - exp [)(2’ - 2 cosh E) = q2, (15) c(m) = (- 1)” exp ( - m [ ) , m # A,

c(X) = T / ( Z ’

- 2 cash E),

}

(16)

with E‘ = -cosh E. The wave-function coefficients given by Equations (14) and (16) are not normalized. We now investigate how the occurrence of localized states is governed by the values of the parameters z, z’, and q which define the interaction between the foreign atom and the crystal. Localized states exist if either one or both of Equations (13) and (15) have real roots [. Real roots exist for given q in regions of the 22’-plane defined by the two hyperbolas (2

f l)(z’ f 2) =

92.

(17)

These are plotted in Fig. 2 for 12 = 1. Localized states occur in the six regions indicated. P2means that there are two 6 states, 6% that there is one 6 state and one 51 state, and so forth. We see that the system may have two or one or no localized states. The area of the region where there are no localized states decreases as q2 increases, and such a “forbidden region” exists only if q2 < 2. The maximum number of localized states which can be formed is two. This result depends on our assumptions that only one orbital on the foreign atom and only one band of crystal orbitals are in interaction and that the perturbation of the crystal by the foreign atom does not extend beyond the first crystal atom. If we extend the perturbation (i.e., modify the Coulomb integrals) to the first and second crystal atoms, we find a maximum of three localized states. In general, the maximum number of localized states

10

T. B. QRIMLEY

2’

FIQ.2. The occurrence of localized statea for r)’

= 1.

is equal to the sum of the number of orbitals on the foreign atom, the number of crystal atoms perturbed, and the number of bands of crystal states. Thus, the theory allows for the formation of surface bonds with multiple-bond orders. It is clear, therefore, that the simple onedimensional model contains many features of the general chemisorption problem, and because of this, it merits a rather full discussion. Before doing this we consider briefly the generalization to a threedimensional crystal.

B. THREE-DIMENSIONAL CRYSTAL When we consider the interaction of a foreign atom with the free surface of a threedimensional crystal, it turns out that the difference equation [Equation (4)] and the corresponding boundary conditions cannot be solved directly. However, the technique developed by Baldock (2) and Koster and Slater (3) is applicable (9, 10, 11).To use this method, we need the one-electron wave functions and energy levels of the crystal with a free surface, this free surface being the one a t which chemisorption is to take place. As we have already indicated in Sec. 11, our knowledge of these quantities is very inadequate, and if we are t o proceed very far with the chemisorption problem, we are committed, more or less, to the “tightbinding” approximation once again. This is a poor approximation for all metals. Results obtained (9) by applying this method show that, if the pertur-

11

THE SUBFACE BOND

bation of the crystal by the foreign atom extends only over a group s2 of crystal atoms, then, depending on the values of the interaction parameters, there may be localized states associated with the foreign atom and the group s2. The wave functions for these states fall to zero a t points in the crystal remote from the group 3, and the corresponding energies lie outside the normal bands (including any surface bands) of crystal states. The maximum number of localized states which can be formed is the sum of the number of orbitals on the foreign atom, the number of atoms in 3, and the number of bands in the crystal. The essential features of the onedimensional problem are therefore retained. The strict generalization of the onedimensional model treated in Sec. II1,A leads to a crystal with its surface completely covered by adsorbed atoms. For this system, the tight-binding approximation gives a difference equation and boundary conditions which can be solved directly. The results show an important new feature. For a simple cubic lattice, the energy levels are given by the usual equation

E

=

+ ~ ~ ( CelO+Scos ez + cos e,).

(18)

When a (100) surface is completely covered by foreign atoms, Oz = k g / N , kz = 1, 2, . . . , N , and 63 = k n / N , k3 = 1,2, . . . , N , but is any root of the equation [Z

+ cos el + sin el cot Nel][z’+ 2(1 - q’)(cos ez + cos e,) + 2 cos el] =

92.

(19)

The interaction parameters z, z’, and q are defined in the usual way, and p“/& where 8“ is the resonance integral between nearest neighbors in the adsorbed layer. If q’ = 1, the eigenvalue condition, Equation (19), is the same as for the onedimensional model. The only change is that the discrete localized states (6 and 3t) of the onedimensional model now appear as bands of surface states (6or 3t bands) associated with the adsorbed layer and the crystal surface. At most, two such bands may be formed, and each band contains N 2 levels. This is the number of atoms in the adsorbed layer. Depending on the values of the interaction parameters z and z’, these bands may or may not overlap the normal band of crystal states. All this was to be expected, and Fig. 2 gives the occurrence of 6 and ,3tsurface bands when q2 = 1. It is when q‘ # 1 (and this will be the usual situation) that a new feature arises. In this case, the second term in the second bracket in Equation (19) does not vanish, and the eigenvalue condition is not the same as in the onedimensional model. In fact we have z‘ 2(1 - q’)(cos 02 cos 0 3 ) in place of z’, and this varies between z’ 4(1 - q’) and z’ - 4(1 - q’). We can still use Fig. 2 if we remember that z’ varies between these two limits. Then if, for example, this variation q’ =

+ +

+

12

T. B. GRIMLEY

takes us from the 6 region into the forbidden region, we do not get a complete band of 6 states containing N a levels. The missing states lie in the normal band of crystal states and are no longer localized in the direction perpendicular t o the surface. Of course, the variation in 2’ may be sufficient to take us from the 6 region, through the forbidden region, and into the 3t region. In this case, there is an incomplete 6 band and an incomplete 32 band, the total number of levels in both bands being less than N2.If (21 is not too small (certainly if 121 > l), the variation of z’ never takes us into the forbidden region in Fig. 2. In this case, there are always a t least N 2levels of some sort (either 6 or 3t) in the surface bands. There may be, for example, an incomplete 6 band and a complete 3t band. Other possibilities are easily seen from Figure 2. These observations may be extremely important in the theory of chemisorption. Assume (and this is not yet established) that chemisorption must involve the localization of a pair of electrons between the foreign atom and the crystal surface. Then we require a localized state with energy lying below the normal crystal band. Assume for definiteness that such states are 6 states, then the 32 states lie above the band. For complete surface coverage, we would need a complete band of surface 6 states. But in view of what has been mid above, this may be impossible. It appears, therefore, that there is a mechanism here, not only for a falling heat with surface coverage as is observed with H2 on the transition metals, but also for the existence of fractional surface coverages a t saturation as with N2 on the transition metals ( I d ) . I n the former case, the missing 6 states would be in the normal crystal band; in the latter, some would actually be 3t states with energies lying above the normal band. It is important to realize that these effects occur even when P” = 0, so that there is no direct interaction between the atoms in the chemisorbed layer. The important interaction occurs through the crystal by a delocalization of the bonding electrons in directions parallel to the surface. A more detailed study of this effect is needed, and we shall return t o it again in Sec. II1,D.

C. BONDING AND ANTIBONDING STATES For the onedimensional model of Sec. III,A, we have seen that there are two types of discrete states associated with the foreign atom and the crystal “surface.” These have been referred to as 6 and 3t states. Their location with respect to the normal crystal band depends on the sign of the resonance integral 8. If B is negative, as it would be if the normal band were an s band, the 6 states lie below the band and the 3t states above it. We refer to the former as bonding states and to the latter as antibonding states. The wave functions for bonding states are smoother than those for antibonding states, the latter having nodes between successive crystal atoms because of the factor (- 1)”in Equation (16).

13

THE SURFACE BOND

If the normal band is a p , band (z-axis along the chain), we expect /3 to be positive. In this case, the 37. states are bonding and the 6 states antibonding, but because of the symmetry of the atomic p state, it is still the wave functions for the antibonding states which have the extra nodes between successive crystal atoms. In Table I we summarize the bonding states for a foreign atom and a chain. The z axis is taken along the chain, and the symmetry symbols u and ?r used to describe the orbitals of diatomic molecules are applicable. u states are axially symmetric, ?r states have a nodal plane passing through the z axis. The classification of Table I also holds for a three-dimensional crystal if the foreign atom is adsorbed directly over a surface crystal atom, and the perturbation extends only to this crystal atom. It is possible, however, that the foreign atom is adsorbed over a subsurface crystal atom, for example a t the center of a face on a (100) surface of a body-centered cubic crystal. In this case, the perturbation would have to be taken over four or even five crystal atoms, and the classification of Table I no longer holds. With extended perturbations of this sort, the general effect is that almost any crystal band is in direct interaction with the orbital on the foreign atom. TABLE I Bonding Slates for a Foreign Atom and a Chain Foreign atom orbital

Chain band

Bonding state

D. INTERACTIONS BETWEEN CHEMISORBED ATOMS By considering the extreme case of a crystal completely covered by a layer of foreign atoms, we have already seen in Sec. II1,B that, if chemisorption involves the formation of localized electron pair bonds, some interesting interaction effects are to be expected. In this section, we approach the problem from the other extreme by considering just two atoms chemisorbed on a crystal surface. If the localized level formed by the interaction does not lie too far below the normal crystal band (or any surface band), the wave function for the localized level is damped only slowly in the crystal. Therefore, two chemisorbed atoms will be in interaction a t distances when the interaction between the isolated atoms would be entirely negligible. To investigate this effect, we take the simplest model which may be expected to yield useful results (11).The crystal is represented by a straight,

14

T. B. GIUMLEY

chain of similar atoms, and two foreign atoms are in interaction with i t at two points along the length of the chain (Fig. 3). Let the chain atoms be numbered by an index m (-N m N ) , and let the two foreign atoms X and jt be in interaction with the chain at positions +n and -n. The wave functions for the system are either even or odd in the center of symmetry at the chain atom number 0. It is sufficient, therefore, to consider the range m 0. I n the tight-binding approximation, we now have Equation (4) for all m # n with the boundary conditions

< <

>

+ + c(n - l)]+ a’c(x)J

(E - a’)c(n) = B[c(n 1) (E - CZ”)C(X) = B’C(~).

is changed to a’ on the chain atom n and t o a’’on the foreign atom A, while 8’ is the resonance integral between n and A.

(Y

-n

-N

0

*

0

-I

*

0

0

0

n

I

0

*

N 0

’

0

0

0 P

A

FIG.3. The model for two chemisorbed atoms.

1. Even States.

The solution is c(m) = cos me, m 6 n, c(m) = [cos ne/sin ( N - n)e] sin

(N

- m)e, m 3

n,

with E’ = cos 0 and 0 any root of the equation (z

+ sin e[cot ( N - n)e - tan no]) {z’ + 2

COB

0 ) = 72.

(20)

2. Odd States.

The solution is

c(m) = sin me,m 6 n, c(m) = [sin ne/sin ( N - n)e] sin ( N - m)e, m

3 n,

with 0 any root of the equation [Z

+ sin e[cot ( N - n)e + cot ne])(z’ + 2 cos e) = q2,

(21)

Exactly as in Sec. IIIJAJone or both of Equations (20) and (21) may have a root with e of the form it or r it with [ real and positive. These are localized states associated with the crystal surface and both foreign

+

15

THE SURFACE BOND

atoms. States with 0 = it will again be referred to as 6 states, those with 0 = ?r it as SI states. 6 states are bonding if p < 0. If N - n is large, so that end effects can be neglected, the eigenvalue condition for even 6 states is

+

[z

+ sinh t(1 + tanh n[)](z’+ 2 cosh t ) = v2.

(22)

The wave-function coefficients are

< + +

c(m) = cosh m.$ m n, c(m> = M e x p 2nt 1) exp ( - - m t ) , m c ( X ) = r] cosh nf/(z’ 2 cosh t ) ,

3

n,

}

(23)

and the energy is given by E’ = cosh t. For the odd 6 states, the eigenvalue condition is [z

+ sinh E ( l + coth nt)](z’ + 2 cosh t ) = qa

(24)

and the wave-function coefficients are

< n, - 1) exp ( - m [ ) , sinh ng/(z’ + 2 cosh 5).

c(m) = sinh m5,m c(m) = s ( e x p 2nE c(X) =

r]

m

3

n,

1

(25)

The energy is again given by E’ = cosh 5. The equations for even and odd 3t states are easily derived, but we do not need them if we assume that 6 states are bonding. As n 00 , Equations (22) and (24) both degenerate to

-

(z

+ 2 sinh t)(z’ + 2 cosh t )

= q2.

(26)

This is the eigenvalue condition for the 6 states formed when there is only one foreign atom interacting along the length of the chain. A maximum of two such states can be formed, and their occurrence in the &-plane is shown in Fig. 4 for q2 = 1. As before, P2 means that two 6 states exist. The occurrence of SI states is not shown, but this information is easily added. If this is done, it turns out that localized states are formed for all values of the interaction parameters. Now this is not always the case for a single atom on the surface of a threedimensional crystal (9),and the model which we are using in this section to investigate interaction effects will be inadequate on this account. We return now to the case of two foreign atoms on the surface separated, in our model, by 2n interatomic distances. It is easy to see from the eigenvalue conditions of Equations (22) and (26) that, if there is a single 6 state for one atom on the surface, there is always an even 6 state when two foreign atoms are present, and that if there are two 6 states for one

16

T. B. GRIMLEY

FIQ.4. The occurrence of localized 8 states for one chemisorbed atom.

FIQ.5. The occurrence of odd 6 s t a h for two chemisorbed atoms with n = 1. The broken curves are those of Fig. 4.

THE SURFACE BOND

17

foreign atom on the surface, there are two even 6 states when two foreign atoms are present. The energies of the even 6 states lie below those of the corresponding 6 states for a single atom on the surface, and their energies fall lower as n decreases. The odd 6 states for a pair of atoms on the surface lie above the corresponding 6 states for a single atom on the surface, and their energies are forced higher as n decreases. In contrast with the situation for the even states, it turns out that, for finite values of n, the eigenvalue condition, Equation (24), does not always give an odd 6 state in the 6 region in Fig. 4 and does not always give two odd 6 states in the S2region. The diagram showing the occurrence of odd 6 states for n = 1 (i.e., for a pair of atoms adsorbed on next-nearest neighbors is shown in Fig. 5 for q2 = 1. The broken curves are those of Fig. 4 for a single atom on the surface. In the region A between the two curves, there is no odd 6 state for a pair of atoms with n = 1, although a 6 state exists if only one atom is present. In the region B, there is only one odd 6 state for a pair, although there are two 6 states for a single atom. It is not difficult to show that the odd state which is missing in these regions is to be found as a nonlocalized state lying in the normal crystal band. In view of our results for the extreme case of complete surface coverage in Sec. III,B, we would have expected that, for certain values of the interaction parameters z and z’, the missing odd 6 state for two foreign atoms would be found as an 31 state with energy lying above the normal crystal band. This is not the case, because of the inadequacy of our present model, as explained earlier in this section. To illustrate the interaction effects, suppose that a single atom is chemisorbed by the formation of a doubly occupied 6 state in the region A in Fig. 5. A second atom can be chemisorbed in just the same way on a site remote from the first. As the two atoms are brought together, the individual localized states split into even and odd localized states belonging to both atoms. The even state has energy below the original level, and the odd state is raised above it. Both levels are doubly occupied. Bringing the two chemisorbed atoms closer together forces the odd 6 state higher and higher, until eventually it becomes a nonlocalized state in the normal crystal band (or perhaps appears as an 31 state above the band). It seems clear, therefore, that falling heats of chemisorption with surface coverage can be accounted for in this way and possibly also the formation of saturated chemisorbed layers when only part of the surface is covered. We emphasize again that these effects are not due to any direct interaction between the chemisorbed atoms. In the model used in this section, the resonance integral between the two foreign atoms is assumed to be zero a t all separations. The important interaction takes place through the crystal. This interaction is large if the original localized level for a single atom

18

T. B. GRIMLEY

on the surface does not lie too far below the band of crystal states. As an example, we give in Table I1 the wave-function coefficients in the chain for the 6 state associated with a single foreign atom at m = 0 when z = 0, z' = - 1.5, and 72 = 1. This state has [ = 0.570 and E' = 1.167. The coefficient c(X) on the foreign atom is 1.200. The spread of the wave function in the chain parallel to the surface is measured in terms of the interatomic distance in the chain by 1/E. For our example, this "size" is 1.75, and important interaction effects are to be expected when two foreign atoms are present on next-nearest neighbors in the chain. This situation corresponds to n = 1 in Equations (22) and (24) ; and with the same interaction parameters as before, both even and odd 6 states exist for the two foreign atoms. The even state has [ = 0.645 and E' = 1.215; the odd state has [ = 0.405 and E' = 1.083. The first few wave-function coefficients in the chain are TABLE I1 Wave-Function Coe$kients in the Chain for the 6 State" m

0

fl

*2

*3

f4

f5

44

1 .ooo

0.666

0.320

0.181

0.102

0.058

02

= 0,z' = -1.5, and q* = 1.

TABLE I11 WaveFunction Coeficiento in the Chain for the 6 Stales"

m Even state Odd state 0

n =

c(m) c(m)

0

fl

f2

f3

f4

f5

1.OOO 0.525 0.275 0.144 0.077 0.824 0.000 f1.000 f0.667 50.446 f0.296 f0.198

1, z = 0,z' = -1.5, and

= 1.

given in Table 111. The two foreign atoms are a t the points f l , and the wave-function coefficients on these atoms are 1.075 for the even state and f1.492 for the odd state. We note that the odd state is less well localized along the chain. This is because its energy lies closer to the bottom of the band. The energy difference between the odd and even states is 0.264P. Finally, we note that if an atom is chemisorbed only by a one-electron bond (6state for a single atom only singly occupied), two such chemisorbed atoms should attract each other because the even 6 state for the pair lies below the state for an isolated chemisorbed atom. This observation shows how an activation energy may be involved in the mutual separation of the atoms formed in dissociative chemisorption (11).

THE SUBFACE BOND

19

IV. Types of Surface Bonds I n ordinary molecular orbital theory, the electronic ground state of the combined system, crystal plus foreign atom (or molecule) is obtained by filling the lowest energy levels with two electrons in each level. If, when this is done, there are two electrons in a localized level, we have a localized surface bond; if not, then any binding of the foreign atom to the crystal surface is accomplished without any localization of the bonding electrons. Although it might be natural to assume that chemisorption must involve electron localization, we have very little information on this point. Certainly there is no theoretical reason why strong binding cannot be accomplished without localization of the bonding electrons (see Sec. IV,C). If localization does occur, the molecular orbital theory outlined in Sec. I11 allows for the formation of surface bonds varying from purely homopolar to ionic in character. In this section, we show how the values of the interaction parameters determine the character of the surface bond. Our discussion is given within the framework of the onedimensional model of Sec. II1,A. The three-dimensional model referred to in Sec. II1,B contains no new features, but is a good deal more difficult to handle.

A. THEHOMOPOLAR BOND If the wave function for a localized state is such that the probability of encountering the electron on the foreign atom is the same as that of encountering it in the crystal then, when such a state is doubly occupied, we have a purely homopolar surface bond. The quantity R, defined in terms of the wave-function coefficients by the equation

is the charge order of the state on the foreign atom. R = $5 for a homopolar state. For definiteness, assume that 6 states are bonding (lie below the normal band); then from Equations (13) and (14), we easily show that for a homopolar 6 state (z'

+ 2 cosh

[)2

= $[1

- exp (-2[)].

Given z' and 72, this determines [ and hence the energy and the wave function coefficients. The corresponding value of z is calculated from Equation (13). Pairs of values of z and z' for which homopolar 6 states exist when 72 = 1 lie on the curves in Fig. 6. There are two branches, both having z = z' and z = -2 as asymptotes. Starting high up on the upper branch, we are in the 6% region of Fig. 2. One homopolar 6 state exists with C: very

20

T. B. GRIMLEY

small and with energy therefore lying only just below the bottom of the normal band. The wave function decays only slowly in the crystal, and we have a many-center homopolar state. For example, when z = 1.245, z' = - 1.585, and q = 1, the homopolar 6 state has 4 = 0.100 and E' = 1.005 (the bottom of the band is a t E' = 1.000). The first few wave-function coefficients (unnormalized), including that on the foreign atom (m = A), are given in Table IV. The many-center character is evident. Its size in the crystal (1/5) is 10 interatomic distances.

FIQ. 6. The occurrence of homopolar 6 states for 7' = 1.

Moving down the upper branch, 4 increases, the energy of the homopolar 6 state falls further below the bottom of the normal band, and the wave

function decays more rapidly in the crystal. We also enter the 6 2 region of Fig. 2. At this point, a second 6 state separates from the bottom of the band. This state separates with a many-center character, but is not purely homopolar. Also it has c(h) negative if q = 1. The energy of the homopolar state is now some way below the bottom of the band. Moving further down the curve in Fig. 6, the energy falls steadily and the wave function looses its many-center character. As an example, we give in Table V the first few wave-function coefficients for the homopolar 6 state formed when z = -3.46, z' = -3.72, and q = 1. It has 4 = 1.50 and E' = 2.35. This is essentially a two-center homopolar state, only the foreign atom and the first crystal atom being involved to any extent. Its size in the crystal is only 0.67 interatomic distance.

21

THE SURFACE BOND

TABLE IV Wave-Function Coeficients for a Homopolar 6’ Slatem

m

0

1

2

3

4

5

6

1.000

0.954

0.863

0.781

0.707

0.640

0.579

X

~

c(m)

’z

2.350 =

1.245,Z’ =

- 1.585,q

1.

TABLE V Wave-Function Coeficients for a Homopolar 6 Slatea m

x

0

1

2

3

4

c(m)

1.02B

1.000

0.223

0.050

0.011

0.002

‘z

=

-3.46,

Z’

=

3.72, q = 1.

On the lower branch of the curves in Fig. 6, there are always two 6 states because this branch lies wholly in the P2region of Fig. 2. Only one of these is purely homopolar, and it is the one with the highest energy. It separates from the normal band with many-center character but becomes essentially a two-center state for large negative values of z and 2’. The occurrence of homopolar localized states for the onedimensional model has been discussed in some detail because the possibility of such states is a natural consequence of the molecular orbital approach t o the problem of the surface bond. It is clear, however, that the conditions for their existence are rather stringent. Most sets of interaction parameters do not give a purely homopolar state but give states with ionic character to a greater or lesser degree. B. BONDSWITH IONIC CHARACTER

The ratio R defined by Equation (27) lies between zero and unity. We classify localized states as anionic or cationic according to whether R is greater or smaller than >$. An electron in an anionic state is concentrated more on the foreign atom than on the crystal; for a cationic state the reverse is true. The occurrence of anionic and cationic localized states is shown in Fig. 7. This is a superposition of Figs. 2 and 6 with the extra information on the ionic character of the states. A 6 C X means that there is an anionic 6 state and a cationic 37, state, A 6 C 6 that there is an anionic 6 state and a cationic 6 state, and so forth. The state written first has the lower energy if 6 states are bonding (0 < 0). The ionic character and the location of the localized states with respect to the normal crystal states are both of great importance in connection with

22

T. B. GRIMLEY

FIG.7. Anionic and cationic localized states for q’

= 1.

the theory of chemisorption on semiconductors and insulators. We take up this problem in Sec. V.

C. METALLIC-LIKE BONDS If the interaction parameters fall in the forbidden region, no localized states are formed by the interaction between the foreign atom and the crystal. It does not follow, however, that strong binding of the foreign atom to the crystal is impossible. Binding can result simply because of a general lowering of the energies of the electrons in the system due to the altered boundary condition at the free surface caused by the presence of the foreign atom. All the electrons in the system contribute something to the surface bond, and since this situation is characteristic of the binding in the metals, such surface bonds are conveniently referred to a9 metallic-like. To get some idea of the magnitude of the energy change involved, we again consider the onedimensional model of Sec. II1,A. We assume that there is one electron per atom in the chain, so that the band is half-filled and that B is negative. We remove the foreign atom to infinity and calculate the total electronic energy of the chain. If no “surface” states are occupied, the result is (13).

THE SURFACE BOND

23

Here z is the parameter introduced in Sec. I1 for a chain with a free end. There are no occupied “surface” states if z > -1. To terms in N-I, a (4p/?r) is the mean energy of the electrons in the chain. The second term in Equation (28) is the “surface” energy associated with the free end at m = 0. We note that -@/T is roughly the cohesive energy of the chain. Now bring up the foreign atom to the free end of the chain. I n general, we would have a different Coulomb integral a” on the foreign atom, a different resonance integral 8’ between this atom and the first crystal atom, and a different Coulomb integral a‘ on the first crystal atom. For simplicity, assume that 8’ = p, and a’ = a. The interaction parameters therefore lie on the z’ axis in Fig. 2. If no localized states are occupied, the total electronic energy of the system is

+

Let 8 be the energy of the valence electron in the isolated foreign atom; then A&, the change in the total electronic energy when the foreign atom is in interaction with the chain, is given by A&=&-&N-€.

Using Equations (28) and (29), we have

where A&, is the difference between the “surface” terms in Equations (28) and (29). According to Equation (30), the change in the total electronic energy accompanying chemisorption appears as the sum of two terms. The first, that in square brackets, is the difference between the mean electron energy in the crystal and the energy of the valence electron in the isolated foreign atom. This is the energy change associated with the delocalization of the valence electron on the foreign atom. The second term in Equation (30) is the change in the surface energy caused by the presence of the foreign atom. Evidently, the form of Equation (30) is quite general for chemisorption involving the metallic-like surface bond. The delocalization energy is positive or negative according as e lies below or above the mean energy of electrons in the normal band, while A&, is positive or negative according to whether z’ is greater or smaller than z. Because of this, the two terms in Equation (30) tend to cancel each other. For example, a large negative first term means that the foreign atom level lies well above the middle of the normal band, and because of this we expect z’ to be large and positive so that A&, will be positive. At the other extreme, we have to remember that if E lies well below the middle of the normal band (first term positive), it is likely that for the combincd system, z’ is large

24

T. B. QRIMLEY

and negative; and while this would apparently make the second term in Equation (30) negative, the whole theory has really broken down because there are occupied localized states in the combined system. We cannot calculate A& from Equation (30) for any particular case because we have no knowledge of the values of the parameters z and z’ which determine A&,. Given suitable values of these parameters, however, A& is quite large and negative if t does not lie too far below the middle of the band, i.e., if the delocalization energy is not too large. For example, if z = +1 and z’ = - 1 [if z’ < -1, the combined system has occupied localized states and Equation (30) fails], we find A&, = 28. This is also the value of A & if the delocalization energy is zero. Since 1 e.v., it seems that quite strong metallic-like surface bonds can be formed if the energy level of the valence electron on the foreign atom falls within the range of occupied levels in the crystal. We note that this disposition of the energy levels does not occur with hydrogen and the alkali metals. With sodium, for example, the bottom of the conduction band is a t about -0.6 Ryd., and the hydrogen level is, of course, at -1 Ryd. Obviously, a very large positive delocalization energy would be involved in the formation of a metallic-like surface bond with this system. With nickel, it is just possible that such a bond is formed because here the bottom of the conduction band is at about -0.9 Ryd. Moreover, there is a low-lying narrow partially filled d band with a high density of states; and because of this, the mean electron energy in the solid is not far above the bottom of the conduction band. Hence, the delocalization energy will be small. With copper, the situation is similar, except that here the d band is completely filled and the s band, which overlaps it, is filled to a point about 0.15 Ryd. above the top of the d band. The mean electron energy in the solid and the delocalization energy are therefore probably larger than in the case of nickel. In the absence of any proper quantum-mechanical calculations, however, it is impossible to say whether or not localized states exist for the combined system when hydrogen is chemisorbed on these metals, and it is fruitless to sepculate further on this matter.

-

V. Chemisorption on Semiconductors The current theory of chemisorption on semiconductors as developed by Hauffe (14) assumes that charge is transferred either from or to the solid, so that the chemisorbed species exists on the surface as an ion. The resulting surface charge is balanced by a charge in the solid associated with the discrete electron levels which are responsible for the semiconducting properties of the solid. It would appear at first sight that the existence of localized states for the combined system, foreign atom plus crystal, is required

25

THE SURFACE BOND

for this theory of chemisorption, but we shall see in Sec. V,A that this is not always necessary. Our main purpose in this section is to show how the values of the interaction parameters determine both the nature of the adsorbed species and the manner in which the balancing charge is carried in the crystal. To do this, we need two general results from molecular orbital theory. First, if we have a perfect crystal containing N electron levels and we bring up a hydrogen-like foreign atom, the combined system has N 1 levels, each capable of accommodating two electrons. Second, the sum of the squares 1 levels is equal to unity of the wave-function coefficients c(m) over all N 1 levels are all doubly for all atoms including the foreign atom. If the N occupied, this means that the foreign atom exists on the surface as the anion. Of course, to achieve double occupation of all levels, we would have to add an extra electron to the system. Exactly the same results apply if the crystal is a p-type semiconductor, either because it contains impurities or is nonstoichiometric. The number N must, however, be taken to include only the levels in the normal crystal band, not the discrete levels lying just above it, which confer the p-type semiconductivity onto the crystal. Similar considerations apply to n-type semiconductors.

+

+ +

ON p-TYPE SEMICONDUCTORS A. ANIONICCHEMISORPTION

By anionic chemisorption we mean that the charge distribution between the chemisorbed atom and the crystal is such that there is excess negative charge on the foreign atom. It is clearly of some importance to know in what regions of the diagram in Fig. 7 this occurs and how the balancing positive charge is carried in the crystal. We assume that the interaction problem is between the orbital on the foreign atom and the normally filled valence band of the crystal. Lying just above the top of this band are the discrete levels which confer the p-type semiconductivity on the crystal. At low temperatures, these levels are unoccupied. Certain regions where anionic chemisorption occurs on p-type semiconTABLE VI Anionic Chemisorption a p-Type Semiconductors

Ftegion 6,61 CX, A6CX Forbidden C37, A 6 C X

level -

Between -

Above

Balancing charge

Chemisorption type

Free holes Trapped hole Free hole Trapped holes and occupied impurity levels

Cumulative, type A Cumulative, type B Cumulative, type C Depletive

26

T. B. GBIMLEY

ductors are given in Table VI. This list is not exhaustive, but the important types are illustrated. The second column gives the position of the 32 level with respect to the top of the band and the discrete impurity levels. The entry “Between” means that the 3t level is between these two, while “Above” means that the 3Z level lies above the impurity levels. In the third column, we show how the balancing positive charge is carried in the crystal. The holes are positive holes, and a trapped hole is a singly occupied 32 level. In the fourth column, the chemisorption is cumulative if the amount of chemisorption is not limited by the number of impurity levels in the solid and depletive if it is. Cumulative chemisorption occurs throughout the 6 and S2 regions and also in the forbidden region where no localized states exist. These cases ( A and C) are the simplest. The foreign atom brings one extra level to the system but only one electron. Hence, the combined system has one level only singly occupied, and this will be the highest level in the normal crystal band (any 6 states lie below the bottom of the band). Thus, there is a free positive hole for each foreign atom adsorbed. To verify that there is, in fact, an anion on the surface, we note that if all levels were doubly occupied, the surface species would be the anion. Now an electron is actually missing from a nonlocalized state. The amplitude of such a state on the foreign atom is extremely small (-N-’), and the charge distribution does, therefore, give an anion on the surface. We note that the Coulomb forces between the surface anions and the free positive holes produced result in the building up of an electrical double layer. The extra positive holes produced by the chemisorption are thus confined to the surface region and contribute only an enhanced surface conductivity. There are two points of some interest in connection with anionic chemisorption. The first, that it occurs even though the system has no localized states, we have already mentioned. The second point is that we get anionic chemisorption when the system has localized states associated not primarily with the foreign atom, but with the first crystal atom. This is the situation in the CS region of Fig. 7.As an example, we give in Table VII the first few wave-function coefficients for the cationic 6 state formed when z = -3, z’ = 0, and = 1. It has E’ = 1.785and R = 0.066. The localization of the wave function on the first crystal atom is apparent. When this state is doubly occupied, it contributes only 0.132 to the charge order on the foreign atom. The rest of the charge order (1.868) required to render the foreign stom anionic, is contributed by the nonlocalized states of the system. This example shows that the usual picture of anionic chemisorption, namely, that the foreign atom accepts an electron from the solid into its vacant atomic level, is not a necessary one. Something like the usual picture is valid only in the A S region in Fig. 7. As an example, we give in Table

27

THPJ SURFACE BOND

VIII the first few wave-function coefficients for the anionic 6 state formed when z = 0, 2' = -3.16, and 7 = 1. It has E' = 1.737 and R = 0.900. This state is evidently well-localized on the foreign atom. When doubly occupied, it contributes 1.800 to the charge order on this atom, and the nonlocalized states therefore contribute only 0.200. The energy lies only slightly below the value E' = = 1.580 characteristic of a perfectly localized state. We note that the two examples discussed above are rather extreme cases. On the homopolar line between the A 6 and the CS regions, there is a homopolar bond between the foreign atom and the crystal. In this case, the charge order on the foreign atom is contributed equally by the two electrons forming this bond and those in the nonlocalized states of the system. Finally, we note that the discrete impurity levels play no part in the chemisorption process, and the theory is therefore applicable to insulators also.

-xz'

TABLE VII Wave-FunctionCoeflcientsfor a Cationic 6 States m

h

0

1

2

3

4

5

44

0.278

1.000

0.305

0.093

0.028

0.009

0.003

2 =

-3,

2'

=

0, 7 = 1.

TABLE VIII Wave-Fundion Coeflcientsfor an Anionic 6 State4

~~

a

m

h

44

3.160

0

1

2

3

4

5

1.000

0.316

0.100

0.032

0.010

0.003

~

z = 0, z' = 3.16, q = 1.

Anionic chemisorption of type B in Table VI js interesting because the positive hole produced is trapped in the neighborhood of the first crystal atom because the extra level which the foreign atom brings to the system is a cationic 3t level lying between the top of the crystal band and the discrete impurity levels. This is the level which is only singly occupied, and the vacant place in this level is the trapped positive hole. With this sort of chemisorption, the conductivity of the solid will not be affected a t low temperatures, but as the temperature is raised, electrons will be excited to the 3t level from the filled band. In this way, free positive holes are produced. Chemisorption of this type has been proposed for oxygen on cuprous oxide (16), but we do not expect i t with many systems because of the requirement that the cationic 'Z level should lie in the rather narrow region between the top of the filled band and the discrete impurity levels.

28

T. B. QRIMLEY

The fourth type of chemisorption listed in Table VI is unusual in being both anionic and depletive. The situation is that the extra level which the foreign atom brings to the system lies above the discrete impurity levels, so that the valence electron on the foreign atom goes into one of these levels. Chemisorption is therefore associated with the building up of a depletion layer in the solid. The interesting point is that there is an anion on the surface. The extra level is a CX level, and the wave function for this level is concentrated on the first crystal atom. If this localization is good, the electrons missing from the CX level do not greatly affect the charge on the foreign atom, which therefore exists on the surface as an anion. For each foreign atom chemisorbed, two positive holes are trapped near the first crystal atom, the foreign atom is converted into the anion, and one impurity level is filled. The electrical double layer associated with this type of chemisorption has a structure already familiar in colloid chemistry as Stern’s double layer. The surface coverage would be extremely small because it is limited by the concentration of impurity levels (14). On thin layers of the adsorbent, however, when space charge effects are unimportant, chemisorption may still continue when all impurity levels are filled. The extra electron is in the CX level, and this subsequent chemisorption is cumulative, with one positive hole trapped on the first crystal atom for each foreign atom adsorbed. The situation is therefore similar to that in the cumulative chemisorption of type B in Table VI, except that we no longer have the rather critical placing of the CX level. With the oxide semiconductors, anionic chemisorption would take place over the metal cations, and the interaction problem would be between the orbitals on the foreign atom and the cation band (the 3d band in CuzO, for example). The discussion in this section is relevant if this is the highest filled band.

B. CATIONICCHEMISORPTION ON P-TYPESEMICONDUCTORS The usual picture of cationic chemisorption on a p-type semiconductor is that an electron is transferred from the foreign atom to an impurity level in the solid. The foreign atom is converted to the cation, and a depletion layer is built up in the solid. This occurs in the A51 and C@A% regions of Fig. 7, provided that the X level lies above the impurity levels. In this case, the AX level is vacant and a hydrogen-like foreign atom exists on the surface as the cation. With the oxide semiconductors, cationic chemisorption should occur over the lattice anions, and we would expect therefore to have an interaction problem involving the anion bands as well as the cation band. This makes the whole problem much more complicated ; and because the cation-anion band model is not adequate for the transition metal oxides, we shall not discuss this problem here.

THE SURFACE BOND

29

C. ANIONICCHEMISORPTION ON n-TYPE SEMICONDUCTORS The usual picture here is that the foreign atom accepts an electron from an impurity level. The chemisorption is therefore depletive because the surface coverage depends on the concentration of impurity levels in the solid. The semiconductivity is, of course, reduced. We assume that the interaction problem is between the orbital on the foreign atom and the conduction band of the solid. The usual picture is then found in the A 6 and A 6 C X regions of Fig. 7, provided that the 6 level lies below the impurity levels. An electron is lost from an impurity level for each foreign atom adsorbed, and if the 6 level is anionic, the foreign atom is converted to an anion on the surface. With the semiconducting oxides, we expect anionic chemisorption to occur over the lattice cations, and our simple molecular orbital theory will be adequate if the conduction band is associated mainly with the cation lattice. This is certainly the case with A1203,where there is direct evidence in the soft X-ray emission spectra that the highest filled band is the oxygen 2 p band (16). Finally, we note that if the interaction problem is between the orbital on the foreign atom and the highest filled band of the solid, anionic chemisorption is found in all regions of the diagram in Fig. 7, provided only that the highest localized level falls below the impurity levels in the solid.

D. CATIONICCHEMISORPTION ON TZ-TYPE SEMICONDUCTORS The usual picture is that the foreign atom looses an electron to the conduction band of the solid. The chemisorption is cumulative, and the conductivity of the solid is enhanced. Assuming that the interaction problem is with the conduction band, this sort of chemisorption occurs, for example, in the forbidden region in Fig. 7. The extra electron which the foreign atom brings to the system is nonlocalized, the amplitude of its wave function on the foreign atom is extremely small, and the charge distribution corresponds to there being a cation on the surface. An unusual type of cationic chemisorption occurs in the C6 and C 6 A Z regions of Fig. 7, provided that the 6 level lies below the impurity levels. In this case an electron is lost from an impurity level for each foreign atom adsorbed, and two electrons are trapped in the C6 level. Now the wave functions for these electrons are small on the foreign atom, which exists therefore on the surface as the cation. This chemisorption is depletive. If the C6 level lies between the bottom of the conduction band and the impurity levels, the chemisorption is still cationic, but the electrons in the impurity levels play no part in the process, and only one electron is trapped in the C6 level in the neighborhood of the first crystal atom. This chemisorption is cumulative.

30

T. B. GRIMLEY

On the homopolar line between the A 6 and the CS regions, for example, the usual anionic chemisorption of the last section and the “unusual” cationic chemisorption of this section coalesce, and a homopolar bond is formed between the foreign atom and the lattice. One electron is lost from an impurity level for each foreign atom adsorbed, and this homopolar chemisorption is depletive.

VI. Conclusion An attempt has been made to show how conventional molecular orbital theory can be applied to problem of chemisorption on solids. Koutecky (11)has shown how the theory can be developed in a very general way by using Wannier functions instead of ordinary atomic orbitals, but in this article we have adopted the simplest approach, namely, that of the tightbinding approximation. This approximation is useless for quantitative work on metals, and its value lies rather in giving us some idea of the sort of results to be expected in a proper theory. The bulk of the theoretical work needed to enable us to gain some insight into the chemisorption process on metals therefore remains to be done. In this connection we should mention the transition metals. Our knowledge of their electronic structures is at present very poor; and until more is known about the metals themselves, we can scarcely hope to treat the chemisorption problem adequately. For insulators and semiconductors, the tight-binding approximation can often be used with more confidence, but here we encounter the difficulty that the simple band approximation fails for just those solids, the transition metal oxides, for which a good deal of experimental information is available. REFERENCES 1. Eiachens, R. P., and Pliskm, W. A., Advances in Catdysis 10, 1 (1958). 8. Baldock, G. R., Proc. Cambridge Phil. SOC.,48, 457 (1952). 3. Koster, G. F., and Slater, J. C., Phys. Rev. 96, 1167 (1954). 4. Tamm, I. E., Physik. 2. Sowjetunion 1, 733 (1932). 6. Shockley, W., Phys. Rev. 66, 317 (1939). 6. Goodwin, E. T., Proc. Cambridge Phil. SOC.86, 221 (1939). 7. Artmann, K., 2.Physik 181,224 (1952). 8. Koutecki, J., Phys. Rev. 108, 13 (1957). 9. Grimley, T. B., Proc. Phys. Soe. 73, 103 (1958). 10. Kouteckf, J., 2. Elektrochem. 60, 835 (1956). 11. Kouteckf, J., Trans. Faraday SOC.64, 1038 (1958). 18. Greenhalgh, E., Slack, N., and Trapnell, B. M. W., Trans. Faraday SOC.63, 8G5 (1956). 13. Baldock, G. R., Prm. Phys. SOC.A66, 1 (1953). 14. Hauffe, K., Advance8 in Catalysis 7, 213 (1955). 16. Garner, W. E., Gray, T. J., and Stone, F. S., Proc. Roy. Soc. 8197, 294 (1949). 16. O’Bryan, H. M., and Skinner, H. W. B., Proc. Roy. SOC.8178, 229 (1940).

Magnetic Resonance Techniques in Catalytic Research D. E. O’REILLY Gulf Research & Developmat Company, Pittsburgh, Pennsylvania Page 1. lntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 A. Nuclear Magnetic Resonance (NMR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B. Electron Paramagnetic Resonance (EPR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 11. Nuclear Magnetic Resonance.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 A. Principles and Methods of NMR.. ...... B. Interactions of Nuclei in the Solid State. C. Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ill. Electron Paramagnetic Resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 A. Principles and Methods of E P R . . .................................... 76 B. Influence of Atomic Environment on EPR Spectra.. . . . . . . . . . . . . . . . . . . . 83 C. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 1V. Conclusion.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

I. introduction Atomic nuclei and electrons possess magnetic dipole moments. In the techniques of magnetic resonance spectroscopy, this property of nuclei and electrons is utilized by the application of a magnetic field to produce a number of energy levels by Zeeman splitting of the quantum states of the magnetic moment. I<.elativeto the direction of the applied magnetic field, the magnetic moment takes up definite directions which differ in magnetic energy. Associated with the magnetic dipole moment, nuclei and electrons possess a spin angular momentum. The component of this angular momentum along the direction of the applied magnetic field is an integral or half integral multiple of the fundamental unit of angular momentum, h (Planck’s constant divided by 27r). A riucleus (or system of electrons) with spin I (or S) may have only 21 1 different orientations in a constant magnetic 1 states of different magnetic energy. Transitions of field and hence 21 the magnetic dipole moment between these states are produced by the application of radiation of the proper frequency and polarization so that a resonance absorption of magnetic energy occurs. By observation of the intensities and frequencies of the resonance absorption, details of the environment of nuclei and electrons in the material under observation can be

+

+

31

32

D. E.

O’REILLY

ascertained. Since most materials of interest in heterogeneous catalysis are solids, magnetic resonance of the solid state will be emphasized in the following discussion. A. NUCLEAR MAGNETIC RESONANCE W. Pauli in 1924 ascribed a magnetic dipole moment and associated angular momentum to nuclei in order to account for the hyperfine structure of atomic spectra. The magnitude of these moments is of the order of lo3 to 104 times smaller than that of the magnetic moments of electrons, which give rise to the well-known phenomenon of paramagnetism. In 1946 Bloch, Hansen, and Packard ( I ) a t Stanford, and Pound, Purcell, and Torrey (2) a t Harvard independently discovered the phenomenon of nuclear magnetic resonance (NMR), which is a direct consequence of the existence of nuclear magnetic dipole moments. The initial application of the method consisted of the precise measurements of nuclear magnetic dipole moments and spins, but the work of Bloembergen, Purcell, and Pound (S), Pake and Gutowsky (4) and Pound (6) indicated the far-reaching usefulness of NMR in the investigation of the structure of solids. In the last ten years a large number of publications have appeared on the theory and applications of magnetic resonance in the study of the solid state. The usefulness of the NMR technique in solid state physics stems from the fact that the widths, splittings, and shifts of the magnetic resonance of nuclei in solids often depend in a sensitive manner on the magnetic and electrical environment of the nucleus in the solid. In this sense the nucleus can be considered as a probe by which one may ascertain certain details of the nuclear and electronic structure of the solid under investigation. Considerable attention has been given by numerous authors to the theory of the magnetic resonance phenomenon, and it is considered to be in a satisfactory state a t the present time. Review articles by Gutowsky (6),Shoolery and Weaver (7), Hutchison (8),McConnell (9), and Wertz (10) on magnetic resonance contain many references to applications of the method. Books by Andrew (11)and Losche (12) and a review by Pake (IS) also contain much information. More recently, a book by Saha and Das (1%) and a review by Fraenkel and Segal (2%) have appeared. There have been several initial applications of the NMR method to the study of solids of catalytic interest. Selwood and co-workers (14) have measured proton relaxation times (TI)of water-soaked y-aluminas containing iron oxide, copper oxide, and chromium oxide. By comparison of the observed relaxation times with those observed for water solutioiis doped with the corresponding paramagtietic ion, these authors defined a ‘(catalystaccessibility” which was taken to be a measure

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

33

of the accessibility to the water molecules of the paramagnetic ions supported on the catalyst. Unfortunately, it was found difficult to separate effects of the support on TI from effects of the paramagnetic oxide, as is illustrated by the more recent work of Hickmott and Selwood ( 1 5 ) ;in this investigation proton spin-lattice relaxation times of y-alumina, wetted with various liquids including water, have been measured. Nuclear magnetic resonance measurements of methane adsorbed to various coverages on titanium dioxide have been made by Fuschillo and Renton (16). At a coverage of 0.95 monolayer and at 20.4"K, the A-point for solid bulk methane, these authors observed an abrupt change in the proton resonance line width, presumably due to translational and rotational diffusion of methane molecules. For pure, bulk methane no change has been observed in the line width a t the A-point. Mays and Brady (I?') have published preliminary measurements of water adsorbed on rutile (TiOz) at 77"K, 195°K and 300°K for several different coverages. Zimmerman and co-workers (18) have made extensive magnetic resonance (spin-echo) measurements of protons of water vapor adsorbed on silica gel. Transverse and longitudinal relaxation times have been measured at room temperature at many different surface coverages and a two-phase behavior of the adsorbed water has been observed. Nuclei that are most favorable for NMR studies of solids are as follows: HI,H2, Li7, Be9, B11, Cia, F19,NaZ3,AP7, SiZ9,P31,C136,SC*~, Vsl, MnS6,C O ~ ~ , Cu'33, CUBE,Ga71, AS^^ , Se77l Br79,Bea1,Rn57, Nbg3,Cdlll, Cd113, Sn117,Sn1l9, SbIZ1,TeP >1127 ,XelZ9,C S ~Pr141, ~ ~ Hg199, , TI2O3,TIzo6,Pb207,and Bi209.Those nuclei in heavy type above have I = $5 and are generally the most favorable for observation in amorphous solids. Nuclear spins, moments, natural abundances, and resonance frequencies are summarized in a tabulation available from Varian Associates, Palo Alto, California and reproduced in ,the review article by Pake (IS) and the book by Losche (12). In Section II,C,3 results on the H', Fig, and AI2' resonances of solids of catalytic interest are discussed. B. ELECTRON PARAMAGNETIC RESONANCE

Since the discovery of the phenomenon of paramagnetic resonance absorption by Zavoisky (19) in 1945, this method has been extensively applied to the study of the properties of unpaired electrons in various substances. A large amount of information has been obtained concerning the transition group elements in various valence states and is summarized in review articles (20) ; generally these elements have been studied in dilute concentration in a diamagnetic host crystal of known structure. Most substances do not possess an appreciable number of unpaired elec-

34

D. E. O'REILLY

trons; however, many materials of interest to chemists because of their catalytic properties contain odd electrons which partially determine the catalytic properties of the materials. A large amount of EPR data has been obtained on organic free radicals (21);however, in view of the relative importance of the ions of the transition elements to catalysis, the following discussion will be limited mainly to these materials. Paramagnetic resonance experiments on ions of transition elements in solids can yield information on : (a) the strength and symmetry of the crystalline electric field environment of the ion (20, 22); (b) the amount of electron transfer from the paramagnetic ion to surrounding cations (23-27) ; and (c) the strength of exchange interactions between paramagnetic ions (26, 28-31). Also of importance are paramagnetic defects in the solid state such as color centers produced by irradiation of solids and donors and acceptors in semiconductors. E P R measurements have been made on electrons trapped in anion vacancies in alkali halides (32-34), on holes trapped near A12' impurity atoms in irradiated quartz (36,36),on Li7, Pal,As"?,SbI2land Sbl*adonors in silicon (37), on irradiated diamonds (56, 36), and on H atoms produced in irradiated frozen acids (38, 39) and ice (40, 41). By EPR measurements on defects of this type, detailed information as to their electronic structure and solid state environment can be obtained. Results of E P R measurements on defects in solids are summarized in a review article by Bagguley and Owen (42). The techniques and results of EPR of conductors, cyclotron resonance in semiconductors, and ferro-, ferri-, and antiferromagnetic resonance are also reviewed in this article. These aspects of magnetic resonance are not discussed in this chapter. In Section III,C, results of E P R studies on systems of interest to catalysis are given.

II. Nuclear Magnetic Resonance A. PRINCIPLES AND METHODS OF NMR 1. Magnetic Resonance Spectroscopy Most nuclei possess an angular momentum, whose maximum component along any specified axis, in accordance with quantum mechanical principles, is an integral or half integral multiple of the fundamental unit of angular momentum A, Planck's constant divided by 2 ~This . integral or half integral number is known as the nuclear spin I . Since atomic nuclei are made up of charged particles, there is a magnetic dipole moment p associated with those possessing nonzero spin angular momentum. Both angular momentum and magnetic dipole moment are vectors and it can be shown (43) quite generally that they are linearly related by a scalar, called the magnetogyric ratio 7. That is

MAGNETIC RESONANCE I N CATALYTIC RESEARCH

35

p = yAI

(1)

The quantity y is different for different nuclci and in particular for different isotopes of the same element,. A magnetic dipole moment, when placed in an external magnetic field, will have an energy of interaction E with the field which is the negative of the product of the magnetic field H and the component of the magnetic moment along the field direction ~ L H

E = - PIIH

(2)

Quantum mechanics allows the component of angular momentum mr along any specific direction in space to have only 21 1 values ranging from - I t o + l . Thus, a nucleus with a magnetic moment when placed in a static magnetic field will have 21 1 states of different magnetic orientation and energy relative to the external magnetic field. The energy difference AE between adjacent states is

+

+

AE

=

yhH,

(3)

or in terms of an angular frequency w is w = yH

(4)

FIG. 1. Energy levels of nucleus with I = 56 in an external magnetic field. Arrows denote transitions caused by rf field; wavy line denotes net transitions due to spinlattice relaxation.

An energy level scheme is shown in Fig. 1 for a nucleus with I = $6, such as the proton (y = 2.675 X lo4 gauss-' second-') where 2 X 55 1 = 2 energy levels occur. Equation (4) is the fundamental spectroscopic relationship of NMR. As one may verify by direct quantum mechanical calculation (9), the application of an oscillating magnetic field, HI,of angular frequency w , will cause transitions of the nuclear spin between adjacent magnetic energy

+

36

D. E. O’REILLY

states. A nuclear spin undergoing a transition to a higher energy state will absorb a quantum of energy hw from the electromagnetic field, and a spin in transition to an adjacent state of lower energy will emit a quantum h. The transition probabilities per nucleus for these up and down transitions are equal. However, a t a temperature T in thermal equilibrium, the upper states of an ensemble of nuclear spins will be less populated than the lower states, as given by the Boltzmann statistics. For example, for I = $6 the number in the upper state N- is related to the number in the lower state N+ by

N-

=

N+e-hw/kT

(5)

Hence, a t thermal equilibrium there will be a net absorption of energy from the electromagnetic field. As can be seen from the value of y given above for the proton, the frequency required for resonance iii a magnetic field of several kilogauss is in the radiofrequency range and of the order of 107 c.p.s. The oscillating magnetic field is most effective in causing transitions when its direction is perpendicular to the static field and causes no transitions when parallel to the static field. The reason for this behavior is made clear by an examination of the kinematical properties of a magnetic moment in a static magnetic field. A magnetic moment in an external field H will experience a torque L tending to turn it about the direction of magnetic field. L is given by

L=pXH

(6)

The torque is simply the rate of change of angular momentum and since magnetic moment is related to angular momentum by Equation ( l ) , one may solve Equation ( 6 ) to find the motion of the spin vector. The spin precesses about H and the angular frequency of this precession, known as the Larmor precession, is y H . This situation is illustrated in Fig. 2. Nuclear spins will precess a t only certain angles, classically speaking, relative to the static field direction; in the case of I = $5 nuclei only those angles such that mI = +M and mI = -%. The component of magnetic moment in the plane perpendicular t o the magnetic field will rotate about in this plane a t the angular frequency y H and if the rotating magnetic field HI is applied in this plane, a “secular” interaction with the magnetic moment will occur when the angular frequency of H I is y H . For this condition a steady torque will act on p tending to turn it about the direction of HI. In the classical case a nutation of the original precession occurs; in the case of a nuclear spin, the spin makes a transition or flips from one quantum state to another, as described above. The maximum effect occurs when HI is rotating in the plane perpendicular to the direction of H.

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

37

Consider now an ensemble of nuclear spins in a homogeneous, static magnetic field. When the frequency of H1 is far from y H , there will be no absorption of energy and no coherent transversal components of nuclear magnetization for the sample as a whole. When H I is rotating at the angular frequency y H , there is a net absorption of radiofrequency energy and a rotating nuclear magnetization in the plane perpendicular to H . A useful equivalent way of looking at the resonance phenomenon is in a coordinate system rotating with the angular frequency of H1 about the z axis which coincides with the direction of Ho, the applied static field (44). In this rotating coordinate system the effective fields are H1,which is now time-independent, and a field H o - w / y , where w is the angular frequency

I

i FIG.2. lllustration of the Larmor precession of a magnetic moment p in a field H with the rf field H I perpendicular to H as in magnetic resonance.

of the rotating coordinate system. The field Ho is reduced by o/y since this is the effective field needed in Equation (6)for ( 6 ) to be valid in the rotating coordinate system. As resonance is approached by varying w , the net field in the rotating coordinate system moves into the transverse plane and after passage through resonance points in the opposite direction to the original one. Viewed from the rotating coordinate system the nuclear spins will precess about this effective field. Consideration of the energy level diagram of Fig. 1 leads to the conclusion that there must be a mechanism by which the Boltzmann thermal equilibrium distribution can be maintained during resonance absorption. For, if there were no such mechanism, upon application of a field H I at the resonance frequency initial absorption of energy would occur, but would

38

D. E. O’REILLY

soon cease as the levels become equally populated. On the other hand, if a mechanism for maintaining thermal equilibrium is present-that is, a way by which spins in the upper state of Fig. 1 may lose quanta to their surroundings and drop down t o the lower state-resonance absorption of energy will persist, due to the constant difference in population between the two energy states. These transitioiis are schematically illustrated by the wavy line of Fig. 1. Such a mechanism is referred to as a relaxation mechanism and the time constant for the system, with initial equal population of both states, for exponential approach to the equilibrium state is known as the thermal or spin-lattice relaxation time T I .This time is directly dependent on the coupling of the nuclear spin with its surroundings or the “lattice.” T I in experiment is found to range from the order of microseconds to several hours. By the definition of TI given above, the equation of motion of the component of nuclear magnetization M , in the direction of the static field is given by dM,/dt = (440 - M,)/TI

(7)

where M o is the thermal equilibrium value of M,. There is, in addition, another generally different time required to specify the radiofrequency behavior of the nuclear spin system. This time is called the transverse relaxation time and is the time constant for the exponential decay of the transverse ( x and 3) components of nuclear magnetization M , and M u dM,,,/dt = -Jf,JTz

(8)

The physical significance of the time T2 follows from the fact that it is the time constant to describe the decay of the transverse magnetization and hence the time constant required for the individual spins to lose rotational phase coherence with one another. If the nuclear spins are in slightly different magnetic fields, due to an inhomogeneity of the static field or difference in local magnetic fields due to the magnetic dipoles of their neighbors (Sections II,A,2 and II,B,l), then they will precess with slightly different Larmor frequencies and thus eventually become phase-incoherent. Flipping of magnetic moments due to spin-lattice relaxation will also contribute to this effect and hence to T2. Since the resonance absorption line width may clearly be due to any of the above effects, Tz is, as quantitative analysis shows, inversely proportional to the line width. T2 is also referred to as the spin-spin interaction time or spin phase-memory time. Combination of Equation (6) with (7) and (8) gives a set of differential equations which may be solved (46) to give the steady state behavior of the nuclear magnetization as the frequency of HI or the field H is varied. These differential equations are known as the Bloch equations and are

MAGNETIC RESONANCE I N CATALYTIC RESEARCH

39

sufficient to describe the radiofrequency (rf) behavior of the nuclear magnetization for a large number of systems. There are two components of the transverse nuclear magnetization : one in phase with the field H1, and one ?r/2 out of phase with H1. The former is known as the dispersion mode or u mode magnetization, and the latter as the absorption mode or v mode magnetization. That is, referring to Fig. 2, peel will lag or lead H I as the resonance is traversed. The magnetic radiofrequency susceptibilities are defined by

M

=

(x’ - ix”)H1

(9)

where is the real part and x” the imaginary part of the complex susceptibility. X I is associated with the dispersion mode and XI’ with the absorption mode. Two cases are distinguished : “slow” and “rapid” passage through the resonance (1). If the time spent traversing the resonance is long compared to TI,a slow passage case results. The dependence of x’ and x” on H - H o as given by the Bloch equations in the case of slow passage is shown in Fig. 3. The shapes of the absorption and dispersion are

IX

I

I

- 4 -3

I

I

-e

-I

Y

A

I

I

I

I

I

2

3

4

I

-1 FIG.3. Imaginary (x”) and real parts of rf susceptibility aa a function of magnetic field atrength H. Field modulation and resulting NMR signal are schematically illustrated for the absorption curve ( X I ‘ ) .

40

D. E. O’REILLY

those for the optical absorption and dispersion of a damped harmonic oscillator, namely, the Lorentzian shape. Physically, the dispersion signal results from alignment of nuclear magnetization along H1 and may be experimentally detected by the change in frequency of oscillation of a radiofrequency oscillator whose inductance contains the sample. The presence of the radiofrequency magnetization causes a slight change in the radiofrequency inductance and hence a change in the resonant frequency of the oscillator. As may be seen in a qualitative manner by the above discussion and as predicted by the Bloch equations, a saturation of the resonance absorption and dispersion susceptibilities occurs a t sufficiently high rf field strengths. That is, the transverse nuclear magnetization decreases as HI is increased, eventually falling to zero. x” will begin to saturate rapidly when rH1is of the order of (T1T2)-,4.The Bloch formulation predicts a saturation of the dispersion a t the same value of HI. Behavior of this type is generally found for liquids; however, for solids the dispersion generally does not saturate a t the same rf level as the absorption but persists to much higher rf levels. Redfield (46) has given a modified description of the saturation phenomena in solids which is in agreement with experimental observations. 2. Line Widths and Shapes

A common source of the line width of the magnetic resonance abmrption of nuclei in solids is the distribution of local magnetic fields in the solid caused by the magnetic dipole moments of the nuclei. As shown in Fig. 4 the magnetic field produced by n magnetic dipole varies in both strength and direction at a fixed distance from the dipole. As a result, the actual field experienced by a nucleus due to a large number of near neighbors will depend on the orientation of the neighbors relative to it. In the presence of a large external magnetic field, the neighbors will be oriented relative t o the field and there will be a large number of possible local fields which a nucleus can experience in addition to the external field. For a completely random distribution of a large number of near neighbors, a Gaussian distribution of local fields is expected, with the result that the shape of the resonance absorption line is Gaussian or bell-shaped. The magnetic field a t a distance of one angstrom and an angle of a/2 relative to the dipole axis of a proton is 14.1 gauss so that local fields and resulting line widths can be of the order of tens of gauss due to the dipoledipole interaction. A quantitative discussion of the magnitude of this effect is given in Section II,B,l. In general the line shape caused by dipolar fields deviates somewhat from the pure Gaussian shape due to the ordered arrangement of the dipoles on a lattice. I n the case that two nuclei are relatively close together, with

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

41

other nuclei possessing magnetic moments relatively far away, such as in gypsum (47) CaS04 .2H20, the resonance of equivalent Hz0 molecules in the crystal consists of two distinct peaks due to the two predominant local fields a proton experiences due to the two possible orientations of its partner. The line shapes of larger clusters of nuclei, such as -CH3 and NH4+ (@), also show considerable structure. Lowe and Norberg (49)have derived a general expression for the line shape resulting from the dipolar interaction. This shape is generally not Gaussian. "0

#

FIG.4. Lines of flux of a magnetic dipole j relative to another dipole k in a magnetic field Ho. Molecular and atomic motions, which frequently occur in solids, have a profound effect on the width and shape of nuclear resonance lines. These motions, if sufficiently rapid, cause a narrowing of the resonance absorption line and, if sufficiently isotropic in space, give rise to a Lorentzian line shape. This effect is referred to as motional narrowing. If the mean period of rotation or the time between jumps of the nuclei is shorter than Tz, the phase-memory time, then the nuclei will experience a range of different local fields in a time short compared to Tz, the time required for nuclei t o get out of precessional phase with one another. This will make the average local fields, experienced by different nuclei in a time short compared to Tz,more equal t o one another and hence narrow the resonance line. Graphically speaking, the nuclei are jumping from one position in the

42

D. E. O’REILLY

original resonance line to another in a time short compared to the time required to define the original resonance line. The amount of decrease of the resonance width may be simply estimated in the following way (60). Let the motion of the spins be characterized by a time re,that is ro is the average time a spin stays in a definite environment or the correlation time for the motion. This environment will causc a difference 6w in the precessional frequency of the spin which may be positive or negative from some average value w . During the time rethe spin acquires a phase angle 64 = rc6w in addition to that acquired by the uniform precession a t w . If we consider the motion to be a random walk process (51), after n such intervals during a time t the mean square phase acquired will be (A+*) = n ( s 4 ) 2

and since n

.=

t/rc (A@) = t ~ ~ ( 6 w ) ~

During the time t a collection of spins initially in phase will have acquired phase differences characterized by (A&!)and when (A42)N 1, t may be considered to be equal to T z for the system. Thus 1/T2 = (6w)2rc

(12)

If the motion is sufficiently slow so that the spin stays in a particular environment for a time long compared to T2,then rc by definition is Tz and 1/Tg

=

60

(13)

which is the rigid lattice value of T2. A more detailed analysis (3,61) shows Equation (12) to be reasonably rigorous and further shows that for random motion in the limit of re short compared to the reciprocal of the resonance frequency the line shape is Loren tzian. An interesting application of the motional narrowing concept arises in the double N M R technique (63).In this technique the contribution t o the N M R line width of nuclei (A) in a solid by the dipolar fields of dissimilar nuclei (B) may be removed by application of a sufficiently strong rf field a t the resonance frequency of the B nuclei. With HIB >> AHB, AHA where AH is the line width, flipping of B nuclei by the H1B field will cause fluctuations in the dipolar fields of B nuclei at the A nuclei which are rapid compared to TM-I and hence cause narrowing of the N M R line of the A nuclei. This effect has been observed in several different solids of the AB type (65,64.

There are several other sources of line width in nuclear magnetic resonance. An experimentally caused width occurs when the laboratory static magnetic field inhomogeneity exceeds the true line width. In this case the

43

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

line shape is determined by the laboratory field distribution and nuclei in different parts of the sample are decoupled h o m one another; that is, the line shape can be thought of as the envelope of a large number of elementary dipolar broadened lines. One may, for example, saturate only a small portion of the resonance line by applying a large rf field over only a small part of the absorption line and put a “hole” in the otherwise unsaturated line (3). If the thermal relaxation time T1 is sufficiently short, this time may determine the width of the resonance line. This effect is referred to as “lifetime” broadening. The Uncertainty Principle expressed in terms of energy and time is as follows 6E6t = A where 6E is the energy spread of the energy state (line width) and 6t is the that the nucleus spends in a definite state. Clearly T1decreases time (T1) as the line width increases, so that if TIis shorter than the contribution to T2due to other sources, TIwill determine the line width (Tl = Tz). A useful classification of the source of resonance line widths may be made into two types (34).The first is known as homogeneous broadening and this class includes all those cases for which the nuclear spins are coupled together via the dipolar interaction or spin-lattice relaxation, so that the system responds as a whole t o an applied rf field. The second kind is known as inhomogeneous broadening and is characterized by the resonance absorption line being an envelope of a large number of individual homogeneously broadened lines. The behavior of the absorption and dispersion signals a t high rf levels is quite different for these two classes (34),so that they can be distinguished experimentally. General examples of the two types of broadening of nuclear resonance lines are as follows:

I. Homogeneous Broadening (1) dipolar interaction between like spins (2) motional narrowing (3) sufficiently rapid spin-lattice relaxation such that Tl = 11. Inhomogeneous Broadening (1) inhomogeneous laboratory magnetic field (2) anisotropy broadening in polycrystalline samples (a) anisotropic chemical or Knight shift (b) quadrupolar effects (3) dipolar interaction between unlike spins

T2

The nature of cases II(2a) and (2b) is discussed in detail in Section I1,B. In the case of dipolar. produced line width, a rigorous expression for the second moment (Equation 17) of the resonance absorption line allows one to obtain quantitative structural information (Section II,B and C). The

44

D. E. O’REILLY

widths of motionally narrowed nuclear resonance lines allow one to ascertain details of the molecular and atomic motions in the solid by specialization of Equation (12), and finally the shape of the absorption envelope of quadrupolar broadened nuclear magnetic resonance lines from polycrystalline materials often allows structural information to be obtained, in the event that single crystals of the material are not obtainable.

3. Spin-Lattice Relaxation T i m e As discussed in Section II,A,l, the existence of a mechanism by which spins may lose magnetic energy to their surroundings and thus maintain a population difference between magnetic levels is essential t o the steady state phenomena of resonance absorption. This coupling to the surroundings for I = 36 nuclei must be via interaction of the nuclear magnetic moments with fluctuating magnetic fields in the solid. The interaction with the surroundings must be timedependent since a spin must lose or gain quanta at the resonance frequency with the surroundings in order to have a net change in spin orientation. Several important mechanisms for nuclear spin-lattice relaxation are relaxation via the following:

i. timedependent dipolar interaction due to translational and rotational diffusion of nuclei (3, 66) ; ii. electron magnetic moments of impurities, such as paramagnetic ions and F-centers (67); iii. nuclear hyperfine interaction with conduction electrons in metallic substances (68); iv. interaction of nuclear quadrupole moment with phonons and other nuclear motions (69); v. fluctuating magnetic fields produced by motion of nuclei with anisotropic chemical shift (60, 61). In the event of translational or rotational diffusion of nuclei the dipolar local magnetic fields will no longer be static but will fluctuate due to the variation of radii vectors between dipoles and angles between radii vectors and the applied field. In general, a continuous spectrum of frequency of the dipolar fields will be produced. Only a narrow band of frequency near the resonance frequency and twice the resonance frequency will be effective in producing spin-lattice relaxation. Two quanta of the resonance frequency can be lost (or gained) simultaneously to (or from) the surroundings by simultaneous flipping of two spins (3). When the nuclear motion is a random process, one obtains, for (i), from the theory of random processes (61) the normalized spectral density of the mean square dipolar magnetic field versus frequency (3). The spectral density near a NMR frequency is proportional to the probability of a

MAGNETIC RESONANCE IN CATALYTIC FUZSEARCH

45

dipoledipole induced transition taking place. The result of the calculation is as shown in Fig. 5, where j ( u ) is the normalized spectral density and T,, is the correlation time for the random process. Such a behavior is physically reasonable; the spectral density is constant out to a frequency of the order the statistical frequency of the motion, beyond which point it drops of rC-1, off towards zero. The figure is drawn for a case where rc-I is large compared with the resonance frequency Y O . For such a case the intensity of the coupling with the surroundings is proportional to r e ; the proportionality coefficient turns out t o be ( S W ) ~as in Equation (12), and TI = Tz, as may be verified by computation of the square of the energy matrix elements of the dipolar interaction for the transitions involved ( 3 ) .

2 W 0

4

a a

t; W a

cn I 0 vo

(e r q 1-1 FREQUENCY, V

FIG.5. Spectral density caused by Brownian-type motions versus frequency. rc is the correlation time for the random motion and YO is a NMR frequency. When rC-l is of the order of Y O or less than Y O , T1 becomes longer since the spectral density of quanta is less. Thus, for example in a liquid, it is found that T1decreases with increasiiig viscosity (increasing r c ) to a certain point ( ~ ~ -N1 y o ) and then increases with increasing viscosity. A simple proportionality between r c and the viscosity is given by the Debye theory of liquids. This dependence of TI on rc has also been verified for several solids such a s the ammonium halides (62), solid benzene, and partially deuterated benzenes (63). In passing i t is interesting to note that Fig. 5 qualitatively explains the reason for the difference in the effect of motion on spectral lines in radiofrequency and optical spectroscopy. In radiofrequency spectroscopy one refers to “motional narrowing,” while “collisiond broadening” is used to

46

D. E. O’REILLY

describe the effect of increased atomic motion on optical absorptions. The reason for the difference is that for optical spectroscopy the frequency corresponding to Y O lies above rC-l,for the range of rC-l usually encountered (0to 1012 second-’) and the dependence of the lifetime T1 on the magnitude of rc is reversed. Relaxation via processes (iii), (iv), and (v) is treated in a somewhat similar way to that of dipolar relaxation, the source of the coupling to the surroundings being different. Explicit expressions for the relaxation times in terms of the constants of the interactions have been derived. Relaxation mechanism (ii), which is the most frequently occurring one in insulator solids, is proportional to the number of unpaired electrons in the solid, which most frequently are due to the presence of paramagnetic ions in the crystal, but occasionally may arise from the presence of color centers. Electron magnetic moments being of the order of lo3 times larger than nuclear moments produce very large fluctuating magnetic fields in their immediate vicinity and cause rapid nuclear spin relaxation for those nuclei close by. The fluctuating field is caused by the usually short electron spin-lattice relaxation time in insulators (TIelectron c 10-‘‘-10-9 sec.) due to spin-orbit coupling of the electron spin to the lattice (Section III,A,2). Nuclei removed by 10 or more angstroms from the electron spin are not affected greatly by the magnetic field of the electron spin since it drops off with distance as l/ra. However, they are relaxed rather rapidly in the presence of the electron spin due to nuclear spin diffusion. The nuclei removed from the electron spin are “hot” areas, since in the presence of a strong rf field they will be further from thermal equilibrium than those nuclear spins near the impurity, and hence a net spin polarization will be transferred to the impurity center via the dipoledipole interaction by simultaneous spin flips between like spins with no net change in energy. The rate of such spin diffusion will be proportional to l/Tz. A quantitative expression for the nuclear relaxation time in terms of the concentration of impurities, electronic relaxation time and the nuclear spin-spin relaxation time has been derived by Khutsishvili (67) in an apparently rigorous manner for low impurity contents. Several hundred parts per million of paramagnetic impurities can give rise to relaxation times in the range of 10-’ to 10-8 sec. a t room temperature. 4. Experimenlal Methods

a. Instrumentation. There are several different methods that are used in the detection of the magnetic resonance of nuclei in solids; the discussion will be limited mainly to the continuous wave methods and later a short discussion of the spin-echo and free induction techniques will be given. There are essentially three widely used methods for observation of

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

47

continuously excited nuclear magnetic resonance. Two of the methods use variable frequency rf oscillators to supply the HI field and are known as the Bloch (1) or “crossed-coil” spectrometer and the Pound-Knight (64) type of NMR spectrometer. The third utilizes a radiofrequency bridge. The crossed-coil spectrometer detects the radiofrequency components of the nuclear magnetization by means of a pick-up or receiver coil which is placed with its axis perpendicular to both the rf field and the static magnetic field. The nuclear magnetization introduces an emf in this coil which is then amplified by a radio receiver. The Pound-Knight spectrometer on the other hand utilizes the change in rf resistance of the inductance of the oscillator tank circuit containing the sample when resonance absorption occurs. The voltage output of the oscillator or level of oscillation is proportional to the &* of the tank circuit and hence a change in the level of oscillation occurs as the resonance absorption is traversed. Suitable amplification of this change in voltage allows observation of the resonance signal. The initial voltages caused by a detectable resonance absorption range from millimicrovolts to millivolts. In order to conveniently detect and display the resonance signal, audio modulation coils are used to modulate the static magnetic field. Close to a resonance the rf voltage will be audio amplitude modulated in the same way that a carrier wave is audio amplitude modulated in radio broadcasting. In this way by modulating with an amplitude large compared to the line width, the entire resonance signal may be displayed on a cathode-ray oscilloscope. Considerations of the signal-to-noise ratio usually dictate the use of the technique of narrow-banding in nuclear resonance. The modulation magnetic field is reduced to small amplitude compared to the resonance h e width as shown in Fig. 3. The audio signal resulting from rf amplification and detection is amplified and detected in a phase sensitive manner by using the original modulation phase as a reference. Both “mixer” vacuum tubes (66) and mechanical “choppers” are used. The resulting DC voltage is fed into a recorder. For sufficiently small audio modulation amplitudes the first derivative of the resonance absorption or dispersion results from the narrow-banding technique. Figure 6 illustrates a block diagram of a crossed-coil variable frequency spectrometer and associated electromagnet. A calibrator circuit (66) is useful for intensity calibration of absorption and dispersion mode signals. A calibrator circuit for the Pound-Knight type of spectrometer is also used (6n*

* The symbol Q is employed here to denote the quality factor of a resonant circuit, i.e., circulating energy divided by rate of energy loss.

48

D. E. O'REILLY

TAGE

u

&TRANSMITTER RECEIVER

=UAND

V MODE PADDLES

Fro. 6. A block diagram of crossed-coil NMR spectrometer with rf and audio waveforms shown schematically.

In the crossed-coil spectrometer two flux paddles (I) are frequently used to adjust the phase of the flux intersecting the receiver coil relative to the phase of H I . These paddles are metallic and dielectric disks or rings which modify the direction and phase of the rf transmitter voltage near the receiver coil. Lumped parameter circuits are often used (68) to accomplish the same end. By means of this phase adjustment, the absorption (v) or dispersion (u) mode signals may be individually examined, since in the case of a large amount of leakage rf flux compared to signal, a signal voltage at 7r/2 relative to leakage will cause only a very small change in amplitude of the leakage compared to a voltage in phase with the leakage flux. The Pound-Knight type of spectrometer has the disadvantage that the dispersion mode is not observed. The dispersion mode is important for the study of solids, since it does not saturate as readily as the resonance absorption in most solids (46), and in some cases (long thermal relaxation time) is the only mode that gives a measurable signal. On the other hand, high temperatures (up to S O O O ) are more conveniently attained with the PoundKnight type spectrometer; the conventional crossed-coil versions have been somewhat limited (up to 300") in this respect.

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

49

The radiofrequency bridge method was used in the original investigations of Bloembergen, Purcell, and Pound (3).The sample is placed in the inductance of an L-C circuit contained in one arm of the bridge. The bridge serves the purpose of cancelling out fluctuations in voltage or current from the source which excites the bridge. The change in complex radiofrequency permeability a t resonance causes a signal to appear at the balance point of the bridge due to a resulting change in impedance of the arm containing the sample. By adjusting the initial unbalance in phase or amplitude, either a pure dispersion or absorption mode signal is observed. In all of the above methods a linearly polarized rf field is applied t o the sample. Only one of the two circularly polarized components of this rf field is effective in causing transitions, as is illustrated in Fig. 2. The first extensive use of pulse rf fields was made by Hahn (69) who invented the method of spin echoes. With a sample immersed in a static magnetic field Ho, the response of the spin system after application of a strong, pulsed rf field at right angles to Ho is observed. In order to observe what is known as the free induction decay following a pulse, the rf field of magnitude H is left on for a. time n/2yH1 (90" pulsc), so that the nuclcar magnetization originally in the direction of Ho is rotated into the plane perpendicular t o Ho. After removal of the pulse, the spins will precess around the direction of Ho and become out of phase in a time T,, the spin phase-memory time. By application of a second pulse of duration n/yH1 (180" pulse) a t various time intervals after the 90" pulse, the spin-phase memory time TZ can be obtained (70). T1 can be obtained by application of a 90" pulse at various time intervals T after an initial 180" pulse so as to sample the amount of magnetization along the field H O that has been restored a time T after the 180" pulse (70). b. Measurement of Relaxation Times. A brief description of the measurement of T1and T zby pulse methods is given above. For the measurement of T1these methods are the most direct and probably the most accurate. For continuous wave measurements of T1, the method employed will often depend on the magnitude of TI.In the most general of these methods, the saturation method (S), the resonance absorption is scanned at various rf fields and from the values of x'' versus HI, one may calculate TI if H1 and Tzare known. T2 is obtained from the normalized shape function of the resonance absorption, g(H - H o ) , evaluated a t H = H O in the case of homogeneous broadening. When T1 is long enough it may be obtained by observation of the exponential recovery of z direction magnetization after removal of a large HI field or the loss of magnetization after application of the if field. Other cw methods of obtaining T1,generally applicable only to liquids, include measurement of the in and out of phase components of the disper-

60

D. E. O’BEILLY

sion derivative at resonance (71)and rapid passage through the resonance at high rf field and return in times comparable to TIso as to observe the sign reversal of the z component of nuclear magnetization (72).

B. INTERACTIONS OF NUCLEI IN

THE

SOLIDSTATE

1. Magnetic Dipole-Dipole Interaction

As was discussed qualitatively in Section II,A,2, the local magnetic fields produced at a nucleus in a solid by the magnetic dipole momeiits of nuclei around it are often responsible for the observed line widths. Van Vleck (73) has derived, in a rigorous manner, an expression for the second moment of the absorption curve of the nuclei in terms of the magnetic moments, spins, and internuclear distances of the nuclei. The second moment ((AHa))of the shape function g(H - Ho)normalized to unit area is

((AH2))=

1-1-g(H - Ho)(H - H o )dH~

The first set of brackets on A H 2 signifies the quantum mechanical expecta, the second set signifies that a statistition value of AHz = (H - H o ) ~while cal average is taken over an ensemble of systems. ((AHz))may be thought of as the mean square magnetic field an average nucleus experiences due to the magnetic dipole moments of its nuclear neighbors. Figure 4 illustrates pictorially a few of the lines of force from a magnetic dipole. The Ho component of this magnetic field at a dipole k located a distance r j k from the dipole j and at an angle e j k between the radius vector rjband the external field Ho is, for I = $6 nuclei,

where p i is the magnetic dipole moment of nucleus j. Van Vleck’s expression for the mean square local field a t a nucleus in a crystal containing N nuclei of this kind is

This expression is of the order of what one would calculate by squaring Equation (15) and summing to get the mean square field. The difference is due to the fact that two nuclear spins can simultaneously flip so as to conserve magnetic energy since they are coupled by the dipolar interaction. This process limits the lifetime of a spin state and gives rise to an additional line breadth. For two nonidentical nuclei such processes do not con-

MAQNETIC RESONANCE IN CATALYTIC RESEABCH

61

serve energy and do not contribute to ((AH2)),and ((AH2))is M the value given by Equation (16). For a polycrystalline sample one may average the angular factor over a sphere and obtain

(17) where the second term in Equation (16) is the contribution discussed above of unlike nuclei j to the second moment of nuclei j and N , as before, is the number of nuclei of kind j . Van Vleck's second moment formula has been experimentally proven to be correct by Pake and Purcell (74). I t has become a valuable tool in structure determination of the solid state. In the case of the large amplitude molecular or atomic motions which often occur in solids in certain temperature ranges, the resonance line will narrow when the motion becomes sufficiently rapid, as discussed in Section II,A,P. Hindered rotations of groups of nuclei in solids often occur about one direction or axis and there results only a partial "washing out" of the local fields; that is, in the limit of very rapid motion a considerable line breadth may remain (75). Isotropic rotation is necessary for complete aver aging of the dipolar fields. These phenomena make temperature studies of nuclear resonances a very valuable method in the study of motion in solids. In suitable cases activation energies for the motional processes may be obtained (76). The limiting line width for a particular mode of motion of an aggregate of nuclei may be calculated from Equation (16) after appropriate averaging of the angular factor over the motion. 2. Nuclear Exchange Interaction In the investigation of NMR of heavier elements in solids, namely metallic silver, metallic thallium, and thallium oxide, it was found (76)that the NMlt line width greatly exceeds that expected from the dipolar interaction discussed above. Moreover, it was found that in thallium and thallium oxide the line width is a function of the isotopic (T1208,T1206) composition of the solid. These results were explained (77, 78) by postulating an exchange interaction of the form AijIi Ij between nuclear spins, where A i , is the exchange coupling constant between spins i and j . In molecules containing light elements, Aij is of the order of lo2C.P.S. and the energy of the interaction is much less than that of the dipolar interaction. The interaction in this case manifests itself in the NMR spectra of liquids and gases where the molecular tumbling causes the dipolar interaction to

52

D. E. O’REILLY

average to zero. Aij arises from the magnetic interaction of the nuclear spin with the electron spin and is thus proportional to the product of the atomic hyperfine splittings for the atoms considered; these splittings in the free atom are dependent on the square of the atomic (s-state) unpaired electron wave function a t the nucleus. The s-electron density of the valence electrons at the nucleus increases with atomic number and for thallium is twenty times that for hydrogen, so that Aij for metallic thallium will be of the order of 400 times that for the hydrogen molecule (Aij = 43 C.P.S.). Van Vleck showed that the nuclear spin exchange between “like” spins leads to narrowing of the resonance line, while nuclear spin exchange between “unlike” spins gives rise to broadening of the resonance line. As shown by ltuderman and Kittel (77) and Bloeinbergen and Rowland (78), Aij in a solid is dependent on the nature of the energy bands in the solid. For metals Aij is proportional to the product of the square of the electron density of Fermi surface electrons a t the nucleus and the effective mass, and decreases as the inverse cube of the internuclear distance. Insulators have been treated by the energy band method (78) and by a molecular method (79) where each atom is considered to be bonded to its nearest neighbors. Unfortunately, both of these met,hods involve approximations in the evaluation of Aij which a,re quite crude a t present. Nuclear spin exchange has also been observed (80) between nuclei in semiconductors of the heavier dements, such as InSb, GaSb, GaAs, and InAs, and considerable exchange broadening of these NMR lines has been observed. Anderson (81) has given a treatment of the exchange effect in semiconductors. Bloembergen and Rowland (78) have also shown that associated with the exchange interaction is a pseudodipolar interaction, which as the name implies, has the same functional form as the dipolar interaction. This interaction arises from the presence of the electron-coupled nuclear spin interaction and the dipoledipole interaction and its magnitude is dependent on the relative amount of p - or &character of the electronic wave functions in the solid. In summary, nuclear spin exchange effects are to be expected in the NMR of the heavier elements in the solid state. From the exchange coupling constants information on the nature of electronic wave functions in solids may be obtained. 3. Chemical and Knight Shifts

The effective field experienced by a nucleus in a chemical compound is generally different from the applied field due to the shielding by the distribution of electrons around the nucleus. “A shift in NMR frequency, known as the chemical shift, proportional to applied field results.” For closed

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

53

shell, isolated atoms with the resulting spherical symmetry, the shift is simply due t o the diamagnetic circulation of electron density about the nucleus. That is, the electrons of the atom in the magnetic field will circulate in such a way so as to produce a magnetic field a t the nucleus directed opposite t o the direction of the applied field. This is a consequence of Lens’s law applied t o atoms. Lamb (82) has given an expression for the shift in isolated atoms. I n the case of diamagnetic molecules, the situation is more complex, because of the specific bond directions. Itamsey (83) has given expressions for the chemical shift in molecules which require, unfortunately, more infot mation than is presently available for most molecules. Recently, Das and Bersohn (84),using the variational approach of Tillieu and Guy (86), have calculated the chemical shift for the Hz molecule using only expressions for the ground state wave function of the molecule. This procedure has been extended by McGarvey (86) to the hydrogen halides and hydrides of Group VIA elements. The chemical shift is generally a sensitive function of the type of chemical environment around a nucleus. The magnitude of the shift is relatively small for protons, due to the fact that only one or two electrons surround the proton in chemical compounds. However, for heavier elements such as fluorine, it becomes quite large; the FI9magnetic resonance of H F and Fz being separated by about 6 gauss a t 10,000 gauss applied field. The chemical shift is a useful parameter in the study of molecular and solid state structure. Knight (87) observed that the nuclear magnetic resonance of nuclei in metallic copper occurs a t a higher frequency than in CuCI, a diamagnetic salt, The type of shift, which generally occurs in metals, is known as the Knight shift and ranges from 0.1 to 3y0 of the resonance frequency. The Knight shift is generally to higher frequencies (or lower fields) and its origin lies in the unpaired conduction electrons a t the Fermi surface of a metal. The nuclei, via the hyperfine interaction, will experience a net local field due to the net polarization of the unpaired electrons a t the Fermi surface. Since this spin polarization depends linearly on the applied field, except at very low temperatures, the shift is proportional to the applied field. The quantitative expression for the shift (88) involves the square of the wave function of the electronic states a t the Fermi surface and provides a direct check on the validity of various wave functions proposed for metals.

4. Nuclear Electric Quadrupole Interaction Nuclei with spin Z > >$ are not, as a rule, perfectly spherical distributions of charge, as may be shown by quite general quantum mechanical symmetry cwisiderations (89). All nuclei possess the spin axis as a sym-

54

D. E. O’REILLY

metry axis and the charge distribution is an ellipsoid of revolution, which may be oblate or prolate. This deviation from spherical symmetry possessed by nuclei of I > is quantitatively measured by the electric quadrupole moment of the nucleus. The quadrupole moment is a tensor, but may be characterized by a single scalar quantity &, the “electric quadrupole moment.” The importance of the nuclear quadrupole moment in nuclear magnetic resonance lies in the fact that it interacts appreciably with atomic electric field gradients and this interaction generally produces striking effects on the NMR spectrum, especially in solids. A t a nuclear site in a solid an electric field gradient, due to charges around the nucleus, will generally exist, if the atomic symmetry around the site is lower than cubic. For cubic symmetry the gradient of the electric field VE vanishes, since in cubic symmetry the x, y, and z directions are equivalent and in general v . E = 0 (Laplace equation) so that VE = 0. The electric field itself at a nuclear site in a solid is of course zero, since a nucleus is bound to the site. Deviations from cubic symmetry may be caused by the inherent noncubic symmetry of the solid or the presence of defects in an otherwise cubic solid. A simple kind of symmetry which applies to a large number of crystals is axial symmetry; that is, two directions are equivalent, such as z and y. When the quadrupole interaction is small compared to the energy separation between the 21 1 energy levels of a nucleus in a magnetic field Ho, the effect of the quadrupole interaction is to destroy the equal spacing. For axial symmetry the effect may be described in terms of a single parameter (6, 90) eq, as follows:

+

eq = Jp(r)(3 cos2 $t

- l)r*d*r

(18)

Integration is over charge density p(r) at an angle between the radius vector r and the symmetry axis. The application of first order perturbation theory (6, 90) then yields the following expression for the energy levels Em, mccHo e2qQ Em = [3m2- 1(1 + 1)](3 cos2 0 - 1) I + 8 I ( 2 I - 1)

(19)

where 0 is the angle between the external magnetic field and the symmetry axis. The effect of the quadrupole interaction to first order on the energy levels of an Z = 94 nucleus is illustrated in Fig. 7. It will be noted that the energy separation between the and -55 levels is unaffected. In general for half integral spin the $4 t)-56 separation is unchanged by the quadrupole interaction to first order; this separation is, however, changed in second order and for nuclei with even I , all separations are changed in first order perturbation theory. In the event that eq is sufficiently large, but still small compared to

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

p H , it is necessary to include second order effects, which for the m =

55

35,

-% levels give a separation

From Formulas (19) arid (20) it is clear that a first order effect is independent of the applied field Ho*, while the second order splitting decreases as Ho increases. In t.his way the two effects may be experimentally distinguished. From single crystal data of the magnetic resonance a t various angles 8, it is clear from Equations (19) and (20) one may derive the direction of the symmetry axes and the values of q& in the case of axial symmetry. The NMR lines from a single crystal of axially symmetric a-A1201with the magnetic field directed along the symmetry axis are shown in Fig. 8. -2 2

--* Y ( H,

-3

---_

-1

--_

2

2

zI

+2AH]

-

+ ----

8 --*

t 3 e2q Q AH=-(3

40hy

cOs*e-t)

FIQ.7. Energy level diagram for nucleus with I = 44 in a magnetic field Ha without and with electric field gradient of axial symmetry to first order in perturbation theory. The splitting without the axial electric field gradient is hrHo.

In Formulas (19) and (20) the actual value of the quadrupole momelit Q that occurs is not that of the bare nucleus, but the bare nucleus value multiplied by a parameter l - y m . This is necessary because the electron distribution of the atom is distorted when the atom is in an electric field gradient, due t o the interaction of the electrons with the field gradient. This distortion produces an additional gradient which is -7- times the

* Except of course for small enough fields so that the quadrupolar energy becomes comparable to the magnetic energy.

56

D. E. O'REILLY

field gradient due to charges external to the nucleus. rl.is known as the antishielding factor and has been computed theoretically for a number of ions (91,SS). The experimental data yield only the product of q and Q, and hence the nuclear quadrupole moment must be determined by some other method in order to obtain q. Accurate values of quadrupole moments for a number of nuclei are known. Bersohn (93) has calculated values of q for several ionic crystals by performing the summation in Equation (18) and obtains rather good agreement with the experimental values. When the gradient of the electric field does not have axial symmetry another parameter must be introduced to describe the magnitude of the electric field gradients in the solid. This is the asymmetry parameter 7 , which is a measure of the deviation from axial symmetry (6, 94). In addition, the direction of the principal axis of the electric field gradient tensor must be specified. From single crystal rotation patterns, the values of these parameters may be deduced (94).

I3in)

n

\I

4-51

Y

I \L

M, vi) +

\

I

(+%>+%)

un

Powder patterns of crystals with axial symmetry yield the value of qQ but do not, of course, give the direction of the axis of symmetry. Line shapes to be expected for the magnetic resonance in this situation have been calculated (96) and for I = 96,the shape is illustrated in Fig. 11 for polycrystalline corundum (a-Al209). The usefulness of quadrupolar effects on the nuclear magnetic resonance of I # nuclei in the defect solid state arises from the fact that point defects, dislocations, etc., give rise t o electric field gradients, which in cubic crystals produce a large effect on the nuclear resonance line. In noncubic crystals defects of course produce an effect, but it may be masked by the already present quadrupole interaction. Considerable experimental data have been obtained by Reif (96,97') on the NMR of nuclei in doped, cubic, polycrystalline solids. The effect of defect-producing impurities is quite

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

57

marked; for example, in AgBr doped with Cd++, a molar concentration of 5 X lod6of Cd++ produces an observable first order quadrupole interaction effect on the Br resonance line width. The line widths and shapes to be expected for cubic crystals containing point defects have been derived by Cohen and Reif for both first and second order quadrupole interaction (97). In particular, for point defect concentrations greater than about 0.1 (in terms of probability f, of a lattice site being occupied by a defect) distributed in a random fashion over various possible lattice sites, the second order interaction gives rise to a lopsided central component whose shape is given by (97) --(If-Ho)/l~

H-Ho>O

( H -Ho)/Pu

H-Ho
= (l/We

g(H)

= (l/We

(21)

where a is a constant which depends on the strength of the electric field gradients and the probabilities for site occupation by various kinds of defects. The validity of Equation (21) requires that the lattice must be treated as a continuum in the evaluation of the angular dependence of electric field gradients. It has also been shown (97) that the proper factor to use in computing the electric field gradient produced by a point defect, taking into account the effect of polarization of the medium, is (26 3)/5e, where c is the dielectric constant of the medium. This result is based on the continuum approximation for the solid.

+

C. APPLICATIONS 1 . Atomic and Molecular Motion i n Solids

As discussed in Section II,A,2, the motion of nuclei has a very pronounced influence on the nuclear magnetic resonance phenomena. The local fields experienced by the nuclei, after a certain frequency of motion has been exceeded, decrease as the rate of motion increases. The effect of atomic motion in the solid state on nuclear resonance line width is illustrated by the behavior of Na2Sresonance from NaCl as a function of temperature (97).In Fig. 9 is shown the variation of the NaZaline width with temperature for “pure” NaCl and NaCl doped with an atomic of CdC12. As discussed in Section II,A,2 fraction concentration of 6 X the low-temperature, rigid-lattice line width will narrow when the frequency of motion of the nuclei under observation equals t,he line width expressed in set.-'. The number of vacancies present should be equal to the concentration of divalent impurities and the jump frequency of Na+ is the product of the atomic vacancy concentration and the vacancy jump frequency

58

D. E. O'REILLY

which is obtained from conductivity measurements. In this way one estimates the line to begin to sharpen near 230" in good agreement with the data of Fig. 9. From the slope of a plot of log Av versus 1/T, an activation energy of 0.66 ev is estimated (97) for t8hediffusion of Na+. This agrees

FIQ.9. Na" line width as a function of temperature in NaC1. Solid curve is that for NaCl sample doped with molar concentration 6 x 10-4 of CdC12; dashed curve is for "pure" NaCl sample (97).

E

OJ 100

I

I

I

140

I

I &

180

I

- ?\A 220

Temperature ("K )

FIG. 10. Variation with temperature of the second moment of the proton resonance absorption line for polycrystalline cyclohexane CaEIls (101).

MAGNETIC RESONANCE IN CATALYTIC BESEABCH

59

reasonably well with values obtained from diffusion (0.77 ev) and conductivity measurements (0.83 ev). Reif also made intensity and relaxation time measurements on the Br79and Br81lines from AgBr samples which show the effects of defects in the solids. The effect of atomic motion has been measured in many other solids, such as the alkali metals (98),hydrogen in palladium (99),and KHzPOd (100). An instructive illustra,tion of the effect of molecular motion in solids is the proton resonance from solid cyclohexane, studied by Andrew and Eades (101). Figure 10 illustrates their results on the variation of the second moment of the resonance with temperature. The second moment below 150°K is consistent with a Doa molecular symmetry, tetrahedral bond angles, a C-C bond distance of 1.54 and C-H bond distance of 1.10 A. This is ascertained by application of Van Vleck's formula, Equation (17), to calculate the inter- and intramolecular contribution t o the second moment. Calculation of the intermolecular contribution was made on the basis of the x-ray determined structure of the solid. The sharp decrease in second moment between 150 and 186°K is quantitatively interpreted in terms of rotation of molecules about the threefold molecular axis. This agreement is obtained by appropriate averaging of the angular factor of Equation (16) over the motion (76) for both the intra- and intermolecular contributions. The sharp fall in second moment at 186°K shows that molecular motion about other axes than the triad is occurring. The resulting moment between 186°K and 220°K is accounted for by assuming the intermolecular contribution is averaged t o zero. Above 220°K the drop in second moment shows that translational diffusion of cyclohexane molecules in solid is occurring. Andrew and Eades estimate the activation energy for diffusion to be about 8 kcal./mole from the NMR data. Relaxation time measurenients were also made and from the rate of change of log Ti versus 1/T the activation energy E for rotation about the triad axis was found to be 11 f 1 kcal./mole. This was done by making use of the relation between T and T~ derived by Bloembergen et al. (3) and assuming an Arrhenius type relation between T~ and E. Data on some other molecular crystals, such as methane (102), ammonium halides, and various hydrocarbons (103) have been obtained. A NMR study of water adsorbed on silica gel has been made by Zimmerman et aE. (18). Transverse (Tz)and longitudinal (TI) relaxation times of various amounts of water adsorbed a t 25" have been obtained with the use of the spinecho technique and a two-phase behavior of both Tz and Ti relaxation times has been observed as illustrated in Figs. 10a and b. Generally only one TI value is obtained, as for a single phase, except for x / m (g H20/g solid) values in the vicinity of x / m = 0.126. Two values of TZ

60

D. E. O'BEIILLY

no. 10a. Transverse relaxation times for protons of water adsorbed on silica gel (18).

phose Two phose,shcrt time cmpment o Two phase,long time component OsKgle

* 160

FIG.lob. Longitudinal relaxation times for protons of water adsorbed on silica gel (18). are observed for x/m > 0.07. The simultaneous two-phase nature of Ta and one-phase nature of TI are explained by the magnitude of the time that a proton resides in a given phase. This lifetime is generally long compared to T, values but short compared to TI values. The phase associated with the short transverse relaxation time Tal of Fig. 10a is ascribed to the water which has the largest heat of adsorption since this phase predominates at

61

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

low surface coverages. The lifetime of a proton in this “short time” phase sec. and 2.5 X lo-* for the at x/m = 0.104 is estimated to be 1 X phase with the long transverse relaxation time ( Tn). The appearance of two distinct longitudinal relaxation times is due to an abrupt increase of the lifetime of protons in a phase. This increase exceeds a factor of 10 in magnitude and may be due to an ordering of molecules that occurs when the molecular interactions become sufficiently strong. The two phases observed by TI measurements have been shown to be identical with those represented by the T2 data. Bloembergen et al. (3) have presented a relationship between the correlation time for molecular rotation in liquids and the relaxation times assuming that relaxation takes place via mechanism (i) of Section II,A,3. Although the theory can be a t best semiquantitative when applied to the protons of water molecules adsorbed on silica gel, values of the nuclear correlation time have been calculated (18) from the TIdata. These correlation times as a function of x / m show a definite change of slope near a monolayer coverage. This result, if corroborated by data on other solids, may provide a rather unique method for the determination of monolayer coverage. 2. Structural Defects in Solids Watkins and Pound (104) performed an experiment which illustrates the effect of strain on the magnetic resonance of bromine and iodine nuclei in cubic KBr and KI. These crystds were subjected to plastic deformation (a 22% change in dimension occurred along the 100 axis for the K I crystal) and it was found that the intensity of the resonance line in the original undeformed crystals decreased to 0.4 of its original value for the bromine isotopes (BP, Brsl, I = 95) and to 0.3 of its original value for the (I = 96)resonance. The ratio of the intensity of the central component (45 f+ -%) of the 21 lines produced by the quadrupolar interaction in noncubic symmetry to the total intensity including all the satellite components is for nuclei with I = 45 and %s for nuclei with I = 95.The dislocations produced in the crystal by plastic deformation will cause a deviation of the local symmetry from cubic symmet,ry, with resulting electric field gradients which cause the satellite components to be well separated from the central component, which is unaffected in first order by the interaction. A range of eq values occurs and the satellites are not sharp lines but are spread out over a large range of frequency or field strength so that they are not experimentally observed. This “washing out” of the satellites is particularly pronounced for B P , BrS1,and 112’because of the large nuclear quadrupole moments and antishielding factors for these atoms. Effects can be detected

so

62

D. E. O’REILLY

even for the most “perfect” cubic crystals. In terms of dislocation lines Watkins estimated the order of 1Olo lines/cm.2 in the deformed crystals would produce the observed effects (106). The effect of dislocations has also been studied by Bloembergen and Rowland (106) in cold-worked copper (Cue3 and Cuesresonances), and also the effect of alloying in Al-Zn alloys (A127resonance) by Rowland (107). Otsuka and Kawamura (108) have studied the NMR of in KI, Na2* in NaC1-NaBr mixed crystals, and Brsl in KBr-NaBr mixed crystals and have estimated dislocation densities in these materials. Reif (97) has observed the effects of point defects on nuclear resonance lines of B F , BrE1,NaZ3,and Li7 in cubic crystals. The effect of temperature on the line widths and spin-lattice relaxation times was investigated for various impurity levels in AgBr and found to be quite pronounced due to vacancy association and diffusion.

;“63

FIQ.11. A powder pattern of AP7 NMR in a- AlpOI at NMR frequency of 7.20 mc./ second (Ho= 6490 gauss); the magnetic field increases from left to right with a total scan of about 1500 gauss. This is the dispersion mode audio signal at HI = 0.5 gauss and is the absorption envelope except at certain points as described in Section 1I,C,2 (109).

Another example is the A12’ resonance from polycrystalline a-AI2O3and yAlnOa(109), a highly defective form of aluminum oxide. In Fig. 11 is illustrated a recorder curve of powdered corundum (a-A120a).The line shape is that of the absorption envelope defined by a large number of dipolar broadened lines distributed continuously a t various field strengths due to the angular dependence of the splitting in Equation (19) and Fig. 7. The signal of Fig. 11 was obtained at high rf field strength (HI 0.5 gauss) on the dispersion (u)mode. For inhomogeneously broadened magnetic resonance lines one obtains the absorption envelope rather than a dispersion derivative if certain conditions ale satisfied, as have been derived both by Portis (110, 111) to describe analogous effects in electron spin resonances, and by the author (109) to interpret the NMR effects. The audio signal is characterized by the fact that it is A out of phase with the modulation field phase, except at points of the powder pattern where sharp peaks occur and homogeneous dipolar broadening is present. These points correspond

-

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

63

to the dips in the central component of the recorder curve of Fig. 11 and are due to second order splitting in (r-Al203. The separation between the peaks (minima of Fig. 11) is in good agreement with the value calculated using Equation (20). This shape of the powder pattern is that predicted ( 5 ) for an I = 35 nucleus in axial symmetry. This situat,ion occurs for the AlZ7nuclei in (r-A1203 which is a hexagonal close-packed array of oxygen atoms with the aluminum atoms ordered in of the holes octahedrally coordinated with oxygen atoms. The plateau edges on either side of the field Ho = w o / y ~are equispaced a t a field strength of 67re2qQ/40yhas one may calculate (5) from Equation (19). The value of 3e2qQ/40h calculated from the spectrum is 175 kc. per second in good agreement with the single crystal data of Pound (6) for corundum. A similar spectrum was obtained for spinel MgAlZOa, a cubic closepacked array of oxygen atoms with the magnesium atoms in the sites tetrahedrally coordinated by oxygen atoms and the aluminum atoms in Bites octahedrally coordinated by oxygen atoms. The point group at the aluminum sites is Dad (112) and Formula (19) thus applies. From the plateau positions a value of 263 kc./sec. is obtained for 3e2qQ/40h.Second order effects cause splitting of the central component as in Fig. 11. The separation between the peaks agrees well with the value calculated using Equation (20).

FIQ. 12. Powder pattern of y-Al,Oa at 7.20 mc./second. Scanned under same conditions as Fig. 11 except gain X 2. Dashed curve with circled points is given by Equation (211, (109).

Figure 12 illustrates a recorder curve of y-&03 with the same horizontal (field strength) scale as the (r-A1203 spectrum. The vertical scale unit is equal t o 0.5 unit of the (r-Al2O3 spectrum scale. The line drawn above the spectmm base line separates the central component intensity above the line from that below the line due to satellites. The integrated intensity of the absorption envelope above this line is approximately %s of the total integrated intensity of the a-Al203 spectrum. The broadening of this portion of the spertrum should thus be a second order effect. This was checked by scanning the resonance a t twice the frequency and field strength where the central component collapsed by a factor of two in breadth in agreement

64

D. E. O’REILLY

with Equation (20). The line shape for the central component is fairly well approximated by Equation (21) with 2a = 27 gauss. A crystallographic structure of y-A1203 is not known. It is one of a number of aluminum oxides that can be prepared by dehydration of alumina hydrates and which at higher temperatures (-1150°C) convert to a-A12O3. These aluminum oxides are referred to as transition aluminas (119).The x-ray patterns of these oxides are diffuse and similar (113). Fiom the x-lay pattern it is faiily certain that y-A120s has a cubic close-packed oxygen lattice and some interpretations of the pattern consider it to be a disordered spinel-type structure with the A1 ions occupying both the tetrahedral and octahedral sites with some of these spinel cation sites (38 out of 24 in unit cell) being vacant or occupied by protons. It has also been suggested (114) that a first approximation to the y-A1200lattice is the MgO type structure corresponding to the formula A 1 ~ 0with the A1 atoms occupying N of the octahedral holes of the cubic close-packed array of oxygen atoms. An approximate spinel-type lattice is obtained by placing some of the aluminums in tetrahedral holes with an approach to spinel unit cell in 8 volumes of the A l s o “unit cell”. From the point of view of the NMR spectrum, it appears that r-A120J is a highly disordered structure, and one takes as a model for quantitative interpretation the MgO type structure, Also, with the aluminum atoms randomly occupying of the octahedral sites. This is an extremely simple type of lattice for which the necessary lattice sums of l/Re (second order interaction) are known. Aside from the line shape, two convenient parameters which characterize the spectrum are the first and second moments of the central component. These may be calculated for a given structure from knowledge of the values of I , &, and yoofor the atom in question. If the presence of 0-- and AP+ ions in the structure is assumed, the value of a in Equation (21) and also the first and second moments can be estimated, using literature values of I , & and y m . One calculates a value of 2a = 17 gauss for A l s o in fair agreement with the best fit value of 2a = 27 gauss for y-A1203. The first and second moments calculated for the line shape (21) are ( ( A H ) ) = 17 gauss and ( ( A H ) 2 )= 1.8 X loa gauss2 comparing with ( ( A H ) ) = 33 gauss and ( ( A H ) z ) = 3.9 X lo3 gauss2 measured for y-A1203. Calculations on modifications of the model by addition of protons and placing some AP+ ions in tetrahedral sites can be carried out. However, in view of present uncertainties in values of r., due to covalent effects and effects of crystal strain and size on the spectrum, this has not been done. A number of samples of y-alumina with different BET surface area were examined by observation of AP’ resonance as in Fig. 13. The shape and breadth of the Mt, -36 component for these samples were constant,

N

65

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

-

100

0

c f

80

a 4

a

c

60

a

t > 40 W b

3E

20

100 200 300 BET SURFACE AREA, A(meter8*/grorn)

4 00

FIQ.13. Intensity of Al" 36 t-) -36 transition vemw BET area, yAl,O,

(173).

independent of surface area. All the spectra were fitted to Equation (21) equally well with a value of 2a = 28 f 3 gauss. However, the integrated intensity of the (W t)-%) resonance component varied with surface area as shown in Fig. 13. The surface of a solid may be considered as a defect of the solid. Nuclei near the surface of the solid will experiencelarge electric field gradients due to the asymmetry of their environment. If these gradients are sufficiently large, the NMR signal of these nuclei in a polycrystalline sample will be broadened enough so as not to be detected by the instrument. The fraction F of aluminum nuclei so situated will not contribute to the observed intensity I. I is related to F in the following manner

I

=

lo(1

- F)

lois the intensity when F = 0; i.e., in the limit of zero surface area. For estimation purposes, consider the yA1203 surface phase to be similar to the bulk structure-a cubic close-packed array of oxygen atoms with aluminum atoms in interstices. With this model there is one A12' nucleus of

66

D. E. O'REILLY

the first cation surface layer per about every 10-12 bz of surface. The precise amount of surface corresponding to a cation in the first cation layer will depend somewhat on the crystal plane considered to form the surface and the distribution of A127nuclei. If aluminum nuclei in the first layer only contribute to F , then

F E

A

x

104

1.2 x 1022 x 10-16

= 8 X 104A

wheie A is total surface area, meter2/gram. For this model the intensity decrease is linear with A . The best straight line representative of the points of Fig. 13 is drawn and the corresponding slope is 16 X lo-' gram/meter2. Thus, on the average, two layers of AlZ7nuclei must be affected by the surface so as to give a NMR signal broadened beyond detection. The scatter of the data of Fig. 13 may result from dislocations in the bulk solid which may vary from sample to sample. It is reasonable that the spectra of nuclei that are observed are not changed by the surface, since the interaction decreases as q2 by Equation (20) which, in turn by Equation (18), behaves as the inverse sixth power of distance, so that at a given nuclear site the electric field gradient geneially will either be quite different from sites of the bulk or essentially the same as sites of the bulk solid.

3. N M R of Nuclei at Low Concentration in Solids Frequently the properties of solids are considerably altered by small concentrations of impurities. Unfortunately only a few nuclei are suitable for the study of their nuclear magnetic resonance at low concentration in solids. Investigations of the FIQ(I= 36, 100% abundant) resonance from 7-alumina doped with varying amounts of fluorine and the proton magnetic resonance of dehydrated silica gel and silica-alumina are described below. a. F'Q N M R of Fluorine-Doped 7-Alumina. The samples studied (116) were high surface area aluminum oxides doped with fluorine by addition of aqueous H F to alumina and subsequent dehydration. A sufficient number of paramagnetic impurities were present in the samples t o give relaxation times of the order of 0.01 second. The BET surface areas of most of the samples examined were within 20% of 250 meter2/gram. Figure 14 illustrates a recorder curve of the resonance absorption derivative of PI8 for a sample containing 2.7 wt. % of fluorine. The time of scanning the magnetic field through resonance was 2 hours and the time constant of the spectrometer was 90 seconds in order to increase the available signal-to-noise ratio. The FIBresonance absorption was examined in the concentration range of 0.3 to 12.5wt. % fluorine. The chemical shift 6 is defined as

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

6 = (H, - H ) / H , X 10"

67 (22)

where H , is the magnetic field at which resonance occurs for the reference compound and H that for the sample a t fixed frequency. The chemical shifts for fluorine (116) are quite large, ranging from -77 ppm for HF (liquid) bo +548 ppm for Fz (liquid) relative to F- (aqueous), the more ionic type fluorine bonds having smaller 6 values (117). Although anisotropy of the chemical shift is expected for nuclei in noncubic symmetry, the average value obtained for a polycrystalline solid should be comparable to these shifts for liquids, which are also average values. The chemical shift for concentrations of fluoiine in the intermediate and on the high part of the concentration range of the samples examined was found to be (-40 f 40 ppm) relative to F- (aqueous). No large shift for the fluoride ion occurs in the solids examined compared to the heavier halides in the solid state (118), indicative of the ionicity of the A1-F bond involved.

-

-

v=1554mc/r Modulallon 2.35 OOUIS

FIG.14. The F10 absorption derivative of 2.7 wt. % of fluorine in alumina at 15.54 mc./second. Circled points correspond to Gaussian shape (116). Adsorbed water was observed to have a large effect on the FIBspinlattice relaxation time for fluorinedoped aluminas in the dilute and jntermediate concentration range of fluorine (0.3-8 wt. yo F). An increase in TIby a factor of 2 to 3 was observed in these samples when adsorbed water was removed from the solid by heating between 200-300". The effect was completely reversible; addition of oxygen-free water back to the solid resulted in recovery of the original (shorter) relaxation time. This effect was observed by the measurement of the in phase and ?r/2 out of phase components of the dispersion derivative a t resonance ax'/dHo a t high rf power, from which effective values of TImay be calculated (46). Values of TI were also obtained by saturation of the resonance absorption derivative. No dependence of FIBrelaxation time on adsorbed water was observed for concentrated fluorinedoped aluminas (-12 wt. yo F). Since the bulk structure of the solids is known to be unaffected by adsorbed water, the effect of physically adsorbed water on the FIBrelaxation time is a surface phase effect. There are several mechanisms of relaxation by which it is possible to explain the influence of adsorbed water in a qualitative manner;

68

D. E. O’BEILLY

they all require that the fluorine nuclei be in or close to the surface phase of the solid in order that they be affected by adsorbed water. These mechanisms include types (i), (ii), and (v) of Section IT,A,3. The line shapes of the resonance absorption curves were rather well described by a Gaussian shape, as is shown in Fig. 14. Two parameters are necessary in fitting a recorder derivative with a Gaussian shape function: the maximum value of the derivative signal (dx”/dH),. and the width between points of maximum slope of the absorption, 6Hm,, which are given by the maxima and minima of the derivative. In this way the values of 6H,, given in Fig. 15 for various amounts of fluorine were obtained. A check on these values was obtained by the fact that the product of ( d ~ ” / d H ) , and 6H,2 is proportional to the area under the absorption curve and hence the total amount of fluorine, CF.That is K(dx”/aH)mn (6Hmn)’ = CF

(23)

where the number K is a constant for a constant shape of absorption curve. CFwas known from chemical analysis of the samples so that relative values of 6H,, could be checked. The error limits of Fig. 15 were obtained from the reproducibility of the 6H,. values and the difference between the 6 H m . values obtained in the two ways described above.

W1.Y OF FLUORINE

FIG.15. Line width of concentretion (116).

Fl9

NMR of fluorhedoped aluminum oxide v e m fluorine

MAGNETIC RESONANCE I N CATALYTIC RESEARCH

69

For a Gaussian shape there is a simple relationship between 6Hm. and the second moment ((AH)2).

((AH)’) = (6HmJ2/4

(24)

Using Equation (24) and the 6H,. values of Fig. 15, values of ((AH)2)may be calculated.* As is illustrated in Fig. 15: the FI9line width at lowest F concentrations is about 5.60 gauss; it rises sharply for the intermediate fluorine concentrations and then levels off at higher concentrations. The sharp increase in line width can only be due to an increase in the local field a fluorine nucleus experiences due to other fluorine nuclei of the sample being closer t o it. This effect will diminish when a fluorine nucleus has a maximum number of neighbors at minimum distances and accounts for the leveling off of the values of 6H,. at higher fluorine concentrations. Moreover, the effect of physically adsorbed water discussed above and the magnitude of the increase of 6Hm. suggests the fluorine is bound in the surface phase of the r-Alz03. This conclusion is given quantitative interpretation below in terms of a simplified model for the system using Equation (17). Consider the available fluorine sites to be the lattice positions of a cubic, close-packed, two-dimensional lattice. These are the oxygen positions of a cubic, close-packed, oxygen lattice in the (111) type planes. Aluminum ions are situated below this twodimensional anion layer. Suppose a fraction f of all the sites is randomly occupied by fluorine atoms; the remaining sites are occupied by 0l6with zero magnetic moment. Let ((AH)2)A~ denote the limiting second moment for zero fluorine concentration and ((AH)2)~ the second moment of FIBdue to other Flg nuclei when the lattice under consideration is full. Then for any intermediate concentration of FI9the line width for a Gaussian shape is

6Hma

=

2 [ ( ( W 2 ) ~-I1 f((AH)2)~11’2

(25)

where ( ( A H ) 2 )= ~ ~7.84 gauss2from Fig. 15 and Equation (24) and ((AH)”)F depends only on the distance between adjacent fluorine nuclei, as can be seen by inspection of Equation (17). With this distance equal to 2.60 A which is an intermediate value of known F-F distances in solids, ((AH)2)~ = 6.53 gauss2. The value of the wt. % of fluorine for which f = 1 may be estimated by the following considerations. Equation (25) may be written to good approximation (within 5%) as

+

6Hm. = 2((AH)2)~1’2f[((AH)2)~/((AH)2)~1’21

(26)

* ( ( A H ) 1 )may be more .$atisfactorilyevaluated by performing the integral of Equation (14) on a recorder curve, but for low concentrations of nuclei such m in this cme, accuracy is difficult to obtain by integration.

70

D. E. O’REILLY

So up to f = 1, 6H,, is a linear function off to good approximation. If we assume above f = 1 excess fluorine atoms over those required to fdl the available surface are in a bulk solid phase of definite composition, then the second moment of the line is the weighted sum of the second moments of fluorine in the bulk phase ((AH2))band fluorine on the filled surface ((AH2)),,.That is, if n. is the mole fraction on t,he filled surface and 731, the mole fraction of fluorine in bnlk phase, then for f > 1

n.

=

l/f,

[

nb =

(f - l)/f,and

6H,, = 2 71 ((AH)’). +

f

((AH)Z)t,]l’z

For f > 1 linearity of the 6H,. versus f curve will not occur. From the data of Fig. 15, this deviation appears t o occur in the neighborhood of 5 wt. yoF. The drawn curve up to 5.0 wt. yoF was calculated from Equation (25) with an F-F distance of 2.60 A. For f > 1 Equation (27) was used, the best fit being obtained with ((AHz))b= 20.7 gauss’. is the second moment of presumably rather The value of ((AH)2)~1 isolated fluorine atoms bound to a y-AlZOs surface. This value is in good agreement with what one estimates for two A1 nuclei close t o the fluorine, one at 1.70 A and one a t 1.89 A, such as occurs for the Al-F bonding in A1F3, estimating the contribution of the remaining A1 nuclei in the solid a t distances greater than 3 A by considering them to be continuously distributed in the solid with known density. Because of the l/r6 dependence of ((AH)2)A1not much error is involved in this procedure. The value of ((AH)z)bis slightly less than that observed for aluminum fluorides (AIFa, Na.9AIFe) and corresponds more closely to an aluminum oxyfluoride which is magnetically more dilute. The actual surface area a t 5 wt. yo fluorine, calculated by multiplying the area per fluorine atom by the total number of fluorine atoms, is less than one-half of the average BET (nitrogen) area of the samples. Up t o now we have, for simplicity, neglected the presence of protons on some of the sites, presumably in the form of OH- ions or AI-OH groups. These protons, unless in states of large amplitude motion, would contribute significantly to the local fields experienced by fluorine nuclei. I n view of the present lack of extensive information on these protons (inteinuclear distances, state of motion, etc.) they are not included in the above model, except to say they may occupy a sizable fraction of the BET surface area, randomly or in patches. In summary, the NMR data on the samples examined indicate that fluorine occupies the surface phase up to the order of 5 wt, % F, and forms a bulk phase of aluminum fluoride a t higher concentrations of

MAGNETIC RESONANCE I N CATALYTIC RESEARCH

71

fluorine. It is quite possible, however, that the mode of addition of fluorine to the oxide may allow the fluorine to enter the bulk phase a t low F concentration or occupy a larger portion of the available BET area. b. Proton Magnetic Resonance of Dehydrated Silica Gel and SilicaAlumina. A relatively sharp proton magnetic resonance signal has been found (119) in high area silica gel and silica-alumina (12.5 wt. % ' A1&) samples which have been dehydrated for 16 hours in vacuum a t 500". In view of the unique properties and possible importance of these protons in the catalytic cracking activity of silica-alumina, a NMR study of these protons has been made (119, 120). I n Fig. 16 is shown an experimental resonance absorption recorder curve of the above-mentioned protons. This signal is from a Davison silica gel (SG) with a BET surface area of 687 meter2/gram, dehydrated in vacuum a t 500". The width between points of maximum slope of this resonance is 310 milligauss and the corresponding spin-spin relaxation time is 1.8 X lo-'

__I

MODULATION,120mpauss

FIG. 16. Proton magnetic resonance absorption derivative from highly dehydrated silica gel at 7.20 mc./second. The circled points are those corregponding to a Lorentzian ahape (173).

sec. The line shape is Lorentzian out to about 8 times the half-width of the absorption where the signal-to-noise ratio approaches unity. Silicaaluminas (SA) show a similar line shape; a SA sample of B E T area of 425 meter2/gram has a width of 260 milligauss and a spin-spin relaxation time of 2.1 X lO-'sec. For these solids, the proton line width and shape were found to be independent of temperature over the temperature range from -210 to +28OoC. As shown in Fig. 17, the number of protons from a series of silica-alumina samples with differing BET surface areas is a nearly linear function of surface area, indicating that essentially all of the protons are situated in the surface phase of the solid. The samples corresponding to the data of Fig. 17 were prepared by steam sintering of the above-mentioned 425 meter2/gram sample a t various temperatures above 5OO"so as to reduce the surfa.ce area to the values given and then soaked in water for 4 hours, oven-dried a t 110" and evacuated a t 500" for 16 hours. A plot somewhat similar to Fig. 17 has been obtained for silica gel. The slope of the best straight line repre-

72

D. E. O'REILLY

senting the da,ta of Fig. 17 is 1.3 X 10'4 crn.72; the corresponding value for silica gels is 2.6 X 10" cm.". The spin-lattice relaxation time of these protons a t room temperature was found to be strongly dependent on the paramagnetic impurity content of the solids. Values of TIfor several different impurity contents are shown in Fig. 18. The slope of the best straight line through the points of Fig. 18 is -1.2, while the theory of spin diffusion (67)predicts a slope of -1.1. The proton relaxation thus appears to be entirely via the paramagnetic impurity ions in the solid, as would be expected if the protons are rigidly attached to sites of the solid and not undergoing large amplitude motions relative to one another. This conclusion is consistent with the tempera-

0

I 0

I00

I

I

ZOO 300 BET AREA (malorsz/gram)

I 400

800

FIQ.17. Number of protons in silica-alumina (12.5 wt. % Allot) dehydrated at 500" versus BET surface area. Dashed line is the best straight line representing the data (173).

Figure 19 illustrates the spin-spin relaxation time for SA as a function of BET area. T2 is constant for areas above about 200 meter2/gram, below 200 meter2/gram T2rises to a value near 3.6 X lO-'sec. for a sample with an area 5 meter2/gram. A similar plot for SG samples shows T2to be constant at 1.8 X 10-4 sec. for surface areas above 100 meter2/gram. T2 increases slightly below 100 meter2/gram. In Fig. 20 is given the proton saturation behavior of a SA sample with an

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

73

area of 425 meter2/gram. The absorption (x") saturates (y2T1T?Hl2= 1) at H I = 14 milligauss (TI= 0.04 sec.) where H1 is the rf field strength effective in causing spin transitions. The dispcrsion derivative a t resonance dx'/dHo on the other hand drops t.0 one-half its constant value at intermediate rf field strength at H1 = 160 milligauss N l/yT2. A similar behavior is observed for SG samples; Tl= 0.1 sec. for the Davison sample and ax'/dHo saturates at H1'v l/rTz 'v 210 milligauss.

t FIQ.18. Spin-lattice relaxation time 21' for silica gel (SG) and silica-alumina (SA) versus paramagnetic impurity content N. The straight line corresponds to the relation 2'1 0~ N-1.' (173).

The chemical shift 6, d e h e d by Equation (22), was measured at 40.0 and 15.5 Mc./sec. and was found to be -3 2 relative to water for both SA and SG. The derivatives of the resonance absorptions were recorded in the measurements. If the total anisotropy of the chemical shift of protons in the solid is somewhat less than the line width, the cross-over point of the derivative will correspond to the average value of 6 as for liquids, and will be directly comparable with the shifts for protons in the liquid state. Comparison of the shift value with those of H30+ (aqueous) (I,%'), 6 = 4-11, OH- (aqueous) ( I a l ) , 6 = +lo; dilute solutions of alcoholic-type protons

74

D. E. O'REILLY

in nonpolar solvents (122), 6 = -4; and those found for hydride-like protons, 6 = -10 to -19, suggests that the majority of protons on both materials is bound as rather isolat.ed Si-OH groups. Kittel and Abrahams (123) have predicted an approximately Lorentzian magnetic resonance line shape for a system of spins which are randomly distributed over a small fraction of a large number of possible sites. This effect has been obseived in electron spin resonance (124). Kittel and Abrahams estimate that appreciable deviations from Gaussian shape will occur when the fraction of sites occupied, f, is less than 0.1, in the case of spins of I = 4% in a simple cubic lattice with the magnetic field directed 4.00

-

-

3.00

O\

0

\

N

P

'\.---------_-

I

0 u) W

O

If

P.00

-

0

0

100

I

too

0

0

0

I

1.00

N

I

I

300

400

AREA.m'a-' BET AREA.rn*g-l

FIG.19. Spin-spin relaxation t i e of protons in silica-alumina versus BET surface area (i79).

along the 100 direction. If each oxygen atom of the sample is considered to be a possible lattice site for a proton, values of f - 0.03 and f III 0.09 are estimated for SA and SG, respectively. In the case that only surface oxygen atoms are possible lattice sites, the corresponding values are f 'v 0.09 and f N 0.22, as estimated from the BET surface area and assuming a close-packed array of oxygen atoms 2.80 8 apart a t the surface. The value of f below which an approximately Lorentzian line shape results depends on the type of lattice available for the protons. Since this is unknown for the systems studied, it can be said that these values are consistent with the dilute spin hypothesis. The temperature-independence of

75

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

the line width and shape over the temperature interval studied suggests that the protons are rigidly attached to sites of the solid and that the Lorentzian line shape is not the result of motional narrowing. The behavior of the dispersion mode derivative is also consistent with a proton dilute spin system, since if only a small fraction of the possible lattice sites are randomly occupied the majority of the protons will experi-

1.0

'

0.5

:

0.1

:

c

m

3c m 3 51; 0 2

4

-

; 0.05

1 I

1

I I 1l111 5

lot

I

I I I I1111

so

100

t

I

I I I1111 500

00

RF FIELD STRENGTH, HI YlLLlOAUSS

FIG.20. Saturation behavior of NMR absorption (x") and dispersion derivative at resonance (ax'/aHo) for proton resonance of silica-alumina (sample of area 425 metera/ gram) dehydrated a t 500". The audio modulation frequency was 40 C.P.S. Arrows on abscissa indicate values of HI for which saturation of x" and ax'/aHo occurs (173).

ence local fields of the order of l/yTz rather than of the square root of the second moment which, fol a Lorentzian shape, is much laiger than l / ~ T z . Thus, saturation of the dispersion will occur at HI 'v 1/yT2, rather than a t HI of t,he order of the square root of the second moment as is true for concentrated spin systems (46). Silica gel and silica-alumina protons will exchange with deuterium in DzO at 150" or Dzgas at 350", as is evidenced by disappearance of the resonance signal. With partial exchange, the absorption line decreases in

76

D. E. O'REILLY

width and remains Lorentzian. It is quite possible that on silica-alumina there are protons which are bound as OH groups to Al. The line width of such protons may be too large for these protons to contribute significantly to the above-described resonance. In summary, the NMR data indicate that the protons remaining on silica gel and silica-alumina after dehydration at 500" are present as SiOH groups which are distributed randomly about the surface of the solid.

111. Electron Paramagnetic Resonance A. PRINCIPLES AND METHODS OF EPR 1. EPR Spectroscopy EPR is in many respects similar to NMR. The main differences are due to the fact that (a) electron magnetic moments are loato lo4 times laiger than nuclear moments, and (b) elections, due to their rapid motions, generally possess a contribution to their magnetic moment due to orbital angular momentum in addition to intrinsic or spin angular momentum they possess similar to nuclei. A particle of mass m and charge e moving in an orbit with angular momentum hL has a magnetic moment V L which is related to L as follows: V L = (ch/2mc)L (28) The separation AE between adjacent energy levels produced by the interaction of a magnetic moment with an external magnetic field H can be written as follows: AE = gSH (29) where g is known as the spectroscopic splitting factor and B is the Bohr magneton (j3 = eh/2mc). Equation (29) ieflults since the eneigy of a magnetic moment v in the field H is - v * H and the change in angular momentum tLL between adjacent levels is =th.Thus for orbital motion g = 1. The spin angular momentum of electrons is hS and g = 2.00 (or 2.0023 with relativistic correction) for an electron spin. That is VS

= 2/98

(30)

In Equations (28) and (30) L, S, V L and are quantum-mechanical and 181 is [S(S 1)]1/2 operators, i.e., the magnitude of L is [L(L 1)]1/2 where L and S are the orbital and spin quantum numbers respectively. For a single electron S = $6. In a free atom L can take on integral values, i.e., L = 0, 1, 2, . . . corresponding to S , P, D , . . . orbital states. In the free atom the electrons move in a Spherically symmetric potential; in a molecule or solid the potential field is no longer spherically symmetric.

+

+

MAGNETIC BESONANCE IN CATALYTIC RESEARCH

77

The result of this lower symmetry of the environment is the “quenching” of the orbital angular momentum of the electron; the orbital angular momentum is no longer a “good” quantum number and has an average value of zero. Some contribution of the orbital motion however remains, and this causes a positive or negative deviation of the g-factor fIom the free spin value of 2.0023. In addition to affecting the spectroscopic splitting factor, the orbital motion can profoundly affect the EPR spectrum by causing splittings (0.01 to 10 cm.-’) of the ground electronic state of the ion in a solid in the case that the ground electronic state has more than twofold spin degeneracy. This effect is known as the zero field splitting since it occurs in the absence of an external magnetic field and causes a fine structure in the EPR spectrum. A further description and examples of this effect are given in Section II1,B. The electron magnetic moment may also interact with the local magnetic fields of the nuclear dipole moments of nuclei around it. A single electron centered on a nucleus of spin 1 will experience 21 1 different local magnetic fields due to the 21 1 different orientations of the nuclear spin I in the external magnetic field. This interaction, which is of the order of cm.-’, causes a hyperfine structure in the EPR spectrum. This structure is further discussed and illustrated in Section II1,B. In addition, the electron cloud in an atom may have an electrostatic interaction with the electric quadrupole moment of the nucleus, if one exists. This effect is very small (of the order of cm.-l>. Finally there is the energy of the direct interaction of the nuclear moment with the external magnetic field (-lo-* cm.-l) as in NMR. All of these effects may conveniently and quantitatively be described (125, 126) by a spin-Hamiltonian X as follows:

+

+

X = BH.g. S

+S

*

D-S

+ S - T * I+ 1 . P . I - m H . 1

(31)

g, D, T, and P are tensors representing the magnetic interaction of the electron spin S with the externally applied field H,the zero field splitting (fine structure) energy, the interaction of the electron spin and nuclear spin (hyperfine structure), and the interaction of the electron cloud and the nuclear quadrupole moment respectively. The last term represents the interaction of the nuclear spin with the field H as in NMR. In Equation (31) S and I are vector operators, i.e., X is an operator whose eigenvalues are the energy levels between which the applied radiation field induces transitions. The solution of Equation (31) is given for the VO++ ion in Section III,C,l and for the Cr*+ion in Section IIl,C,3. The mechanics of EPR spectroscopy as to Larmor precession and the nteraction of the spin 5’ in the applied radiation are exactly similar to that

78

D. E. O’REILLY

described in Section II,A,l for NMR. In passing it is of interest to note that an analogous resonance phenomenon is not possible for electric dipoles oriented in an electric field under the application of an oscillating electric field, since the electric dipole moment produced by the electrons can take up arbitrary orientations in the static electric field. A well-defined absorption of energy will thus not occur. 2. Line Widths and Shapes In EPR line widths are caused mainly by (a) the dipole-dipole interaction (Section II,B,l), (b) exchange interactions between spins, and (c) spin-lattice relaxation (Section II,A,3). Due to the magnitude of electron magnetic dipole moments, the dipole-dipole interaction can give rise to line widths of the order of thousands of gauss. This source of line width is greatly reduced by dilution of the paramagnetic ions in a solid by replacement of paramagnetic ions with diamagnetic ions of the same charge and similar size. Also, exchange effects often change the line width expected from dipole fields (Section 111,C). Spin-lattice relaxation in EPR most frequently arises f i om the modulation of the crystalline electric fields by lattice vibratjons. Via spin-orbit coupling, the electron spin “sees” a fluctuating magnetic field due to the lattice vibrations, which causes spin flips. Theory (127)shows that T Idue to this effect is directly dependent on the energy separation between the ground and first excited orbital state of the electron, and moreover is strongly temperature dependent, becoming longer as the temperature is decreased. Thus in experiment, when further resolution of EPR lines is required, the temperature is reduced.

3. Experimental Methods From Equation (29) one calculates the frequency Y for resonance of unpaired electrons with g = 2 to be of the order of 10 kMc./sec. for a magnetic field of sevcral kilogauss. Thus for magnetic fields of the order of kilogauss which are readily available in the laboratory, the frequency required for resonance is in the microwave region. Two frequency bands are often used : the “X-band” (8.20-12.40 kMc./sec.) and the “K-band” (18.00-26.50 kMc./sec.). Klystrons are used to generate microwave power (usually of the order of a hundred milliwatts), waveguides to transmit power from one point to another and a microwave cavity to contain the sample and provide the HI field necessary for resonance. A commonly used EPIZ spectrometer, similar to that commercially sold by Varian Associates, Palo Alto, California, is shown diagrammatically in Fig. 21. The spectrometer consists of a four-arm microwave bridge generally known as a hybrid tee. The action of this microwave bridge is somewhat

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

79

similar to low frequency, lumped-circuit bridges such as a Wheatstone bridge. On arm 1 of the bridge is connected a source of microwave power (klystron). On arm 4 is the microwave cavity which contains the sample

80

D. E. O’REILLY

for which resonance is to be observed. To arm 3 is connected a “dummy load” which absorbs practically all the microwave power incident on it. On arm 2 is connected a silicon-tungsten detector crystal. The microwave bridge has the property that when arms 3 and 4 are matched to the bridge, that is, when all the power incident upon the cavity and dummy load is absorbed, no power comes out arm 2. Arm 3 is matched for a broad range of frequency. The microwave cavity can be matched only at certain frequencies corresponding to the modes of oscillation of the cavity. For any particular mode of oscillation the paramagnetic sample is placed in that part of the cavity where the microwave magnetic field is maximum and the microwave electric field is zero. This position depends on the shape and mode of oscillation of the cavity. The cavity is orientated so the microwave magnetic field at the sample (HI field) is perpendicular in direction to the static field of the electromagnet. The coupling of the microwave cavity to the bridge is accomplished by a small hole or iris at the bridge end of the cavity. The size of this iris determines the reflection coefficient of the cavity. The iris size needed for zero reflection coefficient, i.e., a matched cavity, depends on the dielectric and conductivity losses of the sample in the cavity and is adjusted by means of a post which partially extends across the iris. By adjustment of the position of this post, the cavity can generally be matched to the bridge. By means of the slide screw tuner of Fig. 21, the bridge is slightly unbalanced as in the rf circuitry of NMR. EPR absorption is then observed in ways similar to NMR: by display of the EPR line on a CRO or by rectification of the AC components and display of the first derivative of the EPR signal on a graphic recorder. In order to stabilize the frequency of the klystron to approximately one part in lo6 parts, the reflector voltage is modulated a t an intermediate frequency of 10 kc./sec. If the klystron frequency deviates (due to fluctuations in the klystron voltages) from that corresponding to the mode of oscillation of the matched cavity, an error signal of 10 kc./sec. is reflected from the cavity, the phase of which depends on the direction of the deviation of the klystron frequency. This signal is detected, amplified and rectified so as to correct the reflector voltage supplied to the klystron and bring the frequency back to thAt corresponding to the mode of oscillation of the matched cavity. This technique is referred to as automatic frequency control (AFC). The AFC setup is schematically illustrated in Fig. 21. Since the frequency of the EPR cavity is used as a reference in this method of AFC, the dispersion mode is suppressed by the AFC and only the absorption mode is observed. By stabilization on a separate reference cavity both x’ and XI’ can be observed. The magnetic field produced by the electromagnet is modulated at an

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

81

audiofrequency by coils wound on the cavity or on the pole faces of the electromagnet. A NMR gaussmeter, utilizing the H1and Li7NMR, is used to calibrate the magnetic field strength to one part in lo5parts. The klystron frequency is measured by a cavity frequency meter to one part in lo4. Compounds with sharp EPR lines and precisely known g-factors, such as l,ldiphenyl-2-picryIhydrazyl,can be used for precise Comparison measurements of g-factors. The sensitivity of the spectrometer is such that approximately lo-" AH mole of spins can be detected where AH is the EPR line width in gauss.

FIQ. 22. Microwave cavity and cavity arm for EPR measurements below and above room temperature (175).

KEY:A, cylindrical microwave cavity; B, cylindrical tube for sample insertion; C, rectangular waveguide; D, nut for adjustment of sample position; E, thermocouple ports.

A cavity arm is shown in Fig. 22. This arm is used for X-band EPR measurements at temperatures ranging from - 196" to 100". The cavity is operated in the TEoll mode at a frequency of 9.39 kMc./sec. A taper section and undersize rectangular waveguide filled with Teflon is used to accommodate the lower section of the cavity arm in the tail of a glass dewar which fits between the pole caps of a magnet (2.50in. gap between pole caps). Field modulation coils over the pole caps of the magnet are used with the apparatus of Fig. 22. A heater coil immersed in water is used to obtain temperatures up to 100";a thermocouple is attached to the sample container. Samples are inserted into the cylindrical cavity by fastening the

82

D. E. O’REILLY

sample tube t o a long bakelite rod; flexible X-band waveguide is used to connect the cavity arm to a microwave bridge. Several other types of EPR spectrometers are used. These include: (a) spectrometers using high frequency (-100 kc./sec.) magnetic field modulation; (b) spectrometers using supei heterodyne detection; and (c) spectrometers using bolometer detection. The spectrometers of type (a) and (b) have the advantage that crystal detector noise is much less a t a radiofrequency than a t an audiofrequency and this source of noise is thus minimized. Factois pertinent to the design of spectrometers with optimum sensitivity have been treated by Feher (128). 4. Overhauser Effect and ENDOR

Overhauser in 1953 (129) proposed a method for polarizing nuclei in metals by saturating the electron spin resonance absorption. As discussed in Section II,A,l, nuclei with spin $1and magnetic moment p , in a field H will have a ratio of populations of the two spin states given by exp (- 2p,H/kT). Overhauser showed that in metals, UPOR saturation of the EPR, this ratio will change to appioximately exp (-2peHlkT) where p , is the electronic magnetic moment. As a result an approximately thousandfold enhancement of the N M R of nuclei in the metal will occur since the nuclear polarization is enhanced by this factor. Carver and Slichter (130)provided experimental evidence for the Overhauser effect discussed above by observation of the Li7 N M R signal from metallic lithium both before and after saturation of the EPR of the conduction electrons. Carver and Slichter estimated that a hundredfold increase occurred in the Li7N M R upon saturation of the electron resonance. This experiment confirmed the Overhauser prediction, although the full enhancement

was theoretically possible, it was not observed. This was probably due to incomplete saturation of the EPlt resonance. Overhauser’s original derivation of the effect employed the FermiDirac distribution functions for electrons and was an involved calculation. Kittel (131),Slichter ( I S $ ) , and others supplied simple derivations for this effect and Abragam (133) extended it to nonmetallic systems. The essential requirement for the effect to occur is a coupling of the nuclear spins with the electronic spins so that the predominant nuclear spin relaxation mechanism is via the eledtron spin system. In metals this coupling is via the hyperfine interaction. Another source of coupling is via the dipole-dipole interaction between nuclear and electronic spins.

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

83

An example (134) of the Overhauser effect in a nonmetallic system was afforded by diphenylpicrylhydrazyl (DPPH), an organic free radical. For partial saturation of the EPR of the radical, an approximately tenfold enhancement of the proton resonance from the ring protons of the DPPH molecule was observed. The Overhauser effect has also been observed in charcoals (proton resonance) and graphite (CIS resonance) (135), and natural crude oils (136). Another double resonance effect, developed largely by Feher (137),is the electron-nuclear double resonance (ENDOR) technique. If nuclei in the material are coupled to the electrons via the hyperfine interaction, a splitting of the nuclear levels will occur. In the ENDOR technique the electron resonance of the material is saturated. By supplying rf power to the sample a t the proper frequency so as to cause nuclear transitions between the levels separated by the hyperfine interaction, the electron resonance can be “desaturated” and an EPR signal will appear a t certain rf frequencies. In this way the hyperfine interaction energy of the electron with nuclei of the material can be very accurately measured. For example, the EPR of F-centers in alkali halides consists of a single line broadened by hyperhe interaction with a large number of nuclear neighbors, such as Clas and Cl*7 in KC1. Feher (138) has resolved this interaction by the ENDOR technique permitting an accurate evaluation of the nature of the electronic wave function for the F-center. Thus the ENDOR technique is useful in the resolution of hyperhe structure of EPR lines, a gain in resolution of the order of lo4 being possible, since the limiting width is that of the NMR line rather than that of the EPR line.

B. INFLUENCE OF ATOMIC ENVIRONMENT ON EPR SPECTRA 1. Crystalline Electric Fields

It has been known for some time that the optical absorption spectra of transition metal ions in chemical combination differ markedly from the spectra of the corresponding free, gaseous ions. New absorption lines appear in the near infrared, visible and ultraviolet portions of the spectrum upon the formation of a chemical compound. This splitting of the energy levels of a free ion under the influence of electric potentials of varying degree of symmetry was first investigated by Bethe (139). Such electric fields exist a t atomic sites in all solids, the strength and symmetry of the field depending on the constitution and arrangement of the atoms of the solid. Through the use of the group-theoretical properties of the crystallographic point groups and the full rotation group, Bethe demonstrated how the degeneracies of the free ion levels are removed and deduced the basic symmetry types of the resulting energy levels of the ion in the solid or complex.

84

D. El. OIFLEILLY

Penney and Schlapp, Van Vleck and others applied these regults to interpret magnetic susceptibility data of paramagnetic transition group ions in crystals. More recently, the theory has been applied with considerable success to electron magnetic resonance data (126, 140, 141) and to the optical spectra (142) of Paramagnetic ions in solids. Before considering the action of crystalline electric fields on d-electrons, a brief review of the properties of free ions and group theory will be given. Ions of elements of the first transition series have the electron configuration (ls22s22p63s23p8)3dnwhere the parentheses enclose the closed shell electrons and n < 10. The energy operator or Hamiltonian X for the free, gaseous ion has spherical symmetry, since if the system is rotated by an arbitrary angle or set of angles, the energy is unchanged. The result of this symmetry property is the conservation of the total angular momentum J of the system of particles. This fact is compactly expressed as follows: JX

- XJ

=

[J,XI = 0

(32)

Equation (32) states that J commutes with X. Operators that commute have the same set of eigenfunctions. Thus in the quantum states of X, J is also quantized. A similar result obtains for J. and I , the inversion operator. I sends a radius vector r into -r. Since

[ I , X] = 0

(33)

in spherical symmetry the eigenfunctions of X are those of I . I%) = 9 where t,b is a function of coordinates and thus the eigenvalue of I* is 1 and those of I are =tl.9 is said to have even parity if it is an eigenfunction of I with eigenvalue 1, and odd parity if it is an eigenfunction of I with eigenvalue - 1. Each of the energy levels of the free atom corresponds to a definite angular momentum and parity. If, in addition] the energy of the ion does not depend on the total electronic spin angular momentum S, then S is also conserved since S then commutes with X. It follows that the orbital angular momentum L is conserved since J = L S. This is the basis of the RussellSaunders coupling scheme: each atomic energy level can be labeled by a definite L and S value. The atomic levels are denoted by the symbol zs+lLand are called term values.The ground electronic state of an ion with L = 2) ; some 80,000 one 3d electron such as Tia+ or V4+ is aD(S = cm.-l and 148,000 crn.-' respectively above the zD state is the first excited state W,corresponding to the ( ) 4s configuration where ( ) represents the closed shell electrons. For a configuration such as ( ) 3d*, as for Cra+, several terms result from a single configuration. I n Cr3+the ground electronic state is 4F (S = 95, L = 3) and some 14,000 cm.-' above this state is a 'P state (S = Xl L = 1).Other terms are 2P,%,2F,zG,and 2H.One must consider the effect of spin-orbit coupling energy. For the iron group

+

+

s,

MAQNETIC RESONANCE IN CATALYTIC BESEABCH

85

elements this energy is small compared to the electrostatic interaction between electrons. For a single electron the Hamiltonian corresponding to this energy is XL . S where X is the spin-orbit coupling constant. L . S commutes with J but not with L or 5. Thus the levels produced from a given term by the spin-orbit interaction may be labeled by their J value with L and S still good quantum numbers, since the splitting produced is small compared to the energy between terms. The above discussion of spherical symmetry can be generalized to any symmetry. To do this it is convenient to use the concept of a group. A group is a collection of quantities or elements which have a multiplication law. The product of two elements of the group will yield a third which is also a member of the group. Furthermore, every group has an identity element and every element of the group has an inverse such that the product of an element and its inverse yield the identity element. There is an associative law, i.e., A(BC) = (AB)C but not a communative law, i.e., A B # BA, where A , B, and C are elements of the same group. The environment of an ion in a solid or complex ion corresponds to qjmmetry transformations under which the environment is unchanged. These symmetry transformations constitute a group. In a crystalline lattice these symmetry transformations are the crystallographic point groups. In threedimensional space there are 32 point groups. The usefulness of group theory in quantum mechanical problems is farreaching (143). If, for example, an ion is in an environment characterized by the group G , then X commutes with every element of G. The result of this commutation property is that the elements of G may be represented in the reference frame defined by the eigenfunctions of X. The elements of G are abstract entities which may be represented by square matrices such that the product of two elements of the group corresponds to the matrix multiplication of the matrices which represent each of the elements. To every element of G, in a given representation, there corresponds one matrix. The size or dimensionality of these matrices may be arbitrary; however, if the set of matrices of a representation of G cannot be broken down into matrices of smaller dimension, which form representations of G , the representation of G is said to be irreducible. If each of the matrices of the set can be broken down into smaller matrices, each of which forms a representation of G, the original representation is called reducible. To an energy eigenvalue or state of X, there will generally correspond several independent eigenvectors or state functions JI1, . . . , $,; n is the degeneracy of the state. These functions must form a basis for a representation of the group G if $ is invariant under G. If R is an element of G n

R 9i =

C j-1

Dji(R)$,

(34)

86

D. E. O'REILLY

The niat,rix D ( n ) is the matrix representative of R. Furthermore, the representation D ( R ) is irreducible, so that to every energy state of X, an irreducible representation of G can be assigned. There are only a finite number of irreducible representations of a finite group. The sum of the squares of the dimensions of the irreducible matrix representations is equal to the number of elements of the group. The usual WRY of tabulating the irreducible repreeentations of a group is to list the various representations in a column, the elements of G in a row, and the Character of the matrix corresponding to a particular representation and element in the space labeled by a row and column. The character of a matrix is the sum of the diagonal elements of the matrix; this quantity is invariant under changes of coordinate system and hence is characteristic of a matrix independent of reference frame. Elements of G belonging to the same class have the same character for their matrix representative and so are listed in the same row position. Two elements of a group A and B belong t o the same class of G if there is a third element X of G such that A = X-'BX Geometrically, elements which belong to the same class correspond to rotations about similar axes or reflections in similar planes. Consider an ion with one 3d electron situated in a cubic environment such as a Mg++ site in MgO. The symmetry transformations of this environment constitute the point group Oh,the character table of which is given in Table I. Oh contains the following classes of elements: E the identity element Cz rotation by u around 2-fold axes C'Zrotation by r around 4-fold axes Ca rotation by 2u/3 around 3-fold axes C1 rotation by u/2 around 4-fold axes g the inversion operator The character of only those representations of even parity is given (denoted by subscript g) since 3d electrons have even parity. The number of elements in a class is also given in front of the symbol for the class. Under the action of the electric field of the Oh environment, the state 2D of the ( ) 3d configuration will split up into two states. The orbital degeneracy of a D state is 2 X 2 1 = 5. From the above discussion each of the resulting states must belong to one of the irreducible representations of O h given in Table I. The state 2D corresponds to a n irreducible representation of the group of symmetry operations of a sphere, i.e., the full rotation group R(3). The 2D state can be expressed as a sum of irreducible representations of Oh as follows :

+

'D

=

"T2,+ 2E,

(35)

The degeneracy of a state is given by the character of 23 of Table I.

87

MAGNETIC RESONANCE IN CATALYTIC RESEABCH

TABLE I Character Table of Oh for Even Parity

Tap

1 1 2 3

TI,

3

'41,

A(0 Eo

1 1 -1

1 1 2 -1 -1

0 0

1 -1 0 1

-1

1 -1 0 -1 1

Thus the Tea state is 3-fold degenerate and the E, state 2-fold degenerate. Equation (35) is derived by requiring that the sum of the characters of the representations of O h which correspond to '0 for a fixed class of o h be equal to the character of the corresponding class of R(3). In this way sufficient equations are obtained to determine the number of times each representation of O h occurs in Equation (35). Each rotation by an angle 4 about an axis in space forms a class of R(3). The character of an L dimensional, irreducible representation of R(3) is sin ( L

+ 45)4/sin (SB)+

The spin degeneracy of the term is not affected by the crystal field since X is assumed not to contain spin terms.

Under the action of a crystal field component of lower symmetry each and state of o h will split up further. Under tetragonal symmetry (D4h),2T29 'E, decompose as follows: 'T2, = 'E, 2B20 (36) 'E, = 'A1, 'B1,

+ +

where E,, B20, A1, and B1, are irreducible representations of Du. The splittings considered are illustrated in Fig. 23. The positions of the energy states are not given by group theory. These energies must be explicitly calculated. This is most conveniently done by expansion of the potential in spherical harmonics and diagonalisation of the resulting matrices formed by taking matrix elements of this potential between the eigenfunctions of the free, gaseous ion. Such calculations are quite approximate but do illustrate the order of the energy levels. When more than one 3d electron is present three cases must be considered. These are: (a) the energy splittings produced by the crystal field (CF) are small compared to the separations between the free ion terms which are proportional to the strength of the electrostatic interaction between electrons; (b) the energy splitting produced by the C F is large compared to the energy separation between terms; and (c) CF energy splittings are comparable to separations of the free ion levels.

88

D. E. O’REILLY

(b)

FREE GASEOUS ION CONFIGURATION

SPlN-ORBIT COUPLINQ

(a)

(d)

(C)

(0)

lo)+

W+CF (Cl+CF (d)tSTATIC OF CUBIC WITH MAQNET~C SYMMETRY TETRAQWAL FIELD SYMMETRY

FIQ.23. Energy level scheme of a single 3d electron showing the effect of crystalline fields (CF) of various symmetry. Electron occupation of levels is indicated by a circle in (d) and by arrows in (e) to denote spin polarization.

\

\

,\

4Azg(ll

-.*

46,,(1)

p-;;;; ---+

SPHERICAL (0)

OCTAHEDRAL

(bl

TETRAGONAL (C)

SPIN-ORBIT i (c)

MAGNETIC FIELD

(dl

(el

FIG.24. Energy level diagram for 3@ configuration quartet terms under the action of crystal fields of various symmetries. Orbital degeneracy of a state is indicated in parentheses. These situations are known as the weak, strong, and medium field cases respectively. As an example of case (c) consider the Cr3+ ion (3d3).The ground term for the free atom is ‘F and some 14,000 cm.-’ above this state is a 4P state. Under the action of a arystal field of cubic symmetry, such as that

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

89

at a Mg++ site in MgO; the 4F splits up into three states as shown in Fig. 24. The degeneracy of the ‘P state is unaffected by the cubic crystal field. If, in addition to the cubic crystal field, a component of lower symmetry is present, such as one having tetragonal or trigonal symmetry (as for the Ala+ sites in cr-AlzO~),further splitting will occur as shown in Fig. 24. Crystal field splittings for other configurations in both the weak and strong field cases are summarized in a review article by Moffitt and Ballhausen (144)* A very general and useful theorem about the action of crystalline fields on atomic electrons has been derived by Kramers (146). Kramers’ Theorem states that if there is an odd number of unpaired electrons in an atom, then an electric field cannot completely remove the degeneracy of a level and the minimum degeneracy is twofold. Thus no matter how asymmetric the CF is in these cases, the ground state is at least twofold degenerate and EPR can in principle be observed upon application of a magnetic field. For an even number of unpaired electrons the degeneracy of the ground state may be completely removed so that no splitting will be produced by an applied magnetic field and no EPR will be observed. Thus for the ions of the iron group with an odd number of d-electrons, EYR can always be observed under proper experimental conditions. 2. g-Factors, Fine Structure, and Hyperjine Structure

consideration of the spin-orbit interaction and the effect of an external magnetic field on the electronic ground state of an ion in a CF allows evaluation of the various terms in the spin-Hamiltonian of Equation (31). In addition, the interaction of the nucleus of the paramagnetic ion and ligand nuclei with the d-electron cloud must be considered. In this way the experimentally determined terms of the spin-Hamiltonian may be related to such parameters as the energy difierences between levels of the ion in the CF and amount of charge transfer between d-electrons and ligands. Abragam and Pryce (126)have calculated general expressions for the quantities g , D, T , and P of Equation (31). A frequently occurring situation is that of axial symmetry such as when the ion is in a CF with tetragonal or trigonal symmetry. In this case the tensors g and T have two components each, parallel and perpendicular to the symmetry axis. T can be characterized in this case by a single value D. Neglecting the last two terms, Equation (31) becomes in this case as follows: X = BBIIHaSz

+ P g l ( H z S z + HuSu) + D[Ss2 - Q S ( S+ I)] + ASJ‘ + B(SJz + SJv)

(37)

As an example of a system to which Equation (31) applies, consider the energy level diagram of a single d-electron given in Fig. 23. Here S = so matrix elements of Sat - #S(S 1) equal zero. There is no D term in

+

s,

90

D. E. O'REILLY

the Hamiltonian. Also as one can show from the formulas given by Abragam and Pryce (126) 911 = 2.002 - (8X/Az) 91 = 2.002 - (2X/Al) A = P(-$$ - K - Agll) B = P ( w - K - Agi) A811 = 2.002 - gll A 9 1 = 2.002 - gI P = 2ya(i/r3) X is the spin-orbit coupling constant, A1 is the energy difference between

2B2, and 2E,of Fig. 23, A2 is the energy difference between 2B2, and 2B,o and K is proportional to the amount of unpaired selectron density at the metal nucleus. K arises from the fact that the energy of interaction of an unpaired spin in an s orbital state and a nuclear spin is proportional to the charge density of the s-electron a t the nucleus (for p , d, I, . . . electrons the charge density at the nucleus is zero). In the ground state configuration of the transition element ions there are no unpaired s-electrons. However, in order to account for EPR hyperfine structure in these ions, it has been necessary (119) to assume the small admixtures of configurations, such as 3s(3d)"4s,in which a closed-shell s-electron (ls, 2s or 3s) is promoted to the 4s orbital. Van Wieringen (146) has shown that for Mn++ in various crystals K is proportional to the covalent character of the metal-ligand bond. Application of formulae of Equation (38) will be given in Section II1,C. Another example of the use of Equation (37) is for the 3da configuration of Fig. 24. Here A = B Ei 0 since CrMhas zero spin and CrU (9.5% abundant) has a small nuclear moment (see, however, Bleaney and Bowers, 147). One finds (148) : gll = 91 = 2.002 - (8h/A) D E 4X2A'/Aoz A' << Ao (39) where A is the energy difference between 4B20and 'BlO,A' is the energy difference between 'h', and IBZ0and A0 is the energy difference between 4Tz0 and Table I1 (141, 149-162) consists of a summary of g-factors, D values and hyperfine coupling constants observed for ions of the first transition series. A molecular orbital (MO) treatment of the metal ion and ligand orbitals has been discussed by Stevens (163) and Owen (164) to account for covalent bonding and resulting hyperfine structure from ligands of transition element ions. Expressions derived for g-factors and hyperfine coupling constants from a MO treatment allow an estimation of the amount of charge transfer of metal electrons to ligand orbitals. Owen (164) has given a MO treatment of Cr8+, Ni++ and Cu++ assuming no 7r bonding.

MAGNETIC RESONANCE IN CATALYTIC BESEABCH

91

Maki and McGarvey (166) have given a MO treatment of Cu++ in tetragonal symmetry taking into account both u and T bonding. The resulting energy level scheme for Cu++ is shown in Fig. 25. The spin-Hamiltonian of Equation (31) can also be used to describe EPR data (126, 140) of ions of the palladium and platinum transition groups, the rare earths, and the trans-uranic group. Experimental data, however, are not presently as plentiful for these elements as for those of the iron group. Crystal Field Theory (CFT) has also been used considerably to rationalize visible absorption spectra, hydration energies, stabilities of complexes, rates and mechanism of reaction, and redox potentials of transition element ions. These applications of CFT are summarized in a book by Basolo and Pearson (166).

ANTI- BONDINO

*D LS

(a) FREE ION IWITHOUT SPIN ORBIT COUPLING)

-

(b) TETRAGONAL CF

(C)

(b)+ OVERLAP wiin LIGAND ORBITALS

FIG.25. Energy level diagram of 3do configuration (Cu+-')in square planar complex or tetragonal crystal field (CF). Effect of bonding of the 3d-electrons with figan& is shown.

3. Exchange Eflects

Due to the coulombic interactions between electrons centered on adjacent nuclei in a solid, there arises what is known as the electron exchange interaction. Neglecting spin-independent terms, the exchange interaction between two electron spins Si and Sj is of the form J i j S i * Sj where J s j is the exchange coupling constant. In this form the exchange interaction depends only on the separation between ions and not on their relative orientation and is thus referred to as isotropic. The exchange in paramagnetic resonance is generally assumed to be isotropic although anisotropic exchange is known to occur. Van Vleck (73) and Anderson and Weisa (167)have considered the narrowing effect of exchange interactions on the resonance line width. These authors

TABLE I1 Surnmaq of EPR Data on Iron (froup Ions Number of 3d electrons

Reference

Ions

spin iegeneracy inaxial CF

9

Tia+, Mn'+, VOW

2

1.1-1.3

3 4

2.0 1.9 2.0

5

2.0

6 2 2 5 4 2 3 2

2.0

V'+, Ti++C , Cr4+~ V++, C F , Mn4+

0.6-2.6 0-9 2.3 2.3 1.4-7 2.2-2.3 2.0-2.5

5-10 0.001-0.9 2.2 0.001-0.2

0.015 (Mn") 0.016 (Vsl) 0.01-0.02 (V'1) 0.001 (C?) 0.009 WSl) 0.007 (Mn")

0.003 (Mna) 0.005 (V61) 0.03 (P) 0.001 (CP) 0.009 (P) 0.007 (Mn")

0.0064.009 (Mn") 0.01 (Mnu)

A - B 0.004-O.o08(Mn~)

u P 0Ld

E 2

0.2 4.5 0.01-0.03 (Corn)

0.001-0.03 (Corn)

0.002-0.02

O.OO2-0.003

0.14

Note: 1.OOO cm.-1 = 29.98 kc./eecond = 21.42/9 kilogauss. 4 Bleaney, B., Proc. Phys. Soc. 863, 407 (1950); O'Reiiy, D. E., J . C h . Phys. 29, 1188 (1958); 30, 591 (1959). * Abragam, A., and F'ryce, M. H. L., Proc. Roy. SOC.8206, 135 (1951). No paramagnetic resonance aa yet reported. d Davis, C. F., Jr., and Strandberg, M. W. P., Phys. Rev. 106, 447 (1957). e Abragam, A., and F'ryce, M. H. L., Proc. Roy. SOC. 8306, 173 (1951). Low, W., Phys. Rev. 109,204 (1958). Owen, J., Proc. Roy. SOC.8237, 183 (1955).

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

93

have shown that when the spins are considered free the exchange interaction between like spins causes a narrowing of the resonance line width (half width at half height). That is, if one considers the resonance line width caused by the dipole-dipole interactions between spins, the exchange interaction results in a decrease in this width, since it causes fluctuations in the dipolar fields which can he considered to be random. Letting H, be the average dipolar field a spin experiences and H , the average field (-J/g/3) produced by the exchange interaction, then the half width a t half height AH is approximately (167) as follows:

AH = R P 2 / H , (40) where H . >> H,. Hence a narrowing of the dipolar line width (-H,) results and, for conceiitrated paramagnetic systems of like spins, “exchange narrowing” of the resonance occurs. When the exchange between like spins is anisotropic, broadening of the resonance line occurs (73).The exchange interaction between unlike spins also gives rise to broadening of the resonance line (79). A number of cases have been reported in the literature where the exchange between pairs of ions in a lattice is piedominant, i.e., ions are exchange coupled in pairs because of their proximity. An example of this is copper acetate (168),where the copper ions occur in pairs which are relatively close, so that the spins of pairs of copper ions are coupled together to form a singlet state (paired spins) and a triplet state (unpaired spins). Resonance measurements (168) permit determination of the magnitude and sign of J . C. APPLICATIONS Since catalytic solids are generally amorphous or polycrystalline, the EPR spectra of unpaired electrons in these solids constitute an a.verage over all possible orientations of the paramagnetic species relative to the direction of the applied magnetic field. The EPR spectrum of a paramagnetic species with a definite orientation of the applied magnetic field relative to the axes of symmetry of the species will, in general, consist of several lines which vary in position as the orientation is varied. Thus in order to fit an EPR spectrum of these solids to a spin-Hamiltonian, it is necessary to make a suitable average of the allowed transitions of Equation (31) over all possible orientations of the species. Since experimental data on solids of catalytic interest are, at present, rather meager, some of the following examples will be of systems which are not of direct interest t o catalysis. 1.

EPR Spectra of Vanadyl and Copper Porphyrins Vanadium in the +4 valence state as vanadyl (VO*)

readily forms

94

D. E. O’REILLY

J

I

2900 3000 3100 3200 3300 3400 3500 3600 3700 3800

ti, gauss (0)

0

I

0

I

6

6

1

I

I

-

H, gousr

chelate compounds. The vanadyl porphyrins (169) frequently occur in nature and exhibit paramagnetic resonance absorption due to a single 3d electron present in a molecule. Figure 26 illustrates the spectrum of vanadyl etioporphyrin I (VEPI) dissolved in teneene and that of VEPI in an extremely high-viscosity petroleum oil. These spectra can be interpreted ( I @ ) in terms of Equation (37). I n the case that the VEPI molecule is rotating about with a correlation time much shorter than the reciprocal of the spread of the spectrum in frequency (-3 X sec.) Equation (37) reduces to an “isotropic” Hamiltonian, i.e., X = gopH * S a1 * S (41) (8= >5, I(V61) = 75)

+

+

+

with go = g ( g l l 2gl) and a = % ( A 2B).This can be demonstrated by transformation of Equation (37) to laboratory coordinates with the external magnetic field chosen as the new z axis (160). As an illustration of the solution of a spin-Hamiltonian for the energy

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

95

levels, Equation (41) is solved below. Consider the z direction to be that of the applied magnetic field. Equation (41) gives rise to a 16 X 16 matrix and mI = . . , -%; there are thus 16 states for the since mg = f>$ system which are denoted by ImgmI). The matrix elements for an angular momentum operator J are as follows in a representation in which J 2 and J . are diagonal (161)

x, .

where Jf = J , f iJ,. The diagonal matrix elements of Equation (41) are thus (msmIlXlmsmI) = gdHms

Noting that

+ I,S,

I.S,

= $(I+S-

+ amms

(43)

+ I-S+)

the off diagonal elements are (ms - 1, mI

+ 1lXImmI) =

(ms

+ 1, mI - 1IXlmsmr)

a[(t.i - mI)(95 + mI)($5 + ms)(35 - m s ) P / 2

= a[(%

+ md(% - m d (M - ms)(% + ms>lX/2

If a<
+ mIa + (Pi - 95 - m1~)a'/2gdH0

where vo is the resonance frequency. The field strength separation between adjacent lines is thus

7/ where Ho = hvo/go,!3and mI = -7/ /2J * * J /2' The spectrum of Fig. 26 of VEPI in benzene is well represented by Equation (44) with go = 1.974 f 0.002 and a = 0.0089 cm.-l. If the VEPI molecule is rotating about sufficiently slowly, Equation (37) must be used with an average of the allowed transitions over all orientations of the molecule relative to the applied field. To first order of perturbation theory one finds for this case

hvo = g&H

+ mIa + i(Ag@H + bmd(3z2- 1)

(45)

where Ag = 811 - gL, b = A - B, z = cos 8, and 8 is the angle between the symmetry axis of the VEPI molecule and the applied field. Thus

96

D. E. O'REILLY

H=

hvo - am1 - 4bmx(3za - 1) B(g0 Q47(3zP- 1))

+

We now ask what is the intensity of resonance as a function of the applied field for a fixed mx. The number of molecules in a volume element dV is proportional to sin 0 dB = -dz. Letting I ( z ) be the intensity of resonance as a function of z and I ( H ) the intensity as a function of H , one requires that I ( z ) d z = I ( H ) d H . Thus I ( H ) a ( d z / d H ) since I ( z ) is constant. This problem has been solved by Sands (162), and more generally by Bloembergen (163) for go # gv # gs. The resulting line shape is shown by the dashed curve of Fig. 27; the solid curve results when line-broadening due to spinlattice relaxation or dipole fields is included. The spectrum of VEPI in

FIG.27. Absorption envelope versus field strength H for fixed mi. HO = hv/g& Ag = 811 - 8 1 and BOSH A , B (149).

>>

Fig. 26(b) is thus a superposition of the eight resulting envelopes of Fig. 27. From the humps and cross-over points of Fig. 26(b) and the value of go given above, one obtains 911 = 1.948 f 0.009 81 = 1.987 f 0.005 IAl = 0.0159 cm.-' IBI = 0.0052 cm.-'

where A and B have the same sign since

I4

=

IW

+ 2B)I

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

97

Unfortunately the optical spectrum (169) of VEPI in the visible and ultraviolet appears to be dominated by electronic transitions of the porphyrin group such that the spectrum of the 3d electron is masked, and direct comparison of the experimental g-factors with the theoretical ones (Equation 40) cannot be made. The value of K necessary to account for the anisotropy of the hfs is 0.71 with the result that 2 8 8 ~ ( l / r ~=) ~0.0057 cm.-'

This quantity is proportional to the magnetic field at the V61 nucleus due to the unpaired s-electron configurations of the ion and is constant within f20a/, for ions of the iron group, if covalent bonding is not extreme as in cyanides of Mn++ in ZnS.

2564

3007

2765

H.

3213

3413

3561

gouss

FIG.28. Paramagnetic resonance of copper protoporphyrin in a high viacosity oil at 9.47 kmc./second. Broad humps are due to Cu hyperhe structure; sharp lines at high field are due to nitrogen hyperhe structure (164).

In Fig. 28 is shown the EPR spectrum of copper protoporphyrin dissolved in a high-viscosity oil (164). This spectrum can be described using Equation (37) similarly to that of VEPI discussed above. One finds 911 = 2.184

2.046 IAl = 0.0215 cm.-I IBI = 0.0023 crn.-' gA =

In this case the energy level diagram is that of Fig. 25. The g-factors are greater than 2.002 since X is negative corresponding to a 3d hole configuration. One must add a term

2 i

rLiNI,N *

s

98

D. E. O'BEILLY

to the spin-Hamiltonian in order to account for hyperfine structure from nitrogen nuclei which appears in the spectrum of Fig. 28, where a?' is the hyperhe coupling constant and I? is the nuclear spin operator of the ith nitrogen nucleus. From the spectrum of Fig. 28 one obtains aN = 0.0017 cm.-'. With the aid of the MO treatment of Maki and McGarvey (166),these data can be used to obtain coefficientsof the d-orbitals of the unpaired electron centered at the copper nucleus and the value of K . One finds a = 0.85

p1 = 0.90 K

=

0.39

where a is the coefficient of the d-orbital (z2 - y2) in the 2B1,state and is the coefficient of the d-orbital (q) in the 2B,,state. 2@&,?K(l/T') = 0.0088 crn.-'. In the ground state there is thus approximately 6% transfer of unpaired electron spin from Cu to a hybridized (sp') a-orbit on each nitrogen. No nitrogen hyperfine structure was observed for VEPI since the ground , not combine with nitrogen o-orbitals. The magnielectronic state 2 B ~does tude of the nitrogen hyperfine structure splitting (aN) is directly proportional to the charge transfer of the d-electron to nitrogen u-orbitals (156). 2. Ions Adsorbed on Solids from Solution

Faber and Rogers (166) have reported EPR spectra of Mn++, Cufe, and VO++ adsorbed on cation- and anion-exchange resins, activated charcoal, zeolite, and silica gel. Spectra similar to those shown on Figs. 26(b) and 28 were observed for VO++ and Cu++ adsorbed on various substrates, with the omission of the nitrogen hfs of Fig. 28. The spectrum of Mn++ adsorbed on the substrates consisted of 6 hyperfine lines due to the Mn" nuclear spin with I = %. In addition, smearing of hyperfine lines was observed. The spin-Hamiltonian of Mn++ in axial symmetry is fairly well represented by the following equation: X = gpH * S

+ D(SB2-

3%~)

+ A1 - S

(46)

where small terms involving the fourth powers of components of the electron spin operator have been omitted. In cubic symmetry D = 0 and 6 well-resolved hyperfine lines result. On cation exchangers (sulfonic acid-type and carboxylic acid-type), a value of A = 0.0089 cm.-l was observed, corresponding to the hydrated Mn(H20)s++. The effect of axial symmetry (D'$0) was observed as evidenced by a fine structure in the hyperfine lines. A value of D however was not determined. The EPR spectrum of Mn++ on an anion exchanger studied consisted of a single unresolved broad line. A smaller A value and larger

MAGNETIC RESONANCE IN CATALYTIC RESEABCH

99

D than that for Mn++ on cation exchangers is indicated, suggesting a larger covalent character (-50%) in the ion-substrate bond. The results of the EPIZ measurements of Cu++and Cu(NH&++ adsorbed on various substrates are classified as follows: 1. Sulfonic acid-type cation exchanges showed the largest g-factors and smallest hfs intervals of all the samples for Cu++ adsorbed. This is consistent with bond between the Cu++ and the adsorbents being largely ionic. 2. Somewhat smaller g-factors and larger hfs intervals were exhibited by charcoal, zeolite, and a carboxylic acid-type exchange resin, indicating more covalent character in the metal-adsorbent bond. 3. Still smaller g-factors and hfs intervals were observed in the EPR spectra of samples containing ammoniated Cu++. No differences between the various adsorbents were observed. 4. For an amine-type anion exchanger both the Cu++ and Cu(NH&++ adsorbed ions had the same g-factors and hfs intervals similar to those of group 3 above. The tetratartratocuprate complex ion did not bond to an amine-type anion exchange resin, indicating that the CF stabilization energy of the complex ion was sufficiently large so that no appreciable bonding to the resin occurred. Lack of bonding was indicated by lack of color change when a solution of the ion was placed in contact with the resin and absence of a detectable EPR spectrum from the dried resin, presumably due to large dipoledipole broadening in crystallites containing the complex ion. For the vanadyl ion adsorbed on the various substrates examined, the g-factors were found constant, however, the hfs intervals varied, being largest on sulfonic acid-type cation exchangers, slightly smaller on charcoal and considerably smaller on an amine-type anion exchanger. Although the results of these measurements have not been presently completely interpreted in terms of the metal-surface bonding, they indicate the usefulness of the EPR technique m the study of paramagnetic ions adsorbed on the surface of solids. 3. Chromia-on-Alumina Chromia-on-alumina is active as a catalyst in many chemical reactions, such as aromatization, dehydrogenation, and polymerization. The magnetic susceptibility of 7-alumina impregnated with chromic acid and subsequently reduced with hydrogen has been investigated by Selwood and Eischens (166). These investigators found a nearly constant magnetic moment, corresponding to three unpaired electrons, for all concentrations of chromia; the Weiss constant, however, varied from nearly zero at low concentrations (-1 wt. % Cr) up to about 200°K for the higher concentrations (35 wt. % Cr).

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D. E. O'REILLY

From these data it was concluded that the chromia is clustered in patches on the support; these patches become more dispersed as the concentration of chromia is decreased. Further susceptibility data have recently been obtained by Matsunaga (167) for chromia-on-alumina oxidized a t various temperatures. Weller and Voltz have made measurements of the excess oxygen on oxidized chromia (168)and the electrical conductivity of chromia and chromia-on-alumina (169).The solids studied were found most active for the hydrogendeuterium exchange reaction when in the reduced state. The oxidized state on the other hand exhibited the lowest activation energy for electrical conduction. Griffith et al. (170) found chromic oxide to be a p-type semiconductor in oxygen atmosphere, but n-type in pure hydrogen atmosphere by thermoelectric power measurements. Paramagnetic resonance has been observed in a-Crz03 above the antiantiferromagnetic Curie point by Maxwell and McGuire (1'71); antiferromagnetic resonance has been studied in a-CrzOaby Dayhoff (172). EPR studies have been made of chromia impregnated on alumina (173). Samples reduced in hydrogen at 500" and oxidized in air at 500" were examined in the concentration range from 0.08 to 10.0 wt. % chromium. X-band EPR spectra of reduced samples are shown in Figs. 29 and 30. The spectra consist of two distinct resonances as shown by changes in the spectra with increasing concentration of chromium and examination of samples at K-band. The first of these is characterized by the strong derivative peak with a maximum near 1500 gauss at X-band; henceforth this resonance will be referred to as the &phase resonance. The second resonance has a symmetrical derivative centered near 3400 gauss; henceforth this resonance will be referred to as the @-phaseresonance. The &phase resonance dominates in intensity in the low-concentration chromium samples, while the &phase resonance dominates in intensity a t the higher concentrations. This effect is illustrated by the spectra of Figs. 29 and 30. The width between points of maximum slope of the symmetrical &phase resonance ranges from about 700 gauss a t the lower (0.5-1.1 wt. %) concentrations to about 1300 gauss at the higher concentrations (5.6-10 wt. %). At K-band only a @-phasetype resonance was detected from the reduced chromia-on-alumina samples and was unchanged in width. No change in the character of the resonances from the reduced chromia-on-alumina samples was observed a t - 196". Upon oxidation of the reduced samples, an additional resonance is obt,ained. A t X-band this resonance is symmetrical in shape, has a g-factor of 1.967 f 0.003, and has a width between points of maximum slope of 50 gauss. The intensity of this resonance, henceforth referred to as the y-phase resonance, is shown in Fig. 31 as a function of concentration of chromium. A maximum in intensity appears near 2 wt. yo Cr corresponding to

MAGNETIC RESONANCE I N CATALYTIC RESEARCH

101

I

I

I

I

I

I

I

704

1350

20010

30%

3410

4406

5362

H.GAUSS

FIQ.29. First derivative of EPR absorption of 0.55 wt. % chromium on alumina reduced in hydrogen at 500".Y = 9.47 kmc./second (173).

FIQ.30. First derivative of EPR absorption of 3.57 wt. % ' of chromium on alumina reduced in hydrogen at 500". Y = 9.47 kmc./second (173).

1.6 X 1Olo spins per gram. This amounts to one such spin for every 14 Cr nuclei in the sample. These concentrations are based on the assumption that the spin of the species giving rise to the y-phase resonance is 55;that is, there is one unpaired electron per absorber rather than three as in Cr3+

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D. E. O'REILLY

Justification for this assumption is given below. At K-band the y-phase resonance increases in width to about 80 gauss and the derivative becomes slightly asymmetric. No changes were observed in the width or position of the y-phase resonance at -196". The peak in the derivative of the &phase resonance does not change drastically in intensity upon oxidation. The &phase resonance, however, does change considerably in intensity in the intermediate concentration range (0.5-3.6 wt. %) upon oxidation. Upon exposure of reduced chromiaon-alumina samples of low concentration to air at room temperature, a rapid color change from blue to green occurs and the EPR characteristic of the y-phase immediately appears, although reduced in intensity in comparison to the y-phase resonance intensity after oxidation a t 500".

FIQ.31. Concentration of unpaired electrons in 7-phase resonance of chromia-onalumina versus weight per cent chromium (173).

The &phase resonance can be fairly well represented by the spin-Hamiltonian corresponding to Cra+in an axially symmetric crystal field. X = gBH * S

+ D(S.'

- %)

(47)

Equation (47) gives rise to a 4 X 4 matrix the eigenvalues (energy levels) of which were obtained by solving these matrices on a 704 computer as a function of G / D (G = gSH) and the angle 8 of the symmetry axis relative

103

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

to the applied magnetic field. Plots of G / D necessary for resonance versus cos B at a fixed value of D for the various possible transitions were constructed; an example of such a plot is shown in Fig. 32. As shown in Section III,C,l the powder pattern line shape is proportional to d cos B/dH. However, one must in this case consider the transition probability for the particular transition considered, since this probability is not independent of the oiientation between the applied field and the Crs+ion. Transition probabilities for selected orientations are given by Davis and Strandberg (148).

-I

E 0

-0.50

0*0.632GM.-I

1.50

-1-

e-a

-

cos e

FIQ. 32. Plot of a / D = gDH/D value necessary for resonance vewuB cosine of the angle 0 between symmetry axis and applied magnetic field for fixed frequency Y = A E / h . For Y = 9.47 kmc./second magnetic fields for which maxima in powder pattern abgorption occur are given. Integers refer to energy levels numbered from 1 to 4 starting with the highest (175).

Through the use of plots similar to those shown on Fig. 32 and a perturbation theory treatment of Equation (47), it is found (173)that peaks are expected in the X-band powder pattern near 1100, and 1700 gauss for D > 0.2 cm.-'. These correspond to positive humps in the first derivative a t 1110-6H and 1700-6H gauss where SH is the half width of the individual resonance lines in gauss. If 6H N 100-200 gauss agreement is obtained with the positions of the observed peaks in the derivative. The positions of these peaks are independent of D for larger values of D. To account for small additional humps in the &phase derivative of Fig. 29, a term may be added to Equation (47) of the form E(SS2- Sy2).This term accounts for the effect of a CF of lower symmetry than tetragonal or trigonal on the EPR spectra. In Fig. 33 is illustrated the EPR spectrum of a sample of a-chromia at various temperatures. As can be seen from the figure EPR appears at 33°C

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D. E. O’REILLY

and increases in intensity above this temperature. At room temperature and lower temperatures, no paramagnetic resonance signal is observed due to the antiferromagnetic state of the solid (l7f).The @-phaseresonance is somewhat similar to a-chromia cxcept (1) no antiferromagnetic Curie point is observed and (2) the @-phaseline width is laiger by several hundred gauss than the a-chromia resonance. For a-Cr203 the line width due to the dipolar fields (73) is several thousand gauss; the exchange effect reduces this width to about 500 gauss. Thus the 8-phase resonance is interpreted

FIQ.33. Paramagnetic resonance of a-chromia at various temperatures. The antiferromagnetic Curie point is approximately 30” (173).

1832

3037 3781 H. GAUSS

5071

as due to Cr8+ions clustered in such a way that there is sufficient exchange coupling between spins to exchange narrow (167)the resonance and partially “wash out” line broadening effects due to the dipolar interaction and D term of the CF. The relatively sharp y-phase resonance which appears upon oxidation of the reduced chromia-on-alumina is possibly due to single electrons trapped on Cre+ions, i.e., Cr6+ions. In summaryJ the EPR spectrum reveals three distinct chemical species

MAGNETIC &ESONANCE IN CATALYTIC RESEARCH

105

in the chromia-on-alumina system: the b-phase consisting of Cr*+ ions electronically decoupled, the 8-phase made up of CrS+ions coupled electronically and the y-phase which appears t o consist of electrons trapped in the oxidized chromia. The EPR data are of course intimately related to magnetic susceptibility data. The Weiss constant of the &phase is proportional to D which will amount to only a few degrees Kelvin at most, while the Weiss constant of the 8-phase is large due to the large exchange effects in this phase. The Weiss constant obtained from a magnetic susceptibility measurement is thus due predominantly to the 8-phase. One would expect the presence of trapped electrons in the oxidized samples to give rise to n-type conductivity, conduction possibly taking place by jump migration of the odd electron in the lattice of Cra+ions in a somewhat similar manner to the mechanism discussed by Heikes (174) for the migration of Ni3+holes in lithiadoped NiO. The observed p-type conductivity of chromia in an oxygen atmosphere is presumably due to electron holes in a solid which is predominantly CrzOa; for the low concentrations of chromia-on-alumina where the y-phase resonance intensity is maximum, the chromium is predominantly in the +6 valence state (167). The &phase resonance is not affected appreciably by oxidation at 500" and appears to be relatively stable as Cra+. Matsunaga (167) on the basis of susceptibility data at concentrations only as low as 1 wt. % Cr, concluded that at infinite dilution, all chromium in the +3 valence state would be converted to the -1-6 state upon oxidation. EPR data indicate that this is not true; the b-phase predominates a t low concentration and is stable towards oxidation. On the other hand, the @phase at high concentration is apparently rather stable towards complete oxidation a t 500°C; this indicates that the chromia is most susceptible to oxidation when in rather small clusters. Mat,sunaga (176) has reported data on the rate of decomposition of hydrogen peroxide using oxidized chromia-on-alumina as a catalyst. The same solids for which previous magnetic susceptibility data (167) had been obtained were employed. The rate of decomposition of H,Oa per unit weight of chromia as a function of chromium concentration was found to be a maximum at the lowest chromium concentration (-1 wt. yo)examined and to decrease monotonically with increasing chromium concentration. This rate appears to be approximately proportional to the specific number of electrons in the y-phase, since at lowest concentration studied by Matsunaga the number of electrons in the y-phase per gram of chromium is a maximum and decreases monotonically with increasing chromium concentration. If the activity is proportional to the number of these electrons, the rate may drop sharply below 1 wt. % Cr since the specific number

106

D. E. O’REILLY

of trapped electrons in the oxidized samples decreases sharply. On the other hand, the activity may be due to hexavalent chromium in which case the activity below 1 wt. yo may likewise decrease due to the stability of the &phase to oxidation. Eischens and Selwood (176)have made a study of the activity of reduced chromia-on-alumina catalysts for the dehydrocyclization of n-heptane. The activity per unit weight of chromium was found to increase sharply at concentrations below about 5 wt. yo Cr; activities were measured down to 1.9 wt. % Cr concentration a t which point the highest activity was observed. Selwood and Eischens concluded that this effect is due to the fact that the chromia is most dispersed a t these low concentrations, in agreement with the present EPR data. However, if a two-site mechanism (1’77) is necessary for dehydrocyclization, the activity may drop at even lower chromium concentrations due to isolation of individual chxomium spins.

4. Porous Carbons EPR has been observed and studied in porous carbons by numerous authors (178-182). The carbons studied have been prepared by pyrolysis of organic material such as dextrose (180), coal (181), and natural gas or oils (181, 182). Porous carbons are of considerable technological importance and show catalytic activity for the ortho-parahydrogen conversion, the hydrogendeuterium reaction, and many reactions of inorganic complex ions (166). Relationships between the characteristics of the EPR absorption and the catalytic activity of porous carbons for the o-p H2 and Hz-DZ reactions have been demonstrated by Turkevich and Laroche (183). The number of free radicals detected by EPR in porous carbons varies from lo1*to lozoradicals per gram and is strongly dependent on the per cent carbon content of the carbon. Likewise in the carbonization of organic materials the number of radicals is strongly dependent on the temperature of carbonization ; a maximum number of radicals is attained by carbonization between 500 and 600”.Heat treatment of carbon blacks formed by pyrolysis of natural gas and oils also results in a variation (182)of the number of unpaired electrons. The width of the EPR absorption line is also dependent on the temperature of formation of the carbon and depends somewhat on whether the sample is carbonized in air or in vacuo m illustrated in Fig. 34. The difference in width obtained between air and in vamo carbonization is a manifestation of the “oxygen effect.” If oxygen is added to coals and sugars heated above 500’ or activated charcoals heated to a temperature above 100’; a pronounced increase in width of the EPR signal occurs. The total, integrated intensity of the EPR absorption, however, does not change greatly. Thus, in this effect the total number of radicals remains approxi-

107

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

mately constant but the resonance line is broadened by interaction with the paramagnetic oxygen molecule. Other paramagnetic gases and also solutions of paramagnetic ions in very porous carbons cause a similar broadening. Adsorbed diamagnetic gases on the other hand are not known to influence the EPR signal. The effect is quite reversible and the oxygen is considered to be physically adsorbed in close enough proximity to the unpaired electrons so as to cause broadening by the dipole-dipole interaction. A large decrease in the spin-lattice relaxation time TI occurs (184) upon the adsorption of oxygen on sucrose chars.

12 .-

I

YI

1

2

Samples in vacuum Samples in air

3 8.. 5

; -

300

a

400

500

600 Temperature (“C)

700

800

FIG. 34. Width at half height of EPR of charred dextrose verBuB temperature of charring (180).

A second type of “oxygen effect” occurs upon exposing activated carbons to oxygen before heating. In this case no change in the width of the EPR signal occurs but the exposure of the sample t o oxygen is accompanied by a decrease in intensity of the EPR signal. Both of the radical effects are completely reversible. The second type of oxygen effect has been ascribed (181) to a bond formation between the oxygen molecule and the iadical such as the R-0-0 type, where the remaining unpaired electron on the oxygen gives rise to a very broad resonance broadened beyond detection due to the anisotropy of the EPR absorption introduced by strong coupling of the spin to orbital motions. The influence of the two oxygen effects on the EPR absorption signal is illustrated in Fig. 35. Another surface effect has been found in that liquids such a8 water, benzene, cyclohexane, etc., can displace gaseous oxygen from the surface

108

D. E. O'REILLY

of porous carbons so as to remove the broadening effect on the EPR signal and restore the signal to the normal value as with a pump-off of the oxygen. This effect is illustrated in Fig. 36; heating of a carbon with adsorbed water vapor causes an inciease in the EPR signal intensity if heated in vacuo and a decrease in the signal if heated in air. As the water vapor is driven off by heating, radicals are left open t o attack by oxygen.

FIQ.35. Oscilloscope tracings of "oxygen effects." Top: decay of EPR signal of coals, charred Rugars and activated carbons heated above 100" with increase in oxygen pressure. Bottom: decay of EPR signal in-activated carbons with increase in oxygen pressure (181).

P

? - i

F

Fro. 36. The effect of removal of adsorbed water vapor in v m c and in air on the radical concentration of activated carbom (181).

a

c

8 d

#a

TEMPERATURE ('C)

[c

It has been Euggested (181) that the basic mechanism in the trapping and stabilization of unpaired electrons is the presence of ring clusters containing more than a certain number of carbon atoms; the radicals are considered to be formed by breakage of bonds a t the edges of the carbon clusters. The possibility of the presence of unpaired electrons in an excited triplet state has been removed by examination (181) of the signal intensity a t various temperatures down to 20'K. It has also been suggested (182) that electronegative groups, particularly quinone-type oxygen, play an

MAGNETIC RESONANCE I N CATALYTIC RESEARCH

109

important role in the stabilization of unpaired electrons in carbons. As the temperature of charring is increased, the number of carbon units which stabilize unpaired electrons increases up to around 600°C where merging of units occurs, resulting in a pairing of electrons and subsequent decrease in the EPR signal intensity. The narrowing of the EPR absorption occurs concurrently with the sharp increase of the number of radicals and is presumed to be due to exchange narrowing of the EPR due to overlap of unpaired electron wave functions. However, this nari owing is accompanied by a decrease in the hydrogen/carbon ratio and may be due to a decrease in the hyperfine interaction of the unpaired electrons with hydrogen nuclei. Initial experiments (184) on a charred paraffin and its deuterated analog indicate that the line width is not principally caused by hyperfine interaction with protons, although the samples were charred in the temperature region where the resonance is appreciably exchange-narrowed. Measurements (184) of the thermal relaxation time T1show T1to be larger than Tg foi charring temperatures below about 600". At and above 600" TI= T2 and the line width increases with increase in charring temperature. This result is consistent with the increase in mobility of the unpaired electrons above 600". Uebersfeld et al. (185) have observed an increase in the proton polarization of liquids (benzene, toluene) and gases (ammonia, hydrogen sulfide) adsorbed on charcoal by saturation of the electron spin resonance of the charcoal. Enhancements of the order of a factor of 10 are observed in the proton resonance of the adsorbed fluid. The enhancement of the proton NMR signal from the adsorbed fluid is proportional t o the dispersion curve of the EPR as the magnetic field in which the nuclear resonance is observed is vaiied. This effect cannot be explained (185) as an Overhauser effect because of this dependence, but does involve a coupling of the nuclear spins and electronic spins, presumably via the dipolar interaction. A phenomenological equation describing the effect has been given (186). Graham and Phillips (186) have measured NMR chemical shifts of hydrocarbons adsorbed on various kinds of porous carbons. Relatively large proton shifts of bhe adsorbate protons to higher magnetic field at constant resonance frequency ranging up to 400 C.P.S.relative to the free liquid of the absorbate have been observed. The authors suggest that the shifts observed are caused by paramagnetism of the carbon surfaces. Although the total magnetic susceptibility of the carbons corresponds to diamagnetism and no EPR was observed from the solids studied, it is deemed likely that the surface phase of these solids is paramagnetic and this paramagnetism may give rise to the chemical shifts observed. The catalytic activity (185) of charred dextrose in the o-p H:! conversion at - 196"and the Hz-D2 equilibrtltion a t 50" is shown in Fig. 37, where the

110

D. E. O’REILLY

first order rate constants for the reactions are plotted. The rate constant for the 0-p Hs Conversion is a maximum for chars with a minimum line width and maximum number of unpaired electrons. On the other hand the rate constant for the Ha-DZreaction increases monotonically with temperature of carbonization up to the maximum temperature employed. Since the low temperature mechanism for the catalytic 0-p Hz conversion is known to be due to electron magnetic moments on the surface of the solid, it is reasonable that the 0-p H, reaction has a maximum rate constant when the concentration of unpaired electrons in the catalyst is a maximum. The HrDz reaction mechanism involves the rupture of hydrogen-hydrogen

F I ~ 37. . Rate constante of 0 - p H, reaction (per minute) and IlrDn equilibration (per hour) over charred dextrose vers,ua temperature of charring of the dextrose (183).

bonds, which does not readily occur when there are a relatively large number of unpaired electrons near the carbon surface. The rate constant does increase with increase in the line width of the electron resonance, which is due to an increase in the mobility of the electrons. Thus the Hz-D2 equilibration mechanism appears to involve interaction of the hydrogen molecule with mobile electrons rather than with individual localized unpaired electrons. Nicolau et al. (187)have reported EPR absorption of platinum and palladium supported on charcoal. These workers attribute a sharp resonance, centered at g = 2.0034, to a species resulting from the interaction of the metal and the charcoal. The intensity of the EPR signal increases

MAGNETIC RESONANCE IN CATALYTIC RESEARCH

111

with increase in platinum concentration up to 5 wt. % Pt, the highest concentration of Pt on charcoal studied. A corresponding increase in catalytic activity of the Pt-charcoal for the hydrogenation of nitro compounds to amines is reported to have been found. Further investigation of this system, however, appears to be necessary to bear out details of the species responsible for the EPR absorption and its role in catalytic hydrogenation.

IV. Conclusion NMR and EPR techniques provide unique information on the microscopic properties of solids, such as Rymmetry of atomic sites, covalent character of bonds, strength of exchange interactions, and rates of atomic and molecular motion. The recent developments of nuclear double resonance, the Overhauser effect, and ENDOR will allow further elucidation of these properties. Since the catalytic characteristics of solids are presumably related t o the detailed electronic and geometric structure of solids, a correlation between the results of magnetic resonance studies and catalytic properties can occur. The limitation of NMR lies in the fact that only certain nuclei are suitable for study in polycrystalline or amorphous solids while EPR is limited in that only paramagnetic species may be observed. These limitations, however, are counter-balanced by the wealth of information that can be obtained when the techniques are applicable. The author wishes to acknowledge valuable discussions and supply of materials studied by members of the Process Division of Gulf Research & Development Company (Section II1C,3a), Dr. H. P. Leftin (Section II,C,3,b), and Dr. D. S. MacIver (Section 111,C13).Dr. Frank Morgan and Dr. C. P. Poole, Jr., read the manuscript and made helpful suggestions. REFERENCES 1. Bloch, F., Hansen, W. W., and Packard, M., Phys. Rev. 70, 474 (1946). 2. Pound, R. V., Purcell, E. M., and Torrey, H. C., Phys. Rev. 69, 680 (1946). 9. Bloembergen, N., Purcell, E. M., and Pound, R. V., Phys. Rev. 73, 679 (1948). 4. Gutowsky, H. S., and Pake, G. E., J . Chem. Phys. 18, 162 (1950). 6. Pound, R. V., Phys. Rev. 79, 685 (1950). 6. Gutowsky, H. S., Ann. Rev. Phys. Chem. 6, 333 (1954). 7. Shoolery, J. N., and Weaver, H . E., Ann. Rev. Phys. Chem. 6, 433 (1955). 8. Hutchison, C. A., Jr., Ann. Rev. Phys. Chem. 7, 359 (1956). 9. McConnell, H. M., Ann. Rev. Phys. Chem. 8, 105 (1957). 10. Wertz, J. E., Ann. Rev. Phys. Chem. 9, 93 (1958). 1I . Andrew, E. R., “Nuclear Magnetic Resonance.” Cambridge Univ. Press, London and New York, 1955. 12. Liische, A., “Kerninduktion.” Veb Deut. Verlag der Wiss., Berlin, 1957. IS. Pake, G. E., Solid State Phys. 2, 1 (1956). 1Sa. Saha, A. K., and Daa, T. P., “Theory and Applicationa of Nuclear Induction.” Saha Institute of Nuclear Physics, Calcutta, 1957.

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13b. Fraenkel, G. K., and Segal, B., Ann. Rev. Phys. Chem. 10, 435 (1959). 14. Selwood, P. W., and Schroyer, F. K., Discussions Faraday SOC.8, 337 (1950); Spooner, R. B., and Selwood, P. W., J . Am. Chem. SOC.71, 2184 (1949). 16. Hickmott, T. W., and Selwood, P. W., J . Phys. Chem. 60, 452 (1956). 16. Fuschillo, N., and Renton, C. A., Bull. Am. Phys. Soc. [a] 2, 226 (1957); Nature 180, 1063 (1957). 17. Mays, J. M., and Brady, G. W., J. Chem. Phys. 25, 583 (1956). 18. Zimmerman, J. R., Holmes, B. G., and Lasater, J. A., J . Phys. Chem. 60, 1157 (1956); Zimmerman, J. R., and Brittin, W. E., ibid. 81, 1328 (1957); Zimmerman, J. R., and Lasater, J. A., ibid. 63, 1157 (1958). 19. Zavoisky, E., J . Phys. (USSR) 9,211 (1945). M. Bleaney, B., and Stevens, K.W. H., Repts. Progr. in Phys. 16, 108 (1953); Bowers, K. D., and Owen, J., ibid. 18, 304 (1955); Orton, J. W., ibid. 23, 204 (1959); Low, W., “Solid State Physics,” Suppl. 2. Academic Press, New York, 1960. 91. Ingram, D. J. E., “Free Radicals as Studied by Electron Spin Resonance.” Academic Press, New York, 1958. 89. Ingram, D. J. E., “Spectroscopy at Radio and Microwave Frequencies.” Philosophical Library, New York, 1956. 93. Stevens, K. W . H., Proc. Roy. SOC.8319,542 (1953); Gri5ths, J. H. E., and Owen, J., ibid. A226, 96 (1954). 64. Tinkham, M., Proc. Roy. SOC.A236, 535, 549 (1956). 96, Owen, J., in “Ions of Transition Elements,” Vol. 26, p. 53. Aberdeen Univ. Press, Aberdeen, 1958. 66. HayeH, W., in “Ions of Transition Elements,” Vol. 26, p. 58. Aberdeen Univ. Press, Aberdeen, 1958. 67. Wertz, J. E., A U Z ~ P., E , Griffiths, J. H. E., and Orton, J. W., in “Ions of Transition Elements,” Vol. 26, p. 66. Aberdeen Univ. Press, Aberdeen, 1958. 98. Bagguley, D. M. S., and GrifEths, J. H. E., Nature 162, 538 (19481). 89. Pryce, M. H.L., Nature 162, 539 (1948). 30. Bleaney, B., and Bowers, K. D., Proc. Roy. SOC.Aa14, 451 (1952). 31. Bleaney, B., Revs. Modern Phys. 26, 161 (1953). 39. Hutchison, C. A., Jr., and Noble, G. A., Phys. Rev. 87, 1125 (1952). 33. Kip, A. F., Kittel, C., Levy, R. A,, and Portia, A. M., Phys. Rev. 91, 1066 (1953). 34. Portia, A. M., Phys. Rev. 91, 1071 (1953). 36. Gri5ths, J. H. E., Owen, J., and Ward, 1. M., Rept. BristoZ Conf. on Defects in Crystalline Solids, 1964 p. 81 (1955); Nature 173, 439 (1954). 36. O’Brien, M. C. M., and Pryce, M. H. L., Rept. Bristol Conf. on Defects in Crystdine Solids, 1964 p. 88 (1955). 37. Fletcher, R. C., Yager, W. A., Pearson, G. L., and Merritt, F. R., Phys. Rev. 95, 844 (1954); Feher, G., ibid. 103,834 (1956). 38. Zeldes, H., and Livingston, R., Phys. Rev. 96, 1702 (1954). 39. Livingston, R.,Zeldes, H., and Taylor, E. H., Phys. Rev. 94, 725 (1954). 40. Smaller, B., Matheson, M. S., and Yasaitis, E. L., Phys. Rev. 94, 202 (1954). 41. Piette, L. H., Rempel, R. C., Weaver, H. E., and Flournoy, J. M., J . Chem. Phys. SO, 1623 (1969). 48. Bagguley, D. M. S., and Owen, J., Repls. Progr. in Phys. 20, 304 (1957). 43. Feenberg, E., and Pake, G. E., “Notes on the Quantum Theory of Angular Momentum.” Addison-Wesley, Cambridge, Mass., 1953. 44.’Rabi, I. I., Ramsey, N. F., and Schwinger, J., Revs. Modern Phys. 26, 167 (1954). 46._Bloch, F., Phys. Rev. 70, 460 (1946).

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89. Rameey, N.F., “Nuclear Moments.” Wiley, New York, 1953. 90. Bersohn, R.,J . Chem. Phys. 20, 1505 (1952). 91. Foley, H. M., Sternheimer, R. M., and Tycko, D., Phys. Rev. 93, 734 (1954). 98. Dm, T. P., and Bersohn, R., Phys. Rev. 102, 733 (1956). 93. Bersohn, R., Bull. Am. Phys. SOC.[2]1, 215 (1956);J . Chem. Phys. 29, 326 (1958). 94. Volkoff, G. N., Can. J. Phys. 91,820 (1953). 96. Feld, B. T., and Lamb, W. E., Jr., Phys. Rev. 67, 15 (1945). 96. Cohen, M.H., and Reif, F., Rept. Bristol Conj. on Dejects in Crystalline Solids,1964 p. 48 (1955). and Reif, F., Solid Stata Phys. 97. Reif, F., Phys. Rev. 100, 1597 (1955);Cohen, M.H., 6, 322 (1957). 98. Holcomb, D. F., and Norberg, R. E., Phys. Reu. 98, 1074 (1955). 99. Norberg, R. E., Phys. Rev. 86, 745 (1952). 100. Newman, R., J. Chem. Phys. 18,669 (1950). 101. Andrew, E. R., and Eades, R. G., Proc. Roy. SOC.216A, 398 (1953). 108. Thomas, J. T., Alpert, N. L., and Torrey, H. C., J. Chem. Phys. 18, 1511 (1950). 103. Andrew, E.R., J. Chem. Phys. 18,607 (1950). 104. Watkins, G.D., and Pound, R. V., Phys. Rev. 89, 658 (1953). 106. Bloembergen, N.,Rept. Bristol Conj. on Dejects in Crystalline Solids, 1964 p. 1 (1955).The method of calculation and description of other examples is given in this reference. 106. Bloembergen, N., and Rowland, T. J., A d a Met. 1, 731 (1953). 107. Rowland, T. J., A d a Met. 3, 74 (1955). 108. Otsuka, E., and Kawamura, H., J. Phys. Soc. Japan 12, 1071 (1957);Otsuka, E., ibid. 13, 1155 (1958). 109. O’Reilly, D. E., J. Chem. Phys. 28, 1262 (1958). 110. Portis, A. M., Phys. Rev. 100, 1219 (1955). 111. Portis, A. M., Tech. Note No. 1. Air Research and Development Command AF 18(600)-892 (1955). 119. “Structurbericht,” Vol. 1, 1913-1928. Edwards, Ann Arbor, Michigan, 1943. 113. Russell, A. S., Tech. Paper No. 10,Alcoa Research Laboratoriee (1956).A review of the properties of aluminum oxide and hydrates. 11.4. Van Nordstrand, R. A., Am. Chem. Soc., Div. Petroleum Chem., Tech. Catal. Prep. 1, No. 2,43 (1956). 116. O’Reilly, D. E., Research File No. H M l , Gulf Research & Development Co. (1956). 116. Gutowsky, H.S.,and Hoffman, C. J., J. Chem. Phys. 19, 1259 (1951). 117. Saika, A., and Slichter, C. P., J. Chem. Phys. 22, 26 (1954). 118. Kanda, T., J. Phys. SOC.Japan 10, 85 (1955). 119. O’Reilly, D.E., Bull. Am. Phys. SOC.121 3, 143 (1958). 180. O’Reilly, D.E., Leftin, H. P., Hall, W. K., J . Chem. Phys. 29, 970 (1958). 181. Gutowsky, H. S.,and Saika, A., J. Chem. Phys. 91, 1688 (1953). 198. Cohen, A. D.,and Reid, C., J. Chem. Phys. 26, 790 (1956). 198. Kittel, C., and Abrahams, E., Phys. Rev. 90,238 (1953). i84. Davis, C. F., Jr., and Strandberg, M. W. p., Phys. Rev. 106, 447 (1957). 186. Abragam, A., and Pryce, M. H. L., Proc. Roy. SOC.&06, 135 (1951).

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186. Bleaney, B., and Stevens, K. W. H., Repts. Progr. in Phys. 16, 108 (1953). 187. Kronig, R. de L., Physica 6, 33 (1939). 188. Feher, G., Bell System Tech. J . 36, 449 (1957). 169. Overhauser, A. W., Phys. Rev. 92, 411 (1953). 130. Carver, T. R., and Slichter, C. P., Phys. Rev. 92, 212 (1953). 131. Kittel, C.,Phys. Rev. 96, 589 (1954). 138. Slichter, C.P., Phys. Rev. 99, 1822 (1955). 133. Abragam, A., Phys. Rev. 98, 1729 (1955). 134. Beljers, H. G., van der Kint, L., and van Wieringen, J. S., Phys. Rev. 96, 1683

(1954). Abragam, A., Landesman, A., Winter, J. M., Compt. rend. 247, 1852 (1958). Poindexter, E., Nature 182, 1087 (1957);J . Zmt. Petrol. 46, No. 421,9A (1959). Feher, G.,Phys. Rev. 103, 500, 834 (1956). Feher, G.,Phys. Rev. 106, 1122 (1957). Bethe, H.A., Ann. Physik. [5]3, 133 (1929). Bowers, K.D., and Owen, J., Repts. Progr. in Phys. 18,304 (1955). Abragam, A.,and Pryce, M. H. L., Proc. Roy. Soc. 8406, 135 (1951). Orgel, L.E., J. Chem. Phys. 23, 1004,1819 (1955);Dunita, J. D., and Orgel, L. E., Phys. and Chem. solids 3, 318 (1957). 14.9. Wigner, E., “Quantum Mechanics of Atomic Spectra.” Academic Press, New York, 1959;Lomont, J. S.,“Applications of Finite Groups” Academic Press, New York, 1959. 1.44. Moffitt, W., and Ballhausen, C. J., Ann. Rev. Phys. Chem. 7 , 107 (1956). 146. Kramers, H.A., Proc. Acad. Sci.Amsterdam 33, 959 (1930). 146. Van Wieringen, J. S., Discussions Faraday SOC.19, 118 (1955). 147. Bleaney, B., and Bowers, K. D., Proc. Phys. SOC.864, 1135 (1951). 148. Davis, C. F., Jr., and Strandberg, M. W. P., Phys. Rev. 106, 447 (1957). 149. O’Reilly, D. E., J. Chem. Phys. 29, 1188 (1958);30, 591 (1959). 160. Bleaney, B., Proc. Phys. Soc. A63, 407 (1950). 161. Abragam, A., and Pryce, M. H. L., Proc. Roy. SOC.A206, 173 (1951). 166. Low, W., Phys. Rev. 109, 247 (1958). 163. Stevens, K.W. H., Proc. Roy. SOC.8319,542 (1953). 164. Owen, J., Proc. Roy. SOC.A227, 183 (1955). 166. Maki, A. H., and McGarvey, B. R., J. Chem. Phys. 29, 31 (1958). 168. Basolo, F., and Pearson, R. G.,‘fMechanisms of Inorganic Reactions.” Wiley, New York, 1958. 167. Anderson, P. W., and Weiss, P. R., Revs. Modern Phys. 26, 269 (1953). 168. Bleaney, R., and Bowers, K. D., Proc. Roy. Soc. A214, 451 (1952). 169. Erdman, J. G., Ramsey, V. G., Kalenda, N. W., and Hanson, W. E., J. Am. Chem. Soc. 78, 5844 (1956). 160. McConnell, H. M., J. Chem. Phys. 26, 709 (1956). 161. Condon, E. U., and Shortley, G. H., “The Theory of Atomic Spectra,” Chapter 3. Cambridge Univ. Press, London and New York, 1935. 168. Sands, R. H., Phys. Rev. 99, 1222 (1955). 163. Bloembergen, N., and Rowland, T. J., Phys. Rev. 97, 1679 (1955). 164. O’Reilly, D. E., unpublished research, Gulf Research & Development Company, 1958. 166. Faber, R. J., and Rogers, M. T., J. Am. Chem. SOC.81, 1849 (1959). 166. Eischens, R. P., and Selwood, P. W., J. Am. Chem. Soc. 69, 1590,2698 (1947). 136. 136. 1%’. 138. 139. 140. 141. 148.

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Matsunaga, Y., Bull. C h m . SOC.Japan 30, 868 (1957). Weller, S. W., and Voltz, S. E., J . Am. Chem. SOC.76, 4695 (1954). Voltr, S. E., and Weller, S. W., J . Am. Chem. SOC.76, 5227 (1953). Chapman, P. R., Griffith, R. H., and Marsh, J. D. F., Proc. Roy. SOC.8324, 419

(1954). 171. Trounson, E. P., Bleil, D. E., Wangsness, R. K., and Maxwell, L. R., Ph,ys. Rev. 70, 542 (1950); Maxwell, L. R., and McGuire, T. R., Revs. Modern Phys. 26, 279 (1953). 178. Dayhoff, E. S., Phys. Rev. 107, 84 (1957). 173. O’Reiiy, D. E., and MacIver, D. S., Am. Chem. SOC.,Diu. Petrol. Chem., Gen. Papers 4, No. 2, C-59 (1959); O’Reilly, D. E., ibid. 4 , No. 2, C-157 (1959). 17.4. Heikes, R. R., and Johnston, W. D., J . Chem. Phys. 26, 582 (1957). 176. Matsunaga, Y., Bull. Chem. Soc. Japan 80, 984 (1957). 178. Eischens, R. P., and Selwood, P. W., J . Am. Chem. SOC.70, 2271 (1948). 177. Herington, E. F. G., and Ftideal, E. K., Proc. Roy. SOC.8184, 434, 447 (1945). 178. Ingram, D. J. E., and Bennett, J. E., Phil. Mag.[7] 46, 545 (1954); Commoner, B., Townsend, J., and Pake, G. E., Nature 174, 689 (1954); Uebersfeld, J., Etienne, A., and Combriason, J., Zbid. p. 614; Ingram, D. J. E., Tapely, J. G., Bond, R. L., Jackson, R., and Murnaghan, A. R., ibid. p. 797; Castle, J. G., Jr., Phys. Rev. 09, 341 (1955); Bennett, J. E., Ingram, D. J. E., and Tapely, J. G., J . Chem. Phys. 23, 215 (1955); Winslow, F. H., Baker, W. O., J . Am. Chem. Sac. 77, 7451 (1955). 179. Austen, D. E. G., and Ingram, D. J. E., Chem. & Ind. p. 981 (1956). 180. Paator, R. C., Wed, J. A., Brown, T. H., and Turkevich, J., Phys. Rev. 102, 918 (1956). 181. Auskn, D. E. G., Ingram, D. J. E., and Tapely, J. G., Tmns. Faraday Soc. 64, 400 (1958). 188. Collins, R. L., Bell, M. D., and Kraus, Gerard, J . Appl. Phys. SO, 56 (1959). 183. Turkevich, J., and Laroche, J., 2.physik. Chem. 16, 399 (1958). 184. Singer, L. S., Spry, W. J., and Smith, W. H., Proc. 3rd Conf. on Carbon p. 121 (1959). 186. Erb, E., Motchane, J. L., and Uebersfeld, J., Compl. rend. acad. sn’. 248, 2121 (1958). 186. Graham,D,, and Phillips, W. D., Solid-Gas Interface-Proc. 2nd. Internat. Congr. of Surface Activity Vol. 11, p. 22 (1957). 187. Nicolau, C. S., Thorn, H. G., and Pobitschak, E., Tram. Faraduy SOC.66, I430 (1959).

Base-Cata lyzed Reactions of Hydrocarbons HERMAN PINES The Ipatieff High Pressure and Catalytic Laboratory, Department of Chemistry, Northwestern University, Evanston, Illinois AND

LUKE A. SCHAAP Research and Development Department, Standard Oil Company (Indiana), Whiting, Indiana Page 117 11. lsomerization., ............................. . 118 A. Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 B. Monoolefins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 C. Diolefins.. ....................................................... 122 D. Phenylcyclohexane (Hydrogen Transfer). ............................ 126 111. Side-Chain Alkylation of Arylalkanes. .................................. 126 A. Generalities.. ..................................... . . . . . . . . . 126 B. Sodium-Catalyzed Alkylations . . . . . . . . . . . . . . . . . . C. Potassium-Catalyzed Alkylations. ............... D. Relative Rates of Ethylation of Aromatics.. .......................... 134 E. Aralkylation of Aromatics.. ........................................ 137 F. Alkenylation of Aromatics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 IV.’ Nuclear Alkylation of Aromatics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 V. Alkyation of Alkylpyridines., ... ...................... 140 V1. Reaclions of Olefins.. .......... ...................... 141 A. Rteactions of Monoolefins. ..... .... . . . . . . . . . 142 B. Reaction of a-Methylstyrene.. ...................................... 144 VII. Conclusion. . . . . . . . . . . . . . . . . . . . ...................... 146 References.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. introduction The acid-cata,lyzed conversions of hydrocarbons have been extensively studied and are widely reported in chemical literature. Many important petroleum and petrochemical processes involve catalysis by acids. In contrast to this, the use of bases to catalyze hydrocarbon conversions has received little attention except for polymerization of conjugated dienes and styrene to high polymers. Recently alkali metals or compounds of alkali metals were found to act as catalysts for reactions, such as isomerization of olefiiis, dehydrogenation 117

118

HERMAN PINES AND LUKE A. SCHAAP

of certain diolefinic materials to aromatics, alkylation of arylalkanes, and polymerization of monoolefins. Many of these reactions are highly selective and open new routes for t.he synthesis and conversion of hydrocarbons. This chapter is largely limited to reactions of hydrocarbons and related compounds. Reactions in which the metal is involved merely as a reducing agent are not included. The alkali-metal-catalyzed reactions leading t o the formation of high polymers are not discussed because they have been treated elsewhere (1).

II. lsomerization A. GENERALITIES Base-catalyzed ieactions of hydrocarbons have been until recently limited to hydrocarbons having conjugated double bonds or double bonds that may be brought into conjugation, to alkenyl-aromatics, and to hydrocarbons possessing triple bonds (2). Double-bond shifts of such compounds can occur a t about 150" with such bases as alcoholic potassium hydroxide. It was recently recognized that olefinic hydrocarbons containing allylic hydrogen atoms can undergo double-bond isomerization under the catalytic influence of very strong bases. The ease of isomerization may be related to the acidity of the allylic hydrogen of the compound and to the strength of the bases. The bases include potassium amide, as reported by Shatenstein et al. (9), lithium ieacted with ethylene diamine (Q), and organosodium compounds (6-9).Sodium or lithium dispersed on activated alumina forms active catalysts; with these catalysts the temperature needed for reaction is much lower (10-12'). In the presence of these basic catalysts, monoolefins undergo a reversible double-bond shift, whereas cyclic diolehs undergo isomerization plus dehydrogenation, which leads to the formation of aromatic hydrocarbons. No skeletal isomerization of the olefin occurs as it usually does in acidcatalyzed isomerizations. Skeletal isomerizations are unknown in base catalysis except for those involving a noncatalytic reaction of arylalkylhalides with alkali metals, as reported by Gxovenstein and by Zimmerman and Smentowski, and those involving reaction of arylalkenyl halides with organolithium compounds, as reported by Curtin et al. (IS).

B. MONOOLEFINS Double-bond isomerieation reaction of simple olefins requires strong basic catalysts. Various catalyst systems have been reported for this reaction. They include sodium-organosodium catalysts prepared in situ by reacting an excess of sodium with a reactive organic compound, such as o-chlorotolucne or anthracene as reported by Pines and co-workers (6-8).

BASE-CATALYZED REACTIONS OF HYDROCARBONS

119

These catalysts require temperatures above 100' and usually 150-200' for reasonable rates. Alkylsodium compounds at their decomposition temperatures (50-90') have also been used by Pines and Haag (9).Lithium reacted with ethylene diamine has also been reported by Heggel et al. (4) as a catalyst for this reaction. The homogeneous system thus formed seems to lower the temperature requirement t o 100' (4), whereas the use of potassium amide in liquid ammonia requires 120' (9). Sodium reacted with ethylene diamine has been reported t o be an ineffective catalyst (4). The most active catalyst systems reported so far are high-surface alkali metals and activated-alumina supports. They are very effective at or near room temperature (10-12). 1. Alkenes These catalysts have strong basic characteristics such that they are able to abstract allylic protons from the olefins involved. step 1

+

B-Na+ RCHpCH=CHz + BH B = H, NH2, alkyl, aryl, etc.

Na+

+ RcH--CH=CHs

The base thus formed from the olefin has a negative charge on a carbon atom, and so may be referred to as a carbanion. The allylic hydrogen is the most acidic because removing it results in a resonance-stabilized intermediate. Na+ Na+ R ~ H - C H = C H ~ cI RCH=CH-CH~ (1) (11)

Step 8

In the presence of additional olefin, an exchange of metal for allylic proton or transmetallation may take place, resulting in the isomerized olefin and more of the basic intermediate.

(11)

Since the basic or carbanion intermediate can continue to go to product by Steps 2 and 3, we have a chain reaction which is consistent with the rapid isomerizations which may be obtained using these catalysts. This mechanistic interpretation was proposed in one of the first paper8 published on this subject (6);it and similar interpretations have been very helpful in bringing about an understanding of base-catalyzed reactions. The chain-reaction sequence may be terminated by reaction with a formation of a material which is not basic enough to metallate the olefin. Such compounds may be polyunsaturated hydrocarbons which may be formed by elimination of hydride ions from a carbanion.

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HERMAN PINES AND LUKE A. SCHAAP

Na+ CH&H-CH=CH*

+

CHZ=CH-CH=CHZ

+ Na+H-

Traces of butadiene have been found by Pines and Haag (14) in isomerized products of butenes. The catalysts exhibiting the highest activity are the high-surface sodium on activated-alumina catalysts. They were used by O'Grady et al. (IZ), to obtain equilibrium distributions of olefin isomers in short contact times and a t relatively low temperatures, as shown in Table I. Since the same composition was reached with different starting materials and differerit reaction times, equilibrium distributions of products are easily obtained. The preparation of these high-surface sodium catalysts has been described (16). TABLE 1 Isomerization of monoolefine Reaction conditions

Product (mole %)

Milliliters remper ature oleh Contact ("C) (minutes) Per gram catalyst cis-2- Butene trans-2-Butene 1-Butene 1-Pentene 1-Hexene 1-Octane

15 45 0.6 5 150 950 6 60

23 23 20 6.4 6.4 6.4 6.4 6.4

25 25 25 0

7

5.8

25

0

25 0 0

-1-

cis-2- trans-2-

sis-3- trans-3-

3 2 3 1.6 1.3 1.8 1.1 0.6

26 26 26 17 16 18 17.2 13.9

71 72 71 81

83 80

60.2 62.1

1%l-octene, 4% cis-octenes, 9570 trans-octenes

Although the catalyst results in the rapid formation of an equilibrium isomer distribution, Haag and Pines ( I I ) , as well as O'Grady et al. ( l b ) , have found that the rate of formation of isomers differs considerably. Kinetic studies of the reaction of 1-butene over sodium on alumina show that in short contact times 1-butene is predominantly converted into cis-2-butene rather than into the thermodynamically favored 2rans-2butene. On longer contact with the catalyst, cis-2-butene is converted to trans-2-butenc in the amount expected from the equilibrium distribution. By nssuming that the isomerization reaction is first order in each isomer, a

BASE-CATALYZED REACTIONS OF HYDROCARBONS

121

rate expression has been derived that is consistent with experimental results. With sodium on alumina, the relative rate constants for the butene isomerization a t 30" have been determined to be as shown below (A). I-I3C-CIiz--CH=CH*

II,C

\

/ \ 3.6

CH=CH

\

cI13

v 12.3

CH=CH

/ CMs

'CHI

The stereoselectivity of the catalyst results from the rapid conversion of l-butene to cis-2-butene. Therefore butene molecules must be reacting more rapidly with a cis-butenyl carbanion, or the cis-butenyl carbanion is present in greater concentrations. The latter interpretation has been favored, and a n additional resonance-stabilized structure may account for the preferential formation of the cis-butenyl carbanion (11). H

\ c/

-CH,

H

/ \

CH#+

A somewhat similar stereoselectivity has been found for butene isomerization in acid catalysis - both heterogeneous and liquid phase (16). However, this is interpreted as being due to an attraction of the electron system for positive hydrogen ions, whereas attraction of electrons for sodium ions has not been demonstrated. 2. Cyclenes

Isomerization of cycloolefins has been carried out using base catalysis. Sodium-organosodium catalysts were used by Pines and Eschinazi (7) for isomerizing 1-, 2-, and 3-p-menthenas; the same distribution of 1-, 3-, and 8(9)-p-menthenes was obtained from each of the starting materials (B). O'Grady et al. ( l a ) , used a high-surface sodium on alumina catalyst at 25" for the isomerization of 4-methyIcycIohexene and observed the formation of the three methylcyclohexene isomers (C) . 4-Methylcyclohexene has also been isomerized by Reggel et al. (4), using the lithium ethylene diamine system. In general the reaction of cyclenes and the mechanism thereof may be considered to be like that of alkenes.

122

HERMAN PINES AND LUKE A. SCHAAP

8-o.o.o (15%)

(40%)

(45%)

C. DIOLEFINS The study of the action of alkali metal catalysts has been largely confined to cyclic diolefins because of the hydrogen elimination reaction yielding aromatics that occurs with these compounds. 1. Monocyclic Diolejns (Dehydrogenation) The double-bond isomerization of cyclic materials possessing two double bonds takes place readily. When 1,4-cyclooctadieneis contacted with highsurface sodium on alumina at ' 0 for a short time, over 95% of the 1,3cyclooctadiene results (12). However an even more interesting reaction takes place when the cyclic diolefin possesses a six-membered ring. An example is the reaction (D) of d-limonene which yields p-cymene and hydrogen (6).

o-$.. @)

BASE-CATALYZED REACTIONS OF HYDROCARBONS

123

The driving force for this reaction is the formation of the thermodynamically more stable aromatic compound. The mechanism (E) involves doublebond isomerisation, as was discussed previously, until an endocyclic diolefin is obtained.

(El

This can then dehydrogenate by being metalated in an allylic position followed by elimination of a hydride ion (F).

B

=

H,aryl, alkyl, alkenyl (F)

A more detailed study concerning this mechanism was made by Pines and Eschinazi (6) using the terpenes d-limonene and Z-a-phellandrene. An advantage of using these compounds is that changes in optical rotation can be observed which may indicate the progress of the reaction. For d-limonene, refluxing in the presence of a sodium-organosodium catalyst resulted in a very rapid drop in optical activity while hydrogen was slowly evolved. The rapid loss of optical activity may result from conversion of d-limonene into the 2-isomer (G). If the reaction (G) is not carried out to completion, some cyclic diolehs will remain. Those from limonene consist mainly of the exocylic diolefins 2,4(8)- and 3,8(g)-p-methadienes,

124

8

HEBMAN PINES AND LUKE A. SCHAAP

+ B-Na+

++Q-Na+

Q -N ' + + B H --+ Q + B-N a+

R

=

CloH1s or chain initiator

(a) whereas endocyclic diolefins could not be found, probably because an endocyclic diolefin dehydrogenates very rapidly. The reaction of l-a-phellandrene showed this to be true. This compound lost optical activity and dehydrogenated rapidly to yield p-cymene (H). I I

h

A (HI

No other semicyclic or exocylic diolehs were produced, although loss of optical activity was somewhat faster than dehydrogenation. Dehydrogenation of dipentene (d,l-limonene) and 4-vinylcyclohexene has been studied using both the lithium-ethylenediamine catalyst system (4) and the sodium-alumina catalyst system (12).The aromatic compounds p-cymene and ethylbenzene are produced by both types of catalyst; however, while vinylcyclohexene yields ethylbenzene rapidly at 0" over a sodium on alumina catalyst, dipentene yields mainly mixed dienes a t 0" but at 25' is also rapidly dehydrogenated to p-cymene (12). The use of potassium tert-alkoxides for the dehydrogenation of d-limonene has also been reported by Pines and Schaap (I?'). These alkoxides are not strong enough bases to catalyze hydrocarbon conversions, except under conditions of thermal decomposition at about 300". It is postulated that these compounds decompose by elimination of carbanions. (CH&C-O-K+

-+

cH,K+

+ (CHc)&===O

The carbanions thus produced in situ have only a transient existence because of the more acidic materials present, such as the ketones, acids, and condensation products produced. However, they are effective for a reaction with a relatively large driving force, such as limonene dehydrogenation.

BASE-CATALYZED REACTIONS OF HYDROCARBONS

125

2. Geminal Alkylcyclohexadienes (Dealkylation)

Geminal alkylcyclohexadienes having structures similar to some of the cyclic diolefins mentioned previously have been reacted over sodiumorganosodium catalysts by Pines and Eschinazi (8). These compounds cannot undergo the dehydrogenation reaction because of the gemdialkyl group. 5,5-Dimethyl-3-methylenecyclohexene(I) yielded m-xylene and methane when refluxed in the presence of the catalyst and a-pyronene (11) yielded 1,2,3-trimethylbenzene.

(11)

(1)

The mechanism of this elimination reaction may be regarded as being similar to that of the dehydrogenation reaction. Double-bond isomerization leads to formation of a species with both double bonds in the ring. This is then metalated and eliminates the alkyl group (A').

+

+

CH8-Na+ BH + CHI B-Na+ B = CoHla or chain initiator anion

(A9 Alkyl groups differ as to ease of elimination. When 5-methyl-5-ethyl-l13cyclohexadiene is reacted over a sodium-organosodium catalyst, methyl groups are eliminated more easily than ethyl groups (B').

OCH8 CzHs

(B')

Methide ion is eliminated more easily than the ethide ion because the methide ion has greater stability. This stability results from the electrondonating ability (inductive effect) of the methyl group. This agrees with the

126

HERMAN PINES AND LUKE A. SCHAAP

commonly accepted order of carbanion stability: primary tertiary.

> secondary >

D. PHENYLCYCLOHEXENE (HYDROGEN TRANSFER) Pines and Kolobielski (18)have shown that phenylcyclohexene,although it is not a cyclic diolefin, will also undergo reactions similar to those that cyclic diolefins undergo when treated with base catalysts. When heated to 200-220' with a sodium-benzyl-sodium catalyst, it underwent a hydrogen transfer reaction resulting in the formation of biphenyl and of phenylcyclohexane; molecular hydrogen was not produced. The mechanism of this reaction may be pictured as an elimination of sodium hydride from one molecule with the hydride ion being accepted by another molecule (A"-E").

(I) + (111)

-

(V)

+ (11)

(E")

This reaction is favored because a resonance-stabilized anion (111) is formed, whereas with a simple cyclic monoolefin, such as methylcyclohexene, a nonresonance stabilized tertiary carbanion would have to be formed. Phenylcyclohexane also was dehydrogenated under base catalysis a t 240'. This is presumably because of the formation of carbanion (111) by reaction with the catalyst, followed by the elimination of hydride ion to yield phenylcyclohexane, which can then react as before.

111. Side-Chain Alkylation of Arylalkanes A. GENERALITIES The acid-catalyzed reaction of aromatics with monoolefins results exclusively in addition of alkyl groups to the aromatic ring. In contrast, the base-catalyzed reaction of aromatics with monoolefins results in alkylation

BASE-CATALYZED REACTIONS OF HYDBOCABBONS

127

of side chains. Thus this reaction is unique in that it allows one to enlarge the alkyl group of an arylalkane catalytically. Arylalkanes suitable for this reaction possess benzylic hydrogens. The olefins suitable for this reaction are ethylene, propylene, and, to a smaller extent, butylenes. Conjugated diolefins, such as butadiene or isoprene, yield alkenylaromatics, whereas styrene reacts with arylalkanes to yield aralkylaromatic hydrocarbons. The reaction (1) can be presented by the general formula given below. R CsHshH

I

R1

+C H - d

\

I

\

R Ra R, RI, RI, R, being H, or alkyl

Rs

Catalysts and reaction conditions used are generally similar to those used for olefin isomerization. Catalysts reported are sodium-organosodium catalysts prepared in situ by reaction of a “promoter” such as o-chlorotoluene or anthracene with sodium (19-24), alkali metal hydrides (20, 21), alkali metals (22),benzylsodium (26), and potassium-graphite (26). These catalysts are strong bases that can react with alkylaromatics to replace a benzylic hydrogen [Reaction (2)]. R

B-Na’

R

+ CIHKAH + BH + CsHrA-Na-’

(2)

RI I $1 R, RI being H, alkyl, or aryl

Metalation reactions of this type have been extensively studied by Morton et al., Bryce Smith, and others (27-36). The relative ease of metalation indicates that methyl groups are more acidic than ethyl groups, etc. (27, 29). Rates of deuterium exchange in the presence of base catalysts have been the most recent approaches toward studying the relative acidity of aromatics. Exchanges of lithium cyclohexylamidewith a-deuterated hydrocarbons studied by Streitwieser (SS), and exchanges of adeuterated ethylbenzene with higher hydrocarbons in the presence of potassium by Hart and Crocker (34) have shown that the acidity of a benzylic hydrogen decreases with increasing alkyl substitution (both in number and size) of the a-carbon. As the acidity of the benzylic hydrogen decreases, metalation of the ring becomes competitive. The distribution of metalation, however, does not only depend on the aromatic, but also on the metalating agent used. Such reagents as alkylsodium or potassium compounds metalate predominantly the aromatic ring of a compound with a deactivated benzylic hydrogen such as cumene (29, 56), while potassium with metal oxides and amyl or phenylpotassium prepared from potassium metal and amyl chloride or anisole respectively metalate exclusively the a-carbon, as shown by Morton

128

HERMAN PINES AND LUgE A. SCHAAP

and Lanpher (36). Sodium and potassium catalysts yield different results when used for side-chain alkylation, but alkylation of the ring does not take place to any appreciable extent in compounds having benzylic hydrogens. Volts ($1) reported that lithium compounds are not very effective catalysts and have been little studied. Temperatures of 150-300° usually are required for side-chain alkylation; the higher temperatures being necessary only for the higher olefins.

ALKYLATIONS B. SODIUM-CATALYZED Sodium is the metal which has been studied most for base-catalyzed alkylations. The use of it results in the most selective reactions. 1. Ethylation

Of the olefins, ethylene has been most extensively studied (19, 21, 93-26, 36) ;it reacts most readily in base-catalyzed alkylations. In general temperatures of 150-200' are used with relatively low ethylene pressures (0-70 atm.). Benzylic hydrogens are replaced by ethyl groups; i.e., toluene yields n-propylbenzene. Additional substitution on the a-carbon may yield 3-phenylpentane and 3-ethyl-3-phenylpentane [Reaction (3)]. CaHrCH:

CI&

- x""

CeHrCH&H&Ha + GFi4 CeHsCHCH&Ha GH' CsHs CHaCH: &HnCHI

(3)

AHaCHs

Thus ethyl groups may be added to a-carbons as long as benzylic hydrogens are available for replacement. The mechanism which has been proposed by Pines et al. (19) for the reaction consists of the addition of the benzylic carbanion formed by reaction of the aromatic and the catalyst with the olefin followed by a transmetalntion reaction with more of the aromatic [Reaction (4)]. R

R CeHsAH

+ B-Na+ -+

A 1

C6Hs-

: I

CeHs(!FNa+ A1

R

-Na+

+ CH*=CH,

-+

CeHb-

81

AI

t: I

-CH~-CHI-Na+

(4)

8 1

R

R CsHs-

+ BH

-CHr-CHz-Na+

+ CsHh

R

B-

=

+

H -+ C ~ H ~ - - - ~ ~ X ~ C,Hs-(!FNa+ CHI

RI1

Ri

R

beneylic, aryl, alkyl, H, etc.

R,R1 = H, alkyl, or sryl

dl

BASE-CATALYZED REACTIONS OF HYDROCARBONS

129

This is a catalytic-chain mechanism because the agent which adds to the olefins is regenerated in the last step.The addition reaction of the anion to the olefin is similar to the noncatalytic reaction of alkyllithium compounds with ethylene as reported by Ziegler and Gellert ($7) and by Bartlett et al. (38).In this reaction (5), the less stable secondary and tertiary alkyl lithium compounds add most readily. (CH&C-Li+

+ CHFCH~

-+

(CHa)rCCHzCHa-LP

(5)

This addition is energetically favored because a more stable primary carbanion is formed from a less stable tertiary carbanion. The addition step in the side-chain alkylation reaction is probably not energetically favored because a primary carbanion is formed from a resonance-stabilized benzylic carbanion. However, as the rapid and energetically favored transmetalation reaction following it restores the benzylic carbanion, the over-all process takes place readily. An alternative radical combination mechanism has also been proposed by Morton and Ward (39) for the alkylation reaction. A hydrogen-transfer reaction involving the olefin and the addition product of the benzylic carbanion and olefin may accompany the side-chain alkylation reaction. The result is that, alkanes and arylalkenes are produced (19). This hydride-transfer reaction may take place by elimination of a hydride ion from the carbanion adduct followed by addition of the hydride ion to the olefin [Reaction (S)].The amount of this side reaction probably depends largely on the severity of reaction conditions used. R R I I CaH&-CH2-CH2-Na+

-+

RI Na+H-

+ CHFCH~

-+

R

-+

+ Na+H-

RI CHr-CHz-Na+

R I

I C~HKCH + CHs-CHa-Na+ I

CaHsC-Na'

I

+ CHI-CHI

RI

RI

R, R1

CaHKCCH=CH2

I

I

=

H, alkyl, or aryl

2. Propylation and Reaction with Higher Olefins

The reaction of toluene with propylene and higher olefins is similar to that of toluene with ethylene. In contrast to the acid-catalyzed alkylation of aromatics, the base-catalyzed reaction of toluene with propylene takes place less rapidly than the reaction with ethylene. With more severe conditions, such as temperatures of 225-250°, the reaction of toluene with propylene may be made to proceed satisfactorily, but butylenos yield only small amounts of products even at 300°, as reported by Pines and Mark (2'0). Such conditions result not only in more hydrogen transfer, but alkyl-group

130

HEBMAN PINES AND LUKE A. SCHAAP

elimination also results, leading to formation of lower arylalkenes than would be expected from the reactants [Reaction (7)]. CH: GH,CH*Na-’

+ (CHa)rC=CH*

+ CEH~CHZ-~-~HINC~+

AH: -+

CsHsCHsC==CHz

+ eHaNa+

(7)

AH:

Aromatics with larger side chains than toluene, such as ethylbenzene and cumene, may be reacted with propylene, but yields of the expected product are small even at 300’ (20). The reaction of aromatics with higher olefins provides the best evidence that ionic intermediates are involved in base-catalyeed reactions. This is shown by the product formed in these reactions (8, 9). Toluene reacts with propylene to yield isobutylbenzene and with isobutylene to yield neopentylbenzene (20).

+ CaHrCHa + (CHa)I--C-CHz CEH~CHI CHa-CH=CHz

ra

---t

CsH&Hz-

H-CH:

--t

CaH&Hr-c(CH:)rcHa

(8) (9)

This indicates that the benzylic carbanion adds to the olefin t o yield a primary carbanion rather than a secondary or tertiary carbanion. CHa CsHseHaNa+

+ CH:CH=CH,

-+ CIH~CH*-AH-~H~N~+

(10)

Reaction (10) is preferred over Na+

CsHs?%%Naf

+ CH8CH=CH3 + CaH6CHz-CHn--H-CH,-CHI

(11)

This agrees with the theory that resonance-nonstabilized primary carbanions are more stable than the corresponding secondary or tertiary carbanions, whereas tertiary carbonium ions or radicals are more stable than the corresponding secondary and primary species. If radical intermediates were involved in a chain catalytic reaction of toluene with propylene, n-butylbenzene would be the product. (12

This has been shown by Pines and Arrigo (40) to be the case in the thermal reaction of toluene with propylene. Schramm and Langlois (22) reported that some n-butylbenzene may be produced in the base-catalyzed reaction of toluene with propylene. The amount of n-butylbenzene apparently

BASE-CATALYZED REACTIONS O F HYDROCARBONS

131

depends on the catalyst and conditions used. The alkali metal used and the temperature affect the ratio of isobutylbenzene to n-butylbenzene produced, as shown in Fig. 1. The production of n-butylbenzene may be attributed to an inherent lack of complete selectivity in carbanion reactions, because the greater stability of an intermediate does not exclude the formation of the less stable product. This stability is only important when the step in forming intermediates is slow or when energy differences are large. On the other hand, the formation of n-butylbenzene from toluene and propylene may be due to a partial radical character of benzyl alkali metals. The latter would not seem to be the case because the potassium compounds should have greater ionic character, but they yield more n-butylbenzene. This agrees with the idea that lack of selectivity may be due to greater rate of reaction of potassium compounds with olefins. I

W N

'

' / A U M

ALITHIUM

' POTASSIUM

I-4 A

a H IY

0

z \

W 2 W N

6

0-

A

id

B

54-

3-

z

W

m

2-

J

"

I

'Ab7

2;3

2;Z '

2b4

*C .

149

I

107

FIO.1. The effect of temperature and type of metal on the ratio of isobutylbensene

to n-butylbensene in the product from toluene and propylene.

C. POTASSIUM-CATALYZED ALKYLATIONS Aromatics react with olefins very readily when potassium is used as a catalyst. However, potassium is less selective in catalyzing alkylation than sodium because an additional reaction yields indans, as reported by Schaap and Pines (24).Therefore, the products consist of mixtures of arylalkanes and indans; the relative amount of each depends largely on the aromatic used (as shown in Table 11). The degree of alkyl substitution of the a-carbon

132

HERMAN PINES AND LUKE A. SCHAAP

of the aromatic determines the amount of indan formed. In the formation of a five-membered ring, rates of cyclization reactions increase the most when the substitution is in the middle of the chain. This effect is especially large when gemdialkyl groups are present, as reported by Brown and van Gulick (41). TABLE 11 Potassium-Catalyzed Alkylation Reactions of CeHsR Conditions R

-

3lefin

Hr.

"C

-

Yield of nonoadduc t (mole %)

190 f 5

1

53

190 f 2

3

64

192 f 4

7

34

245 f 3

2.5

22

185 f 1 3 . 5

33

186 f 4

13

208-233

5

6.5

-

4.4

Products n-Propylbenzene Lndan sec-Butylbenzene 1-Methylindan tert-Pentylbenzene 1,l-Dimethylindan tert-Pen tyl benzene 1,l-Dimethylindan tert-Pentylbenzene 1,l-Dimethylindan 1-Ethyl-1-phenylcyclohexane Spiro-(cyclohexane-1,1'-indan) 2,3-Dimethyl-2Phenylbutane 1,lJ2-Trimethylindan 1,lI3-Trimethylindan

Distribution mole %)a 98

2 86 14 51 49 49 51 66 34 63

37 52 27 21

Yields are based on olefin charged. One mole of aromatic W ~ reacted E with 0.2 mole of olefin. Potassium, 1.7 g., with 1 g. of anthracene was used as a catalyst. 0

Indan formation [Reactions (13)-(15)] represents an intramolecular alkylation of the aromatic ring by a carbanion. R

R

R

R

BASE-CATALYZED REACTIONS OF HYDROCARBONS

133

R

R, R1 = H or ulkyl 13 = H, alkyl, benzylic, chain interaction

The alkylation of benzene by alkylpotassium compounds has been reported by Bryce-Smith (29) and is probably due to the increased base strength of organopotassium compounds over organosodium compounds. The potassium hydride eliminated in the cyclization reaction may add to ethylene to form ethylpotassium, which then may react with the aromatic to yield ethane and a benzylic carbanion [Reactions (16) and (17)]. K+HR

A

CeHs H II

RI

+ CHz=CHz

+ CHjCH*-K+

(16)

R

c:

+ CHsCHt-K+ + CsH, I -K+ + CHjCH, hl R, Rt = H or alkyl

In this way the cyclization reaction results in some hydrogenation of the olefin used. The proposed mechanism of the indan-forming reaction was supported by an experiment in which 3-methyl-3-phenyl-1-chlorobutanewas treated with potassium in cyclohexane a t 80°, as reported by Pines and Schaap (48).1,l-Dimethylindan was produced; under these conditions of low temperature and pressure, however, side reactions produced some tert-pentylbenzene and 3-methyl-3-phenyl-1-butene.The major products, however, were 2,5dimethyl-2,5diphenylhexaneand ethylene. [See Reactions (1&20).] The formation of 2,5-dimethyl-2,5-diphenylhexaneresults from

134

HEBMAN PINES AND LUKE A. SCHAAP

CHs

CHJ

I

CHS

\

( 19)

CHI

I I

CsHa-C-CHz-CHa

+ K+B-

CHa CHa

D. RELATIVERATESOF ETHYLATION OF AROMATICS The relative rate of addition of ethylene to an aromatic side chain depends on the substituents present not only on the a-carbon but also on the aromatic nucleus. These effects have been studied using both pdialkylbenzenes and mixtures of aromatics. 1. p-Dialkylbenzenes

The competition of the alkyl groups in pdialkylbenzenes for ethylene provides information about the rate-controlling step in base alkylation. Early work by Pines, Vesely, and Ipatieff (19) showod that p-cymene reacted with ethylene to yield predominantly lert-pentyltoluene. It is well known that p-cymene is almost exclusively metalated on the methyl group

135

BASE-CATALYZED REACTIONS OF HYDROCARBONS

by organosodium reagents. Metalation of the methyl group is more energetically stable because the a-carbon of the isopropyl group already has a higher electron density due to the inductive effect of the two methyl groups. However, if addition of ethylene to the isopropyl group predominates, metalation is probably not rate-controlling with these compounds, but the addition to the olefin is. Thus, adding the isopropyl carbanion to ethylene is more favorable than adding the methyl carbanion. This supposition is reasonable because the energy barrier for addition in this energetically unfavorable step must be higher for the more stable methyl carbanion [See Reaction (21)]. CH2 I

6 H z C H ' - BH

Q-

CHa=C€Ia

a

-+

-t

.It

A

\

CHI- - CHI

(11)

:

I

H-CHa

CI-I-CH-CH:

,$ CHa

-+ CHa=CHi

H

\

(1)

CHa

C

+

B-

\ CHI-

CHs-CH-CTI~

C

\ CHs-C-CHs

CH~-CH~ I

8 CHa

BH B-

--i

+

\

CHs-

-CHI JH2-CHa

B = CioHis

Although there should be little of species I1 present, it adds rapidly to ethylene. When potassium is used to prepare the catalyst, species I should add more rapidly since it is more reactive than when sodium is used, and a lower selectivity will result. Various pdialkylbenzenes were studied by Pines and Schaap (2.9) ; product distributions, excluding indans from the potassium catalyzed reactions, are shown in Table 111. Isopropyl and ethyl groups react faster than methyl groups, but the greater metalation of the ethyl group and greater reactivity of the isopropyl group in p-ethylcumene result in nearly equal reaction rates. Therefore, the rate-controlling step may vary, depending on the ease of metalation of a compound. In a compound which is very difficult to metalate and which forms a very reactive carbanion, the rate of ethylation may be faster than that of transmetalation. This was shown by Hart (36) in the reaction of 2-phenylpentane with ethylene. Optically active 2-phenylpentane reacted with ethylene to yield

136

HERNAN PINES AND LUKE A. SCHAAP

TABLE Il,I The Ethylation of p-Disubstituted Aromatic Hydrocarbons Monoethylated Product Hydrocarbons

Catalystb

Yield (mole %)

p-Ethyltoluene

Na

73

p-Ethyltoluene

I<

55

p-Cymene

Na

55

pCymene

K

46

p-Ethylcumene

Na

39

p-Ethylcumene

K

30

Compounds

Distribution (mole %)

p-Ethyl-n-propylbenzene p-sec-Butyltoluene p-Ethyl-n-propylbenzene p-sec-Butyltoluene p-n-Propylcumene ptert-Pen tyltoluene pa-Propylcumene p-tert-Pentyltoluene p-sec-Butylcumene plert-Pentyleth ylbenzene p-sec-Butylcumene p-tert-Pentylethylbenzene

26 74 36 64 28 72 55 45 48 52 73 27

Hydrocarbon, 1 mole, was reacted with 0.1 mole of ethylene. *Alkali metal, 0.044 g. atom, was used with 1 g. of anthracene. Experiments were carried out at 185 f 4". TABLE 1V The Relnticie Rates of Reaction cf Arenes with Ethylene Hydrocarbon Ethylbenzene n-Propylbenzene lsopropyl benzene sec-Butylbenzene lndan 0-X ylene m-Xylene p-Xylene p-Cymene p-tert-Butyltoluene

Relative Rate toluene = 1 2.8 1.2 1.9 0.57 1.35 1.9 1.6 0.62 0.75 0.21

inactive 3-methyl-3-phenylhexane1 but the recovered 2-phenylpentane retained its optical activity. This indicates that practically every molecule of aromatic which was metalated reacted with ethylene without having opportunity to exchange with other molecules of the aromatic. 2. Competitive Reactions of Arenes In competitive ethylations of aromatics studied by Pines and Schaap (W), a large excess of aromatic over olefin was used so that relative rates o

BASE-CATALYZED REACTIONS OF HYDROCARBONS

137

reactions of aromatics could be determined. Relative rates of various aromatics with respect to the rate of toluene are shown in Table IV. Ethylbenzene has a greater rate of reaction than toluene although it must be metalated to a smaller extent. This is due to increased rate of reaction of the less stable carbanion with ethylene, as was discussed for the p-dialkylbenzenes. With larger alkyl substitution, such as with sec-butylbenzene, a relatively slow rate is obtained. This may be due to the greatly decreased metalation of such a compound with additional steric effects if these are important. Relative rates of reactions of dialkylbenzenes are not easily explained. The presence of p-alkyl-substitution generally causes a large decrease in rate, whereas o-xylene. which should have the same inductive effects as p-xylene, reacts very rapidly. Possibly this rapid reaction of o-xylene is caused by an intramolecular transmetalation between the carbanion adduct with ethylene and the remaining methyl group [Reaction (22)]. -

CH*CH2CH2 I

CH2 I

CH~CHZCH~ I

Since the addition of the ethylene and transfer of the proton may be concerted reactions, the energy barrier for the alkylation may be much lower than for an addition followed by an intermolecular proton transfer.

E. ARALKYLATION OF AROMATICS The side-chain alkylation reaction of aromatic hydrocarbons has also been studied using unsaturated aromatic olefins, especially styrene. Pines and Wunderlich (43) found that phenylethylated aromatics resulted from the reaction of styrenes with arylalkanes at 80-125' in the presence of sodium with a promoter. The mechanism of reaction is similar to that suggested for monoolefins, but addition does not take place to yield a primary carbanion; a resonance stabilized benzylic carbanion is formed [Reaction (2% b)l. Na + CeHscH*Na+ CaHsCH=CH* -+ CsHsCH2CH&?HCsHs (238) Na+ C'HSCH&HI~HC~H~CsHsCHs -+C~HSCH&HZCHZCOH~ CsH6cH2Na+ (23b)

+

+

+

This reaction, therefore, does not have the energetically unfavorable addition step that the reaction with monoolefins has. Monoadducts and diadducts of styrene with toluene, ethylbenzene, and cumene were prepared. Although styrene will react with sodium to form an organosodium compound, the addition of promoters is desirable, espe-

138

HERMAN PINES AND LUKE A. SCHAAP

cially when an aromatic which is difficult to metalate, such as cumene, is used. Apparently sodium adds to styrene to form an ion radical [Reaction (24a)], which may initiate either a radical-catalyzed styrene polymerixation (24b) or an ionic alkylation (24c) ;the medium determines which reaction will occur. CaHsCH=CH2

+ Na

--t

[CsHscHCHo.]Na+

-

[ C O H S C H ~ H Z I N ~ +(24a)

Polymerization

CaHsCHCHa.Na+

+ n(C6HsCH=CHp)

-+

Na+ CsHs~HCH2(CHoCH).-1CH~CHCsHs (24b) AaHs

Initiation of alkylation CaHsEHCHz Na+ CaHsCHs CaHrCHEH2Na+

+

1

i

+

CeHscHSNa+

+

CsHoCHoCHz * OT

1

(244

!C~H~CHCHS

Promoters that will form organosodium compounds, such as anthracene and o-chlorotoluene, favor the alkylation reaction as well as sodium isopropoxide, which must act as a chain promoter. These compounds are needed for the phenylethylation of cumene.

F. ALKENYLATION OF AROMATICS The reaction of diolefins with aromatics is similar to that of styrenes with aromatics. Hoffman and Michael (44) reported that toluene and various conjugated diolefins could be reacted at 50-90' in the presence of sodium to yield alkenylbenzenes [Reaction (25)]. CaHrCHi

+ CHFCH--CH=CHZ

-+

CsHsCHzCHoCH=CHCHs

(25)

The mechanism of this addition is similar to that for styrenes only an allylic carbanion is formed instead of a benzylic carbanion [Reaction (26)].

-

+

CJ%CH*Na+ CH1=CH-CH=CH2

-+

Na+ CaH6CH2CH2~HCH=CH2

IJ

(26)

CsHrCHnC zCH=CHCI%Na+

The primary allylic carbanion apparently predominates and reacts with aromatic to yield the alkenylbenxene and regenerate the benxylic carbanion [Reaction (27)]. C8H5CH,CH&H=CHCHII-Ne+

Naf

+ CsHrCHc + C~HSCH~CH~=CH=CHCHS + C&%i

(27)

The formation of resonance-stabilized species throughout Reaction (25) suggests that lower-energy barriers hinder this reaction as compared with

BASE-CATALYZED REACTIONS OF HYDROCARBONS

139

the reaction of ethylene. This accounts for the lowered temperature requirement. Because sodium adds t o conjugated diolefins to form organosodium compounds, these adducts may be the initiators for Reaction (26).

IV. Nuclear Alkylation of Aromatics Acid-catalyzed reactions of aromatics with monoolefins result in nuclear alkylation. But the base-catalyzed reactions of aromatics with olefins do not result in nuclear alkylation as long as benzylic hydrogens are available. This is true even with aromatics, such as cumene, which have deactivated benzylic hydrogens resulting in facile metalation of the ring. Apparently phenyl carbanions do not readily add to olefins. Pines and Mark (20)found that in the presence of sodium and promoters only small yields of alkylate were produced a t 300" in reactions of benzene with ethylene and isobutylene and of t-butylbenzene with ethylene. With potassium, larger yields may be obtained a t 190" (24). The nuclear-alkylation reaction of aromatics is accompanied by f ormation of biphenyls (20, 24.6).They may form by an addition of phenyl carbanion to the aromatic ring, followed by an elimination of a hydride ion [Reaction (28)]. GHs-Na+

+

0

-+

'-

C6:O
CeHs-CsHe

-+

+ Na+H-

(28)

In a study of reaction of phenylsodium with benzene, Morton and Lanpher (@) found that at lower temperatures the adduct was stabilized by transmetalation with another molecule of phenylsodium, yielding a dianion [Reaction (29)]. H

H

C 6 H > a <

-

+ C&Na+

Na

"'o<"

+ C&-

-

+ C6He

(29)

Na

Two anionic mechanisms may be proposed for base-catalyzed nuclear alkylation. One, which is analogous to side-chain alkylation, is Reaction (30a, b). R CsHs-Na+

+ R-C=CH*

-+

CeH6-ChH,Na+

RI I

!

C~HE- -cH2Na+ RI

+ C6Hs

(304

4 1

-+

C6H6-

L A,

R, R1 = H or alkyl

CH,

+ CsH6-Na+

( 3 0 ~

140

HERMAN PINES AND LUKE A. SCHAAP

The other, which is similar to the biphenyl-forming reaction, may be initiated by hydride ions produced by biphenyl formation [Reaction (31a, b, c)]. H

+ RC=CHz

Na+H-

+

R-

I

c:I

-cHzNa+

RI

RI H R-LcHZNn+

I

+ (-J+R-p'(=JLH-

1

H

'QLH

-CHz

RI

Nrt+

(31b)

RI

RI

R-

-

+R-

7 - dNa+ R, R,

=

AI

-CHz-

0

+ Na+H

(31~)

121

H or alkyl

Evidence for reaction by both mechanisms is that isobutylene reacts with benzene at 300" to produce lert-butylbenzene and isobutylbenzene. The first mechanism would pi oduce tert-butylbenzene; the second, isobutylbenzene. These compounds were obtained in a ratio of 1:5 (20). The alkylation product of benzene (20)and tertbutylbenzene (24) with ethylene yields predominantly sec-butyl alkylates. This is the case because the ethylbenzene alkylate formed reacts very rapidly in the normal sidechain alkylation reaction. The sec-butyl aromatic alkylates much less readily. The much greater ease of side-chain alkylation over nuclear alkylation also accounts for the exclusive formation of side-chain alkylates from compounds, such as cumene, that are predominantly metalated on the ring by alkylalkali metal compounds.

V. Alkylation of Alkylpyridines Alkylpyridines have been shown to undergo base-catalyzed alkylations similar to those of alkylbenzenes (46-48). These compounds are included in the present discussion because of the importance theso may have in elucidating the side-chain alkylation mechanism. The reaction mechanism is similar to that of alkylbenzenes, but the conditions differ somewhat. Promoters are often not necessary because sodium adds across the azometine linkage of pyridines to yield ionic sodium species (48, 60). A soluble-catalyst system is formed in contrast to the nonsoluble system in aromatic hydrocarbons. Temperatures of 125-160" are sufficient for both ethylation and propylation of most compounds. The position of the alkyl group on the pyridine ring is very important. 4-Alkylpyridines react readily and much like alkylbenzenes, whereas

BASE-CATALYZED REACTIONS OF HYDROCABBONS

141

2-alkylpyridines react less readily and 3-alkylpyridines yield little alkylate, but mostly condensation products. This may be due to lack of resonance stabilization of the 3-picolyl carbanion due to lack of conjugation with the nitrogen, as discussed by Pines and Wunderlich (47). The compound, however, can be metalated readily as was shown by Brown and Murphey (51). A kinetic study of alkylpyridine alkylation was carried out by Pines and Notari (48) usiiig 4-isopropylpyridine with sodium and ethylene a t 125'. The rate of ethylation was proportional to the amount of sodium, independent of the amount of isopropylpyridine, first order with respect to ethylene pressure in the range of 1 to 15 atmospheres, and independent of ethylene pressure a t 30 to 40 atmospheres. These findings indicate t.hat the rate of addition of the anion to the olefin may be rate controlling a t low Pressures, whereas at higher pressures metalation becomes rate determining. With higher acidity compounds, which would be metalated more readily, the effect of increased pressure should extend over a much larger range. Competitive ethylations were carried out by using 2- and 4-alkylpyridines to study inductive effects. Results of a study on this subject made by Notari and Pines (52)are reported in Table V along with results for alkylbenzenes. The 4-alkylpyridines closely parallel the alkylbenzenes in their relative reaction rates, whereas the 2-alkylpyridines have a different order. A solvation effect of the nitrogen may bo the reason. Steric effects apparently become important with higher alkylpyridines, especially with the isobutylpyridines, which react only about one-eighth 8 8 fast as n-propylpyridines. A side chain having P-methyl groups may hinder the approach of the ethylene with its ?r electrons towards the electrons of the anion (as shown in the diagram, below).

H

VI. Reactions of Olefins Olefins possessing allylic hydrogens undergo reactions similar to those of aromatics with benzylic hydrogen. These reactions lead to combination of the olefins, usually to dimers and trimers.

142

HERMAN PINES AND LUKE A. SCHAAP

TABLE V Competitive Ethylation of 2- and 4-Alkylpyridines and of Alkylbenzenes

R

-c-c

-C

-c-c

-C

/

4-Alkylpyridines

Alkyl benzenes

5.5:l

1:7.5

1:2.8

>25:1

1:l

1.5:l

17: 1

1.9:l

2.3:l

2 5 :l

2.3:l

3.5:l

15:l

10: 1

7:l

8.3:l

8.5:l

16:l

2-Alkylpyridines R:Ri

Ri

R:IL

R:Ri

C

\C

-c-c-c

-c-c -C

/

C

C

/ -C \

\c -C

/

c-c

C

/

-c-c

C

\C

\C

/

-c-c

--cc-c

C

\C C

C

/ -C \

-c/ c-c

c‘ \C C‘

-C

-C

\

-c-c

c-c / \C

/

c-c 6.5:l

\ C C C

C

-c/

\c

13.5:l

‘C \C

A. REACTIONS OF MONOOLEFINS Simple monoolefins and cycloolefinsreact in the presence of base catalysts under conditions similar to those used for base-catalyeed alkylation. The

143

BASE-CATALYZED REACTIONS OF HYDROCARBONS

products are mainly the combination of two molecules to yield a larger molecule. Mark and Pines (65)carried out reactions catalyzed by sodium with promoters, as listed in Table VI. Products of the propylene dimerization are methylpentenes; of the isobutylene dimerization, trimethylpentenes. Ethylene and cyclohexene yielded 1-ethylcyclohexene, whereas propylene and cyclohexene yielded isopropyl- and n-propylcyclohexenes TABLE Vl Olejin Reaction Products

Propylene

Olefin I (moles)

1.67

1.5

Olefin 11 (moles)

-

-

-

-

Temperature of pres. sure drop (“C) Highest temperature (“C) Highest pressure (atm.) Duration (hours) Hydrogenated 1 :1 adduct mole Yield (mole %)

Ethylene

1.0

0.5

280

280

285

225 4.5

216 25.5

Propylene

I

1.0

0.75

Cyclohexene -

1.0

-

250

0.2 24

Cyclohexene

298

0.082 11

1.0

1.0

280

278

282

300

287

287

175 14

121 41

43 34

70 8.5 0.036 7.2

0.009

1.8

0.036 3.6

0.020 2.7

The mechanism of reaction of monoolefins resembles that for basecatalyzed alkylation. An example is the reaction of isobutylene (32a, b, c). (CH&-C=CH,

+ B-Na+ -+

BH

+ CH2=C-EH2Na+

(32a)

AH8 CHa CHFC-EH?Na+

CHFC-CHzCHs I

rs

+ (CHa)2-C=CH2

-cH2Na4

+C

H ~ C - C H d - ~ H 2 N a +(32b) &HI

AH,

+ (CHa)&=4H, AH,

~ H s -+

CH2=C-CH2-

I

CII,

r

-CHa

&Ha

B = CJ&Oor chain initiator

+ CH+-cH?Na+ I

CHs

(32c)

144

HERMAN PINES A N D LUKE A. S C H M P

Therefore, the base-catalyzed reaction of isobutylene yields the same dimer a8 the acid-catalyzed reaction although the mechanisms are completely different. Since olefin isomerizations are also catalyzed under these conditions, an equilibrium distribution of products is expected; for example, the reaction of isobutylene yields 78% of 2,4,4-trimethyl-l-penteneand 22% of 2.4,4-trimethyl-2-pentene.

B. REACTION OF a-METHYLSTYRENE Arylalkenes can undergo various reactions when treated with sodium, since compounds such as a-methylstyrene are both olefins with allylic hydrogens and styrenes, both of which are reactive. The reaction of a-methylstyrene with sodium has been reported by Bergmann et al. (64)to yield tetramers. More recent work by Kolobielski and Pines (66) has shown that dimers and products derived from dimers are formed when this compound is heated with a sodium-benzyl-sodium catalyst. Some of the major products were cumene (VII), p-terphenyl (VIII), and l-methyl-l,3diphenyIcyclopentane (IX).

TABLE V11 Eflect of Temperalure upon the Reaction of u-Methylstyene i n the Presence of Sodium Temperature ("C) 125 160 230

Composition of product (wt. yo) Compounds

Recovered a-methylstyrene 6 2 6

v11

VlII

IX

Trimer

3

0.2 0.2

22 34

39

0.1

3b

31

4 6

42

The relative amounts of these produced at various temperatures are shown in Table VII. The formation of these products may be explained using carbanionic mechanisms. The cyclic material may form by addition of an allylic carbanion to a molecule of the styrene, followed by a cyclization to yield a benzylic carbanion [Reaction (33a, b, c)].

145

BASE-CATALYZED BEACTIONB OF HYDROCARBONS

CHz

%+/ \

CsHsC

'

HJC-

B'

CHj

/

+ CsHs -CHI

C-CsHp

H 4

CsHs-C

AHr

C€Iz

\c/

\ /

I

HzC-CH,

CHI

I \CsHs

B = CIO,HIQ,H, or chain initiator

The adduct of the allylic carbanion with a-methylstyrene may possibly eliminate a hydride ion to form a diaryldiolefin, which may cyclize to yield the p-terphenyl [Reaction (34a-e)l.

CHz CHz CsH6e-CH~CHzk-C8Hs

+ B-Na'

+ CsH,

8"' 8"' + 8"'

--CH&H COHK BH Na+

(34b)

Na+ CHz

I

H

(34c)

CaHs -CHzCH=C-CeHs

Na+ Na+ CHI-CHI

/

-, CEH&-Na+

\

(34d)

\

CHs-CH

/

CHr-CHn

CsHKC-Na+

\

CHI-CH

\

/

CHI-CHz

\

C C s H b + CsHsC

//

H-CH B = H, COHO, etc.

C-CsH,

4-NaH

(34e)

146

HEBMAN PINES AND LUKE A. SCHMP

The cyclic diolefin formed can then dehydrogenate as was discussed previously for this type of compound, and the hydrogen eliminated may be transferred to a-methylstyrene, as was previously discussed for phenylcyclohexene, resulting in the formation of cumene. The diaryldiolefin shown in this mechanism was synthesized and successfully cyclized to p-terphenyl in the presence of sodium (66). The ability of a-methylstyrene in acting as a hydrogen acceptor in basecatalyzed reactions was also studied by Kolobielski and Pines (66). Limonene was reacted with a-methylstyrene to yield cumene and p-cymene [Reaction (35)].

Q

+ Cs&

K Q -CH,

+

+ CJIsC(CHa)r

(36)

This reaction also corresponds to the p-terphenyl and cumene formation from the diphenylcyclohexadiene and a-methylstyrene [Reaction (36)]. Cs& I

VII. Conclusion The use of base catalysis for various reactions, such as olefin isomerization, cyclohexadiene dehydrogenation, aromatic alkylation, and olefin polymerization, has been demonstrated. In some cases, compounds are formed which are difficult to prepare by other means, and some highly selective reactions have been found. Much remains to be done before these reactions are fully understood. Catalytic mechanisms involving carbanion intermediates have been used to explain the reactions. The use of these mechanisms has been very helpful in rationalizing the information on base catalysis, but they must not be regarded as complete and all-inclusive pictures of what happens. These reactions, in as far as the authors of this chapter know, have not been put to any practical use in the chemical or petroleum industry. As time progresses, commercial uses of these catalysts will be developed. In the meantime, the theoretical interest in carbanion chemistry has been

BASE-CATALYZED REACTIONS OF HYDROCARBONS

147

important because our knowledge of organic reactions has been enlarged to include more than the known reactions of hydrocarbon free radicals and carbonium ions.

REFERENCES 1. Morton, A. A., Advances in Cdalysis 9, 743 (1957);J. K. Stelle, Chem. Revs.68, 541

(1958). 9. Egloff, G., Hulla, G., and Komarewski, V. l., “Isomerisation of

-

Pure Hydrocarbons,” pp. 70-90. Reinhold, New York, 1942;F. E. Condon, in “Catalysis” (P. H. Emmet, ed.), Vol. VI, p. 112. Reinhold, New York, 1958. 3. Shatenstein, A. I., Vasil’eva, L. N., Dykhno, N. M., and lzrailevich, E. A., Doklady Akad. Nauk, SSSR, 86, 3bl (1952);Chem. Abslr. 46,9954 (1952). 4. Reggel, L., Friedman, S., and Wender, I., J. Org. Chem. 23, 1136 (1958). 6. Pines, H., Vesely, J. A., and Ipatieff, V. N., J . Am. Chem. SOC. 77, 347 (1955). 8. Pines, H.,and Eschinazi, H. E., J. Am. Chem. SOC.77, 6314 (1955). 7. Pines, H., and Eschinazi, H. E., J. Am. Chem. SOC.78, 1178 (1956). 8. Pines, H., and Eschinazi, H. E., J. Am. Chem. SOC.78, 5950 (1956). 9. Pines, H.,and Haag, W. O., J. Am. Chem. SOC.28, 328 (1958). 10. Pines, H., and Haag, W. O., J. Am. Chem. SOC.23, 328 (1958). 11. H u g , W. O., and Pines, H., J. Am. Chem. SOC.82, 387 (1960). 12. O’Grady, T.M., Alm, R. M., and Hoff, M. C., Preprinta, 136th Meeting Am. Chem. SOC.(Petroleum Division) Atlantic City, 1969. 13. Grovenstein, E., J . Am. Chem. SOC.79,4985 (1957);Zimmerman, H.E.,and Smentowski, F. J., ibid. p. 5455; Curtin, D.Y.,Flynn,E. W., and Nystrom, R. F., ibid. 80, 4599 (1958);Curtin, D.Y., and Flynn, E. W., ibid. 81,4714 (1959). 14. Pines, H., and Haag, W. O., private communication. 16. “High Surface Sodium,” Tech. Bull. National Distillers Chem. Co.,Ashtabula, Ohio, 1953. 18. Haag, W. O., and Pines, IT., J. Am. Chem. SOC.82, 2488 (1960). 17. Pines, H.,and Schaap, L., J. Am. Chem. SOC.79, 2956 (1957). 18. Pines, H., and Kolobielski, M., J . Am. Chem. Soc. 79, 1698 (1957). 19. Pines, H., Vesely, J. A., and Ipatieff, V. N., J. Am. Chem. SOC.77, 554 (1955). 20. Pines, H., and Mark, V., J . Am. Chem. SOC.78, 4316 (1956). 91. Voltz, S. E., J. Org. Chem. 22, 48 (1957). 92. Schramm, R. M., and Langlois, G. E., Preprints, 136th Meeting Am. Chem. Soc. (Petroleum Division), Atlantic City, 1969, Paper B-53. $3. Pines, H., and Schaap, L., J . Am. Chem. SOC.80, 3076 (1958). 24. Schaap, L., and Pines, H., J . Am. Chem. Soc. 79, 4967 (1957). 96. Closson, R. D., Napolitano, J. P., Ecke, G. G., and Kolka, A. J., J. Org. Chem. 22, 647 (1957). 26. Podall, H., and Foster, W. E., J . Org. Chem. 23, 401 (1959). 27. Morton, A. A,, Chem. Revs. 36, 1 (1944). 28. Morton, A. A., and Little, E. E., Jr., J . Am. Chem. SOC.71, 487 (1949). $9. Bryce-Smith, D., J . Chem. SOC. p. 1079 (1954). 30. Claff, C. E., Jr., and Morton, A. A., J. Org. Chem. 20, 981 (1955). 31. Morton, A. A., and Lanpher, E. J., J . Org. Chem. 23, 1136, 1636 (1958). 32. Morton, A. A., and Lanpher, E. J., J. Am. Chem. Soc. 79, 5578 (1958).

148

HERMAN PINES A N D LUKE A. SCHAAP

33. Streitwieser, A., Jr., Abstr. 16th Natl. Organic Symposium, Sedtle, Wash., 1969, p. 74. 54. Hart, H., and Crocker, R. E., J. Am. Chem. SOC.82, 418 (1960). 56. Morton, A. A., and Lanpher, E. J., J. Org. Chem. 23, 1636 (1958). 56. Hart, H., J . Am. Chem. SOC.78, 2619 (1956). 57. Ziegler, K., and Sellert, H. G., Ann. 607, 195 (1950). 38. Bartlett, P. D., Friedman, S., and Stiles, M., J. Am. Chem. SOC.76, 1771 (1953). 39. Morton, A. A., and Ward, F. K., J . Org. Chem. 24, 1571 (1959). 40. Pines, H., and Arrigo, J. T., J . Am. Chem. SOC.79, 4958 (1957). 41. Brown, R. F., and van Gulick, M. N., J. Org. Chem. 21, 1046 (1956); see also Hammond, G. S., in “Steric Effects in Organic Chemistry” (M. S. Newman, ed.), pp. 460-470. Wiley, New York, 1956. 49. Pines, H., and Schaap, L., J. Am. Chem. SOC.80, 4378 (1958). 45. Pines, H., and Wunderlich, D., J. Am. Chem. SOC.80, 6001 (1958). 4 4 . Hoffman, F., and Michael, A., U. S. Patent 2,448,641 (1928). 46. Morton, A. A., and Lanpher, E. J., J. Org. Chem. 23, 1639 (1958). 46. Profft, E., and Echneider, F., Arch. Pharm. 289, 99 (1956). 47. Pines, H., and Wunderlich, D., J. Am. Chem. SOC.81, 2568 (1959). 48. Pines, H., and Notari, B., J. Am. Chem. Soe. in press. 49. F. B. Ahrens, Ber. 38, 155 (1905). 60. Henser, A., and Stoehr, C., J . Prakt. Chem. [2] 4!2,430 (1890); 44, 404 (1891). 61. Brown, H. C., and Murphey, W., J. Am. Chem. SOC.73, 3308 (1951). 66. Notari, B., and Pines, H., J. Am. Chem. Soc. in press. 65. Mark, V., and Pines, H., J. Am. Chem. Soc. 78, 5946 (1956). 64. Bergmann, E., Tanbadel, H., and Weiss, H., Bcr. 64, 1493 (1931). 66. Kolobielski, M., and Pines, H., J. Am. Chem. SOC.79, 5820 (1957).

The Use of X-Ray K-Absorption Edges in the Study of Ca ta I yt ica I I y Active Sol ids ROBERT A. VAN NORDSTHAND Sinclair Research Labwatm*es,Inc., Harvey, Illinois

Page I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 11. Origin of Fine Structure. . . . . . . . . . . . . . . . . 150

B. Transitions to Crystal Levels.. ......

. . . . . . . . . . . . . . 151

111. Experimental... . . . . . . . A. Manganese Spectra.. ..... B. Cobalt Spectra ..................................................... c . Chromium Spectra.. ............................................... D. Titanium Spectra .................................................. E. Comparisons among Elements.. ..................................... V. Spectra of Catalysts ..............

163 168 175 178 180 .......................................... 185 .......... ......... . . . . . . . . . . . . . . 187

1. Introduction X-ray techniques presently well known in catalysis include diffraction, small angle scattering, and fluorescence spectroscopy. X-ray absorption edge fine-structure spectroscopy, although known to the X-ray physicists for thirty years, is not well known in catalysis research. The promise which this field holds for catalysis has been apparent over much of the thirty year interval, but has been overshadowed by difficulties both experimental and theoretical. Some features making X-ray K-edge spectroscopy especially attractive for catalyst investigations are: 1. Remarkable sensitivity to the chemical condition of the element under study; 2. Specificity regarding the element whose chemical condition is being studied; 3. Reduced sensitivity to long-range crystallinity, in contrast to X-ray and electron diffraction; 4. Fortuitive experimental factors which make the catalytically important elements of the first transition series especially easy to study; and 149

150

ROBERT A. VAN NORDSTRAND

5. Ability of X-rays t o penetrate matter, such as reactor windows, catalyst supports and catalyst deposits. Experimental difficulties include sample preparation, intensity and stability of X-ray beam, and resolution. Insufficient resolution in even the best spectra presently attainable obscures some details of the fine structure. The spectra reported here are obtained with resolution of 1 or 2 ev.; the present limit to resolution in the energy range explored here is about 0.5 ev. Theoretical difficulties give rise to various seemingly inconsistent interpretations of spectra. This branch of spectroscopy has not reached the maturity characteristic of most other branches. The present report is based primarily upon spectra of 95 known compounds of 4 elements in the first transition series and of several catalysts, obtained as part of an exploration of catalyst applications of absorption edge fine-structure spectroscopy. A previous progress report has been given (1).

II. Origin of Fine Structure The X-ray K-absorption edge of an element arises in the spectrum where the photon has just sufficient energy to eject a Kelectron from the atom. In the case of a metal, in which empty conduction states are available at the Fermi level, the absorption begins a t the lowest possible energy. In the case of insulators, higher energies are required to promote electrons to the lowest unfilled state. The absorption spectrum contains fine-stiucture details in the vicinity of this K-edge. The general subject has been reviewed by Compton and Allison (d), by Sandstrom (3),and by Tomboulian (4). The review presented here will be brief.

A. TRANSITIONS TO BOUND LEVELS The initial state of the K-electron in a given element may be regarded as independent of its chemical combination. Selection rules for central-forcefield problems require that the 1s state combine with some unfilled p-state in the atom. This is the basis for the explanation by Kossel (6) of some of the fine structure existing very close to the K-edge. The spectrum obtained by L. G. Parratt (6) for gaseous argon is considered a clear example of “Kossel Structure.” In this spectrum the l&p, ls-5p, etc., transitions to bound states apparently extend over a range of about 3 ev. Beyond this 3 ev. range there follows immediately a continuous absorption range in which the electron gains translational freedom. The continuous absorption region of the spectrum shows no h e structure. In the absorption edge spectrum of solid argon obtaincd by C. H. Shaw

X-RAY K-ABSORPTION EDGES

151

(7) the l s 4 p , etc., transitions are no longer apparent. The fine structure extends over a much wider energy range, a t least 50 ev. The Kossel structure appears to be a characteristic feature only of monatomic gases. Diatomic gases have spectra like solid argon, i.e., with fine structure occurring over a range of 50 or 100 ev., in place of the low energy Kossel structure. TO CRYSTAL LEVELS B. TRANSITIONS

Fluctuations in the absorptioii coefficient extend as high as 500 ev. above the principal edge in the case of metals or oxides of relatively simple crystal structure. This extended fine structure has been explained by Kronig (8) in terms of fluctuations in density of electronic states characteristic of the crystal lattice. For example, metals of close packed cubic crystal structure give closely related extended fine structure; corresponding maxima and minima occur a t energy values, E, (measured in ev. from the principal edge), which depend upon the lattice parameters, a, according to: EJEm = (az/ad2 (1) The Kronig theory treats the interference conditions involved between the crystal lattice and the ejected or photoelectron of wavelength, A. This wavelength in A is related to E , the kinetic energy in electron volts, by:

x

l / W E (2) The Kronig theory has been used to explain the extended fine structure, occurring in the energy range 100 to 500 ev. above the principal edge. Closer to the edge, difficulties arise, perhaps related to the interactions of the slow photoelectron with the lattice. A new approach to the explanation of fine structure has been offered by Hayasi (9). Like Kossel, he assumes bound states, but of short lifetime and of positive energy. These states, which he refers to as quasi-stationary, are stabilized by Bragg reflections from important planes in the crystal. In the theory of Kronig the Bragg reflections of the photoelectron lead to minima in the absorption coefficient, in that of Hayasi to maxima. To summarize the prevalent views regarding the origin of fine structure at X-ray absorption edges: Kossel structure, found within 2 or 3 ev. of the principal edge, is explained in terms of transitions to empty optical levels; it is seen unambiguously only in the case of monatomic gases. Kronig structure or extended fine structure is found in the range 100 to 500 ev. above the principal edge; it is explained in terms of transitions to high energy electronic states of the crystal, that is, in terms of the wavelength of the photoelectron and the period of the crystal lattice. It is seen only in the case of the metals and compounds of the simplest crystal structures. However, the majority of the known fine structure extends from 3 to =

152

ROBERT A. VAN NOBDSTRAND

100 ev. (just the gap between the Kronig and Kossel structures) and remains unexplained. It is in this range that polyatomic gases, aqueous solutions, ordinary and complex crystalline inorganic salts, and many of the oxides show all of their fine structure; it is here that empirical correlations with structural chemistry me especially striking. In the current literature of this subject, including papers of Beeman slid Bearden (10) and Cotton and Hanson ( I I ) , there appears a consistent effort to treat t4heK-edge fine structure spectra in this “chemical” range of energies by an extrapolation of the Kossel theory. Bound states of some p-character are thus assumed as high as 20 to 50 ev. above the Fermi level. In this study, however, the spectra have been more readily interpreted using the Kronig type explanations, emphasizing the geometric aspects of the atom and its near neighbors in relation to the wavelength of the photoelectron. This outlook was suggested in the paper of Hartree, Kronig, and Petersen (12)for the gaseous GeC14.

INTERPRETATION C. DIFFRACTION In the approach taken here the emission of the photoelectIon is considered as a scattering by the environment of a complex consisting of the X-ray photon and an electron of wavelength A ; this complex may exist as the photon traverses the atom. If the electrostatic environment of the atom is of proper dimensions for scattering an electron of this wavelength, the absorption coefficient is increased. If not, the absorption coefficient is decreased. It is of interest to attempt to cast the absorption-edge spectrum in a form resembling a diffraction function. I n conventional diffraction of X-rays or electrons by gases, liquids, or crystals, the general diffraction function expresses the ratio of scattered intensity, I,, to incident intensity, lo,as a function of (sin O)/A, where 0 is half the scattering angle;

L/Io

=f

(h) sin 0

(3)

The absorption edge spectrum function expresses p, the K-absorption coefficient, in terms of E,. p is defined here by normalization conditions and the equation: I t r / I o = e-r

(4)

where I t , is intensity transmitted; I0 is intensity incident upon the sample, corrected for absorption by electrons other than the K-electrons of the element under study, and includes sample thickness. Values are normalized to apply only to K-absorption and to make p = 0.0 just below the edge and p = 1.0 about 200 ev. above the edge. This corresponds to a sample

X-RAY K-ABSORPTION EWEB

163

thickness of about 3 microns of the element in the form of metal foil of density 8. The independent variable used here for the absorption function is E,. This is the energy the photon has in excess of Eo that is required to promote to the Fermi level a K-electron of the element in its metallic state. This excess energy, E,, of the photon, is transferred to the photoelectron, predominantly as kinetic energy. To this approximation, and using Equation (2)) E , is proportional to 1/X2. A new independent variable, 1/E1 or 1/X, is thus analogous to the (sin O)/X in the diffraction function. The relationship of the dependent variables for diffraction and absorption, I,/Io and p , is considered here. The transmitted intensity of X-ray photons is equal to their incident intensity minus the intensity of photoelectrons of wavelength X emitted (“scattered”) at all angles, zI.,

Is

=

lo

- zIa

(5)

Attenuation of loby coherent and Compton scattering are neglected here. Hence

or

The “total scattering function,” ( z I a ) / I o ,may thus be derived from p. For values of p encountered here, from 0 to 1.5, the graph of the absorption function p resembles that of the total scattering function, ( z I 8 ) / I o . The absorption spectrum here is essentially

and can be converted to

ZI, I0

+)

(9)

In this form the absorption spectrum is analogous t o the ordinary diffraction function,

The absorption spectrum in the form of Equation (9) is expected to have maxima for values of 1/X which correspond t o reciprocal distances from the center of the atom under study to nearest neighbor atoms. As

154

ROBERT A. VAN NORDSTRAND

nearest neighbors approach the central atom more closely, the maxima in the absorption spectrum should shift to higher values of 1/X or of E,. If significant interactions extend only to nearest neighbors, the absorption spectra bear some formal resemblance to diffraction patterns of liquids. If the element is contained in a crystal of high symmetry, as face centered cubic metals or oxides, the extended fine structure is superimposed, indicative of longer range interference phenomena; and the spectra are analogous to Bragg-type diffraction from crystalline solids. The problems associated with quantitative studies of structure based upon this viewpoint of X ray absorption-edge spectra may be similar to those encountered using electron beams of comparable energy, 3 to 100 ev., to carry out electron diffraction studies of crystal structure. Qualitatively, this analogy can be carried further, as both the X.ray spectra and the electron beam diffraction in this energy range are influenced by only the first few atom layers. Some references are made in the following survey of spectra to this analogy between diffraction and absorption edge spectra. However, the real purposes of the survey are to provide background for application of these spectra t o catalyst problems and to point out the empirical relationships between these spectra and structural chemistry.

111. Experimental Values of the X-ray K-absorption edges for the first transition series elements and for some other elements important in catalysis are shown in Table I, both in wavelength (angstrom) units and energy (electron volt) units. The values represent the mid-point of the first steep rise in the K-absorption spectrum of the element, generally in the form of the metal. All are from the publications of Cauchois (13). Two experimental limitations made departure in either direction from the first transition series increasingly difficult. X-rays of wavelength 3 A. or greater are too soft or nonpenetrating to traverse experimental impediments such as instrument windows, air, catalyst supports, and catalyst deposits. On the other hand, X-rays of wavelength less than 1 A. present serious problems of dispersion. The X-ray absorption spectrometer used in this study is the Norelco diffractometer, operating with copper or tungsten target X-ray tube, onetwelfth degree divergence and scatter slits, 0.003-in. receiving slit, a single quartz crystal mounted at the diff ractometer sample positions, and the standard geiger counter tube as detector. The quartz monochromator crystal has a d-value of 3.343 A. The X-ray tubes are operated at 25 ma. and a t a voltage just below twice the value of the absorption edge. This voltage limitation ensures that second-order reflection of harder radiation does not

155

X-RAY K-AESORPTION EDGES

TABLE I Values of K-Absorption Edge

Element ~

Atomic Number

~

0 Al S

c1 A

K

Ti

v

Cr Mn Fa

co Ni cu

Zn Mo Pd Pt

Wavelength (A.)

Energy (ev.)

~~~

8 13 16 17 18 19 22 23 24 25 26 27 28 29 30 42 46 78

23.4 7.95 5.02 4 . 4 0 (or 4.39) 3 87 3.44 2.50 2.27 2.07 1.90 1.74 1.61 1.49 1.38 1.28 0.62 0.51 0.16

531 1559 2470 2819 3203 3607 4964 5403 5988 6537 7111 7709 8331 8980 9660 20002 24347 78379

obscure the spectra. The operating voltages for the elements studied are: cobalt, 15 kv.; manganese and chromium, 11 kv.; titanium, 9 kv. The absorption sample is mounted in the standard filter holder located between the monochromator crystal and the geiger-counter receiving slit. Pert,inent distances are as follows: target to quartz crystal, 17 cm.; quartz crystal to receiving slit, 17 cm.; absorption sample to receiving slit, 6 cm. Sample thickness and sample uniformity present serious problems. The ideal sample is a uniform foil or a homogeneous solution. For metals the optimum thickness is in the micron range. Most of the samples studied here were powders, ground to pass 300 mesh, dispersed in a ductile microcrystalline wax. This wax dispersion is then spread to a uniform film across a sample holder window. The window has dimensions 3 x 17 mm. Adhesive cellophane tape is frequently spread over the window to assist in the mounting and supporting of the sample. Automatic equipment is used for recording the spectra. A t a given wavelength (goniometer setting) the instrument takes 10,000 counts, then records on tape the time required. The goniometer then advances 0.01 degree for the next wavelength, and repeats the counting and recording. The 0.01 degree interval represents steps of about 1 ev. at the titanium edge and of about 2 ev. a t the coba.lt edge. This represents the minimum useful step in view of the limited resolving power of the instrument, which also appears to be about 1 or 2 ev.

166

ROBERT A. VAN NORDSTaAND

Much of the effort represented in the literature concerning this subject is in the direction of improved resolving power. Double crystal and bent crystal monochromators have been developed with two to four times the resolving power used in this study. The long times required with such high resolution has resulted in spectra of very limited range, extending only 20 or 30 ev. above the edge. The method used here, with commercial X-ray diffractometers, provides consistent and meaningful spectra extending out to 200 ev. The spectra presented in this chapter correlate with structure. They appear to be of suitable resolution to encourage more widespread application of this branch of spectroscopy and to justify comparisons with theory.

IV. Spectra of Known Compounds The present survey of absorption edge spectra of known compounds provides a background concerning the type of information these spectra may provide in catalyst studies. Spectra emphasizing the first 30 ev. range

-

OQ

..

-...*.

-

I

0.8-

0.4O0%i

-

-.*...

I 0

I

I

40 80 120 ELECTRON VOLTS

I 160

200

ABOVE M N EDGE (6537W)

Fro. 1. Four distinct types of X-ray absorption edge spectra of manganese in varying chemical states.

157

X-RAY K-ABSORPTION EDGES

are available in the literature for many of these compounds. Here the emphasis is placed on the 200 ev. spectra, including much of the region of the extended fine structure (Kronig) plus the full intermediate region which is sensitive to chemistry. Four distinct types of spectra are shown in Fig. 1, all of manganese compounds. This figure shows the contrasts which may be encountered within compounds of a single element. These distinctive types of Fig. 1 recur frequently in this study. For convenience they will be referred to by type numbers. The structural correlations with these types are indicated here. Type I spectra are associated with hydrated ionic compounds such as the MnClz 4H20and with many other compounds having a single octahedral coordination sphere. These spcctra are sensitive to ionic charge and to radius of coordination sphere. Type I1 spectra are obtained only with hexacyanides and hexacarbonyls -compounds with a double octahedral coordination sphere. Type I11 spectra, characterized by very low amplitude of the fine structure, are obtained from metals.

-

I

I

I

I

I

ELECTRON VOLTS W E M N E W E (6537eV.l

FIG.2. Type I spectra of crystalline hydrated manganous salts.

158

ROBERT A. V A N NORDSTRAND

04

c i

0.0

.

---'.

I-

z

' .

-

. ..

Ti Se

08-

-

.

.. . _--

DI-CYCLOPENTADIENVLTITANIUM

.

..

-

DICHLORIDE

. . Ti LACTATE

-

-

I I20

1

160

200

Type IV spectra are found with the tetrahedral ions such as permanganate and chromate. Many of the spectra shown here do not fall into the above types. These departures likewise may be correlated with specific structural. features.

A. MANGANESE SPECTRA The K-edge of manganese, a t 1.9 A., is readily studied with the spectrometer used. This wavelength is the best compromise between the transmission and dispersion problems. The variety of compounds and valence states of manganese makes manganese an attractive choice. A previous survey of manganese K-edge spectra, carried out by Hanson and Beeman (14) using a high resolution double crystal spectrometer, provides reference spectra for certain of these compounds. The spectra of ordinary hydrated salts of divalent manganese are of type I, and are essentially indistinguishable. In general, these salts contain the Mn++ ion octahedrally coordinated with oxygen. Figure 2 presents spectra of the crystalline manganous salts; Fig. 3, the noncrystalline. Spectra of manganous salts show maxima at 16 and 60 ev. and a minimum

159

X-RAY K-ABSORPTION EDGES

at 38 ev. In some of them a weak, poorly resolved line appears at 25 ev. The spectra of Fig. 3 include three noncrystalline manganous soaps used as paint driers. These soaps were amoiphous as studied, being either in the form of solid resins or in a thick varnish-like preparation. The identity of spectra of aqueous solutions and those of corresponding crystalline hydrate salts has been pointed out by Beeman and Bearden ( l o ) ,and Boke (16). All of these results indicate that the spectra are not determined or influenced by the long range crystallinity. The features which determine the spectra include apparently oiily the valence and the structure in the first coordination shells.

1.2 0.8 0.4 + 0.0

z

uu.

8

08 0.4

0

5-

F

g

0.8

b 0.0 0.8 04 0.0

-40

0

40

00

120

160

200

ELECTRON WLTS ABOVE MN EDGE (m37ev)

FIG.4. Spectra of two manganous and the corresponding manganic salts; locations and widths of peaks change with valence, but spectra remain of type 1.

The effect of valence is shown in Fig. 4. Here corresponding salts of manganous and manganic ions ale compared as acetates and as acetyl acetonates. The higher valence spectra appear still to be of type 1, but the peaks are broadened and shifted t o higher energies. The main maximum appears

160

ROBERT A. VAN NORDSTRAND

at 25 ev. with the trivalent salts. This shift, attributed to valence change, may be reflecting the change in electrostatic environment, shortened bond distances, and increased polarization of nearest neighbor atoms which accompany an increase in valence. The oxides of manganese give spectra, shown in Fig. 5, where the valence shift from +2 to higher (+3, +4) is the outstanding feature. The MnO spectrum shows extended structure probably related to the simple crys-

I

I

0 8-

I

I

I

1.2

/.-."".".

.....-*..

L A

MN0 2

-

-

04I

I

I::: i-.-**/'c1 I

I-

0.0.

-%..

w C m . -

-

MN&

-

-

g

---.-

'

M 4 4

00

-

.

-*-

I

I

I

I

tallographic system of MnO. The first peak of the MnO spectrum, at 16 ev., corresponds to that of the divalent salts of Figs. 2, 3, and 4. The first peak in the spectra of the higher oxides, a t about 22 ev., corresponds to that of the manganic spectra of Fig. 4, but doos not serve to distinguish +3 and +4 valences. Figure 6 shows spectra of other manganese compounds. The spectrum of manganese 1 ,lo-phenanthroline dichloride matches those of the divalent

161

X-RAY K-ABSORPTION EDQES

salts, but with reduced amplitude. The first peak of the MnS spectrum is unusually weak; however, its location on the energy scale corresponds to that of the divalent salts. MnF3 has a principal peak corresponding to the trivalent salts of Fig. 4, and has an additional poorly resolved 38 ev. peak. The spectrum of Li2Mn03has some resemblance to that of MnOz, and corresponds clearly to that of a higher valence manganese (either +3 or +4).

I .2 0.8

I

0.4

5 0.0 w

2

s

0.8 0.4

I 5

I

0.0 0.8

-

MNS

-

04 I

0.0

I

-\ MN(I,~~-PIIEWTH~WW) (x

0.8

-

0.4 0.0,

0

40

80

I20

I I60

a

3

ELECTRON VOLTS ABOVE MN EDGE (6537eV)

FIQ.6. Spectra of variety of manganese compounds; MnF, has high amplitude, MnS low amplitude h e structure.

Spectra of type I11 are shown in Fig. 7. In all four cases these materials are metallic phases, having metallic luster and conductivit.y. Their spectra have an appreciable absorption coefficient at 0 ev., which may correspond to electrons being promoted to the Fermi level in the conduction band; and very low amplitude of fine structure, i.e., relatively flat absorption plateaus. The low amplitude may be attributed to relatively low electrostatic field strength in the first coordination sphere, to be expected in these electronic

162

ROBERT A. VAN NORDSTRAND

conductors. Low amplitude is observed in MnO and MnS spectra, due possibly to electron exchange and to polarization. Type IV spectra are shown in Fig. 8. The compounds represented are tetrahedral MnO, salts, three permanganates and one manganate. The permanganate spectra are essentially identical, again pointing to the minor role of long-range crystallinity and distant neighbors. Aqueous solutions of the permanganates give the same spectrum.

-

MNSL

-

-

--

Mu +23%Fe -

. 0.8-

.

* OC-MN METAL

-

ELECTRON VOLTS ABOVE MN EDGE (6537eU)

FIQ.7. Type I11 spectra of manganese in four metallic phases, MnSi phase has distinctive spectrum.

The manganate ion haa a tetrahedral first coordination shell of oxygen, just as does the permanganate. The manganate ion is expected to be somewhat larger, due to the increased negative charge. Similarly, the spectra of these two ions are closely related. The first peak for permanganate is a t about 4 ev.; for manganate, about 3 ev. For permanganate, the shoulder and the main maximum occur at about 28 and 48 ev.; for manganate, 20 and 35 ev. These shifts may be accounted for by a linear expansion of 17% c a m 4 by the additional electron in the manganate ion.

163

X-MY K-ABSORPTION EDGES

B. COBALTSPECTRA K-edge spectra of cobalt compounds appear quite similar to those of manganese compounds. The ionic cobaltous salts and hydrates produce type I spectra. In Fig. 9 and 10 the spectra of the salts (except for CoBrs) have their principal maximum a t 18-20 ev. Spectra of the cobaltic salts stabilized with a coordination sphere of ammonia or of ethylene diamine, shown in Figs. 11 and 12, are all very similar, are of type I, and have their

1.2 -

-

08

-

-

thMuCk*H&

-

0.8-

%!&- ...../I

I 0

I

I

40 80 Ix) ELECTRON VOLTS ABOVE M W FDGE (6537eV.l

I 160

xx)

FIG.8. Type IV spectra of salts of tetrahedral MnO, ions, both permanganate and manganate.

principal maximum a t 25 ev. Again, this shift attributed to valence may be interpreted in terms of altered electrostatic environment including shortened bond distances and increased polariza.tion in the trivalent compounds. In Fig. 11, no effect is observed upon substituting one atom of the various halides in the first coordination sphere. Likewise, as shown in Fig. 12, when

164

ROBERT A. VAN NORDSTRAND

one substitutes (either cis or trans) either two chlorine atoms or two NO2 groups for an ethylene diamine in the first coordination sphere, the effect is negligible. The spectrum of sodium cobaltinitrite shown in Fig. 13 is also of type I with the maximum a t 27 ev. The spectrum differs from the ammonia and ethylene diamine coordinated cobaltic compounds in yielding a pattern I

1.2

I

I

I

I

-

oa 04 ~

m9 k 8

CoFORMATE

I

0.0’

I

-

bc03

0.80.4

-

-

-

%,:.-

I

I

-

CoSQ.7HzO

-

.

0.0

-

.*

I

I

~

c

C d - Q h -6HzO

06-

04 0.0-

-

do

..

0

40

en

I

I

120

160

200

appreciably sharper and displaced slightly to higher energies. Whereas the vobaltinitrite spectrum (type I) has but a single principal maximum, the cobalticyanide spectrum (of type 11) has a well-resolved pair of maxima, and the trioxalatocobaltic spectrum has a principal peak showing the same magnitude of splitting as the hexacyanide but without the resolution. The multiplicity of this principal peak may relate to the number of coordination spheres of atoms rigidly attached to the cobalt. The cobalt-hexacyanide spectrum, which has two well-resolved major

X-RAY K-ABSORPTION EDGES

165

maxima to correspond with its two octahedral coordination spheres, provides an example of use of the diffraction analogy. The absorption maximum occurring at the lower value of E, (hence higher value of A) corresponds to the outer coordination sphere, the one containing 6 N atoms. The inner coordination sphere gives rise to the second absorption maximum.

FIO.10. Spectra of cobalt metal and four cobaltous salts, showing progresaive change from low amplitude Type I11 spectrum to high amplitude Type 1 spectrum as the cobalt atom is shielded from heavy element neighbors.

Figure 10 shows a sequence of spectra ranging from the low amplitude, type I11 spectrum of the metal to the high amplitude, type I spectra of the hydrated salts. The CoBrz spectrum has a very low amplitude, resem-

166

ROBERT A. VAN NORDSTRAND

bling the metal spectra. Here again, as in the case of MnO and MnS, some factor such as polarization may be decreasing the electrostatic field. Although the amplitude of the fine structure is greatly reduced in each of these cases, the location of the principal peak remains that of the divalent form. I

0.8

-

I

I

I

I

--

[CO(NH& F] FZ

04 -

-

[G(NHdsCL]C L ~

-

I

[CO(NH~ ~ ~m B] R ~

-

.-. [WNW~ ~ ~ ( N o- J ~

I 120

I

I60

xx)

Spectra of the oxides of cobalt COO and CoaO, are shown in Fig. 14. Locations of the principal peak, at 18 and 24 ev., respectively, correlate with the valences. The extension of the fine structure throughout the 200 ev. range studied is in line with the simple crystal structures of these oxides. The series of mixed spinels shown in Figs. 14 and 15, show one of the important features of this branch of spectroscopy. The spectra of Fig. 14 pertain specifically to the Kedge of cobalt, as they extend from 7700 to

167

X-RAY K-ABSORPTION EDGES

7900 ev. Spectra of Fig. 15 apply specifically to manganese, extending from 6500 to 6700 ev. Yet cobalt and manganese are both present in some of the samples, as is nickel. It is not often in spectroscopy or diffraction that one can so certainly distinguish the elements. 1

I

I

I

I

[&(en),

CISCLZ

1 CL

-

-

-

CIS-

[Wenk (NOZIZINOS

-

-

TRANS [Co(en)z (NO&]

-

No3

-

ELECTRON VOLTS ABOVE Ca EDGE (7709eV.)

FIQ.12. Type 1 spectra of cobaltic-ethylene diamine complexes.

Spectra of the mixed spinels are interpretable in terms of X-ray diffraction studies of the same samples by Adroff (16). Cobalt appears to be in the divalent condition, based upon the location of the principal maximum. Manganese appears in a higher valence state. The extended fine structure, which is supposed to be determined by the lattice, appears identical for all the spectra of Figs. 14 and 15 which are of truly cubic spinels, namely C0304,

168

ROBERT A. VAN NORDSTRAND

CoNiMn40s, NizMn40sand NisMn30a. In the spectra of the noncubic Mn40, and the noncubic CoMnz04, the extended fine structure is missing. It is apparent that the extended fine structure does pertain solely to the crystal lattice and is not dependent on the valence, coordination, or nature of the atom giving rise to the absorption spectrum.

ELECTRON VOLTS ABOVE Co EDGE (7709ev.l

FIQ.13. Spectra of three cobaltic complexes of distinctive coordination types and of two cobaltous compounds.

C. CHROMIUM SPECTW K-edge fine structure spectra of chromium compounds show the same range of sensitivity to nearest neighbors, valence, and other chemical effects as do manganese and cobalt.

169

X-RAY K-ABSOEPTION EWES

Spectra of a variety of chromium compounds in the +3 valence state are included in Fig. 16. The principal peak is centered at about 22-25 ev. in all cases. The Cr203spectrum is almost identical to that of MnOz of Fig. 5. Spectra of the oxalato complex and the ammonia complex are almost identical to spectra of the corresponding cobalt compounds of Figs. 13 and 11.

coo

-

CoNi M N ~ O ~

-

G2MrkOe

-

-

-40

0

40

80

I20

ELECTRON VOLTS ABOVE Co EDGE (7709 eV.)

FIG.14. Cobalt K-edge spectra of two mixed oxides compared to spectra of two common cobalt oxides. ColMn4Os is of hausmanite type tetragonal structure, c0@4 and CoNiMn40aare of cubic spinel structure.

The “simple” hydrated ionic salt, chromic nitrate, has a spectrum quite distinct from the ionic salts of cobalt and manganese. The principal peak shows a splitting. This may be related to the very strong affinity which chromium displays toward its first coordination sphere of water. Figure 17 contains three chromium spectra of type 111, the low amplitude spectra characteristic of metals, and one of type I. Chromium, a bodycentered cubic metal, produces extended fine structure. The chromium carbide sample appears by X-ray diffraction to be the

170

ROBERT A. VAN NORDSTFLAND

Cr,Cs phase as described by Crafts and Lamont (I?‘). The spectrum has extended fine structure not expected in a crystal structure of this complexity. The spectrum shows relatively high absorption at 0 ev. and very low amplitude fine structure in the “chemical” range, features in line with the metallic properties of this carbide. The cyclopentadienyl chromium compound, an open sandwich structure, has a spectrum about as devoid of fine structure as one might expect of a I

I

I

1

I I -

oa 04

I

NLMN,Oe

-

0.0

.-

’

0494O“J0

--..

0

40

80

120

160

0

ELECTRON VOLTS ABOVE MN EDGE (6537ev)

FIG.15. Manganese Kedge spectra of five mixed oxides, including two whose cobalt edge spectra were included in Fig. 14. MnaO4 and ColMn4Oa are tetragonal; others are cubic spinels.

171

X-RAY K-ABSORPTION EDGES

-

monatomic gas. An X-ray diffraction pattern of the material was obtained which showed that at least some major fraction of it had not decomposed. The absence of absorption a t 0 ev. is evidence that the material is not a metallic conductor. There remains the possibility that the NO groups, the Br, and the cyclopentadienyl ligands contribute fine structure which adds up in such a way as to cancel out all fine structure. The spectrum of a second cyclopentadienyl compound, shown in the titanium series, is of type I. The spectrum of the organometallic compound dimesitylene chromium, [CsH3(CH3)3]2Cr, has relatively high amplitude. The location of the principal peak, 18 ev., corresponds to that of divaleiit chromium. I 1.2

-

08

-

I

I

I

I

-

-

04-

I- 0 0

. ..*'

5 08-

Q

C R ( N O ~ ) ~ . S H ~O

L

-

10.4-

. . -

.

g,, 0.0

.

-

.

*

KdCR(CzO&]

-

.-

-

0.8 -

[CR(NH&CL]CL~

-

-

040.0-40

-3H20-

*

.

.

0

I

I

I

I

40

80

120

160

200

The effect on the spectrum of the [Cr(en)*] ion caused by successive replacement of ethylene diamine by the thiocyanate ion, NCS, is shown in Fig. 18. The starting compound [Cr(en)a](NCS)3has a spectrum essentially identical to those of [Cr(NH3)&1]CI2in Fig. 16 and [C~(en)~]Cl, in Fig. 12.

172

ROBERT A. VAN NORDSTRAND

The other end of the series, Ka[Cr(NCS)a],has a spectrum with a pronounced preliminary peak at 16 ev., which peak increases in magnitude throughout the series in Fig. 18. The location of the peak might imply divalent chromium. However, from diffraction type arguments and the interpretation of the K3Co(CN)aspectrum of Fig. 13, this new peak introduced by the NCS group may be attributed to the Cr-C distances, i.e., to the second octahedral coordination sphere. As two and then four NCS ions are introduced into the coordination sphere, this preliminary peak is

1

n.n L

04 -

0.8

00

CR DIMESITVLENE

.

-

I

1

I

I

I

FIQ.17. Spectra of b.c.c. chromium metal, of a noncubic carbide (Cr,C8), and of two organometallic chromium compounds.

a t 18 ev.; with all six introduced the peak is a t 16 ev. This change is in the direction of increased Cr-C distances for the six-substituted compound. The principal maximum of the [Cr(en),] spectrum, at 25 ev., is attributcd to the Cr-N distance. This maximum shifts to 30 ev. in the [Cr(NCS)e] spectrum, attributed to a shorter Cr-N distauce. Figure 19 shows spectra related to this problem, namely, spectra of compounds with two distinct octahedral coordination spheres. The top two

173

X-RAY K-ABSORPTION EDGES

spectra, of type 11, provide strong evidence that ionic charge plays a minor role compared to geometric factors in the first coordination spheres. In the three spectra, a sequence of effectiveness is apparent, namely, C > N > 0. This sequence is derived by qualitative comparison of magnitudes of the peaks. The K3[Cr(NCS),J was prepared specifically for this study by F. Basolo to check the possibility that the third octahedral coordination sphere might show up in the spectrum as an additional maximum a t about 8 or 10 ev. The absence of this maximum is however, not surprising; the Eulfur, bromine, and other heavy atoms in the coordination sphere contribute little to the amplitude of fine structure. I

I

I

I

I

-

120.8

-

-

k~(en)&Ncs)3

-

0.4

5@ O’O

08-

-

TRANS-

0

[CR (en12 (SCN)z]

NCS

04-

5

-

. ..

0.0-

-

I

F

NH~[CR(NH&(SCNW -

08-

3

0.4-

....

0.0

0.8

-

-

-40

0

40

I

I

I

80

I 20

160

200

ELECTRON VOLTS ABOVE CR EDGE (5988ev.)

FIG.18. Spectra of a series of chromium complex salts with successive replacement of ethylene diamine by the SCN ion.

Figure 20 contains spectra of compounds in which the chromium is of nominal valence +6 and is tetrahedrally coordinated. The chromate ion shows a type I V spectrum extending out to about 100 ev. which is inde-

174

ROBERT A. VAN NORDSTRAND I

1.2

-

0.8

-

I

I

I

I

(NH& b0.a

-

WzChQJWJ

-

ELEClRON WLTS ABOVE CR CD(K (6988eV.)

FIQ.19. Spectra of two chromium complexes with double octahedral coordination sphere (type 11) and of a complex with triple octahedrnl coordination sphere. I

I

I

1

1

I

clr (COh

K3[b(CN)d

K3 CcdNCS)el

ELECTRON VOLTS

ABOVE Ca EDGE (5988 eV.)

Fro. 20. Type 1V spectra of salts of CrO, and CrOaClions.

-

175

X-RAY I(-ABSORPTION EDGE8

pendent of the associated crystal structure and positive ions. Replacement in the tetrahedral coordination sphere of one of the oxygens by a chlorine has little effect on the spectrum.

D. TITANIUM SPECTRA The spectra of the usual titanium compounds differ somewhat, as does the chemistry of titanium, from that of the elements described above.

o'81 I

TETRAPHENYL TITANATE

94

-

0.0-

08

-

TETRASTEARYL TITANATE

04-

-

-

0.0 08

0.4

-

HYDROXYTITANIUM STEARATE

-

-

00

-

0.8 -

ISOPROPYLTITANIUM STEARATE

0' 0.?40

0

40

80

120

160

200

ELECTRON VOLTS ABOVE Ti EDGE (4964 W.)

FIQ.21. Spectra of four compounds of tetravalent titanium coordinated through four oxygens to various organic groups or hydrogen.

The four spectra of tetravalent titanium shown in Fig. 21 are closely related. All have a low energy peak at about 5 ev., similar to the characteristic low energy peak in the chromate and permanganate spectra. This peak is also present in the spectra of the other tetravalent titanium compounds, TiOzand the lactate. In Fig. 21 the principal peak reaches a maximum at about 22 ev. However, it is split and reaches a second maximum

176

ROBERT A. VAN NORDSTRAND

at about 30-35 ev. The two spectra, corresponding to the titanium ortho esters, Ti(OR)r, appear identical. Both compounds have a double tetrahedral coordination sphere, first of oxygen, then of carbon, which may account for the splitting of this principal peak. The third spectrum is that of the compound trihydroxytitanium stearate; the fourth of triisopropoxytitanium stearate. The small differences between these spectra and those of the ortho esters are in the splitting of the principal peak.

1

Y

k

FIG.22. Spectra of successive oxides of titanium] showing effect of increased oxygen on amplitude of h e structure, and showing distinction between rutile and anataae.

Figure 22 presents the spectra of the common oxides of titanium. The two common forms of Ti02, anatase and rutile, give clearly distinguishable spectra. These distinctions in the spectra have been confirmed in several samples extending over a wide range of crystallite size. The packing within the first coordination shells of anatase and rutile is different and may account for the spectral differences. The tetravalent titanium spectra are

177

X-BAY E-ABSORPTION ICWES

mutually distinguishable by the distribution of intensity in the double principal peak which extends from 30 to 40 ev. The fourth spectrum on Fig. 22, that of TiO, has lost the 5 ev. peak which characterized the tetravalent compounds. The amplitude of this spectrum is reduced compared to that of Ti02. The spectrum of Ti20eretains the 5 ev. peak of the tetravalent form. This spectrum is compatible with the assumption that Ti20ais a mixture of tetra- and divalent titanium.

-

TI 38

Ti LACTATE

-

ELECTRON VOLTS

ABOVE T~ EDGE (4964ev.)

FIG.23. Spectra of titanium metal, of metallic appearing Ti&-, phase, of organometallic compound of divalent titanium, and of the tetravalent titanium lactate.

The spectrum of titanium metal foil is in Fig. 23. The foil, originally of 12p thickness, was reduced by etching in HF to about 4p. A corresponding spectrum of titanium metal powder (not shown here) contained the same peaks but with only about half the amplitude, and with greater scatter of data points. This is an illustration of the advantages of having uniformity of thickness, which is especially difficult to achieve with metal powders. The titanium metal spectrum appears to be Kronig type fine structure.

178

ROBERT A. VAN NORDSTRAND

The TiSn spectrum does not show the low energy peak characteristic of tetravalent titanium, and in other ways is difficult to classify. Again sulfur as a coordination atom does not give rise to fine structure of appreciable amplitude. The spectrum of di-cyclopentadienyltitanium dichloride is the simple type I spectrum that might be expected of a hypothetical hydrated divalent titanium salt.

0.4 0.8

-

00

5

&I 0.0-

COO

u

-

04-

8

0.0

%

I--

-

0 00 0

-

0.4 0.0-

-40

-

r 40

80

TO

-

,

I20

160

FIG.24. Spectra of three compounds with rock salt structure and one nearly cubic compound (TiO), showing variations of extended fine structures, general similarity of spectra, and special low energy absorption of the metallic Tic. E. COMPARISONS AMONG ELEMENTS Spectra up to this point have been compared only to other spectra of the same element. Three figures are shown here comparing similar compounds of the four elements; the sodium chloride, the tetrahedral, and the hexacyanide type molecules. Spectra of the compounds with sodium chloride crystal structure (Fig. 24) show strong resemblance. Quantitative correlation between lattice parameters and absorption maxima is poor as seen on Table 11.

179

X-RAY K-ABSOBPTION EDGES

TABLE I1 Lattice Parameters and Location of Maxima in Related Compounds

Locations of maxima (ev.) Compound

Lattice parameter

Ti0

4.16 4.24 4.32 4.44

(A.1

Coo Tic MnO

First

Third

20 18 15 16

61 64 60

75

1.2 -

0.8

-

0.4

-

a%

“)2

0.0

i5 3 08-

KMNO~

104-

6 OQI-

1JI

KzMNCL

0.0

08-

04 0.0

TETRAPHENYL TITANATE

-

-40

40

I

00

120

I

160

2

ELECTRON VOLTS ABOVE EDGE

FIQ.25. Spectra of three simple tetrahedral salts, all of Type lV, compared with the tetrahedrally coordinated titanium orthoester.

The TiO, though of proper stoichiometry, lacks full cubic symmetry as seen by splitting of the X-ray diffraction lines. The lattice parameter given in Table I1 is an average value.

180

ROBERT A. VAN NOBDSTRAND

The titanium carbide spectrum shows strong absorption at 0 ev., which may be attributed to the metallic nature of this carbide or to the tetravalent state of titanium. This ambiguity is not appreciably resolved by the discussion of Rundle (18), who explains how the tetravalent nature of the titanium in T i c leads to its metallic character. The Ti0 spectrum does not show this low-lying absorption peak; Ti0 is not metallic and does not contain tetravalent titanium. Figure 25 compares spectra of three elements tetrahedrally coordinated with oxygen. The identical nature of the chromate and permanganate spectra (even those obtained from a variety of crystalline compounds and aqueous solutions) suggests that identical electrostatic fields exist around both the Cr and the Mn, and that these fields are sufficiently characterized by the first one or two coordination spheres. The spectrum of the tetrahedrally coordinated tetraphenyl titanate does not resemble the type IV spectrum, primarily due to enlargement of the 20 ev. absorption peak. The second tetrahedral coordination sphere in this compound, consistjng of carbon atoms, may account for this change. An analogous change, also attributed to the second coordination sphere, is observed for the octahedral hexacyanides as compared to the other octahedral compounds. The spectra of three hexacyanides and a hexacarbonyl, all of type 11, are shown in Fig. 26. The close relationship between structure in the first coordination shells and the fine structure spectra is shown here. The common structural feature giving rise to the type I1 spectrum appears to be the octahedral coordination of the linear ligands CN or CO. The general features of these spectra appear unaffected either by changes in the identity of the central atom, by replacing CN by CO, by changing crystal structure, by dissolving in water, or by changing the over-all charge on the complex. Figure 26 supports the general idea that the distribution of atoms within 5 to 8 A. of the central atom determines fine structure spectra out to 100 ev. The distinct first and second octahedral coordination spheres may account, respectively, for the two distinct maxima a t 40 and 20 ev.

V. Spectra of Catalysts A few applications of X-ray absorption edge spectroscopy t o specific catalysts have been reported. Boehm et al. (19) have published spectra of the cobalt K-edge in the vitamin Bla catalyst, Ca144H86-g2014NlrPCo, showing that the cobalt is trivalent. Hanson and Milligan (20)examined K-edge spectra of a number of supposed higher oxides of nickel, of catalytic interest. They found no evidence of trivalent nickel. Keeling (21) examined the K-edge spectra of cobalt catalysts supported on silica and alumina and

181

X-RAY K-ABSORPTION EWES

compared these with spectra of COO, Co304and CoAlzOa. These catalysts, which were prepared by impregnation, contained the cobalt predominsntly as CoaO,. Examples cited from the present studies of catalyst applications include all four of the elements whose reference spectra are described in the previous sections.

t.2

0.8 0.4

0.0 0.6

5w 00

8

6

0.8

0.4

4

ao 0.8

0.4

0.0 08 04 90 -40

0

40

80

120

160

ELECTRON VOLTS ABOVE EDGE

FIQ.26. Type 11 spectra of double octahedral coordination sphere compounds, hexacyanides, and one hexacarbonyl.

The first instance of successful application was in the examination of some supported chromia catalysts. A pronounced variation in catalyst performance, caused by certain oxidative pretreatments, was found to correlate with variations in absorption edge spectra. Spectra involved were

182

ROBERT A. VAN NORDSTRAND

those of the chromate ion and chromic oxide, which are very readily distinguished, as seen in Figs. 16 and 20. The second problem of catalytic interest was in connection with supported permanganate catalysts. The spectra of two such catalysts are shown in Fig. 27. Both were made by impregnation with aqueous NaMnOa. I

I

I

I

I

v.... --------... MN02

-

-

/--\-.-

-

~ M N Q ON ACTIVATED CARBON

NAMN& ON SILICA GEL

04 -

-

08

EUZCTRON VOLTS ABOVE MN EDGE (6537ev)

Fro. 27. Spectra of permanganate supported on silica gel and on activated carbon; change in chemical form is clearly shown in the carbon supported case.

Neither catalyst showed any evidence of crystalline components by X-ray diffraction. The permanganate on silica gel apparently remains as permanganate. The permanganate on activated carbon appears from the spectrum to have been reduced to MnOz or to some other hydrous manganic oxide. Spectra of four supposedly identical catalysts containing cobalt supported on an activated carbon are shown in Fig. 28. The spectra show that the two “good catalysts,” B-1 and B-2, contained the cobalt mostly a5 COO; the “poor catalysts,” A-1 and A-2, contained the cobalt in the metallic form. This wa8 supported by ferromagnetic comparisons of the

183

X-RAY K-ABSORPTION EDGES

catalysts. Some preliminary X-ray diffraction patterns confirmed the identity of the cobalt metal catalysts, but were too diffuse to permit any identification of t,he two good catalysts. The top three spectra of Fig. 29 represent an effort to use the spectra to identify the environment of cobalt in a typical cobalt-molybdena-alumina catalyst of approximate composition 5Oj, cobalt, 10% Mo03. The X-ray I

I

I

I

I

Co-ON-CARBON CATALYSTS 0.8

-

8-2

04 -

0-1

A-2

A- I

0

ELECTRON VOLTS

ABOVE Co EDGE (7709eV.) Fro. 28. Spectra of four catalysts of cobalt on activated carbon. Inactive catalysts A-1 and A-2 are in metallic state; active catalysts B-1 and B-2 appear to be COO.

diffraction pattern shows only an activated alumina. Two experimental preparations were made: the compound cobalt molybdate, and a coprecipitated cobalt-alumina catalyst. These were calcined in air under the same conditions as Co-Mo03-Alz03 catalyst. The spectra indicate cobalt molybdate contains cobalt in a form similar to the divalent salts of Fig. 9. The cobaltalumina catalyst and the cobalt-molybdena-alumina catalyst contain the cobalt in a state comparable to that of the cobalt in the mixed spinel CoMn204of Fig. 14, described as divalent in a spinel lattice. This is evi-

184

ROBERT A. VAN N0RDSl"D

dence that the cobalt is associated with the alumina in the catalyst, not with the molybdena. The additional comparison on Fig. 29 shows that in the coprecipitated cobalt-alumina catalyst the cobalt is altered when the catalyst is reduced in hydrogen. The change is noted in the high energy region of the spectrum. This change is receiving additional study.

I

I

I

I

I

I

I

I

I

1 1

Co-A~203

CATALYST

I

I

I

.YL

o. CO-AL~O~

REDUCED IN Hz

04

00 -40

0

40 ELECTRON 80 VOLTS 120

160

200

ABOVE Co EDGE (7709 ev.)

FIQ. 29. Spectra of cobalt-molybdena-alumina catalyst and related compositions, &MOO,, and a coprecipitated cobalt alumina catalyst (all three samples were calcined in air); also apectrum of cobalt-alumina catalyst reduced in hydrogen.

Figure 30 compares spectra of three hydrous titania cat,alysts-one straight titania and two mixed metal oxides. All three had relatively high surface area; all were amorphous t o X-ray diffraction. The catalysts were prepared by cogelation. The admixed metals were different in the two cases and were present in concentration equivalent to that of the titanium. The X-ray absorption edge spectra provide the following information concerning the titanium in these three high area amorphous catalysts:

185

X-BAY K-ABSORPTION EWES

1. All three have the titanium in the tetiavalent state. 2. All are coordinated in about the same manner.

3. They are not coordinated in the manner of rutile or anatase. 4. The coordination most nearly resembles tetraphenyl titanate, of all reference compounds studied; this implies tetrahedral coordination. 1

1

I

I

I

TlTANlA CATALYSTA MIXED OXIDES

AMORPHOUS

Q8

-

TlTANlA CATALYST B

MIXED OXIDES AMORPHOUS 00. 0.8

-1 -

-

-

. .

-

T1Oz-xH20 AMORPHOUS

-

-

QO---*Lm.-..'

0.8

-

0.4

-

WTILE

-

ELECTRON VOLTS ABOVE Ti EDGE (4964 W.)

FIQ.30. Spectra of three high area, amorphous, hydrous oxides of titanium compared with that of the crystalline anhydrous oxide, rutile. One is a straight titania gel, two are coprecipitated with different elements to form mixed metal hydrous oxide gels.

VI. Summary Fine structure spectra obtained at the X-ray K-absorption edge of an element are not yet completely resolved theoretically or experimentally. However it appears that this branch of spectroscopy even now may be of aid to catalyst research. Meaningful spectra of elements of the first transition series, even in concentrations sometimes as low as >$%,can be readily obtained; this is also true in conditions inaccessible by diffraction

186

ROBERT A. VAN NORDSTRAND

methods but of greatest significance to catalysis, e.g., as adsorbed layers, in aqueous solutions, and in amorphous solids. Thew noncrystalline forms give spectra which appear to provide structural information previously available only for crystalline solids, information concerning the nature and configuration of atoms immediately surrounding the atom under study. Spectra of 95 known compounds of four different elements are shown here, extending through the energy range from below the K-edge to 200 ev. above it. These spectra emphasize the relationship between the extended (Kronig type) fine structure and the intermediate or chemical range fine structure (0 to 100 ev.). lt is this chemical range fine structure which seems independent of the crystallinity of the element but sensitive to chemical effects such as the valence and the first one or two coordination spheres. The correlations between the spectra and the configurations of immediate neighbor atoms may be fitted into the Kronig theory, perha.ps in a way analogous t o tho way diffraction by liquids is related to diffraction by crystalline solids. The photoelectrons are of such low energy that coherence of wavelength may be lost in a few atomic distances. This should mean that an absorption process giving rise to these slow photoelectrons involves a final state whose density of states has no fluctuations with energy. The absorption process however has a transition probability sensitive to energy because of the fluctuations of the electric field surrounding the atomfluctuations having distance parameter of the same order of magnitude as the wavelength associated with the photoelectron. The field is considered here to “scatter” with greater or lesser efficiencythe photoelectron of given wavelength from the center of the atom of origin. Atoms most efficient at causing high amplitude fine structure in the 0-100 ev. range are carbon, nitrogen, oxygen, and fluorine. Proximity in the first or second coordination sphere of an element such as sulfur or an element of greater atomic weight appears to depress the amplitude of the fine structure. Metals, sulfides, and bromides have very low amplitude (type 111) spectra. Elements well insulated with first row atoms, for example MnOz, have much stronger fine structure than thosc Irss well insulated, as MnO, which in turn has a stronger fine structure than metallic manganese. Spectra of types I, 11, I V arc associated, respectively, with single octahedral, double octahedral, and single tetrahedral coordination shells.

ACKNOWLEDGMENTS The writer is greatly indebted to the management of Sinclair Research Laboratories for making possible this study and its publication; to many of the staff members including specifically W. E. Kreger, J. L. Gring, M. F. L. Johnson, R. R. Chambers, J. A. Perry, and R. L. Foster. The writer owes much to F. Bttsolo for his interest and for his

X-RAY K-ABSOBPTION EDGES

187

samples of 27 key compounds; to L. V. Azhoff for his samples of spinels; to S. H. Bauer, A. I. Snow, L. G. Parratt, and J. A. Prins for discussions of spectroscopy; to the Union Carbide Metals Co. (for the carbide and the lower oxides of titanium); and to P. Moews for the dimesitylene chromium.

REFEREKCES 1. Van Nordstrand, R. A., in “Non-Crystalline Solids” (V. D. Frechette, ed.), in

press. Wiley, New York, 1960. 8. Compton, A. H., and Allison, S. K., “X-Rays in Theory and Experiment,” p. 662. Van Nostrand, New York, 1935. 3. Sandstrom, A. E., in “Handbuch der Physik” (S. Flugge, ed.), Vol. XXX, p. 78. Springer, Berlin, 1957. 4. Tomboulian, D. H., in “Handbuch der Physik” (S. Flugge, ed.), Vol. XXX, p. 246. Springer, Berlin, 1957. 6. Kossel, W., Z . Physik 1, 119 (1920); 2, 470 (1920). 6. Parratt, L. G., Phys. Rev. 66, 295 (1939). 7. Shaw, C. H., in “Theory of Alloy Phases,” p. 13. Am. SOC.for Metals, Cleveland, 1956. 8. Kronig, R. de L., Z . Physik 70, 317 (1931); 76, 191, 468 (1932). 9. Hayasi, T., Sn’. Repts. Tdhoku Univ., First Ser. 33, 123 (1949); 34, 185 (1951). 10. Beeman, W. W., and Bearden, J. A., Phys. Rev. 61, 455 (1942). 11. Cotton, F. A., and Hanson, H. P., J. Chem. Phys. 26, 619 (1956); 28, 83 (1958). 18. Hartree, D. R., Kronig, R. de L., and Petersen, H., Physica 1, 895 (1934). 13. Cauchois, Y., and Hulubei, H., “Tables de Constantes et Donn6es numeriques.” Hermann, Paris, 1947. 1.6. Hanson, H. P., and Beeman, W. W., Phys. Rev. 76, 118 (1949). 16. Boke, K., 2. physik. Chem. 10, 45, 59 (1957). 16. Adroff, L. V., 2.K k t . 112, 33 (1959). 17. Crafts, W., and Lamont, J. L., Trans. AZME 185, 957 (1949). 18. Rundle, R. E., Acta Crysl. 1, 180 (1949). 19. Boehm, G., Faessler, A., and Rittmayer, G., Naturwissenschaften 41, 187 (1954); Z . Naturforsch. 9b, 509 (1954). 80. Hanson, H. P., and Milligan, W. O., J . Phys. Chem. 60, 1144 (1956). 21. Keeling, R. O., J. Chem. Phys. 31, 279 (1959).

This Page Intentionally Left Blank

The Electron Theory of Catalysis on Semiconductors TH. WOLKENSTEIN Institute of Physical chemistry of Academy of Sciences U.S.S.R., University of MOSCMO, Moscow Page

I. Introduction.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Types of Chemisorption Bonds.. . . . . . . . . . . . . . . . . . . 111.

IV. V. VI.

A. “Strong” and “Weak” Bonding in Chemisorption.. . . . . . B. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Radical and Valence-Saturated Forms of Chemisorption.. . . . . . A. Free Valencies of a Catalyst.. . . . . . . . . . . . . . . . . . . . . . . . . . . B. Reactivity of Chemisorbed Particles.. . . . . . . . . . . . . . . . . . . . . C. Dissociation of a Molecule upon Adsorption.. . . . . Electron Transitions in Chemisorption. . . . . . . . . . . . . . . . A. Transitions between Different Forms of Chemisor B. Equilibrium between Different Forms of Chemisorption Catalytic Activity of a Semiconductor.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 . . . . . . . . . . . . . . 215 A. Radical Mechanism of Heterogeneous Reactions.. B. Acceptor and Donor Reactions.. . . . . . . . . . . . . . . . Interaction of the Surface with the Bulk of the Semiconductor.. . . . . . . . . . . 224 A. Relation between Surface and Bulk Properties.. . . . . . . . . . . . . . . . . . . . . . . 224

. . . . . . . . . . . . . . . . . .235 B. Mechanism of Promoter

IX. Chemisorption and Catalysis on a Real Surface., . . . . . . . . . . . . . . . . . . . B. Thermal and Biographical “Disorder” on the Surface. . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction This article presents a concise account of the present state of the electron theory of catalysis on semiconductors. It aims to describe the main outlines of the electron theory primarily as it has been developed in the past ten years by the author and co-workers. It also contains a short summary of the results of a number of experimental works dealing with electronic phe189

190

TH. WOLRENSTEIN

nomena in catalysis, carried out mainly in the U.S.S.R. The mathematical treatment has been reduced to a minimum, and all the quantum-mechanical calculations have been completely omitted. The electron theory of catalysis has a two-fold aim: 1. Firstly and piimarily, it seeks to disclose the elementary (microscopic) mechanism of the catalytic act. Every heterogeneous catalytic process, like any chemical process, is based in the final reckoning on an electronic mechanism. It is the aim of the theory to elucidate this mechanism. This is necessary if the theory of catalysis is t o rise above vulgar empiricism and to show how to control the activity and selectivity of catalysts, i.e., how to vary them to the required degree and in the required direction. 2. Secondly, the electron theory seeks to elucidate the relation between the catalytic and electronic properties of a semiconductor. At the present time we possess a vast amount of experimental material which allows us to infer that the electronic processes taking place in a semiconductor and determining its electrical, optical, and magnetic properties also determine its chemisorptive and catalytic properties. It is the aim of the theory to establish the connection between these two groups of properties. The electron theory of catalysis cannot as yet be regarded as a complete theory. It resembles a building from which the scaffolding has not yet been removed. It is being erected on the foundation of the modern theory of the solid state and thus introduces new concepts and ideas into the theory of catalysis. This does not mean, of course, that it excludes other concepts and ideas prevalent today in other theories of catalysis. On the contrary, it makes use of these while attempting to disclose their physical content. The electron theory of catalysis and other, mainly phenomenological, theories of catalysis are not as a rule mutually exclusive. They deal with different aspects of catalysis and thus differ from one another mainly in their approach to the problem. The electron theory is interested in the elementary (electronic) mechanism of the phenomenon and approaches the problems of catalysis from this point of view. The existing phenomenological theories of catalysis bear approximately the same relation to the electron theory as the theory of the chemical bond, which was prevalent in the last century and which made use of valence signs (and dealt only with these signs), bears to the modern quantummechanical theory of the chemical bond which has given the old valence signs physical content, thereby disclosing the physical nature of the chemical forces. The father of the electron theory of catalysis is L. V. Pisarzhevsky (Kiev). His work, begun in 1916, formed part of an extensive series of investigations dealing with electronic phenomena in chemistry. L. V. Pisarzhevsky was the first to attempt to relate the catalytic properties of solids to

THE ELECTRON THEORY OF CATALYSIS

191

their electronic properties. The electron theory of Pisarzhevsky, however, was developed before the appearance of quantum mechanics. It was based on Bohr’s theory and, naturally, remained within the bounds of this theory, which greatly curtailed its possibilities. At present (beginning from 1948) the electron theory is being developed on a modern, more advanced theoretical basis. In the U.S.S.R. the initiator of this new electronic quantum-mechanical trend in catalysis is S. 2. Roginsky (Moscow), from whose laboratory a whole series of experimental and theoretical works has issued. Electronic phenomena in catalysis are also dealt with in a number of papers by A. N. Terenin and his school (Leningrad), V. I. Lyashenko and co-workers (Kiev), S. Y. Pshezhetsky and I. A. Myasnikov (Moscow), and others. In recent years the electronic trend in catalysis has also been developing rapidly abroad (Dowden in England, Boudart in the United States, Germain and Aigrain in France, and especially Hauffe and co-workers in Germany, and others). I t may today be considered the main trend in the development of the theory of catalysis. In its present stage of development, the electron theory of catalysis deals with catalysts which by their electrical properties belong to the class of semiconductors. Catalysis on semiconductors, as is well known, is extremely widespread, far more so than might appear at first sight. This is due to the circumstance that in most cases a metal is enclosed in a semiconducting coat and the processes which apparently take place on the surface of the metal actually take place on the surface of this semiconducting coat, whereas the underlying metal frequently takes practically no part in the process. The results of the electron theory as developed for semiconductors are fully applicable to dielectrics. They cannot, however, be automatically applied to metals. Contrary to the case of semiconductors, the application of the band theory of solids to metals cannot be considered as theoretically well justified as the present time. This is especially true for the transition metals and for chemical processes on metal surfaces. The theory of chemisorption and catalysis on metals (as well as the electron theory of metals in general) must be based essentially on the many-electron approach. However, these problems have not been treated in any detail as yet.

II. Types of Chemisorption Bonds A. “STRONG” AND “WEAK” BONDING IN CHEMISORPTION Every heterogeneous catalytic process begins with the act of adsorption. Therefore, the theory of heterogeneous catalysis should proceed from the

192

TH. WOLKENSTEIN

theory of adsorption. We thus begin our article with a consideration of adsorption problems. A system of adsorbed particles is often treated as a two-dimensional gas covering the adsorbent surface. Such an approach is quite justified and fruitful, as long as we are dealing with physical’ adsorption when the influence of the adsorbent on the adsorbate can be regarded as a weak perturbation. In case of chemical adsorption (the most frequent in catalysis), the concept of a two-dimensional gas becomes untenable. In this case the adsorbed particles and the lattice of the adsorbeiit form a single quantum-mechanical system and must be regarded as a whole. In such a treatment the electrons of the crystal lattice are direct participants of the chemical processes on the surface of the crystal; in some cases they even regulate these processes. We shall proceed from a concept which in a certain sense is contrary to that of the twodimensional gas. We shall treat the chemisorbed particles as “impurities” of the crystal surface, in other words, as structural defects disturbing the strictly periodic structure of the surface. In such an approach, which we first developed in 1948 ( 1 ) , the chemisorbed particles and the lattice of the adsorbent are treated as a single quantum-mechanical system, and the chemisorbed particles are automatically included in the electronic system of the lattice. We observe that this by no means denotes that the adsorbed particles are rigidly localized; they retain to a greater or lesser degree the ability to move (“creep”) over the surface. In such an approach there is no fundamental difference between the chemisorbed particles and the “biographical” structural defects which are always present on any real surface. The only difference is that the chemisorbed particles are free to leave the surface for the gaseous phase and to return to the surface from this phase, whereas the “biographical” defects must be considered as rigidly bound to the surface and incapable of interchange with the gaseous phase. In a number of theoretical papers (2-4) it has been shown that a chemisorbed particle considered as a structural defect of the surface is a center of localization for the free electrons of the lattice, serving as a trap for them and thus playing the part of an acceptor for the free electrons. Or (depending on the nature of the particle) it may serve as a center of localization of a free hole, thus playing the part of a donor. I n the general case, as has also been shown, the same chemisorbed particle on the same adsorbent may simultaneously be both acceptor and donor, possessing a definite affinity both for a free electron and a free hole. We observe that structural defects which are simultaneously acceptors and donors are well known ia the theory of the solid state. Take, for example,

THE ELECTBON THEORY OF CATALYSIS

193

the so-called F center, which, as is well known, can capture a free electron and become transformed into a so-called F‘ center (which causes a change in the coloring of the crystal) ;or it can capture a free hole, causing the disappearance of the F center (bleaching of the crystal). It has been shown (this is highly essential) that the localization of a free electron or hole on a chemisorbed particle (or near it) causes a change in the character of its bond with the surface and a strengthening of the bond. Now the new electron (or hole) takes part in it. In accordance with this, we distinguish two forms of chemisorption: 1. “Weak” chemisorption, in which the chemisorbed particle C (considered together with its adsorption center) remains electrically neutral and in which the free electrons or holes of the lattice do not contribute to the bond between the lattice and the particle. We shall denote such a bond by the symbol CL,where L is the symbol of the lattice. 2. “Strong” chemisorption, in which the chemisorbed particle captures a free electron or a free hole of the crystal lattice (thus representing an electrically charged system) and in which the free electron or the free hole participate directly in the chemisorption bond. We observe that the terms “weak” and “strong” are here used in a relative sense. We simply have in mind stronger and weaker forms of binding in chemisorption. In “strong” chemisorption, either a free electron or a free hole can participate in the bond; hence, we distinguish two types of “strong” bonds which we shall call: a. “Strong” n-bond (or acceptor bond) if a free electron captured by an adsorbed particle is involved. We shall denote such a bond by CeL, where the symbol eL denotes a free electron of the lattice. b. “Strong” p-bond (or donor bond) denoted by CpL, where pL is the symbol of the free hole, if a hole captured by the adsorbed particle is involved. By its nature, the acceptor bond, like the donor bond, may be purely ionic or purely homopolar or, in the general case, a mixed one. As we shall see below, this depends on how the electron or the hole captured by the particle and participating in the bond is distributed between the adsorbed particle and the adsorption center. In other words, thjs depends on the type of localization of the electron or the hole, which in turn, is determined by the nature of the adsorbate and the adsorbent. To illustrate, we draw attention to Fig. 1, depicting various forms of chemisorption for a particle C on an ionic crystal of the type M R composed of the singly-charged ions M+ and R-. It is to be recalled that the presence of a free electron in such a crystal denotes the presence of a neutral state

194

TH. WOLKENSTEIN

M which migrates among the M+ ions of the lattice. A free hole, as a rule, denotes the presence of a neutral state R, which wanders through the lattice from one R- ion to the next R- ion. Figures l a or Id correspond to so-called “weak” bonding. Which of these two cases (a or d) actually takes place depends on the nature of the particle C and the lattice. Figures l b and l c depict the “strong” acceptor bond. These two figures represent two limiting cases, the first of which (Fig. lb) corresponds to a purely homopolar and the second (Fig. lc) to a purely ionic bond. In reality, as a rule, we deal with cases intermediate between Figs. l b and lc. Figures l e and If depict a “strong” donor bond. These figures also correspond to two limiting cases. In reality, we deal, as a rule, with intermediate cases.

--We observe that for the bonds depicted in Figs. l b and le, an atom M or an atom R, to which the chemisorbed particle C is attached, are more weakly bound to the lattice than the normal ions M+ or, respectively, R-. As a result, in some cases we can expect that the molecule CM or CR may evaporate; that is, the particle C upon desorption may carry off with it an atom of the lattice, thereby violating the stoichiometric composition of the crystal. In all cases such adsorption should facilitate surface creep which plays such an important role in the sintering, recrystallization, and disintegration of solids in reaction. This may also explain the well-known influence of adsorption on the surface mobility of the adsorbent atoms. Note further that the electrons or holes taking part in the bonding need not necessarily be drawn from the supply of free electrons or holes. They may also be drawn from the atoms or ions of the lattice itself. For example,

THE ELECTRON THEOBY OF CATALYSIS

195

an M+ ion which serves as an adsorption center (Fig. la) can get an electron by removing it from a neighboring ion R-. A s a result, a hole appears which, breaking its bond with the electron, can begin to migrate through the crystal, thus becoming a free charge carrier. In Fig. Id, an ion Rwhich is an adsorption center may become neutralized; i.e., it may pick up a hole and utilize it to form a “strong” donor bond with the particle C chemisorbed upon it, transferring its electron to a neighboring M+ ion. This electron begins t o wander through the lattice, thus becoming a free charge carrier. We see that the appearance of “strong” forms of chemisorption does not necessarily lead to the depletion of the electron or hole population of the crystal. On the contrary the concentration of the free carriers may be increased in chemisorption. The presence of an electron or a hole gas is therefore not a necessary condition for the formation of “strong)) bonds in chemisorption.

B. EXAMPLES We shall give several examples illustrating different bonding types for a given particle on a given adsorbent. Figure 2 depicts different forms of chemisorption for a Na atom and a C1 atom on the NaCl lattice (6). Figure 2a corresponds to “weak” binding of a Na atom to the lattice. We investigated this type of bond in 1947 (6-8).The bond is effected by the valence electron of the Na atom, which is to a greater or lesser degree drawn into the lattice. In other words, the electron cloud surrounding the positive framework of the Na atom, which in case of the isolated atom was spherically symmetrical, is now deformed and

196

TH. WOLKENSTEIN

somewhat drawn into the lattice. The case may be treated as a one-electron problem if the positive and negative ions of the lattice are regarded in the first approximation as point charges. The wave function of our electron is damped: it falls off inside the crystal as the distance from the adsorption center increases, this center being in this case one of the Na+ ions in the surface layer of the lattice. In the case considered, we have to do with a one-electron bond of the same type as in the molecular ions HZ+ or Naz+. We observe that the chemisorbed Na atom (considered together with its adsorption center) acquires a dipole moment of a purely quantum-mechanical origin; its value may be several orders of magnitude greater than that of the dipole moment induced in physical adsorption. In the case of “weak” chemisorption of a C1 atom depicted in Fig. 2a’, the bonding electron is that drawn from the C1- ion of the lattice, the latter ion serving as the adsorption center. In other words, the bonding is due to a hole being drawn from the C1 atom into the lattice. We have here a bond of the same type as in the molecular ion Cln-. The dipole moment which arises in this case is opposite in direction to that of the preceding case. Figure 2b depicts a “strong” acceptor bond for a Na atom. It is formed from the “weak” bond depicted in Fig. 2a, for example, as a result of the capture and localization of a free electron, that is, as a result of the transformation of a Na+ ion of the lattice serving as an adsorption center, into a neutral Na atom. We obtain a bond of the same type as in the molecules Hz or Naa. This is a typically homopolar twoelectron bond formed by a valence electron of the adsorbed Na atom and an electron of the crystal lattice borrowed from the free electron population. The quantum-mechanical treatment of the problem (2, 8) shows that these two electrons are bound by exchange forces which in the given case are the forces keeping the adsorbed Na atom at the surface and a t the same time holding the free electron of the lattice near the adsorbed atom. Figure 2c corresponds to a “strong” donor bond of a Na atom which is formed from a “weak” bond (see Fig. 2a) as the result of ionization of the adsorbed Na atom, i.e., as the result of its valence electron going over into the free state (the free electron population in the crystal is thus increased by one electron), or, what amounts to the same thing, as the result of the capture of a free hole by an adsorbed Na atom (4-8). In this case, the adsorption bond is of a purely ionic nature: we obtain a quasi-molecule NaC1. Figures 2c’ and 2b’ depict, respectively, a “strong” donor and a “strong” acceptor bond of a C1 atom formed from a “weak” bond (see Fig. 2a’), when a free hole or, respectively, a free electron, is drawn into the bond. In the first case (Fig. 2c’) we have a quasi-molecule Clz with typical homopolar bond, in the second case (Fig. 2b’) a quasi-molecule NaCl with its characteristic ionic bond.

THE ELECTRON THEORY OF CATALYSIS

197

Take another example. Figure 3 depicts two forms of chemisorption of an O2 molecule on ZnO and CuOz crystals which are regarded as purely ionic crystals (this is permissible in the first approximation). We observe that in the ZnO crystal the presence of a free electron denotes the presence of a Zn+ ion among the regular Zn++ ions of the lattice; a free hole denotes the presence of an 0- ion among the 0- ions. In the CuzOcrystal which is composed of Cu+ and 0- ions, a free electron corresponds to a neutral Cu atom, and a free hole corresponds not t o a singly charged 0- ion, but to a doubly charged Cu++ ion.

[o--zrYo--z~+llo--zlr+o--zhq

Icr-cli o--cu+I ~o--cu+o--cu+ I ( h’)

(a’)

FIQ.3

Figures 3a and 3a‘ depict the “weak” bond of an O2molecule with the lattice. It is formed by an electron being drawn from an ion of the lattice to an OZmolecule. Owing to the greater electron affinity of the 0 2 molecule, the electron may be considered completely transferred from the lattice to the molecule; as a result, a molecular ion Oz- is formed and a localized hole appears in the lattice attached to the ion 0,. The entire system (the adsorbed Os molecule adsorption center) acquires a noticeable dipole moment with negative pole directed outward, but remains electrically neutral as a whole. The bond is effected without the participation of a free lattice electron. The transition to a “strong” acceptor bond entails the localization of an electron, or, what amounts to the same thing, the delocalization of a hole. Such a “strong” acceptor bond is depicted in Figs. 3b and 3b’. As another example, consider the adsorption of a H*molecule on an ionic crystal of the type MR. A “weak” bond with the lattice (see Fig. la, in which the symbol C denotes a H2 molecule) can be formed by the two electrons of the Hz molecule, which while remaining paired are somewhat

+

198

TH. WOLKENSTEIN

drawn into the lattice, forming the quasi-molecule (MH2)+. We obtain a two-electron bond of the same type as in the molecular ion Ha+. In this case, there can be no transition to a “strong” bond, for, as can be shown (this question will be discussed in Sec. 111),if a free electron or a free hole is involved in the bond, then the bond between the H atoms in the Hz molecule is broken ; that is, the molecule dissociates. The concept of different forms of chemisorption which differ in the character of the bond between the adsorbed particle and the adsorbent lattice is the first important result of the electron theory. The possibility of different bonding types in chemisorption is due to the ability of the chemisorbed particles t o form bonds to which either free electrons or free holes of the lattice can contribute. In other words, it is due to the ability of the chemisorbed particle to generate a free electron or a free hole and to give them up to the lattice.

111. Radical and Valence-Saturated Forms of Chemisorption A. FREEVALENCIESOF A CATALYST We see that the free electrons and holes of a crystal lattice are important factors in chemisorption and hence in catalysis. Both of them stand out as full and equal participants in the chemical processes involving chemisorbed particles. This is because, in these processes, as was shown in (2, 9-11), the free electrons and holes perform the functions of free valencies capable of breaking the valence bonds in the chemisorbed particles and themselves becoming saturated by these bonds. These functions of the free electrons and holes follow from the very concept of a “free electron” or a “free hole.” We shall illustrate this on the two limiting cases of a purely homopolar and a purely ionic crystal. As a n example of a homopolar crystal, consider a crystal of germanium. In such a crystal each Ge atom, being tetravalent, is surrounded by four nearest neighbors to which it is bound by four valence bonds. Each bond involves two electrons: an electron of the given atom and an electron of its neighbor. Thus, in the germanium lattice all four valence electrons of each atom go to make bonds and cannot participate in conductivity. A free electron or a free hole in such a crystal denotes that there is, respectively, a Ge- ion or n Ge+ ion among the Ge atoms. Such ionic states can migrate through the lattice passing from one Ge atom to another. The Ge- ion is pentavalent; since it is surrounded by four Ge atoms, its fifth valence is unsaturated. The Gef ion is trivalent, so that the valence of one of its four neighbors is unsaturated. Thus, a free electron or a free hole in the germanium lattice may be regarded as free (unsaturated) valencies wandering through the crystal.

THE ELECTRON THEORY OF CATALYSIS

199

As a typical example of an ionic crystal, consider a crystal of NaCI. The Na+ and C1- ions possess closed electron shells and in this sense are analogoues of the zero group atoms. A free electron in a NaCl crystal means that there is a n “extra” electron attached to a Na+ ion outside the closed shell. Such an electron may be regarded as a free positive valence. A hole denotes that one of the C1- ions lacks an electron from its closed shell. Such a hole can therefore be regarded as a free negative valence. As another example, consider a CuzO crystal which we shall treat as an ionic crystal. As already observed, in this case a free electron corresponds to the state Cu and a free hole to the state Cuff-, both of which wander among the normal Cu+ ions of the lattice. In the Cu atom and in the Cu+ and Cuff-ions, the electrons are distributed as follows:

. . . (1s)2(2s)2(2p)6(3s)z(3p)6(3d)10(4s)1 Cu+ . . . (1s)z(2s)2(2p)6(3s)2(3p)6(3d)10

i

Cu

Cu++

(1)

. . . (1s)2(2s)2(2p)6(3s)2(3p)6(3d)g

The Cu+ ion possesses a closed electron shell (valence 0); the Cu atom is characterized by one electron in excess of the closed shell (valence +1), while the Cu++ ion lacks one electron in its closed shell (valence - 1). Thus, in this case, too, a free electron is equivalent to an unsaturated positive valence and a free hole to an unsa,turated negative valence. It should be noted that, besides free electrons and holes, the role of the free valencies in the crystal may be played by the so-called Frenkel excitons. The latter are, roughly speaking, excited atoms or ions of the lattice which can transfer their state of excitation to similar neighboring atoms or ions. As an example, we may take again the CUZOlattice in which a Frenkel exciton (in the same rough model) is represented by an excited Cu+ ion with the following electronic structure: Cu+

. . . ( 1 ~()2~ ~(2p)y3s)* )~ ( 3 p )6(3d)9(4s)

(2)

This differs from the normal structure (1) in that an electron in the Cu+ ion has been transferred from the 3d shell to the 4s shell. In such a state of excitation, the Cu+ ion naturally retains its charge unchanged but acquires a free valence. Free valencies of such an exciton nature may be significant in semiconductors, one component of which is a transition metal possessing an unfilled inner electron shell or a shell that can easily give up an electron. This may, perhaps, explain certain specific catalytic properties of such semiconductors. However, the role of Frenkel excitons in the phenomena of chemisorption and catalysis has been as yet investigated to a very small extent, and in the following we shall not consider free valencies of such an exciton origin.

200

TH. WOLKENSTEIN

The treatment of free electrons and holes as free valencies is very convenient in describing chemical processes on the surface of a semiconductor. The following properties (10, 11) must be attributed to the free valencies of the catalyst in such treatment: 1. Every free valence has a mean lifetime; that is, the valencies can appear and disappear. A crystal continually produces and absorbs free valencies. 2. The free valencies are not localized in the lattice but migrate through the crystal. In other words, as long as we are dealing with an ideal lattice, there is an equal probability of finding a free valence at any point of the crystal. 3. The equilibrium concentration of free valencies in the crystal and on its surface depends not only on the nature of the crystal, but also on external conditions: it increases with a rise in temperature and may be artificially increased or decreased under the influence of external agents (illumination, impurities, etc.). 4. There is a continuous interchange of valencies between the bulk and the surface of the crystal: valencies pass from the surface into the bulk, and vice versa, so that the bulk of the crystal is like a reservoir, absorbing the free valencies of the surface and supplying them back to the surface. 5. The free valencies of a crystal can form pairs, each such pair wandering through the crystal as an entity until it breaks up. Such formations are well known in the theory of the solid state. A pair of opposite valencies in an ionic crystal (electron hole bound by Coulomb interaction) forms what is called a Mott exciton. A pair of like valencies (electron electron or hole hole bound by exchange interactions) forms a so-called doublon. Such formations have recently been investigated ( I d , 13).

+

+

+

B. REACTIVITY OF CHEMISORBED PARTICLES Since the free electrons and holes in a crystal act. respectively, as free positive and negative valencies (we are dealing with crystals with more or less sharply defined ionic bonds), it follows that the “weak” form of chemisorption is that in which the free valencies of the surface play no part, whereas “strong” chemisorption takes place when the free valence of the surface contributes to the bond, this valence being localized and attached to the valence of the adsorbed particle. We have the acceptor or donor form of “strong” chemisorption, depending upon which of the free valencies of the surface (positive or negative) is involved. The participation of a free valence of the surface in chemisorption leads to the transformation of a valence-saturated particle into an ion-radical and, vice versa, to the transformation of a radical into a valence-satuxated electrically charged formation. Thus, among the different coexistent forms

201

THE ELECTRON THEORY OF CATALYSIS

of chemisorption, we must distinguish those in which the chemisorbed particles exist on the surface as radicals or ion-radicals, and those in which the same particles make valence-saturated formations with the surface. Naturally, in radical forms of chemisorption, the chemisorbed particles possess enhanced reactivity, i.e., enhanced ability to form chemical compounds with other chemisorbed particles or with the particles arriving from the gaseous phase. We come to the conclusion that the various forms of chemisorption differ not only in the character and strength of the bond, but also in the reactivity of the chemisorbed particles. This is the second important result of the electron theory. We shall illustrate this by several examples:

nmn

w

W

Figure 4 depicts the different forms of chemisorption for a Na atom by means of the symbolic valence signs. In “weak” bonding the valence electron of the Na atom remains unpaired (see Fig. 2a), and in this sense the free valence of the Na atom may be considered unsaturated. This form Of bond thus represents the radical form of chemisorption, which is symbolically depicted in Fig. 4a. Upon transition to “strong” n- or p-bonding a free electron or, respectively, a free hole of the lattice becomes involved in the bond; the electron becomes localized and coupled to the valence electron of the Na atom (see Fig. 2b) or, respectively, the free hole recombines with the valence electron of the Na atom (see Fig. 2c). In both cases we may consider that the free valence of the Na atom is saturated by the (positive or, respectively, negative) valence of the surface. The mutual saturation of two valencies of the same sign (positive valence of Na atom free positive valence of the surface) leads to the formation of a homopolar bond (Fig. 2b); the mutual saturation of two valencies of opposite sign (positive valence of Na atom free negative valence of the surface) leads to the formation of an ionic bond (Fig. 2c). In the given case, the “strong” n-bond and the “strong” p-bond thus represent valence-saturated forms of chemisorption. They are symbolically depicted in Fig. 4b and, respectively, Fig. 4c. Figure 5 illustrates a “weak” and a “strong” acceptor bond for an 02

+

+

202

TH. WOLKENSTEIN

(a)

(b)

FIQ.5

molecule. In the “weak” bond (Fig. 5a) all the valencies are closed; the 0 2 molecule forms a valence-saturated unit with the surface (compare Fig. 3a or 3a’). In the “strong” bond (Fig. 5b) the chemisorbed 0 2 molecule is an ion-radical (compare with Fig. 3b or 3b’). In this case we have the radical form of chemisorption. Figure 6 illustrates the different forms of chemisorption for a COZmolecule. In the “weak” form of chemisorption the COZ molecule is attached to the surface by two valence bonds, as depicted in Fig. 6a. This is an example of adsorption on a virtual Mott exciton, that is, not on a pre-prepared Mott exciton which, as already observed, represents a pair of free valencies of opposite sign (electron hole) wandering through the crystal as an entity, but on an exciton produced in the very act of adsorption.* As appears from Fig. 6a, this is the valence-saturated and electrically neutral

+

(b)

(0)

(C)

FIQ.6

* The possibility of adsorption on a virtual exciton was indicated by E. L. Nagayev (14) on the simplest example of the adsorption of a one-electron atom. This problem is an example of the many-electron approach in chemisorption theory. Recently, V. L. Bonch-Bruevich and V. B. Glmko (16) have treated adsorption on metal surfaces by the many-electron method.

THE ELECTRON THEORY OF CATALYSIS

203

form of chemisorption. As a result of the electron being delocalized, this form goes over into the “strong” donor form depicted in Fig. 6b; when the hole is delocalixed, we obtain the strong acceptor form depicted in Fig. 6c. Both these forms are the ion-radical ones. We observe, however, that the ion-radicals obtained in these two cases, as can be seen from Figs. 6b and 6c, are essentially different and may cause the chemical reaction to proceed in different directions. Thus, the contribution of the lattice electrons and holes to the chemisorption bonds can be described in the formalism of the valence signs, the latter being but the chemical aspect of the electronic mechanism. We observe that valence signs are frequently used in papers on catalysis (for example, in descriptions of the radical and chain mechanisms in catalysis). The physical meaning of these signs, however, remains hidden ; and their properties, which predetermine the possibility or impossibility of given valence configurations, are completely ignored. We have seen, and this is highly essential, that in speaking of the valencies of a catalyst, we must distinguish two types of valencies (positive or negative) which perform different roles. It is also essential that valencies of like sign on the surface of a catalyst repel one another and thus avoid coming into contact.* This circumstance being taken into consideration, we are forced to regard many valence diagrams figuring in the theoretical papers on catalysis as physically untenable. In conclusion we must stress that, as we have seen (Sec. II,A), it is not necessary that free valencies pre-exist on the surface for valence bond to be formed between a chemisorbed particle and the surface. The free valencies may be produced in the very act of chemisorption and they are always produced in pairs (positive negative).

+

C. DISSOCIATION OF A MOLECULE UPON ADSORPTION It should be noted that particles in the chemisorbed state may differ in nature from the corresponding molecules in the gaseous phase, representing not these molecules themselves, but just parts of them, which lead an independent existence on the surface. In other words, the very act of adsorption may in some cases be accompanied by dissociation of the molecule; this may be considered an experimentally established fact. Such adsorption accompanied by dissociation, requires an activation energy, as was shown by Lennard-Jones (16) on the example of the Hz molecule. The mechanism of such dissociation, which is one of the simplest examples of a heterogeneous reaction has, however, until recently not been investigated. To elucidate this mechanism, the following problem was considered

* Complexes of valencies of like sign can be formed near surface imperfections (see Sec. IX,B).

204

TH. WOLKENSTEIN

(9, 1 1 ) . A molecule A B composed of the two monovalent positive atoms A and B (for example, an HZ molecule) approaches the surface of a semiconductor as depicted in Fig. 7a. We observe that in such a configuration the molecule AB, as can be shown, does not form a “weak” bond with the surface. The author investigated the behavior of a free electron in the semiconductor and the energy of the system as a function of the distance b, which figures in the formulas as a parameter. The problem was treated as a three-electron one (one electron in each of the atoms A and B a free lattice electron).

+

(b)

FIG.7

As the molecule A B approaches the surface of the crystal, the free lattice electron, as was shown, becomes more and more localized near the point which the molecule is approaching (point M in Fig. 7a). A bond arises between the atom B and the surface involving the localized electron and growing stronger and stronger as the molecule AB approaches, whereas the bond between the atoms A and B becomes gradually weaker. As the distance b decreases, the distance a increases, with the result that the atom B becomes attached to the surface by a strong n bond, whereas the atom A becomes free and remains in the gaseous phase (as depicted in Fig. 7b) or becomes attached to the surface by a “weak” bond. The reaction proceeds according to the equation:

AB

-+ eL+

ABeL-tA

+ BeL

and has been shown to entail the surmounting of an energy (“activation”) barrier. The unstable transition state ABeL in which bonds of the type of the Ha molecule are formed corresponds to the peak of this barrier.

THE ELECTRON THEORY OF CATALYSIB

205

This problem is fully analogous to the well-known problem of Slater (l7), who discussed the case of three monovalent atoms A , B, C lying on a straight line and investigated the substitution reaction :

AB

+ C +A + BC

In our problem the role of atom C is played by the crystal lattice considered as a whole. We see that in our case a free lattice electron again plays the part of a free valence. This free valence, as it migrates through the crystal, breaks the valence bond of the molecule AB and becomes saturated by the newly freed valence. The crystal here plays the part of a free radical, and our reaction may be written down as an ordinary reaction involving a free radical :

AB+LA+BL where L denotes the lattice and a dot over a letter denotes a free valence. Suppose now that the chemisorbed molecule AB, composed of two atoms or two atomic groups A and B connected by a simple bond, is in a state of “weak” bonding with the surface. When a free valence of the surface comes into play, the valence bond inside the molecule is broken; that is, the chemisorbed molecule dissociates into two radicals A and B, the valence of one of them becoming free, while that of the other is saturated by the free valence of the surface. Thus, one of the dissociation products is in a state of “weak” and the other in a state of “strong” bonding with the surface. The law of conservation of valencies is satisfied: the free valence of the surface is saturated and reappears as a free valence of the newly produced radical. We observe, however, that a free valence of the surface need not necessarily be involved in the dissociation of the molecule. A molecule may break up upon adsorption without the agency of a free valence of the surface. Consider, for example, the molecule H20, in which the H atom and the OH group are connected by a single slightly polarized bond (with the positive pole on the H atom and the negative pole on the OH group). Suppose that such a molecule approaches the surface of an ionic crystal as depicted in Fig. 8a. If the adsolbent has an appropriate crystallographic structure, then as the molecule approaches the surface, the H-OH bond will become more and more polarized, with the result that the molecule may be broken up by the field of the lattice into two ions: H+ and OH(see Fig. 8a). Each of the dissociation products will be attached to the surface by a “strong” bond (donor or, respectively, acceptor), and these bonds need not necessarily be purely ionic. The degree of ionic nature will be determined by the character of the distribution of the electron (which belongs to the OH group) and of the hole (belonging to the H atom) between

206

TH. WOLKENSTEIN

the adsorbed particle and the corresponding adsorption center (see Sec. I, Fig. 1). In Fig. 8b this mechanism of dissociation is depicted by means of the valence signs. The free valence of the surface does not participate here. The breaking of the valence bond in the molecule is due to the production of surface valencies in the very act of adsorption.

Finally, the dissociation of the molecule upon adsorption may also proceed in such a manner that both dissociation products will form not “strong” but “weak” chemisorption bonds. Take, for example, the 0 2 molecule, in which the double valence bond between the oxygen atoms may

THE ELECTRON THEORY OF CATALYSIS

207

be broken as a result of two electrons from two negative ions of the lattice going over to the 0 2 molecule and two localized holes being formed (as symbolically depicted in Fig. 9). The oxygen atoms formed upon dissociation of the O2 molecule are attached t o the surface by a “weak” bond and may be considered as entirely inactive or slightly reactive (valencesaturated form of chemisorption) . The subsequent delocalization of the hole or, vice versa, localization of the free electron, which recombines with the hole, brings the oxygen atom into a reactive state (radical form of chemisorption). Whether the 02 molecule will dissociate upon adsorption according to the above mechanism (Fig. 9) or will become attached to the surface as an entity without dissociating (Figs. 3 and 5 ) will depend, of course, on the nature and the crystallographic structure of the adsorbent. Here the role of the geometrical factors in chemisorption is especially vividly expressed. These factors have been analyzed in detail by A. A. Balandin and co-workers in their papers (see, for example, ref. 18) on the multiplet theory of catalysis, in which they show their prime importance in a number of cases of the catalytic process. The electronic mechanism of chemisorption does not at all exclude these factors, but just stresses their role; it retains the geometrical schemes of the multiplet theory but gives them physical content.

IV. Electron Transitions in Chemisorption A. TRANSITIONS BETWEEN DIFFERENT FORMS OF CHEMISORPTION A third important result of the electron theory can be formulated as follows: one form of chemisorption may change into another; in other words, a chemisorbed particle while remaining in the adsorbed state may change the character of its bonding with the surface: it may pass from a state with one type of bonding to a state with another type of bonding. Such transitions denote that a free electron or a free hole is localized or delocalized on the adsorbed particle (or near it). This has been illustrated in several of the preceding examples (Figs. 4,5, and 6 ) . It is convenient to describe such transitions in terms of the energy band scheme of a semiconductor depicted in Fig. 10. The y axis in Fig. 10 is parallel to the adsorbing surface of the semiconductor (assumed to be plane). There are two energy bands (a valence band and a conduction band, hatched in the figure) separated by a forbidden region of width u.As shown in refs. 2-4, a foreign particle C , chemisorbed on the surface and “weakly” bound to it, has its counterpart in the energy band scheme of the crystal. A particle possessing affinity for a free electron is depicted by an acceptor level (level A in Fig. 10);a particle possessing affinity for a hole corresponds to a donor level (level D in Fig. 10). I n the general case, when a chemisorbed

208

TH. WOLKENSTEIN

particle “weakly” bound to the surface possesses affinity both for a free electron and a free hole, it is simultaneously depicted by two levels: an acceptor level and a donor level. The position of levels A and D in the forbidden region depends on the nature of the lattice and the adsorbed particle C (3,4, 10). Electron transitions can take place between the valence band and the conduction band, as well as between the energy bands and local levels depicted in Fig. 10. In the case of a semiconductor and not too low temperature, these transitions are of thermal origin. Because of them an electron may pass to the conduction band or to an acceptor level A , or it may be removed from a donor level D. E

FIQ. 10

The appearance of an electron on a level A denotes the transition of the chemisorbed particle C from a state of “weak” to a state of “strong” acceptor bonding with the surface. This may be effected in two ways, as is seen from Fig. 10: by a free electron of the conduction band falling onto level A or by an electron of the valence band being thrown onto level A . The removal of an electron from the level D denotes the transition of the chemisorbed particle C from a state of “weak” to a state of “strong” donor bonding. This may also be effected in two ways: by the recombination of an electron of level D with a free hole wandering in the valence band or by the ejection of this electron from level D into the conduction band. These electron transitions, depicted in Fig. 10 by vertical arrows in bold type (transitions 1, 2, 3, 4, and 5 ) may be written down in the notation of Sec. I,A as follows:

1) 2) 3) 4)

5)

.u CL + eL ~ r CeL ? . . . vC L + p L e C p L . . . w+ CeL -l- pL s CL . . . v+ C p L + e L e C L . . . weL+pLaL..

!

(3)

THE ELECTBON THEORY OF CATALYSIS

209

In formulas (3) the arrows pointing from left to right correspond to exothermal transitions and the arrows directed from right to left to endothermal transition, that is, to the transitions depicted in Fig. 10 by arrows pointing, respectively, upwards and downwards. On the right-hand side of Equations (3) are denoted the energies released or spent in the corresponding transitions (Fig. 10). In some particular cases we may have u+ > u or w- > u (Fig. lo), which denotes that the given particle does not form an acceptor or, respectively, donor bond with the given adsorbent. Transition No. 1 represents the recombination of a free electron with a free hole, i.e., the annihilation of two valencies of opposite sign. The reverse transition is the formation of a pair: free electron free hole. This denotes the formation of two free valencies of opposite sign. Transitions No. 2, 3, 4, and 5 denote transitions between various forms of chemisorption, i.e., transitions of the chemisorbed particle from a state of “weak” to a state of “strong” bonding with the surface, and vice versa. We see that the transition from “weak” to “strong” bonding may be accompanied by the disappearance of a free valence of the catalyst (transitions No. 2 and No. 3); but it may also take place without the participation of a free valence, leading not to the disappearance but, on the contrary, to the appearance of a new free valence on the surface of the catalyst (transitions No. 4 and No. 5). In the first case, the “strengthening” of the bond leads to a reduction in the energy of the pre-excited system, while in the second case, on the contrary, it denotes the excitation of the system. We see that the participation of the electrons and holes of the semiconductor in the chemisorption processes may be described in the lang’uage of the energy band scheme, which thus represents yet another (energy) aspect of the electron mechanism of chemisorption. The electron transitions depicted in Fig. 10 correspond to transitions of the system between states characterized by different adsorption curves. Such adsorption curves which represent the energy of the system E as a function of the distance T between the particle C and the adsorbent surface for the case when particle C is a monovalent atom are schematically depicted in Fig. l l (3,4). The curve 1 represents adsorption on an unexcited crystal, i.e., on a crystal that does not contain free electrons and holes. Curve 1’ represents curve 1 shifted a distance u upwards parallel to itself; that is, it corresponds to adsorption on an excited crystal containing a free electron (in the conduction band) and a free hole (in the valence band). Curves p and n represent the adsorption curves for, respectively, “strong” donor, and “strong” acceptor chemisorption (curve n can lie either below or above curve p ) . The minima of curves 1, n,p , 1’ correspond to the states CL, CeL pL, CpL eL, CL eL pL. An ascent on the curves of Fig. 11 to the right of the minimum denotes

+

+

+

+ +

210

TH. WOLKENSTEIN

FIG.11 the desorption of the atom C. This process of desorption for the states I , n, p , and 1' may be depicted by the following equations: 1)

CL+C+L..

. qo

CeL+pL+C+eL+pL . PI CpL+eL+C+eL+pL.. 1') C L + e L + p L + C + e L + p L . .

n)

. . q-

. q+

. qo

]

(4)

On the right-hand side, we have the energies spent in the respective processes where, evidently (see Figs. 10 and 11) :

+ w+ = qo + v-

q+ = qo

q-

(5)

The product of desorption in all the cases considered is a neutral particle C. As T increases, i.e., as particle C moves away from the surface, the level A in Fig. 10 can be shown (2) to approach the conduction band and to merge with it in the limit r = ; at the same time the level D in Fig. 10 descends to the valence band and merges with it at r = m . In other words, an electron localized on an acceptor level A (making an n bond) or a hole localized on a donor level D (making a p bond) becomes delocalized as r increases and in the limit (at r = a) returns to the conduction band or, respectively, to the valence band, that is, becomes again one of the free electrons or holes. Between the states 1, n, p , 1' in Fig. 11 the following transitions are possible: 1' e 1, I' $ n, 1' p , n $ 1, p $ 1 . These are the transitions depicted in Fig. 10 by the vertical arrows in bold type 1, 2, 3, 4,and 5, respectively [see also (3)]. We observe that these electron transitions [reaction (3)] are Q)

THE ELECTRON THEORY OF CATALYSIS

211

characterized by heats of reaction of the Same order of magnitude as the heats of adsorption [reactions (4)]: in the case of semiconductors, this is of the order of tenths of an electron-volt. Hence, in the study of chemisorption processes, the electron transition reactions (3) which take place simultaneously with the reactions of adsorption and desorption cannot be ignored.

B. EQUILIBRIUM BETWEEN DIFFERENT FORMSOF CHEMISORPTION It should be noted that in a number of theoretical papers on chemisorption by various authors known under the general heading of the boundarylayer theory of adsorption (see, for example, refs. 19-23> the removal of an electron from an acceptor level A or of a hole from a donor level D, which in the energy spectrum of the crystal (Fig. 10) denote a chemisorbed particle are considered as the desorption of this particle, that is, as an act denoting the disappearance of the level itself. Such a treatment of an acceptor level which exists only as long as it is occupied by an electron, or of a donor level which always lacks its electron, makes the very concept of a level capable of accepting and giving up an electron devoid of any meaning. The removal of an electron from an acceptor level or a hole from a donor level denotes, as we have seen, not the desorption of the chemisorbed particle but merely its transition from a state of “strong” to a state of “weak” bonding with the surface. The neglect of this “weak” form of chemisorption (i.e., electrically neutral form) which is characteristic of all papers on the boundary-layer theory of adsorption makes it quite impossible to depict the chemisorbed particle in terms of an energy level, i.e., to apply the energy band scheme depicted in Fig. 10 and used in these papers.* If the direct and reverse electron transitions (3) are in equilibrium (case when electron equilibrium a t the surface is established), then a certain portion of the total number of acceptor levels A will be occupied by electrons, while a certain portion of the total number of donor levels D will be unoccupied; that is, out of the total number N of the particles of a given kind chemisorbed on unit surface, a certain fraction of particles will be in a state of “weak,” “strong” acceptor, and “strong” donor bonding with the surface. Let us denote, respectively, by No, N-, N+ the number of particles per unit surface in each of these states and introduce the notation:

where, evidently,

* When there is nol‘weak”bonding at all,one returns within the frameof the boundarylayer theory. In this case, however, the chemtsorbed particles do not produce any levels in the crystal energy spectrum.

212

TH. WOLKENSTEIN go

+ 7- +

g+ = 1

The quantities go, 7-, q+ characterize the equilibrium relative amounts of the different forms of chemisorption, or, in other words, the probabilities that a chemisorbed particle will be in a given state (characterized by a given type of bonding to the surface), or, otherwise, the mean relative lifetimes af the chemisorbed particle in the respective states. According to Fermi statistics, we have (24):

N-

1

+ N- - 1 + exp I(€.- v-)/kT] N+ 1 N o + N + - 1 + exp - w+)/k~] No

[(en+

where 6,- and e,+ are, respectively, the distances from the Fermi level (the electrochemical potential) F to the conduction band and to the valence band (Fig. 12a).* Hence, we obtain

” = 1 + 2 exp (-Au/kT)

1 cosh [(c,+

exp [- (AulkT) 4-

(en+

exp I- (Au/kT) -

(c,+

- u+)/kT]

- u+)/kT] - u+)/kT] - u+)/kT]

g- =

1

+ 2 exp (-Au/kT) cosh [(c.+

g+ =

1

+ 2 exp ( - A u / k T ) cosh

[(en+

(7)

- u+)/kT]

The meaning of the notation adopted is apparent from Fig. 12a. Note that Equations (7) may be derived as well from the law of mass action for reactions (3) (4, 24). The dependence of go, g-, g+ on e,+, according to (7) is schematically depicted in Fig. 12b. We see that as the Fermi level moves upward in Fig. 12b (i.e., as it moves away from the valence band and approaches the con-

* Strictly speaking, these equations should abo contain pre-exponential factors related to the degeneracy ratios of the states considered (966). This is,however, irrelevant for what follows.

THE ELECTRON THEOBY OF CATALYSIS

213

duction band) q- increases monotonically, while q+ decreases monotonically, i.e., the relative number of particles making acceptor bonding to the surface increases while the number of particles making donor bonding decreases. On the other hand, the quantity qo characterizing the relative amount of "weak" chemisorption passes through a maximum as the Fermi level is shifted monotonically. If the Fermi level FF lies deep enough below the level CC (depicted by the horizontal dotted line in Fig. 12), then q+ >> q-; i.e., practically all the chemisorbed particles play the part of donors. If, on the contrary, the Fermi level lies high enough above the level CC, then 1- >> q+; i.e., practically all the chemisorbed particles act as acceptors. We see that once electron equilibrium is established, the relative amounts of the different forms of chemisorption on the surface, and hence the reactivity of the chemisorbed particles, are uniquely determined by the position of the Feimi level. This may be considered as the fourth important result of the electron theory. Suppose now that in addition to electron equilibrium on the surface we also have adsorption equilibrium between the surface and the gaseous phase. The condition of adsorption equilibrium (for the sake of simplicity we limit ourselves to the region of small coverage) has the form

aP = N'e-"/kT

+ N-e+-/kT + N+e-+/kT,

(8)

where P is the pressure and a is a coeficient which need not interest ua further. (We suppose the frequency factors to be of the same order of magnitude for all three types of bonding.) On the basis of (6) and ( 5 ) , Equations (8) may be rewritten as follows:

or according to (7)

We see that the adsorptivity of the surface with respect to molecules of a given kind, i.e., the total number of molecules of this kind N bound t o unit surface under conditions of equilibrium with the gaseous phase (i.e.,a t given pressure P and temperature T)depends on the position of the Fermi level. By shifting the Fermi level (other conditions being fixed), one can vary the adsorptivity of the surface. If the electron and hole gases on the semiconductor surface are nondegenerate, then (by definition) e-*.-lkT

<< 1

and

e-t.+IkT

<< 1

214

TH. WOLKENSTEIN

and we have

aP or, according to (7), N = b{ 1

= qoNe+lkT

+ 2e-AulkTcosh [(e,+

- u)/kT])P

(9)

where b = ae

q’lkT

In this case, as we see, equilibrium with the gaseous phase is maintained entirely by the “weak” form of chemisorption. In other words, only “weakly” bound particles are desorbed, whereas “strongly” bound ones play practically no part in exchange with the gaseous phase. To avoid misunderstanding, we note that Equation (9) does not represent the Henry isotherm, as might seem at first sight, since the quantity en+ in (9), as will be seen from the following (see Sec. V,A), is itself a function of N. It should be recalled that according to the boundary-layer theory of adsorption, which deals with only one form of chemisorption (“strong” donor or “strong” acceptor form), the adsorptivity of the surface is negligibly small. Within the framework of this theory, the maximum possible coverage, according to the calculations of Weisz (26)is of the order of 1%. This limitation is the result of the neglect of “weak” bonding which, as already observed, is characteristic of the boundary-layer theory. When the “weak” (i.e., electrically neutral) form of chemisorption is taken into consideration, this limitation disappears. The existence of the ‘(strong” form of chemisorption on the surface, that is, of the form in which a lattice electron or hole is localized near the chemisorbed particle, leads, among other things, to the appearance of a charge on the semiconductor surface. Denoting by u the surface electric charge density due to chemisorption we obtain, according to (7) and (9), u =

q(N+ - N-) =

q(q+

- q-)N

= 2qbe-AUlkT sinh

€+.

- u+ . P

kT

(10)

where q is the absolute magnitude of the electron charge. We see that the degree and the character of charging, i.e., the magnitude and sign of the surface charge arising in chemisorption, depend not only on the nature of the chemisorbed particles and the degree of surface coverage, but also on the position of the Fermi level, i.e., on the state of the entire system as a whole. The dependence of u on E,+, according to (lo), is depicted in Fig. 12c. We see that a t e.+ < u+ the surface is charged positively and at ei+ > u+ negatively, while at en+ = u+, when the acceptor and donor types of bonding are equally represented, the surface remains electrically neutral despite the presence of chemisorbed particles on it.

THE ELECTRON THEORY OF CATALYSIS

215

V. Catalytic Activity of a Semiconductor A. RADICALMECHANISMS OF HETEROGENEOUS REACTIONS As we have seen, the participation of the free electrons and holes of the catalyst in chemisorption bonds results in the chemisorbed particle spending a part of its lifetime on the surface in a radical state. Thus, the very fact that a molecule goes over from the gaseous phase to the chemisorbed state leads to an incuease in its reactivity. The radicals and ion-radicals which appear on the surface in the act of chemisorption provide the radical mechanism of heterogeneous reactions. Any heterogeneous reaction may be regarded as proceeding by a radical mechanism. This does not, of course, mean that nonradical mechanisms a1e excluded in heterogeneous catalysis. However, when radical or ionradical forms appear on the surface in sufficient concentrations (and they do appear), the leading role in the heterogeneous catalytic process devolves naturally upon them. We shall consider different types of heterogeneous reactions and their possible radical mechanisms (10, 27). Consider a reaction between two molecules A B and CD, where A , B, C , D denote the separate atoms or atomic groups. 1. Let A and B, and also C and D, be connected by single bonds. Consider the exchange reaction A B -l- C D - i AC BD

+

in the course of which two single bonds are broken and two others formed. An example is the reaction of chlorination of ethane: CzHa

+ Cla

+ CaHiCl

+ HCl

which takes place, for example, on the catalyst ZnCl2. Figure 13 shows a possible radical mechanism of the reaction which proceeds by way of the dissociation of the two reacting molecules on a free valence of the surface. This is an example of a chain mechanism, the chain being sustained by the free valencies of the catalyst. 2. Suppose now that one of the reacting molecules, CD, for example, contains a double bond, whereas A and B in molecule A B are connected by a single bond. Consider the reaction.

AB

+ CD + ACDB

A simple example is the reaction of hydrogenation of ethylene: CZH4

which takes place on MoOl, ZnO

+ Hn + CZHE

+ Cr203,and other catalysts. Figure 14

216

TH. WOLKENSTEIN

( c ) CjH3pLtCleL * ClHSCI+L

(d) ClL + HeL

FIG.13

-

HCI + i L

FIG.14 depicts a possible radical (chain) mechanism of this reaction which proceeds with the formation of surface radicals. A slightly different chain mechanism of heterogeneous hydrogenation (also possible in the frame of the electron theory) was discussed by Thon and Taylor (68). Other examples of reactions of this type are the reactions of addition of hydrogen-halides to olefins, for example, C2HI

+ HC1+

CnHsCl

3. In a similar manner may proceed reactions in which the number of single bonds is increased, as a result not of the breaking of a double bond, but of a valency change of one of the atoms. Thus, for example, the mechanism of the reaction

217

THE ELECTRON THEORY OF CATALYSIS

CO

+ Hi0 + HCOOH

taking place on.the surface of the crystals CuCls, CuJs, NaBr and others may be represented by a similar scheme (Fig. 15). 4. Consider finally the case when both molecules, A D and CD,contain double bonds. Consider the reaction

AB

-+ CD -+ ABCD

which leads t o the formation of a cyclic compound. As an example we can take the reactions of diene synthesis: CH:-CHi (CHP.=CH-CH=CH:)

+ (CH-CHZ)

/

\

\

/

CHi

CH:

-i

CH=CH

(cl COOH pL + HL * HCOOH+ bL

(b) COpL + H20-c COOHpL + HL

FIQ.16

which, however, proceed sufficiently easily in a homogeneous case as well (without chains). On the surface of a catalyst they could take place according to a chain mechanism as, for example, in Fig. 16. It should be noted that the radical mechanisms for a number of reactions given here (Figs. 13 to 16) should be regarded only as theoretical possibilities. In general, a given reaction may proceed by different radical mechsnisms depending upon which bonds of the reacting molecules are broken in the course of the reaction and in what sequence this takes place. The above mechanisms serve merely to illustrate how a complex reaction may break up on the surface into consecutive elementary acts, each of which involves the breaking of one and only one bond in a molecule, and proceeds with the participation of a surface radical. The role of the catalyst consists in producing such surface radicals. They

218

TH. WOLKENSTEIN

appear at the expense of the free valencies of the catalyst existing on the surface on arising there in the course of the reaction. Note that the supply of free valencies existing on the surface is extremely slowly used up in the course of the reaction, since these valencies are brought to the surface from the bulk of the semiconductor, which represents a practically inexhaustible reservoir of electrons and holes. The flow of valencies from the bulk to the surface is limited only by the surface charge arising in chemisorption, which at a given critical magnitude prevents the further access of free valencies to the surface. (a)

FIG.16

The catalyst thus acts as a sort of “polyradical” influencing the course of the reaction in the same manner in which the introduction of free radicals into a homogeneous medium affects the course of a homogeneous reaction. In both cases, the reaction is accelerated because of the participation of the free valencies. In the case of heterogeneous catalysis, these free valencies are introduced by the catalyst itself. In the final account, it is they who sustain and regulate the process.

B. ACCEPTOR AND DONOR REACTIONS Any given reaction does not involve all the particles of a given kind chemisorbed on the surface, but only those in a reactive state. In other

THE ELECTRON THEORY OF CATALYSIS

219

words, among the different forms of chemisorption coexisting in equilibrium with one another, we must distinguish active and inactive forms with respect to the given reaction. The reaction rate for a given coverage, other conditions being equal, will evidently be determined by the relative amount of the active forms on the surface. Hence, the expression for the reaction rates will contain the magnitudes to,q-, q+ and hence the Fermi level. The reaction rate will therefore depend on the position of this level in the energy spectrum of the crystal. We shall illustrate this general result by several concrete examples.

(01 1 C2HsOH+ L Z= CZHsOeL+ HpL

(b) CzHsOeL+HL*

C$l4OeL+

H2

FIQ.17

As a first example, consider the experimentally well-known reaction of dissociation of ethyl alcohol which, generally speaking, proceeds along the two paths CHaCHO Ha . . dehydrogenation

+

.

/*

C2HsOH I

C2H4

+ H20 . . . dehydration

Let us assume that the reaction proceeds by the mechanism depicted in Fig. 17 (dehydrogenation) or in Fig. 18 (dehydration). In both cases, the reaction consists of three stages: (a) adsorption of an alcohol molecule, (b) a surface reaction, (c) desorption of the reaction products. The reaction path (dehydrogenation or dehydration) is determined in this mechanism at the very first stage and depends on what bond is broken

220

TH. WOLKENSTEIN

in adsorption: the 0-H bond (Fig. 17) or the C-OH bond (Fig. 18); this in turn depends on the nature of the catalyst. In general, both may occur on the same catalyst; in this case, the relative activity of the catalyst for dehydrogenation and dehydration will depend, as we shall see, on the lowering of the Fermi level, varying as this level is shifted. We observe that in the alcohol molecule the 0-H and C-OH bonds are polarized, the center of gravity of the electron cloud in the former case being displaced towards the 0 atom and in the latter case towards the OH group. Hence, when these bonds are broken by the field of the lattice (dissociation at adsorption, see Sec. II1,C) , electrically charged formations will arise on the surface, as depicted in the right-hand side of Fig. 17a and, respectively, Fig. 18a.

(a) ClHsOH + L G= C&pL + OHeL

18

Neglecting adsorption of the reaction products and the formation of by-products which may appear in the given reaction, and denoting for the sake of brevity A = CHaCHO, E = CtHI, R = CHsCHZO, Q = CHaCI-IZ we obtain (I) In the case of dehydrogenation (Fig. 17):

or, in equilibrium:

THE ELECTBON THEORY OF CATALYSIS

+

/31N~-Nn+ Y ~ N R - N H + YINR-NHO= &NAO = g A =

22 1 (11)

where 9.4 is the reaction rate (the appearance of acetaldehyde in the gaseous phase), P the vapor pressure of the alcohol, and N R , N H ,N A the surface concentrations of the corresponding molecules, the superscripts denoting, as formerly (Sec. IV,B), the type of bond the chemisorbed particle makes with the surface. (11) I n the case of dehydration (Fig. 18):

or, in equilibrium :

where BE is the reaction rate (desorption of ethylene). From Equations (11) we obtain

Similarly, from Equation (12) we obtain

where, according to (7) (seealso Fig. 12a)

The dependence of the reaction rates 94. and gE on the position of the Fermi level, as given by Equations (13), (14), and (15), is schematically depicted in Figs. 19a and 19b, respectively. We see that the lowering of the Fermi level retards dehydrogenation and accelerates dehydration. This gives us a key to the regulation of catalyst selectivity. Factors which bring down the Fermi level (for example, an acceptor impurity introduced into

222

TH. WOLKENSTEIN

the crystal, see Sec. VI1,B) poison the reaction of dehydrogenation and promote the reaction of dehydration. Factors which raise the Fermi level (for example, a donor impurity) have the opposite effect. This is in agreement with the experimental data (see, for example, 29). The dehydrogenation and the dchydration of alcohol are examples of reactions of two opposite classes. One of these classes includes reactions which proceed the faster the higher the Fermi level (other conditions being equal). These are reactions accelcrated by electrons. We shall call them acceptor, or n-type, reactioiis. The other class includes reactions whose rate, on the contrary, is the greater the lower the Fernii level. We shall call them donor, or p-type, reactions. These are reactions accelerated by holes. The dehydrogenation of alcohol, as we have seen, is an acceptor reaction, while the dehydration of alcohol, on the contrary, is a donor reaction. This result is in agreement with Garner’s opinion (SO).

We observe that not only different reactions, but also the different stages of a given heterogeneous reaction may belong to different classes. An acceptor stage may be followed by a donor stage, and vice versa. This can be illustrated by the reaction of oxidation of CO. This reaction which takes place both on n-type (for example, on ZnO) and on p-type (for example, NiO) semiconductors has been thoroughly studied by numerous authors. (A summary is given, for example, in the paper by Takaishi 31 and in the book by Germain, 32.) It should be noted that the results of different authors often disagree with one another. (Compare, for example, the results of Schwab and Block, 33, an electronic interpretation of which was attempted by Hauffe and Schlosser, 34, with the results of Parravano, 35, and Keyer et al., 36.) We shall consider one of the possible mechanisms of this reaction. We assume that the surface of the catalyst is saturated by chemisorbed atomic oxygen (so that its concentration on the surface, N o , does not depend on the

223

T H E ELECTRON THEORY OF CATALYSIS

lC0 1

FIG.20

pressure of 0,) and that it is these chemisorbed oxygen atoms which in the ion-radical state serve as adsorption centers for the CO molecules. Then, upon adsorption of the CO molecules surface ion-radicals COZ- are formed as intermediate compounds; these, after being neutralized, desorb as C02 molecules, as depicted in Fig. 20 (see Sec. III,B and Fig. 6 ) . Neglecting adsorption of the C02 molecules and assuming that the different forms of chemisorption of C02 are in equilibrium (case when electron equilibrium is established), we have

or a t dNcoa/dt = 0, aNo-Pco

- BNco,-

=

~NcolO= g

(16)

where g is the reaction rate (rate of desorption of CO,). From (16) we obtain

if YNCO~O >> BNco,-, i.e.,

= ">> 7B tlcoz

(17a)

2!24

TH. WOLKENSTEIN

where, evidently, Equation (17a) corresponds to the case when the reaction is limited by the adsorption of CO, and Equation (17b) to the case when the limiting stage is the desorption of COz. Figure 21 shows schematically the reaction rate g as a function of the position of the Fermi level e,+, as given by Equations (17a,b) and (7). As the Fermi level is shifted upwards, the reaction is accelerated, the reaction rate becoming a maximum at a sufficiently high position of the Fermi level; with its further rise the reaction becomes retarded. In the region denoted by a in Fig. 21, the reaction is limited by the adsorption of CO (acceptor stage) and in the region b by the desorption of COz (donor stage).

FIQ.21

We see that the reaction rate (and, hence, the catalytic activity of the semiconductor with respect to the given reaction) is determined (other conditions being equal) by the position of the Fermi level on the surface of the semiconductor. The position of the Fermi level determines not only the reaction rate at given partial pressures, but also the reaction rate a t given surface coverages. (In the first case the catalytic activity of the .semiconductor depends on its adsorptivity with respect to the reacting gases; in the second case the catalytic activity and adsorptivity may be regarded as two independent characteristics of the semiconductor.) This is the fifth important result of the electron theory. The role of the Fermi level as a regulator of catalytic activity was first indicated by us in 1950 (S?').This problem was later considered by Boudart (58) and quite recently by Hauffe (54, 39).

VI. Interaction of the Surface with the Bulk of the Semiconductor A. RELATION BETWEEN SURFACE AND BULKPROPERTIES We have seen that all the principal chemisorptive and catalytic properties of the surface are determined by the position of the Fermi level on the surface of t.he catalyst. The Fernii level determines (see Secs. IV,B and V,B) :

THE ELECTBON THEORY OF CATALYSIS

225

1. The chemisorptivity of the surface, that is, the total number of chemisorbed particles on the surface in equilibrium with the gaseous phase a t a given pressure and a given temperature. 2. The magnitude and sign of the surface charge for a given coverage of chemisorbed particles. 3. The relative amounts of the different forms of chemisorption on the surface which are distinguished by the character of the bonds between the chemisorbed particlw and the surface. 4. The reactivity of the chemisorbed particles, i.e., the probability of their being in radical or valence-saturated states. 5. The catalytic activity of the surface for the given reaction. 6. The selectivity of the catalyst for two (or more) simultaneous reactions. The Fermi level thus acts as a regulator of the chemisorptive and catalytic properties of the surface. It provides the key to the regulation of the catalytic activity of the catalyst. Note that the position of the Fermi level uniquely determines the concentration of the electron and hole gases on the surface of the crystal. This explains the physical significance of the part played by the Fermi level in the phenomena of chemisorption and catalysis, and at the same time establishes a characteristic correlation between the adsorptivity and catalytic activity of the surface, on the one hand, and the surface concentration of free electrons and holes on the other. What are the factors determining the position of the Fermi level on the surface of the crystal? What agents acting on the crystal can change the position of this level? To find the answer to these questions, let us first consider a certain consequence of the very fact of the existence of the “strong” form of chemisorption, i.e., the form in which the chemisorbed particle attaches to itself (or near itself) a free electron or a free hole of the crystal lattice. A consequence of this, as we have seen (Sec. IV,B), is the appearance of a charge on the semiconductor surface in chemisorption. Now, a consequence of the surface charge is the appearance of a space charge in the surface layer of the semiconductor, opposite in sign to the surface charge and compensating it, This causes a bending of the energy bands near the semiconductor surface. Such bent bands are depicted in Fig. 22. Figure 22a corresponds to a negative surface charge, Fig. 22b to a positive charge, and Fig. 22c to an electrically neutral surface. The z axis in Fig. 22 is directed into the crystal perpendicular to the adsorbing surface which coincides with the surface ar = 0. The distance 1 in Figs. 22a and 22b, at which the bending of the bands may be considered significant (in comparison with kT),is called the “screening length.”

226

TH. WOLKENSTEIN

Once electronic equilibrium is established, the surface and the volume of the semiconductor have a common Fermi level, i.e., the same electrochemical potential (depicted by the horizontal line FF in Fig. 22). However, owing to the bending of the bands the position of the Fermi level in the energy spectrum of the crystal (its position relative to the energy bands) will, generally speaking, depend on the distance from the surface. We shall characterize the position of the Fermi level by its distance from the top of the valence band, denoted by c+. Evidently, e+ = e+(x). We introduce the notation e*+ = e+(O) ey+

Note that the condition E

e+

= e+( a)

= e.+ is practically satisfied already a t

E

E

t

t

x=o

X I 0

x

> 1.

X

x=o (a 1

(b)

(C)

FIQ.22

Thus, the position of the Fermi level on the surface of the crystal is displaced with respect to its position in the depth of the crystal by an amount Ae+ = eu+

- c,+

(18)

which characterizes the degree of bending of the bands, or, in other words, the potential of the surface relative to the bulk. The magnitude e,+ which determines the chemisorptive and catalytic properties of the surface depends on the magnitude cy+; the latter is determined by the nature of the crystal and in turn determines its numerous bulk properties. The form of the relation between e.+ and e,+ can be obtained from the condition of electrical neutrality of the crystal as a whole: u

+ 1' p ( z ) dx = 0

(19)

227

THE ELECTRON THEORY OF CATALYSIS

u being the surface charge density and p(x) the space-charge density in the x plane. It can be shown (40) [see also (lo)] that u = a(P,T; t*+)

im(&1; p(z) dx =

p ( e + ) de+)’

=

R(T;e,+,

c.+)

(20)

where x is the permittivity of the crystal; thus, from Equation (19), on the basis of (20), we can determine (in principle, a t any rate) el+ as an explicit function of eo+: e,+ = f ( P , T ;€,+).

(21)

Inasmuch as the surface properties (e.g., the catalytic activity) are determined by e,+ and the bulk properties (e.g., the electrical conductivity) by e,+, Equation (21) establishes the correlation between these two groups of properties. el+ is determined by Equation (21) when (other conditions being equal) t.+ is given ; the latter is determined by the equation p(ew+) =

0

(22)

which represents the condition of electrical neutrality in the bulk of the crystal (at z 1). [Condition (22) involves the assumption that the dimensions of the crystal are greater than the “screening length.” We shall use this assumption.] It can be shown in a most general way (41) [without solving Equation (19) with respect to e.+] that the condition

>

de,+

ds+>O is always valid; i.e., when the Fermi level eW+ inside the crystal shifts up or down in Fig. 22, the Fermi level on the surface, generally speaking, is also displaced in the same direction. (The shift of e,+ may be effected, for example, by introducing the required type of impurity.) This may be regarded as the sixth important result of the theory. We shall consider a number of consequences of this result in Secs. VII and VIII. Note in conclusion that by substituting Equation (21) into (9), one obtains the equation of an isotherm. The isotherm thus obtained is definitely of a non-Langmuir type. Kogan and Sandomirsky have shown (40) that in some particular cases it goes over into a logarithmic isotherm, a Freundlich isotherm, and other types. This violation of the Langmuir relations for a homogeneous (even ideal) surface may be regarded as the first consequence of the theory. In this case the non-Langmuir types of isotherm are due to the proper-

228

TH. WOLKENSTEIN

ties of a given adsorption center (the character of its bonding with the chemisorbed particle) being changed during the lifetime of the particle on the surface. In the final account, they are due to long-range Coulomb interaction between the chemisorbed particles in a state of “strong” bonding with the surface. This interaction is automatically taken account of in our formulation of the problem.

B. “QUASI-ISOLATED” SURFACE

It can be shown (41, 42) that under certain conditions (to be formulated later) the surface of a semiconductor possesses the following property: the position of the Fermi level on the surface of the crystal e,+ depends but weakly (practically does not depend a t all) on its position inside the crystal t.+. This denotes that when the Fermi level inside the crystal is displaced, its position on the surface remains practically unchanged (changes by a small amount compared with kT). E

X‘ ‘

E

‘

L

X

A surface possessing such a property will be called a “quasi-isolated” surface. This is the case when the bulk ceases to influence the surface and, hence, the relation between the bulk and the surface properties of the semiconductor ceases to hold. In the case of a “quasi-isolated” surface, a change in e,+ causes an equal change in the bending of the bands At, so that e.+, according to (18), remains unchanged. This is illustrated in Fig. 23, the right-hand side of which depicts the same semiconductor as the left-hand side, except that the value of e,+ is different, although c,+ is the same. It has been shown (41) that a surface possesses this property (i.e., is “quasi-isolated”) when the quantity

(n. and p , are the surface concentrations of electrons and holes, localized,

THE ELECTRON THEORY OF CATALYSIS

229

respectively, on all the acceptor and all the donor surface levels) is sufficiently small in absolute magnitude (compared with a critical value which is differentfor different surfaces, but does not exceed unity). In the particular case when the Boltamann approximation applies to the distribution of the electrons and holes on all the surface levels, the sufficient condition for “quasi-isolatedness” has the simple form IYI

<< 1

A “quasi-isolated” surface possesses the following property. From Equation (24) we have (l - Yln8 - (l Y)p8 = 0

+

whence (since in the case of a “quasi-isolated” surface we always have IYI << 1) n8 - p 8 = 0

This denotes that in the case of a “quasi-isolated” surface the magnitudes and t,+ are determined not from the system of equations (22) and (21), but from the two independent equations e,+

P(E,+) = u(e,+) =

0 0

(22) (25)

the first of which contains only the parameters characterizing the bulk of the semiconductor and the second only the parameters characterizing the surface. Hence, there is no longer any relation between t.+ and e,+. We see that a “quasi-isolated” surface may also be called “quasineutral,” since Equation (25) is approximately satisfied for it. We are not, however, dealing here with a truly neutral surface. According to (24), at 171 << 1, Equation (25) merely indicates that the absolute magnitude of the difference between the positive and negative charges on the surface is sufficiently small compared with their sum. However, the absolute magnitude of this differencemay itself be quite large. In this case, “quasi-isolatedness” of the surface obtains only for sufficiently large values of the sum n, p,, which condition is fulfilled only if the density of surface states is sufficiently large. We observe that three types of surface states must be distinguished, each of which can be responsible for the “quasi-isolatedness” of the surface: 1. States belonging to the surface energy bands (43, 44). Such bands, if they exist (the surface conductivity band and the surface valence band in which an electron and, respectively, a hole may migrate freely over the surface, but cannot penetrate into the crystal), have a large density of states. States of this type may be formed both on a real and on a n ideal surface.

+

230

TH. WOLKENSTEIN

2. States due to different biographical structural defects existing on any real surface and playing the part of local disturbances in the strictly periodic structure of the surface (Sec. IX,A). These include vacant lattice sites in the surface layer of the lattice, atoms or ions of the lattice ejected onto the surface, and foreign atomic inclusions in the surface of the lattice (surface impurities). 3. And, finally, the chemisorbed atoms or molecules themselves, which fulfil the same functions on the surface as the structural defects, contributes their part to the total density of surface states. We thus see that under certain conditions both a real and an ideal semiconductor surface may be of a “quasi-isolated” nature. An estimate shows that a surface will be “quasi-isolated” at no pa > 1OI2cm.-2. It seems that in the case of real adsorbents and catalysts we rather frequently deal with such surfaces. The existence of “quasi-isolated” surfaces has also been directly established experimentally on a number of semiconductors in experiments which show that the semiconductor work function is independent of the position of the Fermi level in the bulk (e.g., 42). In the case of a “quasi-isolated” surface, the bulk of the semiconductor (e.g., impurities inside the crystal) no longer influences its chemisorptive and catalytic properties, the latter depending only on the structure of the surface. This dependence is implicit in Equation (25), according to which the position of the Ferriii level on the surface E.+ (and hence the chemisorptive and catalytic properties of the surface) depends on the concentration and nature of the chemisorbed particles and also on the concentration and nature of the structural defects on the surface. In particular, one obtains from Eq. (25) E,+ = e,+(N) where N is the surface concentration of the given kind of chemisorbed particles. It also follows that the reactivity of a given kind of chemisorbed particles depends on the total number of such particles on the surface (i.e., on the degree of surface coverage). It is as if each particle felt the presence of the other particles on the surface. We have t o do here with a sort of long-range “interaction” which is transmitted by way of the electron (hole) gas (1, 37, 46). We observe that this effect, however, is not specific for a “quasi-isolated” surface. It exists, of course, as well in the general case of a “non-quasiisolated” surface, when according to Eq. (21), the magnitude E.+ depends, among other factors, upon en+.

+

C. EFFECTS DUE

TO

SURFACE CHARGE

In the remaining part of the present article, we shall consider further consequences of the main results of the theory formulated in the preceding paragraphs. We shall begin with the mechanism of the influence of chemisorption on certain properties of the semiconductor.

THE ELECTRON THEORY OF CATALYSIS

231

As we have seen, the appearance of “strongly” bound chemisorbed particles on the semiconductor surface gives rise to a surface charge, which, in turn, leads to a bending of the energy bands inside the semiconductor. Of course, a similar bending of the bands may arise as well in the particular case of a “quasi-isolated” surface. If, in addition to the surface states due to the chemisorbed particles, the semiconductor also possesses surface states of other origin (surface energy bands, structural defects, surface impurities), then the surface may remain charged in the absence of chemisorbed particles. In this case the appearance of chemisorbed particles causes a change in the magnitude (and occasionally in the sign) of this surface charge. Let u and gobe, respectively, the surface charge in the presence and in the absence of chemisorbed particles, so that u = a0

+ AO

where Au is the contribution of the chemisorbed particles. In this case the appearance of chemisorbed particles on the surface of the semiconductor leads to a change in the degree (and occasionally in the sign) of the bending of the bands. The bending of the bands (or a change in the bending) due to chemisorption leads in turn to the following two experimentally observed effects. The first effect is a change in the work function of the semiconductor. In Fig. 22 the work function is denoted by Q. By definition this is the distance between the Fermi level and the level corresponding t o the value of the potential outside the crystal. (We have in mind the thermoelectron work function which figures in Richardson’s formula.) We have cp = cpo

+ Acp

where cpo is the work function in the case of a (‘clean” surface, i.e., in the absence of chemisorbed particles. If the contribution of the chemisorbed particles to the surface charge is positive, i.e., if Au > 0, then Acp < 0 (the work function decreases; see Fig. 22b); if the contribution is negative, i.e., if Au < 0 then Acp > 0 (the work function increases; see Fig. 22a). We observe that the sign of Acp determines the sign of Au only in the case when it is possible to neglect the additional potential jump on the surface of the semiconductor due to the electric double layer, which arises on the surface in adsorption and figures as one of the terms in the experimentally measured work function. Such an electric double layer may be the result of the polarization of the chemisorbed particles (when the dipole moments of the chemisorbed particles are directed normally t o the surface). This can be the case, for example, in (‘weak” chemisorption (when the total charge of the surface remains unchanged). The second effect caused by the change in the bending of the bands is a

282

TH. WOLKENSTEIN

change in the electrical conductivity of the semiconductor K. Indeed, both the concentration of the free electrons in the conduction band (to be denoted by n) and the concentration of holes in the valence band (to be denoted by p) are determined by the position of the Fermi level in the forbidden region. If the electron and hole gases are nondegenerate, then in the z plane parallel to the adsorbing surface we have (Fig. 22)

A and B being constants which need not interest us further. (We may assume that A 2: B, which denotes approximate equality of the effective masses of free electrons and holes.) Thus, the electrical conductivity is different in different cross sections parallel to the adsorbing surface (i.e., at different z). Chemisorption, by changing the bending of the bands, may lead to a noticeable change in the electrical conductivity of the subsurface layer of the crystal, which in the case of a sufficiently small crystal may effect the total electrical conductivity of the sample. Even more, so the very type of conductivity in the subsurface layer may change under the influence of chemisorption: n conductivity (e- < t+) may go over into p conductivity (e- > c+), or vice versa (the so-called “inversion” of conductivity). If KO is the conductivity of the sample in the absence of chemisorbed particles on its surface, then in the presence of such particles we have K

=

KO

+ AK

Evidently, a positive surface charge (Au > 0) causes an increase of electrons and a decrease of holes in the subsurface layer; a negative surface charge (Au < 0) has the opposite effect. Thus, In the case of an n-type semiconductor In the case of a p-type semiconductor

1 1

AK > 0,

if Au > 0 AK < 0, if Aa < 0 AK > 0, if Au < 0 AK < 0, if Au

>0

In case of an intrinsic semiconductor (is., a semiconductor possessing mixed conductivity), it can be shown that we always have AK > 0, regardless of the sign of Au. Thus, the sign of the surface charge contributed by the chemisorbed particles may be determined if one obtains from experiment the sign of AK (in the case of a “doped” sample, if the type of conductivity is known) or the sign of Acp (if the polarization effect can be neglected); i.e., these

THE ELECTRON THEOBY OF CATALYSIS

233

measurements may give evidence of the acceptor or donor role of the chemisorbed particles, or in other words, of the character of their bonding with the surface (24). Inasmuch as the character of the bonding, as has been seen (Sec. IV,B), is determined not only by the nature of the particles themselves, but as well by the nature and biography of the surface, it can be expected that a given adsorbate may lead to a positive surface charge on one adsorbent, and to a negative charge on another. Indeed, if the condition q+

>> q-

is satisfied for particles of a given kind on one adsorbent (Sec. IV,B), the condition q-

>> q+

may be satisfied for the same particles on another adsorbent. This means that particles acting as donors when chemisorbed on one semiconductor may act as acceptors on another; physically this means merely that in these two cases the chemisorbed particles make different types of bond with the lattice of the adsorbent, in the first case the donor form of chemisorption predominating and in the second case the acceptor form predominating. More so, inasmuch as the surface treatment can, generally speaking, lead to a displacement of the Fermi level, it follows that if the condition (27) is satisfied for a given sample, the condition (28) may be satisfied for another sample of the same material (which has undergone a different treatment). This means that particles of a given kind may act as donors or acceptors depending not only on the chemical nature of the semiconductor, but also on the biography of the adsorbent sample. In this connection let us consider the case when adsorption is accompanied by a slight solution of the adsorbate atoms in the bulk of the crystal. Suppose, for example, that hydrogen atoms are chemisorbed on a semiconductor surface and that the condition (27) is satisfied; i.e., the chemisorbed hydrogen atoms act as donors charging the surface positively. Suppose, in addition that, a part of the hydrogen atoms penetrate into the crystal lattice occupying interstitial positions. The hydrogen atoms in the interstitial positions are typical donors. The semiconductor thus obtains an addition of donor impurities which always leads to an upward displacement of the Fermi level, i.e., brings it closer to the conduction band (Fig. 12). At a sufficient concentration of impurity, i.e., a t a sufficient amount of dissolved hydrogen condition (27) may become replaced by condition (28), as can be seen from Fig. 12b. In this case the hydrogen atoms remain adsorbed at the surface, but lose their donor properties and become acceptors. Thus, if the adsorbent surface is charged positively at small quanti-

234

TH. WOLKENSTEIN

ties of adsorbed hydrogen, the sign of the surface charge may change with an increase in adsorption, and the surface may become negatively charged. The change in the work function and the electrical conductivity of the semiconductor due to chemisorption is the second important consequence of the theory. These effects have been theoretically considered in detail by Sandomirsky (46-48). They have been observed experimentally by a number of authors (49-64). Some of the experimental data are presented in TabIe I, where the signs and - denote, respectively, positive and negative surface charging upon chemisorption (Au > 0 or Au < 0) ; these data have been obtained from the variation of the work function or of the electrical conductivity or both simultaneously. The symbol x in the table denotes that the surface charge is not affected by chemisorption (Au = 0); the figures in brackets refer to the literature.

+

TABLE I Adsorbent Cu*O

a

b

CUO

NiO

MnOn

Ge

ZnO

High temperatures. Room temperature.

As can be seen, the data presented indicate, in the first place, that chemisorption, as a rule, leads to the appearance of an electric charge on the surface of the semiconductor (or to a change in the magnitude of such a charge). In the second place, we see that the sign of the surface charge arising in chemisorption is determined not only by the nature of the chemisorbed particles, but depends as well on the nature (and sometimes on the biography) of the adsorbent itself. We see also from the data that in some cases adsorption does not affect (or hardly affects) the magnitude of the surface charge. This does not necessarily mean that in these cases we have to do with physical adsorption (although this is poesible), for a similar effect (constancy of the surface charge) may also exist in chemisorption (in the case of ((weak” chemisorption or when the “strong” donor and (I strong” acceptor forms of chemisorption are present more or less to the same extent).

THE ELECTBON THEORY OF CATALYSIS

235

VII. Promoters and Poisons in Catalysis A. RELATION BETWEEN CATALYTIC ACTIVITYAND ELECTRICAL CONDUCTIVITY OF A SEMICONDUCTOR The third important consequence of the theory is the relation between the catalytic activity and the electrical conductivity of a semiconductor. The electrical conductivity of a semiconductor is uniquely determined by the position of the Fermi level inside the crystal cv+ and by the degree of bending of the bands. The latter factor, however, is significant only in the case of sufficiently small crystals (Sec. IV,C). The relation between the electron and hole components of the conductivity depends on the position of the Fermi level in the forbidden region. The higher the Fermi level (Lea,the closer it lies to the conduction band and the farther from the valence band), the bigger will be the electron component and the lesser the hole component. We have an n-type semiconductor or a p-type semiconductor when one of these two components can be neglected in comparison with the other. When both components are comparable in magnitude, we have to do with “intrinsic” (mixed) conductivity. The catalytic activity of the semiconductor is determined by the position of the Fermi level on the surface of the crystal e6+. Here, as we have seen (Sec. V,B), it is necessary to differentiate between two classes of reactions: those which are accelerated and those which are retarded as the Fermi level rises (i.e., as t 6 + increases; see Fig. 22). We have called these reactions n-type and p-type reactions, respectively. We have also seen (Sec. VI,A) that the position of the Fermi level on the surface of the crystal +.B is determined, other conditions being equal, by its position inside the crystal c,+. An increase of t,.+ entails an increase of e,+, and a decrease of ev+ a decrease of t.+. We are thus led to the conclusion that the factors which shift the Fermi level in the bulk of the crystal, i.e., which affect the electrical conductivity, will also shift the Fermi level on the surface (in the same direction); i.e., they will affect the catalytic activity. Furthermore we come to the conclusion that the factors directly displacing the Fermi level on the surface without affecting its position in the bulk (i.e., the factors affecting the degree of bending of the bands) will also affect both the electrical conductivity and the catalytic activity simultaneously. Hence, there must exist a certain parallelism between the changes in the electrical conductivity and in the catalytic activity. The physical origin of this parallelism is clear: the electrical conductivity is determined by the concentration of free charge carriers in the semiconductor; on the other hand, these take part in the reaction (as its components) and thus determine its rate. An example of a factor which changes the electrical conductivity of a semiconductor is the method of preparation, in particular, the introduction

Catalyat

Reaction

H,

+ Df

Hz

+ Ix

-+

2HD

---*

2HD

CHsOH -+ CO C&OH 2co

+

2Nt0

GHis

-+

0 2

-+

-+

ZnO with different admixtures of Li,o, ALOI

era,

+ 2Hz

GH60

-+

2N:

2

+ H2

a

+ Oz

CcHjCHi 4-4H2

variously treated in as atmosphere of HS and 0: ZnO with different admixtures of supersbichiometric Zn ZnO with Merent admixtures of chemisorbed 0, NiO with different admixture of L i z 0 NiO with different admixtures of Al*oa C r 9 0 1 . &OI samples of varying constitution

Conductivity type

Simultaneous variation of electrical conductivity and catalytic activity

n

Symbatic

Heckelsberg et al. (69)

P

Antibatic

Weller and Voltz (66)

n

Symbatic

Matveyev and Bomkov (68)

n

Symbatic

Myaenikov and Pshezhetaky (66)

P

Antibatic

Keyer et al. (36)

P

Symbatic

Rieniicker (70)

-

Symbatic

Chapman el al. (67)

Authors

THE ELECTBON THEOBY OF CATALYSIS

237

of impurities (of a given nature and in a given concentration) into the surface or in the bulk of the semiconductor. Thus, different samples of the same semiconductor, which have been prepared differently and which differ in their electrical conductivity, should also differ in their catalytic activity. As one passes from sample to sample the electrical conductivity and the activity should vary in parallel. This parallel change in the electrical conductivity and in the activity may take place in the same or in opposite directions depending on the type of reaction (n-type or p-type) and on the type of semiconductor (n-type or ptype). In the case of an n-type reaction on an n-type semiconductor or of a p-type reaction on a ptype semiconductor, the electrical conductivity and the activity vary in the same direction. On the contrary, in the case of an n-type reaction on a p-type semiconductor or a p-type reaction on an n-type semiconductor, they vary in opposite directions. The existence of a correlation between the catalytic activity and the electrical conductivity which follows from the theory was indicated by us back in 1950 (37,65)) when there were as yet no measurements available that could either corroborate or refute this theoretical prediction. To date we have already a whole series of experimental work in which such a correlation has been observed (e.g., 36, 56, 66-70). A number of authors have measured the electrical conductivity and the catalytic activity of various samples of a semiconductor which differed in the method of preparation and have discovered that these two properties of the semiconductor vary in the same or in opposite directions from one sample to another. The results of some of these experiments are presented in Table 11. If the conductivity type and the character of the relation between the electrical conductivity and the catalytic activity for the given reaction are known and the validity of Equation (23) is assumed, one may conclude from the experimental data to what type (n or p ) the given reaction belongs. This may be useful in a theoretical analysis of the reaction mechanism. It should be observed that in several cases the relation between the electrical conductivity and the activity may break down. This will occur in thoFe intervals of variation of e,+, in which the reaction rate is independent of e.g., for the reaction of dehydrogenation of alcohols in the region of sufficiently high values, and for dehydration in the region of sufficiently low values of e,+ (Sec. V,B and Fig. 19). It may also occur in the case of a semiconductor with a “quasi-isolated” surface, when e.+ is independent of e,+ (Sec. VI,B) if the dimensions of the crystal are not too small (Sec. V1,C). It should be observed in addition and especially stressed that, in general, parallelism between the electrical conductivity and the activity can be expected only when the changes in these properties are due to the same factor acting on the semiconductor, all other conditions being equal. There are

238

TH. WOLKENSTEIN

no grounds for expecting a parallelism between changes in the electrical conductivity and activity when comparing semiconductors of different chemical nature. Indeed, as we have seen (Sec. V,B), the reaction rate is determined not by the position of the Fermi level relative to the energy bands, but by its position relative to those discrete surface levels that correspond to the chemisorbed particles participating in the reaction. The position of these levels in the energy spectrum is, generally speaking, different in semiconductors of different nature. For this reason, the parallelism between the electrical conductivity and the catalytic activity may in these cases he completely hidden. For the same reason, there are no grounds for seeking a relation between the catalytic activity of semiconductors and their conductivity type (n-or p-type conductivity) when dealing with semiconductors of different chemical nature.

B. MECHANISM OF PROMOTER AND POISONINQ ACTIONOF IMPURITIES The position of the Fermi level on the surface of the crystal can he varied to some extent, as we have seen, by doping the surface or the bulk of the crystal with the properly chosen impurities in proper concentrations. It is this displacement of the Fermi level that comprises the mechanism of the influence of impurities on the adsorptivity of the surface (i.e., on the extent of coverage at given values of P and T) and on the catalytic activity (at the given surface coverage). This mechanism helps t o illustrate the way in which insignificant amounts of impurities can cause a noticeable acceleratioil or retardation of a reaction without coming into direct contact with the reacting particles. The physical essence of the mechanism consists in the following: the impurity regulates the surface concentrations of the electron and hole gases, which in turn regulate the reaction rate. Thus, the influence of a n impurity on the catalytic activity on the one hand, and the parallelism between the catalytic activity and the electrical conductivity on the other hand, merely represent two aspects of the same effect. The word “impurity” does not necessarily denote chemically foreign atoms introduced into the lattice. As usual in the semiconductor physics this concept has a broader meaning. It includes any local disturbances in the strictly periodic structure of the lattice. These may be vacancies, foreign atoms replacing the regular lattice atoms, interstitial foreign atoms or atoms of the lattice which have been thrown into interstitial positions or out0 the surface of the crystal. In this sense, stoichiometric disturbances or any deviations from the ideal crystal structure are “impurities.” Foreign chemisorbed particles not participating in the reaction, as well as the reacting chemisorbed particles and chemisorbed reaction products may also play the part of impurities (surface impurities in this case). Thus, foreign

239

THE ELECTRON THEORY OF CATALYSIS

gases may either raise or lower the activity of the catalyst. The accumulation of reaction products on the surface may either raise or lower the activity in the very course of the reaction. Two types of impurities should be distinguished: namely, acceptor and donor impurities which play the part of “traps” (i.e., localization centers) for the free electrons and the free holes, respectively. It should be especially stressed that foreign particles dissolved in the crystal may act as acceptors or donors depending not only on their nature, but also on whether they enter the lattice (interstitially or substitutionally). For example, the interstitial Li atoms in the NiO lattice are donors, but the same Li atoms when replacing the Ni atoms act as acceptors. In the case of a substitutional solution, the foreign atoms of a given type may be either acceptors or donors depending on the lattice in which they are dissolved. For example, Ga atoms are donors in the ZnO lattice and acceptors in the Ge lattice. Thus, if the adsorbed particles are, say, acceptors, the same particles when dissolved in the volume of the crystal may act as donors, and vice versa. Any doping of the crystal leads, generally speaking, to the displacement of the Fermi level on the surface. Surface impurities directly affect el+, leaving en+ unchanged; bulk impurities affect tv+ and hence (Sec. V1,A) cause a change in el+. Acceptor impurities always lower the Fermi level, while donor impurities raise it. At a given surface coverage we have =

€+ ,

€,+(T,Z)

(29)

where Z is the (surface or bulk) concentration of a given kind of impurity centers. The following relations are always satisfied:

a + < 0, a€.+ 3

In the case of an acceptor impurity: -5-

az

In the case of a donor impurity:

a4+ 3

aT

0,

a€,+

0

<0

(30)

With an increase in the temperature or a decrease in the impurity concentration, the Fermi level always moves towards the middle of the forbidden band. The reaction rate g on the surface depends, as we have seen (the surface coverage being fixed) on T and el+: 9

=

s(T,ea+>

We have (by definition)

as > 0 for acceptor reactions: a€#+

for donor reactions:

ag a€,+ < 0

240

TH. WOLKENSTEIN

Equations (31) and (29) explain the mechanism of the promoter and poisoning action of impurities. An impurity is a ag a€,+ ag = promoter if * -> O

az

poison if

a€,+

az

as = a9 .a€#+ -<

az

ael+ az

It follows from Equations (30), (32), and (33a,b) that acceptor reactions are accelerated by a donor impurity and retarded by an acceptor impurity, and vice versa in the case of donor reactions. Thus, a given impurity on a given catalyst may be a promoter for one reaction and a poison for another. This is frequently observed in practice. For example, the addition of Li20 to ZnO promotes the reaction of dissociation of NzO (71)and a t the same time poisons the reaction of oxidation of CO (60). If a reaction proceeds in two (or more) consecutive stages, one of which belongs to the acceptor, and the other to the donor type, then as the impurity concentration 2 increases, i.e., as the Fermi level is displaced monotonically according to (30), the limiting stage may change from, e.g., an acceptor to a donor stage. Consider Fig. 21, which depicts the dependence of the reaction rate g on the position of the Fermi level e,+ for such a twostage reaction. As a result of an increase in the impurity concentration, we may find ourselves transferred from point A on the lower branch of the curve to point €3 on the upper branch. Consequently, an impurity which acts as a promotor in one concentration may become a poison for the same reaction in another concentration. This effect has been observed by numerous authors. As an example we cite the paper by Zhabrova and , studied the reaction of dissociation of hydrogen peroxide Fokina ( B ) who on crystals of MgO doped with SbzOa.The reaction was promoted by small concentrations and poisoned by large concentrations of the impurity. We may also be transferred from a point A to a point B in Fig. 21 (or vice versa) by a change in temperature [at 2 = const., as appears from (30)]. Thus, a given impurity (at a given concentration) may act as a promoter at one temperature and as a poison at another. This has also been observed experimentally. As an example, we cite the reaction of ethylene oxidation on MgO CrzOadoped with NasS04,according to the data of Krylov and Margolis (73). We see that the promoter and poisoning action of an impurity are determined not only and not so much by the nature of the impurity and the character of the reaction as by the position of the Fermi level on the surface of the crystal, i.e.,by the state of the system as a whole. The condition (33a), which is valid at certain values of T and 2, may be replaced by the

.

THB) ELECTRON THEORY OF CATALYSIS

241

condition (33b) a t other values of T and 2. The concepts of “promoter” and “poison” are frequently replaced by the more general concept of “modifier.” The phenomenon of catalyst modification by impurities (promoting by poisons, poisoning by promoters) was discovered in 1940 in the laboratory of S. Z. Roginsky. A summary of the experimental data is given in (74, 6). A theoretical interpretation of the phenomenon was given in the first papers on the electron theory of catalysis (1, 3’7, 66, 47). The effect of impurities on the activity of a catalyst may be regarded as the fourth consequence of the theory. By varying the impurity concentration in the semiconductor, one may regulate not only the activity of the catalyst but its selectivity as well. Indeed, if the reaction proceeds along two parallel paths, one of which is of the acceptor type and the other of the donor type, then upon the monotonic displacement of the Fermi level (i.e., upon the monotonic change of 2)the reaction will be accelerated on one path and retarded on the other, as appears, e.g., from a comparison of Figs. 19a and 19b. Doping of the crystal may accelerate the reaction on one path and retard it on the other. We observe in conclusion that the effect of impurities on the activity and selectivity of the catalyst may in some cases be reduced to nil. The reaction rate becomes insensitive to the bulk impurity (dissolved inside the crystal) when the reaction takes place on a quasi-isolated surface, and also in the case of a sufficiently high temperature corresponding to the region of intrinsic conductivity in the semiconductor, when the Fermi level inside the crystal is stabilized in the middle of the forbidden band and is practically unaffected by the impurity. In such cases, only surface impurities continue to be operative. Hence, if the reaction does not become insensitive to impurities a t the temperatures of intrinsic conductivity, this may be regarded as a criterion denoting that the admixtures which show a promoting or poisoning influence are distributed (completely or a t least partially) on the surface of the semiconductor. In the range of e,+ in which the reaction rate is independent of e,+, both the bulk and surface impurities cease to be effective. In this case, the electron mechanism of the promoter and poisoning action of the impurity is no longer operative.

VIII. Factors Affecting the Adsorptivity and Catalytic Activity

of a Semiconductor A. ILLUMINATION The fifth consequence of the theory is that the adsorptivity and catalytic activity of a semiconductor are affected by illumination. When a crystal absorbs light waves of photoelectrically active frequencies (i.e., frequencies exciting the internal photoeffect), this leads, generally speaking, to a change

242

TH. WOLKENSTEIN

in the concentration of the electron and hole gas on the surface and hence to a change in the relative content of different forms of chemisorption. In other words, the quantities qo, q-, v+ for an illuminated crystal will in general have different values from those for an unilluminated one. This explains the mechanism by which illumination affects the adsorptivity and catalytic activity of the surface. We consider first the effect of illumination on the adsorptivity (76). For the sake of simplicity we limit ourselves to the case when the chemisorbed particles are of a purely acceptor nature. Let them correspond to the acceptor surface levels A in Fig. 24. The level FF in this figure depicts the E

F

F

X

x= 0

FIQ.24 position of the Fermi level in the absence of illumination. Let N and N O be the concentrations of chemisorbed particles (surface coverage) in the presence and in the absence of illumination, respectively, then AN = N - No is the change in concentration due to illumination on the assumption that the pressure P remains the same in both cases. Evidently

+ N+ No-,

N = No No = Noo

where N o and N - denote, respectively, the concentrations of “weakly” and “strongly” bound particles upon illumination; NO”and NO- denote the same quantities in the absence of illumination. At P = const. we have (see Sec. IV,B):

No

=

Noo = bP

and hence AN _

No

- N--

No-

No

= qo-(cc

- 1)

(34)

where qo- =

No-, No

p=-

NNo-

(35)

THE ELECTBON THEOBY OF CATALYSIS

243

Formula (34) gives the relative change in the surface coverage due t o illumination (in other words, the relative change in adsorptivity). The quantity p indicates the increase in the concentration of “strongly” bound particles upon illumination. To determine p, we utilize the condition of electron equilibrium on the surface. In the absence of illumination, this is of the form (principle of detailed balance)

where no and p o are, respectively, the surface concentrations of free electrons and holes (in the plane z = 0, see Fig. 24) in the absence of illumination. The terms on the left-hand side of Equations (36) correspond to the electronic transitions depicted in Fig. 24 by the vertical arrows 1, 2, 3, 4, respectively. We observe that (yl

=

Ple-v+lkT,

cy3

=

&e-v-lkT

(37)

and from (36) we obtain ff2

No’

1

-01, No- PO

= -*

ff(

=

1 -.NO’ no

No-

Upon illumination the condition of electron equilibrium takes the form

alN” - azpN-

=

a3N- - aqnN’

(39)

where n and p are the surface concentrations of free electrons and holes under illumination. Evidently, the quantities

An = n - no Ap = p - PO represent the increments to the corresponding concentrations due to illumination. In view of Equation (38) and introducing the notation [see Equations (371, (61, and (7)1

we obtain from Equation (39) :

and, hence, according to (34),

244

TH. WOLXENBTEIN

We see that illumination can lead both to an increase in adsorptivity (photoadsorption, A N > 0) and to its decrease (photodesorption, A N < 0). This depends on the ratios A n / n o and Ap/po, i.e., on the relative changes in the surface concentrations of the electron and hole gases due to illumination. We have Photodesorption Inactive light absorption

(43) An AP

Photoadsorption

if->a-

no Po

Here, according to (40) and (26),

?!= Po

@(w--a,-)lkT

(4)

where fl is a factor independent of c.-. The effect of illumination on the adsorptivity of the surface has been observed by a number of authors and studied in detail on various adsorbents for different adsorbates and in different frequency intervals (e.g., 76-84; a review of the experimental work is given in 81). I n some cases photodesorption was observed, in other cases, on the contrary, photoadsorption. Why one or another of these two opposite effects takea place has not yet been experimentally elucidated. This remains a problem for a further experimental investigation. From the theoretical point of view, the answer to the question whether photodesorption or photoadsorption will take place depends not only on the conditions of illumination, not only on the nature of the adsorbent and the adsorbate, but also on the biography of the illuminated sample, i.e., according to (44), on the position of the Fermi level in the unilluminated a m ple. According to Equations (43)and (@), when the sample is doped with an acceptor impurity leading to the lowering of the Fermi level, other conditions (including those of illumination) being equal, photodesorption may be replaced by photoadsorption. On the contrary, when the sample is doped with a donor impurity, leading to a rise in the Fermi level, photoadsorption may give place to photodesorption. This theoretical prediction seems to agree with the recent experiment of Kwan and Fujita (86). These authors have studied the adsorption of 02 and ZnO and observed photodesorption on the reduced samples and photoadsorption on the oxidized samples of ZnO . Consider now the effect of illumination on the catalytic activity of a

THE ELECTRON THEOBY OF CATALYSIS

245

semiconductor (photocatalysis). This effect may be due to a change in the reactivity of the chemisorbed particles resulting from illumination. Let us explain this by the following example. Suppose that of the total number N of particles of a given kind adsorbed per unit surface, only those particles take part in the reaction (i.e., are reactive) which are in a state of “strong” acceptor bonding with the surface; their concentration is N- = 7-N. An example of this is the 0 2 molecule, which in a state of “weak” bonding may be considered as valence-saturated and in a state of “strong” bonding is a surface ion-radical (see Sec. 111,B). If the partial pressure P is held constant (both in the presence and in the absence of illumination), then according to (34) we have

N- = pNowhere the index “0” denotes the absence of illumination and p is given by Equation (41). In this case the quantity p indicates how many times the number of reactive particles adsorbed per unit surface increases under illumination (other external conditions remaining the same). Evidently, the rate of the heterogeneous reaction in which these particles participate will be a function of p and thus will be sensitive to illumination. If An = A p = 0 (photoelectrically inactive absorption of light), then according to (41) p = 1, and illumination has no effect on the reaction rate. The experimental data on the effect of illumination on the catalytic activity are as yet extremely scarce. Nevertheless, there are some papera in which this effect seems to have been detected (86-89). In conclusion we stress once more that the above-considered mechanism of the effect of illumination on the adsorptivity and catalytic activity of a semiconductor holds in the case when the absorption of light increases the number of free electrons or holee (or both) in the crystal. This, however, does not always take place. The absorption of light by the crystal may proceed by an exciton mechanism. This seems to be the case in the region of intrinsic absorption, which is as a rule photoelectrically inactive. In this case the initial act of light absorption leads to the formation of an exciton, rather than a free electron or hole. Such an exciton, as it wanders through the crystal, may meet a lattice defect and annihilate on it, the energy of the exciton being utilized to ionize the defect, i.e., to transfer an electron or hole localized on the defect to the free state (the mechanism of LashkarevJuze-Ryvkin, see 90, 91). If such a defect is a foreign particle chemisorbed on the crystal surface, the result will be a change in the character of the bond between this particle and the surface. Thus, the interaction of the lattice excitons with the chemisorbed particles may cause a change in the relative content of the different forms of chemisorption and

246

TH. WOLKENSTEIN

hence a change in the adsorptivity and catalytic activity of the surface. Such a possible exciton mechanism explaining the effect of illumination on the adsorptive and catalytic properties of the surface has not, however, been theoretically investigated as yet.

B. EXTERNAL ELECTRIC FIELD.DEGREE^ OF DI~~PERSION Let us consider the sixth consequence of the theory-the effect of an external electric field applied to a semiconductor on its adsorptivity and catalytic activity. Suppose we have a slab of semiconductor of thickness L placed in an external homogeneous transverse electric field. In this case the electron concentration on one of the surfaces will be increased as compared with the case of no field; i.e., the Fermi level will be raised. On the opposite surface, on the contrary, the electron concentration will be reduced; i.e., the Fermi level will be lowered. This is illustrated in Fig. 25, where the continuous lines indicate the band edges in the absence of the field, and the dashed lines indicate the band edges in the presence of the field. (To be definite, the surfaces are assumed to be negatively charged; the field in Fig. 25 is directed from left to right.) E

FIG.25

Thus, under the influence of the field, the adsorptivity of one of the surfaces should increase, while that of the other decreases (Sec. IV,B), though not by the same amount. (This fact can be demonstrated and is highly essential.) As a result, the adsorptivity of the sample as a whole should change. This effect might be detected by a change in pressure in the adsorption volume. At the same time, the catalytic activity of the sample should also change. One may expect a change in the reaction rate under the influence of the external field. This effect predicted by the theory (effect of an external electric field on the adsorptivity and catalytic activity of a semiconductor) has not been

247

THE ELECTRON THEORY OF CATALYSIS

as yet experimentally investigated. Calculations show (92) that under certain conditions it should be experimentally observable. Perhaps this effect might explain the results of Pratt and Kolm (9S),who observed a slow change in the work function of a semiconductor under the influence of an external electric field. These results seem to indicate that adsorption equilibrium is upset by the field. Now consider another effect which also follows from the theory. This is the dependence of the specific (per unit surface) adsorptivity and catalytic activity on the dimensions of the sample, i.e., on the degree of disperseness of the catalyst. This effect becomes apparent only in the case of sufficiently small crystals for which

v

351 where S is the surface area, V the volume of the crystal, a i d 1 the screening length (as a rule I = 10+--10-6 cm.). In this case, as can be shown (94), the position of the Fermi level on the surface of the crystal (and hence the adsorptivity and the catalytic activity per unit surface) depends on V / S . A

F

E

E

E

I

A

F F

I-t-4 (b)

Lx-4 (C)

FIG.2ti

We shall explain this by means of the following model. Imagine a planeparallel slab of semiconductor of thickness L, both surfaces of which contain chemisorbed particles. The energy band scheme of such a semiconductor in the case of negatively charged surfaces is shown on Fig. 26. Suppose first that L >> I (Fig. 26a). Then the inner region of the semiconductor is electrically neutral, and the energy bands inside it are horizontal, as shown in Fig. 26a. From this condition for electrical neutrality, one determines the position of the Fermi level e,+ inside the crystal; e,+ is thus insensitive

248

TH. WOLKENSTEIN

to the surface (Sec. V1,A). The appearance of chemisorbed particles on the surface and the resulting change in the surface charge do not effect ev+ in this case. Let us now consider a thin slab for which L 5 1 (Fig. 26b). Here the bulk of the crystal is no longer electrically neutral and the bands are less bent than in the preceding case for the same surface charge density. The Fermi level both in the bulk and on the surface is shifted compared with the preceding case. It can be shown that as the slab becomes thinner, the potential difference between the surface and the center of the crystal decreases and the bands gradually straighten out. For a su5ciently thin slab when L << I (Fig. 26c) the bands may be considered completely straightened and the entire volume of the semiconductor uniformly charged. We shall confine ourselves to this limiting case and consider e.+ = E.+ = E+ or e,- = e,- = e-. The position of the Fermi level (e+ or e-) can he easily determined from the condition for electrical neutrality of the crystal as a whole. This condition has thc form u

+ q ( p - n)L = 0

(45)

where a,as above, is the surface charge density, q the absolute magnitude of the electron charge, and n and p the total electron and hole concentrations in the bulk of the crystal (both in the energy bands and discrete levels). We shall assume that the electron and hole distributions in the respective bands as well as on the impurity levels in the bulk are Maxwellian. In addition, we shall consider for simplicity’s sake that the entire surface charge is due to the chemisorbed particles, i.e., that the “clean’’ surface of the semiconductor is electrically neutral. We shall thus neglect the structural defects of the surface, which are always present to some degree on a real surface and act as additional traps for the electrons and holes. With these assumptions we may take expression (10) for u and consider

where A and B are coefficients that depend on the nature of the crystal and on the nature and concentration of the defects (impurities) ; it follows from Equation (45) at u = 0:

where m+ is tho position of the Fermi level on a “clean” surface. Substituting (10) and (46) into (45) we obtain on the basis of (47):

THE ELECTRON THEORY OF CATALYSIS

249

where =

~ b A e(w++~-)IzkT B

The other notations are clear from Fig. 26c. It follows from Equation (48) that as L decreases (at P = const.) the Fermi level approaches the level depicted in Fig. 26c by the dashed line CC (descending if eo+ > u+ and rising if eo+ < u+) and, therefore, the specific adsorptivity of the surface, according to (9),should decrease monotonically as the dimensions of the crystal decrease. At the same time, the specific catalytic activity of the surface should change. This result, obtained for the case L << b, holds qualitatively in the case L ,< I as well (94). Perhaps it is this mechanism which accounts for the change in the specific catalytic activity of semiconductors with an increase in the degree of dispersion, so fiequently mentioned in the literature. The effect should evidently become important the earlier (ie., the less the degree of dispersion) the greater the screening length 1 in the specimen. One could expect to observe it at S/V >, los cm.-l, i.e., when the surface area is of the order of tens of square meters per gram.

IX. Chernisorption and Catalysis on a Real Surface A. THE ROLEOF STRUCTURAL SURFACE IMPERFECTIONS

A real semiconductor surface, in contrast to an ideal plane surface, contains different kinds of imperfections perturbing the strictly periodic structure of the surface. Such a surface is distinguished by a number of peculiarities in its adsorptive and catalytic properties (96). One must distinguish between macroscopic and microscopic imperfections existing on a real surface. Macroscopic imperfections are perturbations of the periodic structure covering a region of dimensions considerably greater than the lattice constant. They include cracks on the surface of the crystal, pores, and various macroscopic inclusions. We shall not deal with such imperfections here. Microscopic imperfections are perturbations of dimensions of the order of a crystallographic cell. Microscopic imperfections include vacancies in the surface layer of the crystal, foreign atoms or lattice atoms on the surface, different groups of such atoms (ensembles), etc. We shall limit ourselves to a consideration of this kind of imperfection. Surface imperfections may affect the adsorptive and catalytic properties of the surface in two ways: First of all, they may displace the Fermi level, the position of the latter, as we have seen (Sec. VI1,B) depending on the nature and concentration of the imperfections. On the other hand, this position determines the

250

TH. WOLKENBTEIN

adsorptivity and catalytic activity of the surface (Secs. IV,B and V,B). This is the first mechanism by which imperfections affect the properties of the surface. Secondly, the imperfections may directly participate in the act of adsorption, inasmuch as they may play the part of adsorption centers. This is the second mechanism. The first of these mechanisms has already been discussed (Secs. VI,B and VII,B). It hns several specific consequences in the case when the imperfections nre irregularly distributed on the surface. Let us consider this case.

-Y FIG.27

Suppose, for simplicity’s sake, that we are dealing with oiily one type of imperfection. We aasume that the surface contains regions of greater and lesser concentration of these imperfections. The position of the Fermi level (relative to the energy bands) will vary in the different regions. This means that the energy bands will be bent as depicted, for example, in Fig. 27. In this figure the y axis is directed parallel to the surface (which is assumed to be plane): the A and D levels represent acceptor and donor levels of the given species of chemisorbed particles, and the imperfection levels are not depicted in this figure. We assume tlint in the region denoted by I in Fig. 27 the level CC lies considerably lower than the Fermi level FF, while in the region I1 it is considerably higher, and in the region I11 close to the Fermi level. In this case (Sec. IV,B and Fig. 12) practically all the particles in region I make an n bond with the surface, those in region I1 a p bond, while the particles chemisorbed in region 111 are almost all in a state of “weak” bonding with the surface. If, for example, we are dealing with COOmolecules, then on these three regions of the surface we find the three types of chemisorption of the COa molecule depicted in Figs. 6c, 6b, and 6a, respectively.

THE ELECTBON THEOBY OF CATALYSIS

251

We thus have different surface areas on which chemisorbed particles of a given kind possess different properties. The idea of such regions, which

may be termed “acceptor” and “donor” regions (regions I and I1 in Fig. 27, respectively), was first formulated by Roginsky (96,97).These regions are evidently characterized by different catalytic activity, some having higher and others lower activity (“active” and “inactive” regions of the surface). Such a surface, as we see, is inhomogeneous with respect to its properties. Its inhomogeneity is due, in the given case, to a single cause: the irregular distribution of defects which in themselves, however, take no part in the catalytic process. We observe, however, that as adsorption proceeds, this inhomogeneity is to a certain extent smoothed out. Indeed, the appearance of acceptor forms of bonding on an “acceptor” region (region I in Fig. 27) tends to lower the Fermi level, while donor forms of bonding on a “donor” region (region I1 in Fig. 27), on the contrary tend to raise it, so that the energy bands straighten out somewhat. The inhomogeneity also evens out somewhat with heating, owing to the resulting migration of the imperfections and the equalizing of their concentrations. Let us now consider another mechanism by which the imperfections affect the adsorptive and catalytic properties of the surface. This is based on their participation in the adsorption process as adsorption centers. The problem of chemisorption on an atomic imperfection has been treated quantummechanically by Bonch-Bruevich (98);it was discussed from the viewpoint of the boundary-layer theory by Hauffe (99) and has been investigated recently by Kogan and Sandomirsky (95). To elucidate some of the features of adsorption on imperfections, we shall consider the example of the adsorption of a monovalent electropositive atom C on an F center in the lattice MR composed of ions M+ and R-. Such an F center, representing a vacant R--site with an electron localized near it, is depicted in Fig. 28a. We shall denote it by the symbol DL. From the chemical point of view this is a localized free valence which can take on a foreign particle. Figure 28b shows this same F center minus its electron. Such an ionized F center we shall denote by the symbol DpL. Figure 28c and 28d depict the two forms of chemisorption for the atom C: Figure 28c corresponds to “strong” acceptor (twoelectron) bonding, Fig. 28d to “weak” (oneelectron) bonding. We shall denote these two forms by CDL and CDpL, respectively. In the first case (Fig. 28c) we are dealing with adsorption on an F center, in the second case (Fig. 28d) with adsorption on an ionized F center. In Fig. 29, which represents the energy band scheme of the crystal surface (the y axis is parallel to the surface) the F centers (Fig. 28a) are depicted by the donor levels D, and the F centers with chemisorbed C atoms (Fig. 28c) by the donor levels CD.

252

TH. WOLKENSTEIN

(a 1

(b)

C+ DL

I

Ct

I

I

DpL+cL

21t

E

I

.~\\\,\,\,

.. -Y

FIQ.29

We observe that in adsorption on an F center (in contradistinction t o the case of an ideal surface) the “strong” form of chemisorption is electrjcally neutral, while the “weak” form, on the contrary, is charged. In this case the chemisorbed particle is bound to a vacant R--site which is equivalent to n positive point charge equal in absolute magnitude to the charge of the electron. In the case of “strong” bonding, the charge of the vacancy is

THE ELECTRON THEORY OF CATALYBIS

263

compeiisated by the charge of the electron participating in the bond; in case of “weak” bonding, this charge remains uncompensated. Note, in addition, that in the case considered both the “strong” and the “weak” bonds are stronger than the same types of bonds on an ideal surface. Indeed, in the present case these bonds are made in the field of the vacant R-site (i.e., in the field of a positive charge), which, as can be shown, leads to a strengthening of the bond. The “weak” and the “strong” bonds are strengthened to different degrees so that, in general, the ((weak” (oneelectron) bond may be stronger in this case than the “strong” (two-electron) bond. The structural forms depicted in Figs. 28a,b,c,d can be transformed into one another, which can be written down as follows (the arrow pointing to the right denotes the exothermal direction of the reaction; at the right in (49) the heats of reaction are given) : I)

2)

C+DL@CDL.. C+DpL@CDpL .

+

. q. . go

3) D p L CL@ D L . . . vD4) C D p L + e L @ C D L . . . VcD-J

1

I

I

(49)

Reactions 3 aiid 4 represent the electron transitions depicted in Fig. 29 by the arrows 3 and 4. From (49) n.r obtain: 9- = qo

+

(ZICD-

- UD-),

whence it follows that (Fig. 29)

If 9If q-

> Po, < go1

then then

UCD-

VCD-

> uD< VD-

(504 (50b)

As adsorption proceeds, the levels D in Fig. 20 disappear, to be replaced by the same number of levels CD. This leads to a displacement of the Fermi level: in the case (50b) it is displaced upwards; i.e., the atoms C act as donors. In the case (50a), on the contrary, it is displaced downwards; i.e., the atoms C act as acceptors, although they are depicted in Fig. 29 by donor levels. If the levels D and CD in Fig. 29 lie far enough beneath the conduction band (i.e., VD- and VCD- are sufficiently large), as is the case, for example, with the alkali halide crystals, then the transitions 3 and 4 may be neglected (in the absence of any other ionizing agents besides the temperature), and adsorption processes on the neutral and on the ionized F centers will be independent of each other. In this case the adsorptivity (at small pressures) of a “colored” crystal (i.e., a crystal containing neutral F centers) will be

254

TH. WOLHENSTEIN

times greater than that of an “uncolored” crystal (i.e., containing an equal amount of ionized F centers). This effectwas observed by Bauer and Staude (loo),who investigated the adsorption of quinone on crystals of AgBr; the adsorptivity of the “uncolored” crystals was practically equal to zero, but after preliminary “coloring” of the crystals, it increased to a noticeable magnitude. The investigators were undoubtcdly dealing with the adsorption of F centers. F centers may act as adsorption centers not only in the alkali halides, but in any other crystals as well. Take, for example, a crystal of ZnO, in which the F center is an oxygen valency with two (not one!) electrons localized near it, as depicted in Fig. 30. From the chemical point of view such a center represents two adjacent localized free valencies of like sign which on an ideal surface could never meet because of Coulomb iepulsion between them. (This should be especially stressed.) As a result of this property, such an F center may play a specific role in catalysis acting as an active center for a number of reactions.

Not only F centers, but also other surface imperfections may act as adsorption centers. For example, the foreign gas molecules adsorbed on the surface may act as adsorption centers for the molecules of another gas (e.g., chemisorbed 0 atoms may act as adsorption center for CO molecules, as in Sec. V,B).

B. THERMAL AND BIOGRAPHICAL “DISOF~DER” ON THE SURFACE The microscopic surface imperfections, whatever their nature, possess a number of common properties: 1. They all possess a mobility which increases with the temperature (Lee,which demands a certain activation energy). They may be regarded as fixed on the surface only a t not too high temperatures.

THE ELECTRON THEORY OF CATALYSIS

255

2. Upon collision they can combine with one another to form groups (ensembles); these are to be regarded as new imperfections possessing, generally speaking, other properties. The idea of such ensembles which play the part of active centers in catalysis was advanced in a number of papers by Kobozev and co-workers (101, 102); these authors, however, regarded such ensembles (and this is characteristic of the papers cited) as formations which are independent of the lattice. In reality, individual surface imperfections and their ensembles form as a rule an entity with the crystal lattice, and their properties are determined to a considerable extent by the state of the lattice as a whole. By considering the ensemble apart from the lattice (i.e., by regarding the lattice merely as an inert substrate, which in some cases is permissible), we lose sight of the specific nature of the heterogeneous case and are in fact returning to the homogeneous process, but transferred from the three-dimensional to two-dimensional space. From the point of view of the electron theory, the part played by individual imperfections and their ensembles in catalysis depends on the fact that they represent groups of localized open valencies: a simple example is the F center in the ZnO crystal (Sec. IX,A). 3. Imperfections of a given kind “reacting” with the other imperfections may be either produced or annihilated. In addition, they may be swallowed up and generated by the lattice itself. As an example, take the displacement of the regular lattice atoms (or ions) into interstitial positions. It results in a formation of two kinds of imperfections. The inverse process is the recombination of interstitial atoms (or ions) with vacancies. This leads to the disappearance of imperfections, as if they had “swallowedy’one another. Another example is the reactions of ionization and neutralization of an F center leading to a change in its properties; these can be regarded as reactions of transmutation of one imperfection into another. The equilibrium concentration of each kind of imperfection depends on the biography of the sample and on the temperature. Poltorak (103, 104) has shown that in real crystals, characterized by non-equilibrium forms of boundary faces, this concentration may be quite considerable corresponding in order of magnitude to the concentration of active centers, a8 determined from the catalytic data. The total number of imperfections per unit surface characterizes what may be termed the “disorder” of the crystal surface. Two parts should be distinguished in the “disorder” : biographical disorder, which is retained at the absolute zero of temperature and depends on the method of preparation of the sample and on its entire preceding history; and thermal disorder, which increases on heating and is superposed on the biographical “disorder.’y If imperfections of some kind take part in adsorption as adsorption centers, then, as has been shown (lob),a consideration of thermal “disorder”

256

TH. WOLKENSTEIN

leads t o an essential change in the relations governing adsorption. To elucidate, this role of thermal “disorder” consider the following example. Suppose that the surface contains two kinds of imperfections which we shall denote by A L and BL, and let only the imperfections A L serve as adsorption centers for the given molecules (which we shall denote by C). We assume that the imperfections take part in the following reactions:

{

C + A L a C A L . . . qc B L + A L S B A L . . . qA

the first representing the reactions of adsorption and desorption and the second the reactions of blocking and unblocking the adsorption centers AL. (The arrow pointing to the right corresponds to the exothermal reaction path.) We denote by N A , N B , NCA,N B A the concentrations of the respective imperfections. ( N Ais evidently the concentration of free adsorption centers, N C Athe concentration of occupied centers, i.e., of chemisorbed particles, and N B A the concentration of blocked centers.) We then have (under equilibrium conditions) :

NA

= aNcA

N A N B = BNBA and

NA

where a =

(514

e-QclkT

where /3 = @oe-g~’kT

+ N B A+ N C A NB

P

+

(51b)

NA* N B A = NB* =

>

where NA* and NB* are known constants. (We shall consider NA* NB*.) If the total “disorder” a t temperature T is characterized by the concentration N = NA N C A ,i.e., by the concentration of unblocked adsorption centers, then N* = NA* - NB* will represent the biographical “disorder” and N - N* the thermal “disorder,” while NA* is the maximum “disorder” possible on the given surface (corresponding t o T = m ) . From Equation (51b) on the basis of (52)) we obtain

+

This equation represents the law of decrease of the number of free adsorption centers with increasing surface coverage. The dependence of N and NCA,according to (53) (at T = const.) is schematically depicted in Fig. 31 by the heavily drawn curve. We see that the total number of unblocked adsorption centers, N = N A NCA: does not remain constant in the process of adsorption (i.e., as N C Aincreases) , but increases. The adsorption

+

THE ELECTRON THEORY OF CATALYSIS

257

process itself leads to the formation of new adsorptioii centers on the surface. Substituting (53) into (51a) and solving Equation (51a) for NcA, we obtain the equation of an isotherm. It can be seen that the resulting isotherm is of a definitely non-Langmuir type, but at NB* = 0 (i.e., when thermal “disorder” is neglected), it goes over into the ordinary Langmuir isotherm. Thus, our surface, which contains only one kind of adsorption center (characterized by a given heat of adsorption qc) and is therefore a homogeneous surface (in the ordinary sense of the term), nevertheless acts as if it were inhomogeneous. This effective inhomogeneity, which shows itself in the violation of the Langmuir relationships, is the result of the concentration of adsorption centers, which are being changed in the very process of adsorption; i.e., in the final reckoning, it is the result of our taking into account thermal “disorder.” N

CA

F I ~31 .

If the total “disorder” is of thermal origin (i.e., N* = 0) and if the maximum disorder possible for the given surface, NA*, is sufficiently great (NA*>> then Equation (53) for the small surface coverage (NCA<< N A ) reduces to

a),

N A

=

m

p

=

dmie+A12kT

(54)

For the adsorption rate in this region of surface coverage, we have

Substituting (54) into (55), we obtain a kinetic equation typical of activated adsorption (with an activation energy ?&A), although in our case there may be no potential barrier near the surface. This is a result of the increase in the number of adsorption centers on heating. In the usual theories of

258

TH. W0LB;ENSTEIN

activated adsorption, which invoke the concept of a potential barrier near the crystal surface, the number of gas particles incident on the surface increases with the temperature, while the number of adsorption centers remains unchanged. In our case, on the contrary, the number of adsorbtion centers increases with temperature, whereas the number of incident particles may remain practically constant. W 4 (a 1

W

(b)

In the case just considered adsorption requires a preliminary excitation of the adsorbent, the degree of this excitation falling off as a result of adsorption. Suppose that q A > qc; i.e., the energy expended on the formation of an adsorption center is greater than that released in adsorption on this center. (This is possible in general.) Then we are dealing with endothermal adsorption (although each adsorption act itself remains exothermal). The possibility of endothermal adsorption was suggested by de Boer (106). Within the framework of the concept of a potential barrier, the endothermal character of adsorption denotes that the height of the activation barrier on the adsorption curve is greater than the depth of the adsorption well. Such adsorption curves for activated adsorption are depicted in Fig. 32. (W is the energy of the system and T the distance between the particle to be adsorbed and the surface.) Figure 32a refers to the case of ordinary exothermal adsorption, and Fig. 32b to endothermal adsorption. We see that the consideration of thermal “disorder” (adsorption on centers of thermal origin) may be another cause of the appearance of endothermal adsorption.* *To avoid confusion it should be emphasized that the terms “endothermic” and exothermic” adsorption are defined here relative to the sign of the energy change (but not the sign of the heat of adsorption). I1

THE ELECTRON THEORY OF CATALYSIS

259

We observe in conclusion that an increase in the number of adsorption centers upon heating may also take place on an ideal surface if the free electrons and holes (free valencies) are regarded as such centers. We have seen (Secs. I1 and 111) that these may be regarded as such if we neglect “weak” bonding in chemisorption and limit ourselves to one type of “strong” bonding (acceptor or donor). Under these assumptions, which return us within the limits of the boundary-layer theory, a particle remains attached to the surface as long as it is charged (bound to an electron or a hole of the crystal lattice) and desorbs in the act of neutralization. The concept of the electrons and holes of a semiconductor as adsorption centers was discussed in refs. 2 and 107,and is also implicitly contained in all thc papers on the boundary-layer theory (see, e.g., 19-23).

X. Conclusions We have seen throughout the present paper that the exposition of the theory can be carried out in terms of three different formalisms: 1. The formalism of the energy band scheme, which reveals the electronic mechanism of the phenomenon. Figures 10, 22 to 27, and 29 may serve as examples. 2. The formalism of valence signs, which is useful for elucidating the chemical features of the phenomenon. This is illustrated in Figs. 4 to 9, 13 to 18, and 20. 3. The formalism of demonstrative models, as exemplified in Figs. 1 to 3, 28, and 30. This formalism is convenient for describing the geometrical aspect of the phenomenon. The energy band formalism is exact. The other two describe the corresponding valence and geometrical schemes (which are, as usual, more or less conditional and approximate). These schemes are, however, very useful and are conveniently employed in a number of problems. As a rule, each problem permits of a translation from one formalism to another. We now formulate the main content of the theory in its present stage of’ development. The quantum-mechanical treatment of the interaction of a foreign molecule with a crystal lattice, as carried out for the simplest models and generalized to more complex systems, leads to a number of results that may be regarded as the fundamental propositions of the theory. The following are the principal ones: 1. Different forms of chemisorption are possible. They are distinguished by the type of bond, which the adsorbed particle forms with the lattice of the adsorbent, and depend on the ability of the chemisorbed particle to involve the free lattice electrons and holes in the bond (Secs. II,A and B). 2. A chemisorbed particle possesses different reactivity in different forms

260

TH. WOLKENBTEIN

of chemisorption, inasmuch as some of these forms are valence-saturatcd and others radical or ion-radical forms (Sec. 111,B). 3. The various forms of chemisorption can go over into one other; i.e., the chemisorbed particle can change the character of its bonding with the surface during its lifetime in the adsorbed state. This is a result of the localization or delocalization of a free electron or hole near the particle (Sec. IV,A). 4. Once electron equilibrium is established, the relative content of the different forms of chemisorption on the surface, and hence the reactivity of the chemisorbed particles is determined by the position of the Fermi level on the crystal surface (Sec. IV,B). 5. The position of the Fermi level determines, all other conditions being equal, the adsorptivity of the surface for each species of particles (Sec. IV,B) and the catalytic activity of the semiconductor for the given reaction (Sec. V,B). 6. The position of the Fermi level on the surface of the crystal depends, in general, on its position in the bulk of the crystal (Sec. V1,A). A relation is thus established between the surface properties and the bulk properties of the semiconductor. These main results lead to a number of consequenceswhich can be experimentally verified. The following are the principal consequences of the theory : 1. The laws of adsorption on a homogeneous ideal surface are essentially of a non-Langmuir type: in particular cases one obtains Langmuir, Freundlich, logarithmic, and other isotherms (Sec. V1,A). This is due to the circumstance that during the lifetime of the particle in the adsorbed state at a given adsorption center the character of the bond which it forms with the center may change. In the final account this is the result of Coulomb interaction between the “strongly” bound chemisorbed particles. 2. Chemisorption leads to a change in the work function and the electrical conductivity of the semiconductor (Sec. V1,C). This is caused by charging of the surface in chemisorption, which fact is in turn a result of the existence of the “strong” forms of chemisorption. 3. There is a correlation between the catalytic activity and the electrical conductivity of the semiconductor (Sec. VI,A), inasmuch as both these properties of the sample are determined by the same factor: the position of the Fermi level. Depending on the character of the reaction, these two factors may change in the same or in opposite directions. 4. Doping of the crystal (both in bulk and on the surface) causes a change in its catalytic activity. This is because doping shifts the Fermi level. This results in either an acceleration or retardation of the reaction. This explains

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the mechanism and the fundamental laws of the promoter and poisoning action of impurities, as well as the mechanism by which impurities affect the selectivity of the catalyst (Sec. VI1,B). 5. Illumination of the semiconductor by photoelectrically active light leads to a change in its adsorptivity and catalytic activity (Sec. VI11,A). This is because illumination causes a change in the surface concentrations of the electron and hole gases. This leads to a change in the relative content of the different forms of chemisorption and, consequently, in the reactivity of the chemisorbed particles. 6. An external electric field applied to the semiconductor also causes a change in its adsorptivity and catalytic activity (Sec. VI11,B). This is the result of a mechanism similar to the preceding case: the field causes a change in the surface concentrations of the free electrons and holes. 7. At sufficiently high dispersion of the semiconductor, its adsorptivity and catalytic activity are sensitive to the degree of dispersion (Sec. VI11,B). This is because, in the case of sufficiently small crystals, the position of the Fermi level depends on the dimensions of the crystal. 8. The transition from an ideal semiconductor surface to a real surface introduces some specific features. At a sufficiently large density of surface states the surface properties of the semiconductor may be independent of its bulk properties (case of a “quasi-isolated” surface, Sec. V1,B). 9. Different surface areas may possess different adsorptive and catalytic properties. This may be because the position of the Fermi level relative to the energy bands varies from one part of the surface to another, this occurring because of the irregular distribution of impurities on the semiconductor surface (Sec. IX,A). 10. The surface imperfections being the centers of localization of free valencies may act as adsorption centers. In this case a real, but homogeneous surface may adsorb as an inhomogeneousone. This is because of thermal “disorder” on the surface of the crystal. We have formulated some of the principal results of the theory and some consequences of these results. Taken together these results lead to a definite conclusion regarding the mechanism of the catalytic action of semiconductors. This mechanism consists in brief in the following. The crystal surface of a semiconductor, having a supply of electrons and holes that participate in the process as free valencies, acts as a sort of “polyradical” in heterogeneous catalysis. It brings the free valencies into play, and this is its function as a catalyst in the process. I n the long run, it affects the heterogeneous reaction rate in the same manner, in which free radicals introduced into the gaseous phase affect the rate of a homogeneous reaction. This may be regarded as the principal conclusion of the theory. The

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concept of a crystal catalyst as a “polyradical” refutes the long-standing opinion that there exists a fundamental difference between heterogeneous catalysis and homogeneous kinetics.

REFERENCES 1. Th. Wolkenstein, J. Phys. Chem. (U.S.S.R.) 22, 311 (1948). 8. Th. Wolkenstein, 6. Phys. Chem. (U.S.S.R.) 26, 1462 (1952).

3. Th. Wolkenstein, J. Phys. Chem. (U.S.S.R.) 28, 422 (1954).

4. Th. Wolkenstein and S. Z. Roginsky, J. Phys. Chem. (U.S.S.R.) 29, 485 (1955). 6. Th. Wolkenstein, Advances in Phys. Sci. (U.S.S.R.) 60, 249 (1956). 6. Th. Wolkenstein, J. Phys. Chem. (U.S.S.R.) 21, 1317 (1947). 7. V. L. Bonch-Bruevich, J. Phys. Chem. (U.S.S.R.) 26, 1033 (1951).

8. Th. Wolkenstein, Bull. Acad. Sci. U.S.S.R., Div. Chem. Sci. 1967, 916; J . chim. phys. 64, 175 (1957). 9. Th. Wolkenstein, Bull. A d . Sci. U.S.S.R., Div. Chem. Sci. 1967, 143. 10. Th. Wolkenstein, Probtems of Kinetics and Caiulysis 8, 79 (1955) (in Russian); Trans. Znst. Chcm. Acad. Sci. Belorussian S.S.R. No. 6 , 3 (1958) (in Russian). 11. Th. Wolkenstein, Bull. A d . Sci. U.S.S.R., Div. Chem. Sci. 1967, 924; J . chim. phys. 64, 181 (1957). 18. Th. Wolkenstein and V. L. Bonch-Bruevich, J. Exptl. Theoret. Phys. (U.S.S.R.) 20, 624 (1950). 13. Th. Wolkenstein, J. Ezptl. Theoret. Phys. (U.S.S.R.) 22, 1% (1952). 14. E. L. Nagayev, Trans. 1st Caf. Higher Educ. Znsts. on Catalysis in press (in

Russian). 16. V. L. Bonch-Bruevich and V. B. Glaako, Compt. rend. m d . sci. U.S.S.R. 124, 1015 (1959). 18. J. E. Iannard-Jonea, Tram. Faraday SOC.28, 333 (1932). 17. J. C . Slater, Phys. Rev. 38, 1109 (1931). 18. A. A. Balandin, Problems of Chemical Kinetics, Calalysis and Reactivity p. 461 (1955) (in Russian). P. Aigain and C. Dugaa, 2. Elektrochem. 66, 363 (1952). J. E. Germain, Compt. rend. 236, 238,345 (1954); J . chim. phys. 61, 263 (1954). H. J. Engel and K. Hauffe, 2.Elektrochem. 67, 762 (1953). H. J. Engel, Nalbleiterproblm No. 1, 249 (1954). 93. K. HaufTe, Angew. Chem. 67, 189 (1955). 84. Th. Wolkenstein, Bull. Moscow Slate Uniu. No. 4, 79 (1957) (in Russian); J. Phys. Chem. (U.S.S.R.) 82, 2383 (1958). 86. S. M. Kogan, J. Phys. Chem. (U.S.S.R.) 33, 156 (1959). 88. P. B. Wekz, J . Chem. Phys. 21, 1531 (1953). 87. V. V. Voyevodeky, Th. Wolkenstein, and N. N. Semenov, Probkms of Chmnical Kinetics, Calalysi. and Recrctivity p. 423 (1955) (in Russian). 88. N. Thon and H. A. Taylor, J . Am. Chem. Soc. 76, 2747 (1953). 90. 0. V. Krylov, 5. Z. Roginsky, and E. A. Fokina, Bull. A d . Sci. U.S.S.R., Div. Chem. Sci. 1067, 422. 30. W. E. Garner, Advances in Catalysis 9, 169 (1957). 31. T. Takaishi, 2.Naturforsch. 118, 297 (1966). 38. J. E. Germain, “Catalyse heterogene.” Dunod, Paris, 1959. 33. G. M. Schwab and J. Block, 2.physik. Chem. (Frankfurt) [N.S.] 1, 42 (1954). 34. K. HaufTe and E. G. Schlosser, Dechemu-Monographien 26, 222 (1956).

19. 80. 81. 99.

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36, G . Parravano, J . Am. Chem. SOC.74, 1194 (1952); 76, 1448, 1452 (1953). 86. N. P. Keyer, S. Z. Roginsky, and P. S. Sazonova, Compt. rend Acad. Sci. U.S.S.R. 106, 859 (1956); Bull. Acad. Sci. U.S.S.R., Div. Phys. Sci. 21, 183 (1957). 3Y. Th. Wolkenstein, J . Phys. Chem. (U.S.S.R.) 24, 1068 (1950). 38. M. Boudart, J . Am. Chem. SOC.74, 1531 (1952). 39. K. HaufTe, Advances in Catalysis 9, 187 (1957). 40. 5.M. Kogan and V. B. Sandomirsky, Problems of Kinetics and Catalysis 10, in press (in Russian); J . Phys. Chem. (U.S.S.R.) in press. 41. Th. Wolkenstein and S. M. Kogan, 2. physik. Chm. (Leiprig) 211, 282 (1959); J . Phys. Chem. (U.S.S.R.) in press; Trans. 1st Conf. Higher Educ. Insts. on Catalysis in press (in Russian). 49. J. Bardeen, Phys. Rev. 71, 717 (1947). 43. I. E. Tamm, 2. Physik. 76, 849 (1932); Physik. 2.Sowjetunion 1, 733 (1932). 44. E. T. Goodwin, Proc. Cambridge Phil. Soc. 36, 205 (1939). 46. V. L. Bonch-Bruevich and Th. Wolkenstein, J . Phys. Chem. (U.S.S.R.) 28, 1219 (1954); Problems of Kinetics and Catalysis 8, 218 (1955) (in Russian). 46. V. B. Sandomirsky, Candidatc’s thesis, Inst. Phys. Chem., Acad. Sci. U.S.S.R. (1955). 4Y. Th. Wolkenstein and V. B. Sandomirsky, Problems of Kinetics and Catalysis 8, 189 (1955) (in Russian). 48. V. B. Sandomirsky, Bull. Acad. Sci. U.S.S.R. Div. Phys. Sci. 10, 211 (1957). 49. W. E. Garner, T. J. Gray, and F. S. Stone, Proc. Roy. SOC.8197, 296 (1949). 60. T. J. Gray, Discussions Faraday SOC.8, 331 (1950). 61. V. I. Lyashenko and I. I. Stepko, Bull. Acad. Sci. U.S.S.R., Div. Phys. Sci. 16, 211 (1952). 62. J. A. Dillon and H. E. Farnsworth, J . Appl. Phys. 28, 174 (1957). 63. V. I. Lyashenko, Trans. Znsl. Phys. Acad. Sci. Ukrainian S.S.R. No. 4, 33 (1953) (in Russian). 64. G. Heiland, 2.Physik. 138, 459 (1954). 66. V. I. Lyashenko and I. I. Stepko, Problems of Kinetics and Catalysis 8, 180 (1955) (in Russian). 66. I. A. Myasnikov and S. Y. Psherhetsky, Problems of Kinetics and Catalysis 8, 175 (1955). 67. S. Y. Elovitch and L. I. Margolis, BuU. Acad. Sci. U.S.S.R., Div. Phys. Sci. 21,206 (1957). 68. N. P. Keyer and L. N. Kutseva, Compt. rend. Acad. Sn’. U.S.S.R. 117, 259 (1957). 69. G. Parravano and C. A. Dominically, J . Chem. Phys. 26, 359, (1957). 60. N. P. Keyer and G. I. Chizhikova, Compt. rend. Acad. Sci. U.S.S.R. 120,830 (1958). 61. L. I. Margolis, Bull. Acad. Sci. U.S.S.R., Div. Chem. Sci. 1968, 1175. 62. V. I. Lyashenko and V. G. Vitovchenko, J . Tech. Phys. (U.S.S.R.) 28, 447, 454, (1958). 63. E. H. Enikeyev, L. I. Margolis, and S. Z. Roginsky, Compt. Tend. Acad. Sci. U.S.S.R. 124, 606, (1959). 64. E. H. Enikeyev, Problems of Kinetics and Catalysis 10, in press (in Russian). 66. Th. Wolkenstein, J . Phys. Chem. (U.S.S.R.) 26, 1244 (1951). 66. S. W. Weller and S. E. Voltz, J . Am. Chem. SOC.76, 5227 (1953); Z. physik. Chem. (Frankfurt) [N. S.] 6, 100 (1955). 6Y. P. R. Chapman, R. H. Griffith, J. D. F. Marsh, Proc. Roy. SOC.224, 419 (1954). 68. K. I. Matveyev and G. K. Boreskov, Problems of Kinetics and Catalysis 8, 165 (1955) (in Russian).

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69. L. F. Heckelsberg, A. Clark, and G. C. Bailey, J . Phys. Chem. 60, 559 (1956). 70. G. Rienacker, Berichtsband von der Chem. Gesellschaft in der D.D.R., in press. Yl. G. M. Schwab and J. Black, Z.Elektrochem. 68, 756 (1954). 72. G. M. Zhabrova and E. A. Fokina, Bull. A d . Sci. U.S.S.R., Div. Chem. Sci. 966,963. Y3, 0.V. Krylov and L. I. Margolis, J . Org. Chem. (U.S.S.R.) 20, 1991 (1950). 74. G. M. Zhabrova, Advances in Chem. (U.S.S.R.) 20, 450 (1951). 76. Th. Wolkenstein and S. M. Kogan, J . chim. phys. 66, 483 (1958); Bull. Acad. Sci. U.S.S.R., Div. Chem. Sci. 1969, 1536. 76. A. N. Terenin, J . Phys. Chem. (U.S.S.R.) 6, 189 (1935). 77. J. A. Hedvall, 2. physik. Chem. B32, 383 (1936). Y8. L. N. Kurbatov, J . Phys. Chem. (U.S.S.R.) 14, 1049 (1940). 79. A. Luyckx, J. Bodart, and G. Rens. J . chim. phys. 39, 139 (1942). 80. J. A. Hedvall and S. Nord, 2.Elektrochem. 49, 467 (1943). 81. A. N. Terenin, Problems of Kinetics and Catalysis 8, 17 (1955) (in Russian). 82. I. A. Myasnikov and S. I. Pshczhetsky, Problems of Kinetics and Catalysis 8, 34 (1955) (in Russian). 83. A. Kahayashi and S. Kawaji, J . Phys. Sac. Japan 10, 270 (1955); 11, 369 (1956). 84. D. A. Melnick, J . Chem. Phys. 26, 1136 (1957). 86. T. Kwan and Y . Fujita, Bull. Chem. Sac. Japan 31, 380 (1958). 86. E. Bauer, C.Neuweiler, Helv. Chim. Acta 10, 901 (1927). 87. W.M. Ritchey and J. G. Calvert, J . Phys. Chem. 60, 1465, (1956). 88. G. M. Schwab, Advances in Catalysis 9, 239 (1957). 89. G. A. Korsunovsky, J . Phys. Chem. (U.S.S.R.) 31, 2351 (1957). 90. V. P. Juze and S. M. Ryvkin, Compt. rend. Acad. Sci. U.S.S.R. 77, 241 (1951). 91. V. E. LaRhkarev, S. Z. Vavilov Commemoration Volume p. 324 (1052) (in Russian) 9.2.Th. Wolkenstein and V. B. Sandomirsky, Compt. rend. Acad. Sci. U.S.S.R. 118, 980 (1958).

93. J. W. Pratt and H. H. Kolm, “Semiconductor Surface Physics,” p. 297. Univ. of Penn. Press, Philadelphia, 1957. 94. S. M. Kogan, Problems of Kinetics and Catalysis 10, in press (in Russian). 96. S. M. Kogan and V. B. Sandomirsky, Compt. rend. Acad. Sci. U.S.S.R. in press; Bull. Acad. Sci. U.S.S.R., Div. Chem. Sci. in press. 96. S. Z. Roginsky, Problems of Kinetics and Catalysis 8, 110 (1955) (in Russian). 97. S. Z. Roginsky, Chem. Sci. and Znd. 2, 138 (1957) (in Russian). 98. V. L. Bonch-Bruevieh, J . Phys. Chem. (U.S.S.R.) 27, 662, 960 (1953). 99. K. Hauffe, Bull. sac. chim. belg. 67, 417 (1958). 100. E. Bauer and H. Staude, Katalyse. Bericht v m der Hauptjahrestagung 1968,Chem. Gesell. i n der DDR, p . 121, 1959. 101. N. I . Kobozev, Acta Physicochim. U.R.S.S. 13,469 (1940). 10.2. N. I . Kobozev, Advances in Chem. (U.S.S.R.) 23, 545 (1956). 103. 0. M. Poltorak, J . Phys. Chem. (U.S.S.R.) 29, 1650 (1956). 104. 0. M. Poltorak, J . Phys. Chem. (U.S.S.R.) 32, 534 (1958). 106. Th.Wolkenstein, J . Phys. Chem. (U.S.S.R.) 23, 917 (1949); Problems of Kinetics and Catalysis 7, 360 (1949) (in Russian). 108. J. H. de Boer, Advances in Catalysis 9, 472 (1957). 107. Th. Wolkenstein, J . Phys. Chem. (U.S.S.R.) 27, 159, 167 (1953); Advances in Phys. Sci. (U.S.S.R.) 60, 253 (1953).

Molecular Specificity in Physical Adsorption D. J. C. YATES Department of Colloid Science, University of Cambridge, Cambridge, England* Page I. Introduction .......................................................... 265 11. The Perturbation of Solids by Adsorbed Molecules.. ...................... 266 A. Surface Energy and Surface Tension of Solids.. ........................ 266 B. Changes in Surface Energy and Tension Due t o Adsorption.. . . . . . . . . . . . 268 C. Volume Changes in Solids on Adsorption.. ............................ 270 D. Implications of These Effects on Theories of Physical Adsorption. . ...... 282 111. Perturbation of Adsorbed Gases.. ....................................... 284 A. The Nature of the Adsorbed Phase.. ................................. 284 B. Newer Experimental Techniques. .................................... 285 IV. Over-All Changes at the Solid-Gas Interface ............................. 290 A. Effects Due to the Presence of Surface OH Groups on Porous Glass. . . . . . 290 B. Some Considerations of Surface Topography.. ......................... 303 V. Conclwion. ..... ................................................ 307 References ........................................................... 308

1. Introduction This article consists of a review of certain specific effects that occur during the process of physical adsorption, in which the writer has been especially interested. While it is hoped that all work directly relevant to these aspects of adsorption has been covered in a comprehensive manner, this review does not aim to cover all the specific effects that are known to occur on adsorption. Some surprise may be occasioned by the title, as the statement is sometimes found ( 1 ) that physical adsorption is essentially nonspecific in nature, particularly when nonpolar gases are used as adsorbates. I t will be shown, however, that this is an oversimplification of the process and that specificity is almost as prevalent, although not as obvious, in physical adsorption as in chemisorption. A general review of physical adsorption has been given in this series by de Boer (d), and other specialized topics have been discussed by Kemball (S), Hill (4),and Halsey (6); they may be consulted for the many aspects of the subject not considered in this article. Conceived in its widest terms, the aspect of ?physical adsorption con-

* Now a t the School of Mines, Columbia University, New York 27, N. Y. 265

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sidered here is that of the perturbations resulting from adsorption. In Sec. 11, various aspects of the perturbation of solid adsorbents are considered. The other half of the adsorption pair is considered in Sec. 111; namely, the changes that take place in the adsorbed molecules themselves. Finally, in Sec. IV, some consideration is given to systems in which both types of perturbation have been measured.

II. The Perturbation of Solids by Adsorbed Molecules A. SURFACE ENERQY AND SURFACE TENSION OF SOLIDS As in so many other fundamental aspects of the thermodynamics of surfaces, we are indebted to Gibbs (6) for pointing out that for solids the surface tension ( 7 ) and surface free energy (F') are not equivalent quantities. Nevertheless, as Shuttleworth (7) mentions in an excellent review, the two terms have been (8) and still are (9) confused. The relationship between the quantities is y = F'

+ A dF'/dA

(1)

where A is the surface area. For a liquid, dF'/dA is zero and the surface tension is numerically equal to the surface energy. For a solid, in contrast, Shuttleworth has shown that F' and A dF'/dA are expected to be of the same order of magnitude. Theoretical calculations of the surface free energy of solids date back to 1928 with the work of Lennard-Jones and Dent (10). Displacements of the positive and negative ions when a given interior layer becomes a surface layer were allowed for by Verwey (11).Calculations by Shuttleworth (12) showed that van der Waals terms make a significant contribution to surface energy. Benson and his co-workers have made an extensive study of alkali-halides (13-16) and of magnesium oxide (17). Some of the difficulties involved may be gathered from the fact that the values calculated for LiF vary from +550 ergs/cm.2 ( I S ) to a negative value (16). Similar difficulties occur with MgO (17),variations in the van der Waals and repulsive terms produced values for F' ranging from - 151 to +885 ergs/cm.2 according to the model used. Following the original measurements of the surface energy ofzsodium chloride by heats of solution by Lipsett et al. (I8), much more accurate determinations have been carried out recently by Benson and his co-workers (19-22). Other substances which have been investigated include magnesium oxide (W), calcium oxide and hydroxide (24), and silica, unhydrated and hydrated (26). When precautions are taken with the purity of the solids (go) and care

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is taken to prepare a series of samples of accurately known surface area (19, 24), reliable data can be obtained. For sodium chloride, the best value (21) is 276 ergs/cm.2. Strictly, the heats of solution experiments measure the surface enthalpy, not the surface free energy. The difference between the two quantities has been shown, however, to be about 5% ( 2 6 ~ It ) . can be concluded that the experimental techniques a t present in use give reliable values of surface energies. The same cannot be said about the surface tension of solids. The paper by the late Dr. Nicolson (26) is practically the only extensive theoretical treatment of the subject. It is of interest to note that for NaC1, the calculated surface tension is 562 dynes/ cm. (26), and the calculated surface energy (16) is 187 ergs/cm.2. Thus, the surface tension, rather than having the same numerical value as the surface energy, is about three times as large. There is a corresponding paucity of experimental determinations of the surface tension of solids, probably because no direct experimental method has been developed. A review of the work on the surface tension of solid metals has been given by Shaler (27). These values were obtained, in most cases, near the melting point of the metals and thermodynamic equilibrium was achieved. These experiments are thus quite different from those where the nonequilibrium state persists, with incomplete relief of surface stress. As this review is mainly concerned with high surface area adsorbents in a state of considerable surface stress (in vacuo a t least), the above results with metals will not concern us further. Magnesium oxide crystals about 500 A. in diameter were prepared in uacuo by Nicolson (26).Lattice determinations by X-rays showed that the parameter of these small crystals was smaller than that of large crystals. The surface tension obtained from these experiments (+3,020 dynes/cm.) was 46y0of the theoretical value. Similar experiments were carried out with sodium chloride crystals made in vacuo (size about 2000 A), and the agreement between experiment and theory was better, the observed surface tension (+390 dynes/cm.) being Toy0of that calculated. While other experiments specifically performed to measure the surface tension of solids seem lacking, other changes in lattice constants due to surface effects have been reported. Rymer and Butler (28) found that the electron diffraction rings obtained from thin gold leaf were not those expected from the lattice constants of bulk gold. This they attributed to the surface tension of the material. Boswell (29) made small particles (less than 150 A) of NaCI, NaBr, KCl, LiF, gold, and bismuth by evaporating mm. the substances in an electron diffraction camera with a vacuum of The lattice constants became smaller in a regular fashion as the particle size decreased, indicating the existence of a positive surface tension. Calculations, by the writer, using the compressibility values used by Nicolson

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(26) give a value for NaCl of $300 dynes/cm. for the surface tension. It is of interest to note that Rymer in a recent review (S9a)has questioned the validity of Boswell's data. His experiments indicate a negative surface tension for LiF, in agreement with Shuttleworth's calculations (7). It can be concluded that much remains to be done before even the sign of the surface tension of alkali halides is known with certainty.

B. CHANGES IN SURFACE ENERGY AND TENSION DUE TO ADSORPTION Direct experimental determinations of these quantities do not exist. The nearest approach seems to be in some observations made by Nicolson (26) in his work on surface tension. He found that when he made magnesium oxide particles by burning magnesium in air, their lattice constants were the same as those of the bulk material. When the crystals were made by the decomposition of magnesium carbonate in vacuo, the expected change in lattice parameter took place due to the surface tension. These negative results obtained in the first method of preparation were attributed to the presence of gases adsorbed from the air. The problem has been treated theoretically by the use of the Gibbs adsorption isotherm, which has been used with success in treating the interfaces between liquids and gases (30).One of the most easily measurable properties of a liquid is its surface tension, and changes in this quantity can be determined with great accuracy. The surface tension of a liquid is numerically equal to its surface energy, as also are changes in these quantities. No such simplicity exists for solids. Accurate methods for determining their surface tensions do not exist, and neither do methods for measuring changes in this quantity. By direct analogy with liquids, Bangham and his co-workers (31, 32) showed that the Gibbs adsorption isotherm could be applied to solids. If F,' is the surface energy (in ergs/cm2) of the solid in vacuum and F' that of the solid with adsorbed material on it, we have T =

-AF'=F'-F,'=RT/rdlnp

(2)

The decrease in free energy is equal to T , the spreading pressure, a quantity which has been widely used in studies a t liquid interfaces. As the free energy is reduced, the spreading pressure becomes larger. The pressure of gas above the solid is p, and r is the concentration of adsorbed material. Converting into the experimental variables usually measured, we have

where M is the molar volume at s.t.p., z the surface area in crnm2/g.,and v

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the volume of gas adsorbed (at s.t.p.). The assumption involved in the conversion of r to v has been examined by Boyd and Livingston (33). It is to be noted that this equation does not apply to the capillary condensation region (if this exists for the particular adsorbent used), since true equilibrium cannot be obtained in this region (34). In general ?r cannot be obtained from a theoretical adsorption isotherm equation, since they are not accurate enough over wide ranges of pressure. Graphical integration is necessary, and procedures and precautions for this have been discussed in detail by Jura and Harkins (8). In particular, they stress the need to have accurate data in the very low pressure region of the isotherm, since a t these pressures very high values of v / p are found. For instance, when argon was adsorbed on porous glass at 79' K. at a pressure of 2 X cm., the value of v / p was 1,410,the coverage then being 0.07. When the pressure was increased to 4.0 cm., v / p had dropped to 10.5 a t monolayer coverage (36).At somewhat lower relative pressures, values of over 3,000 were found with nitrogen and oxygen. The importance of the low-pressure region of the isotherm has been discussed elsewhere (36). Many calculations have been reported in the literature (8,32, 33,36-41) of the surface free energy lowering on adsorption. The accuracy of these results is very difficult to judge, since only in some cases were ?r values given, or of molecular and even then ?r was plotted as a function of pressure (8,38) area (41), methods which give highly curved plots. Furthermore, the necessity of obtaining accurate isotherm data at low pressures was often ignored. Consequently, there are no values in the literature to enable a comparison to be made of the ?r values on various adsorbents with, say, a monolayer of argon or nitrogen adsorbed on them. While there is an obvious physical meaning to the ?r values obtained at the liquid surface, the significance of the values obtained a t the solid interface is in considerable doubt. Everett (42) considers that, although spreading pressures measured on liquids have a definite meaning and are extremely useful in any theoretical approach, this is not the case for solids where he considers that the meaning of the spreading pressures is uncertain. Pierce and Smith (43)mention the effect of nonuniformity of the surface. Because of possible localization on sites of high energy, they think that spreading pressures calculated from isotherms on heterogeneous surfaces may be misleading. When it is remembered that the majority of solids used as adsorbents in physical adsorption studies have very heterogeneous surfaces, the significance of these remarks will be appreciated. The nature of the surface migration provides the key to the differences between adsorption on liquid and solid surfaces. For liquid surfaces, it is, to a good approximation, possible to assume that the heat of adsorption (AH) is the same at all points on the surface. In other words, such a surface

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D. J .

C. YATES

is completely homogcneous in its adsorptive properties. For such a surface the adsorbed molecules behave as an ideal two-dimensional gas, sliding along in all directions. Their random motion is only disturbed by completely elastic collisions. This motion is the analog of an ideal gas, with its chaotic molecular motion in three dimensions. For a real liquid, the thermal motion of the surface molecules upsets this simple picture, but not severely (44). In contrast to this, for a crystalline solid, the free movement of the adsorbed molecules is very much restricted by the periodic nature of the force fields a t such surfaces. Then the activation energy to move from one place of adsorption t o another (AH') becomes very important. Little is known, theoretically or experimentally, about the size of AH' relative to AH, but it is generally considered (46-47') that'AH' is about AH/2 or less. Movement of molecules along this surface takes place by a series of jumps from site to site rather than by a sliding motion. Little consideration has been given to the equality, or otherwise, of the surface energy (and a) values calculated by the above methods and the surface tension changes. For liquids the two changes will be equal. For solids, Bangham (31) has shown that when the adsorbed phase can be considered to behave as a two-dimensional gas, the surface tension lowering and the surface energy lowering are equal and are also equal to the spreading pressure. He did not specifically consider the intermediate case where mobility takes place by a series of hops, but did consider chemisorption. Then the molecules are fixed (for times long relative to the time of the experiment) to the sites of adsorption. Consequently, a will be zero, since no surface migration will take place, and the surface tension of the solid will be unchanged. Nevertheless, the free energy will be decreased. Similar remarks have been made by Crawford and Tompkins (@), who think that there will be a relation between a and AH' for solids, and that when AH' is large enough, T will be zero. In conclusion it is considered that when adsorption takes place on solids with AH' small relative to AH, the following relation holds: where the surface tension of the solid in vacuo is yoand is y1with an adsorbed film,and F,' and F' are the corresponding surface free energies.

C. VOLUMECHANGES IN SOLIDS ON ADSORPTION 1. Historical Development In the development of this type of work, the first experiments were some ten years or so in advance of a theoretical explanation of the facts, 80 this aspect will be dealt with first

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271

This review will be confined to volume changes produced only by adsorption, the molecules of the adsorbate being confined to the surface. Penetration of the adsorbate into the adsorbent is known to occur in systems as diverse as hydrogen in palladium, caesium in organic salts (49),and graphite by bromine, fluorine, potassium, sulfuric acid and nitrogen dioxide (50). Generally, this absorption process takes place most easily with the graphite type of structure, where the adsorbate penetrates between the layers, where the forces holding the solid together are relatively weak. As an instance to show how easily penetration can occur, McDermot and Arne11 (51) have suggested that it takes place in the graphite-nitrogen system, although this is not certain. The swelling of rigid solids by surface adsorption has been studied by fewer workers, and in the main has been confined to the use of charcoal and coal as adsorbents. Changes in size of a cube of charcoal on adsorption were first observed by Meehan (52).Carbon dioxide was adsorbed a t room temperature, and it was shown that the expansions were isotropic. Following this, Bangham and his co-workers (6540) made a thorough study of the phenomenon over the years 1928 to 1946. Most of the work was done with charcoal, but some experiments on coal were also reported (69, SO). A wide range of adsorbates were used, including water, ammonia, sulfur dioxide, carbon dioxide, benzene, pyridine, and several lower alcohols. These gases were nearly all adsorbed a t room temperatures, the length changes being measured with a mechanical lever extensometer. Values of the percentage linear expansion varied from 1-2 with pyridine to 0.16 with carbon dioxide. Other early workers in this field include Briggs and Sinha ( G I ) , who measured the effect of carbon dioxide on coal and McBtlin et wl. (62),who adsorbed water, heptane, and benzene on sugar charcoal. Later workers were able to put their results on a quantitative basis, which Bangham was unable to do, because of the classical work of Brunauer et al. (SS),which provided, for the first time, an accurate method for determining the surface area of any finely divided substance. Haines and McIntosh (64)developed a capacitance type of extensometer and using rods of zinc chloride activated charcoal, adsorbed dimethyl ether, butane, and ethyl chloride. Wiig and Juhola (65) used a charcoal with a very high surface area and measured with a cathetometer the expansion due to water adsorption of a long rod of the material. Razouk and El Gobeily using a mechanical-lever extensometer and willow-wood charcoal, adsorbed methyl alcohol, carbon dioxide, oxygen, ammonia, and sulfur dioxide (66). Since 1950, the scope and nature of these effects have been studied in greater detail. Amberg and McIntosh (67) were the first to use porous glass as the adsorbent and studied water adsorption. In later work (68, 69) butane, ethyl chloride, and ammonia were adsorbed. Flood and Heyding

272

D. J. C. YATES

(70) worked with zinc chloride activated charcoal rods and adsorbed water and nitrogen a t room temperatures. By the use of a very ingenious device for winding fine wire round the rods, radial changes were measured; it was shown that they were isotropic. Length changes were observed in another apparatus by means of a traveling microscope. Further work with helium, argon, krypton, and hydrogen has been reported (71) and, more recently with ethane, propane, butane, methanol, and carbon tetrachloride (72,78). Apart from the work of McIntosh and co-workers (67-69) with porous glass, all the above experiments were conducted with charcoals and carbons of varied degrees of surface complexity. It seemed necessary to study lengthchange effects where the surface processes were a little better defined. In particular, heats of adsorption had been reported in only one case (67') on the same adsorbent as that used in a length-change experiment. Consequently, it was uncertain whether the process producing the expansion was solely due to physical adsorption, or whether a small amount of chemisorption dominated the whole process. For any theoretical understanding of the effect, this knowledge is essential, since only physical adsorption is completely reversible and can be treated satisfactorily thermodynamically. Irrespective of the surface they adsorb on, only the rare gases, which form few, if any, true chemical compounds, will be held solely by physical or van der Waals' forces. Although porous glass has a complex surface, it was considered to be somewhat better defined than charcoals, whose complexity and irreproducible behavior are notorious. It was found possible to measure length changes a t temperatures as low as 77' K. and the effects of argon, krypton, nitrogen, oxygen, and hydrogen were measured (74). Using the same apparatus and sample, the effects of range of polar gases were also studied (76-77). 2. Theory of Volume Changes In this particular review, volume changes that occur on adsorption are viewed from the information and relevance they have to the process of physical adsorption per se. It is now well known that under suitable conditions physical adsorption can continue far beyond the monolayer (where the coverage B = 1) to form multilayers (78). In this multilayer region, the process is formally defined as physical adsorption, but it really has more in common with condensation processes that occur in the bulk transitions from vapor to liquid than anything else. When multilayer adsorption takes place on an adsorbent which has small pores in it, the process of capillary condensation (79)occurs. This is associated with hysteresis in the isotherms and, as they are not reversible, the application of thermodynamics to this region is very difficult. McIntosh and co-authors (67-69) have utilized, in an interesting way, volume changes on adsorption to get more information about this hysteresis than can be gleaned from isotherms alone. These

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273

effects, interesting as they are, seem to be relatively unrelated to adsorption effects which occur a t coverages less than unity, and to be a function of the porous nature of the adsorbent. Both for this reason, and because they seem to be largely nonspecific in nature, they will not be discussed further here. Apart from a few cases where entropy changes predominate (80),the process of adsorption occurs spontaneously because of the decrease in the free energy which takes place (81).This free energy is that of the surface on which adsorption takes place. An atom in the surface of a solid is subject to unbalanced forces, the inward pull being larger than the outward. Physically, this is the reason for the finite surface tension that occurs in all surfaces. Any gas molecules adsorbed on such a surface saturate some of the unbalanced surface forces, decreasing the surface tension and energy. Bangham and Fakhoury (64, 66) suggested that the phenomena of adsorption expansion was related to this change in free energy and proposed the equation :

XdF‘ (5) where x is the percentage linear expansion, dF‘ the free energy lowering, and X a constant. The relation between dF‘ and the spreading pressure T has been discussed in the previous section and also the determination of dF’from accurate isotberms on a solid of known surface area. Further work by Bangham and Maggs (59) related the constant X to the elastic constants of the charcoal. The solid is considered made up of one long thin nonporous rod such that its specific surface is equal to that of the porous solid. The spreading pressure is assumed to act as a tangential stress tending to increase the length of the rod. Then it is found that

x

E

=

ZP = 100 y A

where E is the Young’s modulus of the solid, r, the specific surface in cm.*/g., and p the density of the nonporous rod. This equation has also been shown by Bangham to be valid if the solid is considered as a planecontinuous lamina. Meehan (62) showed in the first experiments on the subject that the expansion was isotropic. This has later been confirmed more accurately by Flood and Heyding (70). It would seem that a better model would be obtained of the process by relating the expansion constant X to the bulk modulus of the solid rather than the Young’s modulus. In measurements of bulk modulus the size changes are isotropic, while in the measurement of Young’s modulus, an expansion along one axis is accompanied by contractions along the other two. Instead of a long thin rod, we shall take as our model a system composed of spheres lightly sintered together. The proper-

274

D. J. C. YATES

ties of such an aggregate will probably have the elastic properties of the material of the sphere. Mackenzie and Shuttleworth (82) have shown that sintering is probably due to the surface forces causing the surface layers to flow together a t the contact between the spheres. Thus, the “neck” holding the sintered spheres will have elastic properties identical with the material from which the spheres are made. Other more sophisticated models of porous solids have been suggested (70). Until much more is known about the real geometry of the porous solids used in this type of work, the simplest possible model is to be preferred. We will now consider surface tension (y) changes in one of these spheres. The surface tension of an isolated solid must be balanced by elastic strains induced in the solid. For a solid sphere it has been shown (7’) that

p = -27 T

(7)

where T is the radius and P the pressure difference across the interface. It might be thought that this effect would be negligible, but for high area solids which have small “effective” radii, this is not the case. Let T be 80 A and if y is taken (for silica) as 780 dynes/cm. (three times the surface energy value (26)), we find P = 1.95 X lo0 dynes/cm.2 rr 2,000 atm. Hence, we can think of the sphere i n vacuo as being under a hydrostatic pressure of 2,000 atm. provided by its own surface tension. This stress in a sphere of this size with a bulk modulus of 1.0 X 10” dynes/cm.2 produces a decrease in radius of about 1.2%, relative to its radius with zero surface tension. When gases are adsorbed on such a system, the reduction in y brings about a reduction in the stress and the solid expands. It has been shown (74)83)that for such a system the expansion constant X is related to the bulk modulus K by

K = -200 - zp 9 x

Furthermore, by combining Equation (5) with Equation (8), it can be shown that the total change in free energy dF (==dF‘A), where A is the area, divided by the volume change, is given by

In this derivation the expansion of the solid is assumed to be isotropic. 3. Experimental Results

This section will be restricted to results obtained when the coverages were less than about 1.5 monolayers and because of this, all work where the surface area of the solid is very uncertain (62-62) is excluded.

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275

Haines and McIntosh (64) used zinc chloride activated rods of length between 8 and 13 cm., the length changes being measured with a capacitance extensometer. The ratio of the smallest length change detectable to the original length (Al/Z) was about 2 X for this system. As adsorbates butane, dimethyl ether, and ethyl chloride were used a t room temperatures. Results for rod No. 13 (average surface area 960 m."g.) are given in Fig. 1, drawn from Table I (64). It will be seen that for both gases used, contractions took place. They were not observed in all cases; when dimethyl ether was adsorbed on rod No. 11 (at 20" C.), only expansions were observed. Values of R a t Vmand Vm/2 are given for ethyl chloride and dimethyl ether on Fig. 1. Beyond the minimum in the curve, the relatiori 2 = X dF'

Free energy lowering ~ , e r g s / c m ?

FIG.1. Expansions of an activated charcoal rod produced by the adsorptioii of ethyl chloride ( 0 )at 10"C. and dimethyl ether (+) at 6.5" C. (6'4).

is quite well obeyed. The cause of the contractions was considered in some detail, but no unique mechanism was suggested. Values of the Young's modulus ( E ) were calculated from Equation ( 6 ) . Water was also adsorbed a t 20" C., and only small length changes took place at low relative humidities. Large hysteresis effects were found in the capillary condensation region. In the next paper (67), the same extensometer was used with a rod of porous glass 11 cm. in length. The surface area was 117 m.2/g. calculated from water isotherms. Length changes were measured with a sensitivity Al/l of 2 X 10-6 and were measured for water adsorbed a t 11.8, 18.7, and

276

D. J. C. Y A W

25.8" C. The main interest was in the capillary condensation region, and for each of the three isotherms, only the first three points of each one was in the region below 0 = 1.5. Probably for this reason, their plots of r against Al/l (Fig. 2) were quite good at coverages greater than unity but showed quite large deviation a t lower coverages. The Young's modulus ( E ) obtained from the initial expansion region was 3.8 X 10" dynes/cm.2. Heats of adsorption were calculated from the three water isotherms, and were about 15.5 kcal./mole a t monolayer coverage. All effects were found to be reversible. 0.12 0.10 0.08 0)

-

I

1

1

1

1

1

-

-

0

20

40

60

80

100

I20 140

s,ergs /cm?

RQ.2. Length changes of poroue glass produced by water adsorption aa a function of free-energy lowering ( x ) (87). Later experiments were performed using a similar extensometer with a different porous glass rod. Butane (at -6.2" C.), ammonia (-39.2' C.) and ethyl chloride (6.0' C.) were adsorbed. As the capillary condensation region was again that of main interest, no details were given of the expansions at below monolayer coverage, although isotherms down to fairly low relative pressures were presented (68). Graphs were given of length changes due to butane, especially detailed in the capillary condensation region, and discussed (69). No details were given of the ethyl chloride length changes except that Bangham's equation was tested for butane and ethyl chloride. Length-change data were not obtained with ammonia or with ethyl chloride a t low coverages. Some irreversibility was found in the adsorption isotherms for all the gases used, especially the polar ones, since the hysteresis loops did not close on desorption. No mechanism was suggested for this nonclosure effect. Earlier work with porous glass showed similar anomalous effects with oxygen (84-86), which were attributed (86) to small amounts of chemisorption on the grease sometimes present on this surface.

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277

Flood and Heyding (70) compared results obtained by earlier workers (64, 65, 67) from the standpoint of volume average stresses in the solid created by the adsorbate in the adsorptive force field. In addition, length changes were measured for a zinc-activated carbon rod. The rod was 8.8 cm. long and the traveling microscope used measured the length changes to f 2 X lo+ cm. The sensitivity AZ/Z is thus about 2.5 X le6. In addition to length-change measurements, the radial changes of the rod were determined by a winding device. No surface area values were reported although

PV Units adsorbed

FIQ.3. Contractions and expansions of an activated carbon rod as a function of pressure-volume units of adsorbed material. KEY:0 , ethane; X, n-propane; 0, n-butane; V, n-pentane; 0 , 2,2dimethyl propane;

+, carbon tetrachloride. (75).

the isotherm was given for water. As the length changes were plotted as a function of pressure, an indirect method, it is difficult t o estimate the length changes in the monolayer region. Considerable attention was paid to effects in the capillary condensation region. Later work (71) was with another carbon rod of similar properties. Improved optical equipment encm. abled length changes of the 11.0 cm. rod to be measured to f 2 X Helium, hydrogen, nitrogen, argon, and krypton at room temperatures

278

D. J. C. YATES

were used as adsorbates a t pressures up to 2,000 lb/in.2. Further theoretical discussions wcre given in a later paper (72), together with some results a t lower pressures with saturated hydrocarbons. Carbon rod No. 4 was used (73), and ethane, propane, butane, pentane, carbon tetrachloride, and methanol were adsorbed a t 24.8" C. Contractions were found in all cases to take place a t low relative pressures (Fig. 3). Volumes adsorbed were given, but not monolayer capacities. These results will be discussed later in Sec. IV. A vacuum interferometer was developed by Yates (74) which was capable of use over the ranges of temperature normally used in adsorption work, namely, from 4-450 to -1196" C. This makes possible pretreatment of the sample under conditions usually used in physical adsorption, with an ultimate vacuum of about mm. Easy removal of grease from the surface of porous glass by burning it off with oxygen in silu is possible. This pretreatment with oxygen has been shown to be important in obtaining completely reproducible results (87). A tube of porous glass 5.1 cm. long was used, the minimum length change that could be detected was 0.1 of a cm.), so that the sensitivity (AI/l) was 5.4 X lo-'. fringe (2.73 X Heats of adsorption were determined from isotherms at 90 and 79" K for argon, nitrogen, oxygen, and hydrogen. For the first three gases, the variation of the heat of adsorption with coverage is very similar to that reported in accurate calorimetric work with rutile (88, 89). Earlier work with porous glass (84-86) did not include any direct determinations of heats of adsorption. In all the work reported earlier with charcoals, and even with water on porous glass (67),it is possible that small amounts of chemisorption might have been the dominating factor. Rare gases (argon and krypton) were studied to eliminate this; the expansions for argon, together with those for nitrogen and oxygen are shown in Fig. 4 as a function of volumes of gas adsorbed (74). The length changes are given in fringes, a change of 1 fringe (a mercury lamp was used) corresponds to a percentage length change of 5.4 X The average monolayer capacities were 41.0 for A, 41.8 for Na and 46.3 for 0 2 in cm.*/g. giving an average surface area of 173.3 m.a/g. In addition, an equation relating the bulk modulus to the expansion, which had been derived earlier [Equation (S)] was tested. It was demonstrated (Fig. 5) that the relation found by Bangham between the expansion (Al) and the free-energy lowering ( T ) was valid for this system with some deviations a t low coverage. These deviations are probably due to the difficulty of getting accurate T values in this region. Since the expansions were measured as a function of fringe shifts ( N ) , the gradient of the expansion-x plots is given by dN/dr. Average values are: argon, 1.01; nitrogen, 1.12; oxygen, 1.16; krypton, 0.76; and hydrogen, 1.83. The differences between

MOLECULAR SPECIFICITY IN PHYSICAL ADSORPTION

x-

279

A

v, cm3 /g.

FIG.4. Expansion, in fringes, of porous glass after the adsorption of argon, oxygen and nitrogen. 0 ,90" K.; X, 79" K. (74).

H , ergs /cm?

FIG.5. Length changes of porous glass aa a function of free-energy lowering ( T ) . 0, 90" K.; X, 79" K. (74).

the first three gases, of similar boiling points, are small, but the accuracy of the data is sufficient to make them significant. Consequently, the bulk modulus theory was compared with Young's modulus theory only for the values obtained with argon, not with all the gases. The bulk modulus obtained from the expansion results is about half as large again as the value determined by the usual methods (go), but the Young's modulus is about three and one-half times as large. Later work was reported with the same sample (76),which enabled accurate intercomparisons to be made with the earlier results. The first

280

D. J . C. YATES

polar gas that was used was carbon monoxide, and contractions took place before expansion, in a manner similar to that observed earlier for charcoals (64). It seemed likely that these contractions were related to the polar nature of the molecule (87), and the anomalous behavior of nitrogen t o its quadrupole moment (91, 92). The quadrupole moments of argon and krypton are zero, and those of hydrogen and oxygen are small. The finite quadrupole moment of nitrogen and its effects on adsorption have been discussed by Drain (93).Carbon dioxide was also adsorbed; this molecule is of interest, since it is similar t o nitrogen, having a quadrupole moment and no dipole moment. It was found (76) that the expansion curves with carbon dioxide were very similar indeed to those of nitrogen; in fact, if plotted as a function of coverage rather than volume of gas adsorbed, the curves for nitrogen are almost identical with those of carbon dioxide. More accurate results were given for hydrogen, and neon was also studied (Fig. 6).

8-

m

-

0

2

4

6

V.

I

0

I

4

I

I

8

I

I

12

I

I

I

16

v, cm? /g.

FIQ.6. Length changes produced in porous glaaa by the adsorption of hydrogen and neon. Neon, 0 , 90" K.; X, 79°K. Hydrogen 90°K.; run 41; 0,run 42; 79°K.; run 35; X, run 38 (76).

+,

The adsorption of gases with larger dipole moments showed very much greater contractions than did carbon monoxide (76). Sulfur dioxide gave a contraction about three times as large, and ammonia thirty times as large. These results were later extended by a detailed investigation of the effect over a wide range of temperatures (77). I n addition to sulfur dioxide and ammonia, methyl chloride, and dichlorodifloromethane (CC192) were adsorbed. In keeping with its rather inert nature, CCLf produced results similar to carbon monoxide. Except for carbon monoxide, the detailed results showed that for all adsorbates a small expansion preceded the con-

MOLECULAR SPECIFICITY IN PHYSICAL ADSOBPTION

281

traction. This occurred to only a small extent with CChF2. The effect can be seen in Fig. 7, where results for sulfur dioxide are given. As the temperature of adsorption is increased, the contractions become smaller and finally disappear. Contractions of similar size were observed with methyl chloride, but with ammonia niuch larger contractions took place (Fig. 8), persisting

v, cm? /g.

Fro. 7. Contractions and expansions of porous glass produced by the adsorption of sulfur dioxide. Temperature, O C.: 0 , -78; 0;8 ,24; X , 50; Q , 75; 0,100 (77).

+,

v , c m ? /g.

FIQ.8. Length-change effects produced in porous glass by the adsorption of ammonia. Temperatures, "C., 0; 0,25; X, 75; 8 , 100; 0 , 150; 0 , 200 (77).

+,

282

D. J. C. Y A T M

even a t 150" C. The reversibility of these changes was investigated and also the time effects near the minimum in the contraction curves. The cause of the contractions has been sought using other techniques and will be discussed in detail in Sec. IV.

D. IMPLICATIONS OF THESEEFFECTS ON THEORIES OF PHYSICAL ADSORPTION A summary of developments in physical adsorption during the period from 1943 to 1955 has been given recently by Everett (94). The chief difference between the approach used by Brunauer in his book published in 1943 and that in vogue in 1955 is in the great development of the thermodynamic aspects of the subject. Prior to 1943, the main effort was in developing theories to predict the shape of adsorption isotherms. Since then, emphasis has shifted towards the thermodynamic properties of the adsorbed phase, particularly its entropy. Advances in the thermodynamics of physical adsorption have been reviewed up to 1952 by Hill (4). One of the main interests in the use of thermodynamics is its ability to give information about the nature of the adsorbed phases-degrees of freedom of movement over the surface, of rotation, and so on. One method of approach has been to treat the surface as smooth, the adsorbed molecules then behaving as an ideal gas. This assumption is very rarely, if ever, valid on solid surfaces, although it is of great utility on liquid surfaces (3). Other methods have been developed which consider the periodic nature of solid surfaces, but they apply to cases where the heat of adsorption does not vary with coverage (94). This type of behavior is also rare, since most adsorbents that have been studied have energetically heterogeneous surfaces. The most general thermodynamic approach is that outlined by Guggenheim (94a), where both components of the solid-gas system are considered in detail. This two-component treatment gives a rigorous description of adsorption experiments. Nevertheless, the very generality of this approach renders it somewhat sterile. By the use of other assumptions, the thermodynamic treatment can be simplified and more progress can be made. In particular, Hill has shown that a system of considerable utility can be obtained by considering the adsorption process as a pseudo one-component system. Only the adsorbate is considered as taking an active part. The adsorbent is assumed inert and the only effect of its presence is that its surface provides an attractive force field for the adsorbate molecules. Many investigations both from the theoretical (4, 42, 96) and experimental (38,88, 89, 96-100) aspects have been reported using the one-component approach. Apart from the simplicity it offers, this convention has

MOLECULAR SPECIFICITY IN PHYSICAL ADSORPTION

283

the attractive feature that all the measured heat and entropy changes can be considered as taking place only in the adsorbate molecules. When, and only when, values of heats of adsorption and heat capacity are measured over a wide range of temperature can accurate information about the nature of the adsorbed film be obtained. This technique is both difficult and expensive, and the only solid that has been investigated in such a fashion is rutile; argon, nitrogen and oxygen were adsorbed (88,89,96-98). While there is no ambiguity about the physical reality of heat effects on adsorption, a t least when calorimeters are used, the same cannot be said of their interpretation. If the solid is perturbed, some of the entropy changes will take place in the solid and some in the adsorbed gas. Drain and Morrison (88)have considered this point: The perturbation of the surface is automatically included in any meaaured thermodynamic property. In the presence of such a perturbation the thermodynamic properties of the adsorbed gaa alone have no direct physical meaning, although the experimentally meaaured quantities are still well defined.

Exception to this inert adsorbent assumption has been taken by Cook It has been stated (24), “The theoretical arguments advanced in favor of this assumption were inadequate, and experimental data wholly lacking.” The dimensional changes which take place when rare gases are adsorbed on to rigid adsorbents provide conclusive evidence that the assumption of inert adsorbents (for physical adsorption) is invalid. Many of the experiments on dimensional changes are not relevant here, in some cases because of the lack of heats of adsorption; and in others because of the somewhat illdefined nature of carbon and charcoal surfaces, a small amount of chemisorption may have taken place. It is generally accepted that adsorbents are not inert when chemisorption occurs. Although it is difficult to express the perturbation of the adsorbent in a quantitative manner, it is perhaps of interest to note that when a monolayer of argon was adsorbed on porous glass, it expanded 6.85 X lo-‘ cm. from its original length. For a length change of the same size to take place by thermal expansion, the sample would have to be heated by 250” C. (76). The absolute length change due to adsorption is small, but in rigid solids it is not negligible in comparison with other processes affecting the size of the solid. Recent work has shown (103) that for alkali halides the Debye characteristic temperature is not very sensitive to volume changes produced by thermal expansion. This probably indicates that, in general, volume changes of an adsorbent will not markedly affect its bulk thermodynamic properties. et al. (101) and by Brunauer (24, 102).

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D. J . C. YATES

Consequently, for such systems the use of the one-component convention may not introduce serious errors. A study of the effects of the adsorbent perturbation on the B.E.T. theory has been reported by Peticolas (104). The frequency of an adsorbent molecule, in an adsorbent site, is expected to increase by 10% when it interacts with an adsorbed molecule. Other consequences of the perturbation of the adsorbent have been discussed by Tykodi (106, 106) and Copeland (107). In conclusion, it can be stated that for physical adsorption it is not rigorous to treat the process as if the solid were inert. No data seem available, however, to express the perturbation of the solid in a quantitative fashion, to help in estimating the errors involved in the use of the one-component approach.

Ill. Perturbation of Adsorbed Gases ADSORBED PHASE Little precise information seems available on this topic. I n particular, few answers are known to such questions as whether the adsorbed molecules are to be thought of as foxming a twodimensional gas, a liquid, or a solid, what are the degrees of freedom of movement along the surface, the rotational freedom, and the distortions (if any) induced by the surface forces, and how the critical and melting temperatures of a substance are affected by the adsorption process. Attempts have been made, using helium, t o measure the density of the adsorbed phase (108-110) to try to h d out whether the fJms are t o be thought of as gaslike or liquidlike. The volume of the adsorbent was determined before adsorption, and then after a known amount of gas had been adsorbed. It was concluded (109) that the adsorption of helium, although small, was finite, introducing uncertainty in the results. Furthermore, while the concept of density is useful when multilayers are considered, it is not necessarily so a t coverages less than unity. The surface forces affect the melting point quite considerably. Morrison et al. (111) showed that a melting region rather than a melting temperature existed when nitrogen was adsorbed on rutile. At a coverage (e) of .4.8, the adsorbate was all melted a t 61.4"K., 1-74"below the melting point of bulk nitrogen, while a progressive decrease in the melting point took place a t lower coverages until at 0 = 2.2, melting had finished by 55OK. This result is expected, since the surface forces have a greater effect at low coverage. At e = 2.2, the width of the melting region increased, and this increase may be due to the energetically heterogenous nature of the rutile surface. Deductions about the degrees of freedom (with respect to both mobility and rotation) have been made by many workers (2, 3, 4, 89, 100) from A. THENATURE OF

THE

MOLECULAR SPECIFICITY IN PHYSICAL ADSORPTION

285

entropy considerations. While the data for adsorbed species on liquids (3) are free from ambiguity, the same cannot be said for solid surfaces. One of the difficultiesin the latter case is the uncertainty in the size of the energy barriers between sites. These results have been discussed elsewhere by many authors.

B. NEWEREXPERIMENTAL TECHNIQUES Thermodynamic methods, which have been those most widely used in the past, utilize isotherms and heats of adsorption as their foundations. Entropy changes calculated from such data are not easy to transform unambiguously into specific descriptions of the adsorbed phase. Another approach developed by McIntosh and his co-workers (112-11 7) has been to measure the electrical properties of the adsorbates while they are adsorbed; it is found that changes in the capacitance curves take place at the monolayer point. However, interpretation of the data to provide, say, the polarizability of the adsorbed species has proved to be difficult. An apparent dipole moment of infinity was obtained for sulfur dioxide adsorbed on rutile. It was concluded (116) that no satisfactory way of obtaining the apparent electrical properties of adsorbed matter has been developed, and until this is achieved, no great clarification of the observations seems likely. Among the other information which it can provide, the field-emission microscope gives direct evidence of the mobility of adsorbed layers. These results have been reviewed elsewhere by Gomer (118)and will not be further discussed here. Nuclear magnetic resonance of surface groups of the adsorbent and of the adsorbed gas has been studied recently (119-126); these effects are very specific to certain nuclei. The easiest resonances to detect are those of hydrogen and fluorine, while A12’ and SiZ9give much weaker signals. Although rather limited in the number of nuclei which can be studied, this technique is certain to have many applications to surface phenomena. Spectroscopic methods, in the infrared region, have been rapidly developed in scope and power since 1949. Excellent reviews of this topic have been given by Eischens and Pliskin (126)and, more recently, by Sheppard (127).In chemisorption, new species are formed and drastic changes take place between, say, the frequencies of a CO molecule in the gas phase and those of one adsorbed on platinum (128). Extensive work has been done in the physical adsorption field by Terenin and his co-workers (reviewed elsewhere, see 126, 1.27).Most of this work has been concerned with changes which adsorption produces in the surface OH groups of porous glass. These groups may be considered part of the adsorbent; spectral studies of the adsorbate as such have been less frequently made.

286

D. J. C. YATES

In this type of work, it is of importance t o obtain as accurate an idea as possible of the coverage of surface at the time the spectra are taken. If this factor is completely unknown, its absence can lead to great difficulties in interpretation (at least in physical adsorption). For instance, in a porous adsorbent, so much adsorbate may be present that the capillaries are filled. The spectra obtained of such a system will approximate t o that of bulk liquid adsorbate and may be unrelated to spectra obt.ained a t lower coverages. Both regions of coverage are of interest, but it ia essential to know which region the spectra were taken in before the results can be correlated with those obtained by classical adsorption techniques. Partly for this reason and partly because geneial reviews of the subject have been published recently, the results discussed here will be limited to those obtained on physical adsorption at known coveiages. The first such studies were reported by Pimentel et al. (129),who adsorbed heavy water on silica1 gel; spectra were given for coverages 6 from 0.35 to 1.8.To reduce light scattering, the gel was embedded in paraffin wax. Quite apart from the fact that the paraffin has absorption bands which make certain spectral regions inaccessible, the wax probably interacted with the surface of the gel. This may have affected the adsorption of the DzO. Other workers have also reduced scattering by immersing the adsorbent in KBr disks (130,131). Both these techniques introduce considerable uncertainties when they are used in surface studies; Pliskin and Eischens (132) showed that the adsorption of ammonia on alumina is drastically affected when the system is embedded in KBr. However useful in other fields of spectroscopy, it is considered that when surface phenomena are to be Etudied that are to be related to surface data obtained by other means, immersion in waxes, alkali halides, or similar media should not be used. The results obtained by such methods must be considered of doubtful validity. General requirements for sample preparation have been discussed by Sheppard (127‘). Using a tube of porous glass of effective thickness 0.28 cm., Sheppard and Yates (133) were able to measure spectra of adsorbed methane at coverages down to 0.01 (Fig. 9). Ethylene, acetylene, and hydrogen were also adsorbed, all a t liquid-air temperatures. The surface area (185.5 m.z/g.) and weight (4.63 g.) of the glass used made possible a direct measurement of coverage in situ, despite the rather large volume of the cell. The spectra of methane, adsorbed at 9O0K., showed a weak band at 2,899 cm.-’, in addition to a strong band (YS) at 3,006 cm.-l. This weak band was assigned to the v1 symmetrical “breathing” frequency of methane, which is normally observed only in the bulk state in the Raman spectrum at 2,916 cm.-’. No over-all dipole change is associated with the v1 vibration; consequently, it is forbidden in the infrared spectra of liquid and gaseous methane. The appearance of this band is a direct measure of the

MOLECULAB SPECIFICITY IN PHYSICAL ADSORPTION

287

distortion in shape of the molecule due t o the asymmetric nature of the surface forces. A weak shoulder appears at 3,010 cm.-' in the spectrum of adsorbed ethylene. This band is probably due to the normally forbidden v 1 vibration of ethylene, which has a frequency of 3,019 cm.-' in the H.aman region. 75 50 25

75

50

.-rg

25

a L

0

r5

a

8

50 25

2000

2500

3000

3500

4000

50

25

Frequency, cm?

F h . 9. The infrared spectra of adsorbed molecules. The lowest line on each spectrum is the background obtained after evacuating the porous glaas. Measured surface coverages (e) are given for a11 spectra (1%).

Both the above forbidden bands lie a t frequencies close to that of a normally allowed one. Once a molecule is distorted, the new band may gain considerably in intensity by resonance with the allowed one. When hydrogen was adsorbed, a t a coverage of 0.2, a band appeared a t 4,131 cm.-I, the corresponding Raman frequency being 4,160 cm.-'. There are no allowed bands for hydrogen, and the appearance of this new band is entirely due to the effect of surface forces. This hydrogen band a t e = 0.2 was also studied with a diffraction grating spectrometer, and its optical density was found to be 0.1 and its half-width to be 21 cm.-' (Fig. 10). Condon (134) showed that infrared spectra were expected t o be induced by high electric fields and that the selection rules

288

D. J. C. YATEB

for such spectra should be the same as those for the Raman spectrum. Furthermore, the intensity of such induced bands was expected to be proportional to the square of the field. These predictions were confirmed by Crawford and Dagg (I%), who measured the specific absorption coefficient of hydrogen in a field of loKv./cm. It is likely that the intensity of the band of adsorbed hydrogen depends on the fluctuations of the dipole moment induced by the surface. Comparison of the intensity and half-width of the band a t known coverage, with the absorption coefficient found by Crawford and Dagg, enables an estimate to be made of the effective field at the surface. It is found to be 7 X lo6 v./cm. The calculation of the surface field of ionic solids at distances appropriate to an adsorbed molecule is highly dependent on this distance. No experimental method of measuring this distance has been developed as yet. If an assumed distance is used, a field value for argon adsorbed on caesium iodide is found to be 5.7 X lo7 v./cm. (136) and for argon on KC1 to be 4.3 X lo7v./cm. (137).As the surface of silica glass is not completely ionic, the above experimental value of the field (7 X 10’ v./cm.) is in reasonable agreement with these theoretical figures. By studying heats of wetting of adsorbents by liquids of varying dipole moments, Chessick and co-workers (158) have found the surface field of rutile to be 8.1 X lo7v./cm. Other values reported later (139) are 7.5 X lo7 for calcium fluoride and 3.3 X lo7for Cabosil. It now seems that the interpretation of heat of wetting data can be rather difficult. A recent discussion (140) has shown that, for example, the breaking of hydrogen bonds during the immersion process can contribute to the heat effect when alcohols are used as the wetting agent. Direct information about the degrees of rotational freedom has been obtained (133) using a high resolution spectrometer. No fine structure was observed in the spectra of adsorbed methane, although the resolving power was the same as that used for the gaseous material (Fig. 10). Even if the molecules are freely rotating, however, individual rotational lines would not necesaarily be resolved. The frequency of vibration of an adsorbed molecule perpendicular to a surface is about 10l2sec.-l (141,142). These vibrations will interrupt the free rotational motions to such an extent that the intrineic widths of the lines will become similar to their separation; under such conditions, no fine structure is to be expected. Allowance was made for this “interrupted free rotation” effect and the experimental data compared with three possible rotational motions distinguishable spectroscopically. Model I was that of no free rotation, model I1 was that of free rotation about one axis, and model I11 was that of free rotation about all three axes in the molecule. The widths of the observed lines ruled out model 111, and detailed examination of the data indicated that model I1 was to be pre-

MOLECULAB SPECIFICITY IN PHYSICAL ADSORPTION

289

ferred. It is of interest to note that of all the small molecules commonly used as adsorbates, methane is the most symmetrical (apart from the rare gases). Consequently, as mentioned by Hill ( I @ ) , CHI (and CCl,) are the molecules most likely to have completely free rotation in the adsorbed state. From these geometrical considerations, it is probable that even if completely free rotation is absent, free rotation about one axis is present in adsorbed methane. Although much more difficult to investigate spectroscopically, it is probable that nitrogen and oxygen adsorbed on silica have much less rotational freedom than methane because of their shape.

0 .+

2 Y) 0

2

I

2850 2900 2950 3000 3050

I

4200

1

I

I

3100

3150

I

4150 4100 4050 4000

Frequency ,crn:I

FIQ.10. High-resolution spectra of (a) adsorbed methane, (b) gaseous methane, and (c) adsorbed hydrogen. Coverage for methane 0.08 and for hydrogen 0.2. Weak and irregular absorption bands are present because of atmospheric water vapor (133).

Water adsorption on silica gel has been studied by Benesi and Jones (148).It was shown that all the surface OH groups could be exchanged by deuteration. This was of use in differentiating certain SiO bands from OH bands. In addition, adsorbed water was shown to consist mainly of OH groups. Thin layers (0.1 to 1.0 mg./cm.2) of gel were used, evacuated a t room temperature. Coverages were obtained by comparing measured water vapor relative pressures with the isotherms of Sing and Madeley (144). It was not stated, however, which of the three isotherms was used for this comparison. These gels (144) varied widely in water adsorption according to pH

290

D. J.

C. Y A W

of preparation. At a relative pressure of 0.25, near monolayer coverage, gel A (surface area 693 m.”g.) adsorbed 0.17 g./g. of water, while gel C (695 m.*/g.) adsorbed 0.08. In addition, earlier work by Sing and Madeley (146) showed the need for evacuation a t temperatures higher than 100” C. to obtain reproducible results. Heating of the sample by the radiation of the spectrometer was not mentioned; this would almost certainly have raised the temperature of the gel in the beam to about 30 to 40” C. (146, 14?’), while the isotherms were obtained a t 25” C. Any conclusions based on such obscure estimates of amounts adsorbed need to be treated with caution. Spectra taken a t 0.6 and 1.3 coverage were interpreted as making it “likely that capillary condensation begins before the completion of the fiist monolayer.” While this may be correct, the data presented seem inadequate to substantiate this statement. While discussing this subject, it is of interest to riote that a recent advance in technique has been t o obtain spectra when only one layer of material is adsorbed a t a coverage of unity. Francis and Ellison (148) have obtained spectra of layers of metal stearates adsorbed on mirrors, and Pickering and Eckstrom (I48a) have studied low molecular weight gases (such as Ha and CO) chemisorbed on metal mirrors.

IV. Over-all Changes at the Solid-Gas Interface A. EFFECTS DUETO

THE

PRESENCE OF SURFACE OH GROUPSON POROUS GLASS

1. Changes Produced by the Replacement of the OH Groups by Methyl Groups. The length-change techniques discussed earlier provide an indication of the changes in the adsorbent on adsorption, while infrared spectroscopy can show directly the changes in the adsorbate on adsorption. In some cases, moreover, where certain groups foreign to the bulk lattice are held to the surface by strong forces, the presence and nature of such groups can be detected by their infrared absorption spectrum. If these groups (such as the OH groups), are considered part of the solid, the infrared spectrometer can be used to detect changes in the adsorbent. It is evident that if both techniques could be applied to one system, there is a much greater probability of assessing the over-all changes that take place on adsorption. Furthermore, the information obtained from each technique will supplement the other. An example of this is a study of the effects due to replacement of the surface OH groups. In earlier work with porous glass, the anomalous curves, and the contractions a t low coverage,

MOLECULAB SPECIFICITY IN PHYSICAL ADSOBPTION

291

found with nitrogen and carbon monoxide were correlated with the quadrupoles and dipoles, respectively, in the adsorbed gas (76). Experiments with gases with higher dipole moments showed, however, that this was not correct (76).The contractions produced by sulfur dioxide and ammonia were different by a factor of about 10, and the dipole moments are 1.60 and 1.46. Preliminary infrared experiments with ammonia (149) showed that strong hydrogen bonding took place between the ammonia and the surface OH groups. Consequently, it was thought that the contractions were due to a hydrogen bonding process, and i t is now known that hydrogen bonding is always found to coexist with contractions. This is discussed in detail later. The much larger contractions that occur with ammonia as against sulfur dioxide (76,77) fit in with this supposition. From the general nature of hydrogen bonding, it is likely that much weaker hydrogen bonds would be formed with sulfur dioxide than with ammonia. Two methods can be used to investigate this idea. The first is to replace the OH groups with some other group, of different hydrogen bond forming characteristics and to see what effect this would have on the contractions. The second is to take the unaltered system and measure the strength of the hydrogen bonds formed with various adsorbates. It was expected that as the bond became stronger, the contractions would become larger. It is to be expected that an increase in the concentration of surface OH groups would have the effect of increasing the contractions, other variables being held constant. The usual technique (74) was to evacuate the interferometer for a day at 320" C. between runs. To increase the water content of the sample, about a monolayer of water was adsorbed at room temperature, and the sample was evacuated afterwards a t 120" C. A contraction experiment was repeated after this treatment, and it was found that the results were much the same as those obtained by normal evacuation a t 320" C. While the reason for this negative result is unknown, long times are needed under some conditions for water to produce changes in a silica surface. In these experiments, the water was only on the surface for a few hours before being pumped off again. This experiment is typical of many that are conducted using classical adsorption techniques, such as the measurement of isotherms and control of evacuation temperature and pressure. There is a high probability that such a treatment will increase the number of OH groups on the surface, but there is no direct evidence of this. An improvement could be made if the sample were continuously weighed during the cycle in a vacuum microbalance (160),but even this would not be entirely free from ambiguity. The use of infrared spectra to identify and measure the number of surface groups is of great utility in such circumstances. The OH groups on porous

292

D. J . C. YATES

glass are extremely strong absorbers of radiation because they have a high extinction coeficient. This makes the detection of these groups easy, but has the disadvantage that if the adsorbent has a high surface area, unless very thin samples (about 0.2 mm.) are used, the whole OH region becomes one of complete absorption of light (133, 149). Replacement of OH groups with methyl groups was studied as an alternative to increasing the OH content. This produces bands due to the C-H stretching vibrations, in regions where the glass transmits light and which are remote from the OH region. The spectroscopic examination of such surface exchanges has been mainly developed by the Russian workers (146, 161). Most of the work has been in the formation of OD groups (161) and methyl groups (146'). The extensive experiments of Sidorov (146) on methylation using methanol are an extremely valuable contribution. Unfortunately, the lack of any values of surface area and coverage make interpretation difficult. Although the detailed nature of the porous glass used by Sidorov may well be different from that made by the Corning Glass Company, it was found possible to methylate this latter glass (162). It was not found possible to methylate it a t the temperatures used by Sidorov (430470"). Under these conditions, a carbonaceous opaque deposit rapidly formed on the glass, and a temperature of 360" had to be used. Glass of 0.04 cm. in thickness, with a surface area about 200 m.a/g., had a peak optical density in the OH region (3,730 cm.-l) of 1.35 after evacuation for 6 hr. at 450" C. After 9 hr. of methylation, the OH band had decreased in density to 0.66, indicating that about 50% of the groups had been replaced by methyl groups. No further methylation took place when longer times were used. This phenomena of incomplete methylation was also shown in Sidorov's spectra (146'). Although it can sometimes be misleading to compare these results with those on silica powders (such as Cabosil) made by different techniques, it is of interest to note that McDonald (153)was also unable to methylate all the OH groups on Cabosil. This result he attributed to possible residual water present in the methylating agents. Incomplete methylation with porous glass may be due to the water formed in the reaction, but this is not certain. Inaccessibility of the OH groups is not likely to be the main reason, since all the OH groups of porous glass can be replaced with chlorine groups (164). It was also found that the methyl groups remained attached to the surface even after long times of evacuation at 320' C. After the above study of methylation for this type of glass, the lengthchange sample was methylated in situ (162).As the methyl groups formed by this treatment were stable, a sequence of experiments could be conducted without the need to remethylate the sample at an intermediate

293

MOLECULAB SPECIFICITY IN PHYSICAL ADSOBPTION

stage. Drastic changes took place in the subsequent contraction behavior; Figs. 11 and 12 show that contractions do not occur on the adsorption of sulfur dioxide (similar curves being found with methyl chloride) and that only small ones occur with ammonia. Results using unmethylated glass are shown on Figs. 11 and 12 for comparison. The presence of the small contractions and plateaus found in these experiments is probably due to the residual OH groups left after long times of methylation. It is important to note that this methylation does not introduce any irreversible changes in the sample. The methyl groups could be easily burned off with oxygen a t 450" C.; after this was done, the infrared spec-

v ,cm? /g.

FIG.11. Changes in expansion characteristics produced by methylation. Sulfur dioxide adsorbed at -78" C., 0 before methylation, x after, At 0" C., 0 before, after (162).

+

v , cm? /g.

FIG. 12. Changes in expansion characteristics produced by methylation. Ammonia adsorbed at 25" C., before methylation; X after. At 100"C., 0 before, after (166).

+

294

D. J.

C. YATES

trum was the same as that originally obtained. The length-change sample was given the same treatment, and subsequent adsorption of methyl chloride and ammonia gave curves identical with those obtained previously (77). These results lead to the conclusion that contraction effects occur only when a certain number of OH groups are present on the surface of porous glass. Reducing the number of OH groups reduces the contraction effect by a very large factor. The contractions found by Haines and McIntosh (64) and Lakhanpal and Flood (72, 73), using carbon rods, are not necessarily connected with OH groups which may be present on their surfaces. Since no infrared spectra of high area carbons have been published, no direct information is available. On general grounds, the surface characteristics of ash-free carbons indicate that few OH groups are likely to be present. It has recently been reported (73) that saturated hydrocarbons produce contractions in carbon of similar size to those produced by methanol. On porous glass, saturated hydrocarbons produce only expansions, while methanol gives a contraction. It is therefore probable that the mechanism of contraction on carbon is dissimilar from that operative on glass surfaces. 3. Hydrogen Bonding between OH Groups and the Adsorbed Molecules.

The actual length-change sample could not be used for investigations of hydrogen bonding, since its thickness (2.8 mm. total) was such as t o give complete absorption between 3,820 and 3,450 cm.-'. A much thinner piece (0.4 mm.) of porous glass was used, and a simple adsorption system with a fused silica cell was constructed (162).The adsorption isotherm could be obtained at the same time that the sample was in the light beam of the spectrometer. This obviates the necessity of measuring the temperature of the sample; with the intensities of radiation normally used in infrared spectrometers this effect can be quite significant, since most adsorbents are bad conductors of heat. To establish the relation between the contractions and hydrogen bonding, it is necessary t o show that the contractions become larger when the hydrogen bonding becomes stronger. This change can be studied in two ways-either by adsorbing a series of adsorbates a t one temperature, of varying contracting power or by using one adsorbate and changing the temperature of adsorption over as wide a range as possible. The contraction effects were found to be very temperaturedependent (77). Typical spectra obtained a t room temperature are given in Fig. 13. Other spectra were obtained in all cases, but a selection is given only of those that are suitable for calculation of apparent optical density. With such broad bands as those occurring in hydrogen bonding, the absorption spectra obtained directly from the spectrometer give little direct information,

MOLECULAR BPECIFICITY IN PHYBICAL ADBOBPTION

295

especially when the sample, in the reference state, has a spectrum with widely varying transmission. Porous glass has this spectral characteristic : the lower line in each of the curves of Fig. 13 is the spectrum obtained after evacuation a t 450" C. Optical density curves were calculated from all

Frequency,

Cm-!

FIG.13. Infrarcd spectra of porous glass (0.4 mm. thick) at 20' C., with volumes of gas adsorbed in cma../g. Methyl chloride (a), sulfur dioxide (b), acetone (c), and ammonia (d) were used (169).

spectra, and some obtained on the adsorption of ammonia are given in Fig. 14. How the monolayer capacity (V,,,) of ammonia changes over such wide temperature ranges is unknown. V,,, for argon for this sample was 60.5 cm.*/g. at - 195" C. Ammonia (at -33" C.) and argon (at - 195" C.)

296

D. J.

C. YATES

had V , values on another bample of porous glass differing only by about 6% (77). Consequently, the coverages in the experiments shown in Fig. 14 are all about 0.1. The nature of the hydrogen bond is still somewhat obscure, but it is well established that the energy of such bonds varies from some hundreds to several thousands of calories per mole. If X and Y are two atoms which are hydrogen-bonded, the system can be represented as X-H----Y, where H----Y is written for the hydrogen bond and X-H for a normal bond. When the hydrogen bond is formed, the stretching frequency of the X-H bond is shifted to lower frequencies. This shift (AY)has been shown (166, 166) to be related to the energy of the hydrogen bond, although in general energies cannot be deduced directly from these shifts. It has also been shown (167) that the distance between the X and Y atoms becomes smaller in many crystals as the energy of the hydrogen bond increases.

O'

do0

'

do0

'

do0

'

3;oo

F r e q u e n c y , cni!

FIQ.14. Spectra of porous glass after the adsorption of ammonia, expressed in optical density units. Volumes adsorbed in cm.$/g.:5.5at 20" C., 5.9, 75" C., 6.0; 100" C., 5.6; 150' C. (162).

The intensity (and also the half-width) of the band due to the XH vibration is greatly increased when the hydrogen bond is formed. This increase has been explained in terms of an increase in the ionic character of the bond (168) and also in terms of a charge transfer (169). Possibly both mechanisms operate together, but recent experiments (160) indicate that the charge transfer model is probably t o be preferred. In such a case, the X atom becomes negative by an electron transfer from the Y atom, the + X-H - Y+. This explains change being represented by X-H----Y why the proton-accepting properties of the Y atom are related to the energy of the hydrogen bond formed.

297

MOLECULAR SPECIFICITY IN PHYSICAL ADSOBPTION

The shift in frequency of the OH groups due to hydrogen bonds being formed is given by Av = 3,730 - V O H , where U O H is the peak frequency of the OH groups perturbed with adsorbed gas, and 3,730 cm.-' is the position of the peak OH intensity of the evacuated sample. Other workers with silica surfaces have found (146, 147) a frequency of 3,749 cm.-' for the latter band. Considerations of shape of the band indicate that hydrogen bonding, between adjacent OH groups, lowers the peak frequency somewhat for the porous glass used (152). The shifts due to hydrogen bonding are given in Table I, together with contraction data. For comparison, some shifts in the narrow OH band found on Cabosil a t 3,749 cm.-' (147) are also shown. TABLE I Comparison between Shifts on Forming Hydrogen Bonds and Contractions of Porous Glass

Adsorbate

A Kr 0 2

N, CH( CHIC1

so2 Acetone Acetone Acetone NHa NHa NHs NHa Hz0 CHsOH

Temp., O

c.

- 170 - 170 - 170 -170 - 170 25 25 25 75 135 25 75 100 150 25 25

Shift (Av) in frequency of OH groups, ern.-' 80 16" 124 24" 320 110" 115O 33OC 305c 270" 820c 750" 710" 640" 290" 380'

Contraction, fringes (1 fringe change is 5.38 X lo-'%) Ob

ob Ob

Change in slopeb Change in slope 0.6"0d 0.6C*d 15.OC*d 10.5"*d

-

25.0CBd 21.0"Sd 17.5"d 10.208* O'J

2.6"

4 McDonald, R. S., J . Am. Chem. SOC. 79, 850 (1957). 'Yates, D. J. C., PTOC. Roy. SOC.8224, 526 (1954). Folman, M., and Yates, D. J. C., PTOC. Roy. SOC.da46, 32 (1958). d Folmnn, M., and Yates, D. J. C., Trans. Faraday SOC.64, 429 (1958). 8 Folman, M., and Yates, D. J. C., Trans. Faraday Soc. 64, 1684 (1958). Amberg, C. II., and McIntosh, R., Can. J. Chem. 30, 1012 (1952).

Very good correlations exist between the shift and net contractions for sulfur dioxide, methyl chloride and ammonia. Acetone gave a shift of 330 cm.-', which was intermediate between that of methyl chloride and sulfur dioxide on the one side and ammonia on the other. This implies that a length-change experiment should give results intermediate between those

298

D. J. C. YATES

of methyl chloride and ammonia. This implication was confirmed by experiments a t 25' and 75" C. (Fig. 15). A tentative model of the contraction process has been sought in terms of pairs of OH groups on the surface hydrogen bonded together. This is the simplest model to consider, although it is quite possible that larger interconnected patches exist on the surface. The hydrogen atom on the left (Fig. 16) is attached only to the OA oxygen atom, while the other

v ,cm?/g.

Fxa. 15. Length changes produced by the adsorption of acetone at 26°C. ( 0 )and at 75'

c. ( 0 )(16.8).

FIG.16. Suggested model of arrangement of OH groups on the surface of porous glass (166).

hydrogen is attached directly to OB and hydrogen-bonded t o OA.When a hydrogen bond is formed between the OAH group (the so-called free OH group) and an adsorbed molecule such as methyl chloride, the electron distribution changes in the system. In terms of the charge transfer model (169), this change means that OA becomes more negative. As a result, the strength of the hydrogen bond originally existing on the surface increases and a decrease in the distance between OA and OB can take place. AS OA and OBare rigidly bound to the lattice, this effectcould result in an over-all contraction of tlie solid.

299

MOLECULAR SPECIFICITY IN PHYSICAL ADSOBPTION

Although infrared data are not available, it is possible that some lengthchange effects found (16Oa) with simple hydrocarbons (Fig. 17) may fit in with this over-all picture. Methane and ethane do not produce contractions, while ethylene and acetylene do. The molecular size, polarizability, and boiling points of the three heavier molecules are similar, so it is surprising, at first sight, to find such a great contrast in the length changes. Strong interactions between ethylene, acetylene, and hydrogen chloride took place (161, 162), attributed to effects of the T electrons. No such interaction took place with ethane (161).

8 -

0

2

4

6

8

10

12

14

16

18

20

v, cma/g.

Fra. 17. Length changes produced by the adsorption of methane at - 183”C. (O), and by the adsorption at -78” C. of ethane (+), ethylene (X), and acetylene (a).

9. Effects Due to OH Groups in the Adsorbate Molecules.

None of the adsorbates used in the length-change work with porous glass reviewed in Sec. I1 contained OH groups, with the sole exception of the work reported by Amberg and McIntosh, using water (67). Water is a molecule whose hydrogen-bonding properties are extremely pronounced. Consequently, if the contractions are due to the formation of hydrogen bonds between the adsorbed molecules and the “free” OH groups on the surface, it is expected that water will produce marked contractions. Experiments (163)on the same sample as that used for all the previous lengthchange work showed that at low coverage only expansions took place (Fig. 18), in agreement with earlier work (67). As well as adsorption on the “free” OAHgroups, it is evident that at least three other modes of adsorption may occur with water. It may adsorb in two ways on sites other than

300

D. J. C. YATEB

the OH sites, either without any drastic change or with the breaking up of the water molecule and the formation of new OH bonds. The third possibility is that it may interact with the existing bound OBHgroups and extend the bound OH system. In terms of the mechanism previously suggested, it is expected that only hydrogen bonds formed with the free OAH groups will produce contractions. The infrared absorption band due to the surface OH groups of porous glass is asymmetric. On the high-frequency side, the band is due to the presence of the free OAH groups, and the broad component a t lower frequency is probably due to the presence of hydrogen-bonded OH groups

0

c .-

+II

0

I

4

I

8

I

I2

I

16

1

20

v , cm?/g.

FIG.18. Length changes produced in pororw glass by the adsorption at 20' C. of methyl alcohol (a) and water (b) (165).

of various sorts (such as OeH). Results with thin (0.25 mm.) porous glass (168) evacuated a t 450°C. showed that a hydrogen-bonded system was formed when water was adsorbed. A shift of 290 cm.-' indicates bonds of strength a little weaker than those of acetone. It is difficult to assign this broad band unambiguously. It may be due to changes in the original OH band (as occurs with acetone), or it may be due entirely to the newlyadsorbed water. Observations on 3,730-cm.-' band show that it becomes weaker as water is adsorbed, which may indicate some interaction with the OBH groups. The high-frequency side of this band remained unchanged by this process, indicating that few of the water molecules are interacting with the contraction-producing OAHsites. Furthermore, the time of adsorp-

MOLECULAR SPECIFICITY IN PHYSICAL ADSOBPTION

301

tion is long (146, IS$), possibly because a slow hydration process forms new OH groups. The above experiments agree with Sidorov's results a t low pressures (146), which showed that water is not adsorbed on the free OH groups under these conditions. No detailed comparison can be made, since Sidorov gave no surface area or coverage values for his glass. Similar observations have been reported by Nikitin et al. (161), but have been questioned by McDonald (153),whose results with Cabosil are a t variance with those on porous glass. This discrepancy is probably to some degree due to the qualitative nature of the data. Both McDonald and the Russian workers quote the pressure of the water vapor as an estimate of the amount of water adsorbed. Aside from the heating of the sample, this information is of little use without adsorption isotherms. These were not given in any of the papers. The uncertainty can be removed by measuring the amount adsorbed directly, while the sample is in the beam (163).In these experiments, the largest g . area of the sample (210 mS2/g.)was amount adsorbed was 9.35 ~ m . ~ / The measured using argon. Comparison of the molecular areas of argon (14.6 A.*) and water (10.5 A.2) gives a monolayer capacity for water of 74.4 cm.a/g. Consequently, for porous glass evacuated a t 450' C. with coverages less than 0.13, i t seems that few of the adsorbed water molecules are on the OAH sites, while some are on the OBH sites. Although it is impossible, a t present, t o estimate the fraction of adsorbed water molecules that are interacting with both types of OH groups, these difficulties may be removed in the fut,ure. Differences between results on Cabosil and porous glass may also be sought in the different distribution and concentration of OH groups on the two media, making comparisons inadvisable, as illustrated by differences between water isotherms on porous glass (6'7) and on silica powders (164) formed by a high-temperature process. As these powders were made by generally similar processes, they probably have surface properties similar to Cabosil. The isotherms on glass were type I1 in Brunauer's classification (78), while those on the powder were similar to type 111. This type 111 tendency became more pronounced as the sample was evacuated a t higher temperatures over the range 25 to 450' C. (164). The times of adsorption on these powders were much shorter than those commonly observed on porous glass (146,163).Despite the great effort that has been expended on silica-water systems, it is evident that they are imperfectly understood and of great complexity. Wide variations in properties exist, depending both on the mode of manufacture and on the pretreatment of the surface. When methanol was adsorbed, a t coverages below about 0.4,the intensity of the band due to the surface OH groups decreased, both components being

302

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C. YATW

affected (163). The strength of the hydrogen bond formed (a shift of 380 cm.-l) is a little stronger than that formed with acetone (Table I). The net contraction is much smaller, however (Fig. IS), possibly because the percentage of adsorbed molecules on the OH sites is smaller than it is with acetone. Furthermore, quite strong bonds may be formed between the OH group of the methanol and the oxygen sites of the surface; molecules adsorbed in this way would cause an expansion of the glass. The spectra obtained with methanol are quite complex and are discussed in detail elsewhere (163). TABLE I1 Shifts in Freqwncy of Surface OH Groups on the Adsorption of Bases al Room Temoerature on Silica Surfaces. GRs

NH: NH: NH: NH:

Hs0 Ha0 H:O Hi0 CHIOH CHIOH CHIOH CHIOH COHO CH6 CeH4 Acetone Acetone Acetone

Shift (Av, from 3,750 cm.-'), crn.-'

120 800 830 820 300 330 350 310 240 360 350 400 0 110 110 370 350 330

Reference a b C

d

b e

f B a b e

B a b e a

b d

Sidorov, A. N., Doklady Akad. Nauk S.S.S.R. 96, 1235 (1954). 'Sidorov, A. N.,J . Phys. Chem. (U.S.S.R.) 80, 995 (1966). a Yates, D. J. C., Sheppard, N., and Angell, C. L., J . Chem. Phys. 28, 1980 (1955). * Folman, M., and Yates, D. J. C., Proc. Roy. Soc. A246, 32 (1958). McDonald, R.S.,J . Am. Chem. SOC.79, 850 (1957). f McDonald, R. S., J . Phys. Chem. 62, 1168 (1958). I Folman, M., and Yates, D. J. C., Trans. Faraday SOC.64, 1684 (1958). a

In view of discrepancies noted in an earlier review (126) between values of the shifts of the OH band when hydrogen bonding occurs, a collection of data has been made and is given in Table 11.All the results, except those

of McDonald, have been obtained with porous glasses of various types.

MOLECULAR SPECIFICITY IN PHYSICAL ADSORPTION

303

Despite the variations in the surface properties of silica, i t is remarkable that such good agreement exists. It would appear that the data in the earlier paper of Sidorov (165) are unreliable.

B. SOMECONSIDERATIONS OF SURFACE TOPOGRAPHY 1. Silica Surfaces.

For the first time, it now becomes possible to hope that we may soon be ' i able to have some detailed information about real surfaces. #I On silica, infrared spectra (146, 147, 151) have shown clearly that two general sites of adsorption exist. Type I comprises the OH sites that remain firmly bound to the surface even after long times of evacuation a t 450" C., and the other (type 11) is the oxygen (or possibly the silicon) atoms in the surface. It is probable that the surface of most oxides consists of oxygen, but little is known in detail about this. Models of the arrangement of the OH groups have been suggested (162,153). On silica surfaces formed a t high temperatures with little water present (e.g., Cabosil), it seems that the concentration of the surface OH groups is low enough for only a small degree of interaction between the OH groups to occur after evacuation at 500" C. (147). When evacuation took place a t 940" C., however, even as short a time of evacuation as 15 min. sufficed to change the OH band into a completely symmetrical peak (153). This symmetry indicates that the OH groups are situated sufficiently far apart after this treatment that only a negligibly small percentage of the OH groups interact with each other. Given the latter conditions, it may be possible to speak of "the OH sites" without too much vagueness. In contrast with this, the spectra of porous glass (146, 161, 152) indicate that quite a large percentage of the OH groups interact with others even after long times of evacuation a t 450" C. The surface of these glasses are formed under aqueous conditions a t relatively low temperatures. Similar spectra to those of porous glass have recently been reported (153) for silica powders made under aqueous conditions. For such substances, it becomes clear that there must be, at the very least, two types of OH groups-the "free" OAH groups and the hydrogen-bonded OBH groups (Fig. 16). A direct estimate of the concentration of the surface OH groups is difficult to obtain. The extinction coefficient of an OH group will be markedly increased when it interacts with other OH groups. Such enchancements are a well-known characteristic of hydrogen-bonded systems. For nearly isolated OH groups, this factor is not so important, and a value for the extinction coefficient has indeed been given by McDonald (153). Recent results ( 1 6 5 ~obtained ) with porous glass evacuated a t 920" C. show that the broad OH band disappears. A very sharp symmetrical band

304

D. J.

C. YATES

remains a t 3,749 cm.-l, very similar indeed to that found on Cabosil after evacuation a t 940" C. (165). Apart from the two types of sites, information about the way in which equilibrium is reached in adsorption can be obtained from infrared studies. Although the existence of slow adsorption processes in physical adsorption has been known for many years, their cause has remained largely obscure. Attempts have been made to explain it either by diffusion times through small capillaries, or by surface diffusion, but with little success. The essential step in the process may be the slow desorption of adsorbed molecules from sites of one sort, and resorption, for longer times, on sites with different properties. Such a process has been observed with methanol on porous glass (165), both spectroscopically and by length-change experiments. All other adsorbates which form hydrogen bonds with the surface (and consequent contractions) have shown this peculiar length-change pattern with time (76, 77). Other effects are shown by a detailed examination of spectra taken on desorption, as well as adsorption, at known coverages (166). In a discussion of the causes of the over-all shape of the contraction-expansion curves, it was assumed (162)that the initial expansion (at coverages less than 0.05) was produced by the majority of the molecules being adsorbed on sites other than OH sites. This is somewhat unexpected on general grounds, so it is of interest to examine the validity of this assumption. When successive doses of gas are adsorbed, it is found qualitatively that the band due to hydrogen bonding becomes stronger. To obtain a quantitative estimate of this effect, optical densities were calculated from all the transmission spectra. As a common basis for comparison, the apparent peak optical density of the shifted OH band, due to hydrogen bonding, was used (166). For ammonia a t all temperatures, the curve of peak optical density against amount adsorbed does not pass through the origin (Fig. 19), indicating that, until about 1 cmqS/g.(0 2 0.014) is adsorbed, most of the molecules do not interact with the OH sites. At coverages higher than this, a t any given temperature, a straight line is obtained. The simplest interpretation of this straight line is that in this region the ratio of the adsorbed molecules on the two sites is constant. The same phenomena are observed when acetone is adsorbed (Fig. 20); this is a somewhat simpler case than ammonia, since there is less ambiguity in the type of hydrogen bond formed. Furthermore, the line for acetone a t 25" C. passes close to the origin. The expansion curve for this temperature (Fig. 15) shows only a very small initial expansion. The constant ratio found spectroscopically is, perhaps, unexpected. The largest coverage, however, for ammonia in the spectroscopic experiments, was 0.18 at 150" C. and 0.1 for acetone at 75" C. Under these conditions,

MOLECULAR SPECIFICITY IN PHYSICAL ADSORPTION

305

the minima in the length change plots (77) were not reached, and to this extent the expansion data agree well with the spectroscopic data. At higher coverages, relatively fewer OH sites probably become involved, as indicated by the length-change data, but this was not investigated spectroscopically.

0.2 0

0.6 0.4 .0.8

c

-

g

0.2

.c

1.6

2

4

0

2

6

"

8

LO

6

8

1.4

0

1.2 1.0 0.8 0.6

0.4

0.2 0

0

4

v , cm?/g.

FIG.19. Peak optical density of the perturbed OH groups as a function of the volume of ammonia adsorbed. The temperatures of adsorption are given in the diagram. Points obtained by adsorption 0 ,by desorption X. 2. Other Surfaces.

It has been noted elsewhere (127) that even when used solely as a support, silica has been the substance most studied by infrared means. Some of the data obtained on these surfaces have implications for other surface phenomena. One of the properties of porous glass is that it adsorbs hydrocarbons from the atmosphere (67, 7 4 , 8 7 , 1 6 7 ) .This adsorption turns it yellow, and if the glass is heated in uacuo, the color becomes darker and darker until

306

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C. YATES

i t finally goes black. The carbon can he removed in a few hours by heating a t 450°C. in either air or oxygen. Expansion experiments carried out before the glass was degreased gave values substantially different from those after degreasing (87). The degreasing was repeated after exposing the sample to the atmosphere and was found to bring the glass into a reproducible state. The optical characteristics of porous glass are such that it is especially easy to detect small color changes. Unless the mechanism of adsorption of

v,cm?/g.

FIQ.20. Peak optical density of the perturbed OH band produced by the adsorption of acetone at 20,75, and 135" C. and methyl chloride at 20" C. Peak optical densities of the 2,970-cm.-l CH stretching band of adsorbed methyl chloride are also given. Value obtained on adsorption 0,after deaorption X .

grease from the air is unique to this material, it is likely that many other surfaces will have been contaminated in this way. The infrared technique is especially useful for detecting this contamination; very small contaminations due to vacuum waxes could be detected, while no visible effect was produced (168). On other silica surfaces (Cabosil), spectra have been published (165) that show bands in the C-H stretching region. These could be removed by oxygen a t 500" C. and were attributed t o a surface contaminant.

MOLECULAR SPECIFICITY IN PHYSICAL ADSORPTION

307

A great deal of adsorption work has been carried out using titanium dioxide as an adsorbent, following extensive work with this material by Harkins and Jura (169). In one series of accurate calorimetric experiments, the initial temperature of evacuation was 300" C. (96). Any grease present on the rutile before degassing would not have been removed by this treatment. Recent work (170) has shown that it is possible that rutile may be subject .. to hydrocarbon contamination. ,One other property of rutile makes it disadvantageous for surface studies. This material is particularly liable either to take up an excess of oxygen during heating in this gas or to be reduced by hydrogen, or a vacuum, at 500" C. These effects have been discussed in connection with surface properties by Reyerson and Honig (171) and Sandler (172) and in the bulk material by Cronemeyer (173, 174). Considerable changes in the infrared spectra of the bulk material were found (173, 174) to occur after slight reduction a t 600" C. How this relative instability affects its surface properties is largely unknown, but the importance of these effects in determining surface topography is great.

V. Conclusion When physical adsorption takes place on solid surfaces, the free energy is reduced and also the surface tension. The surface tension induces significant strains in high area adsorbents in uucuo. Calculations show that the relief of these strains should produce quite marked volume changes in rigid adsorbents. These effects have been studied on the adsorption of inert gases, and it was found that the length changes were a linear function of the free energy lowering. The two quantities are related to each other by the bulk modulus of the adsorbent. I n addition, this adsorption expansion shows that the adsorbent is not inert during the process of adsorption. In many theoretical treatments of physical adsorption the solid is considered inert, since this assumption leads t o a great simplification. It follows that these treatments are not rigorous. Because of great experimental difficulties, little progress has been made with classical adsorption techniques in understanding the effects which physical adsorption produces in adsorbed molecules. The application of infrared spectroscopy to these problems in recent years has enabled very important advances to be made. This technique has shown that the symmetry of a molecule undergoes drastic changes on adsorption because of the asymmetric nature of the surface forces. In addition to this, the presence of new bands in the spectra of adsorbed molecules, a t frequencies similar to those found in the Raman region, shows directly the existence of induced dipoles. The strength of these bands is proportional to the square of the electric field at the surface. Comparison of the spectra of hydrogen adsorbed

308

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C. YATEB

a t a known coverage with the spectra induced in hydrogen by a uniform electric field enables an experimental estimate t o be made of the field at a solid surface. High-resolution spectroscopy can provide dircct information about the rotational degrees of freedom of adsorbed molecules in some cases. These experiments provide information on the perturbation accompanying adsorption, both of the adsorbent and of the adsorbate. The two methods have been used together t o investigate the unusual contractions of porous glass on the adsorption of polar molecules. Hydrogen bonding between the adsorbates and the surface OH groups of the solid was found to be present whenever contractions occurred. The stronger the hydrogen bond formed, the larger the contraction. The special case of adsorbates containing OH groups is also discussed. This information has enabled some progress to be made towards obtaining an idea of the detailed topography of a real surface and of the changes in motion and symmetry of molecules when they go from the gas pliasc to the adsorbed phase.

ACKNOWLEDGMENTS Thanks are due to the following for permission to reproduce certain figures: the Council of the Royal Society for Figs. 4, 5, and 9 to 16; the Council of thc Faraday Society for Figs. 7, 8, and 18; the editor of the Canadian Journal of Chemistry for Figs. 2 and 3; the editor of the Journal of Physical Chemistry for Fig. 6; and the editor of the Journal of Chemical Physics for Fig. 1.

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96. Hill, T. L., in “Structure and Properties of Solid Surfaces” (R. Gomer and C. 5.

Smith, eds.), p. 384. University of Chicago Press, Chicago, 1953. 98. Morrison, J. A., Los, J. M., and Drain, L. E., Trans. Faraday SOC.47, 1023 (1951). 97. Drain, L. E., and Morrison, J. A., Trans. Faraday Soc. 48, 316 (1952). 98. Drain, L. E., Sn’. Progr. 42, 608 (1954). 99. Schreiber, H. P., and McIntosh, R., Can. J . Chem. 32, 842 (1954). 100. Garden, L. A., and Kington, G. L., Proc. Roy. Soc. 8334, 24 (1956). 101. Cook, M. A., Pack, D. H., and Oblad, A. G., J . Chem. Phys. 19, 367 (1951). 10.2. Brunauer, S., in “Structure and Properties of Solid Surfaces” (R. Gomer and C. S. Smith, eds.), p. 395. University of Chicago Press, Chicago, 1953. 103. Barron, T. H. K., Berg, W. T., and Morrison, J. A., Proc. Roy. SOC.A243, 478 (1957). 104. Peticolas, W. L., J . Chem. Phys. 27, 436 (1957). f06. Tykodi, R. J., J . Chem. Phys. 22, 1647 (1954). IOB. Tykodi, R. J., Trans. Faraday Soc. 64, 918 (1958). 107. Copeland, L. E., private communication (1959), to be published. 108. Danforth, J. D., and de Vries, T., J . Am. Chem. Soc. 61, 873 (1939). 109. Tuck, M., McIntosh, R., and Maass, O., Can. J . Research B26, 20 (1948). 110. Juhola, A. J., and Wiig, E. O., J . Am. Chem. SOC.71, 2069 (1949). 111. Morrison, J. A., Drain, L. E., and Dugdale, J. S., Can. J . Chem. 30, 890 (1952). 11.2. McIntosh, R., Johnson, H. S., Hollies, N., and McLeod, L., Can. J . Research B26, 566 (1947). 113. McIntosh, R., Rideal, E. K., and Snelgrove, J. A., Proc. Roy. Soc. 8308, 292 (1951). 114. Snelgrove, J. A., Greenspan, H., and McIntosh, R., Can. J . Chem. 31, 72 (1953). 116. Channen, E. W., and McIntosh, R., Can. J . Chem. 33, 172 (1955). 116. Waldman, M. I€., and McIntosh, R., Can. J . Chem. 33, 268 (1955). 117. Benson, G.C., Channen, E. W., and McIntosh, R., J . Colloid Sci. 11, 593 (1966). 118. Gomer, R., Advances in Catalysis 7, 93 (1955). 119. Hickmott, T. W., and Selwood, P. W., J . Phys. Chem. 60, 452 (1956). 1.20. Fuschillo, N., and Renton, C. A., Nature 180, 1063 (1957). 191. Mays, J. M., and Brady, G. W., J . Chem. Phys. 26, 583 (1956). 1.22. Zimmerman, J. R., Holmes, B. G., and Lasater, J. A., J . Phys. Chem. 60, 1157 (1956). 1.23. Zimmerman, J. R., and Brittin, W. E., J . Phys. Chem. 61, 1328 (1957). 1.24. Zimmerman, J. R., and Lasater, J. A., J . Phys. Chem. 62, 1157 (1958). 1.25. O’Rcilly, D. E., Leftin, H. P., and Hall, W. K., J . Chem. Phys. 29, 970 (1958). 196. Eischens, R. P., and Pliskin, W. A., Advances in Catalysis 10, 2 (1958). 1.27.Sheppard, N., in “Molecular Spectroscopy” (E, Thornton and H. W. Thompson, eds.), p. 277. Pergamon Press, London, 1959. 128. Eischens, R. P., Francis, S. A., and Pliskin, W. A., J . Phys. Chem. 60, 194 (1956). 1.29. Pimentel, G. C., Garland, C. W., and Jura, G., J . Am. Chem. SOC.76, 803 (1953). 130. French, R. O., Wadsworth, M. E., Cook, M. A., and Cutler, I. B., J . Phys. Chem. 68, 805 (1954). 131. Eyring, E. M., and Wadsworth, M. E., Mining Eng. 6,531 (1956). 13.2. Pliskin, W. A., and Eischens, R. P., J . Phys. Chem. 69, 1156 (1955). 133. Sheppard, N., and Yates, D. J. C., Proc. Roy. SOC.8338,69 (1956). 134. Condon, E. U., Phys. Rev. 41, 759 (1932). 136. Crawford, M. F., and Dagg, I. R., Phys. Rev. 91, 1569 (1953). 136. Roberts, J. K., and Orr, W. J. C., Trans. Faraday Soc. 84, 1346 (1938).

312

D. J. C. YATES

137. de Boer, J. H., Advances in Colloid Sci. 3, 36 (1950). 138. Chessick, J. J., Zettlemoyer, A. C., Healey, F. H., and Young, G. J., Can. J . Chem.

33, 251 (1955). 139. Zettlemoycr, A. C., Chessick, J. J., and Hollabaugh, C. M., J . Phys. Chem. 6a, 489

(1958). 140. Hollabaugh, C. M., and Chcssick, J. J., Meeting of American Chemical Society, 141. 14.2. 143. 144. 146. 146. 147. 148. 148a. 149. 160. 161.

Boston, April 5-10, 1959, Division of Colloid Chemistry. Orr, W. J. C., Trans. Faraduy Sac. 36, 1247 (1939). Hill, T. L., J . Chem. Phys. 16, 181 (1948). Benesi, H. A., and Jones, A. C., J . Phys. Chem. 63, 179 (1959). Sing, I<. S. W., and Madeley, J. D., J . Appl. Chem. 4, 365 (1954). Sing, K. S. W., and Madeley, J. D., J . Appl. Chem. 3, 549 (1953). Sidorov, A. N., J . Phys. Chem. (U.S.S.R.) SO, 995 (1956). McDonald, R. S., J . Am. Chem. SOC.79, 850 (1957). Francis, S. A,, and Ellison, A. H., J . O p f . SOC.Am. 49, 131 (1959). Pickering, H. L., and Eckstrom, H. C., J . Phys. Chem. 63, 512 (1959). Yatcs, D. J. C., Sheppard, N., and Angell, C. L., J . Chem. Phys. 23, 1980 (1955). Rhodin, T. N., Advances in Catalysis 6 , 40 (1953). Nikitin, V. A., Sidorov, A. N., and Karyakin, A. V., J . Phys. Chem. (U.S.S.R.)

SO, 117 (1956). 166. Folman, M., and Yates, D. J. C., Proc. Roy. SOC.8346, 32 (1958). 163. McDonald, R. S., J . Phys. Chem. 62, 1168 (1958). 164. Folman, M., and Yates, D. J. C., unpublished work (1957). 166. Badger, R. M., and Bauer, S. H., J . Chem. Phys. 6 , 805, 839 (1937). 166. Badger, R. M., J . Chem. Phys. 8, 288 (1940). 167. Pimentel, G. C., and Sederholm, C. H., J . Chem. Phys. 24, 639 (1956). 168. Barrow, G . M., J . Phys. Chem. 69, 1129 (1955). 169. Tsubomura, H., J . Chem. Phys. 24, 927 (1956). 160. Higgins, C. M., and Pimentel, G. C., J . Phys. Chem. 60, 1615 (1956). 160a. Yates, D. J. C., unpublished results (1956). 161. Cook, D., Lupien, Y., and Schneider, W. G . , Can. J . Chem. 34,957 (1956). 166. Cook, D., Lupien, Y., and Schneider, W. G., Can. J . Chem. 34, 964 (1956). 163. Folman, M., and Yates, D. J. C., Trans. Faraday SOC.64, 1684 (1958). 164. Young, G . J., J . Colloid Sci. 13, 67 (1958). 166. Sidorov, A. N., Doklady Akad. Nauk S.S.S.R. 96, 1235 (1954). I66a. Yates, D. J. C., Unpublished results (1959). 166. Folman, M., and Yates, D. J. C., J . Phys. Chem. 63, 183 (1959). 167. Nordberg, M. E., J . Am. Ceram. SOC.27, 299 (1944). 168. Yates, D. J. C., unpublished results (1957). 169. Harkins, W. D., and Jura, G., J . Am. Chem. SOC.66, 1362 (1944). 170. Gebhardt, J., and Herrington, K., J . Phys. Chem. 62, 120 (1958). 171. Reyewon, L. II., and Honig, J. M., J . Am. Chem. Soe. 75, 3920 (1953). 176. Sandler, Y. L., J . Phys. Chem. 58, 54 (1954). 173. Cronemeyer, D. C., Phys. Rev. 87, 876 (1952). 17.4. Cronemeyer, D. C., Phys. Rev. 113, 1222 (1959).

Author Index Numbers in parentheses are reference numbers and are included to assist in locating references when the authors' names are not mentioned in the text. Numbers in italics refer to the page on which the reference is listed.

A Abrahams, E., 74, 114 Abragam, A,, 77(125), 82, 83(135), 84 (141), 89, 90, 92, 114, 116 Adam, N. K., 268(30), 309 Ahrens, F. B., 140(49), 148 Aigrain, P., 211(19), 259(19), 262 Allison, 5.K., 150, 187 Alm, R. M., 118(12), 119(12), 120(12), 121(12), 122(12), 124(12), 147 Alpert, N. L., 59(102), 114 Amberg, C. H., 271, 272(67), 275(67), 276(67), 277(67), 278(67), 297, 299, 301(67), 305(67), 310 Anderson, P. W., 52, 91, 93(157), 104 (157), 113, 116 Andrew, E. R., 32, 41(48), 45(63), 58 (1011, 59, 111, 113, 114 Angell, C. L., 291(149), 292(149), 302, 31.2

Arnell, J. C., 271, 309 Arrigo, J. T., 130, 148 Artmann, K., 3, 30 Austen, D. E. G., 106(179, 1811, 107 (181), 108(181), 116 Auzins, P., 34(27), 112 Azitroff, L. V., 167, ILV

273, 274(53, 54, 55, 56, 57, 58, 59), 309. 310 Bardeen, J., 228(42), 230(42), 263 Barrer, R. M., 276(86), 278(86), 310 Barrie, J. A., 276(86), 278(86), 310 Barron, T. H. K., 283(103), 311 Barrow, G. M., 296(158), 312 Bartlett, P. D., 129, 148 Basolo, F., 91, 106(156), 116 Bauer, E., 245(86), 254, 264 Bauer, S. H., 296(155), 312 Bearden, J. A., 152, 159, 187 Beebe, R. A., 265(1), 308 Beeman, W. W., 152, 158, 159, 1W Beljers, H. G., 83(134), 116 Bell, M. D., 106(182), 108(182), 116 Benesi, H. A,, 289, 319 Bennett, J. E., 106(178), 116 Benson, G. C., 266, 267(15,19,21,25a), 285(117), 308, 309, 311 Benson, G . W., 266(19), 267(19), 309 Berg, W. T., 283(103), 311 Bergmann, E., 144, 148 Bersohn, R., 41(48), 53, 54(90), 56, 113, 11L Bcthe,'H. A., 83, 116 Black, J., 240(71), 264 Bleaney, B., 33(20), 34(30,31), 77(126), 84(126), 90, 91(126), 92, 93(158), 112, 116 Bleil, D. E., 100(171), 104(171), 116 Bloch, F., 32, 38(45), 39(1), 42(53), 47, 48(1), 111, 112, 113 Block, J., 222, 2G2 Bloembergen, N., 32, 35(3), 42(3), 43(3), 44(3,57), 45(3), 46(57), 49, 51(76, 78), 52, 59, 61, 62, 72(57), 96, 111, 113, 114, 116

B Badger, R. M., 296(155,156), 312 Bagguley, D. M. S., 34, 112 Bailey, G. C . , 236(69), 237(69), 264 Baker, W. O.,106(178), 116 Balandin, A. A., 207(18), 262 Baldock, G. R., 2(2), 6, 10, 22(13), 30 Balk, P., 267(25a), 309 Ballhausen, C. J., 89, 116 Bangham, D. H., 268, 269(32), 270, 271, 313

314

AUTHOB INDEX

Bodart, J., 244(79), ,964 Boehm, G., 180, 187 Boke, K., 159, 187 Bonch-Bruevich, V. L., 195(7), 196(7), 200(12), 230(45), 251, 8G.2, bG3, bG4

Bond, R . L., 106(178), 118 Boreskov, G. K., 236, 237(68), 863 Boswell, F. W. C., 267, 309 Boudart, M., 224, $63 Bowers, I<. D., 33(20), 34(30), 84(140), 90, 91(140), 93(158), 118, 116 Boyd, G . E., 269, 309 Brady, G. W., 33, l l b , 285(121), 311 Briggs, H., 271, 274(61), 310 Brittin, W. E., 33(18), 60(18), 61(18), 11.8, 285(123), 311 C., 141(51), 1 4 F., 132, 148 H., 106(180), 107(180), 116 S., 266(24,25), 267(24), 269 (63), 272(78,79), 273(81), 274(25), 283, 301, 309, 310, 311 Bryce-Smith, D., 127, 133, 147 Butler, C. C., 267, 309

Brown, H. Brown, R . Brown, T. Brunauer,

C Calvert, J. G., 246(87), i?G4 Carr, 11. Y., 49(70), 113 Carver, T. R., 82, 116 Castle, J. G., Jr., 106(178), 116 Cauchois, Y . , 154, 187 Channen, E . W . , 285(115, 1171, 311 Chapman, P. R., 100(170), 116, 236, 237 (671, bG3

Cheasick, J. J., 269(39), 288, 509, 318 Chiahikova, G. I., 234(60), 240(60), b63 Cines, M., 276(85), 278(85), 310 Claff, C. E., Jr., 127(30), 147 Clark, A,, 236(69), 237(69), 864 Clark, H., 269(41), SO9 Cloeaon, R. D., 127(25), 128(25), 147 Cohen, A. D., 74(122), 114 Cohen, M. H., 56(90,97), 57, 58(97), 62(97), 114

Collins, R. L., 106(182), 108(182), 116 Combrisson, J., 106(178), 116 Commoner, B., 106(178), 116 Compton, A. H., 150, 187 Condon, E. U., 95(161), 116, 287, 311 Conger, R. L., M)(72), 113

Cook, D., 299(161,162), 31.9 Cook, M. A., 269(36), 283, 286(130), 309, 311

Copeland, L. E., 284, 311 Cotts, R. M., 42(54), 113 Crafts, W., 170, 187 Crawford, M. F., 288, 311 Crawford, V. A., 270, 309 Crocker, R. E., 127, 148 Cronemeyer, D. C., 307, 318 Curtin, D. Y., 118, 147 Cutler, I. B., 286(130), 311

D Dagg, I. R., 288, 311 Danforth, J. D., 284(108), 311 Das, T.P., 32, 53, 56(92), 111, 113, 114 Davis, C. F., Jr., 74(124), 90(148), 92, 103, 114, 116

Dayhoff, E. S., 100,110 de Boer, J. H., 258, bG4, 265, 270(44,47), 271, 273(80), 284(2), 288(137), 908, 309, 310, 311 Dent, B. M . , 266, SO8 de Vries, T., 284(108), 311 De Witt, T. W., 276(84), 278(84), 310 Dillon, J. A., 234(52), 8G3 Dominically, C. A., 234(59), $63 Drain, L. E., 278(88,89), 280, 282(88,89, 96,97,98), 283, 284(89,111), 307(96), 310, 311 Dugas, C., 211(19), 259(19), 86.9 Dugdale, J. S., 284(111), 311 Dunitz, J. D., 84(142), 116 Dykhno, N. M . , 118(3), 119(3), 147

E Eades, R. G., 45(63), 58(101), 59, 113, 114

Ecke, G. G., 127(25), 128(25), 147 Eckstrom, H. C., 290, 318 Edelhoch, H., 269(40), 309 Egloff, G., 118(2), 147 Eischens, R . P., 2(1), 30, 99, 106, 116, 116, 285, 286, 311 El Gobeily, M. A., 271, 310 Ellison, A. H., 290, 318 Elovitch, S. Y., 234(57), 863 Emmett, P. H., 269(38,63), 276(84,85), 278(84,85), 282(38), 509, 510

AUTHOR INDEX

Engel, H. J., 211(21,22), 259(21,22), 862 Enikeyev, E. H., 234(63,64), 163 Erb, E., 109(185), 116 Erdman, J. G., 94(159), 97(159), 116 Eechinazi, H. E., 118(6,7,8), 121, 123, 125, 147 Etienne, A,, 106(178), 116 Everett, D. H., 269, 282, 309, 910 Eyring, M.,286(131), 311

F Faber, R. J., 98, 116 Faessler, A.,180(19), 187 Fakhoury, N., 271(53,54,55,56,57), 273, 274(53,54,55,56,57), 309, 310 Farnsworth, H. E., 234(52), 263 Feenberg, E., 34, 112 Feher, G., 82, 83, 116 Feld, B. T., 56(95), 11.4 Fletcher, R. C.,34(37), 118 Flood, E. A.,272(70,71,72,73), 273, 274 (70), 277, 278(72,73), 294, 310 Flournoy, J. M.,34(41), 119 Flynn, E. W.,118(13), 147 Fokina, E. A., 222(29), 240, 262, 264 Foley, H. M., 56(9), 114 Folman, M.,272(77), 280(77), 281(77), 291(77), 292(152,154), 293(152), 294 (77,1521, 295(152), 296(77,152), 297, 298(152), 299(163), 300(163), 301 (163), 302, 303(152), 304(77,152,163, 1661, 305(77), 310, 311 Foster, W. E., 127(26), 128(26), 147 Fraenkel, G. K., 32, 112 Francis, 8. A., 285(128), 390, 311, 318 Friedman, S., 118(4), 119(4), 121(4), 124(4), 129(38), 147, 148 French, R. O.,286(130), 311 Fujita, Y.,244, 264 Fuschillo, N., 33, 119, 285(120), 311

G Garden, L. A., 282(100), 284(100), 311 Garland, C. W.,266(23), 286(129), 309, 311 Gamer, W. E., 27(15), 30, 222, 234(49), $68, bGS

Gebhardt, J., 307(170), 312 Germain, J. E., 211(20), 222, 259(20), 268

315

Gibba, J. W., 266, 308 Glasko, V. B., 202, 268 Gomer, R., 285, 311 Goodwin, E. T., 3, 5(6), 30, 229(44), 163 Graham, D., 109, 116 Gray, T. J., 27(15), 30, 234(49,50), 863 Greenhalgh, E., 12(12), 30 Greenspan, H., 285(114), 311 G r a t h , R. H.,100, 116, 236(67), 237 (671, 263 G r a t h a , J. H. E., 34(23, 27, 28, 351, lld Grimley, T. B.,7(9), 10(9), 15(9), 80 Grovenstein, E., 118, 147 Guggenheim, E. A., 282, 310 Gutowsky, H. S., 32, 41(48), 44(61), 51 (751, 59(75), 67(116), 73(121), 111, 113, 114 Guy, J., 53, 113

H Haag, W. O., 118(9,10,11), 119, 120, 121, 147 Hahn, E. L., 49, 113 Haines, R. S.,271, 275, 277(64), 280(64), 294, 310 Halbach, K., 50(71), 113 Hall, W .K., 71(120), 114, 285(125), 311 Halsey, G. D.,265, SO8 Hammond, G. S.,132(41), 148 Hansen, W .W.,32, 39(1), 47(1), 48(1), 111 Hanson, H. P., 152, 158, 180, 187 Hanson, W .E., 94(159), 97(159), 116 Harkins, W . D., 266(8), 269, 307, 308, 309, 312 Hart, H., 127(34), 128(36), 135, 148 Hartree, D. R.,152, 187 Hauffe, K., 24, 28(14), 30, 211(21,23), 222, 224(34,39), 251, 259(21,23), 962, 263, 164 Hayasi, 151, 187 Hayes, W., 34(26), 118 Healey, F. H., 269(39), 288(138), 309, 312 Hecklesberg, L. F., 236, 237(69), 264 Hedvall, J. A,, 244(77,80), 864 Heikes, R.R.,105, 116 Heilmd, G., 234(54), 263 Henser, A,, 140(50), 148 Herington, E. F. G., 106(177), 116

316

AUTHOR INDEX

Herring, C.,53(88), 114, 266(9), 308 Herrington, K., 307(170), 318 Heyding, R. D., 272(70), 273, 274(70), 277, 310 Hickmott, T. W., 33, 112, 285(119), 311 Higgins, C. M., 296(160), 318 Hill, R. M., 280(92), 310 Hill, T.L., 265, 269(34,38), 270(45), 282, 284(4), 288(142), 289, 308, 309, 311, 318

Kalenda, N. W., 94(159), 97(159), 116 Kanda, T.,52(79), 67(118), 113, 114 Kantro, D. L., 266(24,25), 267(24), 274 (251,283(24), SO9 Karyakin, A. V., 292(151), 301(151), 303 (1511,312 Kawaji, S., 244(83), 264 Kawamura, H., 62, 114 Keeling, R. O., 180, 187 Kemball, C.,265, 282(3), 284(3), 308 Keyer, N. P., 222, 234(58,60), 236, 240 (601, 863 Khutsishvili, G. R., 44(57), 46, 72(57),

Hoff, M. C . , 118(12), 119(12), 120(12), 121(12), 122(12), 124(12), 147 Hoffman, C.J., 67(116), 114 113 Hoffman, F.,138, 148 Kington, G. L., 282(100), 284(100), 311 Holcomb, D.F., 59(98), 114 Kip, A. F., 34(33), 112 Hollabaugh, C. M., 288(139,140),31Z Kittel, C.,34(33), 51(77), 52, 74, 82, 112, Hollies, N., 285(112),311 119, 114, 116 Holm, C. H., 44(60), 113 Holmes, B. G., 33(18), 60(18), 61(18), Knight, W. D., 47, 53, 113, l l 4 Kobozev, N. I., 255, 26'4 122, 285(122), 311 Kogan, S. M., 212(25), 227, 228(41), 242 Honig, J. M., 307, 312 (75), 245(41), 247(94), 249(94,95), Howard, R.,280(91), 310 251, 262, 26'3, 86'4 Hrostowski, H. J., 52(80), 113 Kolka, A. J., 127(25), 128(25), 147 Hulla, G.,118(2), 147 Kolm, H . H., 247, 264 Hulubei, H., 154(13), 187 Hutchison, C. A., Jr., 32, 34(32), 111, Kolobielski, M.,126, 144, 146, 147, 148 Komarewski, V. I., 118(2), 147 113 Korringa, J., 44(58), 113 I Korsunovsky, G. A., 245(89), 264 Ingram, D. J. E., 34(21,22), 106(178,179, Kossel, W.,150, 187 181), 107(181), 108(171), 118, 116 Koster, G.F., 2(3), 6, 10,SO Ipatieff, V. N., 118(5), 119(5), 122(5), Kouteckf, J., 3, 6(8), lO(lO,ll), 13(11), 127(19), 128(19), 129(19), 134, 147 18(11), 30, 30 Ierailevich, E. A,, 118(3), 119(3), 147 Kramers, H. A.,89, 116 Kraus, Gerard, 106(182), 116 J Kronig, R. de L., 78(127), 116, 151, 187 Jackson, R., 106(178), 116 Krylov, 0.V., 222(29), 240, 262, 264 Jeffries, C.D., 51(76), 119 Kubo, R., 42(52), 113 Johnson, F. M. G., 266(18), 308 Kurbatov, L. N.,244(78), 264 Johnson, H. S., 285(112), 311 Kutseva, L. N., 234(58), 263 Johnston, W.D., 105(174), 116 Kwan, T.,244, 264 Jones, A. C . , 289, 312 Joyner, L. G., 269(38), 282(38), 309 1 Juhola, A. J., 271, 277(65), 284(110), Lakhanpal, M. L., 272(72, 731, 277(73), 310, 311 278(72,73), 294, 310 Jura, G . , 266(8,23), 269, 286(129), 307, 308, $09, 311, 312 Lamb, W. E., Jr., 53, 56(95), 113, l l 4 Juze, V. P., 245,26'4 Lamont, J. L., 170, 187 Landesman, A,, 83(135), 116 K Langlois, G. E., 127(22), 130, 147 Kabayashi, A,, 244(83), 264

AUTHOR INDEX

317

Lanpher, E. J., 127(31,32), 128, 139, 147, Margolis, L. I., 234(57,61,63), 240, 263, $64 148 Laroche, J., 106, 109(183), 110(183), 116 Mark, V., 127(20), 129, 130(20), 139, 140 (20), 143, 147, 148 Lasater, J. A., 33(18), 60(18), 61(18), Marsh, J. D. F., 100(170), 116, 236(67), 112, 285(122,124), 311 237(67), 263 Lsshkarev, V. E., 245, 264 Leftin, H. P., 71(120), 114, 285(125), 311 Matheson, M. S., 34(40), 112 Lennard-Jones, J . E., 203, 262, 266, 308 Matsunaga, Y., 100, 105, 116, 116 Matveyev, K. I., 236, 237(68), 263 Levy, R. A., 34(33), 112 Maxwell, L. R., 100, 104(171), 116 Lipsett, S. G., 266, 308 Mays, J. M., 33, 52(80), 118, 113, 285 Little, E. E., Jr., 127(28), 147 (121), 311 Little, W. A,, 42(53), 113 Meehan, F. T., 271, 273, 274(52), 309 Livingston, H. K., 269, SO9 Melnick, D. A., 244(84), 264 Livingston, R., 34(38,39), 112 Merritt, F. R., 34(37), 118 Losche, A., 32, 33, 111 Michael, A., 138, 148 Lornont,, J . S., 85(143), 116 Los, J. M., 282(96), 283(96), 307(96), Milligan, W. O.,180, 187 311 Moffitt, W., 89, 116 Moharned, A. F., 271(56,57), 274(56,57), Low, W., 33(20), 90(152), 92, 118, 116 309, 310 Lowe, I. J., 41, 113 Morrison, J. A,, 278(88,89), 282(88,89, Lupien, Y., 299(161,162), 312 96,97), 283, 284, 307(96), 310, 311 Luyckx, A., 244(79), 264 Lyashenko, V. I., 234(51,53,55,62), 263 Morton, A. A., 118(1), 127, 128(35), 129, 139, 147, 148 M Motchane, J. L., 109(185), 116 Maass, O., 266(18), 284(109), 308, 311 Murnaghan, A. R., 106(178), 116 McBain, J. E., 271, 274(62), 310 Murphey, W., 141(51), 148 McCall, D. W., 52(80), 113 Myasnikov, I. A,, 234(56), 236, 237(56), McConnell, H. M., 32, 44(60), 94(160), 244(82), 263, 264 111, 113, 116 N McDermot, H. L., 271, 309 McDonald, R. S., 290(147), 292, 297, 301, Nagayev, E. I,., 202, 262 Napolitano, J. P., 127(25), 128(25), 147 302, 303, 304(153), 306(153), 312 Neuweiler, C., 245(86), 264 McGarvey, B. R., 53, 91, 98, 114, 116 Newrnan, R., 59(100), 114 McGuire, T. R., 100, 104(171), 116 McIntosh, R., 266(17), 271, 272, 275, 276 Nicolau, C. S., 110, 116 (67,68,69), 277(64,67), 278(67), 280 Nicolson, M. M., 267, 268, 309 (64), 282(99), 284(109), 285, 294, 297, Nikitin, V. A,, 292(151), 301, 303(151), 318 298(152), 299, 301(67), 305(67), 308, Noble, G. A., 34(32), 118 310, 311 MacIver, D. S., 71(173), 72(173), 73 Norberg, R. E., 41, 59(98,99), 123, ll4 (1731, 74(173), 75(173), 81(173), 100 Nord, S.,244(80), 264 (173), 101(173), 102(173), 103(173), Nordberg, M. E., 279(90), 305(167), 310, 312 104(173), 116 Notari, B., 140(48), 141, 148 Mackenzie, J. K., 274, 810 Nystrom, R. F., 118(13), 147 McLeod, L., 285(112), 311 Madeley, J. D., 289, 290, 312 0 Maggs, F. A. P., 271(59,60), 274(59,60), Oblsd, A. G., 283(101), 311 310 O’Brien, M. C.M., 34(36), 112 Maki, A. H., 91, 98, 116

318

AUTHOR INDEX

O’Bryan, H. M., 29(16), 30 O’Grady, T. M., 118(12), 119(12), 120, 121, 122(12), 124(12), 147

O’Reilly, D. E., 62(109), 63(109), 66(115), 67(115), 68(115), 71(119,120,173), 72 (173), 73( 173), 74(173), 75( 173), 81(173), 90(119), 94(149), 96(149), 97(164), 100(173), 101(173), 102 (1731, 103(173), 104(173), 114, 116, 116, 285(125), 311 Orgel, L. E., 84(142), 116 Orr, W. J. C., 288(136,141), 311, 318 Orton, J. W., 33(20), 34(27), 118 Otauka, E., 62, 114 Overhauser, A . W., 44(58), 82, 113, 116 Owen, J., 33(20), 34, 84(140), 90, 91 (1401, 92, 118, 116

P Pack, D. H., 269(36), 283(101), 309, 311 Packard, M., 32, 39(1), 47(1), 48(1), 111 Pake, G. E., 32, 33, 34, 41(47,48), 51, 59(75), 106(178), 111, 119, 113, 116 Parratt, L. G., 150, 187 Parravano, G., 222, 234(59), 263 Paator, R. C., 106(180), 107(180), 116 Patterson, D., 266(14), 308 Pearson, G. L., 34(37), 112 Pearson, R. G., 91, 106(156), 116 Petersen, H., 152, 187 Peticolas, W. L., 284, 911 Phillips, W. D., 109, 116 Pickering, H. L., 290, 318 Pierce, C., 269, 309 Piette, L. H., 34(41), 118 Pimentel, G. C., 286, 296(157,160), 311, 319 Pines, D., 42(50), 113 Pines, H., 118, 119, 120, 121, 122(5), 123, 124, 125, 126, 127(19,20,23,24), 128, 129, 130, 131, 133, 134, 135, 136, 139, 140(20,47,48), 141, 143, 144, 146, 147,

148

Pliskin, W. A., 2(1), SO, 285, 286,311 Pobitachak, E., 110(187), 116 Podall, H., 127(26), 128(26), 147 Poindexter, E., 83, 116 Poltorak, 0. M., 255, 264 Porter, J. L., 271(62), 274(62), 310

Portis, A. M., 34(33,34),

43(34),

62,

118, 114

Pound, R. V., 32, 35(3), 42(3), 43(3), 44 (3,591, 45(3), 47, 49, 54(5), 5661, 59(3), 61, 63, 111, 119, 114 Powles, J. G., 41(48), 113 Pratt, J. W., 247, 864 Pro& E., 140(46), 1.48 Pryce, M. H. L., 34(29,36), 77(125), 84 (141), 89, 90, 92, 113, 11.4, 116 Pshezhetaky, S. Y . , 234(56), 236, 237(56), 244(82), 263, 864 Purcell, E. M., 32, 35(3), 42(3), 43(3), 44(3), 45(3,62), 49, 51, 59(3), 61(3), 111, 119

Q Quinn, H. W., 271(68,69), 272(68,69), 276(68,69), 310

R Rabi, I. I., 37(44), I18 Ramsey, N. F., 37(44), 53, 112, 113, 114 Ramsey, V. G., 94(159), 97(159), 116 Razouk, R. I., 268(32), 269(32), 271, 274(58), 309, 310

Redfield, A. G., 40, 47(66), 48(46), 75 (461, 113

Reggel, L., 118(4), 119, 121, 124(4), 147 Reid, C., 74(122), 114 Reif, F., 56, 57, 58(97), 62, 114 Rempel, R. C., 34(41), 118 Rens, G., 244(79), 864 Renton, C . A., 33, 118, 285(120), 311 Reyerson, L. H., 271(50), 307, 309, 312 Rhodin, T. N., 291(150), 318 Rideal, E. K., 106(177), 116, 285(113), 31 1

Rienacker, G., 236, 237(70), 864 Ritchey, W. M., 245(87), 264 Rittmayer, G., 180(19), 187 Roberta, J. K., 288(130), 311 Rogers, M. T., 98, 116 Roginsky, 8. Z., 192(4), 196(4), 222(29, 361, 234(63), 236(36), 237(36), 251, 262, 863, 264 Ross, S., 269(41), 309 Rowland, T. J., 51(76,78), 52, 62, 96 (163), 113, 11.4, 116 Ruderman, M. A., 51(77), 52, 113

319

AUTHOB INDEX

Rundle, R. E., 190,187 Russell, A. S., 64(113), 114 Rymer, T. B., 267(26), 268, 309 Ryvkin, S. M., 245, 864

s Saha, A. K., 32, 111 Saika, A., 67(117), 73(121), 114 Sandler, Y . L., 307, 318 Sandomirsky, V . B., 227, 234, 241(47), 247(92), 249(95), 251, 863, 864

Sands, R. H., 96, 116 Sandstrom, A. E., 150, 187 Sarles, L. R., 42(54), 113 Sazonova, P. S., 222(36), 236(36), 863 Schaap, L., 124, 127(23,24), 128(23,24), 131, 133, 135, 136, 139(24), 140(24), 147, 148 Schlosser, E. G., 222, 224(34), 868 Schneider, F., 140(46), 148 Schneider, W . G., 299(161,162), 312 Schramm, R. M., 127(22), 130, 147 Schreiber, H . P., 266(14,20,21), 267(21), 282(99), 308, 309, 311 Schroyer, F. K., 32(14), l l d Schuster, N . A., 47(65), 113 Schwab, G. M., 222, 240(71), 245(88), 869, 864 Schwinger, J., 37(44), 118 Sederholm, C. H., 296(157), 318 Sepal, B., 32, 118 Sellert, H. G., 129, 148 Selwood, P. W., 32, 33, 50(72), 99, 106, 118, 113, 116, 116, 285(119), 311 Semenov, N . N., 215(27), 868 Sessions, R., 271(62), 274(62), 310 Shaler, A. J., 267, 309 Shatenstein, A. I., 118, 119(3), 147 Shaw, C. H., 151(7), 187 Sheppard, N., 285, 286, 287(133), 288 (1331, 289(133), 291(149), 292(133, 149), 302, 305(127), 311, 318 Shockley, W., 3, 30 Shoolery, J . N., 32, 111 Shortley, G. H., 95(161), 116 Shulman, R. G., 52(80), 113 Shuttleworth, R., 266, 268, 274, 308, 320 Sidorov, A. N., 290(146), 292, 297(146), 301, 302, 303, 318 Sing, K. S. W., 289, 290, 3ld

Singer, L. S., 107(184), 109(184), 116 Sinha, R. P., 271, 274(61), 310 Skinner, 11. W . B., 29(16), 30 Slack, N., 12(12), 30 Slater, J. C., 2(3), 6, 10, 30, 205, 869 Slichter, C. P., 42(50), 67(117), 82, 113, 114, 116

Smaller, B., 34(40), 118 Smentowski, F . J., 118, 147 Smith, R. N., 269, 309 Smith, W. H., 107(184), 109(184), 116 Smith, W . V., 280(91,92), 310 Snelgrove, J . A., 285(113,114), 311 Spooner, R. B., 32(14), 118 Sogo, P. B., 51(76), 113 Sorokin, P. P., 52(79), 113 Staude, H., 254, 864 Sternheimer, R. M., 56(91), 11.4 Stepko, I. I., 234(51,55), 863 Stevens, K . W . H., 33(20), 34(23), 77 (126), 84(126), 90, 91(126), 112, 116

Stiles, M., 129(38), 148 Stoehr, C., 140(50), 148 Stone, F. S., 27(15), 30, 234(49), 963 Strandberg, M. W. P., 74(124), 90(148), 92, 103, 114, 116

Streitwieser, A., Jr., 127, 148 Sypry, W . J., 107(184), 109(184), 116

T Takaishi, T., 222, ,968 Tamm, I. E., 3, 30, 229(43), 863 Tanbadel, H., 144(54), 148 Tapely, J . G., 106(178,181), 107(181), 108(181), 116

Taylor, E. H., 34(39), 11b Taylor, H . A., 216, 868 Taylor, H . S., 269(40), 309 Teller, E., 269(63), 310 Terenin, A. N., 214(76,81), ,964 Thorn, H . G., 110(187), 116 Thomas, J . T., 59(102), 114 Thon, N., 216, 868 Tillieu, J., 53, 113 Tinkham, M., 34(24), l l d Tomboulian, D. H., 150, 187 Tomita, K., 42(52), 113 Tompkins, F. C., 270, 309 Torrey, H. C., 32, 44(66), 59(102), 111, 113, 114

320

AUTHOR INDEX

Weias, P. R., 91, 93(157), 104(157), 116 Weisz, P.B., 214, 262 Weller, S. W., 100, 116, 236, 237(66), 863 Wender, I., 118(4), 119(4), 121(4), 124 (41,147 Wertz, J. E.,32, 34(27), 111, 112, 271(50), 309 Wigner, E.,85(143), 116 Wiig, E. O.,271, 277(65), 284(110), 310, 311 Winslow, F. H.,106(178), 116 U Winter, J. M.,83(135), 116 Woessner, D.E.,44(61), 113 Uebersfeld, J., 106(178), 109, 116 Wolkenstein, Th., 192(1,2,3,4), 195 (5, Uhlenbeck, G. E.,42(51), 44(51), 113 6,8), 196(2,4,5,6,8),198(2,9,10,11), V 200(10,11,12,13),202(15), 204(9,11), 208(3,4,lo), 209(3,4), 210(2), 212(4, van der Hoff, B. M.E.,266(13), 308 24), 215(10, 27), 224(37), 227(10, van der Kint, L.,83(134), 116 41), 228(41), 230(1,37,45),233(24), van Gulick, M . N., 132, 148 234(47), 236(37,65), 241(1,6,37,47, Van Nordstrand, R. A., 64(114), 114, 65), 242(75), 245(41), 247(92), 255 150(1), 187 (1051,259(2,107),262, 963, 264 Van Vleck, J. H., 50, 91,93(73), 113(73), Wunderlich, D., 137, 140(47), 141, 148 113 Wyluda, B. J., 52(80), 113 Van Wieringen, J. S.,83(134), 90, 116 van Zeggeren, F., 266(15,16,20,21,22), Y 267(15,21),908, 309 Ysger, W. A., 34(37), 112 Vasil’eva, L. N.,118(3), 119(3), 147 Yasaitis, E. L.,34(40), 112 Verwey, E.J. W., 266, 308 Vesely, J. A., 118(5), 119(5), 122(5), 127 Yates, D. J. C., 269(35), 272(74,75,76, 771, 274(74,83),278, 279(74,75), 280 (191, 128(19), 129(19), 134, 147 (75,76,77,87), 281 (771, 286, 287 Vitovchcnko, V. G.,234(62), 263 (133), 288(133), 289(133), 291(74,75, Volkoff, G.N . , 56(94), 114 76,77,149),292(133,149,152,154),293 Voltz, S. E.,100, 116, 127(21), 128, 147, (152), 294(77,152), 295(152), 296(77, 236, 237(66), 263 152, 160), 297, 298(152), 299(160a, Voyevodsky, V. V., 215(27), 26.2 163), 300(163), 301(163), 302, 303 W la), (152,165~1,304(75,77,152,163, 305(74,77,87), 306(87,168), 310, 312 Wadsworth, M .E.,286(130,131),311 Young, G . J., 269(39), 288(138), 301 Waldman, M.H., 285(116), 311 (1641,309, 31.9 Wang, M.C.,42(51), 44(51), 113 Wangsness, R. I<., 100(171), 104(171), Z 116 Zavoisky, E., 33, 112 Ward, F. K., 129, 148 Zeldes, H., 34(38,39), 112 Ward, I. M., 34(35), 112 Zettlemoyer, A. C., 269(39), 288(138, Watkins, G.D., 47(67), 61,113, ll4 139), 309, 319 Weaver, H. E.,Jr., 32, 34(41), 48(68), Zhabrova, G.M.,240, 241(74), 264 111, 112, 113 Ziegler, K.,129, 148 Weil, J. A,, 106(180), 107(180), 116 Weise, C. H., 266(24,25), 267(24), 274 Zimmerman, H.E.,118, 147 Zimmerman, J. R., 33, 60, 6l(l8), 119, (251,283(24), 309 286(122,123,124), 311 W e h , H.,144(54), 148

Townes, C. H., 53(88), 114 Townsend, J., 106(178), 116 Trapnell, B. M.W., 12(12), 30 Trounson, E.P.,100(171), 104(171), 116 Tsubomura, H.,296(159), 298(159), 312 Tuck, M.,284(109), 311 Turkevich, J., 106, 107(180), 109(183), 110(183), 116 Tycko, D.,56(91), 114 Tykodi, R.J., 284, 311

Subject Index A Absorption edge, X-ray, 149-186 measurement of, 154 Adsorbed phase, nature of, 224 Adsorption and catalytic activity of semiconductors, 241 chemical, 8ee Chemisorption Alkylation, base catalyzed of aromatics, 126, 137-139 of pyridines, 140 potassium catalyzed, 131 rates of sodium catalyzed, 134-136 side chain, of arylalkanes, 128 of aromatics, 137 sodium catalyzed, 128 Alkylpyridine alkylation, base catalyzed, 141 a-Alumina, N M R Bpectra of, 55, 62, 64 y-Alumina, crystallographic structure of,

64 N M R spectra of, 32,62 of fluorine doped, 66 sodium on, a9. catalyst, 119 Anionic chemisorption on semiconductors, 25, 29 Antibonding states, 12 Arylalkane alkylation, base catalyzed, 126 Atomic motion in solids, 57

B B,, catalyst, absorption edge spectra of, 180 Bond, homopolar, 19 metallic like, 22 Bonding states, 12 Bonds, strong and weak in chemisorption, 193 with ionic character, 21 Benzene alkylation, base catalyzed, 140 Bloch equations, 38 321

Butene isomerization, base catalyzed, 120

C Carbanion reactions, 119-145 Carbon dioxide, chemisorption of, 202 monoxide, mechanism of oxidation of, n2 porous, 106 Catalysis by semiconductors, 249 promoters and poisons in, 235, 238 Catalyst, free valencies of, 198 Catalysts, basic, 119-145 Catalytic activity of semiconductors, 215, 241 and Fermi level, 224 Cationic chemisorption on semiconductors, 28 Chemical shifta in NMR, 52 Chemisorption, anionic, 25, 29 bonds, 191 cationic, 28 equilibrium between ditTerent forms of, 211 on semiconductors, 24-30 one-dimensional model of, 17 particle reactivity in, 200 radical and valence saturated forms, 198 surface bond wave mechanics in, 1-30, 249 three dimensional crystal model of, 10 a-Chromia, catalysis and EPR spectra of, 100 Chromia-alumina, EPR studies of, 99 Chromia catalysts, X-ray study of, 182 Chromium compounds, spectra of, 168175 Cobalt catalysts, X-ray studies of, 182 Cobalt compounds, spectra of, 163-168 Cobalt-molybedium-alumina catalysts, 183

322

SUBJECT INDEX

Copper oxides, chemisorption of 0,on, 197 free valencies of, 199 Correlation time, 42, 61 Crystal, three-dimensional, 10 Crystalline electric fields, 83 level transitions, 161 Cyclohexene alkylation, base catalyzed, 143 NMR spectra of, 69 Cyclohexadiene dealkylation, base catalyzed, 126 Cyclooctadiene dehydrogenation, base catalyzed, la pCymene alkylation, base catalyzed, 134

D Dealkylation, base catalyzed, 125 Dzraction interpretation of absorption edge spectra, 162 Diene synthesis, mechanism of, 217 E Electronic structure of free surfaces, 3 Electron paramagnetic resonance (EPR), 76-111 applications of, 93 experimental methods in, 78 influence of atomic environment on, 83 line widths and shapes in, 78 principals and methods, 76 Electron-nuclear double resonance (ENDOR), 83 EPR-see Electron paramagnetic resonance Ethyl alcohol, mechanism of dehydrogenation and dehydration of, 219 Ethylene hydrogenation, mechanism of, 216 Exchange effects, 91 hydrogen-deuterium, 110

F F e d level, dependence of reaction rate on, 221 role in catalytic activity of semiconductor, 224 Fine structure origin, 89

G g-Factors, 89 Geminsl alkylcyclohexadiene dealkylation, 126 Glaas, porous, in physical adsorption, 275282

H Hexene isomerization, base catalyzed, 120 Hydrogen adsorption on ionic crystal, 187 bonding in adsorption, 294 -deuterium exchange, 110 transfer, base catalyzed, 126

I Illumination, effect on semiconductors, 241 Ionic crystals, 6 Ions adsorbed on solids, magnetic resonance in, 98 Indan formation, 132 Instrumentation, EPR, 78 NMR, 46 X-ray absorption, 164 Interface, changee at solid-gaa, 290 Interaction, between chemisorbed atoms, 13 nuclei, MM7 in semiconductors, 224 magnetic dipoledipole, 60 nuclear electric quadropole, 63 nuclear exchange, 61 Isobutylene, in base catalyzed alkylation, 143 Isomerisation, of diolefins, 122 of cycloolefins, 121 of hydrocarbons, 118 of monoolefins, 118

K Knight-ahift in NMR, 62

1 Larmor precession, 36 d-Limonene, base catalyzed dehydrogenation of, 122

SUBJECT INDEX

323

Line broadening, homogeneous and in- Pentene isomerization, base catalyzed, homogeneous, 43 120 Lithium-cyclohexylamide catalyst, 127 Platinum-charcoal, 111 Lithium-ethylene diamine catalyst, 124 Porphyrins, copper, 97 vanadyl, 93 M Potassium alkoxides, 124 Magnetic resonance in catalytic res k y 1 compounds, 133 search, 31-111 -catalyzed alkylations, 131 Magnetic resonance spectroscopy, 34-76, -graphite as catalyst, 127 see also Nuclear magnetic resonance Propylene dimerization, base catalyzed, and Electron paramagnetic reso143 nance Q Magnetogyric ratio, 34 Magnesium aluminate, 63 Quasi-isolated surfaces, 228 Manganese compound spectra, 156-162 acceptor and donor, 218 pMenthene isomerization, base cataR lyzed, 121 Reactions, base catalyzed, 117-147 a-Methylstyrene, reactions of, 144 of olefins, 141 Mechanism of heterogeneous reactions, Relaxation time, pin-lattice, 38, 44, 72, 215 of promotion and poisoning, 238 78, 107 transverse, 38 Methane adsorbed on titanium dioxide, thermal, 38, 43 33 Microwave cavity for EPR measureS ments, 110 Semiconductors anionic, chemisorption Molecular orbital theory of surface on, 25 bonds, 7-18 catalytic activity of, 215, 235 Molecular motion in solids, 57 cationic, chemisorption on, 28 Motional narrowing, 41 effect of external electric field on, 248 N due to surface charge on, 230 electrical conductivity of, 235 NMR--see Nuclear magnetic resonance electron theory of catalysis on, 189-262 Nuclear magnetic resonance, 32, 34-76 Silica-alumina, NMR studies of, 71, 72 applications of, 57 N M R study of D, and D,O on, 75 experimental methods for, 46 Silica gel, N M R study of, 33, 71, 75 line widths and shapes in, 40 water adsorbed on, 59, 289 principals and methods of, 34-40 Nuclear spin, electron quadrupole inter- Silica surfaces, topography of, 303 Silver bromide doped with Cd”, 57 action, 53 Sodium on activated alumina, 120 0 Sodium catalysta, 118 Overhauser effect, 82 Sodium chloride Octene isomerization, base catalyzed, 120 chemisorption of sodium on, 195 “Oxygen effects” in activated carbons, free valencies of, 199 104,108 N M R spectra of, 57 Spectrographic splitting factor, 76 P Spectrometer, Bloch, 47 Perturbation of adsorbed gases, 284 Pound-Knight, 47 Phenylcyclohexene, dehydrogenation and X-ray adsorption, 164 hydrogen transfer reaction with, 126 Spin-Hamiltonian, 77

324

BWJECT INDEX

Stability of carbanions, 126 Structural defects in solids, 61 Structure, hyperfine, 77, 89 Surfaces, bond types, 19 hydroxyl group^, 290 “Quasi-isolated,” 228 topography, 303

T Term values, 84 Titanium catalysts, 185 Titanium compounds, spectra of, 175-178 Titanium oxide, 33 Toluene alkylation, 128-131 Transitions to bound levels, 150 to crystal levels, 167

2,4,4-Trimethylpentenes ene, 144

from isobutyl-

V Vinplcyclohexene dehydrogenation, base catalyeed, 124

W Work function of a semiconductor, 231

X X-ray K-adsorption edges, 14S187

Z Zinc oxide, chemiaorption of 0, on, 197