Characterization of Porous Solids III: Proceedings of the Iupac Symposium (Studies in Surface Science and Catalysis) (v. 3)

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expression found from the BET theory (with ~ 1 . 5and ) any other similar relationships between these extremes. The actual calculation of the volume adsorbed or desorbed within the pores being filled or emptied over an increment of pressure (and, thus, P/Po) involves several calculations. One needs to account for the difference in the amount of sorption due to thickening or thinning of the exposed surface and one needs to estimate the exposed surface at each step in the sorption processes. 2.2. Estimating the Incremental Surface Area

Accounting for the thickening or thinning of the adsorbed layer involves multiplying the difference in the thickness of the adsorbed layer by an estimate of the exposed surface area over the increment. The accuracy of this calculation depends on the model by which the thickness of the adsorbed layer is calculated and on the subsequent calculations of increases or decreases in the exposed surface. If, for example, the actual differences in the thickness of the adsorbed layer are greater than the model employed, the analyses will interpret this as ad/desorption from pores that do not exist. Thus, if the actual value of n in the exponent employed in the Halsey equation is less than that employed in the calculations, the analyses will estimate that there are pores where the actual phenomenon involved is a thinning of the exposed surface at a rate greater than the model estimates. Another potential inaccuracy comes from the estimation and the changes in the exposed surface over any pressure increment in the sequential calculations. The actual pore volume is estimated based on the volume ad/desorbed related to the Kelvin radius adjusted for the thickness of the adsorbed layer. During adsorption this means that as a pore is filled, its actual volume is larger than the volume adsorbed since the surface is already covered to a specific thickness prior to the adsorption. Similarly, during desorption, the void space is not emptied to the solid surface, but is emptied to leave a coating on the surface that is in equilibrium at the pressure that the void space is emptied. The calculation of the Kelvin Radius (i.e., the "pore" radius), rK, and the thickness of the adsorbed film, t ,are employed in the analyses. Again, this depends on the model by which the pores are represented, e.g., AV = V(rK/q( +t))n and 6s = nAV/rK where n = 1,2,3 for plates, cylinders and spheres respectively. The last calculation to be performed involves keeping track of the total surface area exposed at any point in the calculations. Adsorption and desorption start at the respective extremes: all of the solid surface is exposed when the pores are beginning to be filled during adsorption and essentially, none of the surface is exposed when one commences desorption from P/Po =l. Ideally, the adsorption could start from the calculated BET surface area and the surface attributed to each pore is then subtracted down to -0. Similarly the desorption would accumulate surface area from zero u p to the total surface area; ideally agreeing with the BET surface area. As these calculations rarely agree with the BET surface area and never with each other, these calculations are essentially ignored in our characterization of pore structure. The calculations are performed at pressures above the point where the adsorption and desorption are coincident (where we believe that pores are being emptied or filled) and involve the same total volumes adsorbed or desorbed. However, the calculations of surface area involves division by rp. The rp used in each calculation are based on the relative pressure averaged over the increment of the calculation. Since sorption hysteresis is a universal phenomena for mesoporous materials (although the shapes can vary), the

155

incremental surface areas calculated during desorption will be higher than those calculated during adsorption (at higher P/Po). Thus, the surface areas calculated for desorption will always be larger than those calculated during adsorption. The differences in these two total surface areas is a reflection of the differences in the adsorption and desorption ,i.e., the hysteresis. A method of quantifying this will be discussed below. 3. COMPARISONS BETWEEN SORPTION AND POROSIMETRY

3.1.Network Influences Porosimetry is a sequential process which is subject to substantial network effects that dictate that the measured distributions of pore or constriction dimensions will differ from the actual size distributions. During intrusion the effect of shadowing shifts the measured throat (constriction)size distribution by measuring constrictions at higher pressures (interpreted as smaller) than they would have been measured if the mercury interface had not been held up at smaller constrictions nearer the periphery of the individual particles. To access the pores it is only necessary an the average to enter one and exit another of the constrictions connecting to adjoining pores. Thus, intrusion porosimetry only measures a fraction of 2/VC where VC is the network void connectivity, i.e., the average number of pores connected to a single pore. Those that are measured are the largest constrictions, i.e., the ports of least resistance. The combined result is that a narrower distribution of constrictions is measured than are present in the void network. Desorption is subject to the same network influences as found for intrusion porosimetry. The desorption starts at P/Po 2 1 with the whole void network filled with liquid adsorbent. Desorption only occurs at the liquid vapor interfaces (assuming that cavitation does not occur spontaneously). Due to surface tension at the constrictions these are the equilibrium points during the desorption process. Retraction porosimetry also is subject to network influences that change the measured pore size distribution from the actual. In general, retraction progresses from existing vapor interfaces within the void network filled with mercury. Mercury does not spontaneously retract from a solid surface with which it is in intimate contact. The energy stored in the mercury surface within the pores is released by retraction with the smaller pores (higher surface to volume ratios) having a tendency to retract first. However, they will not retract if an interface does not exist (usually at an adjoining constriction). These combined effects are the equivalent of the shadowing found during intrusion. The result is a shift between the measured dimensions to larger sizes. Retention of mercury is also a consequence of the network influence on the retraction process (in addition to other phenomena such as snap off of the mercury due to instabilities at the constrictions). Mercury cannot be retracted unless a continuum of mercury exists from the exterior bulk to the mercury retained within a pore. If all the pores surrounding a specific pore have retracted before the pressure where a specific pore would retract, then the pore has no pathway by which it can empty. The larger pores, being the last to empty, are the most probable of being isolated in this manner. Thus, some of the larger pores are not measured as they are never emptied during the retraction process. Adsorption, in contrast to retraction porosimetry, is not subject to substantial network influences. This is because at equilibrium the pressure of the adsorbent and the potential for vapor/pore-condensate equilibrium to be achieved is the same

156

throughout the void network. Pores near the exterior of a particle will fill at the same pressure as an identical pore interior to the particle; thus, there is no equivalent for shadowing. Further, there is no equivalent for retention in the adsorption as all pores accessible to the gas phase are filled during the process. Ironically, most automatic instruments employed for pore size characterization employ, as its primary approach, analyses of desorption which it calls a “pore size” distribution. Analyses of adsorption are awkward at best if, indeed, the instrument even has this option. Yet, only adsorption is characteristic of the pores and is the least subject to network influences on the measured versus the actual distribution of void dimensions.

Intrusion & Desorption

Adsorption & Retraction

[Adsorption]’ [Intrusion & Desorption]

[Retraction]-

shodowina

Dimensions ->increasing Constrictions [throats] Openings [Pores] Figure 2 Schematic representation of the network influences on differences between the actual distribution of dimensions and those that are measured. The characterization of the constrictions by intrusion and desorption on the left is contrasted with the distribution of the larger pores measured by adsorption and retraction on the right. The network influences on the sorption and porosimetric processes are schematically shown in Figure 2. It is readily seen that in all of the processes, except for adsorption, the dimensions that are measured are larger than the actual distribution. Intrusion and desorption give similar shifts; whereas, only retraction porosimetry is subject to substantial network influences for pore dimension characterization. If substantial mercury retention occurs (e.g., >25%of the intruded volume retained), then the other reasons for irreversibility in the retraction of mercury need to be considered. These include: snap-off due to large differences between opening and constriction dimensions; irreversible (and reversible) changes in the solid network due to the measurement process (compression or collapse of the solid); reaction between mercury and the surface of the solid (forming amalgams, for example). 3.2. Inferring Pore Shapes from the Analyses

Porosimetry and sorption are processes whose interpretation presumes thermodynamic equilibrium between two phases. During the analyses of sorption, it is necessary to account for the equilibrium thickening or thinning of the surface exposed to the sorbing species. This calculation of the volume of gas associated with the

157

thickening or thinning phenomena are subtracted from the incremental volumes adsorbed or desorbed to estimate the sorption within the porous network over any increment in pressure. One advantage of the network influences on the different processes is that the Rr/Ri vs. @ plot reflects these influences more than comparisons between adsorption and desorption. Thus, the differences between the morphology at the exterior of a particle in contrast with its interior are more easily visualized in this analysis of porosimetry than it would for sorption analyses. We have shown that plots of the ratios of the interpreted radii of intrusion to that measured during retraction, Rr/Ri, versus the fraction of the pore space filled, 0,were characteristic of the void (pore/throat) shapes[4]. The radius ratio's were easily calculated from the data as the radius ratio's are equivalent to the inverse ratio's of the pressures measured at constant volume. This assumes that the Washburn equation may be employed to calculate relative dimensions as P/r = constant. Thus, it was easy to transform the data directly to a Rr/Ri vs. Cg plot since Rr/Ri = Pi/Pr at constant volume. It would be attractive to perform a similar manipulation of the adsorption/desorption data. There are differences between the various plots but that these differences are more subtle than those found for similar analyses of porosimetric data. First, the relationship between the radii gives Rr/Ri = Pi/Pr for porosimitry whereas the assumed relationship between dimensions and pressure for sorption gives, as in the Kelvin relationship for the radius RK, RK*ln(Po/P) = constant. The equivalent ratio of the radii of adsorption to that of desorption is Rads/Rdes = (I-lnPdes)/(1l e a d s ) for pressures in atmospheres at Po=l. This sensitivity of the radius ratios to the pressure data for sorption are less compared to the simple inverse ratios of pressure as found for porosimetry. There are several other reasons for these differences between calculations based on the data for sorption and the data for porosimetry due to differences in the network influences on the specific processes ( see Figure 2). 4. MODIFIED ANALYSES

There are several reasons why the relationship between P/Po and the thickness of the adsorbed layer will differ depending on the specific real surface as well as on the sorbate. First, the relationship between pressure and the thickening of the adsorbed layer depends on the differences in energetics of adsorption of sequential layers. Large differences between sequential layers will decrease the potential for forming multilayers and, thus, would increase the value of r in equation 1, the general Halsey equation, above. Smaller differences will decrease the value of r in equation 1.This tendency is also reflected in the derivation of the BET expression for multilayer adsorption where differences in the energy of adsorption are reflected in the constant "C". Although it is readily recognized that the value of C can vary between solids by over an order of magnitude, only one value of r is employed in conventional unulyses of pore size distributions. Another reason why r in equation 1 will vary for different solids is that surface roughness can vary between solid surfaces. If the surface is atomically rough, the volume of gas adsorbed in sequential layers will decrease as the sorbate layers present smoother layers to subsequent adsorbates. Surfaces that are more rough on an atomic scale will decrease in volume for the adsorption of subsequent layers. This would tend to decrease the value of r estimated from fitting a general Halsey equation. If, however,

158

the surface is so rough that subsequent layers fill micropores from extensive surface roughness, more adsorption will take place than that estimated assuming an atomically flat surface. Microporosity due to extensive surface roughness will decrease the value of r in equation 1. Thus, physical adsorption can result in changes in the relationship between the relative pressure and volume adsorbed without condensation or desorption within the larger pores. The calculation of pore size distribution depends on the nature of these assumed relationships. It should be noted that whereas surface roughness has been related to recent fractal analyses of adsorption, the pore network structure of real catalysts is not amenable to fractal analyses. Indeed, a fractal pore structure will not exhibit hysteresis in adsorption of porosimetry and represent solids that are either too porous (void fractions >90%) or to dense (void fractions 4 0 % )to represent real catalysts [81. The following facts will be considered in a modified analysis of sorption data: a) All automated adsorption equipment collects the data on adsorption between 0.2

159

adsorbed and the slope of the model employed to estimate the thickening of the adsorbed layer (adjusted for the exposed surface at that point). If the actual thickening of the adsorption is less than the model predicts (a lower slope of dV/aP), pores will be calculated where they do not exist. If the fitting of the general Halsey equation to the actual data yields a lower value of r in equation 1, then use of the fit model for the adsorption will calculate fewer pores than if the conventional Halsey equation were employed. Since the surface attributed to the incremental volume adsorbed involves division of the volume by the radius averaged over the increment in P/Po, this error is magnified in the distribution based on area for the smaller pores. This imposes a magnification of the smaller pores in the pore size distribution plot or even calculates small pores that do not exist.

PIP0 = 1

r -> Pore Size Distribution Figure 3: Schematic representation of the differences in the calculations of pore size distribution (e.g., during adsorption) based either on a "standard" Halsey or a more general Halsey equation based on the thickening of the adsorbed layer for P/Po between 0.2 and 0.5 4.2. Inferring Pore Shapes from Sorption A simple method is available to determine the relationship between the radii that

govern the adsorption (or retraction) and the radii that govern the desorption (or intrusion) processes. The total volumes involved in reversible adsorption-Bdesorption between any two pressures where the adsorption and desorption curves are coincident are the same. Thus the volume adsorbed or desorbed from the point where adsorption and desorption diverge (typically P/Po = 0.5 - 0.7) up to saturation are the same. The

160 total surface area at any point in the adsorption or desorption process is calculated. This is used to account for the incremental volume adsorbed or desorbed due to thickening or thinning of the sorption on the surface exposed to the gas phase. The calculation involves dividing the incremental volume attributed to the pores (openings) or throats (constrictions) by their radii. Thus, the calculation of the incremental surface areas for the adsorption will be smaller than that calculated over the same increment of volume during desorption since the radii during adsorption are larger (filled at higher pressure) than the radii calculated during desorption. These aspects of the differences between the calculation of cumulative surface areas for adsorption compared to desorption are related to the differences in the radii of the pores filled during adsorption to the radii of the constrictions measured during desorption. The simplest approximation is just to divide the calculated total surface areas and to realize that this is an approximation of the dimension ratios. As this ratio of areas decreases, it reflects a smoothng of the pore walls as in the pore space between plates-like subparticles. As the ratio increases, the morphology changes from spherelike agglomerates to rod- and needle-like agglomerates. This simple estimation will enable one to quantify the shift between adsorption and desorption. It further employs analyses not heretofore utilized in pore structure analyses. Normally, these estimations of surface area are neglected; probably because these calculations differ from each other and from the calculations of surface area based on the BET analyses. A more precise calculation of the ratios of the sizes of the constriction to those of the openings is discussed below. Note that changing the sorption analyses, as above, to give a more realistic estimation of the thickening and thinning of the adsorbed layer brings the surface area calculated during adsorption analysis much closer to the BET surface area (typically k 10%)unless there is microporosity (adsorption within the pores below P/Po= 0.2).

Upper Part of Sorption Isotherm PlPo 0.5

P/Po = 1

-

&a

dS= dV(r)/rO.5) dS= 2dV(r)/(rOS*rp/rt)

CdS desorption > CdSadsorption CdS desorption CdS adsorption is related to Pore Shape Figure 4: Schematic representation of the differences between the calculations of the cumulative surface areas during the adsorption and desorption processes. The incremental surface areas (which involves division by the respective radii) for desorption will be greater than those calculated for adsorption.

161 4.3. Iterating the Pore/Throat Ratio

In general, the difference between the incremental surface areas over the same incremental volumes will depend on the ratio's of the radii of adsorption to desorption. This suggests two methods to estimate this parameter which is characteristic of the porous network. One can estimate the ratio of the pore to the constriction dimensions from the ratio's of the total surface areas calculated during the analyses of the adsorption and desorption processes, as above. This does not account for the dependence of the incremental volumes on the ratio's of the actual pore (void space) to that which is being emptied or filled. This calculation involves calculations of the incremental volume of the pores being emptied or filled and calculations of the surface associated with an incremental volume of sorption. One can use the ratio of the dimensions of the pores to the throats as a variable throughout the calculation processes. This variable is then iterated to minimize the difference between the surface area calculated during the analysis of the adsorption and desorption processes. The calculation of the pore dimensions during adsorption and desorption involve a sequence of calculations. As pointed out above, the adsorption is the most accurate (if a proper relationship between the thickness of the adsorbed layer and the pressure are employed). If one assumes that the radii characterized during desorption (the constrictions) have similar ratios to the pore radii being emptied, one can use this ratio, RR, as a variable within the sequential calculation for pore size distribution. This ratio is varied until the total surface area calculated during desorption is the same as that calculated during adsorption. There are two places where this ratio, RR, needs to be incorporated into the sequential calculations. First, the actual pore dimensions are employed in the calculation of the actual pore volume compared to the volume desorbed (after subtraction of the volume due to the thinning of the adsorbed layer). The conventional calculation involves taking the radii of the pores to the radii of the Kelvin raised to the first (for plates), second (for cylinders) or third (for spherical surfaces) power. If we generalize the power as m:

Second, the calculation of incremental surface area from the incremental volume adsorbed involves division by rp. The modified analyses will divide by rp * RR. Since the overall calculation incorporates the sum of these calculated incremental surface areas in the calculation of the volume associated with the thinning of the adsorbed layer on the exposed surface and the pore volume calculations need to be adjusted for RR (as above), the result of these proposed changes in the analyses is not more complex than a simple division of the unmodified cumulative surface area calculations. The results of these iteration are seemingly subtle changes in the resultant calculated throat size distributions.

162 5. CONCLUSIONS

The methods by which we analyze adsorption and desorption show that the use of conventional analysis (employing a fixed Halsey equation) is unrealistic. It can result in calculating pores that do not exist, usually the smallest pores. There is a correspondence between adsorption and retraction and between desorption and intrusion (which represent the network of constrictions in the void network). Adsorption is the most realistic reflection of the pore network. However, the analysis of adsorption should be modified to employ a realistic thickening of the adsorbed layer. It seems apparent from these analyses that the universally accepted version of the Halsey equation should not be used for all samples. Indeed, the value of the exponent that relates the thickness of the adsorbed layer to the relative pressure can vary just as the "C" constant in the BET equation. Further, it is quite simple to calculate the experimental values of the constants in the original Halsey equation based on the data collected between relative pressures where multilayer adsorption commences (P/Po - 0.2) up to the relative pressures above which hysteresis is evident, i.e., over the region where simple thickening of the adsorbed layer is presumed. The use of these experimental constants in a modified Halsey equation gives a more realistic representation of the calculated pore size distribution. Moreover, the total surface area which is calculated during the calculations of the pore size distribution agrees more with the BET area (estimated from adsorption to P/Po = 0.3) than that calculated with the currently accepted version of the Halsey equation. Thus, the modified analysis is more consistent with other analyses of the morphology of high surface area, i.e., porous solids. Further, it is possible to infer the shapes of the pores from the ratios of the dimensions of the constrictions to those of the openings. Since these are measured by the respective techniques (adsorption and retraction or desorption and intrusion), w e have already shown how this can be done for porosimetry[3,4]. These network s h a p e influences are most easily detected in the inmemental and total surface areas calculated during the analyses of adsorption and desorption. The ratios of the calculated areas depends on the respective (pore or throat) dimensions. Thus, the ratios of the total areas calculated during adsorption or desorption is a rough indication of the ratios of the dimensions of the pores and throats. More precisely, the ratio (rpore/rthroat) can be directly incorporated as an iterative variable in the calculations. It can then be iterated until the surface areas calculated during adsorption and desorption agree. The resultant radius ratio is then characteristic if the pore shapes. In summary, four modifications to conventional analyses are suggested to give a more realistic calculation of pore network structure and dimensions. 1) Data should be collected and analyzed from adsorption (preferred) as well as from desorption and/or from retraction as well as from. intrusion. 2) A more realistic thickening of the adsorbed layer can be estimated for mesoporous solids by fitting a Halsey equation to the sorption data between P/Po = 0.2 up to the point where hysteresis is evident. This is then used in the subsequent calculations. 3) Calculations from the adsorption or desorption analyses can be adjusted to give equal total areas. This adjustment gives insight into the shapes of the pores. These suggestions are easy to implement from the volume adsorbed (or intruded) versus pressure data. This flexibility is not yet available on automated sorption or porosimetric instruments. These modifications will provide considerably more insight

163

into the actual pore dimensions and the nature of the pore network. Further, these analyses may be iterated, based on insight into the shapes of the pores (as in 3) and the nature of the interaction between adsorbent and adsorbate (as in 21, to more realistically calculate pore and constriction dimension distributions. 6. REFERENCES 1. W. Conner. J. Cevallos-Candau, S. Mendioroz, E. Weist, A. Cortez and J. Pajares, 151 . Langmuir,(l986) 2. W. C. Conner, A. Lane, K. Ng. and M. Goldblatt, J. Catalysis, 336, (1983); and A. Lane and W. C. Conner " J. Catalysis,-98 217, (1984). 3. W. Conner, K. Coyne, J. Neil, C. Blanco, S. Mendaroz and J. Pajares," Stud. Surf. Sci. Catal., v.39(Charact. Porous Solids), 273-81, Unger et al., eds., Elsevier, Pbs., 27381 (1987) 4. W. Conner, J. Neil, C. Blanco and J . Pajares , J. Catalysis, 106,202 (1987) 5. Halsey, G. ,J. Chem. Physics, 16,931 (1948) 6. Pierce, C., J. Chem. Physics, 63,1076 (1959) 7. Gregg, S., and Sing, K., Adsorption Surface Area and Porosity, Academic' Press (London) pbs. (1982) 8. Bennett, C.O., and W. C. Conner, in press J. Chemical SOC.,Faraday Trans, and submitted to J. Catalysis.

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J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Charactcrizaiion of Porous Solids 111 Studies in Surface Scicnce and Catalysis, Vol. 87 0 1994 Elsevicr Science B.V. All rights rcscrved.

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COMMON ABERRATIONS IN AD-DESORPTION: e.g . POROSITY OF DEACTIVATED CATALYSTS S.V. Christensen', J. Bartholdy', P.L. Hansen', W.C. Conner', J. Fraissard3, J.L. Bonardet3 and M. Ferrero3

' Haldor Topsrae a/s, Research Dept., Lyngby, Denmark Dept. Chem. Eng., Univ. Massachussetts, Amherst, MA. USA Univ. Pierre et Marie Curie, Paris, France 1. ABSTRACT During the course of investigating the morphology of deactivated catalysts, we encountered an unusual phenomenon. The adsorption and desorption branches of the nitrogen isotherms at 77K showed a high degree of low pressure hysteresis. Possible explanations for this phenomenon could be: i) chemical interactions, i.e. strong bonding of nitrogen to the surface ii) internal diffusion being a rate-limiting step['~']and iii) swelling of the adsorbent during adsorption['*']. For the type of samples studied here, especially the two first items were believed to include the potential explanation of the phenomenon. Results from I5N NMR experiments ruled out the first explanation. Also it was seen that low pressure hysteresis was observed with other gasses than N,, too. Adsorption experiments with N, at 77K and 85K (at P/Po=O. I) revealed that the second explanation, i.e. that adsorption is limited by internal diffusion, is the most likely of these explanations. 2. INTRODUCTION Catalysts used for upgrading of residual oils are often heavily contaminated both by the deposition of coke and metals. The deposition of contaminants in the pore system deactivates the catalysts, both by coverage of the active phase, but also by restricting the access of the reactants to the pore system. A thorough description of the pore system of the fresh and deactivated catalyst is important in order to have the best utilization of a given catalyst. In the present study of a deactivated RDS catalyst, the pore system was characterized using e.g. N, ad-desorption. The study revealed that the heavily contaminated catalyst obtained from the top of the reactor had a characteristic non closing ad-desorption isotherm. 3. EXPERIMENTAL 3.1 Sample deactivation and preparation The catalyst used in this study is a commercial hydroprocessing catalyst, TK-771 10% Mo, 3%Ni, 2% P, Surface Area 200 m2/g and avg. pore radius 50 A. TK 771 is an active HDS catalyst with a low tolerance for accumulation of metals. TK 771 is therefore under normal

166 industrial applications protected by a layer of an active HDM catalyst. However, in the present study no protection was used in order to accelerate the deactivation due to metal deposition. The TK 771 catalyst used in the present study had been in service for 3000 hours in an pilot plant experiment on a 90% HDS of Kuwait ATB. Kuwait ATB has 4.3 % Sulfur, 10.5% CCR and 82 ppm Ni V.

+

Samples of spent TK 771 were obtained both from the top and the bottom of the reactor. Before characterizing the spent catalyst, the samples were sohxlet extracted for 16 hours using Xylene and the samples were thereafter dried at 100°C under N, blanket. 3.2 Ad-desorption experiments A Quantachrome Autosorb-6 instrument and a static volumetric apparatus equiped with a Texas Instruments pressure gauge were used for these experiments. N, measurements were conducted at 77K, Ar at S5K and neopentane at 273 K. In one of the experiments made in the automatic instrument, desorption was run to as low pressure as possible. As it is seen in Fig. 1, the adsorption and desorption isotherms are parallel down to P/Po=O.Ol.

160 140 120

0 0 W

100 80

60 40

>

20

0 0.0

0.1

0.2

0.3 0.4

0.5 0.6

0.7 0.8 0.9

1.0

P/Po Figure 1. Ad-desorption isotherms for deactivated catalyst Two batches of sample made from the same catalyst and treated in the same way in the pilot plant (called SVC 55a and SVC 55c), were used for ad-desorption experiments. As for SVC 55a, ad-desorption measurements were made on sample degassed at 100' C and 300' C. Weight loss was 2-3% and 20% respectively. Chemical analysis revealed that, after evacuation at 300°C much of the sulphur deposited on the sample as metalsulphides was lost. As this probably would result in a change in pore structure, it was decided to select a degassing temperature of 100' C instead. Also, ad-desorption experiments on sample degassed at 300°C gave isotherms closing at P/Po < 0.4 for N,, Ar and neopentane indicating that the original pore structure had changed.

167

During evacuation at lOO'C, it was seen that it took long time to achieve a reasonable vacuum. A TGA experiment demonstrated that samples had not been completely liberated from the Xylene used for the extraction procedure, by the drying procedure mentioned above. In fact, additional drying in a N, flow at 100°C for more than 20 hrs (TGA) resulted in the same weightloss at that obtained after evacuation at the same temperature for 1 h.

-

3.3 NMR experiments These experiments were performed at the Univ. Pierre et Marie Curie, Paris, France. Samples were loaded into 5mm NMR tubes and evacuated to Torr at 500"C. The samples were then cooled to 77K in vacuum in a liquid nitrogen bath. 99%"N nitrogen gas was then adsorbed to an equilibrium pressure of 300 Torr (P/Po=0.4) and 530 Torr (P/Po=0.7). One sample was prepared during adsorption and the other during desorption at the higher pressure. These ampules were then pulled off with a torch and remained immersed in liquid nitrogen until they were introduced into the NMR probe of a Brucker 400 CXP spectrometer fitted with the coils appropriate for "N analyses. The samples were subsequently rapidly transferred into the NMR probe which had been precooled to -77K. In this manner the sample temperature was maintained near 77K from the time of adsorption until the actual NMR measurement, 3.4 Chemical and Microprobe analysis Chemical analysis was made in order to determine the concentration of C, V and Ni deposited from the residual oil. Concentration profiles of V were determined by microprobe analysis. 3.5 Scanning Electron Microscopy and Energy Dispersive Spectrometry SEM pictures of fractured cross-sections of extrudates were made to study and compare the structure near the exterior surface and in the interior. Information on the concentration of deposited materials was simultaneously obtained by EDS. 4. RESULTS Table 1 gives the concentration of deposited materials (mainly Carbon, Vanadium and Nickel) of the spent catalyst samples from the top and bottom of the reactor. In table 1 the distribution parameter for the deposited V, Qv, is also given (obtained from microprobe analysis; a concentration profile across an extrudate is shown in Fig. 2 ) .

TOP

Bottom

c , wt%

10.4

13

v, wt%

8.4

1.3

Ni, wt% (deposited)

1.8

0.4

0.17 Q" 0.20 The Q, values given in the tab.e are low, indicating that the major part of the V is deposited

168

9

3

a

8

- .

.

,

.

,

.

,

.

,

,

,

.

,

,

,

,

. . . . . . . . . . : . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . .

7 - ................................................ 6.

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

:..................

5 p...................................................

> -400

-300

-200

-100

0

100

Radial Distance,

200

300

400

m

Figure 2. Distribution of deposited Vanadium through catalyst pellet Ad-desorption measurements were conducted with N, at 77K on SVC 55a as whole extrudates and as crushed material. The isotherms for the whole extrudates did not close, whereas the isotherms for the crushed extrudates did, suggesting that the phenomenon of non-closing isotherms at low pressures could be due to: i) chemical interactions that results in strong bonding of nitrogen to the surface and which is not observed with crushed sample as chemical compounds are decomposed by oxidation during the crushing procedure or ii) transport limitations in constricted micropores of the catalyst due to materials deposited in high concentrations near the exterior surface of the extrudates. The former hypothesis was tested by making ad-desorption with Ar (no dipole effects) and the latter was tested by making neopentane ad-desorption (size of molecule). Both tests resulted in non-coinciding isotherms (Fig. 3) and they did therefore not seem to confirm either of these theories.

0 0

W

> P/Po Figure 3. Ad-desorption isotherms: 0 N2; 0 Ar; A neopentane

169 The 15N NMR spectra for nitrogen adsorbed at P/Po=0.4 or 0.7 or being desorbed to P/Po=0.4 are shown in Fig. 4. The narrow identical spectra for each sample indicate that a liquid-like nitrogen is present in identical environments under all of these conditions. The low pressure hysteresis phenomenon is therefore not due to an adsorbate phase transition, such as that which occurs in zeolites.

T=77K PIP0=0.7

T=77K P/P0=0.4 * -

_c

50

40

30

20

10

0

-10

-20

-30

-40

-50

kHz Figure 4. 15N NMR spectra As the results from chemical and microprobe analyses mentioned above seemed to suggest that rather high amounts of deposited materials could have reduced the porosity drastically near the exterior surface of extrudates, SEM pictures of fractured cross-sections of extrudates were made in order to study the presence of such a dense shell. Fig 5 a) shows a shell of about 25 prn thickness. EDS confirms a high concentration of V and S in the shell. In fact, there is enough V-suiphide to fill the pore volume. A picture of a fresh catalyst reference is shown in Fig. 5 b) (same scale as in Fig. 5 a)). No shell can be seen in this sample.

Figure 5. SEM micrographs of a) deactivated catalyst and b) fresh catalyst; - 5 Pm

170

N, ad-desorption experiments on whole extrudates and extrudates cut into two or more pieces showed clearly, that making the interior accessible for molecules through new exterior surfaces resulted in a higher uptake and in that N, was adsorbed much faster (Fig. 6).

loo 90 n

0)

2

80

\

a I-

70

rn

60

0 0 W

50

cn

40

U

30

>

20

a

10

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.9

1.0

P/Po Figure 6. Ad-desorption isotherms for N, at 77 K: 0 whole extrudates; 0 cut extrudates Experiments were also made in order to study the effect of the time allowed for the molecules to enter into the interior of the extrudates on the low pressure hysteresis phenomenon. The results of these measurements for the whole extrudates are shown in Fig. 7. The "equilibration time" is defined as the period of time where pressure does not change more than 0.6 Torr (definition used in the Quantachrome Autosorb-6 apparatus).

40

30

0 0

W

cn

20

U

a

>

10

0

0.0

0.1

0.2

0.3

0.4 0.5

0.6

0.7

0.8

0.9

1.0

P/Po Figure 7. Ad-desorption isotherms for N, at 77 K: 0 equil. time 2 min.; 0 equil. time 4 min.

171 For the whole extrudates (Fig. 7) the sample adsorbs some more N, at low pressures and some more is condensed at higher pressures, when increasing the time. However, the degree of non-coincidence does not decrease, when increasing the equilibration time with a factor of two. This is probably due to the fact that equilibrium has not been established and that the rate of adsorption is therefore higher than the rate of desorption during the recording of the desorption isotherm. The result of this non-equilibrium condition during the entire measurement is that the low pressure part of the adsorption isotherm is shifted downwards and the desorption isotherm is shifted upwards. The downwards shift results in BET areas and C-constants being very low. For the cut sample the isotherms are completely identical, which is not surprising as there is no low pressure hysteresis. In order to determine how long time it takes to come to true equilibrium, an experiment was made with adsorption of N, at P/Po=O. 1 (77K) in the manually operated apparatus, where pressure as function of time was recorded. This experiment revealed that the 5 - 10 minutes per point used by the automatic instrument, was far from enough to come to equilibrium (Fig. 8). , . , . , .

6 1 . n

10.10

5

cs,

\

E 4 cn 0

3

0 W

0.09

0 &

Q

g 2 a >

1

0

0

1

2

3

4

5

6

7

6

0.06

time (hrs) Figure 8. Adsorption of N, at 77 K and P/Po=O. 1 as function of time In fact the curve shows that it requires more than 7 hours and the amount adsorbed after this period of time is still less than for the cut extrudates (Fig. 6). The same was seen for Ar adsorption at 85K. A similar experiment made with N, at 85K, also recording pressure as function of time, resulted in that, after only 5 minutes the same amount of N, was adsorbed as after 7 hours at 77K (i.e. N, was adsorbed 80 times faster at 85K than at 77K !). As it is seen when comparing the amounts adsorbed after 7 hours at both temperatures (Fig. 9), more N, is adsorbed at 85K than at 77K, suggesting that adsorption is an activated process, i.e. internal diffusion in the constricted micropores occurs faster at higher temperatures.

-

172

n

0)

40

h I-

c/) 0 0 W

30

>

10

20

0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

P/Po Figure 9. Ad-desorption of N,: 0 ad-desorption at 77 K (5-10 min. per point); 0 adsorption at 77 K for 7 hours; A adsorption at 85 K for 7 hours

5. CONCLUSION Of the three possible explanations for the non-coincidence phenomenon mentioned above, the one concerning diffusion limitations and thereby lack of equilibrium during recording of ad/desorption isotherms, now seems to be the most likely. This phenomenon is apparently connected with the deposition of Vanadium, which leads to constriction of micropores, especially near the exterior surface of the extrudates. REFERENCES 1. S.J. Gregg, K.S.W. Sing, 'Adsorption, Surface Area and Porosity', 2nd ed., Academic Press, 1982, (p. 156 Fig. 3.23 and pp. 228-239) 2. S.J. Gregg, 'The Surface Chemistry of Solids', 2nd ed. reprint, Chapman & Hall Ltd, 1965, (p. 79)

J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids 111 Studies in Surface Science and Caklysis, Vol. 87 1994 Elsevier Science B.V.

173

Porous structure and adsorption properties of macroreticular organic polymers K. H. Radek@, D.Asterb, B. Rohl-Kuhnc, H. Schroderd, E. Thieded and E. We@ aINTUSInstitut fiir Technologie und Umweltschutz, Aninstitut der Technischen Fachhochschulen Berlin, Geb. 1.7

bUTE-UmwelttechnologischesEntwicklungslabor,Geb. 1.1 1 cBAM-Bundesanstalt fiir Materialforschungund -priihg, Geb. 8.15 dZentrum iiir Heterogene Katalyse in der KAI e.V., Geb. 1.I

Address for all Institutions: Rudower Chaussee 5, D-12484Berlin, Germany SUMMARY Structural and adsorptive properties of porous organic adsorption polymers (Amberlite XAD 4,Wofatites Y 77 = EP 63 and EP 61) are compared with those obtained fiom active carbon Hydraffin 71.From gas adsorption of benzene and n-hexane at 293 K and nitrogen at 77 K we found the highest micropore volume for Y 77 and large mesopore volumes for XAD 4 and EP 61.The characteristic adsorption energies of organic polymers are smaller than that of the active carbon. The adsorption of phenol fiom aqueous solution was at low concentration stronger onto H Y 71, whereas at high concentration a larger amount of phenol is adsorbed onto Y 77. This behaviour may be explained through the high micropore volume of this polymeric adsorbent whereas the active carbon has due to the smatler micropore diameter the higher adsorption potential at lower concentrationwhich is responsible for its good adsorption capacity in this concentrationregion. 1. INTRODUCTION

Porous organic polymers are increasingly used as hydrophobic adsorbents for removing organic wastes fiom water and humid air because they are easier to be regenerated than active carbons. Their adsorption properties are mainly determined by accessible micropore volume, pore size distribution and surface chemistry. Therefore, we investigate structural and thermodynamic characteristics of Amberlite XAD 4 ( R o b and Haas, USA) and the 2 Wofatites (Chemie AG Bitterfeld-Wolfen) EP 61 and Y 77 (EP 63), and make an attempt to relate them to adsorptive properties. Furthermore, they are compared with those obtained fiom active carbon Hydra& 71 (HY 71) (Lurgi/ Bayer). All resins are produced on the basis styrene-divinylbenzene.

174

2. EXPERIMENTAL

We measured the gas adsorption of benzene and n-hexane at 293 K with a classic static gravimetric equipment (quartz spiral). The pressure ranged from 0.1 to 105 Pa and the lowest measurable adsorbed amount was 0.3 mg/g. The adsorption measurements of nitrogen at 77 K we carried out with a static volumetric equipment and for the Hg-porosimetry we used a porosimeter 4000, both from FISON-Carlo Erba Instruments. Futhermore we measured the adsorption of phenol from aqueous solution by shaking the shmples in solution of well-defined concentration at 293 K for 1 week (resins) and for 2 weeks (carbon). Regarding the concentration before and after adsorption, we obtained the adsorbed amount of phenol. From calorimetric measurements we obtained the immersion heats of the adsorbents in benzene and water. 3. CALCULATIONS

From benzene, n-hexane and nitrogen isotherms we calculated the micropore volumes and characteristic adsorption energies through the DUBININ-RADUSHKEVICH method [ 11:

W = Wo exp [-(A / B Eo)2 where

A = RT In (po / p)

(1)

(2)

Here, W is the volume of micropores filled at relative pressure pdp, Wo is the total micropore volume, Eo is a characteristic energy which depends in a simple way on the microporous structure of the adsorbent: E, = K / x where x is the micropore halfkidth (in nm ), K a constant factor for a given type of adsorbent, e.g. 12,5 for carbons, and E, in kJ/mol. The affinity coefficient D, which depends on the adsorptive, is 1.0 for benzene and 1.31 for n-hexane (estimated from the ratio of parachor of n-hexane and benzene). The distribution of mesopores was determined from the desorption line of benzene and n-hexane isotherms through the method described by ROBERTS [2]. In this method, the amount adsorbed is expressed as liquid volume. The relative pressure is expressed as pore radius utilizing the KELVIN equation [3], a cylindrical pore model, and the thickness of the adsorbed layer for correction of the radius for multilayer adsorption on the pore walls. r=Q+t

(3)

where r is the actual radius of the pore filled with condensate, rk is the Kelvin radius and t is the thickness of the adsorbed layer. For benzene we used the thickness ftom ref. [4] measured by DUBININ on smooth surfaces: t = 0.5 (-1 /

In (~/p~))~’~

(t in nm)

(4)

For n-hexane, a thickness is used as was measured on nonporous graphitized carbon black: t = 0.6 (-1 / In (p/po))4’y

(t in run)

(5)

175

The correction of d e s o k d volume for multilayer adsorption follows the calculations suggested in [2]. From calorimetric measurementswe obtained the specific immersion heats in benzene and in water. Earlier, we found a good correlation between specific benzene immersion heat and total organic adsorption capacity [5] and, for a given type of adsorbents, also between benzene immersion heat and specific surface area. 4. RESULTS AND DISCUSSION

Figure 1 shows the benzene isotherms for the 4 adsorbents. From the shape of isotherms we may expect low mesoporosity for Y 77 and HY 71 and high mesopore volume in EP 61 and XAD 4. Futhermore, Y 77 appears already at first glance as highly microporous. 16 14

adsorbed amount [mmoVg]

12 10 8 6 4

2

0 0

0.4

0.2

0.8

0.6

1

relative pressure Figure 1. Isotherms of benzene at 293 K Table 1 includes the micropore and mesopore volumes and the characteristic adsorption energies, calculated according to the above mentioned models. Table 1 Characteristic values of porous structure and characteristicadsorption energy of the adsorbents I 1 I volume of mesopores 1 Adsorbent Volume of micropores Characteristic energy of 15 A < R < 250 A [cm3/g] adsorption [kJ/mol]

I

I

H Y 71

Y 77 EP 61 xAD4

0.64 0.19 0.35

0.70 0.19 0.28

I

i

Benzene n-Hexane Nitrogen 0.32 0.37 0.33 0.54 0.17 0.30

Benzene 14.8 10.1 7.6 7.9

n-Hexane 10.1 9.4 8.3 8.6

Benzene n-Hexane 0.18 0.26 0.55 1.10

0.16 0.27 0.54 1.06

176 Porous structure as determined from benzene, n-hexane and nitrogen isotherms provides the same qualitative results. Y 77 has the largest micropore volume of the considered adsorbents although a slight error may be in results of Table 1 (and Fig.3) due to the fact that at r=2 rim the Kelvin equation used for evaluation of experiments is not quite applicable because of deformation of liquid meniscus. The resins EP 61 and especially XAD 4 have very large mesopore volumes. Figure 2 shows the Dubinin-Radushkevich plots for benzene adsorption and in Fig.3 are drawn the pore size distributions calculated from benzene desorption. Among the resins, Y 77 has the lowest pore diameter as may also be calculated from characteristic energy.. These findings agree well those in [ 6 ] .

0.5

0

-1

-1.5

I

14

-0.5

I

I

/

0

SO

qh

#

l

EP 61 i

l

I

100 150 200 250 300 350 A*A (A m kJ/mol)

XAD 4

I i

0.5 0 100

10

[A1

Figure 2. Dubinin-Radushkevich plots cal- Figure 3. Pore size distribution calculated culated from benzene adsorption from benzene desorption By mercury porosimetry (Fig. 4) we found the highest macropore volume with an increase at r = 250 A for carbon HY 71 but for resins results are not yet explainable and may be garbled due to higher compressibility or, possibly, partial destruction of the polymer.

lo ^

1

0.8 0.6 0.4 0.2 n " 10

10 I

100

1000

r [A1

10000

100000

1

10

100

1000

10000

concentration [mg/l]

Figure 4. Volume vs radius plot obtained Figure 5. Adsorption of phenol from aqueous from Hg-porosimetry solution at 293 K

177 The characteristic adsorption energies (Table 1) of resins are smaller than that of the active carbon HY 71. This causes a better desorbability (e.g. at lower temperatures or with solvents) of the resins. However, the lower adsorption energy causes also a smaller adsorption capacity at lower concentrations. This is shown by phenol adsorption &om aqueous solution (see figure 5), which at low concentration is stronger onto J3Y 71, whereas at high concentration a larger amount of phenol is adsorbed onto resins, especially onto Y 77. Therefore, the carbon is advantageous for drinking water production and resins for purification of industrial waste water with possibility of recycling. The results of immersion calorimetry includes Table 2. According to the large micropore volume and the narrow pore diameter, Y 77 has the highest specific immersion heat in benzene, whereas the specific immersion heats of Y 77 and HY 71 in water are comparable. EP 61 add XAD 4 are not wettable with water. However, since the measurements were performed under vacuum, the pores were filled nevertheless and a small negative calorimetric effect was obtained. The latter was in order of AH = 2..5J/g and may be probably explained through the energy necessary for extension of the water surf= area in contact with the resin surface as discussed earlier in [S]. Because of the large relative scattering of these heats, in Table 2 a value of 0 is given.

r

Specific Immersion Heat [J/g]

Adsorbent

I

Benzene - 86.0 -103.5

Water -42.2 -46.0

-37.9 -65.8

xAD4

* without vacuum not wettable with water concentration of

0

20

40

60

- A H im, sp, b

80

100

120

[Jkl

Figure 6. Plot of the adsorbed amount of phenol vs A Him.sp- b (specific immersion heat in benzene) for resins

178

For the same type of adsorbents, specific immersion heats in benzene are in the same sequence as adsorbed amounts of phenol for a given concentration (figure 6). The reason for this finding is that both values - immersion heat and adsorption capacity refer to specific surface area. Therefore, immersion heats are a good indicator for the adsorption capacity for organics. However, for different types of adsorbents (additionally carbon or zeolite [7]) no simple correlation may be found between adsorption properties and immersion heats.

-

CONCLUSIONS From our structural investigation of polymeric adsorbents we may draw the following conclusions: - Adsorption method for studying the porous structure yield same ranking of micro- and mesopore distribution for different adsorptives although slightly differing in their absolute values. In any case, Y 77 has a very large micropore volume whereas EP 61 and XAD 4 have the larger mesopore volume. From the Dubinin-Radushkevich plot of benzene adsorption we found for the resins a smaller characteristic adsorption energy and therefore, larger micropore diameters than for active carbon. Among the polymers, Y 77 has the smallest pore diameter. - According to pore diameters and characteristic adsorption energies, adsorption of phenol onto active carbon is stronger for small concentration where the polymers have only little adsorption capacity. At high concentration, in agreement with its large micropore volume, Y77 has the greatest phenol adsorption.

-

REFERENCES I. M. M. Dubinin and L. V. Radushkevich, Proc. h a d . Sci. USSR, 55 (1947) 331. B. F. Roberts, J. Colloid Interface Sci. 23 (1967) 266-273. V. Ponec, Z. Knor and S. Cerny, Adsorption on Solids, Butterworths, London, 1974,404 ibid., 558. K.H. Radeke, Carbon 22 (1984) 473. A. Konig, K. Fischwasser, R. Bohm, Acta hydrochim. hydrobiol. 19 (1 991) 675 K.H. Radeke, U. Lohse, K. Struve, E. WeiB, H Schroder, Zeolites 13 (1993) 69 K.H.Radeke, H.Peters, Z.Phys.Chem.(Leipzig)267 (1986) 656

2. 3. 4. 5. 6. 7. 8.

I. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids lli Studics in Surrace Scicnce and Catalysis, Vol. 87 0 1994 Elsevier Scicncc B.V. All rights rcscrvcd.

179

Water in spherical, cylindrical and slitlike pores Sumio Ozeki, '* Yuichi Masuda; Yuko Nishimoto' and Teruo Henmid "Department of Chemistry, Faculty of Science, Chiba University, Inage-ku, 1-33 Yayoi-cho, Chiba 263, Japan; bDepartment of Chemistry, Faculty of Science, Ochanomizu Woman's University, 2-2-1 Ootsuka, Bunkyou 112, Japan; Department of Chemistry, Faculty of Science, Kanagawa University, Tsutiya, Hiratsuka 259-12, Japan; dFaculty of Agriculture, Ehime University, Tarumi 3-5-7, Matsuyama, Japan

Abstract Adsorbed water in slitlike micropores of ca. 1.0 nm width of jarosite and alunite (nanopile) was distinguished by the dielectric properties and H NMR parameters for mono-, bi-, and trimolecular layers. In a monolayer water molecules seem to have a mode of rotational motion and show no phase transition in the rage 3080 "C, in a multilayer have a mode of translational motion and freeze at about -30 "c and in a three layer (q=1.5) in the 1 nm slitlike micropores change their motional mode from rotation to translation across about -30 "C. The extreme immobilization of water molecules a t q=1.5, which was suggested by a maximum dielectric relaxation time and very small heat of fusion, was attributed to a filling of the slitlike micropores with water molecules which bridge the first layers on both walls of the micropores through hydrogen bonding. Water adsorbed on the inner and outer surfaces of nanotubules, imogolite (pore diameter d=1.0 nm) and chrysotile (d= 7 nm), showed two NMR relaxation rates. The fast and slow relaxation rate for chrysotile are ascribed to water on a n inner and outer surface, respectively. Water with fast relaxation mode had three states at the higher coverage of q>3and are adsorbed in the mesopores by capillary condensation to form a liquid phase that may be supercooled down to -60 "c. The slow relaxation rate for imogolite seems to arise from water immobilized on an inner surface of the cylindrical micropores. Water on a nanobaloon, allophane (d=1.5-3 nm) having small holes (0.3-0.5 nm in diameter) on the wall, also has two relaxation rates. The longitudinal relaxation of water in the micropores is faster in the order of spher icabcylindrical>slitlike . 1.INTRODUCTION Molecules in a potential field, as in pores, may be restricted and thus behave

180

peculiarly. Dynamic properties and structures of adsorbed phase on solids have been investigated by dielectric, N M R and neutron scattering measurements, etc [ 11. Adsorbed water is immobilized in a monolayer like ice and behaves as liquid on flat surfaces and in wide pores. The melting point of water in pores is lower than 273 K,melting point of bulk water, and decreases with decreasing pore size 121. On the other hand, an example showed that water in mesopores of silica have higher melting point, e.g., 278 K,than bulk water [31. When water was adsorbed on porous jarosite and alunite, which have slitlike micropores of ca. 1 nm width, the motional mode of adsorbed water changed dramatically with the micropore filling [41. Such changes of motional mode of adsorbed water will depend strongly on pore shape and size. In this paper, we examine and summarize, by using also the previous results t4-61. properties of water adsorbed on solids having various pores homogeneous in shape and size: 1 nm and 8 nm diameter cylindrical pores (nanotubules) and 2-3 nm diameter spherical pores (nanoballoon), as well as 1 nm slitlike pores (nanopile). 2. EXPERIMENTAL Porous jarosite and alunite (KMaO, (OH),; M=Fe or All were prepared by refluxing a mixed solution (pH 2.0)of 0.3 moYdm' M,(SOJ,, KOH and K,SO, at boiling point for 2.5 h [4,5,71.Chrysotile asbestos (Mg$i,O,,(OH)) was synthesized by autoclaving an aqueous MgC1, solution (pH 13) containing NaOH and Aerosil 380 (Nippon Aerosil Co, Ltd.) at 573 K and 65 atm for 24 h [61. Hydrous and allophane (g=1.25), aluminosilicates, imogolite (SiO$Al, 0, molar ratio ~1.05) were prepared from weathered volcanic ash and pumice 183. The samples were characterized by an XRD method, TEM and SEM observations and chemical and EPMA analyses [4-61. N, and H,O adsorption on the samples, dried at 383 K and 1 mP for jarosite, alunite and chrysotile asbestos and at 423 K and 1 m P for imogolite and allophane for 15 h, was measured by the gravimetric method at 77 and 303 K,respectively.

Table 1. Characteristic values of nanopiles, nanotubules and nanoballoon. pore volume pore size pore shape N2 H20 I q a, vm vm ,ad. materials mg/g nm nm m2/g ml/g jarosite alunite chrysotile imogolite allophane

171 265 70 240 335

0.086 0.166

58.9 82.6 22.2 0.101 102 0.159 160

1.0 1.1 7 1.0 3

7 0.7-1 3-5

slitlike slitlike cylinder cylinder sphere

181

Dielectric properties of water adsorbed on the samples in a concentric, cylindrical aluminum cell were measured with an ac bridge circuit at 0.02 - 100 kHz and 303 K 151. 'HNMR was measured by a JEOL FX-200 Fourier transform spectrometer in the range 193 to 303 K 141. The sample in a NMR cell was dried by the procedure similar to the %O adsorption, and then sealed off after the sample had adsorbed definite amounts of water at 303 K. DSC of the sample in a silver pan, which adsorbed water in vapor of a saturation salt solution under air and then was sealed with a silver cap, was measured with a Seiko DSC 100 191. After the sample pan was cooled down to 173 K or less, the temperature of the sample was raised at a rate 1 degree/min with computer control.

3. RESULTS AND DISCUSSION 3.1. Materials The prepared samples are summarized in Table I. Jarosite and alunite have 1.0 nm slitlike micropores, which was deduced from crystallographical structure and electron microscopic images (thin layered structure) and the t-plot of N, adsorption data (Figure 1) [4,51. The prepared chrysotile is a tubular particle whose averaged size from the TEM observation is a length ( I ) of ca. 600 nm and inner (d,)and

0' PIP.

Figure 1. Adsorption isotherms of N, for prepared samples at 77 K. - -jarosite; -.- ,alunite;.....,chrysotile; ,imogolite; ,allophane

-

-

02

04

06

08

1

P 'P.

Figure 2. Adsorption isotherms of H,O for prepared samples at 303 K. jarosite; -.+unite; .....I ,chrysotile; - ,allophane -,imogolite;

-- -

182

outer (do)diameters of 7 and 300 nm [61. This inner diameter agreed with that from the t-plot of N, adsorption data. Imogolite is very thin tubules having &,=1 nm and d0=2nm. The t-plot for N, adsorption data on imogolite showed that the inner diameter was about 1.0 nm. Allophane as a nanobaloon has di= 2-3.5 nm and d,=3-5 nm, and it is considered there are about 10 holes having 3-5 nm diameter on the wall [lo]. The analysis of N, adsorption showed that allophane has two kinds of pore, ca. '1.0 nm diameter (t-plot) and ca. 3.2 nm diameter (Cranston-Inclay method, using the desorption branch). The inner surfaces of the aluminosilicates comprise SiOilike layer. 3.2. &O adsorption The %O adsorption on the microporous samples was promoted from moderate pressure and the adsorbed amounts were much more than those of adsorbed N,, suggesting that polarity of H,O molecules makes them penetrate into N, nonaccessible pores. The surface coverage of H,O, q, is defined by the ratio of the adsorbed amount u to the monomolecular amountn,.

3.3. Adsorption states of H,O 3.3.L H,O i n 1 n m slitlike micropores (Jarosite a n d Alunite )[4,51 Figure 3 shows a possible model for water in the slitlike micropores. Water is adsorbed on the inner walls of the slitlike micropores, and then more water molecules bridges the first layers on both walls through hydrogen bonding t o fill the 1 nm micropores with three water layers or q-1.5, assuming that diameter of a water molecule is 0.3 nm. In this case, water at q= 1.5 will be immobilized by

*I

x -

5

,, .. *--.

c

w Figure 3. A model for immobilized water in slitlike micropores of a porous jarosite.

Figure 4. Variations of dielectric relaxation time with coverage of H,O adsorbed on a porous jarosite ( - - - - ) and a porous alunite ( at 303 K.

-

183

the bridging hydrogen bonds. The dielectric relaxation time of adsorbed water at 30 "c (Figure 4) was a maximum value of 6 ~ 1 0 s. ~at q =1.6 for jarosite and 1.2 x 10" s at q = 1.3 for alunite, at which their isosteric heat of water on jarosite and alunite also liberated by several kcal/mol, suggesting that some hydrogen bondings should be formed with micropore filling. The immobilized water behaved like ice at mor than -30 "C.Relaxation rate of 'H NMR R, (=Ti', where Tl is the longitudinal relaxation time ) increased with increasing temperature at q>1.3 and decreased at qc1.3. This means a slow motion of relaxation time t>>lO.'' s at q>1.3 and a certain rapid motion of t<1.3 would be different from the motion for q c l , considering the difference in the temperature dependence of R,. We suppose that the motion for q>1 may be lateral diffusion and ttransforthe motion would be much more than 10"O s, since water molecules in the slitlike micropores make hydrogen bonds with those adsorbed on both walls,. Water (ice) adsorbed in the slitlike micropores of alunite melted with an average heat of fusion of Hm=1.4kJ/mol a t T,=-26 "C, and thus was ice-like even at a room temperature, because the H,,,(<0.5 kJ/mol) is much lower than that of free water, 6.0 kJ/mol. This is consistent with the immobilization of water which filled the slitlike micropores by hydrogen bond formation.

3.3.2. H,O in 1 and 7 n m cylindrical pores (Imogolite a n d Chrysotile Asbestos 161) In general, only an averaged R, value for adsorbed water is obtained, since the exchange among water molecules is very rapid even at different sites as well as in different layers. However, a motion of water on the outer surfaces of the tubes may be distinguished from that of water on the inner surfaces, when the average distance, 102-104nm, which a water molecule travels during a time scale of T,(0.01-1 s) is comparable with the average length of particles. In fact, two kinds of the longitudinal relaxation rate for water adsorbed on a chrysotile asbestos (Figure 5 ) and an imogolite were observed. The fraction, f " 4.83, of hydrogens with the slow relaxation rate at q=O agreed with the geometrically expected fraction, 0.81, of the outer surface of chrysotile, and thus the fast (R,?and slow (4')relaxation rates are ascribed to water adsorbed on an inner SiO, and an outer Mg(OH), surface, respectively, of a tubular chrysotile crystal with a cylindrical mesopore with a 7-nm diameter.

184

The R,f values, 17-29 s.' for 3.33 is remarkably similar to that of R, for silica 1123 and charcoal 1141 under saturation vapor (Figure 61, although their pore sizes would be so different. The increase and decrease in R,f across the maximum around -70 "C,respectively, seem to correspond to behaviors of a supercooled water and ice 161. Therefore, judging from R,' liquid water adsorbed on the inner surfaces behave like supercooled water below -30 "Cand is converted t o ice around -70 "C. On the other hand, ice in the mesopores of chrysotile, kJ/mol. which was made by cooling down to -100 "c, had T,=-16 "Cand Hm=3 Water on imogolite showed two relaxation rates, e.g., 40 and 266 s-' at q=1.5 and 25 "c. The slow relaxation rate remained unchanged in the range q=1.5-3.7

i

70

I 0

2

6

4

4 Figure 5 . Variation of R, of water adsorbed on a prepared chrysotile with surface coverage. Temperature/ K , 303.2; -.-.-. ,273.2; ,243.2; ---- - , 213.2; ........., 193.2

-

---

Figure 6. log R , of adsorbed water, supercooled water and ice as a function of T'.R,'() for water adsorbed on the chrysotile a t q=5.7 and R, for water adsorbed on a charcoal (---.- )I4 and a silica gel (.-*...*-)I3 under vapor.

185

and, on the other hand, the fast one decreased with increasing q. Since the 1.0 nm cylindrical micropores of imogolite should be nearly filled with a three water layer (q=1.5) and in fact q=1.5 corresponds to the volume fraction, F=l.O, of the pore filled with water, the slow relaxation rate may be independent of q>1.5, unlike R,' for chrysotile which depended on q because the cylindrical mesopores are not perfectly filled with water at q<5. Therefore, the slow relaxation for imogolite would arise from water in the cylindrical pores. The relaxation rate of proton in the l-nm cylindrical micropores is comparable with R,f for water in a 1.5 layer on chrysotile, ca. 35 s-' at q=1.5 and 25 "C (the inner surfaces of both imogolite and chrysotile are Si0,-like), and is faster than that of proton in the l-nm slitlike micropores of the alunite. The immobilized inner water melted at Tm=-60"c with Hm<0.5kJ/mol. The fast relaxation time for imogolite, which is presumably ascribed to water on the outer surfaces, is much larger than those for the above systems. This might be caused by a contamination of 0.08 atomic % FeUII) which would occupy AH1111 sites in the outer gibbsite layer of the imogolite.

3.3.3. KO in 2-3.6 nm spherical pores (Allophane) Water molecules on the inner and outer surfaces may be distinguished because they are exchanged each other only through several channels of 0.3-0.5 nm diameter. In fact, water on the allophane had two longitudinal relaxation rates at 25 "C.The relaxation rate of water on the inner Si0,-like walls of the spherical pores was 109 s-' at q=1.0 (F=0.75) and 42.4 s.l at q=4.0 (F=3.2). These values are regarded to be much larger than those of imogolite, if the difference in pore size is taken account. The motion of water in the spherical pores seems to be extremely restricted, as shown in its T, and H,, i.e., -70 "C and less than 0.1 kJ/mol, suggesting that a very stable cluster of water should be formed in the sphere. From above results, it is inferred that the relaxation rate of water in micropores is larger in the order of spherical >cylindrical>slitlike, in other words, the order of dimension of the space.

REFERENCES 1. e.g., R. L. McIntosh, Dielectric behavior of physically adsorbed gases, Marcel Dekker, New York, 1966, Chapt.5. J. R. Zimmerman and J. A. Lasater, J. Phys. Chem., 62 (1958) 1157. 2. J. Clifford, Water, Ed. by F. Franks, Prenum Press, 1975, vo1.5, p. 75. 3. W. Drost-Hansen and F. M. Etzler, Langmuir, 5 (1989) 1439. 4. S. Ozeki, Y.Masuda and H. Sano, J. Phys. Chem., 93 (1989) 7226. 5. S. Ozeki, J. Chem. SOC. Chem. Commun., (1988) 1039; Langmuir, 5 (1989) 181.

186

6.S. Ozeki, Y.Masuda, H. Sano, H. Seki and K. Ooi, J. Phys. Chem., 95 (1991) 6309. 7. S.Ozeki and K. Inouye, J. Colloid Interface Sci., 125 (1988)356. 8.T. Henmi, M. Nakai, T. Seki and N. Yosinaga, Clay Miner., 18 (1983)101. 9.S.Fujiwara and Y. Nishimoto, Anal. Sci., 7 (1991)683. 10.R. L.Parfitt and T. Henmi, Clays Clay Mineral., 28 (1980)285. 11. V.V. Morariu, R. Z. Mills, Z. Phys. Chem. (Munich), 79 (1972)1. 12.R. T. Pearson and W.Derbyshire, J. Colloid Interface Sci., 46 (1974)232. 13.D.E. Woessner, J. Chem. Phys., 39 (1963)2783. 14.H.A. Resing, J. K. Thomson and J. J. Krebs, J. Phys. Chem., 68 (1964)1621.

J. Rouquerol, F. Rodriguez-Reinoso,K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids Ill Studies in Surfacc Science and Catalysis, Vol. 87 0 1994 Elsevier Science B.V. All rights reserved.

187

Invasion and transport processes in multiscale model structures for porous media Jean-Frangois Dafana, Xu Keb and Daniel Quenardc aLaboratoire d'Etude des Transferts en Hydrologie et Environnement - Institut de MBcanique de Grenoble (UniversitB J. Fourier, INP de Grenoble, CNRS). BP 53X, F38041 Grenoble cedex. kaboratoire des MatBriaux et des Structures du GBnie Civil (Laboratoire Central des Ponts et Chaussdes, CNRS). 2 allbe Kepler , Cite Descartes Parc Club de la Haute Maison, F77420 Champs sur Marne. CCentre Scientifique et Technique du Biitiment, Service Matbriaux. 24 rue Joseph Fourier, F38400 Saint Martin d'H8res. Abstract

A porous medium is represented by the superposition of several pore networks of different mesh-sizes. The multiscale infinite cluster of the structure is defined using rescaling principles. The model is applied to mercury intrusion and electrical and hydraulic transport properties.

INTRODUCTION

A lot of work has been done until now to build up reliable models for the occupation of porous media by fluids and for transport properties, on the basis of the knowledge of the pore-structure. These studies are used in numerous anplication fields like adsorption and catalysis [11, capillary phenomena 121, interpretation of mercury intrusion [3], single phase or multiphase fluid transport [3], electrical conductivity of rocks [4-61, ionic diffusion... Such models more or less explicitly refer to a network representation of the pore-structure. The representative networks are generally regular and characterised by a given coordination number and a given mesh size related to a single typical pore-size. In the case of materials in which several orders of magnitude of the typical pore-size exist together, the single mesh-size network scheme appears to be unsuitable. In the present work, we attempt to define rigorous rules to deal with occupation and transport in multiscale model structures involving a representation by several superposed networks of various mesh sizes. The

188

i=n=3

i=1

i=2

superposition

Figure 1. Schematics of a multiscale structure with 3 scales. basic idea is to put the pores of each typical size in a network of corresponding mesh-size and to perform the superposition using renormalisation, o r rescaling principles 17-91. Figure 1 gives a schematic idea of the structure studied, in the case of three typical sizes 1,2 and 4. The model proposed aims to deal with media involving much more numerous classes of pore-size. 1. BASIC PERCOLAITON THEORY TOOLS 1.1. Networks pmpertiesi far h m the pemlation threshold Percolation theory [10,111 provides the behaviour of various properties of a random network occupied at a rate p in the vicinity of the percolation threshold pc under the form of power laws. The exponents v for the correlation length ((p), p for the proportion of elements Y(p) which belong to the infinite cluster (Fig. 2) and t for the conductivity of the network H(p) (Fig. 3) are defined: 5(P) = IP- PJ"

Y@) = @- PJP

H(P) = @ - PJ'

(1)

In the present work where we have t o consider networks occupied at any rate smaller or larger than pc, it will be necessary to define the behaviour of these properties far from the percolation threshold. For a low (resp. large) rate of occupation, polynomial expansions of the properties can be found by means of the enumeration of the percolant (resp. non percolant) configurations in a sample of finite adimensional size N, provided that the shape of the network is defined. We use here cubic bond networks (CBN). We propose the following expansions, which cannot be demonstrated in this short paper. For the probability of percolation of a sample of size N, PN(p): p + 0 PN(P)= N' pN (1+ 4Np+ ...) , p +1

PN(P) = 1 - N(l-p)NZt...

(2)

For the proportion of elements which belong to the infinite cluster for p>pc, or which are connected to the boundaries of the sample for p
189

0

0.1

0.2

,

.

.

0.3

0.4

0.5

0.6

P

0.2

0.3

0.4

0.5

0.6

P

Figure 2. Invasion characteristic for a cubic (CBN) (p, = 0.25, p = 0.41)

Figure 3. Conduction characteristic (CBN) (t = 1.9)

A similar expansion can be defined for the statistical conductivity of a finite sample, HN(p) at a low rate of occupation. For large rates of occupation, Kirkpatrick [121 showed that the Effective Medium approximation is valid (see Fig. 3): p + 0 H N ( ~ ) =pN (1+ 4Np+ ...) ,

in E.M. domain H@) = (3p - 1) / 2

(4)

1.2. Resealing, renormalisation The rescaling rules 113-171 will be used in the following developments, in order to study the connection between elements which belong to networks of different mesh-size. We limit ourselves here t o the rescaling by a factor 2. A network of mesh-size a occupied at a rate p can be considered to be equivalent to a network of mesh-size 2a occupied at a rate flp), provided that the statistical size of the clusters is the same in the two networks. The adimensional correlation length 5 must be therefore two times smaller in the rescaled network. In other words, the probability of percolation of a sample of respective adimensional sizes 2N and N in the two networks must be the same. The rescaling function flp) can therefore be defined as the limit when N+ of the function fN(p)which satisfies the following condition 1131: 00

PN[fN@>l = p2N(p)

(5)

The behaviour of the function flp) near the percolation threshold derives from the power law for the correlation length (Eq. 1).Its behaviour for large and small values of p can be deduced from equations (2):

190

0

0.2

0.6

0.4

0.8

1

0

0.2

Figure 4. Rescaling function flp) for the rate of occupation (CBN) (v = 0.845) at p =pc f@,) = pc df/dp = 21N fN@) = 22/Np2( 1 + 8p +...) p+o, p+i, f(p) =I- (1-p)4 + ...

0.4

0.6

0.8

1

P

P

Figure 5. Rescaling functions g(p) for the volume and h(p) for the conductivity (CBN)

f(p) = p2(1 + 8p +...)

Figure 4 shows a ten degree polynomial closed form for the function flp), built up on the basis of these indications.

1.3. Wlume and conductivitym s d h g However, the rescaling operation does not conserve the number of elements which belong to the infinite cluster, or which are connected to the edges of a sample for p
In the following developments (see Section 4) the function g(p)=$p) flp) / p will be used in practice. The value of this function just above the percolation threshold derives from equations (1) and (6). Its behaviour for p small and large are deduced from equations (3) and (6): g@,) = 1/2p'" ; g(0) = 112 with dg/dp = 5 ; when p +l

g(p) = l-(l-p)lo+ ...

(8)

Figure 5 shows a closed form for the function g(p), built up on the basis of these indications and with the help of Monte Carlo simulations for p< pc.

191

The same problem arises for the study of the conductivity, because H[f(p)l + H(p). The problem can be solved in a similar way, by assigning to the elements of the rescaled network a conductivity h(p) such that h(p)H[f(p)l = H(p). The function h(p) is defined as: h@) = lim

m+

OO)

H ~ ( PI)H,

[f~@)l

(9)

The following properties are deduced from equations (11, (4) and (6): h@& = 1/ZVv ; h(0) = 114 with dh/dp = 0 ; in EM domain, h(p) = (3p- 1)/[3f@)-11 2. BUILDING A MULTISCm STRUCTURE

Consider n networks (Fig. l), occupied at the rates pi, of mesh-sizes decreasing with i, ai =2"-l a,, supposed to be representative of the random spatial distribution of the pores of typical diameter 4 = 2"-' d,. The volume of each occupied bond is of the order of ai di2. The elementary volume ai3 can hold at most 3 occupied bonds. For consistency, we suppose that 3ai di2 = ai3, or (di/a$2=ll3. The simple superposition process described in Figure 1 suggests to define the provisional following rates of occupation of the pore space by the various classes of pores: u1 = p1

I

u2 = p2 (1- P I )

7

'.....,

ui =pi (1- pi-1 1

(1- P I )

(11)

2.1. Occupationby a non-wethgfluid Having in view the occupation of the structure by a non wetting fluid, which, at a given stage k (e.g. at a given mercury pressure) potentially occupies the largest pores of classes 1 to k, we account for these pores only. The network of rank k is occupied at the rate pk. We rescale it by a factor 2 according to 6 1.2 and then superpose the pores of class k-1. The network of rank k-1 obtained includes the pores of class k-1 present at the rate pk-1 and the rescaled elements of class k present at a rate (1- ~ k - ~ ) f ( ~Repeating k). the process up to the network of rank 1 yields the following rates of occupation ni,k of the successive networks. In the first index indicates the rank of the network and the second recalls the stage of invasion: Xk,k = Pk

...

Xi,k = (l-Pi)f(Xi+l,k)

+ pi

...

X1.k = (1-Pl)f(n2.k) + P 1

(12)

In the rate of occupation of the final network of rank 1, XI,&, the contribution of the pores of class i is:

Xi,k

I92

1

10'3

diameter (m)

Figure 6. Actual pore-size distribution and mercury intrusion curve for a hypothetical medium The percolation of the non-wetting fluid is achieved at a stage k such that > pc. The complete medium is described by the rate of occupation of the gnd of rank 1at the stage n, xl,n, including the contributions

xl,k

222. Occupation by a wettingfluid At the stage k, the wetting fluid occupies the smallest pores of ranks k to n. The pores of ranks 1to k-1 are present in the structure but must be considered as non occupied elements in each network. The structure representative of the occupation of space by the fluid must be built starting from the rank n. The rates of occupation of the successive networks, denoted P i , k , are now: Pn,k = Pn

Pk,k = (1-Pk)f(Pk+l,k)+Pk

* Pk-1.k = (l-Pk-l)f@k,k)

Equation (13) for the contributions to except for replacing x by p.

P1.k = (l-Pl)f(P2.k)

(14) denoted now Yi,k, is unchanged,

3.MODELLING MERCURY INTRUSION

At the stage k of the intrusion, the mercury pressure allows the fluid to penetrate into the pores of classes 1to k. If xl,kPc, mercury effectively penetrates into the pores which belong t o the multiscale infinite cluster of the structure. The contribution of the elements of class i to the infinite cluster is Y(k1,k) X i , k / x1,k. But these elements have been generated by the rescaling of the successive networks of ranks i, i-1, ... ,2. Therefore, their volume must be corrected according to $ 1.3. This yields the following volumic contributions:

193

The intrusion volume at the stage k is v k = X vi,k. The total porosity of the medium i s V n . Its volumic pore-size distribution is defined by the contributions v ~ , ~Figure . 6 shows an example of the cumulative mercury intrusion characteristic, compared t o the cumulative pore-size distribution. The medium was generated by a Gaussian distribution of the apparent volumes ui and the procedures defined above were performed t o obtain the volumic size ~ connected pores and the intrusion volumes v k . distribution v ~ of, the 4. MODELLING ELECTR.ICAL AND HYDRAULIC CONDUCTIVITY 4.1. Method

Consider a multiscale porous medium at a given saturation. A wetting fluid occupies the pores of classes n to k, the pores of classes k-1 to 1are occupied by a non-wetting fluid. We attempt t o define rules for the calculation of the coefficients for three transport processes of interest: the electrical conductivity of the wetting phase (the conductivity of the fluid being GO>, the relative hydraulic conductivity (m2)of the wetting phase and of the non-wetting phase. The main problem with transport properties is that Percolation Theory deals only with the case where all the occupied elements have the same conductivity. The conduction law was defined in Section 1by the function H(p). In the other cases, the Effective Medium Theory (EMT) [12,16-181 provides a mixing law of which validity strongly depends on the conductivity distribution of the medium[l8]. According t o EMT, the equivalent conductivity, S, of a cubic bond network made of bonds of conductivities' Si present in the proportions Xi, non conductive bonds included, is given by:

We propose to use this formula to calculate the conductivity of a multiscale structure, represented by the network of rank 1 defined in Section 2. The proportions of the conductive bonds are Xi,k-l defined in $ 2.1 for transport in the non-wetting fluid, and Yi,k defined in $ 2.2 for transport in the wetting fluid.' The proportion of non conductive bonds is (resp. l-Pl,k). The values of the conductivities Si in the network of rank i must account for the original conductivities si of the bonds and for the rescaling of the successive networks. The original conductivity is si = od3 for electrical transport3 and

' EMT formula i s originally expressed in terms of conductances, G. In a network of constant mesh-size, a, and therefore constant path section, a', the conductance can be replaced by the conductivity S = G I a. 'A correction in the values of the was introduced to account for the difference between the percolation threshold ( = 0.25) and EM" conduction threshold (=1/3).

3

The electrical conductivity of a cylindrical bond is si = ao(q/ ail2. According to the previous convention, (di/ ai ) 2 = 11 3 , si = a I 3. This is because in a unit volume of porosity 1 including 3 occupied bonds, only the in the direction of the transport contributes t o conduction.

ban!

194

0

0.2

0.4

0.6

0.8

1

saturation

Figure 7. Wetting phase electrical conductivity for a hypothetical medium

0

0.2

0.4

0.6

0.8

1

saturation

Figure 8. Relative hydraulic conductivities of the same medium

si=(1/3)(1/32)di2for hydraulic transport, according to Poiseuille law. The elements of class i in the network of rank 1 have been generated by the rescaling of the successive networks of ranks i, i-1, ... ,2. According t o 0 1.3, their conductivity Si is:

An example of application of these procedures is given in Figures 7 and 8, for the same pore-size distribution as in Figure 6. The irreducible saturation, corresponding to the percolation stage (?rl,k-l or Pl,k> p,) can be clearly seen for each phase.

4.2. Partial validation ofthe method The consistency of the model proposed can be controlled by reference to two well-known semi-empirical laws for transport processes in saturated porous media. Concerning electrical conductivity, Archie's law [ 191 indicates a correlation between the formation factor F = oo/ S and the porosity E: F= oo/S-(~-~g)""

(18)

In the case of poorly connected media, described by structures close to the percolation threshold, the open porosity can be considered to be proportional to the proportion of elements which belong to the infinite cluster, Y(p). According to Equations (l), we have in this case Archie's law with E~ = 0 and m= t /p = 4.6. Katz and Thompson [4] proposed a correlation, based on percolation considerations, between the hydraulic conductivity, ksaP of a saturated medium, the formation factor, and the threshold diameter i n mercury intrusion, d,:

195

1 os

.-88 1

10-10

10-'2

1 @I2

lo-$'

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

- 1 c

.-

U.

;*

.-0 71

3=

Y

n

10-l'

E

1 0-lS

i, 1616

-001

0.1

porosity

Figure 9. Porosity-formation factor correlation for 131 media

1

lo.18

10-17

10-16

10'15

1 0-lB 10.13

Figure 10. Katz and Thompson's correlation for the same media

In order to test our model, a series of media were generated, starting from Gaussian distributions of ui round the median diameter 4, = 1 pm (which has no importance for the electrical conductivity, but determines the hydraulic conductivity). Figure 9 shows the correlation obtained between the calculated formation factor and the porosity for 131 media. For high values of the porosity, a relatively good consistency with Archie's law is obtained for E~ .= 0.25 and m=1.56. This exponent is consistent with the values generally e v e n in the literature. In the domain of low porosity, i.e. for poorly connected media, a power-law behaviour is observed, with an exponent comparable with the value oft /p. Equation (19) was also tested. The correlation obtained is shown in Figure 10. Except for some particular cases, an excellent agreement is found. However the prefactor is found to be 1/57 instead of lI226. Moreover, the correlation observed is improved when the critical diameter d, is replaced in equation (19) by the median diameter 4, of the distribution of ui. This may be due to the fact that Katz and Thompson's assumptions about the pore-size distribution are not satisfied for the media considered.

REFERENCES 1. Parlar M. and Yortsos C., 1988. Percolation theory of vapour adsorptiondesorption processes in porous materials. J. of ColloLd and Interface Science, 124 (l),pp. 162-176.

196

2. Diaz C. E., Chatzis I. and Dullien F. A. L., 1987. Simulation of capillary Pressure curves using bond correlated site percolation on a simple cubic network. Dansport in Porous Media, 2(3),pp. 215-240. 3. Dullien F. A. L., 1991. Characterisation of porous media - pore level. Dansport in Porous Media, 6(5-6),pp. 581-606. 4. Thompson A. H., Katz A. J. and Krohn C. E., 1987. The microgeometry and transport properties of sedimentary rock. Adv. Phys., 36 (51, pp. 625-694. 5. Charlaix E., Guyon E. and Roux S., 1987. Permeability of a random array of fractures of widely varying apertures. Dansport in Porous Media, 2, pp. 31-43. 6. Kostek S., Schwartz L. M. and Johnson D. L., 1992. Fluid permeability in porous media: comparison of electrical estimates with hydrodynamical calculations. Phys. Rev. B , 45(1),pp. 186-195. 7. Neimark A. I?,1989. Multiscale percolation systems. Sou. Phys. JETP, 69 (41, pp. 786-791. 8. Saucier A., 1992. Effective permeability of multifractal porous media. Physica A , 183, pp. 381-397. 9. Dai'an J.-F., 1992. From pore-size distribution t o moisture transport properties: particular problems for large pore-size distributions, in Drying'92, A. S. Mudjumdar Ed., pp 263-282, Elsevier. 10. Stauffer D., 1985. Introduction to Percolation Theory. Taylor and Francis, London. 11. Adler €?,1992. Porous Media. Geometry and Dansports. ButterworthHeineman, London. 12. Kirkpatrick S., 1973. Percolation and conduction, Rev. Mod. Phys., 45, pp. 574-588. 13. Kirkpatrick S., 1979. Model of disordered materials, in I11 condensed matter, R. Ballian, R. Maynard, G. Toulouse Eds, pp 321-404. North Holland Publishing Company. 14. Bernasconi J., 1978. Real-space renormalisation of bond-desordered conductance lattices. Phys. Rev. B, 18(3),pp. 2185-2191. 15. Reynolds P. J., Stanley, H. E. and Klein W., 1980. Large cell Monte-Carlo renormalisation group for percolation. Phys. Rev. B, 21 (3), pp. 1223-1244. 16. Sahimi M., Scrivener L.E and Davis H.T., 1984. On the improvement of effective-medium approximation to the percolation conductivity problem. J . Phys. C , 17, pp. 1941-1948 17. King P. R., 1989. The use of renormalisation for calculating effective permeability. Dansport in Porous Media, 4 (11, pp. 37-58. 18. David C., Gueguen Y. and Pampoukis G., 1990. Effective medium theory and network theory applied to the transport properties of rocks. J . Geophys. Res., 95, pp.6993-7005. 19. Gueguen Y. and Palciauskas V., 1992. Introduction dc la physique des roches. Hermann Ed. Paris

J. Rouqucrol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids 111 Studies in Surfacc Scicnce and Camlysis, Vol. 87 0 1994 Elsevier Scicncc B.V. All rights rcscrvcd.

197

Local porosity analysis of disordered porous matrices

Massimiliaiio Giona and Alessantlra. Adrover Dipartimento di Ingegneria Chimica, IJiiiversitb di Roina ”La Sapienza” Via Eudossiana 18, 00184, Roina, Italy

Abstract We analyze the possibility of descrilling the quenched, disordered characteristics of coiiiplex porous matrices by means of local pointwise functions (local accessibility and local porosity fields). Detailed numerical results are developed for 2-d percolation clusters. It is shown that, even far from criticality, p(~rcolatioiicliisters exhibit an highly heterogeneous structure of the local accessil3ility fimctioii. The c,onnec,tion hetween quenched disorder in porous media and dynamic tlisortler of turbulent flow is discussed.

1. INTRODUCTION

The main problems in the analysis of the structure of pore networks lie in the complete characterization of network geonietry and topology and i n the influence of geometrical and topological parameters on traiis1)ort properties. Extensive research on these topics has been developed over tlie last clecatl(~in coiiiiection with the application of fractal concepts, percolation antl grow t 11 motlrls an tl lat t ire r q m w i i t at ion on disortleretl s t riic t ures [ 1-41. Indeed, experimental results iutlicatr that fractal geometrical concepts antl the analysis of anomalous transport properties we usefiil analytical tools for describing transport in porous media. The fractal a.pproacli to porous media focused attention inainly on the universal features, i.e. on the behaviour near criticality (for which universal features analogous to tlie theory of thermal phase-transition can be observed) [ 5 ] , showing that in the case of purely molecular diffiision a limited niiiiiher of scaling exponents characterize However, i n practical analysis of transport in geometrical and transport anoinalies [(i]. porous media (e.g. in sizc:-tsxcliisioii ~-1i1.oinatog~apliy or in diffiision throiigli molecular sieves) the assuniption of fractality semis to be often restrictive since it depends strongiy on the size and nature of the solute nioleculvs considered, which induce a characteristic lengthscale i n the solute/pore-networlr steric interactions [7]. This implies that we are forced to extend our investigations to lion-universal features, seeking a unifying mathematical modeling of complex but no11 nmessarily critical disordered structures. In other words, theoretical research should be oriented also towards to the analysis of transport in disordered non-fractal pore networks. Percolation clusters far from criticality represent

198 an useful starting point. I n o r t l c ~to piirsiit~this goal, 1)rewiititig a general nietliotl of aiialysis, we develop a local characterization of porosity (by introducing a local accessibility field) in 2-d percolatioii clusters, which can b e easily extended to iiiore general situations. In this way, the characterization of disorder is reduced to t h e analysis of quenclied fluctuations in the local accessibility field (i.e. to a sigilal-processing problem), suitable for a macroscopic description of transport in terms of loc,al balance equations. Tliis article is organized as follows. In tlie following sectioii we discuss t h e evaluation of transport coefficients by considering tlie "Geda.iil;en experi~iiriit'~ of a 1-d hierarchical porous structure and introducing tlie concept of a local a.ccrssil)ility ficdtl. We then define tlie local accessibility for 2-(1 percolatioil clustcw ant1 analyze its propelrties. Even f'ar from criticality, the spatial Iiehavioiir of tlie 1oca.l accessil>ilit,y is highly irregii1a.r and Pxliiliits niiiltifra.ctal ipt,ioii of traiisport in porous nietlia features. We discuss tlie analogy I)c~twrcwt h r tl and the analysis of tiirl>ulent flows.

2. TRANSPORT COEFFICIENTS AND LOCAL ACCESSIBILITY Let us consider t h e ideal model of Iiintltwtl transport in a 1-d structure, under t h e hypotliesis that tlie diffusion corfficirnt niay be tlrfined as a function of tlie position D = D ( z ) . Starting from tlie equi valm ce lwt w w i i t rauspor t an tl stochastic cli ffereiit ial equations, and by making use of tlie exit-tinie cyiiation [S], the eqiiivalent diffusion coefficient D,, is related t o D ( z ) by tlie rehtioii

where 1 is t h e characteristic lengthscale of tlie structure. T h e discretized version of eq. (1) takes t h e form

where z, are tlie tliscrctizetl positioiis. 111 ii compl(*xpore 1lrtwolk, D(.cl) ca.11he coiisitlerctl as stochastic variables. If only strric iiiteractioiis are coiisitleretl, t h e diffiisioii coefficient depends on t h e position tlirougli its fiinctional tlepencleiice on tlie local accessibility 6, D ( x j ) = D ( & ( z ; ) wliicli ) can be t1efiiic.d as tlie ratio between the pore radius a n d the solute radius. In this way a I-rl struc,ture is c1iara.cterized by t h e infinite hierarchy of pdf { g = ( ~ ~. ,. , c , , ) } , where g7Lrepresents t h e ptlf of liaving a t tlie lattice sites 1, ..,n tlie ..E,,. Tlie a.vera.gr difrnsion coefiici(wt < D,, > is given by accessibilities

,

In t h e case of homogcneoiis uncorrrlatetl tlisortlrr, we have 71

dElr..r&n)

= J-Jsl(E,) :=I

and eq. (3) reduces to tlie classical tlrfinition of tlie equivalent diffusion coefficient

(4)

199

Figure 1: a) Schematic representation of a pore network: P is the pore network; M the porous matrix. b) Pictorial representation of the meaning of eq. (9); the principal directions are indicated by arrows.

The introduction of local accessibility in the analysis of hindered transport simplifies the developments because the classical expression for the functional dependence of D ( E )on E can be applied (especially in the case of moderate disorder) [7], or can be derived from theoretical considerations. In the following section we define the notion of local accessihility iigorously and develop its characterization in the case of non-trivial disordered structures such as percolation clusters. 3. LOCAL ACCESSIBILITY IN PERCOLATION CLUSTERS

The introduction of local accessihility 1ia.s important implica.tions in hindered transport phenomena. In order to define it, let us consider a pore-network struc.ture P , figure 1 a). The simplest local function which can lie associa,tetl with P is the Characteristic function XP(4

The characteristic function enables us neither to describe the properties of the pore network in a simple way nor to classify the clusters by mea.ns of non-trivial scaling exponents. For this reason, it is natural to define a local accessibility field by taking into account the local structure around each point x E P , e.g. by specifying at each point c the average distance from the elements of the pore matrix M (figure 1 a). Let c E P Ed ( E dbeing the Euclidean d-tlimensional space). The family of straight lines starting from c is specified by means of rl-l angular variables w = ( W ~ , . . , W ~ - ~so)

200 that &,g*;s) is the point at a distance s from .r: on the straight line characterized by the value w_* of the angular variables passing through s. Consequently, the accessibility +,w) at the point s,in the direction w is the distance from of the closest element of the pore matrix M along the specified direction, and can be expressed as E(C,W)

= inf{slxP(g(z,u;s)) = 0).

The local accessibility directions

&(a)at

.?:

(7)

is the average of the previous expression over all the

where rnis(Rd) is the measure of the solid angle R,i in a rl-climensional space (e.g rnis(&) = 27r, rnis(R3) = 4 ~ ) .Of course, if s does not belong to P it ca.n l.ie conventionally assumed that E(C) = 0. Definition (8) of the local accessibility field can l i e considerably simplified in dealing with lattice models of pore-network striictures. In the case of lattice structures, instead of considering the integral (S), the local accessibility at a lattice site zican be expressed by the sum of the distances fro111 the closest elemrnts of the pore matrix along the principal directions associated with the first nearest ric~ighbours(figure 1 I)),

where N ( s i ) is the number of nearest nrighliouring sites of g i ,( N ( . r i ) = 4 for square lattices), and lj(zi) are the lattice lengths representing the distance from of the closer element belonging to A4 along the j-tli ~irincipaldirection. Definitions (8) and (9) focus attention on accessiliility regarded as a characteristic length associated with the average distance from an element of the porous matrix. It should be mentioned, however, that it is possible to piit forward other definitions based on volume-averaging techniques. As a. example, in a la.ttic-estructure the volume-averaged porosity E " ( Z ; ) may be defined as

+

where I, is the neighbourhood of the first N ( I , , ) newest sites of 4, N ( I r L= ) 2 4 7 ~ -1) 1, n = 1,2, .. in a 2-d square lattice. Of course, for percolation clusters, in the limit of large values of n , &v(zi.) tends to the percolation probability 11 homogeneously on the whole lattice. However, in many transport problem related to stcric interaction and size-exclusion effects, definitions (8) or (9) seems to be more appropriate. The reason is that the fundamental parameter descriliing solute accessibility into the pore matrix is the ratio between solute radius and the average pore radius. It is importa,rit to observe that eq. (9) can be generalized by considering other averages, i.e. by defining ~ ( z ,as ) the average of Clj over Z,. The results obtained i n this way a.re sulistantially analogous to those obtained by averaging l j according to rq. (9).

20 1

50

Y 40

50

Y 40

0'

10

20

30

40

x

50

Figure 2: Structure of the accessibility field in percolation clusters: a ) p = 0.65; b) contour plot of the accessibility field for 11 = 0.65; c) p = 0.95; d ) contour plot of the accessibility field for p = 0.95.

202

Figure 3: Accessibility distribution function g(&) for two-dimensional percolation clusters: a) p = 0.65; b) p = 0.70; c) p = 0.80 tl) p = 0.90; e) p = 0.95.

From the above discussion, the average pore radius c,an be evaluated as the average of the local accessibilities over all the structure, or i n terms of ensemble average by introducing local accessibility distriliution function g ( c ) . In the analysis of the distribution of the local accessibility field, two-dimensional square lattices were considered (the critical percolation threshold is pc = 0.593) for values of the percolation probability p ranging from p = 0.65 u p to p = 0.99 (i.e. far from criticality). The numerical sinmlations were performed on the infinite percolation cluster generated by using the Leath algorithm [9] i n order to avoid the influence of finite subclusters. The ) the correspondiiig contour plots of the local accessibility are spatial behaviour of ~ ( 2and indicated in figure 2 a)-d). For contour plots, the black clusters indicates regions with low values of accessibility. As tlie percolation probalility increases, the darker regions tend to disappear and the lattice is crossed by liuear channels at high local accessibility (lighter regions). Moreover, the spatial irregularity of the accessibility field E ( Z ) does not disappear for high values of p . To this high irregular spatial Iwliaviour corresponds a smooth distribution of tlie accessihility g ( ~ )as , can be seen from figure 3. 4. MULTIFRACTAL FEATURES OF THE ACCESSIBILITY FIELD

As we can see from figure 2, the spatial Iirliaviour of ~ ( xis)highly irregular, iniplying that even for high p the local porosity cannot be described by ineans of a smooth pointwise function. The spatial Iieterogeneity of E ( S ) can be analyzed by using standard techniques appropriate for singular distriliution (multifractal analysis [lo]). Since the local accessibility attains nou-negative values, it can be regartled as a probability measure upon normalization EN(Z)

= E(X)

/J

E(d)

(lT .

Multifractal analysis can be applied directly 011 E ~ , . However, since a percolation cluster well above criticality is spatially Iioiiiqyneous, tlir inea
203

Figure 4: Behaviour of

E N ( . r , y)

for fixed y; p = 0.80.

ized by a one-dimensional restriction of E N ( S ) = EN(.^, y), i.e. by analyzing the porosity distribution along one coordinate (say .r) for fixed v a l i i ~ sof y (figure 4). In this way, by defining the one-dimensional measure as

where S is the box length, tlie spectrum of generalized dimensions D ( q ) [lo] can be obtained from the scaling of the moments

The symbol < . > indicates tlie averagr of tlie iiioiiients with respect to the y-values (in our analysis the averages were calculated over 400 y-valiics in order to ensure an accurate statistical average of the data). In the present analysis, the characterization of tlie lieterogeneity by means of multifractal scaling has been applied in order to show t1ia.t the accessil)ility field i n percolation clusters exhibits singularities. A noit constant distribution of the generalized dimension D ( q ) is an indicator of multifractality. Of course, the analysis of the scaling of pi(y,6) is a simplification of the general niriltifractal aitalysis of the accessibility field considered as a two- or threedimensional measiae. For the tecliiiical details of the evaluation of the multifractal spectrum see [lo]. Figure 5 a) shows some results for the moments 2, for different values of q ( q = -2,2,10). As is apparent from this figure, we obtain power-law behaviour of 2, in the range of length-scales 1 < 6 < 1024, ( 6 is eva1ua.ted i n lattice units), from which we calculate the corresponding slopes D ( q ) , yelding D ( - 2 ) = 1.0s f 0.03, D(2) = 0.94 f 0.03, D(10) = 0.84 f 0.03, for I’ = 0.80. These results iiitlicate the manifestation of multifractality since a constant value for the generalizetl rlimmsions D ( q ) can be excluded also by taking into account the error Inrs. As the percolation probability decreases, the generalized dimension spectrum becomes broader. Of course, in the limit of 11 + 1,

204

1 0 '0

0

~

p

~

o

.

8

,

c

l

p.0.65 16'

0

4

10

20

30

1

x

1) 1

Figure 5: a) Scaling of the monieiits versus box length: log,(Z,) vs logz(S) for p = 0.80. b) Spatial correlation function C(.r) associated with the accessibility field E .

D ( q ) -t 1 for all values of q . Tlie results expressed by multifractal analysis and the spatial distribution of the local porosity (figure 2) are rather surprising, especially in that niultifractal features are present even for high values of p . Tlie local properties of the accessi1,ility field E can be further analyzed by considering the spatial correlation function

C(Z) = ( ( E ( 5

+2)-

< E > ) ( & ( 2 ) -< E >)) .

-

(14)

As shown in figure 5 I)), the correlation fiinction decays exponentially C(:c) exp(--z/A(p)) where the characteristic correlation leiigth A is a iiionotonically increasing function of p . As the percolation probability 11 increases, broader regions with high accessibility are present and the local structure of the accessibility field is correspondingly more correlated.

5. ANALOGY WITH THE DESCRIPTION OF TURBULENCE There is a strong analogy between turbulence and transport i n porous media described by means of a local accessibility field, if m e considers that temporal velocity fluctuations in turbulence correspond to quenched spatial fluctiiations in E ( Z ) . This picture has its macroscopic counterpart i n the classical niacroscopic theories of turt)ulence and transport in porous media based respectively on temporal antl local-volnnie averaging [I 1-12]. This analogy can be further developed by observing that the multifractal scaling characterizes both the distribution of turbuleiit eddies antl the clustering of' low-accessibility regions (see figures 2 and 5). Moreover, as in the analysis of turbulence, a detailed statistical characterization can be obtained, but difficulties are encountered ill deriving niacroscopic equivalent models linking the representatioiis of the fluctuations with their influence on transport properties. The macroscopic description of turbulence requires the introduction of simplified expressions (Prandl and Taylor model, Deissler empirical relation [l11) for the characteristic mixing length, necessary for developing the corresponding balance

205 equations. The same problem is encountered in tlie development of local-porosity analysis froin the level of a geometric characterization of porous matrices up to a form suitable for a macroscopic description of transport in porous media. From tlie definition of a position-dependent accessibility it is possible to develop a macroscopic theory of transport. This aspect will be developed elsewhere. Hovewer, it is important to note that the introduction of spatial fluctuation in the accessibility qualitatively furnishes flow-rate profiles analogous to those experimentally found in packed-beds [13]. Macroscopic equations based on the definition of tlie local accessibility can describe transport in a disordered pore network on the assumption that the structure of tlie network is not fractal or anomalous (in the sense of anoinalous transport as developed in [S]). A somewhat similar approach to heterogeneous porous media (not making use of a local description but applying averaging over particle-size distribution) is developed in [14] for the estimate of permeability. 6. DISCUSSION AND CONCLUSIONS

There are several aspects that should be pointed out. Tlie main thrust of tliis work is to describe a complex pore network as a position-depeiicleiit accessibility field. This enables us to analyze transport i n a classical way by taking tlie structural porosity fluctuations into account i n the expression of tlie coefficients entering in tlie balance equations. The numerical analysis of percolation clusters reveals that tlie local structure of tlie accessibility factor is highly singular and multifractal scaling has been observed even far froin criticality. Of course, tlie definition of tlie local accessibility field is somewhat arbitrary and other expressions can be proposed. Eqs. (8) and (9) are based on tlie physical modeling of size-exclusion plienoniena i n which tlie fundamental parameter governing tlie steric interactions is tlie ratio between solute and pore radii. Tlie application of tliis method of describing of porous structures can easily be transferred (see the general definition (8)) to tlie analysis of real pore networlts by making use of image-proc,essing techniques. This represents a natural generalization of previous analysis based on tlie correla.tion function associated with the characteristic function of a digitalized pore-network representation [I 51. Moreover, and this aspect is not of marginal importance, the definition of a local accessibility function enables us not only to c11ara.cterize a medium but also to apply this characterization in tlie analysis of transport properties. Tlie connection between these two aspects sliould be carefully analyzed in future works, both numerically and experimentally.

REFERENCES 1. M. Saliimi, C.R. Gavalas a n d T.T. Tsotsis, Chrm. Erigng. Scz. 45 (1990) 1443, and references tlierein.

2. E.T. Wilkinson and G . A . Davies, Clie771. Eiigiig. Sci. 44 (1989) 459. 3. M.A. Ioaniiidis and I. Cliatzis, C/wrn. ences tlierein;

E1ig1ig.

Sci.

48 (1993) 951, and rcfer-

206 4. G. Mason, in Characte~irationof Poro,us Solids, K.K. linger, J. Rouquerol, K.S.W. Sing and H. Kral (Eds.), pp. 323-332, Elsevier, Ainsterdam, 1988.

5. D. Stauffer and A. Aharony, Introduction to Percolation Theory, Taylor and Francis, London, 1992. 6. S. Havlin and D. Ben-Avraham, Adv. Phgs. 36 (1987) 695. 7.

H.Determann, Gel Chromatography,

Spriiiger V., Berlin. 19G4.

8. The mathematics of stochastic differential equations and of the exit-time equations can be found in: S. Karliu and H.M. Taylor, A Second Course in Stochastic Processes, Academic Press, New York, 1981; A. Lasota and M.C. Macltey, Probabilisiir Proyrrtks of Dfterrni~ttidic,Systems, Cambridge Un. Press, Cambriclge, 1985. Rclatrtl I)liysicd applications are presented in: R.N. Bliattacharya and V.Y. Gupta, L4'att.r Resour. Rf.s. 4 (1983) 938; M. Giona, A. Adrover and A.R. Gioiia, Procrmliigs I ( h i i f . on Chemical and Process Engineering, Florence 13- 15 May 1993, pp.59-(3. 9. T. Vicsek, Fractal Groudh Phcrioinoia, Wortll Sci., Singapore, 1992. 10. T.C. Halsey, M.H. Jensen, L.K. Iiatlanoff, I. Procaccia and B. Shraiman, Phys. Rev. A 33 (19%) 1141; P. Grasslwrger and I. Procxcia, Physica 13 D (1984)

34. 11. J.C. Slattery, Momentuni, Eric Publ., New York, 1981.

, atid Mass

Tra?tsfw i r i ('oit~tinua,R. Krieger

of Ilinnspo7.t Phenomena i n 12. P. Carbonell and S. Whitalter, in F!~ndnnre7~tnls Porous Media, J. Bear and M.Y. (hrapcioglu (Eds.), 111). 123-198, Martinus Nijhoff Publ., Dordrecht, 1983.

13. D. Vortineyer antl J . Scliiistcr, (,'hem. Engriq. Sci. 38, (1983) 1691; C. McGreavy, E.A. Foiimeny antl K.H. .laved, ( % e m . E1igr1g. Sci. 41 (198G) 787. 14. M.J. MacDonald, (2-F C l i i i , P.P. (iriillot, 1i.M. Ng, A / ( M J . 37, 1583, 1991.

15. P.M. Adler, C.G. Jacqiiin and .].A. Qiiiblim, Ittt. .I. A/lrdtiphase Flow 16, 691, 1990.

J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids Ill Studies in Surface Science and Catalysis, Vol. 87 0 1994 Elsevicr Science B.V. All rights rescrved.

207

HEAT AND WSS TRANSFER IN POROUS MATERIALS 'Ant6nio Heitor, 'Orlando Silva and ','Rui 1 2

Rosa

Departamento de Fisica, Univ. de Evora, Ap. 94, 7001 Evora Codex, Portugal Departamento de Fisica, I.S.T., Av. Rovisco Pais, 1000 Lisboa, Portugal

ABSTRACT Fom a study o f equilibrium states of a fluid inside a porous material, a equation which interrelates wncentration. temperature and pressure changes is obtained. Under the assumption o f local thermodynamic equilibrium this equation is combined with known heat and mass flux/gradient l a m to obtain an equation describing heat and mass fluxes coupled through the gradient o f fluid concentration (apliwbe t o mesopomus materials). From the analysis of some limiting cases it is found that these fluxes are strongly dependent on parameters defining adsorption isotherms and adsorption isobars. Finaly, it is outlined a method with the purpose of dealing with practical situations.

1 - INTRODUGI?ON

Transfer phenomena inside porous materials are of great importance in many areas (civil engineering, agriculture, catalysis, etc.). Heat and mass fluxes are proportional to temperature and pressure gradients through the respective conductivities (generalized thermal conductivity and permeability). Nevertheless, the study of heat fluxes inside a porous material is somewhat more complicated than in the case of a non-porous solid because they are usually strongly coupled to mass fluxes which depend, namely, on the permeability of the medium. The attempts that have been made to correlate the conductivities (for ex: permeability) with the particular morphology of a porous solid have proved that such correlations are neither simple nor widely aplicable [1-31

-

Our purpose is to search for a model for coupled heat and mass fluxes that might be suitable to deal with practical situations. Permeability and generalized thermal conductivity coefficients used in such a model are to be determined from experimental measurements performed in a modified WickeKallenbach cell [4]. 2 - THEORY

Equilibrium states of a fluid inside a porous material may be related to the thermodynamic variables describing the external gas phase of the same fluid. Let subsystem A denote the FluidUporous matrizand let subsystem B denote the e d e m a [ gas phase. Equilibrium states of the whole system AUB are defined in the four-dimensional thermodynamic space (U,S,V,M) by the hipersurfaces: 0, = TSA - PVA +/&A ; 0, = TSB- PVB +/AM, (1) If the whole system undergoes a small perturbation (6T; dP), the quantities U,S,V,M of each system do readjust to the new equilibrium state. In particular for subsystem A:

208

This equation relates the mass change in subsystem A to the magnitude of the perturbation (6T; CP). The coefficients:

relate the changes in the acessible volume and entropy of subsystem A to changes in the chemical potential p which defines the state of the whole system and, therefore, do stand for the particular properties of each pair A-B (adsorbent/adsorbate). In fact,

where FA and HA are the Helmholtz free energy and the enthalpy of the adsorbed phase, respectivelly. Steeper isotherms will be expected when (6FA)N,T/(Cp)is large (vice-versa) and steeper isobars do appear in cases of large (CHA)N,p/(6p)(vice-versa). In practise, the coefficients 11 and 8 may be evaluated from adsorption isotherms and adsorption isobars, respectivelly In general

.

1120;8 5 0 . From (3) one concludes that mass concentration p=aMA (where a-1 stands for the quantity against which M A is measured - (mass or volume of the material)) of a fluid inside a porous material is dependent on temperature ( T ) and vapour pressure ( P ) . If variations 6MA, 6P and 6T are parametrized by spatial coordinates &',it comes from eq. (3): 3

--t

a-1grad p =IIgrad P

+Bgrad+T

(5)

In case of absence of a ljquid phase, mass transfer inside mesoporous media occurs through gas flow +

(JM), foilowing a gradient law:

-i

JM=-(kM/u)gradP

where kM is the permeability

of

the gas. Also, the heat flux

(JQ)(conduction,

the medium and

Y

(6) the kinematic viscosity of

convection and radiation) may

be described by: --+

J,

=-

i

T (7) where h is a generalized thermal conductivity, which has some dependence on T . Under the assumption of local thermodynamic equilibrium, one may insert (6) and (7) into (5) to obtain: grad

-i

JM =- (~M/IL)~-'&P

4

- (ekM/IIYQJJ,

(8)

which shows how heat and mass fluxes are interrelated through the gradient of concentration. On the other hand both fluxes are strongly dependent on parameters II and 8 as one may see from the analysis of eq. ( 8 ) in some limiting situations :

209

: ) e0 ~(flat

isobar-high T range)

In this case mass fluxes are proportional to the gradient of concentration (FicLian reghe) and are insensitive to

temperature gradients and therefore also insensitive to heat fluxes.

::)e/n<
low II (steep isobar, almost flat isotherm usually low T range (water vapor at low P case)) Mass fluxes are strongly dependent on temperature gradients. Heat fluxes play in this case the major role in mass transfer.

8
iii)II>>O,

3 - METHOD AND EXPERIMENTAL PROGRAMME From extensive determinations of data of the mass concentration p of the fluid under isobaric and isothermal conditions it is possible to obtain a thermodynamic chart of the system (materialuadsorbate]. The coefficients II and 8 can obtained from this chart. In cases of adsorption/desorption hysteresis one has a coefficient for each process. From measurements of mass fluxes in a modified Wicke-Kallenbach cell either in the absense and under a temperature gradient one can obtain the permeability kM and the generalized thermal conductivity 8. The d c i e n t a II, 8, kM and 8 enable us to compute the mass conductivity (k IIm) and MJ. the masslheat fluxes coupling coefficient (8kM/IIu8) at each point and thereafter predict the mass flux arising from a concentration gradient and/or from a heat flux (and vice versa).

141, [5]

It is offered, as a consequence, a method to choose the best drying path for a particular material and optimize the pair - energywnsumption/drying rate.

At the moment we proceed with determinations of data leading to a thermodynamic chart of the system porous cement/water vapor. Later on, the coefficients kMandkq will be determined in order to test the method. ACKNOWLEDGElbENTS This work was partially financed by European Community programme STEP (under contract n9CT090-110) and by Programa Mobilizador de CiGncia e Tecnologia (JNICT, Portugal)

REFERENCES 1. W. C. Conner et al., Roc. "COPS2" , 199, Elsevier 1992 2. J . F. quinson et al., Proc. "COPSB", 209, Elsevier 1992 3. T. Sato, Proc. "COPS2", 283, Elsevier 1992 4. E. Wicke and R. Kallenbach, 2. Kolloid., 97 (1941) 135. 5. S. B. Bhowmik et al., Proc. "COPS2", 273, Elsevier 1992

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J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characrerizalion of Porous Solids Ill Studies in Surface Science and Calalysis, Vol. 87 0 1994 Elsevier Science B.V. All rights reserved.

21 1

J. SallBs, J.F. Thovert, P.M. Adler LPTM, Asterama 2, Avenue du TBlBport, 86360-Chasseneuil, France

Abstract Simulation of geological media with the same porosity and correlation function of the pore space as real ones can be performed. Then, programs able to solve the local field equations in any geometry are used to study various transport processes such as convection, diffusion, Taylor dispersion in these media whereby macroscopic quantities such as permeability, formation factor and dispersion tensor are obtained.

1. Introduction

The study of transport in porous media has been spurred on over the years by various industries of vital importance, such as filtration, oil recovery and more recently, hazardous waste repositories. Much has been written on this topic ; among the most recent works are : Dullien (1979), de Marsily (1986), and Adler (1992). This paper deals with the derivation of the local properties of porous media. Our analysis has two original features ; the first is the great emphasis given to the geometrical representation of the porous media. The second original feature is the determination of the macroscopic transport properties of these media from the numerical resolution of the local equations governing transport in samples of reconstructed media. Section 2 is devoted to the generation of reconstructed media from measurements made on thin sections. Section 3 is devoted t o the study of transport in these media. Permeability is addressed first and the Stokes equation is solved ; the numerical results are then compared to data obtained by Jacquin (1964) on Fontainebleau sandstones ; the ratio between them is always smaller than a factor 5 . Studies on diffusion and dispersion are, at the moment, limited to molecules o r particles such as colloids whose size is very small

212

compared to a characteristic size of the pores of the porous material. In the conclusion, some tentative remarks are made on the limitations of this methodology and on its possible extensions to the study of transport and deposition of particles in porous media.

2. Reconstructed media

Measurements Fontainebleau sandstones were selected here because they are known t o have remarkably simple properties. Several thin sections of these sandstones are shown in Figure 1. The pore space is obtained by injecting a dyed glue into the medium ; then the sample is cut and the pore space is replaced by the dyehardened glue. Sections (about 20 pm thick) were obtained by abrasion of the samples. The pore space is clearly defined since the glue is dyed red ; colour pictures of these section can be taken with the help of a microscope. The statistical geometric characteristics of the pore space can be measured when the phase function Z(x) is introduced Z(x) = 1 0

if x belongs to the pore space otherwise

1

where x denotes the position with respect to an arbitrary origin. The porosity

E

and the correlation RJu) can be defined by the statistical

averages (which will be denoted by an overbar)

(2.b)

where u =

&(u) = [Z(x>- E] .[Z(x + u)- El / (E - E2)

I I uI I. Notice that (E - E

~ in )

(2.b) equals var (Z) since Z2(x)= Z(x).

These measurements were made in a single, but otherwise arbitrary, plane since Fontainebleau sandstones are known to be isotropic. They were made by image analysis. The image must first be binarized as indicated in Figure 1. Some experimental correlation functions are shown in Figure 2 ; note that these functions do not depend very much upon porosity, since E vanes by a factor 3 in Figure 2.

213

Figure 1. Thin sections of the Fontainebleau sandstone. The scale is indicated on each picture by a bar which corresponds to 0.5 mm. The surface porosity of each picture is : (a)

E = 0.31 ;(b) E = 0.25 ;(c) E

= 0.21 ; (d) E = 0.1

I

I

I

10

20

30

u

40

Figure 2. Experimental correlation functions R, as functions of the translation u which is graduated in pixels. The length scale a is always equal t o cx = 3.8 pdpixel. Data are for : image a (+) ; image b (x) ; image c (V) ; image d (0).

214

Additional details on image analysis, size of the samples, the checking of the statistical homogeneity, etc., can be found in Adler et al. (1990).

Gemrationof random discrete variables withgiven average and cornlation finetion Let us now briefly sketch the reconstruction of three-dimensional random media. We want t o generate a three-dimensional random porous medium with

a given porosity E and a given correlation function ; the medium is homogenous and isotropic -but this last property is not essential-. It should be emphasized that the correlation function of isotropic media only depends on the norm u of the vector u (see Adler, 1981 not to be confused with the author of this paper). Similarly, we want t o generate a random function of space Z(x) which is equal to 0 in the solid phase and to 1in the liquid phase. Z(x)has to verify the two average properties (2) (Joshi,1974;Quiblier, 1984). It should be emphasized that the point of view is quite different here ;E is a given positive number < 1;R,(u) is

a given function of u which verifies the general properties of a correlation (see Adler, 1981)but is otherwise arbitrary. The analysis and the numerical process are detailed in Adler et a1 (1990). Results and discussion Examples of numerical thin sections inside the same cube are shown in Figure 3. If 1is the arbitrary length of the side of the cube, the horizontal crosssections correspond to values of the vertical coordinate z equal to 0,0.25, 0.5 and 0.75. The visual aspect of these sections is very different from the sections obtained by site percolation (see Lemaitre and Adler, 1990) ; the elementary cubes are gathered in larger pores because of the correlation function. It is believed that most of the isolated elementary cubes do not belong to the general pore system. These reconstructed media can also be represented in three dimensions with adequate software and hardware. An example is shown in Figure 4. The apparent realism of the porous medium is quite striking although some fine features do not exist in the reconstructed media. Further discussion on these media can be found in Yao e t al. (1992).

215

1

1

a

4

F’igure 3. Cross-sections of a sample of reconstructed porous medium. The pores are black ; the solid phase is white ; the boundaries of the sample are indicated by the broken lines. This sample has the same characteristics as the image displayed in Figure Id. The bar corresponds t o 250 pm. Data are for : Nc = 80, Lc = 16.

Figure 4. A three dimensional porous medium

216

3.Transportprocesses In this Section, we show how some of the macroscopic transport properties of these reconstructed media can be numerically determined by solving the local equations with the adequate boundary conditions. When possible, these properties are compared with experimental data.

Permeability Consider an infinite medium made of identical unit cells of size a.Nc. The low Reynolds number flow of an incompressible Newtonian fluid is governed by the usual Stokes equations : (3.a)

v p = pv2v

(3.b)

v.v=o;

where v, p and p are the velocity, pressure and viscosity of the fluid, respectively. In general, vsatisfies the no-slip condition at the wall (4.4

v = 0 on S,

S denotes the surface of the wetted solid inside the unit cell. The volume T~ of this cell is equal t o (NC.a)gBecause of the spatial periodicity of the medium, it can be shown (see e.g. Adler, 1990) that vpossesses the following property (4.b)

vis spatially periodic, with period a.Nc in the three directions of space.

As in Section 2, one considers a finite sample of size Nc.a (see Lemaitre and Adler, 1990). This system of equations and the conditions apply locally a t each point R of the interstitial fluid. In addition, it is assumed that either the seepage velocity vector?; is specified, i.e.

-

-1

v = T~

.

R ds . v = a prescribed constant vector

217

o r else that the macroscopic pressure gradient-

is specified,

(5.b)

Vp = a prescribed constant vector.

Since the system (31, (41, (5)is linear, it can be shown t h a t v i s a linear function of%. These two quantities are related by the permeability tensor K such that

Here K is a symmetric tensor that is positive definite. It only depends on the geometry of the system and thus can be simplified when the porous medium possesses geometric symmetries. A good example is given by the regular fractals studied by Lemaitre and Adler (19901, which possessed cubic symmetry; hence K is a spherical tensor, i.e. (7)

K=KI,

where I is the unit tensor. The same property holds for the average permeability K of the random medium since it is isotropic only in the average. The numerical method which is used here is a finite difference scheme identical to the one used by Lemaitre and Adler (1990). In order to evaluate our 4

methodology, the experimental data of Jacquin (1964) were used. The porosity

E

c

and the permeability K were measured on a large number of cylindrical samples with a diameter of 2.5 cm and a length of 3-4 cm. Note that the thin sections of Figure 1 were taken from some of these samples. The permeability data are shown in Figure 5 and they are seen not to be too scattered for real data. They are also compared to the numerical results ; it is important to note that this comparison does not involve any hidden adjusted parameter and that every quantity is measured or calculated. The calculated permeability differs by, at most, a factor 5 from the measured one. However, the general shape of the experimental curve is predicted in quite an accurate way as if a systematic “error” was incorporated in the measurement of the unit scale. Since Yao et al. (1992) showed that the moments of the phase function are identical up to the fourth order in real and simulated media, the discrepancy is likely to be due to the variations of the sandstone properties at some scale of intermediate length of maybe some few mm.

218

- lo4

..

K Imdyl

*.

- lo3

.

*

A

A :+'a.

-

.

.Em.

**%

.*

lo2

9.

2'

.

t

6.-

._

*. t

'.. 9

- 10

E #

I

I

Figure 5 - Permeability (for air in mD) as a function of the porosity E (Jacquin, 1964). The dots are the experimental data. The average numerical permeability K was calculated for the four previous samples plus an additional one ; they are indicated by crosses ; data are for Nc = 27, L, = 8 ; the vertical bars

L indicate the

interval of variation of the individual permeabilities.

0.05 03

0.2

E

Figure 6 - The formation factor F as a function of the porosity E. The dots are the experimental data. The average numerical formation factor is indicated by a cross. Numerical data are for : N, = 80. The vertical bars 1 indicate the interval of variation of the individual formation factors

219

Formationjktor The formation factor F is usually defined as the inverse of the dimensionless electrical conductivity o/oo of a porous medium filled by a conducting liquid phase of conductivity oo

In order t o determine F, one has to solve a Laplace equation in samples of reconstructed media with periodic boundary conditions at the surface of the unit cell. Again the numerical results can be compared with the experimental data obtained by Jacquin (1964) on the same samples as before. The data and the comparison are displayed on Figure 6. First, it should be noticed that the data are well correlated by the so-called Archie’s law (Dullien, 1979)

with a cementation factor m = 1.64. The comparison between data and predictions is better than for the permeability since the ratio between them is always smaller than 3. This improvement might be due to the fact that the electrical problem does not involve any length scale, while permeability has the dimension of the square of a length and therefore is likely to be more sensitive to any small change than the formation factor. Note that permeability was always underestimated while F is overestimated ; this is consistent since permeability is, so t o speak, a conductivity while the formation factor is a resistance. Again in view of the fact that no external parameter whatsoever is fitted, the agreement between experimental data and numerical predictions is the best one at the moment, to our knowledge (see also Adler et al, 1992).

Dispersion of apassive solute The physical situation can be summarized as follows : a neutrally buoyant, spherical Brownian particle is injected at some arbitrary interstitial position R at time t = 0 ; this particle is convected by the interstitial fluid and

220

simultaneously undergoes Brownian motion characterized by the diffusion coefficient D. Within the limit of long times, the moments of order m of the probability distribution are defined by (Brenner, 1980)

-

(R R')m P(R, Uat) d3R

(10)

where (R - R' Irn represents the m-adic (R - R')

... (R - R'). The probability density

is denoted by P(R, m).The two first moments verify (Brenner, 1980)

(1l.a)

dM1 lim -=v* dt t+

(1l.b)

Id lim -(M2- MIMI)=D* 2 dt t+

where

~

is the mean interstitial fluid velocity vector in T ~ the , portion of the unit

cell T~ occupied by the liquid phase,

(12)

-

1

v* = -

I,

v d3R

TL

The macroscopic dispersion tensor D* can be calculated in two different ways. The first one which is due t o Brenner (19801, can be summarized as follows : a general expression o f F i s derived from an analysis for long times which yields a vectorial convection-diffusion equation. The second classical manner t o d e t e r m i n e F i s to perform a Monte Carlo calculation by simulating the displacement inside the fluid of a large number of particles. In the rest of this Subsection, we shall only deal with the longitudinal component D*// of F. It is customary to represent its variations as a function of the Peclet number

(13)

IF

Pe =-

D

22 1

where D is again the diffusion coefficient of the solute particles in an infinite fluid. 1 is some characteristic length of the medium. Our routines were also checked with respect to existing results such as the ones by Edwards et al. (1991) for square arrays of cylinders and the classical experimental data by Gunn and Pryce (1969) for cubic arrays of spheres. They were also systematically used for various structures such as fractals and random media derived from site percolation. This material will be given in a forthcoming publication (SallBs et al., 1993). Results relative t o reconstructed media are shown in Figure 7. Although porosity is multiplied by a factor 3, the data are quite similar ; this may be explained by the fact that the dispersion tensor is an interstitial quantity like the interstitial velocity?. This figure only gives trends since it is based on a single sample for each porosity. A t large Peclet numbers, i.e. when convection is predominant, the dispersion coefficient can be represented by a power law

where a is approximately 1.6. This intermediate value of the exponent has been confirmed by the extensive calculations by SallBs et al. (1993) in this range of Peclet numbers. This might be due to the limited value of Peclet numbers which were used here, but it was difficult t o investigate higher values with an acceptable accuracy.

4. Concludingremarks

Realistic representations of real porous media are obtained by means of the method of reconstructed media based on the reproduction of porosity and correlation function. This method is very useful when the structure of the medium is not well defined. Transport processes can be systematically studied in these reconstructed media. This was made possible by the development of a series of numerical programs which are able t o solve the local field equations in any geometry made of elementary cubes. So far, the permeability, the formation factor and the

222

dispersion tensor have been investigated. Many extensions of this method can be envisioned. A t the moment, deposition in reconstructed media is actively studied by means of Monte Carlo calculations. A large number of particles is injected into a medium ; they are convected, they diffuse and they interact with the wall ; from time to time, the geometry of the medium is updated. A second important class of extensions is colloidal particles when they are small with respect to the pores. The specific interactions of these particles with the wall can be easily taken into account ; the colloidal forces are the superposition of van der Waals and double-layer forces. Many of the previous calculations can be done with these forces. A last class of extensions is multiphase flow in reconstructed media, a topic which is currently being studied by means of lattice gas methods.

D*/o

0

+ I

I

Figure 7. Dimensionless longitudinal dispersion coefficient D*/D for reconstructed media as a function of the Peclet number Pe = v*L/D. L is the correlation length of the medium. Data are for : 12A13 (E = 0.11, 0) ; C J (E = 0.21, V)

; 2A3 (E = 0.31, +)

223

References Adler, P.M. 1992 Porous media : geometry and transports, Butterworth/ Heinemann. Adler, P.M., Jacquin, C.G. & Quiblier, J.A. 1990 Int. J. Multiphase Flow , 16, 691-712.

Adler, P.M. 1989 Flow i n porous media, in The fractal approach to heterogeneous chemistry (ed. by D. Avnir) Wiley. Adler P.M., Jacquin C.G., Thovert J.-F., The formation factor of reconstructed porous media, Wat. Res. Res., !23, 1571. Adler, R.J. 1981 The geometry of random fields, Wiley. Brenner, H. 1980 Dispersion resulting from flow through spatially periodic porous media, Phil. 1Fans. Roy. Soc., London, A!297,81-133. Edwards, D.A., Shapiro, M., Brenner, H. & Shapira, M. 1991 Dispersion of inert solutes in spatially periodic two-dimensional model porous media, 1Fansp. Porous Media, 6,337-358. Dullien F.A.L, 1979, Porous Media, Academic Press, London Gunn, D.J. & Pryce, C. 1969 Dispersion in packed beds, D-ans. Inst. Chern. Eng. ,T341-T350. Jacquin, C.G. 1964 Correlation entre la permeabilite et les caracteristiques gbometriques du grks de Fontainebleau, Revue Inst. Franc. Pktrole, 19,921-937. Joshi, M. 1974 A class of stochastic models for porous media, Ph. D. Thesis, University of Kansas, Lawrence, Kansas. Lemaitre, R. & Adler, P.M. 1990 Fractal porous media. IV-Three-dimensional Stokes flow through random media and regular fractals, Dansp. Porous Media, 6,325-340. de Marsily, G. 1986 Quantitative hydrogeology, Academic Press, New York. Quiblier, J.A. 1984 A new three-dimensional modeling technique for studying porous media, J. Colloid Interf: Sci., 98,84-102. Sallks, J., Prevors, L., Delannay, R., Thovert, J.F., Auriault J.-L., Adler, P.M. 1993, Taylor dispersion in porous media. Determination of the dispersion tensor, Phys. Fluids A, in press. Yao, J., Frykman, P., Kalaydjian, F., Thovert, J.F. & Adler, P.M. High order moments of the phase function in reconstructed porous media, 1993, J. Coll. Interf. Sci. ,156,478.

This Page Intentionally Left Blank

J. Rouquerol, F. Rodriguez-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characrerizarion of Porous Solids Ill Studies in Surface Scicnce and Calalysis, Vol. 87 0 1994 Elsevier Scicnce B.V. All rights reservcd.

225

Modelling of mercury intrusion and extrusion M.Daf, I.B.Parkef, J.Bell', R.Fletchef, J.Duf€ie', K. S.W.Sing", D.Nicholson'

'ICI Materials, PO Box No 90, Wilton, Middlesbrough, Cleveland, TS6 8JE, U.K. Qxeter University,U.K. "Imperial College, London, U.K.

This paper reports the refmement and further application of the model of mercury intrusionextrusion first described at the COPS lI Symposium. To simulate the general patterns of hysteresis, entrapment and reintrusion observed in our experimental studies it has been found necessary to limit the number of sites available for the initiation of extrusion and to select particular spatial arrangements.This work has revealed that the interpretation of experimental intrusion data should be treated with caution. Thus it is evident that the shape and location of a s u e intrusion curve cannot provide a reliable basis for the assessmentof pore size distribution. We are now able to identifycertain distinctivefeatures of the intrusionextrusion-reintrusioncurves and to begin to classify different systems. In principle it should be possible to apply mercury porosimetry in a more rigorous manner than in the past, and it will be necessary to include the determinationof extrusion and reintrusion curves. 1. INTRODUCTION

Mercury porosimetry is widely used to determine the pore size distribution of porous solids by the analysis of the intrusion curve up to pressures of the order of 414 MPa. When the pressure is released after intrusion, the extrusion, i.e. retraction of mercwy from the porous structure reveals two general phenomena: hysteresis between intrusion and extrusion, and the entrapment of mercury when the pressure is reduced to one atmosphere. Furthermore reintrusion from the entrapped state occurs when the pressure is again increased. It is now believed that intrusionextrusion hysteresis, entrapment and reintrusion are dependent on the three dimensional pore network geometry of the material, and not simply on pore size distribution [l-51. This paper describes a model of mercury intrusion into and extrusion from three dimensional cubic networks. The validity of deriving the pore size distribution from intrusion data is investigated by modelling intrusion and extrusion in networks where the pore sizes can be assigned at random,and where there is some degree of spatial correlation. A simple model was proposed in an earlier paper [6],in which a systematic investigation of experimental intrusion behaviour was also reported. This work has now been extended and a systematic evaluation of the model undertaken, which will be reported in more detail elsewhere. The purpose of the present paper is to draw attention to

226

certain features which we consider to be important, and to propose a number of tentative classes of intrusionextrusion behaviour based on our systematic programme of modelling and experimentalmeasurements. 2. THE MODEL

This consists of a mechanism for intruding and extruding mercury in a three dimensional network whose characteristics can be varied. The network is based on a cubic lattice of nodes, each connected to its neighbour by a pore divided into three segments. In all cases the lattice consisted of 10*10*10 nodes. The radii of all segments, and the size correlation between the radii of the segments in the same pore, are specifiable in three ways: 1. all radii are assigned at random from a unimodal log-normal distribution whose

width, referred to as a "standard deviation" can be varied, 2. radii are assigned from two l o g - n o d distributions, specifying the ratio of the number of segments from each, then randomly assigningradii to each of the segments to generate an "intermingled"bimodal distribution; 3. two log-normal distributions which are physically separate within the network with, for instance, the larger pores on the outside of the network. The central segment may be either the smallest (SIC) or largest (LIC) in the pore, using a process of interchange after the initial random allocation, or left random.

Figure I . Part of the three-dimensional network showing a random distribution of segment size. The mechanism assumes that the Washburn equation holds for intrusion, and proposes that as intrusion proceeds small quantities of gas, termed "middle interfaces" are trapped in middle or end segments. Extrusion can only be initiated from these middle interface sites if there is a continuous path or thread of mercury to the outside of the network. If no path exists, the whole set of segments visited are flagged as "trapped", and therefore play no further part in the extrusion process. The number of middle interfaces declared at the completion of the intrusion stage can be reduced by random elimination in the model. Although it is possible that mercury may be entrapped as a result of an irreversible change in pore structure due to sample compression, this is not considered in the present work.

227

3. EVALUATION OF THE MODEL

Four aspects of the model have been evaluated, namely the effect of reducing the number of middle interfaces, the mode of allocation of segments to pores, the e f f i of the width of the distribution, and a comparison of intermingled and spatially separate bimodal distributions. 3.1. Reduction of middle interfaces Figure 2 shows the effect of varying the number of middle interfaces in a 10*10*10 network with a unimodal distribution, mean segment size of 1lOA and standard deviation (sd)of 18%. A total of 1546 middle interfaces were generated. Extrusion then produced a wedge shaped hysteresis loop, and gave a high level of entrapment (figure 2, curve A). The path of reintrusion was close to that of the extrusion. When middle interfaces were reduced to 30, the shape of the hysteresis changed from a wedge to a parallel loop with a horizontal region at the start of extrusion. Entrapment was reduced and the path of reintrusion closely followed that of the first intrusion. Reduction of middle interfaces to less than 10 had no appreciable further effect (curve 2). (see runs 1,2 in Table 1). Clearly the reduction in middle interfaces is an important parameter in modelling extrusion. 3.2. !%pent allocation Using a unimodal distribution with a mean of 1lOA and a sd of 18%, segments of pores were allocated to the 10* 10*10 network in three ways (i) randomly (R); (ii) with the largest segment in the centre (LIC); (iii) and the smallest segment in the centre (SIC). For extrusion, middle interfaces were reduced to 10 in all three cases. The results are shown in figure 3. There m small differences in the intrusion behaviour. Levels of entrapment were such that SIC>R>LIC. The paths of reintrusion were all close to first intrusion, with the same sequence as observed in the first intrusion. (see runs 3,4 in Table 1).

3.3. Effect of width of distribution Figure 4 gives the results of similar calculations with the sd=65%. The SIC model is omitted here. The effects of a wider distribution are to broaden the intrusion curve and the hysteresis loop, with a longer horizontal region at the start of extrusion. Entrapment is increased and the path of reintrusion does not meet that of first intrusion. (see Table 1). For distributions with a constant mean pore and segment size, the point of inflexion derived from the intrusion curve decreased with increasing standard deviation. In order to maintain a constant point of inflexion as the width of the distribution is increased, the mean pore and segment size of the distribution must be increased. (see Figure 5). This is indicative of percolation effects in the network.

228

Table 1 Unimodal distributions Run Mean Standard Pore/Seg Deviation Diameter %

Segment AGcation

Middle Interface Reduction

Entrapment %

A 1 2 3

4 5

6

7

110 110 110 110 110 110 110

18 18 18 18 18 65 65

LIC LIC LIC SIC Random Random LIC

10 10 10 10 10 10

64 40 40 32 36 63 66

3.4. Bimodal distributions Networks with bimodal distributions were set up in which the smaller set of segments had a mean diameter of 1 loll and the larger set had mean diameters which could be varied from 220 to 440A.The relative numbers of segments in the two sets could be adjusted for equal numbers or for equal total volumes. The widths of the two distributions could be varied from 1% to 50%, but were always equal. In all cases middle interfaces were reduced to 10. Location of the sets of segments was either (1) intermingled or (2) spatially separated as follows: 1.Radii from the two distributions were intenningled in the network. Where the sd and the separation between the means of the dstributions were such that they were clearly dstinguishable, intrusion and reintrusion displayed evidence of bimodality. Extrusion, on the other hand, did not reflect bimodality, and was delayed at the level of maximum intrusion, remaining horizontal over the critical pressure range of both sets of segments. (see Figure 6). The ratio of the volumes of the two distinct intrusions did not correspond to the ratios of the volumes in the two distributions when designatedon the basis of equal numbers of segments from each distribution: the apparent volume of the larger set of segments was significantly lower than that designated. (see Table 2). 2.The radii of the larger distribution were located on the outside of the network, surrounding the smaller set. Intrusion, extrusion and reintrusion all exhibited bimodality, giving rise to two separate hysteresis loops. The volumes apparently intruded into each set of segments corresponded to the volumes designated in the network when on an equal volumes basis. (see Table 2 and Figure 7). Clearly this behaviour can result from other arrangements exhibiting a degree of spatial separation, and is not unique to the one described here. Other workers have made similar observations [fl.

229

Table 2 Normrlised voluma intruded in bimodal distributions Run Type MeanPore DiameterA Normalised Intrusion Volume Designed in Derived from set 1 Set 2 Network Model 0.20 0.85 1 1 110 220 0.80 0.15 2 1 110 0.14 0.83 275 0.86 0.17 0.10 0.80 3 1 110 330 0.90 0.20 0.059 0.80 4 1 110 440 0.941 0.20 5 2 110 0.50 0.50 220 0.50 0.50

In above table type l=intermingled: equal numbers of poredsegments 2=spatially separated equal volumes of poredsegments 4. TENTATIVE CLASSJFICATIONOF INTRUSION-EXTRUSION BEHAVIOUR The results of these simulations taken together with many experimental intrusion-extrusion data on wellcharacterised systems allow us to propose certain tentative hypothetical classes of behaviour illustrated in Figure 8. 1.Class 2 is characterised by a steep intrusion curve and a clear limit to intrusion. Extrusion leads to a m o w parallel hysteresis loop and a small degree of entrapment. Reintrusion rapidly merges with the path of first intrusion. This behaviour represents a narrow unimodal system. 2.Class 2 in which there is a broader range of intrusion and a clear limit to intrusion. Extrusion leads to a broad hysteresis loop and a large degree of entrapment which is indicative of a wide range of pore sizes. The path of reintrusion merges with that of first intrusion more gradually than in Class 1. 3.Clms 3 exhibiting a steep intrusion but almost horizontal extrusion represents a complex system containing either a broad distribution of pores or very narrow entrances into larger cavities. Percolation threshold effects are very likely to play a more important role than usual in this type of structure.

230

4.Cluss 4 represents bimodal structures with a degree of spatial separation. There is evidence of bimodality in intrusion and extrusion, with hysteresis loops narrow and extrusion parallel to intrusion. Reintrusion indicates some characteristic bimodality. The relative pore volumes observed on intrusion can be directly related to the two pore systems. 5.CZuss 5 represents a more complex system than class 4. There is evidence of bimodality from the intrusion curve, but the extrusion curve extends over both intrusion processes. Reintrusion can indicate evidence of bimodality. This is indicative of intermingled sets of pores, leading to uncertainty in assigningvalues to the relative pore volumes of the sets of pores. 5. CONCLUSIONS l.A well-defined terminal plateau in the intrusion curve is indicative of the penetration of mercury into an identifiable total pore volume. On the other hand, an extensive extrusion

plateau is generally associated with a complex pore structure. 2.A very steep intrusion curve does not always signify a narrow unimodal distribution of pore size. This type of uniform pore structure generates unique intrusion-extrusion

behaviour in which both curves are steep and parallel with narrow hysteresis and low entrapment. 3.An intrusion c w e with two inflexion points is consistent with some form of bimodal distribution, but quantification is not possible if the hysteresis is wide and entrapment is large. However, in the special case of parallel curves and narrow hysteresis, it is likely that the two sets of pores are spatially separate and that the majority of narrow pores are entered through the wide pores. 6. FURTHER DIRECTIONS

This work has indicated the need for a clearer understanding of the mechanism of intrusion and extrusion and the limitations of the Washbum equation. In addition the simulation could be extended to other model network systems. 7. REFERENCES 1. Mann, R., Androutsopodos, G.P. 2. Conners, W.C., et al. 3. Gladden, L., Portsmouth, R.L. 4. Payatakes, A.C., Tsakirogloy C.D. 5.Matthews, G.P., Spearing, M.C. 6. Day, M., et al.

7. Park,C.Y.,Ihm, S.K.

Chem Eng Science, 1979,34,1203 J. Catal 1983,83,336 Chem Eng Science, 1991,46,3023 J. Colloid Interface Science, 1990, 137,315 Transport in Porous Media 1991,6,71 Characterisationof Porous Solids II, ~75,1991, Elsevier Characterisationof Porous Solids II, 1991, Elsevier

23 1

P

Intrusion

*

Rdnbusbn

200

150 PORE DIAMETERA

-I0

100

50

B=10MI A=1546MI ..__._.

__

Figure 2. Effect of reduction of middle interfaces (Ml) on intrusion-extrusion and reintrusion in unimodal distribution (Av. diameter = 1 1 OA,sd = 18%)

0

w

“3 z

204

200

180

160

120

140

100

80

PORE DIAMETER A

SIC

LIC

__

Random

...._.

Figure 3. Comparison of random-LIC-SIC allocation of segments in unimodal distribution (Av. diameter = 1 lo& sd = 18%)

60

0

232

-

_.._ ____-----

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

Intrusion

Extrusion

*

RNnlrusim

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

I

I

I

- 0

Figure 4. Effect of width of distribution on intrusion-extrusion and re-intrusion in unimodal distribution (Av. diameter = 1 lo& sd = 65%)

300

4

250 -

150 -

1000

'

I

20

'

I

40

"

60

'

'

80

I

100

"

120

'

140

WIDTH OF DISTRIBWION (SDK)

Figure 5 , Relationship between width of distribution and its mean pore size for constant point of inflexion

233

Figure 6. Behaviour of bimodal intermingled distributionswith equal numbers of pores (Av. diameter = 11 OA,440A, sd = 18%)

7 / /

Figure 7. Behaviour of spatially separate bimodal distributions of equal volumes (Av. diameter = 11OA,220& sd = 18%)

Im

234

Class 1

Class 2

I

Pressure

Class 3

Class 4

Intrusion

Pressure

Class 5

7

loo'

Normalised

Pressure

['+Intrusion

I +Extrusion

I

Figure 8. Tentative classes of intrusion-extrusion behaviour

J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterizalion of Porous Solids I l l Studies in Surface Scicnce and Catalysis, Vol. 87 0 1994 Elsevicr Scicnce B.V. All rights rcscrvcd.

235

NEUTRON SCATTERING INVESTIGATIONS OF ADSORPTION IN MICROPOROUS ADSORBENTS HAVING CONTROLLED PORE GEOMETRY. J.D.F. Ramsay CNRS, Institut de Recherches sur la Catalyse 69626 Villeurbanne C&ex, France.

Abstract An understanding of adsorption processes in porous materials is of fundamental importance in processes such as gas separation, catalysis and chromatography and also in the uptake and removal of molecular species in liquid media. Neutron scattering is a powerful technique which can provide direct information on the structure and dynamics of adsorbed molecules and in particular the role and influence of the adsorbent microstructure (porosity, surface characteristics) on these properties. Here the applications of several neutron scattering techniques : small angle scattering (SANS), diffraction, incoherent quasielastic and inelastic scattering (IQENS) are reviewed. These techniques have been applied in investigations of several porous systems having a controlled pore geometry : silica gels, smectite clays (montmorillonite, hectorite) and microporous carbon fibres. Particular emphasis is given to the mechanisms of adsorption of water. Here the perturbation of the intermolecular H-bond structure, resulting from molecular confinement in micropores is discussed, together with the steric orientation of water molecules in aligned samples having a highly anisotropic pore structure. 1. INTRODUCTION

Understanding of the mechanisms of adsorption in microporous solids has improved considerably over the past ten years . This progress has arisen from advances in several areas. These include : theoretical analysis of adsorption isotherms ; computer simulation (refs.1-3) ; the synthesis of model porous solids (refs.4-5) and the application of new spectroscopic techniques (refs.6-8). These advances have been coupled with a marked growth in the technological interest in microporous materials, which include : carbons, zeolites, oxides and layered structures such as clay minerals. These materials have great potential in numerous catalytic and separation processes due to their exceptional porous structure, where often the pore shape is uniform and in the range of molecular size. In such a confined microporous environment molecular interactions are enhanced and this can lead to remarkable selective properties in adsorption and diffusion, which arise from steric effects (molecular sieving) and adsorption specificity for example. These features occur when the pore width is typically < 2 nm, which is the accepted criteria for distinguishing a microporous from a mesoporous solid (ref.9). It has long been realised that due to the enhanced adsorption interaction in

236

micropores, the fluid structure and thermodynamic properties of adsorbates are different from those in the bulk state. Consequently conventional methods for determining pore size and specific surface area from adsorption isotherms are no longer valid. This difficulty has led to the development of alternative spectroscopic techniques, such as NMR (refs.67) and neutron scattering (ref.8), to measure the microscopic properties (e.g. diffusion) of adsorbed species. Here the adsorbate molecule can act as a probe, which is sensitive to the confining pore environment, and can thus provide indirect information on pore size and shape. The object of this review is to outline the different types of neutron scattering technique which can be applied in the characterization of both the structure of porous solids and the mechanisms of gas adsorption processes. Emphasis will be given to investigations of adsorption in microporous solids having uniform pore geometry. These have especial interest for two main reasons : firstly, they can compliment developments in the computer simulation of adsorption in idealized model pore structures (ref.lO) ; secondly they can provide a more confident basis for the structural characterization of microporous materials having less defined properties. In this review we will cover three main topics : A - The nature of water in porous oxide gels and clay systems.

B - The mechanisms of capillary condensation and volume filling in oxide gels. C - The structure and adsorption behaviour of microporous carbon fibres.

Several neutron scattering techniques will be demonstrated : (i) (ii) (iii)

Incoherent Quasielastic (IQENS) and inelastic scattering. Diffraction. Small Angle Neutron Scattering (SANS).

2. ADSORPTION PROCESSES

Both incoherent and coherent scattering, can be used to investigate adsorption processes as is illustrated below. 2.1 Incoherent scattering The application of incoherent scattering is particulary applicable to the study of molecules containing hydrogen (1H) atoms due to its very large incoherent scattering (see Table 1). Incoherent scattering has been used extensively to cross-section, u investigate the #fusion and vibrational modes of adsorbed molecules (ref. 11). These result in a change of energy, of the scattered neutrons. For example for water, diffusive motions (translational and rotational) correspond to energy changes in the range of approximately 1 meV (Quasielastic) and librational modes arise in the range up to about 100 meV (Inelastic). The librational modes are very sensitive to hydrogen bonding and reflect perturbations in the structure of water confined in small pores and at surfaces (refs.1213). Some of these features have been demonstrated from IQENS measurements of water in porous silica gels for example. The energy spectrum of the neutrons which are scattered incoherently by the water has been measured by time of flight spectroscopy (TOF). It is observed that temperature has a marked effect on the TOF spectra. We note that the breadth of the quasielastic peaks (Figure I) decreases as the temperature is reduced from = 310 to 200 K indicating a reduction in the rate of diffusion. However the

237 water remains in a supercooled liquid state and cannot crystallize to give an ice phase. Cooling also results in marked changes in the inelastic spectrum corresponding to quantised rotations and librational modes. These are agah different from bulk ice and indicate a supercooled liquid or vitreous state. It can bc shown that perturbation in the structure of water becomes pronounced when the pore size is < 5 nm.

TIME O F F L I G H T ( A R B . UNITS)

Figure 1. TOF spectra of water adsorbed in porous silica at different temperatures: (a) 310; @) 273; (c) 255; (d) 240; (e) 200 K. N.B.The central narrow peak is due to quasielastic scattering and the bands to the left are in the inelastic region. Table 1 Incoherent scattering cross-sections, uinc of different atoms.

Atoms 1024 qnc/cm2

H

D

0

C

Si

79.7

2.0

0.0

0.0

0.0

238 Another area where IQENS measurements have been used extensively is in the investigation of the translational and rotational dynamics of different hydrocarbons (methane, propane, butane, hexane and benzene) in different zeolites (ref. 14). Thus it has been shown that the intracrystalline diffusion of molecules within the channels or cavities corresponds well with molecular dynamics simulations of hydrocarbon mobility. 2.2 Coherent scattering Coherent scattering has its counterpart in X-ray scattering which is an elastic scattering process (no-energy change). However the scattering cross sections of atoms for X-rays and neutrons are different. For neutrons the cross-section can be related to a coherent scattering length bc h. Values of bco can vary for ifferent isotopes of the same element. This is particuyary important fortydrogen (1H ; H) (See Table 2) ; and allows the important technique of contrast variation to be exploited (ref.15) as will be demonstrated. The mechanisms of adsorption processes in porous solids can be investigated by two different types of coherent scattering measurement (i) Diffraction and (ii) Small Angle Neutron Scattering (SANS), as illustrated below.

1

Table 2 Coherent scattering lengths, bcoh, for different elements

Element

10 2bcoh/Cm-2

H

D

0

C

Si

-0.374

0.667

0.58

0.665

0.42

Ti

-0.34

2.2.1 Diffraction Diffraction measurements can be used to distinguish the structural organisation of adsorbed atoms or molecules in porous media. This technique has not been widely exploited and has mainly been used to investigate water behaviour in meso and microporous oxides, as will briefly be described here. More recently however the technique has been applied successfully by Rouquerol and co-workers (refs. 16-18) to study phase transition behaviour of different gases (argon, krypton, methane, nitrogen, carbon monoxide) in MFI - type zeolites, as is discussed in the present meeting. Studies of water in silica gels and hydrated clay systems, with particular emphasis on the H-bond structure of the adsorbed phase compared with that in the bulk will be illustrated here. The diffraction of bulk liquid water (D 0) and ice are markedly different (see Figures 2a and 2b). For ice the diffraction is c?aracteristic of a hexagonal structure where there are four H-bonds associated with each oxygen atom as shown in Figure 3a (ref. 19). The structure of liquid water is shown schematically in Figure 3b. Here there are statistically on average between 3 and 4 H-bonds per oxygen atom. Although there is no Iong range order in liquid water there is however a short-range structure which fluctuates dynamically. This dynamic short-range intermolecular structure is influenced by temperature in the bulk (ref.20) and may be perturbed in a porous medium for example.

239

Figure 2. Neutron diffraction of (a) liquid D 0 at 298 K and (b) ice at 263 I?The peaks indexed in (b) correspond to the structure of hexagonal ice, Ih.

10

20

30

LO

50

201 deg.

I 0 OXYGEN

Ibl WATER

I

la1 ICE

WYOROGEN

Figure 3. Diagram depicting hydrogen-bonded structure in (a) hexagonal ice and @) liquid water.

240

It is well established that the freezing of water in mesoporous silica and other solids occurs at temperatures below 273 K - the bulk transition temperature. The depression in the freezing temperature is related to the pore dimension and this feature can indeed be used to determine pore shape and size (refs. 21). However when the size approaches the micropore range, = 2 nm, a regular H-bond network is unable to form in the confined pore space and the water remains in a supercooled vitreous state. This is demonstrated in Figure 4, which shows the effect of temperature on the neutron diffraction of hydrated porous silica (pore size = 2nm). It will be noted that the band at a 2 8 value of 22" narrows progressively, but even at 123 K the water remains in a vitreous state and the diffraction is quite different from bulk ice (cf. Figure 2b).

70 20 30 LO 50

10 20 30 LO 50 281deg.

10 20 30 LO 50

Figure 4. Effect of temperature on the neutron diffraction of hydrated porous silica, S1 (27 % w/w D20). Temperatures (K) are: (a) 298; (b) 255; (c) 250; (d) 245; (e) 233; and (0 123, respectively. Another application of neutron diffraction to determine the organisation of water in a confined pore geometry has been demonstrated with smectite clay gels, such as montmorillonite and hectorite. Here the porous structure is formed by the parallel alignment of the thin ( = 10 A) sheet like particles to give slit-shaped pores. The interlayer zone in these structures contains water and as the uptake increases the sheets swell apart but remain highly oriented (ref.22). It is indeed possible to investigate the ordering of water molecules with respect to the clay surface in such materials as a function of interlayer spacing. In such neutron diffraction experiments the bulk samples are oriented with respect to the neutron beam (viz.either parallel or horizontal). Although full details are not possible here neutron diffraction of D20 at different uptakes (corresponding to interlayer separations demonstrate that a fraction of water ( 2 3) layers is oriented and structured with respect to a surface. This water gives rise to the defined peak in the samples of parallel alignment : because of orientation effects it is not detectable in the horizontal alignment. For the latter a broader band is observed, which intensifies with increasing uptake. This band corresponds to water which is not significantly perturbed by the clay surfaces (viz. "free" water).

24 1 2.2.2 Small angle neutron scattering This is a very powerful technique for obtaining information about the properties of porous solids (refs.23-26). This is obtained from measurements of the scattered intensity, I(Q), as a function of angle, 2 8 or Q where Q = 4r sin

€)/A.

Examples of some recent developments are discussed in the following section and are covered by several authors in the present volume (refs.27-30). One exciting application, which has considerable potential for future development, concerns the SANS investigation of adsorption processes in porous media (refs. 31-32). This is made possible by the use of contrast variation which exploits isotope substitution effects, a unique feature of SANS which is not possible with SAXS. Thus SANS arises from fluctuations in coherent scattering length density in a material. Such fluctuations are caused by heterogeneities in a continous phase of uniform scattering density for example, such as particles in a liquid or pores in a solid, where the dimension of the heterogeneity is typically in a range = 10 - lo3 A. The processes of adsorption and fluid penetration in a porous medium may thus be investigated by selecting the scattering length density of the adsorbed phase, pa, to be identical to that of the solid, p For an evacuated solid the pores have a scattering density, p which is effectively zeros: P’ K contains information on the distribution of the size and form of the pores, the nature of the interfacial structure, and the respective volume fractions of the two phases. The value of p can readily be varied for water - by using mixtures of H 0 and D 0 for xample which ?or the bulk liquids have scattering length densities of -0 5% and 6.38 x 1018 cm-2 respectively. This novel approach has been applied to study the mechanisms of capillary condensation and micropore filling of water in the oxide gels, Si02 and Ce02 (ref. 32). Here the gels were composed of globular type parkings of spherical particles, giving materials of controlled pore size. Scattering was measured at progressively increasing P/Po and it was shown that the results for mesoporous gels were in accord with theoretical predictions of multilayer adsorption and capillary condensation. In contrast with microporous gels, the behaviour was consisent with volume filling, with a density of the adsorbed phase markedly less ( = 70 %) than in bulk water. In the present meeting, this feature of contrast variation has been applied by Hoinkis and Allen in SANS studies of C D6 adsorption in porous graphite (ref. 30). Other investigations by Schmidt and Smitg and their co-workers (ref. 27) discuss pore structure analysis using SAXS where the effects of contrast matching are applied. In this field further developments using SANS seem likely, particulary to investigate percolation effects in porous networks for example. Both kinetic effects of penetration, and different equilibrium conditions in adsorption and desorption processes are amenable to study.

3. STRUCTURE OF POROUS SOLIDS 3.1 Small angle neutron scattering Neutron scattering techniques can provide an insight into adsorption mechanisms and the microscopic properties of molecules and atoms in the adsorbed state as has been described. These developements are recent and somewhat specialised. However SANS is a technique which is now well established for the characterization of the structure of porous solids (refs. 23-25). There are however some recent advances which are likely to become increasingly important in the future. One in particular concerns the investigation of materials which contain an oriented porous struture, such as fibres and layer-like materials

242 (see Table 3). Frequently the pores are highly anisotropic and aligned with respect to a specific particle orientation. For these materials unique microstructural information can be derived from small angle scattering measurements with both neutrons and X-rays. These details are not obtainable from bulk measurements, such as adsorption isotherms. This application of SANS has recently been demonstrated with ceramic alumina fibres by Stacey (ref.33) and microporous carbon fibres by Ramsay and co-workers (ref. 34). Here we will illustrate the information obtainable by describing in outline the latter investigation.

Figure 5. Orientation of ACF. (a) horizontal and (b) parallel to the incident neutron beam with respect of the two axes on the two-dimensional detector. In activated carbon fibres (ACF) the micropores are slit-shaped and are formed by the parallel alignment of microcrystals of graphite along the axes of the carbon fibres (refs.35-37). This has been established by SANS with ACF samples oriented in two different directions to the incident neutron beam (see Figure 5). Results showing SANS along the two axes of the two-dimensional detector for ACF samples oriented horizontally indicate that the scattering is anisotro ic see Figure 6 ) . In (i) the scattering arises from the surface of the microcrystals (> 103 mig-1) which have a "smooth" surface; this gives a power law decrease in scattering of 4-4. In (ii) the scattering arises from the edges of the microcrystals which are "rough" and have a surface fractal dimension of = 3.5. This gives rise to a Q-3.5 power law as shown. When the fibres are oriented with their axes parallel to the incident beam (see Figure 7), the scattering is isotropic, as can be inferred from a theoretical analysis of scattering from oriented particules (ref. 22). In this situation the scattering contribution comes from both the surfaces and edges of the microcrystals, with the former dominating. The power law component is consequently now close to Q-4. Furthermore the neutron diffraction of supercooled water (D20)in this ACF sample shows that the water remains in an unfrozen vitreous state after cooling to 123 K. Such behaviour is similar to that described previously with silica gels and indicates that an ordered H-bond network as occurs in bulk crystalline ice cannot form in the confined volume of the micropores. It will be noted that anisotropic porous structures may occur in a wide range of materials as detailed in Table 3. For such materials analysis of scattering using two dimensional detectors can provide microstructural details (pore size, shape and volume,

243

Figure 6. SANS of oriented ACF. Fibers are oriented horizontally with their axes perpendicular to the incident beam. (i) SANS along the vertical axis. (ii) SANS along the horizontal axis of the detector.

Figure 7. SANS of oriented ACF.Fibers are oriented with their axes parallel to the incident beam. Scattering is isotropic and I(Q) is radially averaged data.

244 surface characteristics) which are important in many technical applications (structural materials, catalysts, membranes, adsorbents). Table 3 Materials containing anisotropic pore structures Carbon fibres Ceramic fibres Ceramic membranes Sol-gel films Clay and zeolite minerals Crystalline solids (during topotactic decomposition) Bio-inorganic skeletal structures With neutrons there are few limitations on the form and thickness of the sample under examination and the type of containment. Nevertheless of particular interest in the future will be the possibilities which arise from X-ray scattering using synchrotron sources. Here the very high intensities available will allow the examination of microscopic samples using microfocussed beams, and the investigation of kinetic processes as in decomposition reactions for example. The object of this review has been to show the value and versatility of neutron scattering techniques in the characterization of porous solids. This is also particularly evident from the growth in the number of papers on this topic covering the period of the three COPS Symposia.

REFERENCES

1 2 3 4 5

6 7 8 8a 9 10 11 12 13

D. Nicholson and N.G. Parsonage, "Computer simulation and the statistical mechanics of adsorption", p.97, Academic Press (London, New-York) (1982). N.A. Seaton, J.P.R.B. Walton and N. Quirke, Carbon, 22, (1989) 853. 2. Tan and K.E. Gubbins, J. Phys. Chem., % (1990) 6061. K.S.W. Sing, in "Characterization of Porous Solids 11", Eds, F. RodriguezReinoso, J. Rouquerol, K.S.W. Sing and K.K. Unger. Studies in Surface Science and Catalysis vol. 62, p.1, Elsevier, Amsterdam (1991). J.D.F. Ramsay and R.G. Avery, Studies in Surface Science and Catalysis, vo1.62, p. 257, Elsevier, Amsterdam (1991). T. Ito and J. Fraissard, J. Chem. Phys., 16 (1982) 5225. D.P. Gallegos, K. Munn, D.M. Smith and D.L. Stermer, J. Colloid Interface Sci., 119 (1987) 127. J.D.F. Ramsay and C. Poinsignon, Langmuir, 2 (1987) 320. J.M. Drake and J. Klafter, Physics Today, p. 46 (1990). S.J. Gregg and K.S.W. Sing, "Adsorption Surface area and porosity", Academic Press, London (1982). R.F. Craknell, P. Gordon and K.E. Gubbins, J.Phys. Chem., 92 (1993) 494. T. Springer, "Quasielastic Neutron Scattering for the Investigation of Diffusive Motions in Solids and Liquids", Springer Tracts in Modem Physics, 64, SpringerVerlag, Berlin (1972). J.D.F. Ramsay, H.J. Lauter and J. Tompkinson, J. Phys., C7 (1984) 73. C. Poinsignon and J.D.F. Ramsay, J. Chem. Soc., Faraday Trans., 82 (1986) 3447.

245

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

H. Jobic, A. Renouprez, M. B k and C. Poinsignon, J. Phys. Chem., 90 (1986) 1065. B. Jacrot, Rep. Prog. Phys., 2 (1976) 91 1. P.L. Llewellyn, J.P. Coulomb, Y. Grillet, J. Patarin, H. Lauter, H. Reichert and J. Rouquerol, Langmuir (In Press). P.L. Llewellyn, J.P. Coulomb, Y. Grillet, J. Patarin, G. Andre and J. Rouquerol, Langmuir (In Press). H. Reichert, U. Muller, K.K. Unger, Y . Grillet, F. Rouquerol, J. Rouquerol and J.P. Coulomb, Studies in Surface Science and Catalysis vol. 62, p. 535, Elsevier, Amsterdam (1991). D. Eisenberg and W. Kauzmann, "The Structure and Properties of Water", Oxford Univ. Press, Oxford (1969). J. Teixeira, M.C. Bellisent-Funel, S.H. Chen, A.J. Dianoux, J. Phys., (1984) 65. M. Pauthe, J.F. Quinson and J.D.F. Ramsay, this meeting. J.D.F. Ramsay, S.W Swanton and J. Bunce, J. Chem. Soc., Faraday Trans., Zp (1990) 3919. A. Guinier and G. Fournet, Small Angle Scattering of X-rays, Wiley, New-York (1955). A. Kostorz in "Treatise on Materials Science and Technology", vol. 15, Neutron Scattering, p. 227, Academic Press, (1979). B.O. Booth and J.D.F. Ramsa , in "Principles and Applications of Pore Structural Characterization", p. 9 7 - l l l Eds. J.M. Haynes and P. Rossi-Doria, J.W. Arrowsmith Ltd, Bristol (1985). J.C. Dore and A.N. North, Studies in Surface Science and Catalysis, vol. 62, p. 245 (1991). P.W. Schmidt et al. (this volume). P.G. Hall et al. (this volume). J.D.F. Ramsay et al. (this volume). E. Hoinkis and A.J. Allen (this volume). J.C. Li, M.J. Benham, L.D. Howe and D.K. Ross, in "Neutron and X-ray scattering Complementary Techniques", Adam Hilger (pub.) (1989) p. 155. J.D.F. Ramsay and G. Wing, J. Colloid Interface Sci., 141 (1991) 475. M.H. Stacey in "Studies in Surface Science and Catalysis", vol. 62, p. 615, Elsevier, Amsterdam (1991). A. Matsumoto, K. Kaneko and J.D.F. Ramsay, in Proc. of 4th Int. Conf. on Fundamentals of Adsorption, Kyoto, Japan (1992), (to be published). K. Kaneko, Y . Yamaguchi, C.Ishii, S . Oseki, S. Hagiwara and T. Suzuki, Chem. Phys. Lett., 176 (1991) 75. K. Kaneko, K. Kakei and T. Suzuki, Langmuir, 3 (1989) 879. K.Kaneko, M. Sato, T. Suzuki, Y . Fujiwara, K. Nishikawa and J. Jaroniec, J. Chem. Soc., Faraday Trans., 82 (1991) 179.

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J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solidr 111 Studies in Surface Science and Catalysis, Vol. 87 0 1994 Elsevier Science B.V. All rights reserved.

247

Characterisation of aluminas by small angle neutron scattering (SANS) and adsorption isotherm measurements. Peter J. Branton, Peter G. Hall, Astrid Mange1 and Ruth T. Williams. Department of Chemistry, Exeter University, England. Abstract

Nitrogen adsorption measurements and small angle neutron scattering (SANS) measurements have been recorded for a series of mesoporous, spherical aluminas with differing particle sizes and capping groups. The results from the two methods are compared and discussed. 1. INTRODUCTION

SANS is a useful technique for the study of surface area and porosity in solids'. The surface area may be obtained directly from the experimental data, without resort to assumptions concerning the system e.g. the volume of gas necessary to form a monolayer, and the shape and size of structures in the approximate size range 1-1ooO nm can be determined for example mixed micellesz. Other research areas in which SANS is used regularly include metallurgy, biology, polymer, glass and ceramic research3. The results obtained from SANS, i.e. the specific surface area and the average pore size have been shown to be in reasonable agreement with those using a standard nitrogen adsorption technique. The aluminas under investigation have been specifically designed for use in chromatography by Phase Separations Ltd4 and are the only commercially available HPLC spherical aluminas5. They all have the type y-structure and have been synthesised by artificial means. They are particulary useful as a normal phase support where there is often specific retention of compounds containing double bonds or substituted aromatics. The mechanism of chromatographic separation imposes many constraints on the supports. They must have a large surface area in order to achieve adequate separations: since the interaction forces in chromatography are weak (physical) the differences between them are small. This is achieved by using highly porous, finely powdered samples with pore diameters between 2 and 50 nm. Spherical particles, uniform in size ensure an even flow of the carrier medium. The supports must be inert and stable to resist physical and chemical attack oflby the solvents and elutes, conditions largely satisfied by silicas and aluminas. However, such compounds are prone to chemical attack as a result of their surface hydroxylations reducing chromatographic activity. Bonding of organic moieties to the surface will allow chromatographic supports with different surface characteristics to be manufactured. The bonded species range from hydrophobic alkyl chains to highly polar or ionisable groups, depending on the intended application. The use of alumina has been reported for the separation of basic drugs using aqueous methanol mobile phases with ion-pair additive&. The separation of peptides' has also been reported as has the use of its ion exchange properties*.?

248 2. EXPERIMENTAL

The y-aluminas investigated consisted of spherical particles of sizes 3, 5, 10 and 20 microns (referred to as A3Y, A5Y, AlOY and A2OY respectively). Two other aluminas with a particle size of 5 microns but with capping groups of (CH2)3CNand (CH2)17CH3 (referred to as A5CN and A5-Cl8 respectively) were also investigated. The precise final make-up of the bonded species is not known since the organic moieties can bridge and bind in different ways. Furthermore, not all surface hydroxyl groups can be displaced, for steric reasons. Thus Guiochonlo reports that even small groups cannot displace more than 50% of hydroxyl groups and large ones only around 25%. However, the residual hydroxyl groups do not usually affect chromatographic activities since they are rarely exposed5. The manufacturing details are not disclosed (by an agreement with Phase Separations Ltd). Isotherm measurements were recorded using a conventional volumetric technique with nitrogen as adsorbate at 77K and the SANS results were obtained on the LOQ diffractometer at the pulsed neutron source, ISIS at the Rutherford Appleton Laboratory, England. Neutrons in the wavelength range 2 - 10 A are used to investigate structures in the size range 10 - loo0 A from data collected over a Q range of 0.005 - 0.22 A-1 (Q is the momentum transfer or scattering vector and is defined as the difference between the wave vectors of the incident and scattered neutrons. For elastic scattering, Q = (4n/L)sin('p/2)where 'p is the scattering angle of the neutrons at wavelength A). 3. THEORY

The small angle neutron scattering phenomenon of X-rays or neutrons has been described in detail by Guinier and Fournetll. There are distinct scattering regimes with distinct slopes corresponding to the values of the wave vector, Q. ) to Porod's law scattering and The scattering in the large Q region (Lim I ( Q ) Q ~corresponds provides information on the surface area. For homogeneous particles (or voids) with sharp phase boundaries of surface area S, the Porod relationship is written Lim I(Q)Q.~= ?nSno*/Qa

for Ql>>l

where I is the shortest dimension of the heterogeneity of scattering length density %. The neutron scattering length density, k,is given by the following equation :

no = Zbp,LIM where b is the coherent scattering length amplitude, ps is the skeletal density, L is Avagadro's number and M is the molar mass. Thus a plot of InI(Q) versus InQ should yield a linear slope, having a gradient of -4 in the high Q range. In practice the density transition cannot be infinitely sharp. The density fluctuations within phases, due to surface irregularities, produce additional intensity components in the small angle region due to internal structure of the phases12. The deviations from Porod's law can be detected by a plot of I(Q)Q4 versus Q2. The finite width of the density transition produces negative deviations, the density fluctuations within the phases, positive deviations. Provided Porod's law is obeyed, the specific surface area can be evaluated by multiplication of the factor lipacking density (pp).

249 pp = mass of solid/volume of (solid+pores+space)

i.e.

S,, = {I(Q)@/%no2}{ "4)

In the small Q range 0.19<4<0.48 nm-1, the Guinier approximation is valid. At small scattering values of Qa. where a is the linear dimension of the particles, the scattering is approximately related to the radius of gyration, R,. For a system of randomly orientated homogeneous particles : Lim I(Q)Q*, = 1(O)exp(-Q2Rg2/3)

QRgsl

I ( 0 ) is the intensity at zero momentum transfer. For a sphere of radius r,. Q = &I5 rs

If a plot of InI(Q) versus Q2 is linear, the slope (-R,2/3) will indicate the presence of isdiametric particles. For the case of narrow cylinders of radius r, and height 2h :

I( Q) = I( 0)(d2Qh)exp(-Q2rc2/4)

QR,sl, Qhm, r,ah

R, = Ji/2 r, Cylindrical particles are characterised by a linear slope (-rc2/4) of a plot of In{I(Q)Q} versus Q2.

If the heterogeneities are polydisperse the Guinier plots will not be linear, indicating a distribution of Rg values. For a system of heterogeneities random in size, shape and distribution, a Debye analysis13 may be attempted. Certain porous solids can be characterised by a correlation function y(r) where y( r) = exp(-r/a) and a is the correlation distance. The scattered intensity is given by I(Q) = A/( 1+@a2)2

For Qa*I , the Porod relationship may be revealed by a Debye plot of which the constants a and A can be evaluated. Gradient = a2/dA and intercept = 1/dA

versus Q2 from

The specific surface area, S,, = (A/a4)(1/2nno2)(lip,) and it can be seen that the quantity A/al is a corrected form of the asymptotic value of I@ from the Porod plot. 4. RESULTS

A N D DISCUSSION

For all the aluminas studied, irrespective of particle size or capping group, normal Porod behaviour was observed as illustrated in Figure 1 using A5Y as example, with plots of InI(Q) versus InQ all having gradients between -3.9 and -4.0.This Q4 dependence on I(Q) indicates that the particles do have relatively sharp interface boundaries with the surrounding material. This is in contrast to some nonporous kaolinites and some microporous molecular sieves

250 investigated by us using LOQ, which deviated considerably from normal Porod behaviour. Any water present will contribute a flat background of incoherently scattered neutrons, that effectively rtxiuces the dependence of I(Q) on Q.

6

0

-2 -5.5

(&,,

-4.5

-1.5

-2.5

Figure 1. Porod plot for A N . Filled points indicate range used. Guinier plots were all of the same shape and are shown for A5Y in Figure 2. All of the aluminas behave according to the Guinier approximation for both isodiametric and cylindrical shapes although the plots were linear over a wider Q range assuming isodiametric shapes. The linearity of both plots suggests that the pores are of regular size and form and are probably a mixture of spherical and cylindrical pores but with predominantly spherical ones.

7 r

I

I

zt 1 '

0

m a

'

'

' 40

50

60

0

-1

0

1

1

10

20

10.''

1

34

o

1

1

,

49,

50

60

/ cm

Figure 2. Guinier plots for A5Y assuming isodiametric pores (left) and cylindrical pores (right). Filled points indicate range used.

25 1

For A5Y using the isodiametric approximation for O.l!kQ/nm-k0.61 , 0.9sQRg/nm-lG.0 giving a pore diameter of 12.5 nm. Using the cylindrical approximation for 0.28
--lo

'ta 8

[

-'mlo r h

8

C

0 *

!34

4

g*

P

. . I

4 0 0

0.

,

0.4

0.6

Rdative Pressure (P/&

1

0

0.2

0.4

0.6

0.8

Relative Pressure (PiPo)

1

Figure 3. Adsorption isotherms of nitrogen on A5Y (left) and AS-CN (right) at 77K.Different symbols denote different runs and filled symbols denote desorption.

252 Table 1 Surface area determination

.--

_ I _ -

Alumina ~

BET surface area I m2g-1

-

~~

A3Y A5Y A 1OY ABY ASCN A5-C 18 ~

..----.---

Modified Porod Debye surface area surface area I m2g-1 I m2g-1 __L-._I-

92 92 94 93

78 73

--

135 126 124 134 116 117 _ I -

--190 200 173 182 182 202

-

I _ -

The spread in surface area values gives an indication of the errors involved. Errors arise from the skeletal and packing densities, adsorbed water (none of our samples were outgassed before the SANS expenment) and experimental error e.g. through which points to draw a straght 1i ne.

5. CONCLUSION The SANS results provide a good insight as to the shape, size and distribution of the pores in the aluminas investigated. These results are well complimented by an analysis of the physisorpdon of nitrogen at 77 K. At small Q, the Guinier approximation is obeyed for both isodiametric and cylindrical shaped pores although there is a slightly better fit using the isodiametric model. The manufacturers value of the pore size agrees well with the Guinier value for spherical pores whilst the Kelvin analysis of the physisorption of nitrogen agrees with the Guinier value for cylindrical pores. Estimates of the surface area using a Debye analysis and a modified Porod analysis at larger Q show that both models are observed although the modified Porod results are in a better agreement with the nitrogen BET areas. The capped aluminas show a smaller BET area than the uncapped ones, however the SANS surface area results are unaffected by these groups. (The Porod region is unaffected by the capping groups). REFERENCES 1. P.G.Hall and R.T.Williams, J. Coll. Int. Sci., 104, 151 (1985). 2. H.Pilsl, H.Hoffmann, S.Hofmann, J.Kalus, A.W.Kencono, P.Lindner and W.Ulbricht, J.Phys.Chem., 97( 1 I ) , 2745 (1993). 3. E.Frikkee, Prospects for Applications of Neutron Scattering in Material Research. In Technicas Experimentales en Haces de Neutrones. Jaca, Spain (1986). 4. Phase Separations Ltd, Deeside Industrial Park, Deeside, Clwyd CH5 2NU U.K. 5. J.H.Knos (Ed), High-Performance Liquid Chromatography, Edinburgh University Press ( 1978).

6. C.J.C.M.Laurent, Ph.D. Thesis (1983). 7. H.Tanaka, M.Koike and T.Nakajima, Analytical Sciences, 2, 385 (1986). 8. G.L.Schmitt and D.J.Pietrzyk, Anal. Chem., 57, 2247 (1985). 9. T.Takeuchi, E.Susuki and D.lshii, Chromatographica, 25,480 (1988). 10. H.Colin and G.Guiochon, J.Chromatogr., 141, 289 (1977). 11. A.Guinier and GFournet, "Small-Angle Scattering of X-rays", Wiley, New York ( 1955). 13,. W.Ruland, J. Appl. Cryst., 4.70 (1971).

253 13. P.Debye and A.M.Bueche, J. Appl. Phys., 20, 518 (1949). 14. K.S.W.Sing, D.H.Everett, R.A.W.Haul, L.Moscou, R.A.Pierotti, J.Rouquerol and T.Siemieniewska, Pure & Appl. Chem., 57(4), 603 (1985). 15. S.J.Gregg and K.S.W.Sing, "Adsorption, Surface Area and Porosity", p.82, 2nd ed., Academic Press, Inc (1982).

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J. Rouquerol, F. Rodriguez-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characrerizaiion of Porous Solids 111 Studies in Surface Scicnce and Cahlysis, Vol. 87 0 1994 Elsevicr Science B.V. All rights rcscrved.

255

Pore Structure Analysis Via Small Angle X-Ray Scattering And Contrast Matching D.W. Hual, J.V. D'Souzal, P.W. Schmidt2, D.M. Smith1 1. UNM/NSF Center for Micro-Engineered Ceramics, University of New Mexico, Albuquerque, NM, USA. 2. Department of Physics, University of Missouri, Columbia, MO, USA.

ABSTRACT Contrast matching is often carried out using small angle neutron scattering (SANS) and adsorbed H20/D20 mixtures in an effort to obtain additional pore structure information. In this work, we explore the use of single adsorbates with similar electron density to those of the matrix so that contrast-matching may be conducted with small angle x-ray scattering (SAXS). In particular, we have used a series of halogenated organic liquids and several porous and particulate silicas and a microporous carbon to demonstrate contrast matching with SAXS. Also, halogenated silylation compounds have been used which yield surface modification groups with electron density similar to silica. From analyzing the change in scattering as a function of adsorbate loading or surface modification, pore morphology, pore size distribution and/or surface texture information is obtained. 1. INTRODUCTION Small angle x-ray scattering is an important technique for structural anaIysis of porous materials on the scale of 10 to 2000A. In scattering studies, the scattering intensity from a structure with a length d can be expressed as a function of qd, where q is the scattering vector and q = (4n/h)sin(0/2),

(1)

where h is the wavelength, and 0 is the scattering angle. Scattering data between the interval 0.1 < qd <1 can be used to estimate d. For qd>>l, information about the pore surface properties can be obtained. In this interval, intensity I(q) is

256

proportional to a negative power of q [1,2]: I(q)=Ioq-".

(2)

From the exponent a,one can find out whether the pore surfaces are smooth or fractal [2,3]. Other information can be obtained from 10 [4,5]. In a two phase system with constant electron density, the small angle scattering intensity can be expressed as

Therefore, the intensity will be zero when the electron density of the two phases are equal, even when the phases contain different materials. This method is often called contrast matching and is very useful in small angle neutron scattering. This technique is also used in light scattering studies by matching the refractive index but has rarely been used with x-rays. By combining SAXS with varying loading of a contrast matched adsorbate or varying coverage of a contrast matched surface modification agent, additional information can be obtained as compared to scattering or adsorption only. These include pore surface roughness, pore morphology (i.e. positive or negative curvature), and pore size. The change in scattering with adsorption/surface modification is conceptually illustrated in Figure 1. Since SAXS probes only changes in density, one is unable to determine if a particular solid exhibits pores of a given size, d, or a solid particle of the same dimension. However, the change in characteristic size as a function of adsorbate loading should indicate the net curvature of the pore space (see Fig 1.a). Pfiefer and co-workers [6] have previously shown that by measuring the change in surface area as a function of the quantity of a film adsorbed on the pore, the surface roughness could be assessed. This same approach may be combined with SAXS to yield roughness information (see Fig 1.b). At higher relative pressures for the adsorbed film, pore blockage will occur leading to pore size information (see Fig 1.c). Although some of these concepts have been demonstrated previously with SANS (for example, Ramsey [7]), we will demonstrate the approach with SAXS which should make the technique more generally available. 2. EXPERIMENTAL For solids, the electron density Pe can be computed from:

257

where v is the number of electrons per molecule, M is the molecular mass is atomic mass units, Pm is the mass density, and No is Avogadro's number. There are a number of liquid halogenated hydrocarbons that have electron density in the same range as silica and carbon and which have a vapor pressure sufficiently high at room temperature to facilitate vapor adsorption experiments. 1.a Pore Morphology

-

1.b Surface Roughness

4 Figurel. Conceptual diagram of contrast-matched adsorbates and SAXS for determining pore structure information. Table I lists the electron densities and mass absorption coefficients that we have calculated for a series of fluids with density that bracket silica and carbon (the solids of interest in this study). We should note that there is some uncertainty in the

258

solvent electron density as a result of uncertainty concerning the physical properties (this is particularly problematic for the fluid density in microporous solids) and in solid density since this depends on surface species associated with the solid (eg, surface hydroxyls). Table I. Electron Density for various compounds for contrast matching. Comvound water graphite silica bromoform chloroform dibromome thane chlorod ibromome t hane 1,2 dibromoethane bromochloromethane

Mass Abs. c d . (u)

Electron Density ( ~ ~ 4 3 ) 0.334 0.683 0.661 0.772 0.436 0.669 0.666 0.601 0.556

9.84 4.22 36.41 85.84 97.72 83.31 70.12 77.37 57.12

For contrast matching/adsorption studies, several porous materials were used; CPG-75, CPG-350 (control pore glasses from Electronucleonics), porous silica gel from Alltech, Amoco super carbon, and a B2 silica xerogel. B2 xerogels were made by a two-step acid/base catalyzed hydrolysis and condensation reaction with TEOS [8]. Particulate fumed silica, grades CAB-0-SIL L90 and EH5 (Cabot Co.), were also studied. Surface area and pore volume for each sample was determined from analysis of low and high pressure portions of nitrogen adsorption isotherms at 77 K and are reported in Table 11. Table 11. Surface area and vore volume determ ined from N:, adsorvtion. Samde CPG75 CPG-350 Alltech silica gel 82 xerogel Amoco super carbon

Surface area (m2/g) 224 67 471 570 2652

Pore volume ( c m 3 ~ 0.37 0.97 0.82 0.87 1.46

For loading the contrast matching reagents, two methods were used, one via vapor and one via liquid. For liquid loading the sample is put in a l m m capillary tube, dried under vacuum at 140 "C, the liquid is added, and the tube is sealed.

259

Vapor loading is accomplished at ambient temperature with a volumetric adsorption apparatus. The vapor pressure was controlled by varying the adsorbate temperature. An equilibrium time of 24 hours was used for each adsorption point. For silylation studies, the two particulate silicas (L90 & EH5) and the porous B2 xerogel were used ( 82 was also used in our previous study on trialkylsilylation [lo]). Two silylating agents were used: ETCS (ethyl trichlorosilane) and DBETCS (dibromoethyltrichlorosilane). If complete reaction of the three C1 groups occur with SiOH groups, the electron density of the DBETCS moiety will be very similar to that of silica. The ETCS will lead to a electron density which is between that of silica and air in the pores leading to a three-density system. For silylation, the silica was either used as received or refluxed with water and dried for a hydroxyl abundant surface, the rehydroxylation process does not change the surface property. Then, silylation was conducted by placing a certain quantity of dried silica into a benzene solution with various concentration of silylating agents, shaking for 24 hrs, and dried at 413 K for two days. The degree of silylation was calculated from the elemental analysis and represented by carbon content. Pore structure analysis was conducted using nitrogen adsorption/condensation, detail inref. [9]. Small angle x-ray scattering was performed at the University of New Mexico with a Kratky U-slit system using a linear position sensitive detector. Cu-Ko! line is used (h = 1.542 A) and the scattering wave vector (4) range is from 0.008 to 0.58 Al. The silylated samples were loosely packed in 0.5 mm thick cell for SAXS study, and the liquid and vapor loaded samples were in a lmm dia. capillary tube fixed in an airtight sample holder. The SAXS data were all corrected for smearing effects and only relative intensities of the samples were compared. 3. RESULTS AND DISCUSSIONS First, we tried to liquid load CPG-75 with the reagents listed in Table I in order to demonstrate complete contrast matching. By liquid loading, we hoped to avoid problems with condensing fluid from the vapor phase in possible large pores. By using fluids with electron density significantly smaller and greater than that of silica, we hoped to show scattering intensity going through a minimum. As can be seen (Fig. 2)., except for chloroform (which has an electron density significantly different than silica), the match is quite good. We should note that under these experimental conditions, I(q) variations less than one order of magnitude over the entire q range are essentially noise arising from background subtraction. According to the scattering curves, the reagents chlorodibromomethane and dibromomethane exhibit the best match. Similar results were observed for the Alltech silica gel and the Amoco super carbon. The relatively small effect of electron density for solvents other than chloroform is a result of the square dependence of the electron density difference (Equation 3). For silica, a difference in q of 0.05 will result in a scattering intensity which is only -1% that for air in the pores of the solid. Therefore, small changes in electron density

260

due to changes in fluid packing density or surface specie concentration will be minor. In order to demonstrate the effects of contrast matching adsorption on SAXS for surface roughness and pore size, the CPG-75 was vapor loaded with dibromomethane at a wide range of relative pressures. The plain (unloaded) CPG75 has a peak in Figure 3 which shows the characteristic feature of the material (pore dia.- 80 A). The slope at large q has been interpreted as a fractal dimension of -2.2. At low relative pressure, the adsorbate fills up the surface roughness. This is manifested in a flat tail at large q which moves to smaller q as the thickness of the film increases. At these low adsorbate relative pressures, the 80 A peak does not move significantly. We think it is because the size change is small (i.e., the film thickness is less than 10 A) and because the pores contain both positive and negative curvature. Since this material exhibits a monomodal pore size distribution, a gradual change in the SAXS pore size is not observed during increasing adsorbate loading but rather a sudden drop in scattering intensity is observed when a relative pressure, PIPo, is reached which causes condensation in the majority of the pores. We have calculated this relative pressure value to be -0.8. There is still a hump for the 100% vapor loaded CPG sample which means that the contrast is still not perfectly matched or, more likely, that all of the pores in the sample were not completely filled during the 24 hour equilibration time. A previous study of silylation with 82 xerogels showed that the pore size distribution of the sample may be narrowed and the pore size is reduced by a dimension comparable to the organic group diameter. Silylation appears to selectively modify the large pores in the size distribution and also smoothes the pore surface. However, for these samples, it seems that silylation does not affect the surface significantly. Also for highly silylated samples, the SAXS curve seems to show a crossover at q-0.2. Below that region, we obtain a Porod slope less than -4 (Fig. 4), we believe this is due to the fuzzy boundary contained on the surface which smears the effect of silylation. Schmidt and co-workers previously observed a decreasing slope with increasing coverage of large R silylating agents with values of the slope approaching -5 and attributed this to the presence of a diffuse layer of varying electron density contrast between the silica and the pore (the so-called fuzzy boundary theory) [10,11]. If one can match out this diffuse layer effect, then the study of silylation by SAXS will be much more straightforward. For testing the fuzzy boundary theory, two kinds of fumed silica (CAB-OSIL) were used. One had a smooth surface (L90) and one with a rough surface (EH5). We found that when silylated with DBETCS, SAXS results (see Figure 5) show that the Porod slope does decrease with increasing concentration of silylating agent. EH5 exhibits a smooth surface (with slope of -4) after silylation whereas the Porod slope for L90 changes slightly for L90. From nitrogen adsorption, as the silylation level increases, the surface area of both L90 and EH5 decrease which also supports a smoothing of the surface. With vapor loaded dibromomethane on these samples, the Porod slope of EH5 goes from -3.45 to -4, while for L90 (which started as a smooth surface with slope of -4 ), it increased to -4.22 (Figure 6 )

26 1

Cheng, Cole, and Pfeifer have studied the adsorption of films on fractal surfaces [12] and showed the above effect. A thick liquid film adsorbed on the fractal surface of a substrate that had the same electron density as the adsorbed film. They found that in this adsorption process, which they call defractalization, an adsorbed film of nominal thickness D is adsorbed mainly on the regions of the surface where the surface roughness is characterized by length scales not exceeding A. The film tends to smooth out the roughness in these regions, which then appear smooth, and for qA >> 1 the calculated intensity of the small angle scattering can be described by Equation I(q) = 10s-a,with a=4. On the other hand, for qA << 1, the surface scatters as if it were fractal, with a = 6 - D. Scattering data will provide direct evidence of an effect that the adsorption data could confirm only indirectly. 4. CONCLUSION In this study, we found out that with a proper contrast matching fluid (similar electron density as silica or carbon), one can successfully match out the scattering from the mother matrix. The combination study of small angle x-ray scattering and adsorption contrast matching should be an effective way for pore structure analysis of porous materials.

5. ACKNOWLEDGEMENTS This work is supported by the US Department of Energy (DE-FG22-91PC91296) and by the UNM/NSF Center for Micro-Engineered Ceramics, a collaborative effort supported by NSF, Los Alamos and Sandia National Laboratories, the New Mexico Research and Development Institute, and the Ceramic Industry. The authors gratefully thank CMEC staff J. M. Anderson and J. L. Thole for the sample preparation. Elemental analysis by R. Ju is also appreciated.

REFERENCES 1. J. E. Martin, A.J. Hurd, J. Appl. Cryst. 20,61 (1987). 2. H.D. Bale, P.W. Schmidt, Phys. Rev. Lett. 53,596 (1984) P.W. Schmidt, in "The Fractal Approach to Heterogeneous Chemistry", Ed. 3. D. Avnir, p.67 Wiley, 1898. 4. P. Pfeifer, P.W. Schmidt, Phys. Rev. Lett. 60, 1345 (1988). A.J. Hurd, D.W. Schaefer, D.M. Smith, S.B. Ross, L. Lemehaute, and S. 5. Spooner, Phys. Rev. B 39,9742 (1989) P. Pfeifer, M.W. Cole,, and J. Krim, Phys. Rev. Lett. 62 (1989) 1997. 6. J. Ramsay, Characterization of Porous Solids 11, Ed. F. Rodriquez-Reinoso, 7. p235, Elsevier, (1990). C.J. Brinker, K.D. Keefer, D.W. Schaefer, C.S. Ashley, J. Non-Cryst. Solids, 48 8. (1982) 34.

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263

Determination of Anisotropic Features in Porous Materials by Small-Angle X-Ray Scattering J. S. Rigden, J. C. Dore and A. N. North8 'Physics Laboratory,University of Kent, Canterbury,Kent, Cl2 7NR, UK. Some synthetic and natural materials exhibit anisotropic features due to the way that they have been fabricated. Small-anglescatteringtechniques with x-rays or neutrons may be used to probe this anisotropy by observation of the azimuthal variation in scattering intensity from an oriented sample. Results will be presented for a series of materials, in either fibre or disk form, which give distinctive patterns corresponding to ordered or disordered structures with spatial characteristics in the 10-2000Arange. The possible extension of the method to other materials and further development of the technique is also considered. 1. INTRODUCTION

Many porous solids show complex structural characteristics, but the information obtainable from most techniquesnormallypermits only an approximatemodel representationof the detailed geometrical features to be made. In most cases the essential properties may be conveniently modelled by a pore-size distribution function, P ( r ) , but it is rarely possible to determine information about the shape or orientation of the actual pores. Some materials have structures in which the alignment of non-spherical pores can play an important role in the functional properties of the sample as a whole. It is therefore desirable to study these anisotropic properties using experimental methods sensitive to orientational characteristics. One of the most suitable techniques for probing such features is small-angle scattering. The present paper reports some preliminary studies by S A X S and USAXS of porous fibres and membranes. 2. THEORY

The general formalism for small-angle scattering of x-rays ( S A X S ) or neutrons (SANS) has been presented in various review papers [l]. The measured intensity, I(Q ) ,as a function of the scattering vector, Q,for each scattering angle 8, may be expressed for x-rays as

for Q = sin where pr ( r ) representsthe spatialdistributionof the electron densitythroughout the medium. In most cases the expression can be simplified by writing model functions for prjr) and considering an average over all orientations. It is also convenient to make a low-Q approximation for many particulate or pore systems:

264 for [)I?,

< 1 where f?,

is the radius of gyration given by

and defines the overall size of the particle or pore. For anisotropic systems, these approximations cannot be made and the observed scattering pattern is not simply a function of the magnitude of the Q-vector. If the sample has a preferential direction represented by an axis of symmetry a, the phase factors iQ.r, in the amplitudes of scattered waves cannot be averaged and the resulting pattern is then dependent on the relative orientation of Q and a, i.e. the I ( Q ) function is no longer radially symmemc. The intensity function has been calculated for many different scatterers [2]; for the case of an oriented rod I ( Q ) is given by [3]:

I ( Q i = .4

Jl(QR,sin3) /' [sin(QHcos3) (Q H c o s 3 ) (QR,sind)

.o

sin 3 d3

(4)

for a rod of radius R, and length 1 = 2H, where '4is a constant, J l ( 5 ' ) is the fust order Bessel Function of the parameter 5 and Y is the angle between the rod axis a and the scattering vector

Q. The main features of the general expression are obviously retained for specific orientations, i.e. for scattering with Q parallel to a the spatial dimension being probed is the length of the cylinder I , leading to an intense but steeply falling distribution; for Q perpendicular to a, the I ( Q j function is mainly influenced by the radius ( a << 1 ) and has a broader, less intense distribution. A schematic representation illustrating this phenomenon is presented in Figure 1.

Q Figure 1. Schematic diagram of anisotropic scattering illustrating the differences between scattering parallel and perpendicular to the fibre axis.

265 3. SAMPLES 3.1. A1202 Fibres Some alumina fibres, made by ICI plc using a sol-gel process, were supplied by M. Stacey. The individual fibres have a typical diameter of 0.4pm and are mesoporous with a solid phase of 11-alumina and an apparent crystallite size of 60A [4]. The porosity is typically, 30-40% and the pores are believed to be cylindrical with a preferred ordering with the pore axis parallel to the fibre axis [4]. 3.2. A1203 Membranes Some alumina membranes, supplied by Anotec Separations Ltd., now part of Whatman Scientific Ltd., have been studied by USAXS. The membranes were developed initially for filtration purposes and show a very narrow pore size distribution, the pores being formed by an extended. honeycomb-like structure. The formation of pores from anodic oxidisation of aluminium [5] has been possible for some time, however, the films lay in contact with the alunliniuin layer. A method developed by Anotec [ 5 ] , of successively reducing the anodising voltage, causing the production of smaller pores near the base layer, eventually causes perforation of the barrier layer and separation from the base aluminium. In this way membranes may be constructed which show varying pore sizes, evolving from the initial m a t h pores. The membranes available for USAXS studies were (a) the initial pore matrix, with pore diameter 0.2p m ,and lengh 60pm, (b) the initial pore matrix (a) above, with a smaller 0.3pm layer of smaller pores, diameter 0.02jIl?l. A micrograph of the top face of membrane (b) and a cross-section through the layers are shown in Figure 2.

Figure 2. Electron micrographs showing the top of, and cross section through, a 0.02pm membrane.

266

3.3. Carbon Fibres Some carbon fibres were provided by the Alicante group [ 6] ,prepared from an isotropic pitch produced by Showa Shell Oil Co. Ltd. The pitch was spun at a temperature of 553K and stabilised at room temperature by a series of temperature steps to give a general purpose microporous fibre of 20-40prn diameter. Gas adsorption measurements (COz and Nz) have characterised the sample as possessing a micropore volume of 0.25 x 10-6m3g-1 and a surface area of 640in2g-'. 4. EXPERIMENTATION

4.1. SAXS The conventional small-angle scattering arrangement is shown schematically in Figure 3. An arrangementof optics produces a monochromaticbeam of wavelength I .SA,which is collimated by a series of slits. The x-rays then pass through the sample and are scattered. The outputs from two ion chambers, one before and one after the sample, are used to monitor the incident beam intensity, and also to account for losses due to absorption. The main path of the scattered x-rays takes place in an evacuated camera to reduce air scatter; increasing the length of this camera reduces the angular range of scattered radiation which may fall upon the detector. A position sensitive detector is used, which is calibrated into Q-space by the use of wet rat's tail collagen. The detector may be a simple linear or a sector (quadrant) detector; for the data presented in the present paper a sector detector of angle 70°is employed.

sensitive detector

Figure 3. Schematic diagram of the SAXS arrangement.

Figure 4. Schematic diagram of the USAXS arrangement.

Since data are collected simultaneously across the whole Q-range, any changes in beam current, absorption, etc., affect all points equally and global corrections may be carried out. The final Q-range available with a typical SAXS camera length ( 3 1 7 7 ) is -0.02 to 0.fi-I. 4.2. USAXS

The USAXS station at Daresbury is based on the arrangement originally proposed by Bone and Hart,Figure 4. The x-ray beam is incident on a first, silicon monolith which produces a highly monochromatic, collimated beam by four successive reflections from the 111 plane.

267 After scattering at the sample, the x-rays pass through a second, similar crystal which may be rotated by accurate stepper motors to isolate scattering from any particular angle. Ion chambers are used before and after the sample to account for changes in the incident beam, however, for USAXS, data are collected sequentially across the available Q-range and therefore each data point must be treated individually. The Bonse-Hart instrument shows extremely high resolution with a minimum step size of 5x to 0.03A-', although typical count rates are low at Q-vectors above -O.OlA-'. 5. RESULTS AND ANALYSIS A1203 Fibres The contrast between the empty pores and alumina is large for both x-rays and neutrons and the fibre may be readily studied using both S A X S and S A N S . Stacey has used a standard Kratky camera for SAXS and a standard S A N S instrument to study tows of fibres in detail. Figure 5 shows the SAXS scattering from a bunch of aligned fibres. The measurement was made at the SERC Daresbury Laboratory; the resolution of the SAXS data being far greater than either the SAXS or S A N S data of Stacey [41.

5.1.

0.2

0.1

-O.f

-0.2 -0.2

-0.1

0.0

0.1

0.2

Grange

Figure 5 . Contour plot of the anisotropic scattering from porous alumina fibres. The use of an area detector would be most appropriate for studying the SAS from the alumina fibres. The data presented in Figure 5 is an amalgamation of a number of data sets obtained using a quadrant detector. A number of measurements were made, in which the fibre axes of the aligned fibres were rotated in the sample plane. The resulting composite scattering pattern is therefore similar to that obtained using an area detector. In agreement with Stacey an anisotropic scattering pattern is observed. There appear to be two independent pore populations, some of the pores being randomly oriented generating isotropic

268 scattering, the other pores give anisotropic scattering which is characteristic of long cylindrical pores aligned parallel to the fibre axis. A detailed analysis of these specific pore distributions is beyond the scope of this short review. 5.2. Alz03 Membranes The scattering distributions for ceramic membranes (a) and (b) were collected using the Bonse-Hart camera of USAXS Station 2.2 at Daresbury. Membrane (a) (0.211172 matrix) showed rod little scattering in the USAXS range, consistent with scattering from an oriented 601~i11 with diameter 0.2pin. However, membrane (b) consisting of the initial matrix and smaller pores showed a varying scattering distribution, depending on the orientation of the pore axis with respect to the scattering vector Q. Figure 6 shows the collected scattering distribution for membrane (b) for the three different orientations illustrated.

0

1

2

3

4 5 .lo-'

6

7

6

Q-value

Figure 6. Scattering from the 0 . 0 2 p membranes at Position A (A), rotated to Position B and rotated to Position C (+).

(v),

For the membrane in Position A, the scattering distribution (A, Figure 6) could closely be fitted to scattering from an oriented 0 . 3n? ~ rod with a 0.0211rn pore diameter, consistent with the scattering from the narrow layer of smaller pores. Scattering from the membrane rotated from Position A to Position C (+, Figure 6 )was very small. In this position the membrane axis is at 45" to both the direction of the incident x-ray beam and the scattering vector Q.It is unclear without further measurements whether the collected distribution differs from the background scattering. Scattering from the membrane rotated 45" from Position A to Position B showed the most interesting form of scattering. At angles near Position B (within +lo") a series of regularly spaced oscillations appeared to be superimposed on a gradual fall offin intensity. Although the

-

269 intensity of these oscillations changed sharply with angle, disappearing within 510" of Position B, the position of the peaks did not change; this discounted theories that the oscillations resulted from the thickness of the pore layer and suggested that they originated from some feature parallel to the axis of the membrane which remained unchanged with rotation.

0

1

2

3

4

5

6

7

8

9

*lo-'

Q -v aIue Figure 7. Scattering from the 0.02pm alumina membrane at Position B showing the Q-3 exponential fall off and the interference function (inset).

In order to isolate these oscillations an exponential ( Q - 3 ) was fitted through the data points and the scattering was divided by this 'form factor'. The fitted exponential and resultant interference function are presented in Figure 7. The fist peak in this distribution occurs at a Q-value of 1.87 >: 10-3A-1, corresponding to an inter-pore distance of 3360A; this seems more likely to occur from the larger pore matrix (pore size 2000A) than the smaller pores (pore size 200A). A radial distribution function, produced from the distribution of pore centres derived from an electron micrograph of a heavily etched 0.2pt7t membrane, seems to corroborate this fact [7]. The derived separation distance between pore centres was found to be 3365A which strongly suggests that the large pore matrix is the cause of the oscillations in the scattering distribution at some orientations. It is unclear why the osciUations resulting from the large pores are only observed with the presence of the layer of smaller pores. This may be due to the fact that the scattering distribution for the larger pores falls off very sharply, due to the large thickness (60pn) of the membrane, so that the oscillations are masked by the experimental noise. It is possible that the presence of the form factor for the shorter pores, as observed in the scattering from the membrane in Position C, increases the scattering in the USAXS range and therefore reveals the presence of

270 the oscillations. An electron micrograph of the top surface of the 0.02pn membrane reveals that the small pores are arranged in small groups at the base of each larger pore, and this may be why the spacing calculated from the oscillations corresponds to the large pore separation. 5.3. Carbon Fibres

The scattering intensity I(Q.4) for the carbon fibres as collected at the S A X S Station 8.2 at Daresbury, is shown as a log-log plot in Figure 8a. It is notable that measurements for 0 = 0 -+ 45" are almost identical, but there is a sharp increase at low @values as the fibre is rotated to the parallel position (0 90"). In Figure 8b, the ratio I ( Q. 4 ) / I ( Q. 0) is shown, c o n h i n g the observations and suggesting that there is a high degree of anisotropy at Q-values below 0.05A-'but little effect at higher values. ---f

-2.0

-1.75

-1.5

-1.25

Log (0)

-1.0

-0.75

0.0

0.05

0.1

0.15

0.2

Q-vohre

Figure 8. a) Log-log plot of scattering from carbon fibres at varying orientations, b) the asymmetryfuncrion I ( Q . O)/I(Q.O). These results demonstrate the different behaviour for the various spatial regimes. The scattering from the micropores gives the main contribution to I(Q ) at large Q-values and suggests that there is no preferential orientation of these features relative to the fibre axis. The anisotropy at low-Q appears to arise from the microstructural features in the strumre of the fibres which result from the spinning process. These measurements were obtained with a sector detector (giving A0 = 135" at 6 = 90") and it seems likely that the actual distribution shows very strongly localised scattering with Q parallel to a. A further measurement with better angular resolution, i.e. using an area detector,would enable more information to be extracted. Additional work on C02-and steam-treated carbon fibres has already been conducted and will be reported separately [81. 6. DISCUSSION

The preliminary results presented in the previous section illustrate some of the advantages in using SAS techniques to study anisotropic features in porous materials of various kinds.

27 1

Further work is in progress to extract quantitative data and to link the information to other experimentalmeasurements. Although the basic concept of scattering from anisotropic systems has been known for many years it seems that relatively little work has been conducted on the subject except in the area of biophysics. The present results show that interesting research can be carried out for materials science and extended to many other areas of mesoscopic systems in soft condensed matter physics.

7. ACKNOWLEDGEMENTS We wish to thank Wm Bras and John Harries of the SERC Daresbury Laboratory for their assistance with the measurements. The carbon fibre sample studies form part of an extensive collaboration programme involving Prof. C. Salinas and Dr. D. Cazorla of Departamento de Quimica, Universidad de Alicante, Spain. We would also like to thank Roy Rigby of Anotec Separations(now Whatman ScientificLtd.) for provision of the aluminamembranes and Martyn Stacey of fCI plc, Runcom, for the alumina fibres. ANN would like to thank the SERC for financial support in the form of an Advanced Fellowship.

REFERENCES 1. J. C. Dore and A. N. North, p245, Characterisation of Porous Solids II, F. RoderiguezReiniso, J. Rouquerol, K. S.W. Sing and K. K. Unger (eds.),Elsevier Publishers.J. C. Dore, A. N. North and J. S.Rigden, special issue of J. Radiation Physics and Chemistry, P. Bames (ed.), to be published 1993. 2. 0. Glatter and 0. Kratky, Small Angle X-ray Scattering, Academic Press, 1982. 3. I. Livsey, J. Chem. SOC.Faraday Trans. It.83 (1987) 1445. 4. A. F.Jones, I. B. Parker, and M. H. Stacey, J. Appl. Cryst. 24, (1991) 607. 5. R. C. Fume-, W. R. Rigby, and A. P. Davidson, Nature 337, (1989) 147. 6. M. A. Gardner, A. .N. North and J. C. Dore, C. Salinas and D. Cazorla, this issue. 7. J. S.Rigden, Development of Ultra Small-Angle X-Ray Scattering for Studies of Heterogeneous Systems, Ph.D Thesis, University of Kent, 1993. 8. D. Cazorla, Private communication.

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Characlerizaiion of Porous Solids 111 Studics in Surfacc Scicnce and Calalysis, Vol. 87 0 1994 Elscvicr Scicncc B.V. All rights rcscrvcd.

273

Characterization of pore size in activated carbons by small-angle x-ray scattering

M.A. Gardnes, A.N. Northa, J.C. Dorea, C. Salinas-Martinez de Leceab and D. Cazorla-Amorosb aphysics Laboratory, University of Kent at Canterbury, Canterbury, Kent, CT?. 7NR, U.K. bDepartamentode Quimica Inorganica e Ingenieria Quimica, Universidad de Alicante, Aptdo, 99-Alicante, Spain.

Abstract Small-Angle X-Ray Scattering (SAXS) studies have been carried out over a wide range of Qvalues (5 x 10-3 - 0.5 A-1) permitting analysis of structural features for a spatial regime of 0.5 200 nm. Experimental and analysis procedures are described and results presented for a series of activated carbons. It is found that the pore size distribution has a complex form that varies according to the degree of activation (burn-off).Additional measurements have been made by neutron diffraction. The results demonstrate the basic graphitic structure of the carbons but show that there is considerable distortion of lattice planes.

1. INTRODUCTION

The high adsorption capacity of activated carbons has lead to many industrial applications involving the separation of liquids or gases, including air purification and solvent recovery; their high surface area has also led to use as catalyst supports. Of particular interest is the microporous nature of these carbons with respect to molecular processes. These processes are often dependent upon the diffusion and adsorption of molecules in microstructures, where motion is restricted. An understanding of the pore size and shape is necessary to determine the use and manufacture of the most economic of a choice of porous carbons. Various techniques have been developed for the characterisation of porous materials. Information on larger pore sizes is easily obtained by microscopy or pomsimeny. Knowledge

274

of smaller meso- and micropores is much more limited. Adsorption methods measure the available pore volume giving an indirect measurement of pore dimensions through the adsorption isotherm equations [l]. Hence there is a need for other methods to obtain information on pore dimensions independently. Among the foremost of these is Small-Angle Scattering (SAS), of x-rays or neutrons, which allows a direct analysis of inhomogenieties in a sample over a size range of a few Angstroms to about 200 nm [2]. The main advantages of scattering techniques are that they are non-destnctive and non-invasive. SAS can be used to detect blocked or closed pores inaccessible to adsorptives. The availability of high intensity x-rays from synchrotron radiation sources enables the use of Small-Angle X-ray Scattering ( S A X S ) to study the meso- and micropore size distributions of many materials. Neutron diffraction measurements give additional information on atomic correlations useful in interpreting the structure of the materials under investigation.

2. SCATTERING THEORY

Scattering theory is covered in detail in various texts [3,4] so only a brief introduction to some of the basic principles will be given here. When x-rays or neutrons with a wavelength, h, are incident on an object they are scattered with scattering vectors, Q, dependent on their angle of scatter, Q, (figure 1).

Scattered Radiation

Incident Radiation

4R 8 Figure 1. IQI = lk - El = --.sin -

A

*

A scattering cross-section is defined

-d o - -

a

no. x-rays (or neutrons) scattered into solid angle dQ/ time incident flux.dS2

275 after correction the scattered intensity from an experiment

Braggs law for diffraction relates the angle of scatter, 8,inversely to the size of the object studied. Small-angle scattering covers a range of low Q-values allowing long range inhomogenieties to be measured. The scattering cross-section is then the average scattering of all the inhomogenieties in the sample. 00

I A p . exp(iQr).d3r

I2

= P(Q)

where P(Q) is the particle form factor which depends on pore size and shape and the scattering density contrast, Ap, between the particle (or pore) and the surrounding medium. For x-rays the scattering density contrast is due to the difference in the electron densities of the different components of the system. A structure factor, S(Q). represents the structural relationships between particles. For a monodisperse ensemble of particles (or pores) the scattered intensity may then be written

For a dilute polydisperse system, assuming S(Q) = 1 (i.e. no inter-particle interactions) 00

I(Q) = IDn(r).&.P(Qr).dr 0 with size distribution Dn(r) and normalised form factor P(Qr).

3. FRACTAL SYSTEMS An object is said to be fractal if its degree of irregularity is the same on all scales [ 5 ] . There are two types of fractal, surface fractals and mass fractals. A surface fractal is an indication of the roughness of the surface. The surface area, A, inside a radius, R, from any origin increases as

276 A = RY where y has a non-integral value between 2 and 3. In porous materials larger pores may

have on their surface smaller pores which in turn exhibit smaller irregularities etc. giving a 'rough surface' down to the atomic scale. A mass fractal system is one where the mass inside a sphere increases as a non-integer power of the radius (i.e. M=4n/3.RX,where x is a noninteger less than 3). Many particle aggregates show this behaviour and it is possible that either the network of pores running through a material or the remaining mamx itself may resemble such a structure. The x-ray scattering mass fractal structure, as used in this work, is approximated by

where r ( D m - 1) is the gamma function and is a length that characterises the size of the mass fractal. Dm is the mass fractal dimension [ 6 ] .

4. SAXS EXPERIMENTATION AND ANALYSIS

S A X S experiments have been carried out on station 8.2 at the SERC Daresbury Laboratory, England, using a Synchrotron Radiation Source. Synchrotron radiation is favoured over radiation from a laboratory source because of its high intensity in the x-ray region (approximately 104 - lo5 times that from a laboratory source) as well as having a wide tunability of energy and high polarisation and collimation.

Monochromator System

Sample

Figure 2. Schematic diagram of a S A X S experiment.

Detector

277 Figure 2 is a schematic diagram of the SAXS instrument. A beam of wavelength 1.54 A is chosen by use of appropriate (focussing) monochromators. Ion chambers before and after the sample allow corrections tobe made for absorption and any fluctuations in the x-ray intensity. A beam-stop protects the centre of the detector from the transmitted primary beam and places a restriction on the lowest Q-value that can be measured. The scattering pattern is recorded over all angles simultaneously using a linear position sensitive detector. The distance between the sample and the detector is known as the camera length and can be changed to allow the scattering in different Q-ranges to be measured. With a short camera length (e.g. 1 m) intensities over a larger range of Q-values can be examined but resolution is much less than for a longer camera length. Various indirect transformation methods of analysis have been developed (e.g. [7])however there are limitations imposed by the Q-range of the expetirnents. Alternative analysis techniques include maximum entropy [8] and the application of specific pore size distribution models. In the present work the scattered intensity has been analysed by the last of these methods using a modified Schultz size distribution and a mass fractal structure factor. The theoretical scattering from these models was calculated and compared with experiment using 'FISH', an interactive fitting program [9] which assumes spherical pores. 'FISH' utilises a standard iterative linear least squares method of fitting using the parameters of a chosen model. A model that fits well to the experimental data is one possibility for the pore size distribution but other models using different pore size distributions or pore shapes may fit just as well. Any possible model must be physically realistic and concur with what is already known about the sample, this determines a good approximation to the pore size distribution within the confines of the model. Although a mass fractal structure factor is used in this work, it is not so simple to determine exactly what the concept of a mass fractal means in terms of in terms of the structure of the sample. It is found [lo] that it may not be possible to separate the Scattering due to polydispersity from the scattering caused by a mass fractal-like structure using S A X S alone.

5. ACTIVATED CARBONS The activated carbons examined in this work are obtained by carbonisation and activation of olive stones [ l 11. Carbonisation removes most of the non-wbon elements and activation clears the less organised carbonaceous compounds and removes some of the carbon. The olive stones were crushed and sieved to a particle size of about 2 mm and then cleaned in acid before being washed in distiled water to remove all traces of the acid. The particles were carbonised for 2 hours in a continuous nitrogen flow at 85OoC. Activation was then carried out in a horizontal furnace using carbon dioxide at 800OC for varying lengths of time. The greater the amount of

278

time, the greater the activation (or burn-off). Burn-off is measured as the percentage, by weight, of material bumt off during the activation process. Integrated studies of the pore volumes of these carbons by nitrogen adsorption and mercury porosimetry give values for the total pore volumes from 45% for an 8% bum-off sample to 77% for 80% burn-off. Most of the pore volume comes from macro- and micropores as can be seen in figure 3. This indicates a very narrow pore size distribution with many micropores and a long tail-off extending into the macropore region. The micropore volume is seen to increase very rapidly with initial activation after which the rate of increasing volume for each of the pore size ranges appears to increase almost linearly with activation.

0 Vmacro V 2 4 k 5 0 run V 0 . 7 4 < 2 nm

3

8

10

34

62

70

80

Bum-off (percentage mass) Figure 3. Pore volumes for activated carbons measured by adsorption and porosimetry.

6. SAXS STUDIES OF ACTIVATED CARBONS

S A X S studies have been applied to the series of activated carbons enabling the change in pore size distribution to be evaluated as activation (bum-off) is increased. The change in the scattering curve for three of these samples is shown in figure 4a. Analysis of the carbons using fitting routines (figure 4b.) shows an increase in the number of pores with a n m w pore size dismbution which broadens with the mean radius, R,increasing only slightly from 4 to 5.sA as activation is increased. A mass fractal dimensionality is fitted which first increases and then decreases with increasing activation (table 1). This, combined with marked differences in the

279

values obtained for the 8, 19 and 34% burn-off samples, indicates a change in the stmcture of the saniple or the mechanism of activation as the bum-off reaches 20 to 40%. The fitted mass fractal dimension does not agree with that obtained from log(1) vs log(Q) plots of the data, it is thought that this may be due to the effect of the polydispersity (as previously mentioned) with the fitted dimension being more accurate.

0-15

-125

-10

-0.75

-0.5

-0.25

0.0

0.1

02

03

0.4

03

Figure 4. (a) Scattering curves from three activated carbons with 19.52 and 80% burn-off. (b) Fit (-) to data (+) from the 19% burn-off sample using the pore size distribution shown (inset), the psd obtained for the 80% burn-off is also shown (--).Residuals of the fit are shown in the lower curve.

Table 1 Change in structure of activated carbons as activation increases. Bum-off in C@ 8% 19% 34% 52% 70% 80%

/mass

Mean Radius 4.1 4.9

5.0 5.1 5.2 5.3

/A

Mass Fractal Dimension 1.8 2.0 2.1 1.7 1.4 1.3

280

The present analysis provides a convenient paranleterised analysis of the data but should not be regarded as a definitive representation. The high internal pore volumes of these samples pose a question about what exactly the x-rays are being scattered by. It is currently believed that at high Q-values the micropores in the carbon matrix are detected, with a pore size distribution as shown above, but at low Q-values the scattering may be that from the tenuous ribbon-like carbon mamx, showing mass fractal-like properties. The effect of activation will be different on each of these regions; where and how these regions overlap is, as yet, uncertain but may shed light on some of the changes seen in the scattering.

7. NEUTRON DIFFRACTION

Neutron diffraction studies of some of the C02 activated carbons have been made on the 7C2 diffractometer at the Orphee reactor, CEN, Saclay, (France) and the diffraction patterns are shown in figure 5 . The shape of the curve is similar at Q-values greater than 3 A-1 for all samples showing that there is little change in the atomic structure. The small-angle scattering is seen to extend beyond the first diffraction peak at 1.5 A-1 and emphasises that the microporosity is linked to distortion of the graphite planes. There are no sharp Bragg peaks as seen for graphite and a preliminary analysis suggests that the graphitic micro-crystallites have considerable disorder in their local environment. A more detailed structural model is under investigation.

-Small-angle

II

scattering

-Broadened

(and overlapping)

1

I

1

0

16

0-value

Figure 5. Neutron diffraction patterns of CQ2 - activated carbons with different bum-off

(percentage mass)

28 1

8. CONCLUSIONS AND FUTURE WORK The results from these studies compare well with current knowledge of activated carbons [ 121 and complement those results obtained by alternative methods [ 13,141. Previous work [I21 has demonstrated that carbons have fractal properties, however, most of the work suggests surface fractals not found in this study, this difference can not yet be fully explained and further investigation is required. Current work includes the introduction of a slit form factor (P(Q)) into the analysis programs. It is hoped that this will improve the accuracy of our results from porous carbon (for which there is much evidence of slit shaped pores). Preliminary results show similar distributions with mean 'radii' shifted to higher values. Studies using Ultra-Small-Angle X-ray Scattering facilities, to investigate pores up to the micron size range, are also underway. Further refinements to the analysis and interpre:.ition should produce more consistent, accurate results making SAXS a useful tool, in combination with other methods, for the study of all porous materials. It is hoped that future work will involve a closer comparison of the results from the available analysis techniques in order to complete the picture of the structure of these industrially important materials and to show how these techniques may be combined to provide a complete analysis of other porous media.

ACKNOWLEDGEMENTS We wish to thank Dr. W. Bras (Daresbury Laboratory) for his help with the S A X S station (8.2) at the SERC Daresbury Laboratory, England. ANN would like to thank the SERC for financial support in the form of an Advanced Fellowship.

REFERENCES 1. C.A. Jessop, S.M. Riddiford, N.A. Seaton, J.P.R.B. Walton, and N. Quirke, in "Characterisation of Porous Solids II", 123, Elsevier Science Publishers, B.V., Amsterdam, 1991. 2. A.N. North, J.C. Dore, R.K. Heenan, A.R. Mackie, A.M. Howe, B.H. Robinson and C. Nave, Nucl. h a . Meths. Phys. Res., B34, 188-202, 1988. 3. 0.Glatter and 0. Kratky. "Small Angle X-Ray Scattering", Academic Press, 1982. 4. G.E. Bacon, "Neutron Diffraction", Clarendon Press, Oxford, 1975. 5. J.E. Martin and A.J. Hurd, J. Appl. Cryst.. 20, 61-78, 1987. 6. J. Teixiera, J. Appl. Cryst. 21, 781-785, 1988. 7. 0. Glatter, J. Appl. Cryst. 10, 415, 1977. 8. S. Hansen and J. Skov Pedersen, J. Appl. Cryst., 24, 541-548, 1991. 9. R.K. Heenan, FISH - Data Analysis Program, 1989. 10. J.E. Martin and B.J. Ackerson, Phys. Rev. A 31, 1180, 1985. 11. J.M. Guet, Q. Lin, A. Linares-Solano and C. Salinas-Martinez de Lecea, in "Characterisation of Porous Solids 11". 379, Elsevier Science Publishers, B.V., Amsterdam, 1991. 12. B. McEnaney, Carbon 26,267, 1988. 13. P.Gonzalez-Vilchez, A. Linms-Solano, 1. de D. Lopez-Gonzalez and F. RodriguezReinoso, Carbon, 17, 441, 1979. 14. M.A. Gardner, "Small-Angle X-ray Scattering Studies of Porous Carbons", Masters thesis, University of Kent at Canterbury, 1991.

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J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids I l l Studies in Surface Science and Catalysis, Vol. 87 0 1994 Elsevicr Science B.V. All righls rescrvcd.

283

Determination of porous texture in zirconia gels from adsorption isotherm measurements, small angle neutron scattering and thermoporometry M. Pauthe*, J.F. Quinson*, J.D.F. Ramsu**

*Laboratoire de Chimie Appliquke et GCnie Chimique CNRS, URA 417 Universid Claude Bernard Lyon I €12622 Villeurbanne Cedex, France. Institut de Recherches sur la Catalyse, CNRS 2, avenue Albert Einstein 69626 Villeurbanne Cddex, France.

Abstract

Zirconia gels have been prepared using a technique where the oxide is precipated within a polymer (polyacrylamide) matrix. With this process large (> lmm) gel spheres can be formed in the wet state. These can be dried using different techniques (solvent displacement, evaporation in air) to give gels of controlled porosity.The microstructural changes which occur on drying the gels have been investigated using nitrogen adsorption isotherms, thermoporometry and small angle neutron scattering (SANS). From SANS, it has been shown that the gels have a fractal structure composed of clusters of small ( < 3 nm) zirconia particles, which are formed by a process of diffusion limited aggregation (DLA). The method of drying has an influence on the size of these clusters, and the extent of their interpenetration. During drying the overal size of individual clusters is reduced and interpenetration of adjacent clusters can occur. The method of drying can have a marked effect on this process and thus may control the resultant porous structure. The pore size and volume of gels determined by isotherm analysis and thermoporometry are in good accord with such a model of the pore structure. 1. INTRODUCTION An understanding of the microstructural changes which occur on drying oxide gels is important for many different applications (ref. 1). This is particularly the case where there is a need to control porosity or to minimize the tendency for cracking during shrinkage. Recently we have shown that the porous properties of oxide gels (Si02, Zr02) can be controlled using solvent displacement drying techniques (ref. 2). In these processes, where water is displaced by a partially miscible solvent, such as an alcohol, less shrinkage occurs, and the gel has a markedly higher porosity than that produced by air-drying. The porous microstructure of these oxide gels has been investigated by nitrogen adsorption isotherms, small angle neutron scattering (SANS) and thermoporometry. The two latter techniques are non destructive and can provide details of the structure of "wet" gels, i.e. either still containing water or organic solvent (refs. 3-7). In this paper, we have compared results obtained on zirconia gels using these three techniques. From SANS, we show that the porous gel has a fractal structure composed of

284

clusters containing amorphous units. The method of drying has an influence on the aggregation or association of these clusters and hence can result in changes in the porous structure. Furthermore, it is shown that the pore size and volume determined by isotherm analysis and thermoporometry are in good accord with such a model of the pore structure. 2. EXPERIMENTAL 2.1. Preparation of zirconia gel spheres of controlled porosity. Zirconia gel spheres were produced by the method described previously (refs. 2, 8). Using this method, dry gel spheres which are either highly porous or of low porosity can be obtained, Feed solutions were prepared by mixing equivalent volumes of 4 % polyacrylamid solution in formamide/water with aqueous solutions of zirconium nitrate (0.8 mol dm- ). Feed droplets ( = lmm diameter) were produced by pumping the feed solution through a vibrating jet. The droplets were allowed to fall through a column containing concentrated ammonia solution ; here the droplets gelled (retaining their integrity as individual spheres) and precipitation of metal hydrous oxide occurred. The gel spheres were washed repeatedly with water to remove salt. Batches of wet gel spheres were divided into three, one portion being retained (sample A) and another dried by evaporation in air (sample B). The third (sample C) was dehydrated by solvent displacement : the aqueous phase was exchanged repeatedly with butanol and the solvent was removed by subsequent evaporation in air. This latter drying process gave spheres with little shrinkage in contrast to air drying where shrinkage was marked.

3

2.2. Adsorption isotherm measurements Nitrogen adsorption isotherms at 77 K were measured volurneticall using a Digisorb 2600 (micromeritics instrument corporation) as described previously (ref( 1). Dried samples were outgassed at ambient temperature for approximately 16 hours. Specific surface areas, SBET, pores volumes, V , and mean pore radii, r were derived in the standard manner as P’ previously (refs. 3, 9). P 2.3. Thermoporometry Full details of this technique and its applications have been described elsewhere (ref. 57), and only brief details of this method will be outlined here. Thermoporometry is a thermal method which is based on the thermal analysis of the liquid-solid phase transformation of a capillary condensate held inside the porous body under study. From the solidification curve it is possible to determine: - the pore radius, R, from the depression of the solidification temperature, dT, due to the Gibbs-Thompson effect. - the pore volume V, from the energy, Q, evolved in the phase transformation. This determination must take into account that the heat of the phase transformation is a function of freezing point depression. - the pore surface, S, from the simultaneous measurements of AT and Q.

By analysing both the melting and the solidification curves, one determines a pore shape factor varying between 1 (spherical pores) and 2 (cylindrical pores). Thermoporometry may be used for rigid materials but also for those whose texture is either modified during drying (wet gels, membranes) or which may swell in a liquid medium. Its range of application covers a pore size range corresponding to mesoporous distribution, essentially. Experimentally solidification and melting curves of water in zirconia gels under study, are determined using a differential scanning calorimeter. The amount, w, of dried gel used

285

and the value, v, of the temperature scanning rate depend on the pore volume and the pore radius to be tested, respectively: - For the sample B, v=S"C/h and w=15mg - For the sample C, v=60"C/h and w = 75mg.

2.4. Small-angle neutron scattering SANS measurements were made at a wavelength, A, of 12A, using the D11 SANS spectrometer at the Institut h u e Langevin, Grenoble (ref.10). Data were analysed using standard programms to normalize for detector efficiency, and correct for sample selfabsorption and background (ref. 3). SANS arises from inhomogeneities in the scattering density, p , of materials which occur over distances dSAS (d M28) in the range 1-1OOO nm. Such inhomogeneities may arise with dispersions colloidal particles in a liquid and porous solids for example. The SANS intensity, I(Q), is measured as a function of the momentum transfer, Q, (where Q = 4 7 sine/X, and 2 8 is the scattering angle) to obtain details of the structure of the scatttering inhomogeneities (e.g. pore size and volume ; porehiid interfacial area and structure). For the gel systems here it has been shown (ref. 2) that the dependence of I(Q) on Q can be ascribed to that of a system of particle aggregates having fractal properties (refs. 12-14).

09

It-

Range/ of fractal self similarity

'Porod region'

\ log 0

Figure 1. Schematic representation of a particle aggregate (a) having a range of self similarity between approximately a l and a2. The form of the scattering is as depicted in (b).

286

For such systems I(Q) scales with an exponent corresponding to the fractal dimension, D, namely :

UQ) = Q-D The value of the exponent relates to the mechanism of formation of the aggregates and the range over which the power scaling occurs to the size or extent of the cluster. Thus for the process of diffusion limited aggregation (DLA), D has a value of 2.5 (ref. 14). Such a scaling effect relates to the mass fractal dimension and arises for a range in reciprocal space, a l , and the primary particle size, a2, (see Figure 1). At higher Q it can be shown that for a two-phase system, with sharp interphase boundaries, a 4-4 power law is obeyed. This occurs in the Porod law region when Qr > 4 where 2r is the size of the scattering inhomogeneity e.g. a particle or pore (ref. 15).

3. RESULTS 3.1. Adsorption isotherms

The method of dehydration has a marked effect on the surface and porous properties of the dried gels, as has been described earlier (ref. 2). This is illustrated by the nitrogen adsorption isotherms in Figure 2 for zirconia gels which have been dried in air (sample C) and by solvent displacement (sample B). The isotherm for sample B is almost Type I1 in character which is typical of structures composed of an assembly of particles with a very open packing (ref. 11). This feature is demonstrated by the very high uptake at saturation, which corresponds to a considerable porosity ( > 0.90) in the gel and the large pore size (see Table 1). In contrast the isotherm for sample C is Type IV in character, and has features which indicate a gel with a considerable reduced porosity where the size of the pores are approaching the micropore range (< 2 nm). This is illustrated by the marked reduction in uptake at saturation and the shift of the hysteresis loop to much lower pressures. The restricted size of the hysteresis loop shows the isotherm is almost reversible and therefore approaching Type I behaviour which is typical of a volume filling process in a microporous solid. Such behaviour is an indication that marked shrinkage has occurred leading to a highly compact assembly of very small particles. The marked differences in specific surface area, SBET, Vp and rp depending on the method of dehydration are listed in Table 1 3.2. Thermoporometry Thermograms for both freezing and melting of water in samples B and C are shown in Figures 3 and 4 respectively. For the solvent displacement dried gel (sample B) we note that d T s is smallcorresponding to large pores, and that d T s > d T m - corresponding to a near cylindrical shape model. Furthermore the energy change in the phase transition is considerable, which can be ascribed to a large pore volume. Values derived from these curves are given in Table 1. The thermograms for the air dried gel (sample C) show a marked difference. Here OT, is much larger, indicating much smaller pores. Furthermore the curve extends to 213 K corresponding to the limit where freezing can occur. This implies the existence of microporosity (an approximate estimate of the micropore volume, derived from the mass of water which remains unfrozen, shows this to be 0.1 cm3 g-1).

287

Table 1. Surface and porous properties of zirconia gels. NITROGEN ADSORPTION ISOTHERM

Rmm

THERMOPOROMETRY

Sample B

Sample C

Sample B

Sample

22

2

22.2

2.3

1.9

2

c

(W

FV/Z

Figure 2. Nitrogen adsorption isotherms at 77K for zirconia gels. ( B ) sample B; ( C ) sample C.

PIP0

288

4-

2

2 E v

K

O

50a -2

4

I d melting

.

-

r /\ T

’\,

freezing

\ii

1

Figure 3. Thermogram for zirconia gel sample B.

Figure 4. Thermogram for zirconia gel Sample C.

289

Again QTs > dT indicating a non-spherical shaped pore, and furthermore the energy associated with tp;Ie' phase change is much smaller than observed with sample B. This indicates a much smaller pore volume - in accord with the nitrogen adsorption isotherm results already described. Considering the widely different basis of these two techniques the accord shown in Table 1 is very satisfactory. Apart from the value of surface area which is lower when determined by thermoporometry. For sample C this may be ascribed to the presence of micropores which will not contribute to the derivation. For sample B, the existence of very large pores (> 30 nm), as evident from the cumulative pore volume distributions determined from thermoporometry in Figure 5 , may also lead to an underestimate in the derivation of a cumulative pore surface area.

m

nsE

w

R(nm)

Figure 5. Cumulative pore volumes of zirconia gels. ( B ) sample 8 ; ( C ) sample C. We will defer discussion of the possible textural structure of the gels, which is consistent with the measurement from these two techniques, until after the SANS results are described in the following section.

3.3. SANS results SANS measurements are shown (Figure 6) for the wet zirconia gel spheres (curve A), and the same gel spheres after drying by solvent displacement (curve B) and directly in air (curve C) respectively). These measurements are in a Q range where the characteristics are due to mass fractal properties. (It has been shown previously (ref.2) that at higher Q ( 1 10-1 A-1) these is a trend to Q-4 scaling behaviour. Here the lower Q range has been entended by over a decade, compared to that measured previously.) Here we note two important features : 1-

A power law slope of = 2.5 (curves A and B) corresponding to a process of DLA giving rise to clusters of zirconia particles (size c 3 nm).

2-

A progressive shift of the lower-limit cut-off in Q-2.5 scaling to higher Q for curves A, B and C. This corresponds to a decrease in the size of the gel spheres during drying (i.e. shrinkage occurs). For curves A B, and C this deviation occurs approximately at 2 x 10-3, 4 x 10-3 and 1.6 x 10-i A-1 respectively.

290

lo4 lo3

lo2 1 (QI 10

1

15*

16'

Figure 6. SANS for ( A ) wet zirconia gel spheres, ( B ) after solvent displacement drying, and (C) after drying in air. 4. DISCUSSION

A schematic depiction of the different structural changes during the drying of the gel spheres which provides a tentative explanation of these results is shown in Figure 7. Thus in the "wet" state the gel spheres are swollen and contain aggregates of small oxide particles which are dispersed in a weak polymer network. Here the aggregates are widely separated. 2 x 10-3 A-1 reflects the approximate separation of The shoulder in the SANS curve at the clusters which is indicated by a. On displacing the water with butanol which is then evaporated, partial shrinkage occurs leading to a highly porous structure, as shown in B. The average separation between the clusters decreases (to approximately d2) and it is probable that a continuous network (percolation) is formed by association of the clusters. Here we note a displacement in the cut-off in the SANS curve to 4 x A-1, indicating a contraction in the effective cluster size. Direct evaporation of water from the

-

-

29 1

"wet" spheres causes a marked contraction and a collapse of the aggregates to give a microporous structure with much lower poros'ty a depicted in C. It is probable that the inflection in the SANS curve at = 1.6 x 10- A- corresponds to the average separation between these collapsed clusters ( = 300 A), within which microporosity is formed in the interstices between the primary particles. Furthermore slightly larger pores ( = 2 nm) approaching the mesopore range may arise in the zones between the packed clusters.

4,s

Figure 7. Schematic depiction of different structural changes during the drying of gel spheres. In the "wet" state (A) the gel spheres are swollen and contain aggregates of small oxide particles which are dispersed in a weak polymer network . On displacing the water with a n organic solvent (butanol) which is then evaporated, partial shrinkage occurs leading to a highly porous structure (B) . Direct evaporation of water from the "wet" spheres causes a marked contraction and a collapse of the aggregates to give a microporous structure with much lower porosity (C) . The relative size of the different microstructures is denoted approximately by the scale a .

Such a model is consistent with both the N2 adsorption isotherm and thermoporometry measurements. Thus by comparing the relative porosity between the gels dried in air and by solvent displacement (Table l), we note that the volume occupied by the zirconia particles within the gel spheres is > 50 % for C but only = 10 % for B. Furthermore there is an approximate ten-fold reduction in the effective pore size in shrinkage from the situation in B to c. 5. ACKNOWLEDGEMENT

Discussions with Dr. M. Kolb and access to facilities at the Institute Laue Langevin, are gratefully acknowledged.

292

6. REFERENCES 1

8

9 10 11 12 13 14 15

C.J. Brinker and G.W. Scherer, Sol-Gel Science : The Physics and Chemistry of SolGel Processing, Academic Press Ltd., London, (1990), p.453. J.D.F. Ramsay, P.J. Russell and S.W.Swanton, Studies in Surface Science and Catalysis, Vol. 62 (1991) Elsevier, Amsterdam, p. 257. J.D.F. Ramsay and B.O. Booth, J. Chem. Soc., Faraday Trans. 1, 79 (1983) 173. J.D.F. Ramsay, Chem. Soc. Rev., 15 (1986) 335. M.Brun, A. Lallemand, J.F. Quinson and C. Eyraud, Thermochim. Acta, 21 (1977) 59. J.F. Quinson and M. Brun, Studies in Surface Science and Catalysis, Vol. 39 (1988), Elsevier, Amsterdam, p.307. J.F. Quinson, J. Dumas, M. Chatelut, J. Serughetti, C. Guizard, A. Larbot and L. Cot, J. Non-Cryst. Solids, 113 (1989) 14. B. Stringer, P.J. Russell, B.W. Davies and K.A. Dansos, Radiochimica Acta, 36 (1984) 31. J.D.F. Ramsay and R.G. Avery, Studies in Surface Science and Catalysis, Vol. 21 (1985), Elsevier, Amsterdam, p.97. K. Ibel, J. Appl. Crystallogr. 9 (1976) 296. R.G. Avery and J.D.F. Ramsay, J. Colloid Interface Sci., 42 (1973) 597. T.A. Witten and L.M. Sander, Phys. Rev. B, 27 (1983) 5686. M. Kolb, R. Botet and R. Jullien, Phys. Rev. Lett., 51 (1983) 1123. P. Meakin, Phys. Rev. A, 27 (1983) 1495. H.D.Bale and P.W. Schmidt, Phys. Rev. Lett, 53 (1983) 596.

J. Rouqucrol, F. Rodrigucz-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characlerization of Porous Solids 111 Studies in Surface Scicncc and Caulysis, Vol. 87 0 1994 Elscvicr Sciencc B.V. All righis rcscrvcd.

293

Adsorption properties of crystalline zirconia and yttria-doped zirconia M.R.Alvarez 1, M.J.Torralvo 1 ~ 2Y.Grillet , 3, F.Rouquerol2 and J.Rouquerol3 1Dpt. de Quimica Inorganica I, Facultad de Quimicas, Universidad Complutense, 28040 Madrid, Spain. 2UniversitB de Provence, Place Victor Hugo, 13331Marseille Cedex 3, France. 3Centre de Thermodynamique et de Microcalorimetrie du C.N.R.S., 26 rue du 1416me R.I.A., 13003 Marseille, France.

The adsorption of argon, nitrogen and carbon monoxide at 77K on crystalline samples of ZrO2,Zr02.2mol%Y203 and Zr02.5mol%Y203, has been studied by volumetric and microcalorimetric techniques. In these materials, which were prepared from the corresponding microporous gels by heating in air at 723K for 20 hours and for 30 days, both micropores and mesopores contribute t o the BET area and, for the same treatment time, doped samples seem to have more heterogeneous porous texture than undoped zirconia, as we can deduce from calorimetric results obtained for argon adsorption. For doped samples, as for undoped zirconia, the differences in the differential enthalpy curves of argon adsorption, with an increase of the thermal treatment, show that the higher differential enthalpy at low coverage for the gels is due to their more developed microporous texture. From the adsorption isotherms and corresponding differential enthalpy curves for argon, nitrogen and carbon monoxide adsorption, we can deduce that specific interaction occurs between the polar surface of doped and undoped samples and N2 and CO molecules which have dipolar (CO) or quadrupolar (N2) permanent moment. INTRODUCTION

Zirconia is often included in heterogeneous catalytic systems either as a promoter or as a support. In recent years there has been an increase in research devoted to the effect of temperature on textural and structural properties of ZrO2 [ 1-41. It is known that the addition of dopants such as La2O3, Y2O3 and others metal oxides, in low concentrations, stabilize the higher symmetry phases of ZrO2 at room temperature [5,6]. Recent work also seems to indicate that with the incorporation of these oxides the thermal stability of the texture of zirconia is considerably improved [ 1,7].

294

In previous work we have shown that the zirconia samples obtained by gelprecipitation followed by calcination at 723K in air, have a mesoporous texture with high specific surface area. This surface area decreases with an increase in calcination time. Moreover, the microcalorimetric results obtained for the adsorption of adsorbates with different permanent molecular moments have shown the specific nature of the surface of the crystalline zirconia MI. In this paper we report the results obtained by microcalorimetric and volumetric adsorption measurements concerning the influence of dopants on the porous texture and specifi nature of the surface in zirconias.

MATERIALS AND METHODS The samples were obtained from ZrO2,Zr02.2mol%Y203and Zr02.5mol%Y203 Y C ~ respectively), Y by heating in microporous gels (which are labeled as C, C ~ and air at 723K for 20 hours and for 30 days. After this treatment, crystalline materials were obtained in the three cases, these crystalline samples being labeled as: starting gel(7Mtreatrnent time). Both C(723/20h) and C(723/30d) are a two-phase mixtures of the tetragonal and monoclinic forms. The doped samples and cubic form correspond to the tetragonal form (C2Y(723/20h)and C2~(723/30d)) of ZrO2. Prior to adsorption, the samples were (C5Y(723/20h)and C5~(723/30d)) degassed under vacuum at room temperature. The adsorption isotherms of Ar, N2 and CO at 77K and corresponding curves of differential enthalpy of adsorption as a function of coverage, were obtained from simultaneous microcalorimetric and volumetric adsorption measurements, applying a slow and continuous introduction of the adsorbate [91. Complete adsorption-desorption isotherms of nitrogen at 77K were determined for each sample by the conventional static procedure. Analysis of the adsorption isotherms was made by the BET and a, methods. BET areas were obtained using the values of 0.138, 0.162 and 0.162 nm2 as molecular cross-sectional area for argon, nitrogen and carbon monoxide respectively. The standard Arhilica isotherm [ 101 was used for the construction of the a,-plots.

RESULTS AND DISCUSSION Representative adsorption-desorptionisotherms of nitrogen at 77K are given in Fig.1. We can observe that with an increase of treatment time at 723K of the doped sample (Fig.la), as well as with pure zirconia [81, the adsorption capacity progressively decreases and simultaneously, the maxima in pore size distribution (results not shown in the figure) are shifted and extended to the larger pore radii. On the other hand, for the same treatment time pure zirconia shows larger BET area than doped samples together with a more developed porous texture (Fig.lb). Continuous recorded adsorption isotherms of argon, nitrogen and carbon monoxide for C(723/20h),C2~(723/20h)and C5~(723/20h) samples, are plotted in Fig.2a, 3a and 4a. Representative a,-isotherms obtained from argon adsorption are include in Fig.2. Characteristic adsorption parameters obtained from the isotherms are given in Table 1and Table 2.

295

a

Vads cmsg-1

Vads cm3g-1

50

L120

40

- 40 *-*

10

I OI.2

0!4

I

0.6

I

0.8

,I

1.0

P/ p,

Vads

0

cm3g-1

6o

Figure 1.Adsorption-desorption isotherms of nitrogen at 77K. a) For C2Y ( 1, C2Y(723/20h) ( ) and C2~(723/30d) ( * ). b) For pure and doped zirconia samples after treatment at 723K for 20 hours. (C(723/20h)( * ), C2Y(723/2Oh)( ) and C5Y(723/2Oh)( x )).

1

b

0

I

I

0.2

I

I

0.4

0.6

r

I

0.8

1.0

PIpo

The corresponding curves of the differential enthalpy of adsorption of the different adsorbates ( I Aads fi I ) are plotted as a function of coverage (VNm) in Fig.2c, 3b and 4b. Fig.2 also includes the differential enthalpy curves of argon adsorption on C2Y, C2Y(723/20h)and C2~(723/30d).

296

Vads

a

cm3g-1 16

b

-

Vads cm3g-1

12C2Y(723/20h)

8-

C 5 Y (723/20h)

C2 Y (723/20h)

8 4-

4 *-

_---

1 1 015 0.05

0!2

0.10

P/ p,

laads t i m

-

IAads A1 k J mol-1

C

1

I

I

0.6

d.4

0.8

as

d

12-

10

-

8-

4-

4I

I

0.5

V/Vm

1.5

O! 5

I

VI Vrn

1.0

Figure.2. Argon adsorption a t 77K. a) Adsorption isotherms. b) %-plots. 4Differential enthalpy curves in function of coverage for pure and doped zirconia after treatment at 723 K for 20 hours. d) Differential enthalpy curves in function of coverage for C2Y, CzY(723120h)and C2Y(723/30d).

Vads c m3 9-1

a

I

18-

164

l2F@

14-

8

10-

+ 6-

&

0.04

- co - Ar N2

-

I

I

0.12

0.08

P/ po

Figure.3. Adsorption of Ar, N2 and CO at 77K on sample C2Y(723/20h). a) Adsorption isotherms. b) Differential enthalpy curves.

Vads

IAads6l

16

rn

a

cm3g-1

b

-

C2Y I723/20 hl

12C2Y l723/20 hl

10 4

4-

C5Y 1723/20hl I

I

0.04

I

IAliq Ul

I

0.08

-

0.12

I

co I

0.2

P/ g

Figure.4.a) Adsorption isotherms of Nz (- -) and CO (-) at 77K. b) Differential enthalpy of CO adsorption at 77K.

0!4

1

0.6

V l Vm

298

Table 1 Adsorption parameters for C2Y, C ~ Y723/20h) ( and C2~(723/30d) . Sample Adsorbate

Ar

V m (cm3 g-1 ) a

82.4 75.5 305.6 329.0 46 54 0.92

SBET (m2 g-1) b C C

Vm(NS)Nm(Ar) Sa&) ( m 2 g-1) e SmpISt f Vo (cm3 8-1) (liq) g Vo (cm3g-1 ) (STP)

Ar

N2

N2

13.0 14.4 52.4 62.8 55 40 1.04 36.0 0.69 0.005 4.0

Ar

N2

6.4 23.7 67

30.5

7.0 64

1.10 16.7 0.70 0.005 2.4

Table 2 Adsorption parameters concerning the zirconia and doped zirconia samples treated at 723K for 20 hours.

Adsorbate

Ar

N2

CO

Ar

Nz

CO

Ar

N2

CO

7.0 15.0 15.7 16.1 13.9 14.4 15.3 6.4 7.0 55.5 68.5 70.0 52.4 62.8 66.5 24.0 30.5 30.6 40 55 45 25 27 32 70 46 47 1.05 38.1 0.69 0.006 4.8

1.07

1.04 36.0 0.69 0.005 4.0

1.10

1.09 16.3 0.68 0.002 1.6

1.09

a BET monolayer capacity.

BET area measured at 77K. BET C constant. Ratio of the monolayer capacities for adsorbed N2 (or CO) and Ar. External surface area from the as-plot of argon adsorption. f Ratio of the surface areas corresponding to the mesopores (Smp) and that obtained by the BET equation (St). g Micropore volume from the as-plot using the density of liquid argon. Micropore volume from the as-plot using the density of gas argon (STP).

299

*The results obtained for argon adsorption show that: -The amount adsorbed at the statistical BET monolayer decreases with the increase of: i) the treatment time in both, pure zirconia [8] and doped zirconia samples (Table 1)and, ii) the yttria content of the sample for the same treatment time (Fig.2a and Table 2). -The as analysis carried out from the results obtained for argon adsorption reveals that a similar contribution of microporosity to the BET area is present in all samples (Fig.2b and Tables 1and 2). -Differential enthalpy curves for samples treated in the same conditions (Fig.2~)may be separated in two parts: the first one, in which the differential enthalpy decreases down to an inflexion point (at V N m -0.7, 0.65 and 0.5 for C(723/20h),C2Y(723/20h) and c 5~(723/20h)respectively) and the second, up to VNm=l, in which IAads 61 decreases in a slight manner. In the first part, corresponding to P/Po c0.02 for C(723/20h) and C2Y(723/2Oh) and P/Po c0.01 for C5Y(723/20h),microporous filling must occur together with the formation of a monolayer in mesopores and external surface. If so, the differences in both, the form of the curves and the values of differential enthalpy may be the result of differences in the microporous texture of the samples. For VNm values higher than the corresponding inflexion points, when the micropore filling is finished, the argon monolayer is progressively completed and the values of I Aads li I obtained in this range of coverage are comparable to those reported for several non-porous solids 1111. In terms of non-specific interactions, we could deduce from these results that doped samples have more heterogeneous porous texture than pure zirconia. *For doped samples, as well as pure zirconia [81, increasing the permanent polar moment of the adsorbate molecule increased both, the amount adsorbed at the BET monolayer and the differential enthalpy value for the same surface coverage (Tables 1 and 2 and Fig.3). These results suggest that, as in previous work [8, 121, some degree of localization and orientation of the N2 and CO molecules must occur on the polar sites of the surface due to specific interaction. If so, it is possible to explain the ratio Vm(Nz)Nm(Ar)(or Vm(CO)Nm(Ar))being higher than those calculated from the molar volumes of the adsorbates in their three-dimensional liquid state (Tables 1 and 2) and also, the high values of I Aadsh I of nitrogen and carbon monoxide observed at low coverage. From the value of 0.138 n m 2 for the molecular cross-sectional area for adsorbed argon and the amount adsorbed at the BET monolayer of N2 and CO we can deduce the values of 0.126-0.135 nm2 and 0.128 n m 2 for the molecular cross-sectional areas of adsorbed nitrogen and carbon monoxide respectively. The curves of the variation of differential enthalpy obtained from nitrogen and carbon monoxide adsorption, are similar for doped and undoped samples treated in same conditions. Moreover, the variation of IAads l i l for CO adsorption (Fig.4b) seems to indicate that for undoped samples, the contribution of specific interaction to the adsorption enthalpy occurs until higher values of coverage than for doped samples and, this fact suggests that doped samples have a more heterogeneous surface. In this stage of the work it is difficult t o relate these results with the concentration of polar sites in the surface of pure and doped zirconia. Although

300

the incorporation of Y 2 0 3 into the ZrOz structure introduces anion vacancies, which must be active centers for specific adsorption, the concentration of these centers on the surface is not necessarily the same than in the bulk [21 and may be influenced by sintering and pore texture of the materials. ACKNOWLEDGEMENTS M.J.T. acknowledges a 2-month invited professorship at Universit6 de Provence.

REFERENCES 1. P. Turlier, J.A. Dalmon, G.A. Martin and P. Vergnon, Appl. Catal., 29 (1987)

305. 2. R.G. Silver, C.J. Hou and J.G. Ekerdt, J. Catal., 118 (1989) 400. 3. P.D.L. Mercera ,J.G. Van Ommen, E.B.M. Doesburg, A.J. Burggraaf and J.R.H. Ross, Appl. Catal., 57 (1990) 127. 4. W. Hertl, Langmuir, 5 (1989) 96. 5.M. Yoshimura, Ceram. Bull., 67 (1988) 1950. 6. R.L. Withers, J.G. Thompson and P.J. Barlow, J. Solid State Chem., 94 (1991) 89. 7. P.D.L. Mercera , J.G. Van Ommen, E.B.M. Doesburg, A.J. Burggraaf and J.R.H. Ross, Appl. Catal., 78 (1991) 79. 8. M.R. Alvarez , M.J. Torralvo ,Y. Grillet , F. Rouquerol and J. Rouquerol, J.Therm. Anal., 38 (1992) 603. 9. Y. Grillet, F. Rouquerol and J. Rouquerol, J. Chim. Phys., 2 (1977) 179 and 7-8 (1977) 778. 10. D.A. Payne, K.S.W. Sing and D.H. Turk, J. Colloid Interf. Sci., 43 (1973) 287. 11.K.S.W. Sing and V.R. Ramakrishna, Colloques Internationaux du CNRS, No. 20 1(197 1) 435. 12. J. Rouquerol, F. Rouquerol, C. Perks, Y. Grillet and M. Boudellal, Characterization of Porous Solids, SOC.Chem. Ind., London 1979, p.107.

J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characlerizaiion of Porous Solids I l l Studies in Surface Science and Caulysis, Vol. 87 1994 Elsevier Science B.V.

30 1

NMR measurement of pore structure William L. Earl,a Yong-Wah

and Douglas M. Smithb

a c h e m i d and Laser Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA bCenter for Microengineered Ceramics, University of New Mexico, Albuquerque, New Mexico 87 13 1, USA

ABSTRACT Several different NMR experiments are described for obtaining information about pore sizes and the physical chemistry of molecules in restricted geometries. These methods include 129Xe chemical shifts, 129Xe freezing, 15N2 freezing, and 13CO2 freezing in pores. We conclude that care must be taken in the application of the mean free path model relating 129Xechemical shifts and pore diameters. The freezing experiments are interesting in providing information about the state of small molecules in pores but they do not yield quantitative pore size information in themselves.

1. INTRODUCTION We have been working on various methods of using Nuclear Magnetic Resonance (NMR) as a tool to measure pore sizes, pore size distributions, and pore structures. The reason for this effort is the realization that NMR is sensitive to short range order and the NMR relaxation times and chemical shifts are potential sources of the type of information required to determine the structure of micropores. This manuscript is basically a progress report of that work. It includes some successes and many unresolved questions in the use of NMR for pore structure characterization. It is not a complete review of the literature or a description of all ongoing work in this field. The references are not intended to be exhaustive; such a review is not possible in this forum. It has long been recognized that the NMR relaxation times of fluids in restricted geometries are sensitive to pore size.' This phenomenon arises because the relaxation time of molecules in contact with the surface of the pore is much shorter than those in the bulk. The rapid exchange between molecules on the wall and those in the bulk results in an average relaxation time, which can be related to the surface to volume ratio of the pores. Considerable effort has been dedicated to understanding this effect and to deriving the proper mathematical formalism to extract pore sizes and pore size distributions from measurements of NMR magneti~ation.~-~ More recently, it was realized that the chemical shift of 129x3,can be related to pore sizes in closed pore systems such as clathrates as well as in open pore materials such as ~ e o l i t e s . ~ . ~ This techniques is relatively easy, the NMR sensitivity is high, and the application requires only

302 simple mathematical analysis. As a result, 129x3,NMR has been applied in a large variety of materials from clathrates and zeolites through ceramics and even in coals where the association of the shift with pore size is tenuous, at best. There is at least one report in the literature, in a silica with large pores, where the measured shift is clearly inconsistent with the theory as applied to zeolites.* The authors suggest that the larger than expected chemical shift is due to surface roughness. There are several other critical studies of Xe shift measurements of pore sizes and several research groups continue this work with the goal of understanding the basic physical chemistry underlying these shifts and giving them a quantitative interpretation.9910 We decided to pursue 129Xe NMR as a pore measurement technique with the goal of understanding the details of the system. We have also investigated other magnetically active nuclei and small molecules as probes of pore size and adsorption sites. This manuscript is a description of some of our attempts not a review of the subject. It includes systems in which we were successful in measuring pore sizes and cases in which we were unsuccessful. We will discuss several "freezing" experiments in which we reduced the temperature well below the freezing point of the pore fluid. This is analogous to thermoporometry using NMR as a detector of the phase transition.ll The distinction between NMR and thermoporometry is that in the latter case one determines the temperature at which a first order phase transition takes place (freezing), and in the NMR measurements one observes the NMR lineshape which indicates the temperature at which molecular motion becomes "slow," where we define slow as having motional correlation times longer than the NMR transverse relaxation time, T2 or about s. These experiments do not yield quantitative information about pore sizes or pore size distributions, but they add to our understanding of the physical properties of molecules in confined spaces. They are also useful in obtaining information about relative pore sizes. We will also describe a few experiments with "quadrupolar" nuclei in which we failed to obtain useful data.

2. EXPERIMENTAL All NMR data were taken on a Varian Unity-400 spectrometer operating at an applied magnetic field of 9.4 T. A special probe was constructed for this work. Temperature control is obtained with an Oxford model CF1200 cryostat. The probe itself is of a transmission line design.12 Samples were sealed in 16-mm 0.d. pyrex tubes, sealed to a 1-m long Pyrex capillary, which is connected to a gas handling system. This configuration allows us to bake out the sample to about 750 K under vacuum, insert it in the NMR spectrometer, and then control the pressure and chemical composition of the gases on the sample without removal from the spectrometer. The temperature, during NMR experiments, can be controlled over the range from about 3 to 430 K. Temperature regulation is achieved with an Oxford temperature controller and sample temperature measured with a carbon-glass thermometer. Once stabilized, temperature fluctuation and accuracy is better than 0.1 K. With this system we can effectively perform adsorption isotherm measurements concurrent with the NMR measurements. The samples reported in this study are: imogolite,l2 commercially available sodium Yzeolite, and an aerogel, and xerogel, which were prepared through gelation of TEOS.13 The samples were dried at temperatures from 480 K for the aerogels to 520 K for the imogolite, to over 670 K for the zeolite. They were dried for at least 16 hours at temperature under a vacuum of less than 10-4 torr.

303 The gases used were "normal" xenon gas where any residual air was removed through condensation and freeze-thaw cycles, l3CO2 (99+ % enriched) purchased from Cambridge Isotope Labs, and 15N2which, was obtained from the Los Alamos stable isotope separation facility.

3.

RESULTS AND DISCUSSION

3.1. Xenon Shift Measurements The earliest applications of this technique can be attributed to Ripmeester6 and Fraissard? who applied 129Xechemical shift measurements at 26°C to understanding the pore sizes and character of clathrate and zeolite pores, respectively. Since those reports, a number of other groups have attempted to use this technique.I5-l8 In zeolitic systems, Fraissard and coworkers have developed a model which relates the 129Xe chemical shift at infinite Xe dilution, 6,, to the mean free path of Xe, 1. The mean free path can, in tum, be related to the pore dimensions with certain assumptions about the pore geometry. This results in a rather simple equation:

6, = 243 x 2.054

2.054 + 1 '

where 6, is the 129Xeshift, corrected for Xe-Xe interactions and 1 is the mean free path. Work by Conner, et a1.8 indicates that there are problems with an indiscriminate application of this mean free path model and resulting equation to the determination of pore sizes. In that work the measured chemical shift was much greater than expected for the packed silica material. We have duplicated measurements on several zeolites reported in the literature. In most cases, our experimental setup allows us to go to significantly lower pressure than previously reported. Our results on zeolites are unremarkable in that they substantially agree with reported data. We note that for these hydroscopic materials, sample treatment can significantly change the NMR shifts measured. We have dedicated a significant effort to measurement of the pore size of synthetic imogolite, a tubular aluminosilicate with a gibbsite structure. The gibbsite sheet is essentially rolled with the SiO4 tetrahedra to the inside of the cylinder. The cylindrical micropore created has a diameters 0.7 nm.19 As synthesized, this imogolite is ordered in having the tubes packed in parallel bundles forming a sort of micro crystallite. This implies that there are smaller micropores between the tubes, which we estimate to be about 0.3 nm in size. These are so small that Xe (atomic diameter = 0.44 nm) cannot enter them. Using the above equation and computing the pore diameter for a cylindrical pore, we obtain 0.75 nm from the Xe shifts. This result is satisfying, but the imogolite has a pore wall composition and pore size very similar to zeolite samples so we might expect to apply the mean free path model without problems. We have also applied 129x3,chemical shift measurements to sol-gel prepared silicas. These samples are prepared from tetraethoxysilane, followed by controlled aging, and drying from pore fluids of varying surface tension.13 We report here on a xerogel dried from tetrahydrofuran and an aerogel prepared by exchanging the normal pore fluid (HZO-EtOH) with liquid CO;! and drying above the critical point. This results in a xerogel with a pore radius of about 4.5 nm and an aerogel with a pore radius of about 30 nm. A straightforward application of Fraissard's "mean free path model" would result in 129Xe shifts of about 22 and 3.3 ppm for the xerogel and aerogel, respectively. In fact we measure shifts of around 102 ppm for the

304 xerogel and 68 ppm for the aerogel. The Xe chemical shifts do not increase linearly as a function of Xe loading. These samples do not contain significant amounts of paramagnetic centers or cations which might cause such a nonlinearity. Cheung suggested that samples with distributions of pore sizes will give curved plots for the 129Xe shift as a function of xenon loading. We also attempted to measure the pore size of pores in a carbonate rock obtained from Texas A&M University. This geological sample is of interest because of its potential as an oil bearing mineral. We measured an infinite dilution shift of about 3.8 ppm corresponding to a pore radius of 13.4 to 26.3 nm, depending on the model chosen for the pore geometry. We are assured that the actual pore radius is about 200 nm. Conner et a1.8 found the chemical shift of xenon adsorbed in pores formed by packing of nonporous microspherical aerosils to be on the order of the shifts found in much smaller pore size zeolites. They suggest that the surface roughness of these materials accounts for the anomalously high 129Xechemical shift. It is possible that Conner's interpretation of the anomalously large measured shift is correct ...the surfaces are very rough and Xe atoms spend a large amount of time adsorbed in small pockets. This would skew the results towards small pores. On the other hand, the explanation may be simply that the mean free path model is valid only in a limited range of sample composition and pore size, e.g., from about 0.5 to 1.5 nm. These results certainly call into question I29Xe measurements of pore sizes in very different materials such as carbons and coals. In such samples, the very different pore shapes and pore wall physics would lead one to believe that the empirical equations, derived for zeolites, could hardly be expected to apply even if the basic model is correct. Carbons have an additional difficulty in that they are invariably paramagnetic and the paramagnetism might be expected to produce significant shift effects. We are continuing work on large pore materials, including a variety of sol-gel prepared silicas and porous glasses with the aim of understanding the effects of pore wall roughness and perhaps the extent to which the mean free path model can be applied in large pore materials.

3.2. Xenon Freezing Cheung and coworkers studied the NMR of 129Xein porous materials at 144 K.20 They observed the changes in line shape associated with the gas-liquid transition in the mesopores of zeolite samples. This can be compared to thermoporometry in which the liquid-solid transition of pore water is monitored calorimetrically. The goal of thermoporometry is to relate the freezing point depression to the pore size.]] Freezing is a cooperative phenomenon that really requires a bulk liquid. In a system where the pores are so small that all liquid molecules are effectively on the walls of the pores, the thermodynamic concept of freezing in a bulk like liquid does not apply. On the other hand, if we observe the I29Xe NMR signal as a function of temperature, we may draw conclusions about density, mobility, and pore size from the chemical shift and relaxation times. Figure 1 contains the 129x3, NMR spectra of xenon in imogolite at about 640 torr near the freezing point of bulk xenon. Our view of this system is that xenon exists in the micropores of the imogolite and in the macroporous space surrounding the "crystallites." At 162 K, just above the freezing point of the bulk liquid (161.3 K) we see a spectrum indicative of liquid xenon and of xenon in the micropores. Unlike some other samples that we have investigated (e.g., aerogels), we see two peaks above the freezing point because the exchange between atoms in the microporous tubes of the imogolite and the bulk-like xenon outside the pores is

305

Xenon in lmogolite

Xe in micropores

hard to freeze

350 340 330 320 310 300 290 280 270 260 250 240 230 ppm

Figure 1. The 129Xe NMR spectra of xenon in synthetic imogolite at different temperatures. The pressure of Xe in the sample was 640 torr. very slow. Thus, we see one peak at about 267 ppm for the Xe in the imogolite tubes and another at about 255 ppm for Xe in the bulk. At about 161 K the Xe in the bulk freezes, giving rise to the peak at about 294 ppm, indicative of solid (frozen) xenon. With decreasing temperature, we see the chemical shifts consistently becoming more deshielded as expected. The slight asymmetry in the solid peak we attribute to xenon on the external surfaces of the crystallites. If we continue to lower the temperature to 82 K, the xenon in the micropores never reaches a chemical shift, indicative of bulk freezing. The increased linewidth of the Xe in the micropores is indicative of decreased motion. We interpret this to be due to heterogeneity in the detailed site structure of the different xenon atoms in the micropore. As the temperature is lowered, a given xenon atom cannot sample as many different sites and the NMR line is inhomogeneously broadened. It is curious that the resonance for Xe in micropores stays relatively symmetrical. In analogy to 129x3,NMR in clathrates, we might have expected to see evidence of chemical shift anisotropy at the lower temperatures. This, too, indicates that Xe atoms in the micropore retain some mobility within a "cage" so they collide with the walls of the pore and with adjacent xenon atoms. This is consistent with the idea that molecules in small pores or on the walls of a pore do not "freeze" in a normal fashion.

3.3. Freezing of C 0 2 and N2 In our studies of imogolite we were interested in investigating linear molecules in the long cylindrical micropores. We were also interested in putting a small molecule into the channels between the imogolite cylinders. One of the goals was to obtain a spectrum that demonstrated a chemical shift anisotropy. In bulk N2 or C02 the NMR lineshape is symmetrical down to quite low temperatures. This is a result of motional averaging of the chemical shift tensor through rapid, isotropic tumbling of the molecules. However, in a restricted pore space nearly the size of the molecules, we would expect the molecular electric quadrupole interaction to slow the rotational motion. This should result in observation of a well known chemical shift anisotropy (CSA) pattern.21

306 Figure 2 contains a series of 13C spectra of C02 in imogolite as a function of temperature. The upper spectrum is the CSA pattern expected when motion is stopped. This spectrum was taken using a "solid echo" NMR pulse sequence, which results in an NMR signal only from molecules that are rigid. The spectrum immediately below it is the Fourier transform of a Bloch decay, which should give signals from all C02 molecules in the sample. It is the superposition of the CSA spectrum from the solid and a rather broad peak due to mobile C02 molecules. As the temperature is raised, we simply see that the "liquid" peak becomes stronger and the solid one weaker. At 150 K all that is observed is a fairly narrow resonance due to mobile C02.

l3cQ on tmogotite Full Loading

64K

Bloch Decay

101K

I , ,I

,,,,I,,,,

I l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

250 200 150 100

50

0

150K I , , (

,,,,,,,,,,,,,,,,

-50 -100 -150 -200 -250 pprn

Figure 2. The 13C spectra of C02 adsorbed on synthetic imogolite at very high loading at different temperatures. Normal nitrogen adsorption measurements of surface area and pore size failed to quantify the small pores between the imogolite tubes. Those pores are so small, equilibration time is very long, and the equilibrium pressure for nitrogen in such small pores is below that detectable by the pressure transducers. However, we attempted to use l5N NMR to investigate the adsorption of nitrogen in this system as a function of temperature. Figure 3 contains the 15N spectra of nitrogen at a pressure which should nearly saturate all of the pores of the imogolite. The large peak at 40 K is indicative of liquid N2 in micropores. The minor intensity at about 180 ppm in that spectrum is the indication of a nitrogen CSA pattern just starting to appear. As the temperature is dropped, we start to see the loss of intensity in the liquid peak and an increase in the solid CSA pattern. At the lowest temperature we see indications of a split CSA pattern from the peak at about 200 ppm. The CSA pattern is not as well defined as the one for C02 in Fig. 3 because of instrumental difficulties with such a broad line at the low resonance frequency of *5N. The apparent splitting of the pattern is probably due to *5N-15N magnetic dipole interactions.

307

500 400 300 200 100 0 -100 -200-300 -400-500-600

ppm

Figure 3. The 15N spectra of N2 adsorbed on synthetic imogolite at very high loading at different temperatures. Figure 4 contains l5N spectra of the same sample, but at a lower loading of nitrogen. The N2 loading was computed to be sufficient to fill the small pores formed by the stacking of the imogolite tubes. In this case we see that the majority of the N2 freezes at 40 K, a much higher temperature than at high loading. We attribute this to nitrogen molecules in the very small pores between the imogolite tubes. The freezing point increase is contrary to the concepts of thermoporometry, where a freezing point depression would be expected for molecules contained in small pores. In this case, the space is so confined and the electric quadrupole and van der Waals forces are much stronger in the pores; enough to stop the tumbling of the nitrogen molecules at a much higher temperature than in the larger pores of imogolite.

500 400 300 200 100

0

-100 -200 -300 -400 -500

pprn

Figure 4. The l5N spectra of N2 adsorbed on synthetic imogolite at low loading at different temperatures. The loading was calculated to fill the very small pores prior to entering the larger pores of the imogolite.

308

3.4. Quadrupolar Nuclei This work was performed in analogy to low field NMR relaxation time measurements of pore sizes as exploited by Smiths and H a l ~ e r i n .In~ NMR relaxation measurements of pore sizes, it is known that pore sizes can be determined from the average relaxation time, T I , of the pore fluid. The basic concept is that molecules on the wall of the pore have a much shorter relaxation time than those in the center of the pore which have relaxation times equal to bulk fluid. There is rapid movement of molecules from contact with the wall to "bulk" positions. It is not necessary to know the mechanism of relaxation on the wall, only that the relaxation time be much shorter. It is also found that the relaxation time for those molecules in contact with the wall is a function of the pore fluid and the character of the pore wall. We concluded that if we were able to use a quadrupolar nucleus where the mechanism of relaxation would always be quadrupolar, it might be possible to select molecules where the detailed character of the wall is unimportant. To that end, we have performed several NMR experiments using I3lXe at different temperatures and 14N2at 77 K as probe molecules. In both cases, we found that the linewidth is so broad that we were unable to obtain an interpretable spectrum. This results from the rather large quadrupolar moment and relatively slow molecular motion that obtains with these probe molecules in contact with the wall. 4.

CONCLUSIONS

There is a great deal of information about molecular motion and interactions available through interpretation of variable temperature NMR experiments. This is true because the NMR technique is sensitive to short range interactions (on the order of 1 nm or less) and to molecular dynamics in the range of 10-2 to 10-6 s. These general principles make NMR techniques interesting and useful for studying pore structures. The work on xenon adsorption and freezing, N2 adsorption, and C02 adsorption reported here is a preview of the potential of these techniques. We are continuing to pursue these experiments in more detail to complete our understanding of the basic physical chemical phenomena and hopefully to obtain better pore size measurement techniques for microporous materials. We have a goal of developing general NMR techniques for easily studying porous solids. Our present view is that NMR techniques are powerful but are not entirely general and still require experienced practitioners of Nuclear Magnetic Resonance as well as integration of the NMR results with other pore characterization techniques.

REFERENCES 1.

2.

3. 4.

R.J.S. Brown, "Measurements of Nuclear Spin Relaxation of Fluids in Bulk and for Largo. Surface-to-Volume Ratios." Am. Phys. SOC., Bull, Ser. II 216, (1956). S.D. Senturia and J.D. Robinson, "Nuclear Spin-Lattice Relaxation of Liquids Confined in Porous Solids."SOC.Pet. Eng. J. 10: 237-244, (1970). K.R. Brownstein and C.E. Tarr, "Spin Lattice Relaxation in a System Governed by Diffusion." J. Mugn. Reson. 26: 17-24, (1977). J.C. Tarczon and W.P. Halperin, "Interpretation of NMR Diffusion Measurements in Uniform- and Nonuniform-field Profiles." Phys. Rev. B 32: 2798-2807, (1985).

309 5. 6. 7. 8.

9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21

D.P. Gallegos, K. Munn, D.M. Smith, and D.L. Stermer, "A NMR Technique for the Analysis of Pore Structure: Application to Materials With Well Defined Pore Structure." J. Colloid Znte@iuce Sci. 119: 127-140, (1987). J.A. Ripmeester and D.W. Davidson, "Xenon-129 NMR in the Clathrate Hydrate of Xenon." J. Mol. Strut. 75: 67-72, (1981). T. Ito and J. Fraissard, "129Xe NMR Study of Xenon Adsorbed on Y Zeolites." J. Chem. Phys. 76: 5225, (1982). W.C. Conner, E.L. Weist, T. Ito, and J. Fraissard, "Characterization of the Porous Structure of Agglomerated Microspheres by 129Xe NMR Spectroscopy." J. Phys. Chem. 93: 4138-4142, (1989). J.A. Ripmeester and C.I. Ratcliffe, "Application of Xenon-129 NMR to the Study of Microporous Solids." J. Phys. Chem. 94: 7652-7656, (1990). C.J. Jameson, A.K. Jameson, R. Gerald 11, and A.C. de Dios, "Nuclear Magnetic Resonance Studies of Xenon Clusters in Zeolite NaA." J. Chem. Phys. 96: 1676-1689, (1992). M. Brun, A. Lallemand, J.F. Quinson, and C. Eyraud, "A New Method for the Simultaneous Determination of the Size and the Shape of Pores: (Thermoporometry)." Thermochim Actu 21: 59-88, (1977). Y.-W. Kim and R. Norberg, Paper in preparation. W.C. Ackerman, J.C. Huling, and D.M. Smith, "The Use of Imogolite as a Pore Size Standard in the Size Range of 0.8 to 1.2 nm." Paper Number 96 at this meeting. R. Deshpande, D.-W. Hua, D.M. Smith, and C.J. Brinker, "Pore Structure Evolution in Silica Gel During AgingDrying. 111. Effects of Surface Tension." J. Non-Cryst. Solids 144: 32-44, (1992). J. Fraissard and T. Ito, ''129Xe NMR Study of Adsorbed Xenon: A New Method for Studying Zeolites and Metal-Zeolites.'' Zeolites 8: 350-361, (1988). P.J. Barrie and J. Klinowski, "129Xe NMR as a Probe For the Study of Microporous Solids: A Critical Review." Progr.NMR Spect. 24: 91-108, (1992). C. Dybowski, N. Bansal, and T.M. Duncan, "NMR Spectroscopy of Xenon in Confined Spaces: Clathrates, Intercalates, and Zeolites." Ann. Rev. Phys. Chem. 42: 433-464, (1991). P.C. Wernett, J.W. Larsen, 0. Yamada, and H.J. Yue, "Determination of the Average Micropore Diameter of an Illinois No. 6 Coal by 129Xe NMR." Energy Fuels 4: 412413, (1990). W.C. Ackerman, D.M. Smith, J.C. Huling, Y.-W. Kim, J.K. Bailey, and C.J. Brinker, "GasNapor Adsorption in Imogolite: A Microporous Tubular Aluminosilicate." Accepted for publication in Langmuir. T.T.P. Cheung, "Low Temperature (144 K) 129Xe NMR of Amorphous Materials: Effect of Pore Size Distribution on Chemical Shift." J. Phys. Chem. 93: 7549-7552, (1989). C.A. Fyfe, Solid State NMR for Chemists, C.F.C. Press, (Guelph) (1983).

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J. Rouqucrol, F. Rcdrigucz-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids 111 Studics in Surfacc Scicncc and Camlysis, Vol. 87 0 1994 Elscvicr Scicncc B.V. All rights rcscrvcd.

31 1

Molecular motion in micropore space by D-NMR J. Fukasawa", K. Kanekob,C.-D. Poon" and E. T. Samulski" a Tokyo Research Laboratories, Kao Corporation, 2-1-3 Bunka, Sumida-ku Tokyo 131, Japan b Department of Chemistry, Faculty of Science, Chiba University, Yayoi, Chiba 260, Japan c Department of Chemistry, University of North Carolina, Chapel Hill, NC 27599-3290, U.S.A. Molecular motion and ordering of the deuterated benzene adsorbed in a micropore was studied by deuterium nuclear magnetic resonance (D-NMR) as a function of the amount of adsorbed benzene. The ideally oriented slit-shaped micropore system which is suited for study with D-NMR was found in the pluglike, ordered aggregate of plate-shaped boehmite primary particles. The deuterium NMR spectra of benzene adsorbed in the micropore space at 303K showed motionally averaged the 2-D powder patterns, which are indicative of a high degree of anisotropic mobility of the adsorbed benzene molecule in conjunction with the uniaxial arrangement of the slit-shaped micropores. The adsorbed benzene ordering decreased as the fractional filling of micropores increases. The surface diffusion constant @,> of benzene at concentrations near the complete filling of the micropores is close to that of liquid benzene itself.

1. INTRODUCTION As the surface adsorption potentials from opposite pore walls are overlapped to enhance physical adsorption [ 1,2] in micropores, adsorbed molecules in the micropore may exhibit special behavior which are different from that of the bulk molecules. Understanding the molecular behavior in micropores is indispensable to elucidate the micropore filling mechanism and to contribute a new ideas to the catalysis field in general. Deuterium nuclear magnetic resonance (D-NMR) is a particularly useful method for determining molecular orientation and dynamics of partially ordered, labeled adsorbates. It has been applied to a variety of adsorbates on a wide range of substrates [3-71. However, the micropore walls in crystalline substrates (the most readily prepared specimens) are randomly oriented, which often precludes simple conclusions because guest compounds adsorbed on disordered micropore walls yield broad, often featureless, NMR spectra. An ideally oriented, slit-shaped micropore system which is suited for study with D-NMR was found in the plug-like ordered aggregate of plate-shaped

312

boehmite primary particles [8]. D-NMR spectra of deuterated adsorbates in the uniquely ordered micropore wall offered an opportunity to derive dynamical information [9] from the DNMR lineshapes. In this report, we examine molecular motion and ordering of the deuterated benzene adsorbed in a micropore with different adsorbate relative pressures. It will be shown that D-NMR can be a new tool for the characterization of microporous solids. 2. BACKGROUND

2.1. Boehmite Structure and Morphology. The unit cell dimensions and atomic structure b (12.4A) of boehmite are shown in Figure la. Two layers of A1 atoms octahedrally coordinated to oxygen are connected by H-bonding bridges [ 101. The *sen 0 Al o unit cell is uniquely oriented in the platelike, ultrafine boehmite primary particles obtained in the sol-gel synthesis of metal oxides from metal alkoxides. The average size of these particles (a) along three mutually perpendicular axes (loo), ( O l O ) , and (001) are 6.0, 2.5, and 4.0 nm, respectively (Figure lb). The b axis of the unit cell is along the (010) direction; hence the platelike particle's thickness corresponds to c (2.864 twice the b-dimension of the unit cell [8]. During the process of synthesizing boehmite, macroscopic, glassy, and monodomain samples with uniform, long-range structural order are (100) 60A prepared. Freeze-drying the sol can produce a (b) glassy plug with a uniaxial arrangement of (001)40A primary particles [8]. This morphology is a result of unidirectional growth of ice crystals in Figure 1. (a) Unit cell dimensions and atomic the phase which form On freezing a structure of boehmite (after ref. 10): the dashed cylindrical sample of the sol solutions in a lines indicate the H-bonding bridges. (b) vertical temperature gradient (-100 "/cm). Ultrafine boehmite P d m W Particle dimensions with the three mutually perpendicular axes These results in a honeycomb of channels whose (olo), (ool) indicated. lengths span the macroscopic, vertical dimensions of the glassy plug. The channel morphology, which remains after the water is removed, consists of delicate and corrugated thin walls (thickness = several tens of nanometers) which are comprised of primary boehmite particles. Approximately cylindrical channels form at high sol concentrations. This unusually regular morphology is schematically illustrated in Figure 2 (left), where the plug's symmetry axis, P, is indicated. X-ray diffraction confirmed in detail the hierarchical morphologies schematically illustrated in Figure 2, showing how the primary boehmite particles are arranged in the channel walls of the plugs. The intensity of the

313 diffraction from the (020) plane is much stronger than that of other scattering when the samples were irradiated with an X-ray beam along the h axis of the glassy plug (parallel top); the opposite intensity distribution is observed when the X-ray beam is normal to the plug axis P. This result indicates that in the glassy plugs, the (010) direction of the boehmite primary particle is normal to the channel wall surface; i.e., the b axis is perpendicular to the channel walls. Figure 2. A schematic illustration of the hierarchical morphology of a glassy plug of Hence in the microscopic plugs the b axis is, on boehmite; the macroscopic symmetry axis (the average, perpendicular to P. Note, however, plug axis P) is indicated and the arrangement of that because the wall of the channel forms a primary particles is shown; n is local surface closed surface (with variable curvature), the b normal and the (010) axis (parallel to the b axis of the boehmite unit cell - see Figure 1) are axes are distributed in a uniplanar orientational shown in successive magnifications. pattern in a cross section normal to P. The particles are stacked within the walls with the unit cell’s b axis essentially parallel from particle to particle (Figure 2 right). Micropores are formed between the (010) planes of the particles [ 113. Thus the slit-shaped micropore spaces are parallel to P and distributed two-dimensionally in a cross section normal to P. The glassy plug is very porous with high surface area. And, the macroscopic anisotropy suggests that adsorbate guests may be uniquely suited for study with D-NMR. Herein we will show that the D-NMR measurements of deuterated benzene delineate the orientational distribution of the baxes in the boehmite plug morphologies. 2.2. Deuterium NMR. The utility of the deuterium NMR technique derives from the fact that the relevant NMR interactions are entirely intramolecular, i.e., the dominant interaction is between the nuclear quadrupole moment of the deuteron and the local electric field gradient (efg) at the deuterium nucleus. The static efg tensor is generally defined in terms of the quadrupolar interactions tensor q. This is a second rank tensor that is usually axially symmetric for deuterium covalently bonded to carbon; its principal component q is along the C-D bond. In mobile phases with long range molecular orientational constraints, deuterium-labeled molecules exercise rapid anisotropic reorientation which incompletely averages the static quadrupolar interaction. A partially averaged tensor results with its principal component (4) along the local symmetry axis of the anisotropic molecular motion (the local symmetry axis is denoted by the unit, apolar director n). Anticipating uniaxial adsorbate motion relative to a director identified with the local substrate surface normal, the average (q) is simply related to the static component q (defined in a molecular fixed frame) by the factor (P,(cos a(t))),where a(t) is the timedependent angle between n and the C-D bond vector (9) = q(P,(cos 4 t ) D (1) (P,(COS a(t))) represents a time average of the second Legendre polynomial, P,(cos a(t))=

314

(3cos2a(t)- 1)/2,over the rapid motion of the bond vector's orientation relative to the local director. In an idealized microsystem-mobile adsorbates at the interface of a single crystalan averaged quadrupolar interaction may be observed with essentially high-resolution NMR techniques. The dominant feature of the deuterium NMR spectrum associated with a monodomain (crystallite) exhibiting an incompletely averaged quadrupolar interaction is a quadrupolar doublet A v whose magnitude is a direct measure of the efficacy of the motional averaging AV = Y,(~)V,(~COS~ e-1 (2) 8 is the angle between the magnetic field B, and the local symmetry axis n. Hence, in the case of a mobile, partially aligned adsorbate, the Av values may be readily interpreted in terms of the average orientation of adsorbed molecule's C-D bond vector relative to the local symmetry axis. In the absence of a peculiar adsorbate-substrate interaction, this local symmetry axis will coincide with the substrate's local surface normal. For symmetric adsorbates such as benzene, the experimentally determined value of (q),i.e., (P,(cos a(t)))may be further decomposed to give the average of the time-dependent orientation of the C, axis of benzene, (P,(cOs ac,(t))) (= -1/2(P,(cos a(t)))). relative to the surface normal. 3. EXPERIMENTAL SECTION 3.1. Sample Preparation. Boehmite sols were prepared according to literature procedures [8-91. Aluminum isopropoxide was hydrolyzed in water under vigorous stimng at 363K. The boehmite powder was obtained by drying the hydrolyzed products with a rotary evaporator at 363K. The boehmite powder was peptized with a minimum amount of 1 N HC1 solution (160 mM HCl) to make a clear sol. The glassy plug is prepared from a 15 wt % sol in a 8 mm (i.d.) X 5 mm glass tube fitted with a 8 mm (0.d.) X 4 mm brass bottom; the solution is unidirectionally frozen by cooling the brass bottom in a 203K bath and then lyophilizing the frozen plug (freeze-drying). The boehmite particles aggregate into sheets forming parallel channels that are continuous from the top to the bottom of the cylindrical plug (-7 mm in diameter and -5 mm long). The glassy plug was dehydrated at 473K under vacuum with a residual pressure of 1 mPa. After cooling to 301K, the plug sample was allowed to equilibrate with weighed amount of benzene-d, vapor within the vacuum manifold . To ensure quantitative transfer of the adsorbate, we cooled the sample to liquid nitrogen temperature and then flame-sealed and disconnected it from the vacuum line.

3.2. NMR Measurements. NMR spectra were recorded with a JEOL EX270 wide-bore spectrometer using a high power probe with a transverse solenoid coil (the B, field is perpendicular to the B, field). For the glassy plug, we used a transverse 10-mm solenoid with a 90" pulse width of 6 ps. All of the spectra were obtained by using a single pulse sequence. The plug adsorbed with benzene-d, was centered in the 10 mm tube. The symmetry axis of plug, P, was set 90" to the magnetic field.

315

3.3. Adsorption isotherm. Adsorption isotherm of benzene-d, was measured at 301K with the aid of the high precisionvolumetric organic vapor adsorption equipment [ 121. N, adsorption isotherms with >70 points were measured statically with the aid of a computer-aided gravimetric apparatus [ 131. The samples were preheated at 473K (1mPa) for more than 2 hrs prior to the adsorption measurement. 4. RESULT AND DISCUSSION

Figure 3 shows the N,adsorption isotherm for the boehmite plug. The adsorption isotherm is the same as that for boehmite film (Type I-like isotherm). The Type I isotherm generally indicates that the sample is microporous having a small external surface. The micropores consist of the “slit-space” between the plateshaped primary particles. The external surface is the only surface of the macrodomain plug that we can see by the naked eye. The Type I-like isotherm with a gradual increase below a plateau indicates that the micropores have a size distribution classified into several groups. This size distribution might be caused by different packing modes of the primary plate-shaped particles. The number of these micropore groups could be determined by the number of the clear bend-transition in the DR plot for the adsorption isotherm. The DR plot of the N, isotherm is shown in Figure 4. The plot can be divided into three linear regions as could that constructed from data using the boehmite film. Thus, in the plug there are three micropore sizegroups where N, molecules can enter. Experimentally the micropore volume for each size micropore can be estimated from the extrapolation of the segments of the DR plots. Table 1 shows the micropore size distribution estimated by the DR plot. Here, the subgroups of micropores are denoted as W,“, W’, and W H O in the order of increasing pore width. L, M, and H arise from the lowest, medium and highest relative pressure regions of the DR plot-

10 1

I

PPO Figure 3. The N2 adsorption isotherm for boehmitePlug.

InzPo/P Figure 4. The DR plot of the N2 adsorption isotherm for the boehmite plug. Table I. The micropore size distribution determined by the DR plots for Nz adsorption isotherms for boehmite plug. W$ml/g) 0.043

w i (ml/g)

W,O(ml/g)

0.049

0.149

316

PPO Figure 5. The benzene adsorption isotherm for boehmite plug.

segment. The volume for each size micropore are almost same as that found in the boehmite film. It is interesting that in both films and plugs, the stacking order of boehmite primary particles is essentially the same though these morphologies are prepared by two distinct routes: (1) air-drying (film) or (2) freeze-drying (plug) sols. Figure 5 shows the adsorption isotherms of benzene-d, for the boehmite plug at 303K. The benzene-d, adsorption is also type I-like in shape, indicating that benzene molecules are adsorbed in the classified micropores. The DR analysis was applied to the benzene isotherm (Figure 6). In this case, the plot can be divided into two linear regions. The benzene-8 molecules must access only the larges of the two kinds of micropores. In order to understand the molecular motion and ordering of the deuterated benzene adsorbed in the two kinds of micropores, D-NMR measurements were made on the different amounts of benzene-d, molecules in the micropore groups in the plug sample. The samples used are (a) 0.32, (b) 0.86, and (c) 1.08 mmol benzene/g boehmite in which benzene-d, molecules fill 60% of medium-size pore groups, 100% of medium and 50% of large pore groups, and 100% of both pore size groups,

In 2p0P Figure 6. The DR plot of the benzene adsorption isotherm for boehmite plug.

(a) 0.32 mmol/g

@)

I

I

I

10

0

-1 0

kHz

Figure 7. Deuterium NMR spectra of benZene-d6 adsorbed on a glassy plug in the j3 = 90' at 303K. The benzene/boehmite ratio (mmoVg) is indicated next to the corresponding experimental spectra.

317 respectively. The slit-shaped micropores are formed between the (010) planes of the boehmite primary particles, which serve as the adsorbing sites for benzene. Benzene molecules enter the micropore and form a domain of an ordered phase on the pore walls. When the molecular reorientation and chemical exchange of adsorbed benzene within a domain are sufficiently rapid, the quadrupolar interaction is averaged. A spectrum is obtained consisting of superposition of spectra due to the various domain orientations. In this mobile benzene phase, the residual interaction is relative to the local normal of the slit pore walls, n. In the plug, the local normals have a uniplanar distribution of 8,where 8 is the angle between the n and B, (a uniform two-dimensionaldistribution). Thus, in the p = 90" orientation of plugs, where p is the angle of the P axis with respect to the magnetic field B,, the D-NMR spectra showed 2-D powder patterns. In Figure 7 we show the spectra of benzene-d, adsorbed on the three samples for p = 90". Distorted two-dimensional powder patterns with small Av values (4 kHz) DR are observed for all samples, indicating the benzene molecules form domains in the slitpores and the mobility is high and slightly O A anisotropic. The low degree of order in the resulting anisotropic motion is confirmed by the general finding that the observed Av values 0.03 are on the order of a few percent of static value (-250 kHz) of the splitting. When the adsorbate concentration increases, the magnitude of Av decreases due to a change to a less ordered type of the benzene motion. The distortion of the D-NMR patterns is as a result 0.1 of a non-negligible anisotropic magnetic susceptibility contribution from the boehmite plug structure. Further, we can realize that the pattern (c) is partially averaged. The partially averaged 2-D powder pattern is given by the l.o rapid adsorbate translational diffusion along to the cylindrical channel walls (the rapid exchange of adsorbate between wall surface segments having local director n). The benzene molecules must exchange between the lo.o domains and diffuse through the aligned micropores. This surface diffusion constant Ds can be inferred from simulated spectra Figure 8. Simulated lineshapes of 2-D powder obtained by modifying the method used to with heinfluence of Ax (4.2) forplanar partially averaged NMR lineshapes in reorientation with different planar diffusion cholesteric liquid crystals [14]. In Figure 8, coefficients h.

A

A 24-

318 we show examples of simulated lineshape of 2-D powder pattern with the influence of anisotropic magnetic susceptibility. The lineshape is influenced by the “planar diffusion coefficient” D, that describes the effective angular reorientation of n brought about by circumferential trance diffusion of adsorbate. Comparing the observed pattern (c) and simulated examples, the D, value of pattern (c) is estimated as 0.03 0.1. Using the EinsteinSmoluchowski relation for surface diffusion, the D, value can derive D, from the use of the radius of curvature r of the channels. The estimated value (3 10 X 10’ cm2/ s) was close to that of liquid benzene itself (D = 2.14 X cm2/ s) [15]. From these results, we can discuss the relationship between the molecular motion and the amount of benzene in each micropore group as follows: When the medium size micropore group is filled with benzene, the molecular motion within the domain in the slit pore is fast and anisotropic. Further addition of benzene half-filling the large size micropores results in no fundamental change of the benzene motion except for less order (more effectively average-via chemical exchange-anisotropic motion). The spectrum onIy shows one 2-D powder pattern (not the superposition of two different powder patterns from the benzene in medium and large micropores. Hence there is fast molecular exchange (on the NMR time scale) between the domains in different sized micropores) irrespective of the amount of benzene. The adsorbate is undoubtedly exchanging between surface-bound sites (with preferred surface orientations) and bulk like, isotropic benzene. Thus the benzene molecules behave as a quasi-liquid that diffuses two-dimensionally in the micropores of boehmite glass.

-

-

REFERENCES 1 D.H. Everett and J. C. Powl, J . Chem. SOC.Furudy Trans. I . (1976) vo1.72,619. 2 S. J. Gregg and K. S. Sing, Adsorption, Surface Area and Porosity Chapter 3, Academic press, New York, 1982. 3 B. Stubner, H. Knozinger, J. Conard and J. J. Fripiat, J . Phys. Chem. (1978) vo1.82, 1811. 4 H. E. Gottlieb and Z. Luz, J. Murgn. Reson. (1983) vo1.54,275. 5 P. D. Majors and P. D. Ellis, J Am. Chem. SOC.(1987) vol.109, 1648. 6 R. Grosse and B. Z. Boddenberg, Z. Phys. Chem. (1987) vol. 152,259. 7 W. Horstmann, G. Auer and B. Boddenberg, Z. Phys. Chem. (1987) vo1.152,281. 8 J. Fukasawa and K. Tsujii, J. Colloid Interface Sci. (1988) vol.125, 155. 9 J. Fukasawa, C.-D. Poon and E. T. Samulski, Lmgmuir (1991) vo1.7, 1727. 10 J. J. Fripiat, H. Bosmans and P. G. Rouxhet J. Phys. Chem. (1967) vo1.71, 1097. 11 J. Fukasawa, H. Tsutsumi and K. Kaneko, Langmuir, to be submitted. 12 M. Sato, T. Sukegawa, T. Suzuki and K. Kaneko Chem. Phys. left.(1991), vo1.181,526. 13 K. Kakei, S. Ozeki, T. Suzuki and K. Kaneko, J. Chem.SOC. Furudy Trans. I . (1990) ~01.86, 371. 14 Z. Luz, R. Poupko and E. T. Samulski, J . Chem. Phys. (1981) vo1.74,5825. 15 D. W. McCall, D. C. Douglass and E.W. Anderson, Ber. Bunsen-Ges. Phys. Chem. (1963) v01.67,336.

J. Rouqucrol, F. Rodrigucz-Rcinoso, K.S.W. Sing and K.K. Ungcr (Eds.) Characterization of Porous Solids 111 Studies in Surracc Scicncc and Catalysis, Vol. 87 0 1994 Elsevicr Scicncc B.V. All rights rcscrvcd.

319

The Use of 15N NMR for the Understanding of Nitrogen Physisorption. J. Bonardeta, J. Fraissarda, K. Ungerb, Diptka Kumarb, M. Ferreroc, J. Rag16 and W.C. Connerc

Wniv. Pierre et Marie Curie, Lab. Chimie de Surfaces, Paris, France bJohannes Gutenberg-Universitat,Maim, Germany CDept. Chem. Engng., Univ. Massachusetts, Amherst, MA. 01003, USA Nitrogen adsorption at liquid nitrogen temperature, 77K, is universally employed to determine pore dimensions. The nature of nitrogen physisorbed within the micropores of ZSM-5 zeolite was studied by in situ 15N NMR as it depends on the partial pressure of the nitrogen and the temperature above and below 77K. An increase in the volume of adsorption of nitrogen at 77K occurs at a relative pressure of 0.18 for this zeolite. The nature of the nitrogen was studied below and above this increase in nitrogen adsorption. We find that two states (phases) of nitrogen are evident. We conclude that two phases can be present but that a solid phase of nitrogen is not evident even as the temperature is decreased to below 11K at a relative pressure of 0.25.

-

1. INTRODUCTION

Nitrogen is the most commonly used adsorbent for the characterization of pore structure by ad-desorption. It is assumed that the adsorbed nitrogen behaves like a condensing liquid on a flat surface. In microporous systems such as zeolites these assumptions are not as clear. Indeed, Unger and Miiller (1-3), among others (41,have found hysteresis in the adsorption at a relative pressure, P/Po of 0.15 for adsorption of nitrogen at 77K in ZSM-5 family of zeolites. This is seen in Figure 1 for adsorption at 77K. These authors speculated that there might be a transition behveen a liquid and solid nitrogen within the pores of the zeolite at this pressure and temperature. The exact nature of this hysteresis loop depends on Si/A1 ratio of the zeolite and the sorption temperature(3), and it also depends on the rate at which the sorption was conducted( 5). However, it is always present in these systems to some extent. To understand the state of the nitrogen above and below this hysteresis, we studied the 15N NMR at temperatures from 4-90K and relative pressures at 77K of 0.08 and 0.25. It is apparent that there are indeed at least two states of Nitrogen adsorbed in the pores of the zeolite at the higher pressure. We, however, conclude that there is no evidence for a solid form of nitrogen under these conditions. Indeed, there is no

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320

evidence for a transition to solid nitrogen even down to below 10K. These results will be presented and the forms of the sorbed nitrogen will be discussed. These are, to our knowledge, the first studies of nitrogen physisorption employing 15N NMR.

E

200

;”

150

n

E Y

100

--

50 -0

I I

-

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I I I 0.25 I

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0.6

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Relative Pressure (P/Po) Figure 1:Isotherm for Nitrogen adsorption at 77K into ZSM-5 (Si/AI -50). 2. EXPERIMENTAL

Prior to adsorption, the samples have been calcined and or degassed to remove any organic sorbents or residual template. Samples of ZSM-5 were loaded into 5mm NMR tubes and evacuated to 1W6 torr at 500OC. The samples were then cooled to 77K in vacuum in a liquid nitrogen bath. 99% 15N nitrogen gas was then adsorbed to an equilibrium pressures of 60 torr(P/Po = 0.08) and 190 torr (P/Po = 0.25). These ampoules were then pulled off with a torch and remained immersed in liquid nitrogen until they were introduced into the NMR probe of a Brucker 500 CXP spectrometer fitted with the coils appropriate for I5N analyses. The samples were subsequently rapidly transferred into the NMR probe which had been pre-cooled to -77K. In this manner the sample temperature was maintained near 77K from the time of adsorption until the actual NMR measurement. The relative pressures of the nitrogen adsorption pertains to the measurements at 77K. At higher and lower temperatures the pressures will vary accordingly in the sealed sample ampoules. However, the gas volume in the sample ampoules was small ( << 1 cm3 STP), the pressure was reduced (<0.25bar), and the adsorption was done in the region of the isotherm where the changes in volume adsorbed with pressure are insignificant (a plateau in the isotherm). Therefore, even these changes in temperature (and pressure) did not substantially change the volume adsorbed within the micropores of the ZSMS. The temperature in the NMR was controlled to within 0.1K by a liquid He cryostat, i.e., ATC4 controller from Oxford Instruments. We confirmed that the I5N NMR spectra for adsorbed nitrogen were completely reproducible by retaking the spectra after the temperature excursions and even after the samples were removed from the cavity for over 24 hours and then were reintroduced.

321 3.15N-NMR RESULTS & DISCUSSION

Our first studies involved adsorption at a relative pressure of 0.25. As the temperature is decreased from 77K,a phase transition from a liquid-like condensate to a restricted/confined liquid with reduced molecular motion is inferred from changes in the NMR signal width. At least two superimposed NMR signals are evident and the broader signal dominates the spectra as temperatures below 65K. This is seen in Figure 2 which shows the decomposition of the signal at 63K and P/Po =0.25. However, the transition from this state (phase) to a solid phase is not evident as the temperature is lowered to below 11K. The micropores restrict the molecular motion and, at the same time, change (depress the transition temperature for) the Liquid-Solid equilibrium of the condensing nitrogen.

40

30

20

10

0 kHertz

-10

-20

-30

-40

Figure 2: Decomposition of the I5N NMR spectra at 50K into two component lines for enriched Nitrogen initially adsorbed in ZSM-5 zeolite at P/Po = 0.25 at 77K. The *5N NMR for nitrogen adsorbed at a relative pressures of 0.08 is shown in Figure 3. There is a difference in the breadth of the N M R signal with temperature. The narrow line seen for the sample at 0.08 relative pressure and 77K is characteristic of nitrogen solely in a liquid state. Note that >>99% of the nitrogen in each of the samples is adsorbed within the zeolite pores, i.e., there is little nitrogen present in the gas phase over the samples. It is apparent that the intensity of the broader signal is increasing as the temperature is lowered and that this increase in intensity is at the expense of the narrower signal.

322

I

I

I

50,000

0

-50,000

Hertz

Figure 3: Changes in the 15N NMR for nitrogen adsorbed at a relative pressure of 0.08 as a function of temperature, (K)shown on the right edge.

323

The broader signal that is evident in the spectra at a relative pressure of 0.25 is in a more restrictive environment than the sample at a relative pressure of 0.08. The rotational motion of nitrogen is substantially more limited at the higher pressure; although, the difference in the volume adsorbed is only ca. 10%. This is seen in Figure 4 for both samples at 63K.

I \

I

I

I

50,000

0

-50,000

Hertz

Figure 4: Comparison of the 15N NMR for nitrogen adsorbed in ZSM-5 at relative pressures of 0.08 and 0.25 at 63K. The change from a liquid-like to a broader signal which reflects a more restricted environment is progressive as contrasted with a standard temperature dependent phase transition. This is seen in the comparison of the 15N NMR signals at 90K and 77K in Figures 5 and 6.

T = 9OK P/Po = 0.08P/Po = 0.25

-

I

I

50,000

0

I

-50,000

Hertz

Figure 5: Comparison of the 15N NMR for nitrogen adsorbed in ZSM-5 at relative pressures of 0.08 and 0.25 at 90K.

324

Hertz

Figure 6: Comparison of the 15N NMR for nitrogen adsorbed in ZSMS at relative pressures of 0.08 and 0.25 at 77K. The transition between a narrow and a broad NMR spectra is not abrupt either as the temperature is lowered or the pressure is increased. It can be inferred that the more restricted phase that is evident in the broader signal is associated with a denser phase than the narrow liquid-like signal evident at a relative pressure of 0.08 and 77K. Thus, a slightly greater volume of nitrogen is required to fill the pores. This more restricted phase is progressively formed with increased gas phase pressure and/or decreased temperature. The two sets of spectra are seemingly shifted one from the other in temperature due to the higher equilibrium pressure and slightly increased adsorption. This is seen in figure 7 which compares the spectra at P/Po =0.08 and 63K with the spectra at P/Po = 0.25 and 77K.The spectra are essentially identical.

T = 63K P/Po = 0.08__ T = 17K P/Po=O.25

-

I

I

I

50,000

0

-50,000

Hertz

Figure 7: 15N NMR spectra for nitrogen adsorbed on ZSM-5 at P/Po =0.08 and 63K and at P/Po = 0.25 and 77K.

325

The mechanism for the relaxation in zeolites is most probably due to dipolar interactions. Other sources of line-width broadening, such as paprmagnetic impurities, are insignificant. These dipolar interactions will increase as the temperature decreases or the molecules are restricted in their molecular motion due to interactions with the microporous network. The result is a broader NMR resonance signal as the temperature is decreased. If, in addition, the molecules are progresively confined to the more restricted void spaces, a broader signal will result from the enhanced dipolar interactions due to the confinement. These steric restrictions may progress from the smaller to the larger pores or they may involve certain multiples of molecular dimension. Thus, a void space that is close to three times a molecular dimension (such as width) might give evidence for molecular adsorption in a more restricted configuration than a void space that is two and a half times the molecular dimension, under the same conditions. Thus, motion (and its change with temperature) can change the nature of the environment for adsorbing nitrogen. The restricted pore spaces can also provide an environment where motion will be reduced and, thus, dipolar interactions are enhanced resulting in a broader NMR spectra. This transition is not a simple "phase" transition from a liquid to a restricted state that occurs at a specific temperature and pressure in the bulk since the void network can be complex (even in a zeolite) and the specific molecular motions can control the influence of the steric interactions. The two "phases" that are simultaneously present within the pores of the zeolite do not readily exchange on an NMR time scale and, thus, two superimposed spectra are evident and not an average of a broad and a narrow line that is averaged by exchange to yield a single spectra with a single intermediate line width. We propose that this is because the two phases are spatially separated, i.e., the two phases are formed within different portions of the void network within the zeolite. Since the new phase that is formed is more restricted in its rotational mobility than the liquid-like phase that is also evident, we propose that the broader spectra is due to a. phase forming within the smaller dimensions of the void network, possibly first in the zigzag channels. Next (with increasing pressure or decreasing temperature), it might be forming in the straight channels and finally at the channel intersections. The progressive nature of the transformation may reflect limited exchange at the interface between these various spatial regions of the void network. Alternately, there might be a matching between the spacing between the nitrogen molecules in the more restricted configuration and the pore dimensions. Thus, if the channel intersections were exactly an integral n times the distance between nitrogen molecules in the more restricted phase, the more restricted phase might first form at the channel intersections. Without further 15N NMR data for nitrogen adsorption in other zeolites (or with variation in the Si/A1 ratio's or within ZSM-11, as an example), we suggest that formation of the more restricted sorbed phase would occur within the smaller dimensions of the void network first. This would be followed, progressively, by formation of this phase within void spaces of increasing dimensions.

326 4. ACKNOWLEDGMENTS

We are indebted to Bruker laboratories in Karlsruhe for the use of their facilities and NMR instruments. Specifically, Dr. S. Steuemaguel is thanked for his running of the NMR. We also thank P. Man for the decomposition of the NMR spectra. The Petroleum Research Fund of the American Chemical Society is thanked for the funds for WCC, under grant 22916-AC5. REFERENCES 1. U. Miiller and K.K. Unger, in Characferimtionof Porous Solids, Eds. K.K. Unger et at. , Vol. 39 (Elsevier, Amsterdam, 1988) 101. 2. U. Miiller, K.K. Unger, D. Pan, A. Mersman, Y. Grillet, F. Rouquerol, J. Rouquerol in Zeolites as Catalysts, Sorbents, and Detergent Builders, Vol46 (Elsevier, Amsterdam, 1989) 665. 3. H. Reichert, U. Muller, K.K. Unger, Y. Grillet, F. Rouquerol, J. Rouquerol, J.P. Coulomb, in Characterization of Porous Solids 11, Eds. F. Rodriguez-Reinoso et al. , Vol62 (Elsevier, Amsterdan, 1991) 535. 4. P.J.M Carrott and K.S.W Sing, Chem. Ind. (1986) Beiheft 1,128. 5. S.W. Webb and W.C. Conner,Characterization of Porous Solids lZ, Eds. F. RodriguezReinoso et al., Vol62 (Elsevier, Amsterdan, 1991) 31. 6. W. Conner, M. Ferrero, J. Bonardet and J. Fraissard, J. Chem. SOC., Faraday Transactions (1993), 89(3), 833

J. Rouquerol, F. Rodrigucz-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids 111 Studies in Surhcc Science and Cat~lysis,Vol. 87 0 1994 Etscvicr Scicncc B.V. All rights rcscrvcd.

327

Characterization of macropores using quantitative microscopy

Brian McEnaney and Timothy J. Mays School of Materials Science, University of Bath, BATH, Avon BA2 7AY, United Kingdom

Abstract The application of quantitative microscopy, or image analysis, to the characterization of macropores is reviewed using as examples different types of porous carbon materials. The principal advantages of the technique are the ability to measure both open and closed porosity and the shape, location and orientation of pores. It is also an advantage to be able to measure these parameters for different classes of macropores in a given porous body. The stereological problems of relating two-dimensional measurements to structural parameters of the threedimensional material are a disadvantage, particularly when dealing with anisotropic and heterogeneous substances.

1.

INTRODUCTION

The performance of porous materials in many technical applications results from an interplay between properties that depend to different extents upon three main pore types: micropores (width, w < 2 nm); mesopores (2 Iw 1.50 nm) and macropores (w > 50 nm) [ 11. For example, the oxidation in air of anode carbons used in aluminium smelting depends upon the specific surface area and therefore mainly upon the extent of meso- and microporosity [2]. However, reactivity also depends upon the temperature of the anode surface, which is related to its thermal conductivity. This property is dominated by the nature and extent of macropores. Examples of other important properties that are influenced by pore structure include adsorption, electrical conductivity, Young's modulus and strength. Consequently, it is often necessary to characterize several pore types, using appropriate methods, in order to assess the overall performance of a material. Here, we focus attention on the characterization of macropores. There are three main methods presently is use for characterizing macropores: mercury porosimetry, fluid flow (i. e., diffusivity and permeability of gases and liquids) and microscopy. The relative merits of these techniques have been considered previously [3]. Porosimetry and fluid flow only probe open pores, i. e., pores that are accessible to fluids penetrating from external surfaces. This is a limitation where both open and closed pores are relevant, e. g., when electrical, thermal and mechanical properties are being considered, but one that does not apply with microscopical methods. A further limitation of porosimetry and fluid flow methods is that simple, model pore structures are usually assumed, e. g., bundles

328

of non-intersecting capillaries, whereas in microscopy pores are viewed directly and therefore an u priori assumption about pore structure is not required. This paper is a review of some of the capabilities of quantitative microscopy for characterizing macropores using examples taken mainly from work in the authors' group on porous carbons and graphites. These examples include measurements made using quantitative microscopy which can also be made using porosimetry and fluid flow, e. g., pore volume fractions, pore size distributions and fractal dimensions. In addition, examples are presented of measurements made using quantitative microscopy, such as pore shape, orientation and location, that are difficult or impossible to make using the other two methods. 2.

EXPERIMENTAL TECHNIQUES

The preparation of a sample for microscopy involves the usual methods of grinding and polishing a flat specimen (often in a resin mount) to yield a planar section through the porous body. Samples can be viewed in an optical microscope (resolution 2 1 pm) or a scanning electron microscope, SEM, for greater resolution. The development of an effective polishing technique is of critical importance to ensure a faithful definition of pore edges and to avoid artifacts that can cause pore enlargement or closure. It is also necessary to ensure effective contrast between pores and the solid matrix to facilitate 'segmentation' (see below). Open pores can be distinguished from closed pores by impregnation with a fluid of high optical or electron contrast, e. g., a fluorescent resin or a liquid metal respectively [4]. While manual techniques can be used to measure the geometry of pore cross-sections, 6'. g., using calibrated graticules either in the microscope system or on micrographs, they are laborious and error-prone. Instead, the most-widely used methods for quantitative microscopy of porosity involve computer-based image analysis. A block diagram of a typical image analysis system using optical microscopy is shown in Figure 1 . I I I I I I I I I I I I I I I

Figure 1. A block diagram of a typical image analysis system for quantitative microscopy. The general mode of operation of the image analysis system, Figure l., is as follows. A monochrome television camera captures the image from the microscope. This image is then

329 digitised by the computer into an array of square picture elements, 'pixels', whose locations in the array are stored in the computer. Each pixel is assigned a grey level corresponding to the average brightness of the image at its particular location. Typically, in modem, commercial image analysers, there are lo5 - lo6 pixels and -lo2 - lo3 grey levels in an image array. The grey image is next converted to a binary image by a process called 'segmentation', in which the operator selects a range of grey levels that corresponds to the objects of interest, i. e., macropores in the present case. In the binary image, the pixels within the segmented grey level range are 'on' while the rest are 'off'. Segmentation is a critical step in the process since it requires the subjective judgement of the operator. It is also for this reason that specimen preparation is so important, since it is necessary to ensure that all of the objects of interest have grey levels that fall within the range selected for segmentation. Modem image analysis systems are equipped with overlay facilities which allow the grey and binary images to be compared and a suite of image refining algorithms which the operator can use to ensure that the binary image is a faithful representation of the objects of interest. The final step in the image analysis process is the computation of geometrical parameters of objects in the binary image (see below). The image analysis system can easily make the large numbers of measurements that are required to ensure results are statistically significant. Typically many thousands of objects in a microscopical field can be measured, and many fields can be measured for a given sample using automatic stepping stages. Thus, once the parameters required for effective segmentation have been selected, a high degree of automation can be achieved. With objects where there is a wide range of grey levels, segmentation may be difficult. In such cases, the objects of interest can be selected and outlined manually, e. g., using a light pen. This circumvents the problem of segmentation, but the advantages of automation are lost. A cross-section through a macropore in a plane, polished surface is sketched in Figure 2. In a binary image, the continuous curve which is the perimeter of the pore section is represented by an irregular polygon whose vertices are the co-ordinates of the boundary pixels. The image analysis system then computes geometric parameters of this polygon. Some examples of such parameters are shown in Figure 2. In addition to simple parameters such as area, A, and perimeter, P, other, more complex parameters may also be measured, e. g., maximum and minimum Feret diameters, d, and dmi,, Figure 2. Derived parameters may also be computed, such as aspect ratio = d,,, / dmin,equivalent circle diameter = d(41cA) and roundness = P2I 4aA. If a reference axis is defined, then orientation parameters can also be determined, e. g., the angle 8 in Figure 2.

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3.

EXAMPLES OF MACROPORE CHARACTERIZATIONS QUANTITATIVE MICROSCOPY

USING

Presented here are some examples of macropore characterizations using quantitative image analysis. While these examples are taken mainly from the authors' work on carbons and graphites many of the points that they illustrate are applicable to a wide range of macroporous solids.

330

'

boundary of macropore cross-section

approximating polygon whose vertices are the centres of boundary pixels smallest superscribed circle, diameter = d (maximum Feret diameter)

; I

perimeter, P

Figure 2. A sketch of a macropore cross-section in a plane, polished surface, and some examples of simple image analysis parameters.

3 . 1 , Distributions of pore areas and pore volumes A basic function of quantitative microscopy is the estimation of pore area distributions. For example, image analysis was used [5] to determine macropore size distributions in carbons made from phenolic resins, which are of interest as porous catalyst supports. The macropore sizes were correlated with fabrication parameters, e. g., pressing conditions and carbonization rates, and mechanical properties such as Young's modulus, flexural strength and toughness. These carbons provide simple images for analysis with sharp contrast between pores and matrix as shown in Figure 3. A typical pore area distribution for such carbons obtained using computer-based image analysis, Figure 4., shows a unimodal pore area distribution with a modal value of 8 pm 2.

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331

20 l m Figure 3. Macropores in a resin-based carbon.

m

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2

1

0

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1 log ( pore area, A / pm2 )

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Figure 4. A pore area distribution for a resin-based carbon obtained from quantitative optical microscopy. To equate the pore area distribution to a pore volume distribution requires an assumption about the stereological relationship between the two-dimensional images and the threedimensional objects from which they are derived. This is Delesse's theorem and, in the present

332 context, it implies that the macropores are spherical and uniformly distributed throughout the sample. This assumption is often made in image analysis studies, including those on materials for which the theorem is clearly inappropriate, e. g., anisotropic materials or on objects which are far from spherical. In the present case a number of initial measurements were made including distributions of aspect ratio of pore sections cut in different directions in the sample which indicated that pores were approximately equiaxed. In addition, observations on a number of fields in different sections indicated that, subject to careful fabrication, pores were distributed uniformly throughout pressed carbon beams. This evidence for isotropy and homogeneity of the macropores in the resin-based carbons suggested that it was reasonable to apply Dellesse's theorem to these materials, i. e., the area fraction of pores, typically around 0.40, was a good approximation to the volume fraction. However, in general, the stereological problem of relating data from a two-dimensional image to structural parameters of the threedimensional body from which it is derived is a serious limitation of quantitative microscopy.

3 . 2 Pore shape and orientation The above example illustrates the application of quantitative microscopy to a class of macroporous materials which are particularly simple, i. e., they contain a single class of uniformly-distributed, near-spherical pores. However, in many solids pore structures are more complex, e. g., they comprise non-uniform distributions of pores of different shapes which originate at different stages in the manufacturing process. Quantitative microscopy has proved very useful in characterising the size, shape and orientation of different classes of pores in complex engineering materials. One class of pores of particular interest are cracks, i. e., pores of high aspect ratio. The orientation of cracks can play an important role in determining a number of properties of porous materials, e. g., strength, electrical conductivity and thermal expansion coefficent. The capabilities of image analysis in this area is illustrated with two examples: (i) grain orientations in an electrode graphite and (ii) cracking around fibres in a carbon-carbon composite. Synthetic graphites, used as electrodes in the smelting of metals, are made by extruding and subsequently heat-treating a mix of liquid pitch and solid, needle-coke filler grains. Figure 5. shows the general microstructure of an electrode graphite, including the macroporous calcination cracks that run parallel to the long axis of a filler grain. Quantitative microscopy was used to determine the angle, 9,between the maximum Feret diameter (see Figure 2.) of a single calcination crack - and hence the long axis of the filler grain - and the extrusion direction in each of a large number of grains across the radius of a graphite electrode [61. The extent of orientation of grains, as measured by the width of the distribution of 8 for localized regions, was greatest at the edge of the electrode log and least at its centre, see Figure 6. This was as expected from consideration of shear forces in the liquid mix during extrusion. The different extents of grain orientation, Figure 6., have implications for the radial variation of electrical conductivity of electrodes and hence their performance in service. This shows how quantitative microscopy of macropores can provide structural information that would be difficult or impossible to obtain using other methods.

333

1 rnm

Figure 5 . Microstructure in an electrode graphite. b - calcination cracks in the needle-coke filler, a-a'. d - globular rnacropores in binder phase, c. Extrusion direction parallel to base of micrograph.

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334

Another example that illustrates this point concerns the nature of cracking around fibres in carbon-carbon composites, CC, i. e., composites consisting of carbon fibres in a carbon matrix. CC have high strength, stiffness and toughness which they retain to very high temperatures; they also have excellent thermal shock resistance. For this reason they have been used extensively in components for rocket engines and re-entry vehicles in aerospace engineering and they are also candidate first-wall materials in the next generation of fusion reactors [7]. However, little is known about the relationships between structure and properties in these materials under irradiation conditions. As part of a programme assessing the prospects of CC in fusion reactors, image analysis studies have been undertaken recently to characterize the nature of cracking around fibres in CC [7]. Such cracks may be important in determining the fracture and thermal expansion of the composites. Distributions of macroporous, fibrematrix cracks in a three-directionally reinforced CC have been measured on images provided by a scanning electron microscope. Figure 7. shows the model for quantifying these cracks in terms of a characteristic angle 8, and it illustrates the frequency of cracks as a function 8. There is preferential cracking in the arc 30 < 8 c 90 ', Figure 7., probably due differential stresses arising from the anisotropic reinforcement architecture of the composite. O

count

a

1"

90.120

21Q240

270-300

Figure 7. Analysis of macroporous fibre-matrix interface cracks in a three-directionally reinforced carbon-carbon composite. a. definition of angle 8; b. distribution function of 8 (from [7]).

3 . 3 Fractal analyses of macropore surfaces The examples of quantitative microscopy above have all involved the use of simple parameters of planar, Euclidian geometry to characterize macropore cross-sections, e. g., ma, Feret diameter, and orientation angle. However, image analysis can also be used to explore the fractal nature of objects, including pores. A simple technique is the divider stepping method derived from Richardson's classical work on the length of coastlines (see [S]). In the present context, if the perimeter of a pore viewed in the image analyser is fractal then the estimate of its length, P(n), using a yardstick of length n is related to the fractal dimension D by

335

where B is a constant. Thus, the value of D may be estimated by measuring the perimeter of the pore using chords (yardsticks) of different lengths. This can be done manually with a light pen or, alternatively, by using pixel size as a yardstick. Figure 2. shows that the image analyser represents the pore perimeter as an irregular polygon whose vertices are the coordinates of the boundary pixels. If the pixel size is varied by viewing the pore image at different magnifications, then the fractal dimension can be estimated. An example of a Richardson plot for a pore in a resin carbon obtained using this method is shown in Figure 8. The value of D = 1.33 obtained from this plot is in the range 1 < D < 2, as expected for a fractal line. However, the fractal nature of the pore perimeter is not clearly established because the range of yardstick size (n = 0.2 - 2.0 pm) is limited. Another limitation of this approach is that microscopical estimations of pore sizes are influenced by the magnification used if the pore edges are rounded as a result of polishing [9]. The estimation of fractal dimensions using image analysis has been reviewed by Kaye [lo].

2.9

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2.8

3.

2.7 2.6 2.5 -0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

log 1o (pixel width / pm) Figure 8. A Richardson plot for a macropore in a resin-based carbon.

3 . 4 Comparison of quantitative microscopy and other methods No systematic studies appear to have been made yet to compare results from quantitative microscopy, porosimetry and fluid flow for characterizing macropores in a particular material. However, cumulative open macropore size distributions for various graphites obtained from image analysis, using metallic and fluorescent impregnants for contrast enhancement, were compared with those obtained form mercury porosimetry [4].This work was part of a study of the influence of pore structure on the oxidation of graphite moderators in nuclear reactors. As Figure 9. shows, porosimetry underestimates mean pore sizes compared with those obtained from image analysis due, it was presumed, to the sensitivity of porosimetry to constrictions in the pore network.

336

OPV 15.2 */a

-

Characlcrtsl~c~ Q T O dimCMOn ( p m l

Figure 9. Comparison of cumulative open pore size distributions for a nuclear graphite obtained from quantitative optical microscopy and mercury porosimeay (from [4]). One implication of the different macropore size distributions in Figure 9. is that, if oxidation is not influenced by pore constrictions, then image analysis is more useful in studies of moderator corrosion than porosimetry. It may be noted that, in a separate study [ 111, it appeared that fluid flow, like image analysis, is not sensitive to pore constrictions. This suggests that macropore size distributions from image analysis and fluid flow might be similar. Further work is required to c o n f i i this expectation. 4 . CONCLUDING REMARKS The principal advantages of quantitative microscopy as a tool for characterising macropores in porous solids are the ability to measure both open and closed porosity and the shape, location and orientation of pores. It is also an advantage to be able to measure these parameters for different classes of macropores in a given porous body. The stereological problems of relating two-dimensional measurements to structural parameters of the threedimensional material are a disadvantage of the technique, particularly when delaing with anisotropic and heterogeneous substances. Acknowledgements

We thank: Dr T.D. Burchell of Oak Ridge National Laboratory, USA, and Dr A.J. Wickham of Nuclear Electric plc, UK, for permission to use Figures 7. and 9. respectively.

337 REFERENCES 1.

2. 3.

4. 5. 6. 7. 8. 9. 10.

11.

K.S.W. Sing, D.H. Everett, R.A.W. Haul, L. Moscou, R.A. Pierotti, J. Rouquerol and T. Siemieniewsaka, Pure Appl. Chem., 57 (1985) 603. K. Grjotheim and B.J. Welch, Aluminium Smelter Technology, 2nd edn., Aluminium Verlag, Dusseldorf, 1988. B. McEnaney and T.J. Mays, in: H. Marsh (ed.), Introduction to Carbon Science, Buttenvorths, London, 1989, pp. 153-196. J.V. Best, W.J. Stephen and A.J. Wickham, Prog. Nucl. Energy, 16 (1985) 127. B. McEnaney, I.M. Pickup and L. Bodsworth, Catal. Today, 7 (1990) 299. Y. Yin, B. McEnaney and T.J. Mays, Carbon, 27 (1988) 113. Y.Q. Fei, B. McEnaney, F.J. Derbyshire, and T.D. Burchell, In: Extended Abstracts 21st American Carbon Conference, American Carbon Society, Buffalo, 1993, pp. 66-67. B.B. Mandelbrot, Fractals: Form, Chance and Dimension, W.H. Freeman and Co., New York, 1983. J. Piekarczyk and R. Pampuch, Ceramurgia Int., 2 (1976) 177. B.H. Kaye, In: D. Avnir (ed.), The Fractal Approach to Heterogeneous Chemistry, Wiley, New York, 1989, pp. 55-66. T.J. Mays, PhD Thesis, University of Bath (1988).

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J. Rouqucrol, F. Rodriguez-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids 111 Studies in Surface Scicnce and Catalysis, Vol. 87 0 1994 Elscvicr Scicncc B.V. All rights rcscrvcd.

339

AN EXPERIMENTAL PROCEDURE AND APPARATUSES FOR MEASUREMENT OF DENSITY OF POROUS PARTICLES B.Buczek, E.Vogt Faculty of Energochemistry of Coal and Physicochemistry of Sorbents, University of Mining and Metallurgy, 30-059 Cracow, Al. Mickiewicza 30, Poland

An apparatus known as Bulk Densimeter was used to measure the apparent density of coarse porous particles by powder densimetry method, and of fine particles by a comparative method. These techniques for the measurement of particle density are competitive for the conventional mercury densimetry approach. Both methods enable lll be measured. Their advantages are a the density of porous particles less than 1 ~llto result of the simplicity of the determinations, which are based on bulk density measurements. The measurements made a standard conditions show high accuracy and reproducibility of the results.

1. INTRODUCTION

The apparent density is one of the basic features of both adsorbents and catalysts. The knowledge of the apparent density together with the true density enables the calculation of the volume of the pores included in the particles of a solid. This is the simplest estimation of a solid’s porous structure based on densimetric measurements. The increasing interest in new techniques of density determination is the result of limitations in standard methods and the need to determine these characteristics more accurately. In this work, two apparatuses were used to measure the apparent density of coarse adsorbents by the powder densimetry method and of tine particles by a comparative method. One of the apparatuses, known as a Powder Characteristic Tester, was made by Hokosawa Micromeritics Laboratory; the other, a Bulk Densimeter, was made by the Faculty of Energochemistry of Coal and Physicochemistry of Sorbents of University of Mining and Metallurgy. The use of these apparatuses led to a high reproducibility of the results and a standarization of the conditions of measurement.

340

Figure 1 . Powder Characteristic Tester 1 - main unit, 2 - dispersibility measuring unit, 3 - amplitude, 4 - vibrating plate, 5 - spatula assembly, 6 - pan base, 7 - tap holder, 8 - rheostat, 9 - timer. 2 /---

, 1

----ITFigure 2. Bulk Densimeter 3 1 - standard 100 cm cup, 2 - extension piece, 3 - pan, 4 - tapper, 5 - timer, 6 - starter.

341

2. EXPERIMENTAL AND RESULTS For the purpose of measuring the apparent densities, the Powder Characteristic Tester accessory, originally designed to measure bulk density, was employed. The bulk density is the mass of particles making up a bed divided by the volume of the bed. In order to perform a bulk density measurement, a calibration cup is filled with excess material, by means of an extension piece attached to increase its volume. The entire set is then placed in an automatic tapper which is adjusted to vibrata with a frequency of 1 Hz for 180 s. A constant level is maintained by adding more material as the previous material becomes more densely packed. After the measurement is over, the excess material from the above calibration cup is removed by means of a ruler. The bulk density is calculated from the known material mass contained in the known cup capacity.

2.1. Determination of apparent density by powder densimetry (1,2) The density was measured using a 100 cm3 standard cup as a powder pycnometer. As the pycnometric medium powders, which according to Geldart's classification belong to easily (dry goods) granular substances ones and hence do not indicate cohesive properties, have been used. The grain diameter of the pycnometric medium powders should be much smaller than porous size of particles, but larger than the largest porosity. In order to find the density values of porous silica gel, active carbon and a molecular sieve, the pycnometcr was filled with the said materials, their amounts corresponding to 30% of the pycnometer capacity. The remaining portion was packed with an appropriate powder pycnometric fluid so as to be sure of the best dispersion of the adsorbent particles within the cup capacity. Subsequent procedures were similar to the bulk density measurement method. Knowing the mass (m ) and bulk density (p,) of the pycnometric powder, as well P as the adsorbent mass inside the pycnometer (ma), its apparent density (p ) was "P calculated from:

where Vn is the pycnometer capacity. The apparent density values thus obtained for adsorbents and non-porous glass beads are listed in Table 1 . Every determination was repeated several times and good repeatability was achieved (k0.02 * 1O'3 kg/rn3). For reference purposes, the apparent density values of the same adsorbents as found by the mercury displacement method and by water pycnometry for glass beads are also included.

342

Table 1 Apparent density of coarse adsorbents by the powder densimetry method Adsorbent (diameter range) Silica gel (2.5-6.0 mm) Active carbon (2.0 mm) Molecular sieve (0.8-1.2 mm) Glass beads (0.4-0.6 mm)

Density ( kg/m3 * bronze steel

) using

zinc

mercury

1.12

1.13

1.16

1.17

0.63

0.63

0.64

0.64

0.92

1.01

1.08

1.10

2.85

water

2.90

2.2. Determination of apparent density by the comparative method (3,4) The density of fine porous particles was measured by a method based on the assumption that the minimum packed bed voidage is the same for similarly shaped particles of a narrow size range. Density measurements by this method involve determining the bulk density of the porous particles to be tested (p ba )and the bulk density of the reference material (p br ) of a known apparent density (p ). Thus: aPr

Where k is a factor defining the correlation between the shapes of the porous particles and the reference material. The factor k is equal to one for spherical particles. For other shape particles’ k will determine experiment. The method was applied to determine apparent densities of narrow fractions of fine porous particles obtained via disintegration and sieving of coarse adsorbents. In addition, the density of a cracking catalyst was measured. The reference materials were the powders originally used as pycnometric fluids in powder densimetry experiments. The experimental results obtained by the comparative method are shown in Table 2. The apparent density values obtained by the above method was compared with the density values resulting from the mercury displacement method (Table 1) by calculating the differences in both determinations. Such comparison is reasonable for these adsorbents. Their structure contains no closed pores, which might be made available in the disintegration process and thus may alter the percentage of pores in the particle volume. For the cracking catalyst the difference was calculated using the supplier’s data.

343 Table 2. Apparent density of fine particles by the comparative method

Particles

(diameter range)

Density ( kg / m3 *

Silica gel: 0.04-0.08 lfl~ll Active carbon: 0.02-0.04 mm Molecular sieve: 0.2-0.4 mm

Cracking catalyst: 0.040 - 0.056 lfl~ll

0.056 - 0.071 mm 0.071 - 0.090 lfl~ll 0.090 - 0.125 ~lllll

Difference (%)

)

1.14 0.67 1.11

-2.56 4.69 0.91

using glass beads

using bronze beads

using glass beads

using bronze beads

1.55 I .56 1.50 1.51

1.59 1.58 1.55 1.54

1.30 2.00 -2.00 -1.30

3.90 3.30 1.30 0.60

3. CONCLUSION mercury method

L r~ 20

comparative method

5

P

I

, Dowder densimetrv method

I

I

I

50

100

200

I I

500

I

1000 ____+

I

1

5000 dP [pml

Figure 3.Application range of various methods to measure the apparent density of porous particles. The mercury displacement method finds wide application for the apparent density determination of coarse particles. However, its applicability is limited to particle sizes over 0.8 mm. Attempts have been made to extend this range by conducting measurements at a pressure over the atinospheric value. However, in order to obtain reliable

344

results, such a method would require a porous particle structure which would be different from its intergranular porosity. The mercury method is also useless for particles of porous metals and catalysts which form amalgams with mercury. The results indicate that both the powder densimetry and the comparative method allow the density of porous particles to be determined which would otherwise be impossible to measure by the mercury method. Furthermore, by using very fine powders as pycnometric fluids, some disadvantages of mercury displacement are eliminated.

REFERENCES 1. 2. 3.

B. Buczek, D. Geldart, Powder Technol., 45 (1986) 173. B. Buczek, Chemia Analityczna, (in Polish), 32 (1987) 969. M.A. Hooker, D.H.T. Spencer, private commun., National Coal Board, (1979). 4. A.R. Abrahamsen, D. Geldart, Powder Technol., 26 (1980) 35. 5. B. Buczek, E. Vogt, Przemysl Chemiczny, (in Polish), submitted.

J. Rouqucrol, F. Rcdrigucz-Reinoso,K.S.W. Sing and K.K. Unger (Eds.) Characierization of Porous Solids I l l Studies in Surface Scicncc and Catalysis, Vol. 87 0 1994 Elscvicr Scicnce B.V. All rights rcscrvcd.

345

Electro-gravimetric measurements of binary coadsorption equilibria

R.Staudt, G. Saller, M.Tomalla, J.U. Keller, Institute of Fluid- and Thermodynamics, University of Siegen, D-57068 Siegen, Germany Abstract

The dielectric behaviour of an adsorption system is an aspect to characterize the porous solid and its adsorbate [ 1-21, Physisorption equilibria of pure gases and of binary gas mixtures on inert porous solids like activated carbon (AC) or molecular sieves on principle can be determined by simultaneously measuring the weight and the (frequency dependent) dielectric permittivity or capacity of the sample adsorbent. Measurements of the dielectric capacity of ACs being exerted to a gaseous mixture of methane and carbon monoxide at T = 298 K and pressures up to.12 MPa are presented in the frequency range 5 Hz - 13 MHz. The molecular structure of the adsorbent / adsorbate system and resulting methods to extract adsorption isotherms from permittivity measurements are discussed to a certain extend. 1. INTRODUCTION

The state of a dielectric medium will be changed in an electric field, due to the shifting of the electric charges in the solid. The resulting dipoles are fixed in the electrical field [3]. Non-polar molecules like N2, Ar, CH4 do not have a permanent dipole moment. However, they are polarized in an external electrical field. The resulting so-called induced dipole moment being usually small, leading to a dielectric permittivity Er z 1 . Polar molecules like CO, H20, H2S etc. exhibit permanent dipole moments which due to thermal motion are orientated at random. However, in an external electrical field they will be oriented in the direction of the field, thus increasing the dielectric capacity of a condenser. In an alternating electrical field both induced and permanent dipoles are forced to oscillate with the same frequency as the field. In case of resonance-oscillation the capacity of the condenser increases considerably and a resonance-frequency can be determined.

346 Microporous carbons are materials which exhibit a rather complicated and quasi-chaotic molecular structure (Fig. 1, [5]). The structure consists of aromatic sheets or strips. There are variable gaps of molecular dimensions between the tube- or slite-like micropores. The highly disorganized structure depends on the production process and the treatment during thermal or chemical activation. In an aromatic strip, every C-atom like in a graphite plane is connected to three other C-atoms. The fourth electron of the C-atom is a free electron, it can build an additionaly x-binding with one of the three other C-atoms. The excitation of the metallic like mobility of the fourth electron is very low, hence the electrons may be considered as a two dimensional electron-gas in a graphite plane with positive charged C-atoms. Hence AC is a dielectric medium with permanent dipoles. The binding forces between two graphite planes in ACs are very small. Therefore it is possible for a dipole to oscillate with a part of the graphite plane in an alternating electric field. To give an example an unloaded AC (Norit R1) shows a peak in the capacity-spectrum with a maximum of 0.42 nF at 0.24 MHz (Fig.3). This frequency is equivalent to a resonance-frequency of a dipole. At such a low resonancefrequency, there exist only dipoles with large masses.

Fig. 1: Activated carbon [5]. In the case o f a zeolite (DAY 5A, Fig.3), the crystal forces are very strong. Therefore, it is not possible to observe a resonance-frequency within the range of 5 Hz to 13 MHz. If the condenser is filled with gas only (N2:123 bar, CO: 135 bar, T = 298 K), a small shift of the capacity-spectrum occures, compared to the vacuum-capacity-spectrum as is depicted in Figure 4. 2. EXPERIMENTAL

The experimental setup for electro-gravimetric and volume-gravimetric measurements [4], of binary adsorption equilibria is sketched in Figure 2. It mainly consists of a micro-balance (Sartorius, M 25D-P), an impedance-analyzer (HP, 4192 A) with a condenser in the

347 adsorption vessel, a storage vessel with electro-polished surfaces (V* = 10 I, stainless steel No. 1.4462, Messer-Griesheim) and a pump for gas circulation (Brey, GK 24-02N). The tubes are made of stainless steel (type 1.4401), inner surfaces provided with electropolishing to reduce adsorption. Valves have been chosen from Veriflo (Type L944, L928). Pressures are measured in the storage vessel and in the adsorption chamber by pressure gauges (VDO, Burster). The temperature is measured at various locations using thermocouples and resistance thermometers (Pt IOO), connected to an indicating device (Kelvimat).

Fin. 2: Experimental setup for electro-gravimetric and volume-gravimetric measurements [4]. After providing the microbalance and the condenser with (physico-chemical identical) adsorbents with known masses ms and mSo and after evacuating the whole system (po < 10-3 mbar), the measurement is started by measuring the capacity-spectrum of the unloaded sample. The capacity-spectrum is measured from 5 Hz to 13 MHz (cp. Fig.3). Now the storage vessel is filled with a binary gas of known molar concentration. Measuring p* and T* in the storage vessel the masses of the adsorptive's components prior to adsorption can be determined via the equation of state [4]. Opening the valve connecting the storage vessel and the adsorption vessel adsorption occures, enhanced by gas circulation. In equilibrium, the pressure p, the temperature T of the adsorptive and the weight G of the loaded adsorbent ms at the microbalance are registrated. The capacity-spectrum is also measured. Figure 7 shows capacity-spectra of the system CH4:C0(90: 10 mol%) / AC Norit R1 at 298 K in the pressure range of 0 - 8 MPa. The volume-gravimetric method is described in [4].

348

0

i2

Fig. 3: Capacity-spectrum of AC Norit R1 and DAY-zeolite 0.38

I

T=298K

0.26 1

0

3

6

9

12

15

frequency f [ MHz]

Fin. 4: Capacity-spectrumof pure gases compared with vacuum.

3. RESULTS Activation urocess: To examine the influence of preadsorbed gases in the AC on its adsorption capacities we investigated samples which had been activated with helium at various temperatures (333 K)

and pressures (12 bar). Figure 5 shows the capacity-spectrum of AC (Norit R1) at various

349 stages of the activation process. At the beginning of the activation process, there are no structures in the capacity-spectrum. The dipoles of the “activated carbon seemingly are neutralized by polar components like CO, HzO from the atmosphere. During the activation process the porous solid will be cleaned by desorption of polar and nonpolar impurities, such leading to the formation of new polar groups within the AC. Indeed at 240 kHz there arises a peak which increases with increasing activation.

I

I : 0.1

0.5

0.3

0.7

0.9

frequency f [ MHz 1 Fig. 5 : Activation of AC Norit R1.

Time dependency: The time dependency of a capacity-spectrum during an adsorption process is shown in Figure 6. First we observe an increase of the maximum capacity (up to 0.5 nF) and a shift of the maximum to higher frequencies. This possibly may be due to preliminary adsorption of COmolecules in large pores where they increase both the capacity and the resonance frequency of the loaded AC. But this is not the final adsorption place of the CO-molecules! Indeed the molecules need some time to reach their final adsorption place, which may be in the slit-like micropores. On these places there is strong attraction between the dipoles of the AC and the dipoles of CO-molecules. Hence adsorption of CO leads to a neutralization of the local electrical field in the AC. The capacity-maximum at resonance-frequency decreases with the adsorption of CO and the resonance-frequency is shifted to lower frequencies. At adsorption equilibria the change of the resonance peak is an indicator for the mass of CO adsorbed.

350

0.6

time

p = 75,O bar

J 0.1

0.3

0.5 frequency f [ MHz ]

0.7

0.9

Fig. 6: Time-dependency of capacity-spectrum of CH4:CO / Norit R1. Adsomtion Isotherm of CH4:CO / Norit R1: In Figure 7 the capacity-spectra of adsorption equilibria states at different pressures

p 8 MPa are given. With increase of the adsorbed mass the maximum of the resonance peak decreases and is shifted to lower frequencies. Figure 8 shows the change of the maximum value of the capacity at resonance-frequency with the adsorptive's pressure. The symbols indicate the data of measurements and the curve is a logarithmic fit of the data.

"."

-c Y

I

T=298K

I

0.4

0.3

0

0.2

0.1 1

0.1

0.3

0.7 frequency f [ MHz ] 0.5

Fig. 7: Capacity-spectrum CH4:C0 / Norit R 1.

0.9

35 I

T = 298 K

t

f

I

0.24 MHz

/-

a3

v-

0

20

40

60

80

Fig. 8: Change of the maximum value of capacity of CH4:CO / Norit R1.

References [I]

Ozeki, S . : Water Immobilized on Porous .Jarosite: Dielectric and Thermal Analyaw; J. Chem. SOC.,Chem. Commun. (1988), 1093.

[2]

Fiat, D., Folman, M., Garbatski, U.: Dielectricproperties of the adsorbate at low surface coverage; Proc. Roy. SOC.London, A260 (1961), 409.

[3]

Frohlich, H.:Z’heoryof Dielectrics; Oxford University Press, Oxford 1990

[4]

J.U. Keller, R. Staudt, M. Tomalla: Volume-GravimetricMeasurements of Binary Gas Adsorption Equilibria; Ber.Bunsenges.Phys.Chem. 96 (1992), No. 1,28-32.

[5]

H.F. Stoeckli: Microporous Carbons and their Characterization: The Present State of the Art; Carbon 28 (1990), 1-6.

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J. Rouquerol, F. Rodriguez-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characlerizalion of Porous Solids 111 Studies in Surface Science and Catalysis, Vol. 87 0 1994 Elscvicr Scicncc B.V. All rights rcscrvcd.

353

A METHOD FOR ESTIMATION OF PORE CHARACTERISTICS OF SOLIDS IMMERSED IN A SOLVENT BASED ON THE CAPILLARY PHASE-SEPARATION CONCEPT Minoru Miyahara and Mono Okazaki Department of Chemical Engineering, Kyoto University, Kyoto 606-01, JAPAN Abstract Based on the capillary phase-separation concept, or a hindered liquid-liquid equilibrium in narrow pore with curved interface, a method for pore characterization of solids immersed in solvents was proposed. The method is considered to be effective for determination of pore characteristics of swelling/shrinking solids in solvents. The method was tested by comparing the pore size distribution calculated from liquid phase adsorption isotherm and that from nitrogen adsorption on a non-swelling solid. The distribution from liquid phase was able to express the pore characteristics satisfactorily to show the potential power of the method proposed The parametric sensitivity of the method and desirable nature of the probe molecule are also discussed.

1. INTRODUCTION Pore characteristics as well as the physico-chemical nature of porous solids play an important roll in many fields such as physisorption, chemisorption, membrane and catalysis. The increasing demands for these techniques and recent advance in production technology for porous material have been yielding various types of porous solids. Among them, as seen in macroreticular adsorbents, some porous materials will swell or shrink when immersed in a solvent in use. The swollen or shrunk state itself is the important characteristic for these kinds of solids. However, conventional methods for pore characterization such as physisorption of gas and mercury intrusion need evacuation before the measurements, which yield only 'dried' states of information. We have already shown [l] that a similar phenomenon to the capillary condensation can occur in liquid phase if the interface of liquid-liquid equilibrium has curvature within narrow pore, and that the liquid phase adsorption isotherms of solutes with limited solubilities can be interpreted on the basis of this concept, Capillary Phase-Separation (CPS). The understanding for total amount adsorbed is quite similar to that of the mesopore analysis by physisorption. Hence the CPS phenomenon is tightly connected with the pore characteristics of solids immersed in a solvent. Thus, we could estimate pore characteristics of immersed

354 solids if we have a quantitative knowledge of the amount of surface adsorption in liquid phase onto non-porous solids. As a simple test for this method, non-swelling porous solids in water were employed in this work. The pore size distributions (PSD) of the solids were estimated from liquid phase adsorption isotherms based on the CPS concept with the information of the amount adsorbed on non-porous solids of similar chemical composition, and compared with those calculated from nitrogen adsorption isotherms. The two distributions, namely, one obtained from adsorption of nitrobenzene from aqueous solution and the other from nitrogen adsorption were in sufficiently good agreement to show the potential power of the method proposed. The influence of the magnitude of surface adsorption, which may firstly bring uncertainty into the method, are further discussed. 2. CAPILLARY PHASE-SEPARATION CONCEPT [I] The capillary phase-separation is a similar phenomenon to capillary condensation from thermodynamic aspect: a hindered liquid-liquid equilibrium could stand within a pore because of the presence of a curved interface of the two liquid phases. In other words, a solute-rich phase could be equilibrium with a solvent-rich phase at a lower concentration than the saturated. The liquid-liquid equilibrium with curved interface is considered as follows to obtain the quantitative description for the phenomenon. Suppose that we have two equilibrium states including components A and B as shown in Fig. 1, namely, one with a flat interface and the other with a curved one existing within a pore which has acylindrical shape with radius r as an example. The interface with the I I interfacial tension (T contacts with the wall with the contact angle 8. The components a-phase P (A-rich) A and B correspond to a solvent and an XBaS interface adsorbate, respectively, in the case of P-phase adsorption. Besides, a-phase corre(B-rich) sponds to a bulk phase and P-phase contributes to the amount adsorbed. Equating the chemical potentials of each Fig. 1 Capillary phase-separation concept component in each system, and applying Young-Laplace equation for mechanical balance between phases, we obtain the equilibrium concentration in the system I1 in terms of mole fraction, X , as Eq.(l), with an assumption that the mutual solubility is small so that the activities are linear with mole fractions.

xG

- 0

..

355 where 2ovijcose (3) ”= rRT r RT where subscript S is pertaining to the standard state with flat interface and v ‘s are molar volumes for which the superscript * is pertaining to dilute state and O to concentrated state. Equation (1) for CPS corresponds to the Kelvin equation for capillary condensation. A rather complicated form is obtained because two components contribute to the phase equilibrium in liquid phase. For other shape of the pore, the correspondingcurvature should be substituted for 2cosBlr. To simplify Eq.(l), a few more assumptions are needed; namely, e = 0, the solubility of A in P-phase is small so that the ratio XBp/X,sp is close to unity, the concentrations of Bcomponent in a-phases are small so that the ratio XBa/XBSacan be approximated by relative concentration CIC,. The resulting equation is ~OV;COS~

$A=

where C, is the saturated concentration of the solute B in the solvent A. Equation (4) is now similar to the Kelvin equation. One has to be careful whether Eq.(4) holds in a given system. Most of assumptions made above are valid if each phase can be treated as an ideal dilute solution. Hence, the equation is applicable to aqueous solutions of, for example, aromatic compounds or aliphatic compounds because they have quite small solubilities.

3. ESTIMATION OF PORE SIZE DISTRIBUTION OF IMMERSED SOLIDS The solute-rich phase of the hindered liquid-liquid equilibrium within a pore would be counted as adsorbed amount at a lower concentration than the saturated. Accordingly, the total amount adsorbed consists of two modes of adsorption, namely, the adsorption which arises from physico-chemical nature of the adsorbent surface, and the apparent amount by CPS which arises from the pore characteristics of the adsorbent especially in the mesopore range. This concept is quite the same as that employed in pore analysis of mesoporous solids by physisorption of gas. Then, the interrelation between liquid phase adsorption isotherm and PSD of an immersed solid can now be understood in the same manner as that between gas phase adsorption isotherm and PSD. Hence, with quantitative comprehension of CPS, PSD of immersed solid could be calculated from a liquid phase adsorption isotherm, and vice versa, if we have a knowledge of the adsorption on surface in liquid phase. For the verification of the method, non-swelling mesoporous solids were used in this work. The PSD’s of a solid were calculated both from nitrogen adsorption isotherm and from adsorption isotherm of an aromatic compound from aqueous solution, and compared. The calculation scheme of PSD for immersed solids from liquid phase adsorption isotherm was similar to that of Dollimore and Heal [2], which is for nitrogen isotherm and

356

was also used here for calculation of PSD from nitrogen isotherm for comparison. Note that the present estimation method for immersed solids do not limit itself into this calculation procedure. Rather, any calculation scheme which is originally proposed for gas physisorption could be applied if its basis is the understanding of the total amount adsorbed as the sum of adsorption on surface and capillary condensate, since the substitution of CPS for the latter adsorption mechanism would make the method applicable to immersed solids. The adsorption on surface in liquid phase was expressed by a similar equation to that of the method for gas phase. Namely, it was expressed as "the statistical thickness" of the adsorption in liquid phase and assumed to follow Frenkel-type formula.

By this assumption, we have only one unknown parameter, to in Eq.(lO) for the calculation of PSD of an immersed solid from a liquid phase adsorption isotherm. The unknown parameter, to ,is considered to be unique for combination of solute, solvent and solid. An aromatic compound in water was used as a solution in the present study. The parameter for carbonaceous solid was determined by using graphite as a nonporous solid, while a value determined in a previous work [ 13 was used for macroreticular adsorbents. Because of relatively large experimental error for the measurement of liquid phase adsorption, a direct use of the liquid phase adsorption data would result in unrealistically oscillated pore distribution. Hence the data were smoothed by a cubic polynomial and the calculation for liquid phase was based on this function. The procedure of the pore analysis is briefly explained below. The CPS phase can be approximated as a pure phase of adsorbate in this calculation because of the small solubility of water into the p-phase. Then the amount adsorbed by CPS can be converted to corresponding volume using density of pure liquid. The critical pore radius rp corresponding to a concentration of an isotherm datum is calculated with r by Eq. (1) and t by Eq. (5).

rp = r +t (6) At any data point of the isotherm, the pores with smaller radii than the critical one corresponding to its concentration are supposed to be filled with the adsorbate while those with larger radii have the surface adsorption expressed by Eq. (5) and the solution with the concentration, which would have almost no contribution to the amount adsorbed. The difference in volume of amount adsorbed between adjacent data, AV , then, consists of volume of CPS in this pore range AV, and the change in surface adsorption dVs . AV = AV,

+ AV,

(7)

The latter is calculated using Eq.(5) together with the information of elemental surface areas of larger pores determined stepwise. Then dVC and the corresponding pore volume in this

357 Table 1 Physical properties of nitrobenzene Molecular weight [glmol] 123.11 [g/cm31 1.19 Liquid density25.7 Interfacial tension with water [dydcm] Saturated concentration [mol%] 0.0320 Table 2 Physical properties of adsorbents Adsorbent Nitrogen surface area Pore volume

SP900

580

0.84

pore range dVp is determined. The calculation proceeds until the concentration become small enough so that the CPS phase do not contribute to the amount adsorbed.

4.EXPERIMENTAL Adsorption isotherms of nitrobenzene from aqueous solution onto porous adsorbents were measured by a conventional batch adsorption method at 308 K. The physical properties of the adsorbate are summarized in Table 1. The reagent of research grade provided by Wako Pure Chemicals Inc. was used with no further purification. The adsorbents are summarized in Table 2. EC, electric conductive porous carbonblacks, and SP900,whose chemical structure is of stylene-divinylbenzeneblock co-polymer, are typical mesoporous solids. So the CPS would show a large contribution for these adsorbents. In addition to porous adsorbents of different origin, a non-porous solid was employed to examine the validity of using Eq.(5) for the statistical thickness of the adsorption in liquid phase. Before experimental usage, the carbonaceous adsorbents were washed with distilled water and evacuated at 383 K for 24 hours while the macroreticular adsorbents were washed first with methanol before done with distilled water, and then evacuated at 333 K for 48 hours. The measurement were made by a conventional batch adsorption method. The adsorbent was added to 300 ml solution in an Erlenmeyer flask stopped by teflon-sealed screw cap to prevent the solute from evaporative loss. The flask was shaken in a thermostatted bath for 7 days. The equilibrium concentration was determined by an ultraviolet spectrophotometer (Shimadzu UV-260). Nitrogen adsorption isotherms at 78 K were measured by the constant volume method to obtain the pore size distributions for comparison. The nitrogen isotherms for the porous solids more or less showed hysteresis. The question, which branch to use for pore analysis, has been under discussion for many years. The PSD calculation in this study utilized the adsorption branches of isotherms for the purpose of comparison of gas phase and liquid phase: the liquid phase adsorption isotherms

358

0.020

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Adsorbent : Graphite Adsorbate : Nitribenzene 0.015 .

.

0.005

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.

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. 0.6 . . 0.8. c/c, [ - I a

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Fig. 2 Surface adsorption of nitrobenzene on graphite are considered to be close to the adsorption branches under the experimental condition of this study. An isotherm obtained by "batch" adsorption may sound closer to desorption branch since the initial concentration is higher than the equilibrium one. However, it should depend on the mass transfer mechanisms. The batch adsorption method might give partial characteristics of desorption branch if the external mass transfer resistance is small since the outermost portion of adsorbent particle would be exposed to to a solution with higher concentration than the equilibrium one. On the other hand, the higher concentration might not be able to touch to the particle surface if the external mass transfer resistance is large, which might be the case in this study because no intensive mixing was made during the course of adsorption and because an acceleration of intraparticle mass transfer by so-called surface diffusion would be possible in the systems examined [3]. 5. RESULTS AND DISCUSSION

1) Adsorption on non-porous solid from solution and surface adsorption parameter The validity of using Eq.(lO) as an expression for the adsorption on surface in liquid phase was tested with non-porous solid. The result of adsorption isotherm of nitrobenzene from aqueous solution onto graphite is shown in Fig. 2. The broken line shows Eq.(5) with to value of 0.58 nm. Though the data were rather scattered because of the only small adsorption amount in this system, the broken line expresses the data fairly well in most part of the concentration examined. In lower concentration range, Eq.(5) overestimates the amount adsorbed to some extent. The important information for the estimation of porosity is, however, the adsorption amount in middle or higher range of the relative concentration. This characteristicof the present method would make the influence of the overestimate quite small. As a whole, the utilization of the Frenkel formula for the adsorption on surface is thought to be appropriate for the present method. This r, value was used in the calculation of PSD for EC while it was 0.59 nm for macroreticular adsorbents, which was obtained as stated below.

359 Table 3 Surface adsomtion Darameter Adsorbate Adsorbent to [nm] 0.58 Nitrobenzene EC EC600JD SP900 0.59 SP206 Activatedcarbon-1 0.58 Activated carbon-3 Benzene EC 0.39 Aniline 0.76 Benzonitrile 0.54 In the previous work [l], the parameter to was determined as shown in Table 3 for various combination of adsorbent and adsorbate, which were obtained not by direct measurements on nonporous solids but by fitting experimental and calculated adsorption isotherms from solution on porous adsorbents using a method for isotherm estimation based on the CPS concept. As seen, the variation of the value is quite small for an adsorbate, nitrobenzene, over the adsorbents examined, while it shows relatively large variation over four kinds of adsorbates. The insensitivity of the to value to the adsorbents examined could be interpreted as follows. In the concentration range considered here the apparent coverage exceeds unity, which implies more opportunity for an adsorbed molecule to interact with other adsorbed molecules. This situation for the molecule reduces the importance of the interaction with the solid surface or with solvent molecules. As a result, the influence of the adsorbent-adsorbate interaction on the to value becomes less important and the adsorbate-adsorbate interaction principally determines the to.

2) Comparison of calculatedpore size distribution The adsorption isotherm from aqueous solution on EC is shown in Fig. 3. The solid line expresses the smoothed curve by the polynomial function. The smoothed curve surely able to express the sigmoidal change of liquid phase adsorption in this system. Figure 4 compares the PSD calculated from the isotherm in liquid phase shown in Fig. 3 by the present method and the one from nitrogen adsorption at 78 K. The distribution from liquid phase has quite a similar form to that from physisorption of gas. Both qualitatively and quantitatively, the agreement is satisfactory in view of the usage of mesopore analysis presently applied. The agreement manifests the validity of the quantitative expression of the CPS, Eq.(4) and the calculation scheme of the present method for immersed solids. Similar results are obtained as shown in Figs. 5 and 6 for the macroreticular adsorbent SP900. In this case, the adsorbent has a rather clear peak in the distribution around 7 nm as shown by the gas phase result. The trial of mesopore analysis of immersed solid succeeded

360

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Fig. 3 Liquid phase adsorption isotherm of nitrobenzene on EC

Fig. 4 Comparison of PSD of EC from liquid phase and gas phase

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Fig. 5 Liquid phase adsorption isotherm of nitrobenzene on SP900

0.0

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[ml

Fig. 6 Comparison of PSD of SP900 from liquid phase and gas phase

to find out this characteristic of the solid to yield fairly good agreement between the two distribution curves. As a whole, the present method has a potential power for the estimation of porosity in mesopore range for solids in the immersed state which could be applicable to swellingJshrinking solids in solvents.

3) Influence of surface adsorption parameter The method needs information of surface adsorption in principle. The amount should be obtained by experiments on a nonporous solid with the same chemical composition as that of the porous solid to be examined. However, this kind of experiments often bring great difficulties because, in addition to generally arising difficulties in liquid phase adsorption, nonporous solids have quite smaIl surface areas in general which result in hard-to-detect amounts adsorbed. Thus the measured surface adsorption may inevitably include large uncertainty. If we have a solute with small surface adsorption compared with the

361

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rp [ m l rp [ m l Fig. 7 Disturbance in pore size distribution by Fig. 8 Disturbance in pore size distribution by error in the parameter; t0=0.6 nm error in the parameter, tO=O. 1 nm

contribution by the CPS phase, the uncertainty involved in calculated PSD is expected to be reduced. By a simulative calculation, the nature of surface adsorption, or parametric sensitivity of to to calculated PSDs are considered as follows. Based on the pore size distribution of SP900, two fictitious solutes were considered. One was with to of 0.6 nm, which was close to that of nitrobenzene, and the other with to of 0.1 nm, which was a model solute with small surface adsorption. With respective value of the parameter, fictitious liquid phase adsorption isotherm for each solute was calculated from the PSD, the procedure of which was the reverse calculation of PSD determination. These isotherms were analyzed with different to values which included f 50 % error from the original one as an example of the uncertainty of the parameter. Thus obtained PSD's with erroneous to were compared with the original one. The disturbed PSD's are shown in Figs. 7 and 8 together with the true PSDs. As seen, the overall feature of the distributions do not change significantlyeven with as much as 50% error in the surface adsorption parameter. Thus the present method has a desirable feature, not too sensitive to a parameter with large uncertainty. Further observation of the results clarifies the superiority of the solute with smaller surface adsorption. The peak height and location of the solute with smaller to are almost identical with the original ones while the other shows higher peak at greater pore radius with +50% error. The disturbance evoked by the error in the parameter is a cumulative one so that the difference will be bigger for solids with smaller pore radius while it will be smaller for solids with larger pore radius, which was confirmed in other simulative calculations made on different model solids though the results are not shown graphically here. Considering the characteristics of the surface adsorption parameter, a solute with smaller surface adsorption is desirable for the present method. It is especially appropriate to a solid

I

362 with smaller pores, for which a larger surface adsorption parameter yields greater sensitivity to the error in the PSD. On seeking a suitable probe molecule for characterization of an immersed porous solid, the selection should be made on the strategy described above. The relatively small sensitivity of calculated PSD on the surface adsorption parameter would suggest a complete neglect of surface adsorption itself in the calculation. For pore analysis by nitrogen adsorption, Brunauer et al. [4] suggested the possibility of the neglect, together with the so-called modelless method, and found no significant change caused by the neglect. It might similarly apply to the present method. By the neglect, the obtained radius would be the "core" radius which does not include the thickness of the surface adsorption and hence is not exactly the pore characteristics. However, such information sometimes may be important in many practical applications, for example, comparison among porous solids with similar base material as seen in materials development. In those cases, one need not count for the surface adsorption, which greatly reduces the experimental efforts for the determination of pore size distribution. 6. CONCLUSIONS A method for estimation of pore size distribution of solids immersed in solvents was proposed, which had its basis on the capillary phase-separation concept, or a hindered liquid-liquid equilibrium in narrow pore with Curved interface. The method shouId be effective for determination of swollen/shrunk states of porous solids in solvents. The method was able to elucidate the pore characteristics of immersed solids from liquid phase adsorption isotherms, which was confirmed by comparing the pore size distribution from liquid phase and that from nitrogen adsorption on non-swelling solids. The error in the surface adsorption parameter, which may be with relatively large uncertainty, was found to bring no significant disturbance into the distribution. This desirable nature of the parameter intensified itself with smaller surface adsorption amount. ACKNOWLEDGEMENTS This work was supported by Mitsubishi Chemical Industries Ltd. and a Grant-in-Aid for Scientific Research 4650852 from the Ministry of Education, Science and Culture of Japan. The authors are grateful to Mr. Toshio Kitamura for the assistance in the experimental work. Acknowledgements are also made to Lion Corp. for providing adsorbents of EC.

REFERENCES [ 11 Miyahara, M. and M. Okazaki: Fundamentals of Adsorption - Proc.Wth Int. Con& on Fundamentals of Adsorption, M.Suzuki, ed., p.445, Kodansha, Tokyo (1993) [2] Dollimore, D. and G.R. Heal: J. Appl. Chern., 14, 109(1964) [3] Miyahara, M. and M. Okazaki: J. Chern. Eng. Japan., 25,408(1992) [4] Brunauer, S., R.S.Mikhai1 and E.E.Bodor: J. Colloid Interface Sci., 24,451(1967)

J. Rouquerol, F. Rodriguez-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterizarion of Porous Solids 111 Studies in Surface Science and Catalysis, Vol. 87 1994 Elsevicr Science B.V.

363

Possibility of chromatographic characterization of porous materials, specially by Inverse Size Exclusion Chromatography. Andre Revillon Centre National de la Recherche Scientifique Organiques Propriktks Spkcifiques, Lyon-Solaize, BP24; 69390 Vernaison, France

-

Laboratoire des Matkriaux

Abstract Size Exclusion Chromatography is a practical well-known technique for molar mass determination and Inverse Size Exclusion Chromatography appears to be a n attractive method for porosity measurement. In fact results may depend on choice of relation between solute size, pore dimension and elution volume. Different laws are applied to test their effect on porosity results. 1. INTRODUCTION

Pore structure may be evaluated by direct or indirect methods, i n dry state or i n presence of a diluent. Classical techniques a r e based on BET a n d B J H isotherms, mercury porosimetry, pycnometry, XR central scattering, scanning electron microscopy in the dry state (1);newer ones a r e thermoporometry (2,3), electrolyte uptake for ion exchangers (4) and Inverse Steric -or Size- Exclusion Chromatography, ISEC, (5). Pore diameter distribution, pore volume a n d surface a r e a i n solids a r e fundamental parameters to be known, since they are governing, for instance, diffusion of reagents and products in catalysis, adsorption, a s well as exchange equilibria i n liquid chromatography. Solid state methods suffer for restrictions, since the material is examined only in dry conditions, which are not those of use. For rigid materials, the pore volume is defined and constant, but this is not true for organic polymers, which may be modified either under the effect of pressure o r the effect of a liquid diluent. Moreover, polymer dimensions depend on solvent and temperature : they vary from unperturbed ones in a poor solvent to extended chain in a good solvent, at a given temperature. Even for networks, structure is depending on the amount (and nature) of crosslinker and porogen agents, so t h a t networks have permanent (macroporous) or variable (gel type) swelling. The problem is more complex for organic-inorganic materials, since chain mobility a n d chain expansion are restricted by attachment of the chain t o the surface. Chromatography may be applied in other ways t h a n fractionation, what opens new approaches for physical investigation. Some exemples in gas or liquid phase are the determination either of surface characteristics or polymer transition (glass and melting) temperature by reverse gas phase chromatography (8) or

364

saturation of solid by a reagent observed by frontal elution, or determination of equilibrium between reagents by measuring their respective peaks areas i n liquid chromatography (9). The newer liquid chromatography method is a dynamic one, which is based on measurement of elution volumes of samples of a given size. This principle is the same of that applied for molecular mass (or size) measurement of molecules by eluting them on a known porous phase (gel permeation or size exclusion chromatography), but applied in the reverse way, so th a t the present name is Inverse Steric -or Size- Exclusion Chromatography, ISEC. Some advantages are ability of pore determination i n a series of solvents of interest, in the conditions of use of the materials. The condition is th a t the process be a n entropic one, in order to avoid side effects : interactions between solute, and solvent or stationary phases. This is realised by fitting their Hildebrand solubility parameters. An other condition is that this dynamic process may be assumed as i n equilibrium, which requests high mass transfer rate a n d a low flow-rate of the eluent. The measure does not request too much time and material. 2.

SIZE EXCLUSION CHROMATOGRAPHY

A lot of papers have been devoted to size exclusion chromatography (SEC) mechanisms and some ones to ISEC possibilities (10-31). Few a r e contradictory or do not give the necessary equations. We begin by trying to recall fundamental SEC relations.

2.l.Basic relations The experimental evidence is the separation of molecules versus size in a definite time (or volume) by flowing them on a porous phase. I t is easy to show that this fractionation of soluble species is performed inside the porous volume, Vp, occuring after the dead volume, VO, this one corresponding to interparticular space of the packing. The general relationship for elution of a solute in a porous medium may be expressed a s :

Ve = K Vp

+ Vo

eq.5

where K is a global and experimental partition coefficient between 0 e t 1. Small molecules enter the whole porous volume (K=l) , larger ones enter only in pores which size is higher (K<1) and are totally excluded if K = l . K = We -vo)Np

eq.6

This coefficient K appears a s a distribution factor (equilibrium of solute) between stationary and mobile phases, a s well a s a probability parameter (dynamic) for probability to enter the pores. Since entering of the various solute molecules depends on stationary phase porous volume, another relation between size (or mass M) and elution volume may be written. It is linear, in semi-log form, in a limited domain : log M = A - BV

eq.7

365

or log M = a - bK or K = (a - log M)/b

eq.8 eq.8'

The two relations (eq. 5 and 7) correspond to experimental measurements, yet a thermodynamic interpretation of K may be given. The standard free energy change for the transfer of solute molecules from mobile phase to the stationary phase a t a given temperature is written AGO = A H 0 - TASo = -RT Alog K

eq.9

For a pure exclusion process, there is only an entropic term, related to order, so that exclusion constant may be written (R gas constant) : K = exp (ASOR)

eq. 10

If side interactions between components occur, resulting in partition and adsorption, a term is added, taking account of this enthalpic process (AH), so that elution can take place in a volume larger than pore domain. 2.2. Relation between solid porosity and solute size Several theories have been built to account for permeation-exclusion in the pore structure of the stationary phase. They were based on either kinetic or thermodynamic static hypotheses. Difficulties arise both from heterogeneity of pore sizes and shapes and definition of particle "size". A t first, pores are assumed to be cylinders of diameter dp and the particle to be spherical, with a diameter ds. From geometrical considerations, it is evident that accessibility coefficient K for hard spheres may be defined either as :

& = 1- (ds/dp)2 (probability of approach to the wall) or Kc = (1- ds/dpP (projected area of particle)

eq.11 eq.12

values which are less than 1 if ds < dp and K = 0, if ds > dp K is similarly defined for a molecule of radius r (of random coil) versus pore of radius R (isomolecular and isoporous systems) : for instance, K proportional to l-(r/R)2. It is t o be noted (32) that the distribution coefficient may be generalized as

K = (1- arm)"

eq.13

with n = 1,a = 2 for slab-shaped pores n = 2, a = 1 for cylinder-shaped pores n = 3, a = 213 for spherical pores and a more complex form for rectangular pores. So that, for an heterogeneous porosity, summation (or integration) versus r must take place. Sophistication of this relation is brought by using a power series development, combining several pore shapes.

366

The following relation may also be found (33)

K = 1-6(n12/6rzR2)0.5, for a linear polymer in random coil (chain with n segments of length 1). The radius of gyration is n12/6 = R2g so that

K = 1-6(r2RE2)0.5 which means an equation different from the preceeding relations :

K = 1 - ur/R

.

eq. 14

Moreover, we shall see later that entrance of molecule in a pore has a probability depending not only of respective projected surfaces areas, so that a coefficient must be applied to the term (r/R). Polymers in solution are assumed to be random coils, what means chains in a sphere envelope constituted essentially of "attached" solvent. In fact polystyrene behave like hard sphere, but being constituted of flexible chains may enter pores of smaller diameter. Freeman (23) presents a review of some equations, which are of a similar form (25). From experimental observations, Giddings has proposed a relation between pore size and solute penetration : s = exp

(-a)

eq.15

where A is surface area per unit pore volume, L is the mean projected solute size. This is related to the distribution coefficient D, using -LnD = B + AL, where B is the maximum pore volume fraction at L O , so that we can write

D = exp (-a) (plus and added term), or K = exp (-2r/R)

eq.16

in the more usual form, for random-planes pore model-spherical solute, or

K = exp (-L/R) for random-planes pore model-rigid solute, where L is the mean external length of the solute (average length of the projection of the solute along axes of random orientations). Large molecules are assumed to be random coils, so that reference dimension is radius of gyration or hydrodynamic radius. Difficulty arises for small molecules to be used as standards. A possibility is to use physical parameters; another is to do mesurement on a rigid solid of known porosity.

2.3. Relation mass-dimension For a polymer chain, in a random coil, this L is twice gyration radius, so for polystyrene in a good solvent (THF, toluene) :

367

L (nm)= 0.0246 Mo.588 Taking account of entrance probability of a molecule in a pore, Halasz obtains a different (factor 2.5) coefficient, so that the relation becomes : D(nm)= 0.062 Mo.59,

eq. 17

Equivalent sphere volume is related t o molar mass M a n d (q) limiting viscosity index by Flory relation, Ve = (q)M l 2 , 5 N (where Avogadro number is N)

eq.18

and to dimensions by Ve = II~ 3 / 6 By applying Mark-Houwink viscosity law eq.19

(q) = K Ma

and combining relations, we get hydrodynamic diameter Re i n function of molecular mass : 2Re = L = (2.4K M(a+1)/IINl1/3.

eq.20

For instance, for a polystyrene of molecular mass 10 000 in solution in THF, L is 4.58 nm (231, but 5.54 nm in (33, p174) o r 7 nm, in (15). For small molecules, L may be taken equal to a term proportionnal to the mass with a n additional constant (23)

L(A) = 3.24 + 0.0375 M

S o for hexane, L is 6.45A. Another values may be found (12) : L(A) = 3.62 + 0.0267 M. Halasz uses extended chain length for alcoylaromatic compounds (4). 2.4. Attempt of conclusion

First, we have seen that numerous equations have been proposed to relate pore size and solute size, with approximate definitions of these two entities. It is strange t h a t K could be written simultaneously as exp or log of size o r mass parameters, since 2r is proportional to Mo.6, for a random coil.

K = exp(-2r/R) and K = (a - Ln M)/b.

respectively eq.16 and 8

Second, the different numerical values are rather confusing.

368

0,o

0.2

0.4

0.6

0.8

1 ,o

Figure 1. Calibration-like curves, Ln(r/R) vs K, with models l-(r/R)20 ; (1-r/Rl2u; l-r/R+; exp-2rR m We have considered the theoretical representations of four relations (eq. 11,12,14,16) and their polynomial approximation (first, second or third order, with a n excellent correlation coefficient value of 1).Since r/R is a relative size, with r proportional t o M, these curves may be considered a s master curves. It is particularly interesting to see t h a t the exponential form fit very well a third degree, which can be interpreted as an assembly of the other models. Decrease of K with r/R may be monitored by applying a coefficient a = l , 2, 3 for r/R (in eq.16). By plotting relations between K and r/R (log scale) a form similar to the classical SEC calibration curve is obtained (Figure 1).

3.POROSITY MEASUREMENT BY ISEC 3.1.Principle of porosity distribution The basis of any pores-size calculation is t h a t the total porous volume is the summ of individual porous volumes brought by each class of pores Vpi, assumed to be isoporous :

To each pore Vpi corresponds the permeation of a solute with a maximal size Li. Elution of a given solute takes place through sampling the series of pores, each one being affected with a n accessibility coefficient Ki : KVp = CKi (Li) Vpj

369

Difficulties are due to the possibility of a molecule either to enter in pores smaller thant its size, or needing a pore much larger than its size to penetrate (34). Since Ve is weakly affected by pores with dp close to L, calcul may be done in 3 hypothesis, which corresponds to Halasz observation taking dpi = 1.5 or 2 or 2.5 b. Results are very satisfactory for rigid samples. Questions arise for flexible organic materials or even with networks. The geometrical volumes must be decomposed like that : column VC, where particles under investigation have a volume Vc - Vo (VO intersticial volume) which is composed of polymer volume, porous volume and an "invisible" part, corresponding t o swollen gel, VSW. By applying Ogston's treatment (10) for pores defined by long randomly distributed rods, Jerabek proposed (12) to use another distribution coefficient t o get access to the organic volumes. Finally, a classical relation holds between volume, surface area and mean pore radius (e.g. ref. 5) : S(m2/g)= 0.04 Vp(cm3/g)/F50(A).

eq.21

3.2. Data treatment From the expression of K (e.g. eq.121, we may derive experimental value of L corresponding to a given pore size dp.

L=(~-((V~-VO)N dp. ~)~.~)

eq.22

A set of standards is injected (their dimensions being Li) and their elution volumes Vi measured. The unknown in the equation is Vpi, which must be >O. Fitting of results involves to minimize C(Vi exp - Vi calc)2, the summ of differences squared. Use of computers allow now effective practical application.

3.3.Experimental arrangement Column preparation, measurement and data treatment have been already published and applied for samples consisting of silica and silica-grafted polymers obtained via a coupling agent and free-radical polymerization (35). 4. ISEC RESULTS AND CONCLUSION

Curve on figure 2 represents experimental data (molecular mass vs VP on silica), with a n attempt of mathematical fit (second order, with excellent correlation coefficient). Polymer-grafted silicas have smaller porous volumes which do not allow a discussion on the exclusion-partition model. Since solute (polystyrene and alcane standards in THF) dimensions are proportional to molecular mass, in a log-log scale (fig. 31, these results may be transformed in dimensions vs K, on figure 4 (for a better fit, two points corresponding to highest mass are omitted).

370

1

y = 14,495 - 0 , 6 9 8 ~+ 0 , 0 3 2 ~ ~R2 = 1,OO

4 . 1 . 1 . 1 . , . 1 . , . 1 . , . 1 ' 1 . 1 . 1 . 1 .

0 0,040,080,130,490,710,83

1 1,08 1,2 1.251,291,331,38 1,4

Figure 2. Experimental calibration curve for elution on s i l i c n H F

102

j

dimension (nm)

4

6

8

10

12

Figure 3. Relation mass-dimension

14

Figure 4. Log dim vs K

The next step is t o transform the elution results into pore size distribution, by using the different models given for the exclusion coefficient (eq. 11, 12, 14): t h e results are presented in the three Fig. 5. The exponential model (eq.16) does not lead to a possible distribution, whereas i t was appearing to give a very satisfactory calibration curve. For a given model, we have shown (35) the sensitivity of t h e method, able to make difference between initial silica and primed silica, o r silica grafted with different polymers, or in different media. But, from the above figures, it is evident t h a t pore distributions depend on the choice for t h e partition

37 1

40

0

50

20

60

40

70

60

80

80

Figure 5. Porous volume distribution vs pore size, respectively (from top) with model r/(l-K)0.5, eq.11; r/(l-K0.5), eq.12,22; r/(l-K), eq.14

312

coefficient. Best fit (few points to discard) is obtained with eq.11. We may recall that, more generally, morphology results depend on pore shape model.

REFERENCE3 1- B. Imelik, J.C. VBdrine Bd. "Les techniques physiques d e 1'Ctude des catalyseurs", Technip, 1988 2- M. Brun, A. Lallemand, J.F. Quinson, C. Eyraud, Thermochim. A c t a 2 1 , 59 (1977) 3- M. Brun, J.F. Quinson, R. Blanc, M. NBgre, R. Spitz, M. Bartholin, Makromol. Chem., 182,873 (19811 4- F. Krska, K. Dusek, J. Polym. Sci., part C, 38, 121 (1972) 5- I. Halasz, P. Vogtel, Angew. Chem. Znt. Ed. Engl., 19, 24 (1980) 6- S. Brunauer, P.H. Emmett, E. Teller, J. Am. Chem. SOC.,60, 309 (1938) 7- E.P. Barett, L.G. Joyner, P.H. Halenda, J. Am. Chem. Soc., 73,373 (1951) 8- J. F. Rabek "Experiniental methods i n polymer chemistry", chap.24, Wiley ed. 1980. 9- A. Revillon, Anal. Chem., 46, 1589 (1974) 10- A.G. Ogston, Trans. Far. SOC.,54, 1754 (1958) 11-H. Kamogawa, A. Kanzawa, M. Kadoya, T. Natto, M. Nanasawa, Bull. Chem. SOC.Jap., 56,762 (1983) 12- K. Jerabek, Anal. Chem., 57, 1598 (1985). 13-K. Jerabek, Anal. Clieni., 57, 1595 (1985). 14- K. Jerabek, K.J. Shea, D.Y. Sasaki, G.J. Stoddard, J. Polym. Sci., Polym. Chem., 30,605 (1992) 15- A. Wang, J. Yan, R. Xu, J . Appl. Potym. Sci., 44, 959 (1992) 16- M. Krejci, D. Kourilova, R. Vespalec, K. Slais, J . Chromatog., 191, 3 (1980) 17- K. Jerabek, K. Setinek, J. Hradil, F. Svec, Reactive Polymers, 5 , 151 (1987) 18- K. Jerabek, K. Setinek, J , Polym. Sci., Polym. Chem., 28,1387 (1990) 19- K. Jerabek, K. Setinek, J. Polym. Sci., Polym. Chem., 27,1619 (1989) 20- K. Jerabek, Polymer, 27,971 (1986) 21- J. Capillon, R. Audebert, C. Quivoron, PoZym,er, 26, 575 (1985) 22- B. Haidar, A. Vidal, H. Balard, J.B. Donnet, J. Appl. Polym. Sci., 29, 4309 (1984) 23- D.H. Freeman, I.C. Poinescu, Anal. Chem., 49, 1183 (1977) 24- D.H. Freeman, S.B. Schram, Anal. Chem., 53, 1235 (1981) 25- 0. Chiantore, J. Polym. Sci., Polym. Letters, 21, 429 (1983) 26- S.B. Schram, D.H. Freeman, J . Liqu. Chrom., 3,403 (1980) 27- J. Yan, A. Wang, R. Xu, Lizi Jiachun Yu Xifu, 5, 292 (1989) 28- K. Jerabek, K. Setinek, J. Molecular Catal., 39, 161 (1987) 29- W.P.N. Fernando, C.F. Poole, J. Planar Chromatog., 5, 50 (1992) 30- W.P.N. Fernando, C.F. Poole, J . Planar Chromatog., 4, 278 (1991) 31- J.H. Knox, H.J. Ritchie, J. Chromatog., 387,65 (1987) 32- W.W. Yau, J . J . Kirkland, D.D. Bly "Modern size exclusion liquid chromatography", Wiley, 1979 33- J.V. Dawkins i n "Comprehensive Polymer Science", Vol.1, chap.12, Pergamon 1989 34- R.L. Albright, chap.7 in "Catalyst supports and supported catalysts", A.B. Stiles ed, Butterworths 35- K. Jerabek, A. Revillon, E. Puccilli, Chronzatographia, 36,259 (1993)

J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characlerizalion of Porous Solids 111 Studies in Surface Science and Catalysis, Vol. 87 0 1994 Elsevier Science B.V. All rights reserved.

373

stochastic Analysis of Dispersion in Size-Exclusion Chrornat ographic Columns

Alessaiidra Adrover", Diego Barbs*, Massimiliano Giona" Daiiiela Spera" "Dipartimento di Ingegneria Chimica, IJnivcrsitb tli Roiiia "La Sapienza" Via Eudossiaiia 18, 00184, Roiiia, Italy *Dipartimento di Ingegneria C%imica, [Jiiiversitb dell' Aqiiila, Monte Luco cli R.oio, 67040 L'Aquila, Italy 'Consorzio di Ricerche Applicate alla Biotecnologia., Strada Provinciale 22, 67051, Avezzano (AQ) Italy

Abstract Dispersion properties of l>iomolccules in size-exclusion chroma togra.phic coluniiis are analyzed both experimentally a.nd tlieoretically. I n order t o explain t h e 1iiiea.r beliaviour of the dispersion coefficient with the soliite vcAlocity, experinienta.lly found for most of t h e bioiiiolecules considered, a stochastic iiioclrl of solute dispersion is proposed based oil tlie exit-time equation.

1. INTRODUCTION

A classical way of charactcriziug tlie tlyiiamir properties of I>:iclied I d s antl chromatographic coluiiins is to make use of nioment aiialysis in order t o evaluate t h e coiivective contribution a.nd the dispersion coeficient of solute molecules [I]. Dispersion analysis furnishes a clear picture of the rrsolution capa,liility antl sc-paratioil performinces of chromatographic columns [2]. T h e usual short-cut prediction of (-liromatogr~tI>Iiic-coliiiiiii perforiiiances makes use of plate-lieight tlic-wry [a], and separa,tion properties are evaluated by iiieans of Gaussian approximation of oiitlct profile [4]. More refined physical analysis of dispersion can b e developed iii terms of physical iiiodels of solute-matrix interactions by considering t h e influeiicc of vdoc-ity fliictiiations, which depends on tlir disorclered structure of t h e porous nia.trix and on tlir IicJkrogrnc-ity of tlie p d i l i g . In this article we analyze dispersion plienomc?ua of glol>ular l>iomoleciilesin SEC coluiiins - in wliicli soliite transport is iiifluenccd solely by t,hr gc~motricalinteraction of t h e molecules with the pore structure of tlie pacliing - ill tlir ~ I Y ~ S ~ of( Ya. s ~ r o i i groiivectivr field ( t h e Peclet nmnl)cr is geiierally in the raiigr 1000-20000 for iisiial op>ratiiigroutlit,ions). The experimental results show that tlie mean squarc tlcviatioii of oiitlet cliroma.togra.ms exhibits a powerlaw behaviour wit,h respect t,o the retention tiill(-, witli an exponent t h a t is iisiially equal to 2. This implies that t h e clispcrsion coe6rieiit scales linearly with tlie soliite velocity.

374

A stochastic inodel of transport based on the presence of velocity fluctuations at the microscopic scales is proposed in order to explain the beliaviour of the dispersion coefficient with the retention time. The model is based on the description of transport as a stochastic-differential equation at tlie microscopic scales and on the evaluation of the macroscopic transport coefficient (in this case tlie dispersion coefficient) from the average exit-time distribution. Tlie first article developing tliese concepts in the case of dispersion in periodic and aperiodic media was published by Bliattacliarya and Gupta in 1983 [ 5 ] . A simple onediinensional stochastic inodel is capable of yielding the experimentally found dependence of the dispersion coefficient with solute velocity. The deviations from the linear dependence of the dispersion coefficient on solute velocity experinientally observed for small-radius highly heterogeneous packing can be qualitatively explained in teriiis of the highly disordered geometry of the packing. Moreover, in order to characterize dispersion proiierties as a function of molecular size, a dispersion length associated with each biomolecule is introduced, representing the characteristic length within wliich the fluctuations in solute velocity are correlated. 2. EXPERIMENTAL APPARATUS

The coluinns used i n performing experiments were: Bio-Sil TSK 250 (packing G 3000 SW); average particle size 10p11, avemge pore radius < 1' >= l25A, and Bio-Sil TSK 125 (paclting G 2000 SW); average pore ratlius < 7' >= G2.5A from Toyo-Soda (column length L = GO cm; coluinn section S = 0.44 cm'). The elution solutions were 0.1 M Na2S04,0.1 M NaH'PO, and 0.02 % Sodium Azitle ( w / v ) for the TSI< 250 column; 0.05 M Na2S04, 0.05 M NaH2P04 and 0.02 % Sotliuni Azide ( w / v ) for the TSK 125 coluinn. The eluents were adjusted at pH G.8 by using a NaOH solution. The processing apparatus consisted of a twin-headed reciprocating pump, Water mod 510, a selectable wavelengtli U.V. detector (481 Lambda Max) and a Rheodyne injector, model 7125, purchased from Millipore 1J.K.The protein concentration varied froin 0.1 to 20 mg/ml and the injection volume from 20 to 40 /A. All the experiiiients were performed at 25 "C. The biomolecules consitleretl were: thyroglobulin from bovine (669 It Da), apoferritin from horse spleen (443 IiDa), ovalhimin from chiclien egg (44 kDa), myoglobin from horse (17 kDa) and cyanocobalainin (1.35 kDa) siipplitd hy Sigma, Poole U.K. 3. EXPERIMENTAL RESULTS

The experimeiital results for the clispersion of solute molecules can be obtained froiii the evaluation of the variance u2 of the outlet chromatograins, starting from an iiiipulsive inlet injection. Figure 1 a,) shows the beliaviour of u2 as a function of tlie retention time t , for both TSK 250 and TSI< 125 coliinins, obta.ined by varying the elution flow rate in the range 0.1-1.0 iiil/min. From this data it is possible to clerive the following correlation between u2 and t,. u2

-

t;.

(1)

375

cr2[rnin2]

lo2+

I

t

i

16’

1o-2 10’

lo2

t,[rnin] lo3

Figure 1: a) uz vs t , for TSK 250 and TSK 125 (only proteins exhibiting total exclusion) column: a: cyanocobalarnin (TSK 250); b: thyroglobulin (TSK 125); c: apoferritiii (TSK 125); d: ovalbumin (TSK 250); e: thyroglol~uli~i (TSK 250). The lines are the power law correlations a2 t:. b) a2 vs t, for the TSK 125 coluinii for snialler biomolecules: a: cyanocobalarnin (TSK 125); b: iiiyogloliin (TSK 125); c: ovalbuiiiiii (TSK 125). The lines are the power law correlations uz t:, witli cu = 1.5.

-

-

Given that for a single-phase coiivection-tlis1,erhioii model of chromatographic dynamics the outlet variance is related to the tlispersioti coefficient D , as u2 = 2D,t:/L2, it follows that

v being the solute velocity and L,l a characteristic leiigth associated witli dispersion (the physical iiieaiiiiig of Ld will be discussed i n section 5). The linear scaling of D, vs I,I is indicative of the strong correlation existing hetween velocity intensity (and hence velocity fluctuations) and dispersion. I11 a ma.croscopic perspective, eq. (2) implies that the dispersion Peclet number Ped = Lv/D,, is iiideprntlent of flow conditions and characteristic of each molecule, (figure 2)

L Ped = Ld

The scaling beliaviour (11-12) was observed for every biomolecule processed iri the TSK 250 column. In TSK 125 column, large biomolecules exhibiting total exclusioii (thyroglobulin and apoferritin) show the same beliaviour. These molecules, according to

376

-Figure 2 : Dispersion Peclet number P c , ~vs solute velocity v for biomolecules liaviiig a linear dependence of D with v. a: t1iyroglol)uliii (TSK 250); b: ovalbumin (TSK 250); c: apoferritin (TSK 125); d: thyloglobulin (TSII; 125); e: cyaiiocobalairiiii (TSK 250). Felgenhauer correlation [6], have m o l c d a r radii respectively of T , = 69.0 and r, = 80.0 and therefore do not penetrate into the packing. For smaller biomolecules, with respect to which tlie packing acts as a molecular sieve, the experimental data (figlire I b ) intlicatr a scaling law of tlie form

with a = 1.50 f 0.05. It is reiiiarl;al,le to ol~servt.tliat the expoiient cy of tlie siiialler biomolecules (cyanocobalainiii, myoglobiir, ovall~uinin)in the TSK 125 coluiiiii is exactly the same (within the natural experimental Riictuatioiis), iiitlira.ting that this exponent is not related to the specific nature of tlic solute Init to the sttlric interaction of sinall biomolecules with the porous structiire of the ~m-lting. A detailed cliaracterization of tlie sIIap(=of tlie outlet chromatogram can be found i n [7]. This article presents a scaling analysis of the outlet cliroiiiatograiiis and shows that the response of SEC coliimiis can I,o tlc ibctl for high Peclet num1,ers by ineaiis of a unique invariant function iiiclepc~iiclciitof tlrr Row ra.tr aiitl characteristic of each solute. 4. THEORETICAL MODELS O F DISPERSION There are several models for rxplaiiiiiig fluitltlynamic dispcrsioii in tubes and in packed beds. The Taylor-Aris motlcl [t;] piwlicts ii. dispersion coefficient proportional to tlie c n t txperiniental results on packed beds. More square velocity, but is not i n a g r ~ ~ t ~ i iwith refined models of dispersion in porous mcdia. arc h s e d on a iiiiiltipliase characterization of transport. The analysis of C:arl~oiicll a i d Wliitalw [9], based on local-scale averaging and on the iiitroduc.tion of a closiire condition into the iiriiltiphase model of transport in porous media, fiiriiislies the scaling law D,, v k 1with:,! = 1.:3- 1.7. Nevcrtlilcss, as noted in Plumb-Whitaker [9], this Itintl of inotlcl appears to he inadrqiiatr as a description of

-

377 transport a t high Pe (greater then lo3). Monte Chrlo simulations of solute dispersion in disordered lattice models are discussed by Sahinii et al. [lo] by assuming the validity of the Darcy law. The simulation results indicate a linear dependence of D, on v at high convective velocity. Lattice simulations in disordered models of porous media indicate that the origin of convection-controlled dispersion comes from the chaotic reorientation of the streamlines in a microscopically disordered porous medium. Finally, attention should be drawn to the probabilistic analysis of Saffman [l11 predicting an axial dispersion coefficient of the form D, = v l l o g ( v l / D ) , where D is the diffusion coefficient. An interesting alternative to tlie previous analysis of dispersion was formulated by Bhattacharya and Gupta in terms of solute motion at the microscopic scales. (i.e. at the scales at which velocity fluctuations are present). Solute motion a t the scales of fluctuations can be formulated in terms of a stochastic differential equation (SDE) [12]. In the stochastic approach, the dispersive contribution can be espressed by means of Brownian motion fluctuations. The dvtails of tlie stochastic analysis of dispersion can be found in [ 5 ] . In the one-dimensional approxiimtion, the stochastic differential equation of motion reads as d z ( t ) = -C(z(t))rlt

+f i d < ( t ),

(5)

where 6 is the fluctuating velocity firltl at tlie microscopic scales and @ ( t )is an infinitesimal increment of a Brownian motion rrlatrtl to nioleculnr diffusion. The expression for the dispersion coeffic,ient D , can be obtained from the average value of the correlation function < z 2 ( t )> evaluated at tlie microscopic scales. By taking into account the Brownian nature of molecular fluctuations, and by assuming that velocity fluctuations are also Brownian and are uncorrelated with ( ( t ) ,the dispersion coefficient can be expressed as

D, = D

+ v2pt, ,

(6)

where p is a constant related to the corrc4ation function of velocity fluctuations and t , is the characteristic time for velocity flnctiiations. The dIarac.teristic. time t , can be evaluated within the fraineworli of the stocliastic theory of transport by considering it equal to the volume-average of the exit-tiinr distribution [ 121 from the unit pore-cell at the microscopic scales < O ( : c ) >. The exit time O(:I:) a.t a, point ;c is tlie time necessary to reach the boundary of the unit pore-cell for a particle suhjrctetl to tlie stochastic equation of motion (4). In three dimensions, the equation for O ( z ) is ail elliptic equation,

DV'B

+ V . ( 6 0 ) + 1 = 0.

(7)

The general application of the exit-time equation iinplies: the definition of a coniplex iiuit pore-cell representing tlie porous structure a t the microscopic scales; the definition of tlie statistical properties of the fluctuating velocity field 6;

378 0

the solution of the exit-time equation on the unit pore-cell with the boundary condition e(z) = 0 at every point of the boundary of tlie cell representing a pore opening, and normal derivative of 0 equal to zero, aO(z)/an= 0, at every point representing the porous matrix.

The problem posed in this way is rather coinplex to solve both numerically and as regarding the physical assumption on tlie velocity field 6. However, it is possible to derive the fundamental features of tlie stochastic model of dispersion by reducing it in a simple and analitically tractable wa.y. A short cut evaliiation of tlie average exit time can be achieved by simplifying tlie tlirre-dimensioiial exit-time equation i n one diinension (reducing the problem to a slab-formiilation of pore structure), and by simplifying tlie expression for the velocity field 6,consitlering it i n the first-order approximation equal to the mean solute velocity w. In this way, the exit-tinie equation retliices to a second-order differential equation with constant codficients

with the boundary conditions O(.c)IT=, = 0, dO(z)/d.cl,,o = 0, where 1 is tlie characteristic length of fluctuation. The last condition expresses tlie symmetric boundary condition for z = 0. The expression for < 0 > reads as (9)

Pe, being the fluctuationa.1 Peclet number ( P e , = d / D ) . The a.vera.gedexit time has tlie limit behaviour, limp,,+m = Z / 2 7 1 , and therefore, substituting it into eq. (8), it follows that D v , which explains why, for high Peclet niinihers, tlie dispersion coefficient exhibits a linear beliaviour with v . Eqs. (6),(8)-(9) constitute the simplest interprt:tation i n terins of the fluctuatioiial approach to transport i n complex poroiis iuedia of the scaling law (1) experimentally found in SEC columns. It is interesting to note that the dispersive behaviour predicted by eqs. (6)-(9) explains with suffirieiit a.ccuracy the experimental results on dispersion in packed beds as a function of Prclet niimber [13]. Finally, a few remarks should be made on the deviatioii from eq. ( 1 ) observed for small molecules in the TSI< 125 column. The deviation from tlie linear delwndence of the dispersion coefficient found in the TSI< 125 column for smaller biomoleciiles could be heuristically interpreted by assnniing that the average fluctmtion velocity < d > for highly heterogeneous porous media does not 1trha.ve liuea.rly with macroscopic solute velocity but follows a scaling law

-

< G > N W Y

(10)

with y = (Y - 1. It is important to olisrrve that this a~r,onrmlor~s dispersive beliaviour ( we define as regular tlie scaling laws ( I ) - ( 2 ) ) cannot be explaiued by the logarithmic correction to dispersion coefficient deriving from Saffman theory. According to this model a2/t: log(w). Figure 3 shows the behaviour of a 2 / t :vs v is normal-log scale. The Saffman theory observed. The predicts a linear beliaviour of u'/t? vs log(.), which is not ex~~erinientally N

379

4 -

3-

21-

-'0 lo-'

" "

10'

I

v [crn/rnin] 10'

Figure 3: u2/t,2 vs 2) i n normal-log scale for the bioinolecules of figure 1 b) a linear regression represents tlie results of the Saffnian theory. a: ovalhiimin; b: myoglobin; c: cyanocobalamin. different dispersive behaviour of sriiall molrcules in TSK 125 and TSK 250 coluinns can be explained in terms of the different rnicroporosity ant1 geoine.tric heterogeneity of the two packings, so that the siniple Euclitlean a.pproximation developed for the exit-time equation can be reasonable for the TSK 250 columii antl seeins to be iiiadeguate for smaller niolecule in TSI< 125 column. Tra.liport a.nd dispersion i n the mobile phase of TSK 125 (i.e. for those molecules exhibiting total exclusion) still show a linear depeiidence of D on u and therefore the exponent y is exclusively related to tlie fluiddynamic conditions inside the pore-network of the packing. From these observations, it becomes clear that only a coniplete analysis of the exittime problem in a two- or three-dimc~isio~ial motlel of tlie pore-network can explain the anomalous features expressed by eq. (4). 5. INFLUENCE OF MOLECULAR SIZE Let us consider the depentleiice of L,l 011 tlie steric cliaracteristics (iiiass or radius) for molecules exhibiting linear Iwliaviour of D with 2). Figure 4 shows tlie results obtained for tlie dispersion length of tlie bioinolecules analyzed 011 tlie TSK 250 column. A physical model for the functional dependence of L,l on mass can be obtained in analogy with the mass dependence of dispersion deriving from the Taylor-Aris theory

where R is the column radius antl D E tlie Stokes-Einstein diffusivity. Eq.( 11) implies that if the velocity term constitutes the niain contribution to dispersion, then

380

1 03 1o3

1

1o4

lo5 M [Dal 10‘

Figure 4: Dispersion length Ld vs niolecular weight for I)iomolecules in the TSI< 250 Colunul. where r , is the solute radius and conseqimitely

i.e. Ld monotonically increases with tlir miss. Tlie numerical results for Ld can be indicative as an estimate of the scale of fluctiiations coinpared with tlie size of the gel beads. A dispersion length of ahoiit 50 ge-beads diameters was found for the larger bio~nolecules(e.g. tliyroglobulin) antl one of 2-3 dia.meters for the smaller ones. This is fairly reasonable considering that tlie motion of tlie heavier niolecules develops priniarly in the mobile phase and the velocity fluctuations are highly correlated as a consequence of the doniinance of tlie convective teriii. On tlie contrary, for small bioniolecules the correlation length of the fluctuation is comi~arablewith tlie diaineter of the gel beads since the main contribution to vchrity fluctuations derives from the geometrical and topological disorder of the porous matrix. 6. DISCUSSION AND CONCLUDING REMARKS

Tlie experimental results obta.iiietl fur tlie tlispcrsion of globular bioniolecules in SEC columns can be well interpreted by a p ” r law 1)eliavioiir ( I ) , wliicli in the regular case has an exponenent cy = 2. Tlie stoclia.stic approach can expla.in this phenomenon in a simple way and can also be extcntlctl to more complc=xgeometrical modeling of the porenetwork. The anoillalous beliavioiir ( 0 < 2) found for smaller solutes in the TSK 125 column is probably due to tlie roniplrx geometrical pore-network experienced by these molecules. Comparative aiialysis of tlir c~xprriitientalresults of dispersion in SEC coliinins indicates three different dispersive rc,gimcs: 0

dispersion in large pores (sucli R S i n the TSIi 250 coluniii) cliaracterited by an exponent N = 2 antl by a dispersion lcngth that incrctases with the niolecular size;

38 1

2.01

1.4

0.5 1.0 rs’cr’ 1.5 Figure 5: cy vs the geometric ratio T ~ for thc T S I i 125 coliiinn. A sudden transition 0.0

in dispersive behaviour is evident Iwtwcvn molecules pwinrating into the gel-beads and those presenting tot a1 exclusion . 0

0

dispersion in the mobile phase (for niolrculrs exliilitiiig total exclusion i n the TSK 250 colunm) chara.cterizetl 1)y N = 2 and with a dispersion that is practica.lly coilstant, but s e e m to decrease with tlie niolecirlar size (even if tliis conclusion should be carefully checked by fiirthcr rxperiinents); dispersion in sinall pores (TSK 125) with a n exponent cy less than 2 , wliich may well depend on the liighly Iirtrropieous poroiis struc,ture, and a tlie dispersion that increases with size.

The sudden transition in the dispvrsive l.iehaviour of solute molecules experiencing the geometrical complexity of packing i n the TSI< 125 coliimn is s h o w n in figure 5 , i n which the resulting exponent cy is represented as a function of tlie steric parameter rs/ < r >, where r, is the solute radius. Ilufortiinately, \vc have not at disposal experiinental data near rs/ < o’ >= 1, whic,li are important to chrify the nature of t,lir transitioii found in the behaviour of the exponent a. Futiire exlirrinient;rl work will lie oriented on this topic. The anomalies i n the dispersive Iwhavioiir can prol)aljly still lie explained in tlie framework of the stochastic theory by extending tlie niiinrrical simiilation to complex pore-cells, and including the influence of tlie fliiidodynainics i n porous niedia expressed as a. noxiconstant velocity field. Nrvertlielrss, a f u r t h e r iinprovemmt of the theoretical models can be achieved by detailed simultnnroiis a,na,lysis of the niicrostructural properties of the porous packings and of the tlispersivc fmtures of solute molecules. Initial results on tlie dispersive behaviour obtained by solving the exit-time equation (7) on lattice models of disordered porous structures (percolat,ion lattices) indicate that ail exponent N less than two is observed i n the presence of‘ liigli geometrical tlisorcler [14].

REFERENCES 1. J .H . Seinfeld an (1 L . La 11 id us, A Int h e mnt icnl Mfthods in Chemicnl Engin ecring, Volume 3, Prentice Hall, Eiiglrwwotl ClifFs, 1974; E. Kiicera, J . ~ / l r o n z n t .19

382 (1965) 237. 2. W.W. Yau, J.J. I
3. G. Guiochon and M. Martin, .I. Clwouint. 326 (1985) 3; B. Aiispacli, I1.U. Gierlicli arid K.K. Unger, J . Cht-onrnt.443 (1088) 45. 4. W.W. Yau, J.J. Kirkland, D.D. Bly and I-I.J. Stoklosa, .I. C/t.r0?7Lat. 125 (1976) 219. 5. R.N. Bliattacharya and V.K. Gupta, M’atfr Rr.sonr. RFS.19 (1983) 938; R.N. Bhattac1ia.rya and V.K. Gupta, in Dyriniirics of Fluids i n Hiwarehied Porous Media, J.H. Cushman (Ed.), 111). 61-96, Acaclcmie. Press, London, 1990. r k Physiol. Cl)wn)..355 ( 1074) 1281. 6. K. Felgenhauer, H o y p c - . ’ ; ’ r ? ~ l ~2.

7. M. Giona, A . Atlrover, D. Barha antl D. S p m t , Siniplificd arialysis of cliromatographic column tlynatnics, < , ” / t f ! t i . Eiign9. Sci., accrptrtl for publication (1993). 8. G.I. Taylor, Proc. Roy. Soc. A219 (1953) 1%; R. Aris, Proc. Roy. SOC. A235 (1956) 67. 9. P. Carboilell and S. Whitalter, in Fmdnntwntals of Transport Phe~ioineiiai7i Porozis Media, J . Bear and M.Y. Corapcioglu (Etls.), 111). 123-198, Martinus Nijhoff Pulil., Dordreclit, 1983. 10. M. Sahimi, B.D. Hughes, L.E. Scriveii antl I-I.T. Davis, Cltwm. Engiig. S c i . 4 1 (1986) 2103; M. Saliimi, A.A. I l c i h , H.T. Davis and L.E. Scriven, Clirin,. Engng. Sci. 41 (1986) 2123. 11. P.G. Saffnian, J. Fluid. A4eel1~6 (1959) 321; ibitleni 7 (1960) 194. 12. S. I<arlin and I-I.M. Taylor, A Sccond Conrsc in Stoclrnstic Proec.ssfs, Academic Press, New York, 1981; N.S. Got.1 antl N. Richter-Dyn, Sfochnstic Model.5 in Biotogy, Aca.deinic Press, Ncw Yorl;, 1974. 13. The results obtained from tlir siiiiple ow-climrnsion niotlrl of dispersion reported i n this article are i n close agreeiiiriit with tlir comprehensive data on axial dispersion in pacl;etl I)& wportrtl hy O.A. Plutiili and S. Whitalter in Dynam.ics of Fluids in Hieinnlricnl Poroiis hlrrlin, .J. Cuslinian (Ed.), lip. 97-148, Acadeniic Press, New York, 1990. With reference to these data, tlie le nun]fluctuational Peclet numher P e j slioultl lie relatrtl to tlir ~ ~ a r t i rPeclet ber Pep. 14. M. Giona, A. Adrover and A.R.. Giona, Numerical analysis of diffusion in disordered media Insed on tlie exit-titw cyua.tioii, First Conferc?trceon Chemical and Process Engineering, Floreiire 1:3-15 May, 1993, pp.59-63 .

J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterization of Porous Solids I11 Studies in Surface Scicncc and Cahlysis, Vol. 87 0 1994 Elsevicr Scicncc B.V. All rights reserved.

383

Molecular interactions on porous solids under magnetic field Sumio Ozeki,* Hiroyuki Uchiyama, Shinji Ono, Chihiro Wakai, Junichi Miyamoto and Katsumi Kaneko Department of Chemistry, Faculty of Science, Chiba University, 1-33Yayoi-cho, Chiba 260,Japan

Abstract The chemical and physical interactions of a paramagentic NO and a diamagnetic water with solid surfaces were enhanced and depressed by static magnetic field. The micropore filling of a supercritical NO onto microspaces of zeolites and pitch-based activated carbon fibers a t 303.2 K was enhanced by a 7.6 kG static magnetic field via magneto-micropore filling (MMF), for which preferential pore sizes were 0.5 and 1.0 nm in diameter or width. An NO dimer seems to be formed via a magnetic effect on a radical pair on a NO dimer in microspaces which fit mono- and bimolecular layers of NO dimer. Water on a carbon black, a pitch-based activated carbon fiber and a zeolite was attracted to the surfaces under a 9.6 kG magnetic field. Only water weakly interacting with the surfaces, such as water in multilayers and cluster and on hydrophobic surfaces, was apt to respond the magnetic field. The magnetic micropore filling of water in slit-like micropores of P-10 was depressed stepwise with an increase in amount of adsorption, as if the adsorption process of water into micropores may occur by multilayer adsorption. 1. INTRODUCTION The chemisorption of NO on metal oxides was enhanced and depressed by the external magnetic field [ll. The magnetoad- and magnetodesorption related intimately to porosity of solids and adsorption state (surface sites) rather than the magnetism of solid. Using activated carbons (AC) and activated carbon fibers (ACF), we examined an role of porosity and surface functional groups in magnetoadsorption 121. Super critical gases usually cannot be adsorbed by physisorption onto porous materials. However, a supercritical NO near room temperature can be adsorbed extraordinally much amount on ACs and ACFs [31.

384

When NO molecules are adsorbed in micropores of ACFs and zeolites, NO dimers are formed in the micropores [31. In the previous papers [21, we reported that NO adsorption onto activated carbons are enhanced by magnetomicropore-filling (MMF) in slit-like micropores less than 1.1nm in width and MMF should relate close to micropores, i.e., formation of NO dimer. At the same time, however, MMF is also subject to amount of surface functional groups of carbons. Therefore, the role of micropore in MMF might be somewhat ambiguous. Zeolites have cylindrical micropores with no distribution of pore size, unlike activated carbons having slit-shaped micropores which will be accompanied with some pore size distribution. In addition, there are little functional groups on zeolites. Therefore, zeolites would be suitable for examination of pore effect on magnetomicropore-filling of NO, distinguishing from the effect of surface functional groups on it. Generally, water adsorbed on surfaces are immobilized in the first layer and approaches monotonously to bulk liquid water with amount of water adsorbed. Thus, adsorbed water experiences a variety of states which result in both solid-water and water-water interactions, as water adsorption progresses. Recently, we examined the magnetic effect on water adsorption on oxides as a function of amount of intensity of magnetic field and water adsorbed and found that only water in multilayer, not in first layer, responds to magnetic field [41. In this paper, we discuss the role of micropores in magnetomicropore-filling of paramagnetic NO and diamagnetic water for various zeolites and pitch-based activated carbon fibers (relatively free from surface functional groups) having different pore sizes. 2. EXPERIMENTAL

Samples used here, zeolites (MS3A, 4A, 5A, 13X, mordenite, TSZ-500 (Toso Co.)), pitch-based activated carbon fibers (PIT: P-10, 15, 25, and P-10-1173), and a nonporous carbon black (NPC) and a carbon black (PC) having slight amount of micropores, are relatively free from surface functional groups. P-10-1173 was prepared in order to remove surface functional groups by heating P-10 in air at 1173 Kfor 1h “21. N, adsorption on zeolites, which was pretreated at 573 K and 1mPa for 1h, was carried out at 77 K. The amount of NO and water adsorbed was determined volumetrically at 303.2 f 0.1 K, as described in the previous paper 111. The sensitivity of the adsorption measurement was about 1pg/(g-adsorbent). The changes of gas pressure were measured upon applying the static magnetic field of 7.6 kG for NO and 9.6 kG for water t o the gas-adsorbent systems which had been equilibrated for

385

40 h or more. The homogeneities of the magnetic field at the position of the adsorption cell is within 2 %. The samples were pretreated at 1mPa for 1h prior to the adsorption experiments.

3. RESULTS The specific surface area, pore volume, and pore width of the samples were analyzed by the t-plot of N, adsorption isotherms at 77 K using the standard thickness for N, film on the graphitized nonporous carbon [21. Figure 1 illustrates changes of amount of NO adsorbed on various zeolites by application of 7.6 kG which was applied at zero of the time axis and removed at 60 min. A nonporous carbon black as a reference showed no MMF. Magnetoadsorption of NO onto the adsorbents occurred just after application ON

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Figure 1. Examples of the increment of adsorption amount of NO due to 7.6 kG static magnetic field which was applied with the permanent magnet to the quasi-adsorption equilibrium at 303.2 K and 15 Torr NO. The time at which the magnetic field is applied to (ON) and removed from (OFF) are 0 and 60 min. respectively. Adsorbents: A, MS5A, B, MS13X.

Figure 2. Magnetic-field-induced adsorption of NO at 303.2 K and 7.6 kG as a function of pore size (diameter for cylinder and width for lamellael of solids. Samples: 0 , zeolites (MS3A, MS4A, MS5A, mordenite, TSZ-500, MS13X);o,pitch-based activated carbon fibers (P10, P15, P25, P10-1173); 0, carbon blacks (PC, NPCl

386

of the magnetic field, reached a constant value or a maximum value (Au)within a few minutes, and in the latter case exponentially decreases during application of the magnetic field. After removal of the magnetic field, NO was reversibly desorbed. The characteristic time for the exponential decrease was, e.g., 28 min for MS5A and 38 min for MS13X. Figure 2 shows the relationship between Au and pore size of the adsorbents. Here Au for the carbons are reduced by multiplying a factor 0.27 so that the point for P-10 may fall on the plot for zeolites in the figure. The pore sizes of the zeolites are effective size and those for the carbons were estimated from the t-plot analysis of N, adsorption isotherms [21. In the plot, two preferential pores for MMF appear markedly at 0.5 and 1.0 nm. The amount of water adsorbed on NPC, P10 and MS5A changed just after application of magnetic field, as in the case of NO, and reached to a constant value within a few minutes. A 9.6 kG magnetic field promoted water adsorption. The Au value for MS5A reached up to 5 ?4 of total amount of adsorbed water. When the magnetic field was removed, the adsorbed amount recovered the initial value. The magnetic effect appeared when water was adsorbed beyond 110 (0.3) mglg (Torr) on MS5A or at the apparent surface coverage 8 > 1(Figure 3). On the other hand, the amounts of water adsorbed on NPC and P10 increased by a 9.6 kG magnetic field even in the monolayer region (if water covers the surfaces which N, molecules access) (Figure 4). 4. DISCUSSION 4.1. Porosiry effect on MMF of NO Very weak interaction of NO with graphite 151 causes small adsorptivity of the nonporous carbon black (NPC) for NO. However, when a carbon black has micropores, such as PC, typically AC and ACF, adsorbs more NO. This dependence of NO adsorptivity on microporosity is parallel t o that in MMF 121. The relationship between Au due to 7.6 kG magnetic field and pore size (width of slitlike micropore) of ACs and ACFs (Fig.10 in Ref.3) suggests that there are two preferential pore regions, 0.7-0.85 nm and near 1.1 nm, which we did not point out previously [21. Since the discrete micropore size distribution of ACFs, e.g., 0.70-0.84 and 0.98-1.18 nm for cellulose-based ACF [61 may be smeared by contributions from surface functional groups, it is difficult to conclude what size of pores is most preferable for MMF of NO. In the current results (Figure 21, obtained by using adsorbents relatively free from surface functional groups, the preferential pore size for MMF appeared at 0.5 and 1.0 nm. Both zeolites and PITS seem to prefer 1.0-nm micropores for

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Figure 3. Magnetoadsorption of H,O as a function of total amount ( u ) and apparent surface coverage (0) of water adsorbed on MS5A under 9.6 k G at 303.2 K. 5 4 02

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Figure 5. Magnetoadsorptivity of H,O as a function of total amount of water adsorbed on P-10 under 9.6 kG at 30 3.2K.

Figure 4, Magnetoadsorption of H,O as a function of total amount of water adsorbed on hydrophobic surfaces of NPC (upper) and P-10 (lower) under 9.6 KG at 303.2 K.

MMF, on the other hand, the preference of 0.5-nm pore appears only in zeolite systems. This may be only because activated carbon fibers (ACFs) have little micropores of less than 0.70 nm in width [61. Therefore, consulting with the results obtained here, we may deduce th at most preferential pores for MMF are 0.5 and 1.0 nm in diameter (width). The pore shape (cylinder and slit) effect on MMF may be expected but the experiments showed no desicive indication about it from the comparison of MMF between ACFs and zeolites, Kaneko and coworkers [31 found th at in the micropores of zeolites and ACFs

388

some NO molecules are dimerized even above room temperature via the enhancement in the intermolecular interaction of NO, about 10 kJ/mol. A paramagnetic NO having a n unpaired electron forms a diamagnetic dimer (NO), in the condense phase at low temperature [71 and the adsorbed layers on a flat surface below 90 K [8]. MMF was promoted with decrease in pore size and particularly preference of 0.5 nm micropores in MMF agrees with that in micropore filling of NO L31. The dimers are most strongly stabilized in 0.5 nm micropores which just fits the geometry of the dimer (0.53 x 0.41 x 0.30 nm' for the trans 191 and cis 1101 forms). MMF was also enhanced in 1.0 nm micropores, although the micropore filling of NO was not specifically enhanced in 1nm pores of zeolites and ACFs [31. Since the excess stabilization energy of the dimer steeply decreases with pore size, it is inferred that magnetic field promotes the dimer formation in 0.5 nm and, especially, 1.0 nm micropores through a specific effect on adsorbate-adsorbent and/or adsorbate-adsorbate interactions, which were neglected in the micropore filling theories. The 1.0 nm micropores can just accept bilayers of NO dimer. Considering that MMF waa observed in zeolites having small channels and cages, short range interactions between NO molecules, rather than long range interactions as in cluster, are important for MMF. Most plausible species in the MMF process is (NO),. Since NO dimer has a boiling point in contrast with a supercritical NO, further micropore filling of NO may occur. The diamagnetic NO dimer has a weak chemical bond which arises from electron pairing between two NO (n2) molecules, but the coupling between two interacting NO molecules will be still weak and the unpaired electron will mainly be localized on each NO molecule ill]. Then, one may regard a n (NO), molecule as a two spin system. The ground state of (NO), is a singlet (S)H21. The radical pair theory successfully explains the kinetics and the production yield for radical reactions L131. 4.2. Porosity Effect o n Magnetoadsorption of Water Generally, water in first layers on solids is strongly adsorbed, e.g., by hydration around exchangeable cations and interations between water dipole and electric field of zeolite, while condensed water in pores and water in multilayers interact weakly with each other via hydrogen bonds. Thus, the small magnetic energy (cO.1 cm.') seems to affect only the weakly interacted water molecules in the multilayers, subject to the adsorption field. In fact, the magnetic response from water in the narrow pores of MS5A was weaker than that from the chrysotile and silica gel 141, while water which interacts very weakly with hydrophobic

389

surfaces of NPC and P10 responded to magnetic field even in the first layer (Figure 4). Figure 5 shows magnetoadsorptivity of P10 for water as a function of total amount of water adsorbed on P10. There seems to be two steps on the curve:the onsets of the first and second decrease corresponds, reffering to the micropore size distribution, roughly to half-filled adsorption onto walls of the micropores with ca. 0.7 nm width and t o complete monolayer adsorption onto both walls of the micropores with 1.0 nm width, respectively, in which water molecules must be loosely adsorbed on the hydrophobic inner surfaces. Further adsorption of water into the half-filled 7 nm-pores and completely-covered 1.0 nm-pores give rise to hydrogen bonding between water molecules on both walls to make a kind of large cluster (a tightly-bonded two dimentional cluster). This may bring about steep reduction of magnetic responce of water adsorption and subsequent constancy. Since both H,O and all solids used are diamagnetic, water on the surfaces may be removed by free energy loss under magnetic field. On the contrary, the magnetic promotion of physical adsorption of water is a remarkable phenomenon. The apparent stabilization of the adsorbed water under magnetic field should be ascribed to a kind of magnetic transition or a structural change. The magnetoadsorption of NO seems to occur via NO dimer formation due to the singlet(S)-triplet(T) transition of a radical pair on a (NO), molecule. It is well known that a magnetic field affects the pardortho (p/o) conversion of H, on solids 114-161:a nuclear spin S / T transition via the interaction with paramagnetic center on surfaces [ E l . The mechanism for the both cases is quite analogous to each other [161. We presume that the magnetic effect may come up via a hypothetical p/o-water conversion due to extrinsic magnetic field. Then, the two nuclear spins in a water molecule must interact with each other and should experience the inhomogeneous dipolar magnetic field due to the paramagnetic spin to change their relative spin alignment via different precession 115,161. The p/o conversion requires energy exchange (-100 cm-') with the translational freedom during a collision with paramagnetic center [16,171. This seems consistent with the fact that the magnetic water adsorption onto the chrysotile at 9.6 kG was enhanced with increasing temperature, despite an exothermic adsorption process, and also that a calf thymus DNA, which have probably zero paramagnetic centers showed no magnetoadsorption at 9.6 kG. The ohter adsorbents here may have some paramagnetic centers on their surfaces 114,181. When the two nuclear spins in a water molecule are coupled via an oxygen atom, one might expect that the p/o conversion may propagate through hydrogen bond networks.

390

The experiments suggest that water under adsorption field from solids may be so different from bulk water. as demonstrated by magnetic-field-induced adsorption.

REFERENCES 1. S. Ozeki, H. Uchiyama, J. Phys. Chem. 92(1988) 6485. S. Ozeki, H. Uchiyama and K. Kaneko, J. Phys. Chem. 95 (1991), 7805. 2. H. Uchiyama, S. Ozeki and K. Kaneko, Chem. Phys. Lett. 166(1990), 531; Langmuir. 5 (1992) 624. 3. K. Kaneko, N. Fukuzaki and S. Ozeki, J. Chem. Phys. 87 (1987) 776. K. Kaneko, A. Kobayashi, A. Matsumoto, Y. Hotta, T. Suzuki and S. Ozeki, Chem. Phys. Lett. 163 (1989),61. 4. S. Ozeki, C. Wakai and S. Ono, J. Phys. Chem. 95 (1991) 10557. 5. W. Dianis and J. E. Lester, Surf. Sci. 43 (1974) 603. 6. S. Ozeki, Langmuir 5 (1989) 186. 7. E. Lips, Helv. Phys. Acta 8 (1935) 247. W. J. Dulmage, E. A. Meyers and W. N. Lipscomp, Acta Crystallogr. 6 (1953) 760. F. E. Wang, W. R. May, E. L. Lippert, Acta Crystallogr. 14 (1961), 1100. 8. A. Enault and Y. Larher, Surf. Sci. 62 (1977), 233. 9. (a) Kagaku Binran (3rd ed.), Maruzen, Tokyo, 1986. (b)J. R. Ohlsen, J. Laane, J. Am. Chem. SOC.100 (1970) 6948. C. M. Western, P. R. Langridge-Smith, B. J. Howard, Mol. Phys. 44 (1981) 145. 10. B. M. Hoffman and N. J. Nelson, J. Chem. Phys. 50 (1969) 2598. 11. C. Y. Ng, P. W. Tiedemann, B. H. Mahan and Y. T. Lee, J. Chem. Phys. 66(1977)3985. 12. Ph. Brechignac, S. De. Benedictis, N. Halberstadt, B. J. Whitaker and S. Avrillier, J. Chem. Phys. 83(1985)2064. 13. H. Hayashi and S. Nagakura, Bull. Chem. SOC.Jpn. 51 (1978) 2862. Y. Sakaguchi, H. Hayashi and S. Nagakura, Bull. Chem. SOC. Jpn. 53 (1980) 39. 14. (a) M. Misono and P. W. Selwood, J. Am. Chem. SOC. 90 (1968) 2977. (b) P. W. Selwood, Adv. Catal. 27 (1978) 23. 15. E. Ilisca, Phys. Rev. Lett. 24 (1970) 797. E. Ilisca and E. Gallais, Phys. Rev. B6 (1972) 2858. E. Ilisca, Phys. Rev. Lett. 40 (1978) 1535. E. Ilisca, M. Debauche and J. L. Motchane, Phys. Rev. B22 (1980) 687. 16. U. E. Steiner and T. Ulrich, Chem. Rev. 89 (1989) 51. 17. E. Ilisca and S. Sugano, Phys. Rev. Lett. 57 (1986) 2590. 18. V. F. Kiselev and 0. V. Krylov, Adsorption Processes on Semiconductor and Dielectric Surfaces I, Springer-Verlag,New York, 1985, Chapter 3.

J. Rouquerol, F. Rodriguez-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterizalion of Porous Solids 111 Studies in Surface Scicnce and Catalysis, Vol. 87 0 1994 Elsevicr Science B.V. All rights rcscrvcd.

39 1

Characterization of Solids by Thermal Desorption in Solution M.D. MerchAn, F. Salvador Dpto. de Quimica Fisica. Universidad de Salamanca. 37008 Salamanca. Espafia.

Abstract The use of equipment for thermoprogrammed desorption in solution for the characterization of porous surfaces is described and the calculations and results of the thermoprogrammed desorption of a dye in an aqueous solution from two porous adsorbents are given. The versatility of the equipment is demonstrated with other useful assays in the analysis of surfaces, such as the construction of isotherms in solution at elevated temperatures and the test for the detection of diffusional phenomena. A new technique is also described, along with some results: thermoprogrammed adsorption-desorption as a broader variant of thermoprogrammed desorption in solution.

1. INTRODUCTION The characterization of porous surfaces and structures is specially important in processcs such as catalysis, adsorption, corrosion, etc. In recent years, numerous experimental methods for surface analysis have been developed. In a recent article, the IUPAC makes an extensive review of these experimental techniques. describing more than thirty (Ref. 1). One way of approaching the problem of characterizing a surface is to study the desorption process of a substance that has previously been adsorbed onto it. There are several techniques for inducing desorption. Among these are thermal desorption, electron impact desorption, field desorption, photon- and phonon-induced desorption, etc. The method of thermal desorption is probably used most frequently because of its simplicity. The desorption rate is extremely temperature-sensitive and is normally described by an Arrhenius equation. Thermal desorption may be performed isothermally or by a temperature programme. Isothermal desorption experiments are simpler to analyse but more difficult to adjust experimentally. Furthermore, if several desorption processes occur. it is not possible to deduce the individual rates from the total rate. To do this, a number of isothermal experiments must be carried out at different temperatures. Clearly, the technique of thermoprogrammed desorption, in which the information can be obtained with only one experiment, has obvious advantages. Since its discovery in the late forties (Ref. 2). thermoprogrammed desorption (TPD) has been used profusely and can be considered the technique most often employed in the

392 investigation of gas-solid interactions. Basically, it provides information on surface composition, the binding states of the adsorbates, the population of these states, as well as the desorption kinetics and mechanisms (reaction order, rate constant, activation energy, etc.). At present, TPD is a useful tool in adsorption and catalysis studies. In spite of being a well-known technique, its application has always addressed desorption of gases and never desorption in solution. Only very recently, with the use of equipment (Refs. 3.4) permitting the maintenance of the liquid phase at high temperatures has it become possible to approach thermal desorption in solution. This work demonstrates the usefulness and versatility of this equipment for carrying out a great variety of analyses in solution, not only of TPD. but of others related to adsorption, desorption and catalysis such as: thermoprogrammed adsorption-desorption; adsorption isotherms at high temperatures; the test for detecting diffusional phenomena; pulse adsorption; reactions to programmed temperature; isothermic reactions of adsorption and desorption; treatment of adsorbents and catalyzers. etc. The present work will discuss results and examples of some of these studies that are directly related to surface characterization.

2. EQUIPMENT The problem of maintaining the liquid phase at high temperatures has been solved by a flow device in which the carrier fluid is subjected to high pressures. The equipment is basically the same as that described in other works (Refs. 3.4) with some modifications. Here, therefore, an oven (Fig. 1) that facilitates handling of the equipment and permits higher temperatures and faster heating rates is used as the heating chamber. This oven has a powerful fan which rapidly homogenizes the temperature imposed by the programmer and facitlitates the transmission of heat in the preheater (1) and in the desorption chamber (2).

FIGURE 1: Photograph of the oven interior. I: Preheater; 2: Desorption chamber; 3: Refrigeration system of the oven interior.

393 The oven also has a refrigeration system (3) connected to a cryostat which allows the oven to cool after each experiment and to be thermostated when working in isothermal conditions.

3. RESULTS

Exueriments of Thermourowammed Desorution The fundaments and theory of TPD in the gas phase are described in depth in the works of Cvetanovic, Schmidt and King (Refs. 57)and its application to catalysis in the works of Falconer and Schwarz (Ref. 8). There is no reason not to assume that these fundaments and theory are still valid and applicable to thennoprogrammed desorption in solution. Two typical desorption spectra are shown in Figure 2. They correspond to desorption in an aqueous solution of crystal violet dye (CV+) from two porous adsorbents, granular activated carbon (20-40 mesh) from Aldrich and silica gel for chromatography (0.2-0.5 mm) from Merck. The spectrum may show several peaks, such as occurs in the case of desorption from carbon; these can be assigned to different adsorption sites with different binding energies, or different desorption mechanisms for a single binding state. The second peak has greater binding energy than the first one because it appears at higher temperatures. However, the quantity of CV+ adsorbed with this energy is less. The relative quantity of one or the other type of sites can be determined from the peak areas. Perhaps the first information, apart from the number of adsorption forms, their quantification and relative stability, is that provided by analysis of the shape of the peaks in the spectrum. For a first order kinetic process. the peak is asymmetrical with respect to its maximum, with a greater slope in its ascending stretch (Ref. 9).Such seems to be the case of the

FIGURE 2: Thermoprogrammed desorption in solution of crystal violet from: a ) Activated carbon. Flow rate = 3.5 cm3 min-'; Heating rate = 2.17 "C min-'; Initial coverage = 9.29 mol g-'; Adsorbent mass = 0.086 g. b) Silica gel. Flow rate = 3.5 c d min-'; Heating rate, = 2.18 "C min-'; Initial coverage, = 1.80 IPS mol g-'; Adsorbent mass = 0.040 g.

394 desorption of CV+ from silicagel. A detailed analysis of the shapes of desorption peaks and of the complex desorption spectra can be found in the work of Dawson and Walker (Ref. 10). The adsorption energy can be calculated from a quantitative analysis of the spectrum. As a result of practical interest in the knowledge of this parameter, quite a few methods have been proposed (Refs. 8, 11). One of the simplest, and the one which has been most extensively applied, was initially proposed by Redhead (Ref. 12) and is based on the change in the position of the maximum with the heating rate. According to this method, there is a relationship between the linear rate of heating, 6, and the temperature at wich the maximum, T, appears:

p = (A R TM2/ E) exp (-E / RT,) where A and E are the pre-exponential factor of the Arrhenius equation and activation energy, respectively. This energy can be determined from the slope of the plot of In (p /TM2) against InM. This procedure was followed in the case of desorption of CV+ from silica gel. Figure 3 shows this plot for seven thermograms obtained with different heating rates between 0.44 and 3.97OC min''. Three of these thermograms are shown in Figure 4. The activation energy obtained by Redhead's method is 58.8 kJ mol-*, and can be attributed to binding by hydrogen bridge.

-10 1 N h

+E: -1 1 -12

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1 /T, ( K ' ) FIGURE 3: Calculation of the activation energy of the desorplion of crystal vwletj'torn silica gel in aqueous solution. Activation desorption energy = 58.8 W rnol-I. Another TPD study is shown in Figure 5. This shows the effect of the flow of carrier liquid in the desorption of the dye adsorbed in silica gel. It can be seen that as flow increases, the maximum is displaced to lower temperatures. This displacement tends to disappear when the flow selected is large and this could be due to two facts. One is the possible readsorption of the adsorbate which has just been desorbed and the other is that the diffusion of the molecules desorbed inside the pores may be the limiting step in the desorption process. Both phenomena, readsorption and diffusion, can modify the position and form of the spectrum when the flow of the camer liquid is changed (Ref. 11).

395

'I'EMPERATURE ( " C )

FIGURE 4: Influence of heating rate on TPD in solution of crystal violer from silica gel. mol g-'; Adsorbent tnass = 0.040 g ; Flow = 4.5 cm3 min.'; Initial coverlrge = 8.02 Heating rote = a) 0.44 "Cmin.'; b) 0.79 "Cmiti'; c) 3.97 "C min.'.

TEMPERATURE ("C)

FIGURE 5: Influence of flow rate on TPD in solution of crystal violet from silica gel. Heating rate = 2.19 "C min-1; Initial coverage = 8.02 10-6 mol g - l ; Flow rate = a) 2.0 em3 min-'; b) 3.5 cm3 min-'; c) 5.0 cm3 ntiti'.

Construction of adsorvtion isotherms at high temperatures The construction of adsorption isotherms can be considered as being one of the most classic methods in the characterization of solids. On many occasions, the parameters and the information provided by these isotherms are used in other studies; they are thus extrapolated to zxperimental conditions very different from those in which the isotherms were originally sbtained. In practice, when adsorption isotherms are constructed in solution they are usually

396 restricted to a narrow temperature range, due mainly to evaporation of the solvent. One of the most interesting applications of the TPD equipment described here is the possibility of obtaining adsorption isotherms in solution, even at temperatures much higher than the normal boiling point of the solvent. T o do this, it is sufficient to substitute the carrier liquid with an adsorbable solution and place a known quantity of clean adsorbent in the desorption chamber. After thermostatting the oven at the selected temperature, the solution is made to circulate through the adsorbent at a high speed after which it is returned to the deposit. Equilibrium is said to be reached when the signal in the detector does not vary in time. The quantity retained by the adsorbent is determined by the difference between the initial concentration and the equilibrium concentration. The equipment has other advantages which facilitate the laborious and tedious work that the construction of isotherms always entails: a) It is possible to monitor the development toward equilibrium continuously. b) Using high flow rates and elevated pressures, the time needed to reach equilibrium is drastically reduced. This procedure is much more effective than any other form of stirring and has the advantage of not disrupting the adsorbent. c) Quantification of the amount adsorbed is very simple and precise. d) It is possible to construct several points of the isotherm with the same sample, by simply modifying the concentration of the circulating solution. Figure 6 shows two adsorption isotherms in an aqueous solution of p-nitrophenol onto activated carbon at temperatures of 80 and 15OOC. According to the IUPAC classification (Ref. 13). they can be considered type I isotherms. A sharp decrease in the adsorption capacity of the monolayer is observed when the temperature increases. The adsorption of 4-nitrophenol in an aqueous solution has sometimes been used to estimate the specific surface area of adsorbents (Ref. 14). assuming a cross-section of the molecule adsorbed of 25 A2. Calculation of the specific surface area using this cross-section leads to values of 184 and 105 m2 g'' at 80 and 150°C, respectively, much lower than those obtained by the BET method from the adsorption isotherm of N, at 77 K which is 621 m2 g-*.

FIGURE 6: Adsorption isotherms in solution of 4-ni~ofenolon activated carbon.

397

Test 0-f interruption The surface phenomena of adsorption and desorption on porous solids are quite often affected by diffusional problems, diffusion being the limiting step to the rate of the total process. There are different assays for determining these limitations. Some are based on the effect that the variation in particle size has on the rate of the process (Ref. 15). Others are based on the interruption of the process, by isolating the adsorbent (Ref. 16). During the period of interruption. if there are diffusional limitations, a homogenization of the concentration inside the pores will take place, such that when the process is resumed, the rate will be greater than at the moment of interruption. Owing to the versatility of the equipment described, it is possible to easily apply this “test of interruption” to desorption in solution, and is thus a great help when interpreting the TPD spectra from porous solids. The experimental procedure is very simple. After placing a small sample in the desorption chamber, desorption is begun by increasing the temperature in the oven. When the rate is appreciable, the temperature programmer is stopped in order to proceed with the thermodesorption, now under isothermal conditions. The interruptions are made by stopping the flow of the carrier liquid. Figure 7 shows the application of this test to the desorption of phenol at 7OoC from activated carbon. The desorption process was interrupted four times for 25 minutes each time. In all the cases when the flow of the carrier liquid was resumed, the desorption rate was seen to be greater than the rate at the moment of interruption. This demonstrates the importance of the transport process in the pores during the desorption of phenol from activated carbon.

I

I

TIME

FIGURE 7: Test of interruption. Desorption of phenol from activated carbon at 70°C. niol g-’. Adsorbent inass = 0.0350 g ; Flow rate = 3.5 crd min-’; Initial coverage = 7.44

Study of thermopronrammed adsorption-desorption Although the usefulness of TPD in the characterization of surfaces is unquestionable, correct interpretation of the desorption spectra is sometimes difficult and laborious, hence the

398 need to complement it with other techniques. Complications arise as a consequence of the fact that the desorption process is usually accompanied by other phenomena such as readsorption of the adsorbate that has just been desorbed, or the slowness of the adsorbate in diffusing in the pores of the adsorbent. Furthermore, TPD is a technique which provides kinetic data and parameters only for the desorption process and not for adsorption, which are just as or even more important. For these reasons, we propose a new tecnique: “Thermoprogrammed adsorptiondesorption”, wich we are developed as a variant of TPD (Ref. 17). Because it offers wider possibilities, it has certain advantages and it complements the information obtained in TPD since it provides data on the adsorption process. The technique consists of passing a flow of adsorbable solution with a constant concentration through a clean adsorbent and recording both the adsorption and the subsequent desorption under thermoprogrammed conditions. Experimentally this is very easy to carry out with the apparatus described, since one only needs to substitute the carrier liquid with an adsorbable solution and proceed as for aTPD experiment. At the beginning of the experiment, when the adsorbent is free and the temperature is low, surface begins to become occupied, capturing adsorbateladsorbent from the circulating solution and producing a net adsorption process. However, if the experiment is continued, a moment arrives when the saturation of the adsorbent is considerable and the temperature is high enough for the opposite process to occur, the adsorbent desorbs part of the adsorbate, yielding it back to the solution. The spectrum of thermoprogrammed adsorption-desorption (Figure 8) clearly shows these two stages of the process, the first with a net balance in favour of adsorption and the second with a net balance favourable to desorption.

TEMPERATURE (K)

FIGURE 8: Simulated spectrum of thermoprogrammed adsorption-desorption. A characteristic point of these spectra is that in which the balance of what the adsorbent captures from the solution and what the adsorbent yields to the solution is zero. This corresponds to a situation in which the adsorption rates and the desorption rates are equal; this

399 is thus a situation of thermodynamic equilibrium. The fact that at this point there is no mass transfer between the adsorbent and the solution guarantees that at that moment there are no diffusional phenomena. A detailed study of the spectrum at this point allows us to calculate the kinetic parameters of both adsorption and of desorption, with the guarantee that they are not distorted by diffusional processes. (Ref. 17). In an adsorption-desorption experiment the net rate can be expressed as v = Va - vd, where V a and vd represent the adsorption and desorption rates, respectively. According to the Langmuir principles and developing the equation for the point of thermodynamic equilibrium in which dWdT = 0 is fulfilled, one obtains the following expression:

which relates the values of the desorption rate constant kd and AE = Ed-Ea with the initial concentration of camer liquid C,, and with N,, T, and me, which are the number of actives sites occupied, temperature and the slope of the tangent at the point of equilibrium. Treatment of a series of different adsorption-desorption thermograms according to this equation and the Arrhenius equation allows one to calculate the activation energies of adsorption and desorption. Ea and &. An experimental spectrum of thermoprogrammed adsorption-desorption in solution is shown in Figure 9. It corresponds to the adsorption-desorption of 2,6-dichloro-4-nitrophenol on activated carbon. It shows how the point of thermodynamic equilibrium is reached at 141°C with adsorption proedominating at lower temperatures and desorption prodominating at higher temperatures.

I

TEMPERATURE ( " C )

FIGURE 9: Spectrum of thermoprogrammed adsorption-desorpiion of 2,6-dicloro-4nitrofenol on activated carbon. Adsorbent mass = 0.0258 g; Initial concentration = 5.89 in01 dm"; Flow rate = 3.5 cm3 min-'; Heating rate = 1.06 "Cmin-1.

400 As may be seen, this new technique is specially good for studying processes in which other phenomena, such as readsorption and diffusion, occur such that it finds an important application in the characterization of adsorbents and porous catalysts, in which these phenomena are always present. The special characteristics of the thermodynamic point of equilibrium permits the simultaneous calculation of the true adsorption and desorption activation energies without needing to introduce the mathematical complexity of differential equations. This way of working i s much more precise than other TDP methods, in which when one suspects the existence of diffusional effects one has to minimize them by changing the experimental conditions, such as using very low heating rates (Ref. 8); these methods are therefore only approximate. Thus, thermoprogrammed adsorption-desorption can complement and help to interpret the characterization of porous solids by TPD.

4. REFERENCES 1 . IUPAC, Pure and Appl. Chem., 62 (1990) 2297. 2. E. Urbach, "Solid luminiscent Materials", G.R. Fonda and F. Setiz (eds.), Willey, N.Y., 1948. 3 . F. Salvador; M.D. MerchBn, Langmuir, 8 (1992) 1226. 4. F. Salvador; M.D. MerchBn, Patent No P92-01729 (1992). 5 . R.J. Cvetanovic; Y. Amenomiya, Cat. Rev., 6(1) (1972) 21. 6 . L.D. Schmidt, Cat. Rev.-Sci. Eng., 9 (1974) 115. 7 . D.A. King, Surf. Sci., 47 (1975) 384. 8. J.L. Falconer; J.A. Schwarz, Cat. Rev.-Sci. Eng., 25 (1983) 141. 9 . M. Smutek; S . Cerny; Buzek, Advn. in Catal.. 24 (1975) 343. 10. P.T. Dawson; P.C. Walter. "Experimental Methods in Catalitic Research". vol 111. R.B. Anderson and P.T. Dawson (eds.), Academic Press. N. Y., 1976, p-211. 11. P. Malet, Stud. Surf. Sci. Cat., Spectrosc. Charact. Cat. pt(B), 75 (1990) 333. 12. P.A. Redhead, Vacuum, 12 (1962) 203. 13. IUPAC, Pure and Appl. Chem., 57 (1985) 603. 14. C.H. Giles; T.H. MacEwan; S.N. Nakhawa; D. Smith, J. Chem. Soc.,(1960) 3973. 15. R.M. Koros; E.J. Nowak; Chem. Eng. Sci., 22 (1967) 470. 16. J.S. Zogorski; S.D. Faust, J.H. Haas, Jr., J. Coll. Int. Sci.. 55 (1976) 329. 17. M.D. Merchiin. Tesis Doctoral. Universidad de Salamanca (1992).

J. Rouqucrol, F. Rodriguez-Rcinoso, K.S.W. Sing and K.K. Unger (Eds.) Characterizaiion of Porous Solids 111 Studies in Surfacc Scicncc and Catalysis, Vol. 87 0 1994 Elsevicr Scicncc B.V. All rights rcscrvcd.

40 1

The porosity of solids by thermal desorption of benzene J. Goworek and W. Stefaniak

Faculty of Chemistry, Maria Curie-Skiodowska University, 20-031 Lublin, Poland Abstract

The pore size distributions and total pore volumes of a variety of porous solids including silicas, aluminas and carbon adsorbents, have been determined using thermogravimetric method. The method is based on the measurements of thermal desorption of benzene at quasi-isothermal conditions. The results were compared with those from nitrogen method. 1. INTRODUCTION

Recently, we have applied temperature programmed desorption of benzene and n-butanol for the characterization of the porosity of silica gels [l-31. The approach, being at an early stage of development appeared to offer valuable information concerning the pore structure of adsorbents. The experiment consists in the measurements of weight loss of the liquid wetting the sorbent perfectly against temperature using quasi-isothermal program of heating. The main feature of this program is a constancy of temperature within the time when the transformations connected with weight changes take place in the sample. Usually, this heating mode is used in the investigations of thermal decomposition or dehydration. (see e.g. 4-6). Desorption of adsorbed species from porous material is a process of a different type and takes place within some temperature range. However, the desorption of liquid adsorbates from the pores of different dimensions may be treated as a process which is the sum of several isothermic processes. Each isothermic process corresponds to desorption from a given group of pores of uniform dimensions. Thus, during the desorption experiment carried by using quasi-isothermal program the temperature and the heating rate are not constant. If evaporation of liquid is slow the fixed weight loss level (usually = 0.5mg/min) regulating the run of the program is not exceeded. As a result the linear increase of temperature within this measuring range is realized. At a certain temperature when intensive evaporation occurs, the above mentioned level is exceeded and quasi-isothermal conditions are established. The sharp evaporation of liquid takes place at the boiling point of the liquid out of pores or at

402

temperature for which the pressure of the saturated vapours above the liquid meniscus in the pore becomes equal to atmospheric pressure. Fig.1 shows the typical desorption curve (solid line) for a liquid which wets the adsorbent perfectly and interacts with its surface only physically [3]. The results have been expressed as conventional TG curves, weight loss against temperature, .Lm=f(t). In Fig.1. the dependence of temperature against time for the same desorption process is also 2000

I

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

I

.. .............. ..... _ _ _

l

a

.

U

e,

1500

ard 43

0

rn rn

500

2 0

40

80

Temperature

120

160

[ O C ]

Fig.1. a - desorption curves of n-butanol from silica gel Si-100 at different heating programs: quasi-isothermal program (solid line), linear program (dotted line), b - dependences of temperature of desorption against time for quasi-isothermal program (solid line) and linear program (dotted line). shown. For illustrative purposes, the dotted curves represent the results obtained by applying dynamic heating program with continuously increasing temperature. In this last case the characteristic points on the desorption curve connected with the textural properties of solid disappear. Two main conclusions can be drawn from Fig.1. The first, and most obvious is that, the total time of analysis depends on the heating mode. The second is that, linear heating mode is inadequate in the investigations of the porosity. Segment I of TG curve represents the bulk liquid outside the pore structure of the adsorbent. Intensive evaporation at this stage of the process takes place at the boiling point of the liquid (perpendicular segment). When the first stage of desorption is completed the temperature increases and starts the desorption from pores. Segment II corresponds to desorption of adsorbate within the pores together with the adsorbed film on the walls of pores and is, therefore, a measure of the total pore volume. The steepest part of the curve above the boiling point of the liquid corresponds to the desorption from pores of a greatest part

403 of the total pore volume. The plot Am=f(t) may be converted into a plot volume loss versus pore radius hV=f(R) using the Kelvin equation [7].Differentiating the dependence AV=f(R) the pore size distribution for a given sorbent may be derived. It follows from our previous studies that the choice of appropriate heating rate of quasi-isothermal program is very important for obtaining the meaningful results [3]. The heating program must be neither too slow nor too fast. In both cases the pore distributions are deformed and the location of the pore size distribution peaks differs considerably from those obtained from the nitrogen method or mercury porosimetry. The differences between the peak location of the pore size distributions from the nitrogen and TG methods were discussed in terms of the surface film effect [8].However, it is always possible to find for a given adsorbate optimal desorption conditions for which the surface film effect is minimized. The work reported here was carried out as part of a larger study concerning the application of the thermogravimetric technique for the characterization of the porosity of solids. The aim of the present work was to extend the application of TG method for other highly porous materials. 2. EXPERIMENTAL

The following porous materials were used in the experiment. 0

silica gels: 9-60, Si-500 (Merck, Germany)

0

aluminum oxides: 60H (type E), 150 (type T), (Merck, Germany)

0

active carbon Norit RKD-3 and carbon black Vulcan 3 (Cabot)

0

silica gels, mixed samples: Si-40/Si-l00 (Merck, Germany), at different weight ratios 1:1, 3:l and 1:3

Oxide adsorbents were dried by prolonged heating at 18OoC. These conditions are sufficient to remove the physically bonded water. Benzene (POCh, Poland) puriss grade was carefully dried and stored over 3A-4A molecular sieves. Temperature programmed desorption experiments were made with Derivatograph 1500C (MOM, Hungary) using the quasi-isothermal program at a heating rate of 3OC/min within the linear heating range. The samples in the form of pastes were prepared by adding an excess of liquid adsorbate to the dry adsorbent. Next, portions (about 50mg) were placed in a platinum crucible of the labyrinth type. Time of temperature programmed analysis was about 1.5h. The adsorption/desorption isotherms of nitrogen at -195OC were measured with an automated Sorptomatic 1800 apparatus (Carlo Erba, Italy). Specific surface areas, SBET, were calculated from the BET equation over the linear range of relative pressure between about 0.05 and 0.4, taking the cross-sectional area of the nitrogen molecule to be 16.2A2. The pore size distribution curves were calculated

404

from the desorption isotherm by using the BJH method [9] with corrections of the pore radii with respect to the surface film thickness. 3. RESULTS AND DISCUSSION

Desorption curves of benzene for silica gel Si-60 and Si-500 are shown in Fig.2a. Fig.2b contains appropriate adsorption/desorption isotherms of nitrogen plotted as points at -195OC. The amount adsorbed A is displayed in cm3 of nitrogen at STP per gram of adsorbent. Fig.2a demonstrates that, in the case of silica Si-500 above

E

Y

I

I

I

800

a -

1000 =.......___.

I

I

I

0.2

0.4

0.6

A

' b

600

400

200

n

0.0

Temperature

0.6

1.0

P/P,

[OC]

Fig.2. a - desorption curves of benzene from silica gels Si-500 (1) and 3-60 (2) measured at quasi-isothermal conditions, b - adsorption/desorption isotherms of nitrogen at -195OC on silica gel Si-500 (1) and Si-60 (2), A - adsorbed amount cm3/g at STP. Adsorption - hollow points, desorption - filled points. 0.04

0.03

5

5 a

0.02

0.01

0.00

40

ao

Radius

120

180

[A]

Fig.3. Pore size distribution curves for silica gels Si-60 (1) and Si-500 (2) calculated on the basis of thermogravimetric data - solid and broken line, respectively. Points represent pore size distribution from nitrogen method.

405

100°C no changes of sample weight occur. It means that below this temperature the total amount of the adsorbate present in the pores and bonded physically with the surface is desorbed. A good accordance of the recorded temperature for the desorption of the bulk liquid with the boiling point of benzene under normal conditions is observed. Fig.3 demonstrates pore size distribution for both silicas derived from thermogravimetric data by using Kelvin equation in the manner described earlier (lines) [ l ] . The points represent the pore size distributions derived from nitrogen desorption data. As can be observed both curves are close together. In a similar way aluminum oxides AI2O3-60H (type E) and A1203-150 (type T) were investigated (see Fig.4a,b). The shape of thermogravimetric curves as well as 600

E

Y

a

eL

A

I

a, 4

400

0 vl

a 200 %w

0 vl vl

2

c

0 60

120

100

80

Temperature

140

" 0.0

0.2

0.4

0.6

0.8

1.0

P/P,

[OC]

Fig.4. a - desorption curves of benzene from A1203 60H (1) and A1203 150 (2) measured at quasi-isothermal conditions, b - adsorptionidesorption isotherms of nitrogen at -195OC on A1203 60H (1) and A1203 150 (2), A - adsorbed amount cm3/g at STP. Adsorption - hollow points, desorption - filled points. 0.010

e: a

\

3

a

0.005

0.000 20

40

60

Radius

80

100

[A]

Fig.5. Pore size distribution curves for A1203 60H (1) and A1203 150 (2) calculated on the basis of thermogravimetric data - solid and broken line, respectively. Points represent pore size distribution from nitrogen method.

406

adsorption/desorption isotherms of nitrogen differ considerably indicating appropriate differences in their textural properties. Pore size distributions for these adsorbents are shown in Fig.5. Similarly as in the case of silica gels discussed above the pore size distributions derived from TG and nitrogen adsorption data for both aluminas are in good accordance. Fig.6a shows thermodesorption curves of benzene from two carbon adsorbents i.e. activated carbon Norit RKD-3 and carbon black Vulcan 3. These adsorbents have been selected, considering their different origins and porous texture, to test the influence of the porosity on the shape of desorption curves. In the case of Norit RKD-3 the shape of the nitrogen isotherm (Fig.Gb), which exhibits a step rise at very low relative pressure indicates the micropore nature of the adsorbent. The hysteresis above p/p0=0.4 suggests some mesoporosity. However, the shape of the nitrogen adsorption isotherm for Vulcan 3 indicates mesoporous character and lack of micropores. Similarly, for both carbon adsorbents thermodesorption curves are different in shape.

-;

I

I

I

.a

I

A

I

I

b

f

$ 1

0.0

Temperature

[OC]

0.2

0.4

0.6

0.8

1.0

PIP,

Fig.6. a - desorption curves of benzene from activated carbon Norit RKD-3 (1) and carbon black Vulcan-3 (2) measured at quasi-isothermal conditions, b - adsorption/desorption isotherms of nitrogen at -195OCon Norit RKD-3 (1) and carbon black Vulcan-3 (2),A - adsorbed amount cm3/g at STP. Adsorption - hollow points, desorption - filled points. For Norit RKD-3 on segment II of the desorption curve the step at about 90°C is observed then the curve continuously drops. For Vulcan 3 desorption takes place at lower temperature and within a small temperature range. Comparing these data with pore size distributions from nitrogen adsorption (Fig. 7) one can conclude that the long extended segment of the desorption curve for activated carbon corresponds to micropores. The steepest segment on the desorption curve for activated carbon represents desorption from mesopores. Although, the accurate measurement of

407

0.06

p: U

0.05

L== U

0.03

\

0.02

0.00 20

40

60

80

100

Radius [A]

Fig.7. Pore size distribution curves for Norit RKD-3 (1) and carbon black Vulcan-3 (2) calculated on the basis of thermogravimetric data, - solid and broken line, respectively. Points represent pore size distribution from nitrogen method. the desorption curve is a matter of routine, its inversion to yield a reliable pore size distribution in the case of adsorbent containing micropores is much more difficult. Within the mesopores Kelvin equation is useful for the estimation of the pore radii and the derivation of appropriate pore size distribution curves. However, Kelvin equation is derived from thermodynamic considerations and is hence exact in the limit of large pores, but it becomes progressively less accurate as the pore size decreases. Thus, in the case of activated carbon only a part of the desorption curve may be used for the derivation of the pore size distribution. However, pore volume corresponding to a given radius range e.g. smaller than 20A can be estimated precisely. Fig.7 shows pore size distribution for activated carbon Norit RKD-3 within the range of mesopores derived from TG (solid line) and nitrogen adsorption data (filled points). The curve'2 represents the pore size distribution for carbon black from TG method. Application of the nitrogen method for carbon black leads to doubtful pore distribution. Finally, in Fig.8a the desorption curves for mixed samples of silica gel Si-40 and Si-100 at different w/w ratio are presented. These mixed samples contain the mesopores in the wide size range. As it was stated earlier, pore size distributions for separate Si-40 and Si-100 silica gels do not overlap [ l ] . It means, that these silicas do not contain the pores of the same dimensions. In this connection analysis of the desorption data for mixed silica samples is a test of efficiency of TG method. As expected, in the case of mixed silica gels two inflection points on the TG curves are present. Depending on the amount of a given silica in the sample the increase or decrease of the appropriate segment of this curve is observed. The heights of the steepest segments are proportional to the pore volumes of the greatest part of the total pore volume. As Fig.9 illustrates, pore size distributions derived from these data for mixed silica gel samples are of bimodal type.

408

E

I

I

M

1000 .-

Y

.-

I

a

1-

0.0

T e m p e r a t u r e ['C]

0.2

0.4

0.6

0.8

1.0

P/P,

Fig.8. a - desorption curves of benzene from mixed samples of silica gels Si-40 and Si-100 at different w/w ratio: (1) - 1:3, (2) - 1:1, (3) - 3:1, measured at quasi-isothermal conditions, b - adsorption/desorption isotherms of nitrogen at -195OC on mixed sample of silica gels Si-40 and Si-100 (wlw ratio - l : l ) , A - adsorbed amount cm3/g at STP. Adsorption - hollow points, desorption - filled points. 0.04

0.03

5 \ 0.02

0.01

0.00

20

40

60

Radius

80

100

[A]

Fig.9. Pore size distribution curves for mixed samples of silica gels Si-40 and Si-100 at different w/w ratio:(l) - 1:3, (2) - 1:1, (3) - 3:1, calculated on the basis of thermogravimetric data. Points represent pore size distribution from nitrogen method for mixed sample of silica gels Si-40 and Si-100 (w/w ratio - 1:l).

Figures 2a to 8a demonstrate the series of basic types of liquid desorption curves obtained by using quasi-isothermal program and corresponding to them pore size distributions. Generally, one can say that the there exists a good consistency between these pore size distributions and those derived from nitrogen adsorption data. Looking at parts a and b of each pair of figures 2, 4, 6 and 8 it can be seen

409 that there exists direct correlation between the shape of TG curves and nitrogen desorption isotherms. Taking into account the amount of liquid desorbed above its normal boiling point the total pore volumes V, for investigated adsorbents were calculated. Appropriate corrections with respect to changes of liquid density against temperature were introduced. Table 1 contains the radii corresponding to the peaks of pore size distributions and total pore volumes obtained by using different methods. The V, values from nitrogen data were estimated at p/ps=0.98 (interpolationfor 0.95