Коллоидная химия: Методические указания к практикуму

Fbgbkl_jkl\hh[s_]hbijhn_kkbhgZevgh]hh[jZah\Zgby JhkkbckdhcN_^_jZpbb G:Y...

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Fbgbkl_jkl\hh[s_]hbijhn_kkbhgZevgh]hh[jZah\Zgby JhkkbckdhcN_^_jZpbb
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2

JZ[hlZFhe_dmeyjgZyZ^khj[pby gZih\_joghklbjZa^_eZjZkl\hj\ha^mo >ey dheehb^guo mevljZfbdjh]_l_jh]_gguo kbkl_f oZjZdl_jgh gZeb qb_ h]jhfghc ih\_joghklb jZa^_eZ f_`^m nZaZfb b dZd ke_^kl\b_ wlh]h [hevrhcaZiZkk\h[h^ghcih\_joghklghcwg_j]bb K\h[h^gZyih\_joghklgZywg_j]by-lZqZklvk\h[h^ghcwg_j]bbkbkl_fu dhlhjZy h[mkeh\e_gZ gZebqb_f f_`nZaghc ih\_joghklb Bklhqgbdhf ih\_jo ghklghc wg_j]bb y\eyxlky kbeu f_`fhe_dmeyjgh]h \aZbfh^_ckl\by g_kdhf i_gkbjh\Zggu_ \ ih\_joghklghf keh_ \ke_^kl\b_ jZaebqghc wg_j]bb \Zg^_j-\ZZevkh\Z \aZbfh^_ckl\by fhe_dme ih\_joghklgh]h kehy k fhe_dmeZfb kf_`ghcnZaubf_`^mkh[hc Ijb h[jZlbfhf baf_g_gbb iehsZ^b ih\_joghklb 6 \ bah[Zjghbahl_jfbq_kdbomkeh\byobaf_g_gb_wg_j]bb=b[[kZ* kbkl_fuhij_^_ey_l ky\ujZ`_gb_f dG = σ · dS ]^_σ -m^_evgZy\_ebqbgZk\h[h^ghcih\_joghklghcwg_j]bb σ = ( ∂G/ ∂S)

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l_σ -k\h[h^gZywg_j]by=b[[kZ_^bgbpuiehsZ^bih\_joghklb baf_jy_lky\>`f 2 ). E_]dhihdZaZlvqlhm^_evgZyk\h[h^gZyih\_joghklgZywg_j]byqbke_ggh jZ\gZ kbe_ ih\_joghklgh]h gZly`_gby ^_ckl\mxs_c gZ _^bgbpm ^ebgu dhglmjZ h]jZgbqb\Zxs_]h ih\_joghklv b klj_fys_cky khdjZlblv ih\_jo ghklvjZa^_eZnZa<_ebqbgZih\_joghklgh]hgZly`_gbyσbaf_jy_lky\Gf >`f 2 Gf e_]dh hij_^_ey_lky wdki_jbf_glZevgh gZ ]jZgbpZo `b^ dhklv]Za`b^dhklv`b^dhklv blZdbfh[jZahf^Z_l\_ebqbgmm^_evghck\h [h^ghc ih\_joghklghc wg_j]bb dhlhjZy g_ ih^^Z_lky wdki_jbf_glZevghfm hij_^_e_gbx

3 Mf_gvr_gb_ k\h[h^ghc ih\_joghklghc wg_j]bb kbkl_fu ijhbkoh^bl kZ fhijhba\hevgh b fh`_l j_Zebah\u\Zlvky ^\mfy kihkh[Zfb aZ kq_l mf_gv r_gby iehsZ^b f_`nZaghc ih\_joghklb gZijbf_j \ ijhp_kk_ dhZ]meypbb ^bki_jkguo kbkl_f iml_f baf_g_gby khklZ\Z ih\_joghklgh]h kehy Z^khj[pbb. :^khj[pby - wlh gZdhie_gb_ dhgp_gljbjh\Zgb_ jZkl\hj_ggh]h beb Z^ khj[bjh\Zggh]hdhfihg_glZkbkl_fugZih\_joghklbjZa^_eZnZa <_ebqbgmZ^khj[pbb=]ZffZ beb:h[uqghbaf_jyxldhebq_kl\hfZ^ khj[bjh\Zggh]h\_s_kl\Zijboh^ysbfkygZ_^bgbpmih\_joghklbfhevf 2 ) bebgZ_^bgbpmfZkku\kemqZ_l\_j^h]hZ^khj[_glZfhevd] JZkkfhljbf kemqZc Z^khj[pbb fhe_dme jZkl\hj_ggh]h \_s_kl\Z gZijb f_j h^gh]h ba kibjlh\ `bjgh]h jy^Z gZ ih\_joghklb jZa^_eZ jZk l\hj\ha^mo Fhe_dmeu kibjlh\ 5HG \ ih\_joghklghf keh_ jZkl\hjZ kZfhijhba \hevghhjb_glbjmxlkylZdbfh[jZahfqlhg_iheyjgucm]e_\h^hjh^gucjZ^b dZe 5 \uoh^bl ba \h^u \ khk_^gxx g_iheyjgmx nZam \ ^Zgghf kemqZ_ \ha^mo Z iheyjgZy ]b^jhnbevgZy ]jmiiZ -HG bgl_gkb\gh \aZbfh^_ckl \mxsZyk\h^hchklZ_lky\\h^ghcnZa_jbkZ LZdZyhjb_glZpbyh[_ki_qb \Z_lkgb`_gb_k\h[h^ghc ih\_joghklghc wg_j]bb jZkl\hjZ ih\_joghklgh]hgZly`_gbyσKm\_ebq_ gb_f h[s_c dhgp_gljZpbb jZkl\hjZ \_ ebqbgZZ^khj[pbbjZkl_lfhe_dmeuI:< \Z^khj[pbhgghfkeh_k[eb`Zxlkyb \ ij_^_e_ ijb K →∞ h[jZamxl iehlgh miZdh\Zgguc gZkus_gguc fhgh kehc qZklhdhe ³E_g]fxjZ´ jbk[ <_ebqbgZ σ ijb wlhf kgb`Z_lky ^h fbgbfZevgh]hagZq_gbyZZ^khj[pby^hklb]Z_lij_^_evghc\_ebqbgu

4 <_s_kl\Z kgb`Zxsb_ ih\_joghklgh_ gZly`_gb_ jZkl\hjZ b h[jZamxsb_ Z^khj[pbhggu_kehbkih\ur_gghcdhgp_gljZpb_cgZau\Zxlkyih\_joghkl gh-Zdlb\gufb Ihfbfh kibjlh\ d gbf hlghkylky ^jm]b_ iheyjgu_ hj]Zgbq_kdb_ kh_^b g_gby dZj[hgh\u_ b kmevnhdbkehlu b bo kheb kheb Zedbeh\uo wnbjh\ k_j ghcdbkehluZedbekmevnZlu Zfbgubbokhebbl^ Ih\_joghklgh-Zdlb\gu_k\hckl\ZlZdbo\_s_kl\h[mkeh\e_gugZebqb_f\ bo fhe_dmeZo ^\mo jZaebqguo ih ijbjh^_ iheyjghklb qZkl_c dhlhju_ kh h[sZxlbfkjh^kl\hdjZaebqgufihiheyjghklbnZaZf Wg_j]by \Zg-^_j-\ZZevkh\Z \aZbfh^_ckl\by m]e_\h^hjh^gh]h jZ^bdZeZ 5 - k iheyjgufb fhe_dmeZfb \h^u f_gvr_ q_f wg_j]by \aZfh^_ckl\by fhe_ dme \h^u f_`^m kh[hc Ihwlhfm gZ ]jZgbp_ jZa^_eZ \h^guc jZkl\hj\ha^mo bebm]e_\h^hjh^ jZ^bdZeu5kZfhijhba\hevghi_j_oh^yl\ulZedb\Zxlky \ khk_^gxx g_iheyjgmx nZam qlh wg_j]_lbq_kdb \u]h^gh b h[gZjm`b\Z_lky dZd mf_gvr_gb_ ih\_joghklgh]h gZly`_gby ih\_joghklghc wg_j]bb σ Ih eyjgu_]jmiiugZijhlb\Zdlb\gh\aZbfh^_ckl\mxlk^biheyfb\h^u]b^jZ lZpby b khh[sZxl fhe_dmeZf I:< ]b^jhnbevgu_ k\hckl\Z fhe_dmeyjgh_ kjh^kl\h d \h^_ lh]^Z dZd m]e_\h^hjh^gu_ jZ^bdZeu y\eyxlky ghkbl_eyfb ]b^jhnh[guok\hckl\]b^jhnh[ghklvhagZqZ_l\f_kl_kl_fhe_hnbevghklv - kjh^kl\h d g_iheyjguf nZaZf -m]e_\h^hjh^Zf fZkeZf IhkdhevdmgZebqb_ fhe_dme I:< \ ih\_joghklghf keh_ wg_j]_lbq_kdb \u]h^gh ∂σ/∂F lh ijhbkoh^bl kZfhijhba\hevgh_ dhgp_gljbjh\Zgb_ jZkl\hj_ggh]h \_s_kl\Z gZ f_`nZaghc]jZgbp_G_hj]Zgbq_kdb_khebdbkehluhkgh\Zgbyih\urZxlih \_joghklgh_ gZly`_gb_ \h^guo jZkl\hjh\ b ihlhfm bo Z^khj[pby hljbpZ l_evgZdhgp_gljZpby\_s_kl\Z\ih\_joghklghfkeh_f_gvr_q_f\h[t_f_ Wlhih\_joghklgh-bgZdlb\gu_\_s_kl\Z L_jfh^bgZfbq_kdb_ mkeh\by jZ\gh\_kgh]h jZkij_^_e_gby I:< f_`^m h[t_fhfbih\_joghklgufkeh_fhij_^_eyxlky\ujZ`_gb_f

5

D = D H[S −

µ − µ 57

]^_Zµ0 bZµ0 -khhl\_lkl\_gghZdlb\ghklbbobfbq_kdbcihl_gpbZejZkl\h j_ggh]h\_s_kl\Z\ih\_joghklghfkeh_bh[t_f_jZkl\hjZ
=

& Gσ 5 7 GF

(1)

MjZ\g_gb_ =b[[kZ iha\hey_l jZkkqblZlv bahl_jfm Z^khj[pbb -aZ\bkbfhklv=K ihbahl_jf_ih\_joghklgh]hgZly`_gbyσK jbk >eywlh]hijbjZaguoKgZoh^yl qbke_ggh_agZq_gb_ijhba\h^ghc ( dσGK h[uqgh]jZnbq_kdbf iml_fl_ihgZdehgmdZkZl_evguoddjb\hcσK \jZaebqguo JbklhqdZo Bahl_jfZ fhghfhe_dmeyjghc Z^khj[pbb hibku\Z_lky mjZ\g_gb_f E_g ]fxjZ $

$ ∞

.& , . &

(2)

]^_K-jZ\gh\_kgZydhgp_gljZpbyI:<\h[t_f_jZkl\hjZD-dhgklZglZZ^ khj[pbhggh]h\aZbfh^_ckl\by:∞ -ij_^_evgZyZ^khj[pbybeb_fdhklvfh ghkehy - \_ebqbgZ Z^khj[pbb hl\_qZxsZy h[jZah\Zgbx gZ f_`nZaghc ih \_joghklbgZkus_ggh]hfhghkehykfjbk[ =b[[kh\kdZy Z^khj[pby = jZkkqblu\Z_lky dZd ba[ulhd jZkl\hj_ggh]h \_s_kl\Z \ Z^khj[pbhgghf keh_ ih kjZ\g_gbx k h[t_fhf ih E_g]fxjm Z^ khj[pby : - ihegh_ _]h dhebq_kl\h \ Z^khj[pbhgghf keh_ \ h[hbo kemqZyo gZ_^bgbp_ih\_joghklb Ijbmkeh\bbK→:≅=

6 Bahl_jfm Z^khj[pbb E_g]fxjZ lZd`_ fh`gh jZkkqblZlv ih aZ\bkbfhklb σK >eywlh]hg_h[oh^bfhgZclbagZq_gbydhgklZgl:bDBofh`ghih emqblv bkihevamy mjZ\g_gb_ Rbrdh\kdh]h hibku\Zxs__ bahl_jfm ih\_jo ghklgh]hgZly`_gbyσK σ = σ 0 - a ln ( 1+bK ) ,

(3)

]^_σ 0 -ih\_joghklgh_gZly`_gb_jZkl\hjbl_eyabb -dhgklZgluWlhwf ibjbq_kdh_ mjZ\g_gb_ H[t_^bgyy mjZ\g_gby =b[[kZ b E_g]fxjZ _]h fh`gh ihemqblv\ke_^mxs_f\b^_ σ=σ 0 -RTA ∞ ln(1+KK)

(3’)

BamjZ\g_gbc b’)ke_^m_lqlh a = RL:∞ , b = D

(4)

AZ\bkbfhklvσK kh]eZkghmjZ\g_gbyf b’ g_ebg_cgZ>eyjZkq_ lZdhgklZgl:∞ bDmjZ\g_gb_bahl_jfuih\_joghklgh]hgZly`_gbyijb\h^yl d ebg_cghfm \b^m < h[eZklb g_ hq_gv fZeuo dhgp_gljZpbc DK!! lh]^Z ij_g_[j_]Zy_^bgbp_cih^agZdhfeh]ZjbnfZihemqbfmjZ\g_gb_ \\b^_ ∆σ=σ 0 - σ =Z lnb + a lnK ,

(5)

l_∆σebg_cghaZ\bkblhlOQKBa]jZnbdZaZ\bkbfhklb∆σOQK gZoh^yl dhgklZgluDbEZihkhhlghr_gbyf -:∞ bD AgZy \_ebqbgm :∞ fh`gh jZkkqblZlv iZjZf_lju Z^khj[pbhggh]h kehy iehsZ^v ijboh^ysmxky gZ fhe_dmem\gZkus_gghfZ^khj[pbhgghfkeh_6 ³fhe_dmeyjgZy iehsZ^dZ´ blhesbgmZ^khj[pbhggh]hkehyKjZ\gmx^ebg_ fhe_dmeukfjbk[ bake_^mxsbokhh[jZ`_gbc GZf 2 ih\_joghklbZ^khj[bjh\Zgh: ∞ 1fhe_dme1-qbkeh:\h]Z^ jh hlkx^Zke_^m_lqlh S m = 1/ A ∞ N

(6)

FZkkZ\_s_kl\ZPZ^khj[bjh\Zggh]hgZf 2 ih\_joghklbjZ\gZ P :∞ ·F

7 F-fheyjgZyfZkkZI:< K^jm]hcklhjhgu\_ebqbgmP fh`gh\ujZ ablv dZd fZkkm \_s_kl\Z gZoh^ys_]hky \ h[t_f_ Z^khj[pbhggh]h kehy k ieh sZ^vxkf 2 blhesbghcK m = ρ· h (ρ -iehlghklv\_s_kl\Zd]f 3 ). LZdbfh[jZahf$∞ ⋅F ρ ⋅Khldm^ZK $∞ ⋅M /ρ Wdki_jbf_glZevgZyqZklv P_ev jZ[hlu jZkkqblZlv bahl_jfm fhe_dmeyjghc Z^khj[pbb I:< gZ ih\_joghklb jZa^_eZ jZkl\hj\ha^mo \uqbkeblvfhe_dmeyjgu_oZjZdl_jb klbdbgZkus_ggh]hZ^khj[pbhggh]hkehy < dZq_kl\_ I:< ijbf_gyxl h^bg ba kibjlh\ `bjgh]h jy^Z < lZ[ebp_ ijb\_^_gu g_dhlhju_ oZjZdl_jbklbdb I:< b j_dhf_g^m_fu_ mkeh\by ijh\_ ^_gbyhiulh\. K\hckl\Z

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fheve Babkoh^gh]hjZkl\hjZI:<]hlh\yljy^jZkl\hjh\lZdbfh[jZahfqlh[u dhgp_gljZpby dZ`^h]h ihke_^mxs_]h jZkl\hjZ[ueZ\^\h_f_gvr_ij_^u^m s_]h >ey wlh]h \ f_jgmx dhe[m gZ fe \\h^yl ba [xj_ldb ihke_^h\Zl_evgh fe bkoh^gh]h jZkl\hjZ I:< b ^h\h^yl kh^_j`bfh_ dhe[u^hf_ldb^bklbeebjh\Zgghc\h^hc

8 Ohjhrh i_j_f_rZ\ kh^_j`bfh_ dhe[u i_j_eb\Zxl jZkl\hju \ qbklu_ kmob_kdeygdb Baf_jyxlih\_joghklgh_gZly`_gb_ijb]hlh\e_gguojZkl\hjh\\ihjy^d_ \hajZklZgby dhgp_gljZpbb Baf_j_gby ijh\h^yl f_lh^hf kq_lZ dZi_ev klZ eZ]fhf_ljbq_kdbc f_lh^ Nbabq_kdb_ hkgh\u f_lh^Z aZdexqZxlky \ ke_ ^mxs_f
Vρg = 2π R σ n >eyklZg^Zjlghc`b^dhklbkba\_klgufih\_joghklgufgZly`_gb_f

9 ρJ = π5 σ Q Ih^_eb\h^gh\ujZ`_gb_gZ^jm]h_ihemqbf

σ ρ Q = hldm^Z σ σ ρ Q

σ

ρ Q ρ Q

(7)

>eyhij_^_e_gbyqbkeZdZi_evh[jZam_fuoijb\ul_dZgbbhij_^_e_ggh]h h[t_fZ`b^dhklbihevamxlkyklZeZ]fhf_ljhfjbk Hg ij_^klZ\ey_l kh[hc kl_deyggmx ljm[dm k jZkrbj_gb_f ihk_j_^bg_ aZdZgqb\ZxsmxkydZibeeyjhfBgh]^Zljm[dZbf__l]hjbahglZevgmxqZklvjbk[ \dhlhjmx

9 \iZyglhgdbcdZibeeyjqlh[uaZf_^eblvbkl_q_gb_`b^dhklbeyjZkq_lZσhij_^_eyxlqbkehdZi_evn 0 bQ Jbk dhlhju_ h[jZamxl khhl\_lkl\_ggh klZg^ZjlgZy `b^dhklvh[uqgh^bklbeebjh\ZggZy\h^Z bbkke_^m_fZy`b^dhklvijb\ul_ dZgbbhl\_jog_c^hgb`g_cf_ldb KlZeZ]fhf_ljbq_kdZy mklZgh\dZ bah[jZ`_gZ ko_fZlbq_kdb gZ jbk Ba f_j_gbyijh\h^ylke_^mxsbfh[jZahfI_j_dju\djZg ijbhldjulhfdjZg_ke_]dZ k`bfZxlj_abgh\mx]jmrm ihke_q_]hdjZgaZdju\Zxl Ijbih^gy\dx\_lmklZdZgqbd ih]jm`ZxldhgqbdklZeZ]fhf_ljZ\bkke_^m_fmx`b^dhklv Jbkdx\_lZ^he`gZ[ulvaZiheg_gZgZa h[t_fZ Ke_]dZ ijbhldju\ djZg f_^e_ggh aZkZku\Zxl `b^dhklv \ klZeZ] fhf_ljDZdlhevdhf_gbkdi_j_k_q_l\_jogxxf_ldmg_f_^e_gghaZdju\Zxl djZg gh g_ himkdZxl dx\_lm G_h[oh^bfh \u`^Zlv g_dhlhjh_ \j_fy ihdZ g_ ij_djZlblky ih\ur_gb_ mjh\gy `b^dhklb \ klZeZ]fhf_lj_ bgZq_ \ g_]h ihiZ^_l\ha^moDh]^Zf_gbkdhklZgh\blkydx\_lmhimkdZxlgZklhebd@b^ dhklv gZqbgZ_l f_^e_ggh ih dZieyf \ul_dZlv ba klZeZ]fhf_ljZ Ijb[hj kh h[sZ_lkykZlfhkn_jhcq_j_alhgqZcrbcdZibeeyj[eZ]h^Zjyq_fm^hklb]Z _lky^hklZlhqghfZeZykdhjhklvh[jZah\ZgbydZi_evh^gZdZieyaZa k DZd lhevdh f_gbkd ^hklb]Z_l \_jog_c f_ldb gZqbgZxl kq_l dZi_ev ijb ^hklb`_gbbgb`g_cf_ldb-aZdZgqb\Zxl

10 KjZkl\hjZfbdZ`^hcdhgp_gljZpbbgZqbgZyk^bklbeebjh\Zgghc\h^u ijh\h^yl baf_j_gby g_ f_g__ lj_o jZa Ih hdhgqZgbb jZ[hlu klZeZ]fhf_lj ijhfu\Zxl^bklbeebjh\Zgghc\h^hc J_amevlZlubaf_j_gbcaZibku\Zxl\lZ[ebpm Bkke_^m_fh_ Dhgp_gljZ\_s_kl\h

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Ih\_joghklgh_ gZly`_gb_ jZkkqblu\Zxl ih nhjfme_ AgZq_gb_ σ 0 ijbl_fi_jZlmj_hiulZ[_jmlbakijZ\hqgbdZeb[hjZkkqblu\Zxlihnhjfme_ σ 0 = σ + α ( T- 293), ]^_σ -ih\_joghklgh_gZly`_gb_\h^uijbl_fi_jZlmj_0 D fGf α - l_fi_jZlmjguc dhwnnbpb_gl ih\_joghklgh]h gZly`_gby ^ey\h^uα =-fGf⋅D Hlghr_gb_ρ/ρ0 ^eybkihevam_fuo\jZkl\hj_ jZa[Z\e_gguojZkl\hjh\I:eyjZkq_lZbahl_jfuZ^khj[pbbE_g]fxjZgZoh^yldhgklZgluwlh]hmjZ\ g_gby :∞ bDiml_fkijyfe_gbybahl_jfuih\_joghklgh]hgZly`_gby\dh hj^bgZlZomjZ\g_gbyRbrdh\kdh]h\_]hebg_cghcnhjf_ ∆σ = Z lnb + aOQK Kljhyl djb\mx aZ\bkbfhklb σ hl K GZ wdki_jbf_glZevghc djb\hc aZ \bkbfhklbσK \u[bjZxl-lhq_d\uqbkeyxl^eygbo∆ σbOQKKljhyl ]jZnbdaZ\bkbfhklb∆σOQK jbk Ih gZdehgm ijyfhc ∆σ OQK gZoh^yl \_ebqbgmdhgklZgluZmjZ\g_gbyRbrdh\kdh]hbjZkkqblu\Zxlij_^_evgmxZ^khj[pbx:∞ bkihevamynhjfmemZ :∞ ⋅RT.

11 Jbk Ijb jZkq_l_ gZdehgZ ijyfhc ∆σ OQK g_h[oh^bfh ihfgblvqlh^ebgudZl_lh\lj_m]hevgbdZ\u[jZggh]h^eyjZkkq_lZ^he`gu [ulv \ujZ`_gu \ _^bgbpZo l_o \_ebqbg dhlhju_ hleh`_gu gZ hkyo dhhj^b gZlkmq_lhffZkrlZ[Z WdkljZihebjmxlijyfmx∆σOQK ^hi_j_k_q_gbykebgb_cghjfZevx d hkb Z[kpbkk ijhoh^ys_c q_j_a lhqdm OQK b gZoh^yl hj^bgZlm lhqdb i_ j_k_q_gby Kh]eZkgh mjZ\g_gbx ijb OQK ∆σ = Zlnb Bkihevamy gZc ^_ggu_ agZq_gby Z b ∆σ jZkkqblu\Zxl b<_ebqbgZ b jZ\gZ D \ mjZ\g_gbb E_g]fxjZ?^bgbpZbaf_j_gbydhgklZgluZ->`f 2 ,D-efhev Ih mjZ\g_gbx E_g]fxjZ jZkkqblu\Zxl agZq_gb_ : ^ey jZaebqguo dhgp_gljZpbc b kljhyl bahl_jfm Z^khj[pbb : K G_h[oh^bfu_ ^ey jZkq_lZ ^Zggu_aZibku\Zxl\lZ[ebpm Dhgp_gljZ-pby DK

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14 Bkoh^y ba wlbo ij_^klZ\e_gbc kljh_gb_ fbp_eeu fh`_l [ulv \ujZ`_gh nhjfmehc dhlhjZy hljZ`Z_l ijbjh^m ^bki_jkghc nZau ijbjh^m b jZkij_^_ e_gb_ ihl_gpbZehhij_^_eyxsbo bhgh\ b ijhlb\hbhgh\ GZijbf_j ^ey hljb pZl_evgh aZjy`_ggh]h ahey $J- \ \h^ghc nZa_ dhlhjh]h kh^_j`blky .- nhjfmeZfbp_eeubf__l\b^ fbp_eeZ { m [ AgJ] ⋅ nJ - ⋅ (n-x) K + ]

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x - jZkklhygb_ hl ]jZgbpu kehy Rl_jgZ ^h ^Zgghc lhqdb χ =λ

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lb\gZy lhesbgZ ^bnnmaghc qZklb >WK Nbabq_kdbc kfuke λ ke_^m_l ba mjZ\g_gby ijbo λ

ϕ = ϕ 0 _l_λ -wlhjZkklhygb_gZdhlhjhfihl_g

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(2)

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16 K\yav f_`^m ζ - ihl_gpbZehf b kdhjhklvx we_dljhnhj_aZ

hibku\Z_lky

mjZ\g_gb_f

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εε + ζ, η

X

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U=

2 εε0H ζ 3 η

(4)

8 = IχU

εε+ η

ζ,

(5)

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17 AgZq_gby dhwnnbpb_glZ IχU \ aZ\bkbfhklb hl \_ebqbgu χU ijb\_^_gu \ lZ[ebp_³JZkq_lubaZ^Zqbihdheehb^ghcobfbbIh^j_^;ZjZgh\hc<BF-K χr f

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22
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25 _eZ_lky ^hims_gb_ qlh ijbkbgl_a_aheyj_Zdpby]b^jhebaZ ijhoh^bl ^h dhgpZ lh]^Z bhggZy kbeZ hij_^_ey_lky dhgp_gljZpb_c h[jZah \Z\r_]hkyoehjh\h^hjh^Z\ahe_ZlZd`_dhgp_gljZpb_cwe_dljheblZ_kebhg \\h^bekyijbwe_dljhnhj_a_Dhgp_gljZpbx+KOjZkkqblu\ZxlihmjZ\g_gbx j_Zdpbb ]b^jhebaZ k mq_lhf dhebq_kl\Z \ayluo dhfihg_glh\ kmffZjgh]h h[t_fZ kbkl_fu b ijhba\h^b\r_]hky jZa[Z\e_gby ahey \^\h_ ijb we_dljhnh j_a_ Wdki_jbf_glZevgu_bjZkq_lgu_^Zggu_k\h^yl\lZ[ebpm

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26 DZd baf_gy_lky ihl_gpbZe >WK k jZkklhygb_f hl ih\_joghklb" GZib rbl_ khhl\_lkl\mxsb_ mjZ\g_gby ^ey iehkdh]h Z^khj[pbhggh]h b ^bnnma gh]hkeh_\ijhlb\hbhgh\ Qlh ihgbfZxl ih^ wnn_dlb\ghc lhesbghc ^bnnmaghc qZklb >WK" Hl dZdbonZdlhjh\bdZdhgZaZ\bkbl" QlhlZdh_we_dljhdbg_lbq_kdbcihl_gpbZe"DZdbhldZdbonZdlhjh\hg aZ\bkbl" DZd baf_gblky ζ - ihl_gpbZe hljbpZl_evgh aZjy`_ggh]h ahey ijb \\_^_gbb\g_]hoehjb^h\1D%D/D" DZd gZau\Z_lky we_dljhdbg_lbq_kdh_ y\e_gb_ h[jZlgh_ we_dljhnhj_am "
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27 Njheh\X=Dmjkdheehb^ghcobfbb-F-k =e<-K-63. =eM<-K-230 . Njb^jbok[_j]>:Dmjkdheehb^ghcobfbb-E-k =eO-K-226. EZ[hjZlhjgu_ jZ[hlu b aZ^Zqb ih dheehb^ghc obfbbIh^ j_^ X=Njheh\Z:K=jh^kdh]h-F-k =ejZ[-K99-101.

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28 db_ kehb khev\Zlbjh\Zggu_ ^bki_jkbhgghc kj_^hc ij_^klZ\eyxl kh[hc ih \_joghklgu_klm^gbbeb]_eb -l_eZijhy\eyxsb_l\_j^hh[jZagu_k\hckl\Z Ihke_^gb_^\ZnZdlhjZy\eyxlkyg_we_dljhklZlbq_kdbfbboaZsblgh_^_c kl\b_ h[mkeh\e_gh f_oZgbq_kdhc ijhqghklvx khev\Zlguo keh_\ b klm^g_]_e_- h[jZaguoZ^khj[pbhgguokeh_\ >_ckl\b_wlbob^jm]bo nZdlhjh\h[_ki_qb\Z_l^ebl_evgh_kms_kl\h\Z gb_ dheehb^guo kbkl_f [_a baf_g_gby bo k\hckl\ l_mklhcqb\hklvGZebqb_ b hlghkbl_evgZy jhev dZ`^h]h ba nZdlhjh\ mklhcqb\hklb hij_^_ey_lky ]eZ\ guf h[jZahf ijbjh^hc b dhgp_gljZpb_c klZ[bebaZlhjZ \kblkl_f_ijbjh^hc ^bki_jkghc nZau b ^bki_jkbhgghc kj_^u JZaebqZxl ^\Z \b^Z mklhcqb\hklb Kihkh[ghklv kbkl_fu khojZgylv \h \j_f_gb ihklhyggmx kl_i_gv ^bki_jkgh klb mklhcqb\hklv d Z]j_]Zpbb qZklbp gZau\Z_lky Z]j_]Zlb\ghc mklhcqb\h klvx :M Hl :M ke_^m_l hlebqZlv k_^bf_glZpbhggmx mklhcqb\hklv - kih kh[ghklv ^bki_jkghc kbkl_fu khojZgylv jZ\ghf_jgh_ jZkij_^_e_gb_ qZklbp ihh[t_fm^bki_jkghckj_^umklhcqb\hklvdhkZ`^_gbxqZklbpih^^_ckl\b _fkbeuly`_klb >_ckl\b_ aZsblguo nZdlhjh\ fh`_l [ulv kgylh beb hkeZ[e_gh jZaebq gufb\ha^_ckl\byfbgZijbf_j\\_^_gb_fwe_dljheblh\\wlhfkemqZ_ijh bkoh^bl k`Zlb_ ^bnnmaguo bhgguo Zlfhkn_j \hdjm] qZklbp mf_gvr_gb_ ]b^jZlZpbb bo ih\_joghklb b ^jm]b_ y\e_gby < j_amevlZl_ mf_gvrZxlky kb euhllZedb\Zgby\hagbdZxsb_ijbk[eb`_gbbqZklbpbi_j_dju\ZgbbboaZ sblguokeh_\bklZgh\blky\hafh`gufkebiZgb_qZklbpkh[jZah\Zgb_f\k_ [he__mdjmigyxsbokyZ]j_]Zlh\dhZ]meypby Kdhjhklv dhZ]meypbb aZ\bkbl hl bgl_gkb\ghklb dhZ]mebjmxs_]h \ha^_c kl\by gZijbf_j dhgp_gljZpbb we_dljheblZ aZjy^Z dhZ]mebjmxsbo bhgh\ b ij LbibqgZy aZ\bkbfhklv gZqZevghc kdhjhklb dhZ]meypbb 90 hl dhgp_gljZpbb we_dljh eblZ-dhZ]meyglZ ij_^klZ\e_gZ gZ jbk

29 <_ebqbgZ gZqZevghc kdhjhklb dhZ]meypbb hij_^_ey_lky\ujZ`_gb_f90 = - (d γ/dt ) t→0 ]^_γ

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30 ]^Z lhesbgZ >WK agZqbl_evgh f_gvr_ jZ^bmkZ qZklbp l_ ih\_joghklv fh `_ljZkkfZljb\ZlvkydZdiehkdZy GZjbkij_^klZ\e_gZaZ\bkbfhklv8hll , U ij bkmffZjghcihl_gpbZevghc wg_j]bb 8 hl jZkklhygby f_`^m qZklbpZfb Fh`gh \b^_lv qlh wg_j]bb hllZedb\Zgby b ijb ly`_gby j_adh jZklml ijb k[eb`_ gbbqZklbpZkmffZjgZyih l_gpbZevgZy wg_j]by ijb g_dhlhjhf jZkklhygbb f_`^m qZklbpZfb ijhoh^bl q_j_a fZdkb fmf8max \iheh`bl_evghch[eZklb<_ebqbgZ8max ij_^klZ\ey_lkh[hcih l_gpbZevguc [Zjv_j hllZedb\Zgby dhlhjuc oZjZdl_jbam_l Z]j_]Zlb\gmx mklhcqb\hklvahey Ijbm\_ebq_gbbdhgp_gljZpbbwe_dljheblZkbeuwe_dljhklZlbq_kdh]hhl lZedb\Zgby mf_gvrZxlky \ke_^kl\b_ k`Zlby ^bnnmaguo >WK qZklbp b ih l_gpbZevguc[Zjv_jhllZedb\Zgby8max kgb`Z_lkyjbk Djb\Zy oZjZdl_jbam_l Z]j_]Z lb\gh mklhcqb\uc ahev ihl_gpb Zevguc [Zjv_j hllZedb\Zgby ^hk lZlhqgh \ukhd lZd qlh dbg_lbq_ kdhcwg_j]bbqZklbpijb boklhedgh\_gbyog_^hklZlhqgh^ey_]hij_h^he_gbydhZ]meypbyhlkmlkl\m_l lhqdZk 1 kfjbk Djb\u_blhqdbk 2 bk 3 kfjbk hl\_qZxlkemqZx dh]^Z dhgp_gljZpby we_dljheblZ ij_\urZ_l g_dhlhjh_ ihjh]h\h_ agZq_gb_ (ihjh] dhZ]meypbbID kfjbk ijbdhlhjhf8max kgb`Z_lkygZklhevdh qlhklZgh\blky\hafh`ghcdhZ]meypbyghg_\k_klhedgh\_gbyqZklbpwnn_d lb\gu l_ ijb\h^yl d kebiZgbx ld hklZlhqguc ihl_gpbZevguc [Zjv_j U max !bg_\k_qZklbpuZebrvgZb[he__³]hjyqb_´ fh]ml_]hij_h^he_lv Ih f_j_ ih\ur_gby dhgp_gljZpbb we_dljheblZ 8max kgb`Z_lky ^hey wnn_d

31 lb\guo khm^Zj_gbc jZkl_l b kdhjhklv dhZ]meypbb m\_ebqb\Z_lky f_^e_ggZy dhZ]meypby Djb\Zyhl\_qZ_lgZklmie_gbx[ukljhcdhZ]meypbbijbk I;D8max =0, ijb ex[uo jZkklhygbyo ij_h[eZ^Zxl kbeu ijbly`_gby ENHijb\h^bldkhhlghr_gbx

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FRQVW bebF] 6 = const , ]

(3)

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= 64 : 1 : 0,09

Ihemq_ggh_ khhlghr_gb_ ohjhrh kh]eZkm_lky k wdi_jbf_glZevgufb ^Zggufb \ kemqZ_ lZd gZau\Z_fhc dhgp_gljZpbhgghc dhZ]meypbb dh]^Z mf_gvr_gb_ we_dljhklZlbq_kdh]h ihl_gpbZevgh]h [Zjv_jZ hllZedb\Zgby ^hk lb]Z_lky lhevdh aZ kq_l k`Zlby ^bnnmaguo >WK qZklbp ijb wlhf bo ih\_jo ghklgucaZjy^bihl_gpbZehklZxlkyg_baf_ggufb Khhlghr_gb_ g_jZk ijhkljZgy_lkygZkemqZcg_cljZebaZpbhgghcdhZ]meypbbijbdhlhjhc\\h ^bfu_ bhgu obfbq_kdb \aZbfh^_ckl\mxlkihl_gpbZehhij_^_eyxsbfbbhgZ fb gZ ih\_joghklb qZklbp k\yau\Zy bo \ g_jZkl\hjbfh_ beb g_^bkkhpbb jmxs__ kh_^bg_gb_qlhihgb`Z_laZjy^bihl_gpbZeqZklbpLZdijbdhZ]m

32 eypbb eZl_dkh\ kheyfb k ^\mo- b lj_oaZjy^gufb dZlbhgZfb ihke_^gb_ qZk lbqgh k\yau\Zxl Zgbhgu I:< -klZ[bebaZlhjZ 5&22- , RSO 4 - b ^j \ Z^ khj[pbhgguo kehyo gZ ih\_joghklb qZklbp ihebf_jZ k h[jZah\Zgb_f g_jZk l\hjbfuokhe_cqlhkgb`Z_laZjy^bihl_gpbZeqZklbp´Ijbf_kv´g_cljZeb aZpbhgghcdhZ]meypbbijb\h^bldhldehg_gbxhlijZ\beZF] 6 FRQVWHghg_ \uihegy_lky lZd`_ _keb mklhcqb\hklv ahey h[_ki_qb\Z_lky g_we_dljhklZlb q_kdbfbnZdlhjZfb

Wdki_jbf_glZevgZyqZklv P_ev jZ[hlu hij_^_eblv ihjh] [ukljhc dhZ]meypbb kbgl_lbq_kdh]h eZ l_dkZkheyfbkjZagufaZjy^hfdhZ]mebjmxs_]hbhgZijh\_jblv\uiheg_gb_ ijZ\beZF] 6 = const. >ey hij_^_e_gby I;D g_h[oh^bfh gZclb aZ\bkbfhklv gZqZevghc kdhjh klbdhZ]meypbbhldhgp_gljZpbbwe_dljheblZ-dhZ]meyglZH[uqghijbf_gyxl f_lh^ ³fbgmlghc fmlghklb´ ijb dhlhjhf aZ f_jm gZqZevghc kdhjhklb dhZ]m eypbb ijbgbfZxl \_ebqbgm fmlghklb eZl_dkZ dhlhjZy ^hklb]Z_lky aZ fbg ihke_gZqZeZdhZ]meypbbhlfhf_glZ\\_^_gbywe_dljheblZ-dhZ]meyglZ Nbabq_kdb_ ij_^ihkuedb f_lh^Z lZdh\u Dheehb^gu_ qZklbpu kihkh[gu jZkk_b\ZlviZ^ZxsbcgZgbok\_l\ke_^kl\b_ba\_klgh]hnbabq_kdh]hy\e_gby -^bnjZdpbbBgl_gkb\ghklvjZkk_yggh]hk\_lZ,j_adh\hajZklZ_lkm\_ebq_ gb_fjZaf_jZqZklbp>eykn_jbq_kdbog_ijh\h^ysbolhdqZklbpkjZ^bmkhfU ihmjZ\g_gbxJwe_y I=I 0 ·k

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33 Hlghr_gb_ , , 0 =τ gZau\Zxl fmlghklvx Fmlghklv qbke_ggh jZ\gZ bg l_gkb\ghklb kbe_ k\_lZ jZkk_b\Z_fh]h _^bgbp_c h[t_fZ kbkl_fu ijb bg l_gkb\ghklbiZ^Zxs_]hk\_lZjZ\ghc_^bgbp_ Kh]eZkgh mjZ\g_gbx Jwe_y fmlghklv ijhihjpbhgZevgZ dm[m jZ^bmkZ qZklbp LZdbf h[jZahf ijhp_kk mdjmig_gby qZklbp Z]j_]Zlh\ \ dhZ]meb jmxs_f ahe_ khijh\h`^Z_lky \hajZklZgb_f fmlghklb \h \j_f_gb qlh iha\h ey_lhp_gblvkdhjhklvdhZ]meypbb F_jhcgZqZevghckdhjhklbdhZ]meypbb90 kem`bl\_ebqbgZ V0= (

Gτ ) t→0 GW

HgZijZdlbq_kdbqbke_gghjZ\gZ³fbgmlghcfmlghklb´τ1 lddjb\u_τ - t \gZqZe_ijhp_kkZebg_cgu Bgl_gkb\ghklv k\_lhjZkk_ygby fmlghklv baf_jyxl k ihfhsvx g_n_ ehf_ljh\ Bkihevam_fuc \ jZ[hl_ ijb[hj fZjdb GNF iha\hey_l baf_jblv bgl_gkb\ghklv k\_lZ jZkk_yggh]h ih^ m]ehf 0 d gZijZ\e_gbx iZ^Zxs_]h emqZKihfhsvxijbeZ]Z_fh]hdijb[hjmwlZehgZfh`gh_]hijhdZeb[jh\Zlv bjZkkqblu\ZlvZ[khexlgu_agZq_gbyfmlghklbbkke_^m_fhckbkl_fu HibkZgb_bihjy^hdjZ[hlugZg_n_ehf_lj_GNF Bgl_gkb\ghklv k\_lhjZkk_ygby \ g_n_ehf_lj_ baf_jy_lky iml_f kjZ\g_ gby^\mok\_lh\uoihlhdh\h^bgbadhlhjuojZkk_ygbkiulm_fufjZkl\hjhf Z^jm]hcwlZehggufjZkk_b\Zl_e_fjbk K\_lh\hcihlhdhleZfiujZa^_ey_lkyihemijhajZqghcieZklbgdhc gZ^\_qZklbh^gZbadhlhjuoihiZ^Z_l\dZf_jmk^bklbeebjh\Zgghc\h^hc \dhlhjhcihf_sZ_lkydx\_lZkahe_fZ^jm]Zyijhoh^blq_j_ajZkk_b\Zl_evieZklbgdZbafhehqgh]hkl_deZ K\_ljZkk_yggucqZklbpZfbahey JbkHilbq_kdZybk\_lhkeZ[e_ggucjZkk_b\Zl_e_f

34 ko_fZg_n_ehf_ljZijhc^yh[t_dlb\bebgamihiZ^Z_l\ nhlhf_ljbq_kdbcma_edhlhjuc\dexqZ_l\k_[y baf_jbl_evgu_ ^bZnjZ]fu k hlkq_lgufb [ZjZ[ZgZfb h[t_dlb\u ijbafu nhdmkbjmxsmx ebgam k\_lhnbevlj b hdmeyjQ_jgZyrdZeZ[ZjZ [ZgZ - rdZeZ k\_lhijhimkdZgby HgZ ihdZau\Z_l ^hex ijhoh^ys_]h q_j_a ^bZnjZ]fmk\_lZkl_i_gvjZkdjulby^bZnjZ]fu \ijhp_glZo
35 ?keb fmlghklv h[t_dlZ ij_\urZ_l fmlghklv jZkk_b\Zl_ey lh iheghklvx hldju\Zxl ijZ\mx ^bZnjZ]fm ijZ\uc [ZjZ[Zg klZ\yl gZ b mjZ\gb\Zxl yjdhklbihe_caj_gbye_\uf[ZjZ[Zghf >ey jZkq_lZ fmlghklb ijb[hj dZeb[jmxl mklZgZ\eb\Zy \f_klh ahey wlZ ehg-ijbafmkba\_klgufagZq_gb_ffmlghklbHlkq_luijhba\h^ylihq_jghc rdZe_ijZ\h]h[ZjZ[ZgZ Fmlghklvaheyτkf -1 jZkkqblu\ZxlihnhjfmeZf τ=τw ·

Qij Qw

eb[h

, τ=τw Q e_ \Q w

]^_Q j bQ e_\ -hlkq_lihijZ\hfmeb[hihe_\hfm[ZjZ[Zgmkhhl\_lkl\_ggh Q

τw -fmlghklvwlZehgghcijbafuQ w -hlkq_l^eyijbafu Ijbf_qZgb_dZeb[jh\dZijb[hjZijh\_^_gZaZjZg__j_amevlZlu k\_^_gu \ lZ[ebpm aZ\bkbfhklb τ hl Q bf_xsmxky \ eZ [hjZlhjbb Ihjy^hd\uiheg_gbyjZ[hlu Ij_`^_ \k_]h ke_^m_l ih^h[jZlv jZa[Z\e_gb_ eZl_dkZ g_h[oh^bfh_ ^ey g_n_ehf_ljbq_kdbo baf_j_gbc MjZ\g_gb_ Jwe_y kijZ\_^eb\h ^ey jZa[Z\e_g guo ahe_c dh]^Z dZ`^Zy qZklbpZ fh`_l jZkkfZljb\Zlvky dZd hl^_evguc jZk k_b\Zxsbc p_glj b hlkmlkl\m_l y\e_gb_ \lhjbqgh]h jZkk_ygby Ihwlhfm ^ey g_n_ehf_ljbq_kdbo baf_j_gbc lj_[m_lky agZqbl_evgh_ jZa\_^_gb_ eZl_dkZ h[uqgh\ 3 - 10 4 jZa Ijb_fe_fuf h[uqgh y\ey_lky lZdh_ jZa\_^_gb_ ijb dhlhjhf hlkq_l ih rdZe_ k\_lhijhimkdZgby ijZ\h]h [ZjZ[ZgZ g_n_ehf_ljZ khklZ\ey_l g_ [he__ 50. J_dhf_g^m_fh_^eybkiulm_fh]hh[jZapZeZl_dkZjZa\_^_gb_bko_fZjZa [Z\e_gbymdZaZgugZwlbd_ld_ Ijbf_j

36 J_dhf_g^m_fh_ jZa\_^_gb_ eZl_dkZ 1: 10 4 jZaJZa\_^_gb_ijhba\h^blky\ ^\_klmi_gbihko_f_ 1/ 10000 = 1/ 100 ⋅ 0,5/ 50 Ze__ fe eZl_dkZ ijhf_`mlhqgh]h jZa[Z\e_gby \ghkyl \ f_jgmx dhe[m gZ fe ^h\h^yl \h^hc ^h f_ldbIhemqZxldhg_qgh_jZa[Z\ e_gb_-keZ[hhiZe_kpbjmxsbcjZkl\hj Baf_jyxl fmlghklv ihemq_ggh]h jZkl\hjZ τ0 k ihfhsvx g_n_ehf_ljZ dZdhibkZgh\ur_?kebihdZaZgb_ijZ\h]h[ZjZ[ZgZ[hevr_q_flhm\_eb qb\Zxl jZa[Z\e_gb_ gZ \lhjhf wlZi_ l_ [_jml g_ fe Z f_gvr_- ^h[b\Z ykv\uiheg_gbymkeh\byQ >Ze__ijh\h^ylhij_^_e_gb_³fbgmlghcfmlghklb´τ1 ijb\u[jZgghfjZa [Z\e_gbb bkihevamy jZkl\hju we_dljheblh\ 1D&O &D&O 2 , LaCl 3 bkoh^gZy dhgp_gljZpbybfhevekhhl\_lkl\_ggh J_dhf_g^mxlky ke_^mxsb_ bgl_j\Zeu dhgp_gljZpbb we_dljheblh\ ffheve 1D&O-200...1200 ; CaCl 2 - 10...50; LaCl 3 - 1...5.
37 e_caj_gbyblhqghihbkl_q_gbbfbgaZ\_jrZxlwlmijhp_^mjmAZibku\Zxl ihdZaZgb_Q rdZeuijZ\h]h[ZjZ[ZgZ Hihjh`gb\bhihehkgm\dx\_lmbdhe[mijh^he`Zxlbaf_j_gby\\h^y\ dhe[mihke_^h\Zl_evghfejZkl\hjZwe_dljheblZGZqbgZykg_dh lhjhc dhgp_gljZpbb we_dljheblZ mjZ\gb\Zgb_ ihe_c aj_gby k ihfhsvx ijZ \h]h[ZjZ[ZgZklZgh\blkyg_\hafh`gufIjbQ ijZ\Zyiheh\bgZihey aj_gby hklZ_lky k\_le__ e_\hc ld kbeZ jZkk_yggh]h k\_lZ klZeZ ij_\urZlv kbem k\_lZ ijhr_^r_]h q_j_a jZkk_b\Zl_ev Lh]^Z baf_j_gby ijh\h^yl gZ e_\hf [ZjZ[Zg_ mklZgh\b\ ijZ\uc gZ hlf_ldm J_amevlZlu ihf_sZxl \ lZ[ebpm EZl_dk H[t_f l\hjZ

jZk Dhgp_gljZpby we_d we_dljheblZ

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); τ0 =

.

IhdZaZgby

Fmlghklv

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τ1 ·10 3 kf -1

ffheve

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ffheve

K bko =

ijZ\uce_\uc

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38 GZah\bl_ \b^u mklhcqb\hklb ^bki_jkguo kbkl_f \ q_f hgb aZdexqZ xlky" Ih dZdhfm ijbagZdm ^bki_jkgu_ kbkl_fu ^_eyl gZ ebhnh[gu_ b ebh nbevgu_"DdZdhfmdeZkkm^bki_jkguokbkl_fke_^m_lhlg_klb ahev$J, wfmevkbx[_gaheZ\\h^_ fbp_eeyjgucjZkl\hjhe_ZlZgZljby eZl_dk ihebklbjheZ jZkl\hj[mlZ^b_g-klbjhevgh]hdZmqmdZ\[hgahe_" DZdb_ ba wlbo kbkl_f fh]ml h[jZah\u\Zlvky \ j_amevlZl_ kZfhijhba\hev gh]h^bki_j]bjh\Zgby" Q_f h[mkeh\e_gZ Z]j_]Zlb\gZy mklhcqb\hklv ebhnh[guo ^bki_jkguo kbkl_f" DZdb_ ijhp_kku \_^msb_ d mdjmig_gbx qZklbp kZfhijhba\hevgh ijhl_dZxl\lZdbokbkl_fZo" DZdhc ijhp_kk gZau\Zxl dhZ]meypb_c" Q_f hg aZ\_jrZ_lky" DZdbfb kihkh[Zfbfh`_l[ulv\ua\Zg" I_j_qbkebl_ b hoZjZdl_jbamcl_ nZdlhju Z]j_]Zlb\ghc mklhcqb\hklb ebhnh[guo ahe_c DZdb_ nZdlhju h[_ki_qb\Zxl Z]j_]Zlb\gmx mklhcqb\hklv Z eZl_dkZihebklbjheZkh^_j`Zs_]h\dZq_kl\_klZ[bebaZlhjZhe_ZldZeby[ wfmevkbbklbjheZ\\h^_kh^_j`Zs_c\dZq_kl\_klZ[bebaZlhjZg_bhgh]_ggh_ I:< gZijbf_j 52 &+2 CH 2 2 + \ lhc `_ wfmevkbb klZ[bebah\Zgghc `_ eZlbghc" QlhgZau\Zxl[ukljhcbf_^e_gghcdhZ]meypb_c"
39 < q_f jZaebqb_ f_`^m dhgp_gljZpbhgghc b g_cljZebaZpbhgghcdhZ]m eypb_c" < dZdhf kemqZ_ kijZ\_^eb\h ijZ\beh Rmevp_-=Zj^b" Fh`gh eb i_ j_g_klbwlbihgylbygZkbkl_fuklZ[bebabjh\Zggu_g_bhgh]_ggufbI:<" Ebl_jZlmjZ Njheh\X=Dmjkdheehb^ghcobfbb-F-k =eM-K-352. Njb^jbok[_j]>:Dmjkdheehb^ghcobfbb-E-k =eO-K-257. EZ[hjZlhjgu_ jZ[hlu b aZ^Zqb ih dheehb^ghc obfbbIh^ j_^X=Njheh\Z:K=jh^kdh]h-F-k =eMjZ[-K-171. >hihegbl_evgZy Dheehb^gZyobfbykbgl_lbq_kdboeZl_dkh\Mq_[ihkh[b_Ih^j_^JW G_cfZgZ-
,N9 ν Ij = , (1) λ

40 ]^_ N-dhgklZglZ oZjZdl_jbamxsZy jZaebqb_ hilbq_kdbo k\hckl\ ^bki_jkghc nZau b ^bki_jkbhgghc Fj_^u k ihdZaZl_eyfb ij_ehfe_gby khhl\_lkl\_ggh n 1 bQ 0 ):  Q − − Q   k = 24 π   Q + Q 

3

MjZ\g_gb_ Jwe_y kijZ\_^eb\h ^ey jZa[Z\e_gguo fhgh^bki_jkguo ahe_c kh^_j`Zsbokn_jbq_kdb_g_ijh\h^ysb_lhdg_ih]ehsZxsb_k\_lqZklbpu JZkk_b\ZxsZykihkh[ghklvaheyoZjZdl_jbam_lky\_ebqbghcfmlghklb ( τ dhlhjZyhij_^_ey_lkyhlghr_gb_fτ = I j / I 0 . Fmlghklv beb dhwnnbpb_gl jZkk_ygby qbke_ggh jZ\_g k\_lh\hc wg_j ]bb jZkk_b\Z_fhc _^bgbp_c h[t_fZ kbkl_fu \h \k_o gZijZ\e_gbyo ijb bg l_gkb\ghklbiZ^Zxs_]hk\_lZjZ\ghc_^bgbp_ <_ebqbgZτfh`_l[ulvlZd`_\ujZ`_gZq_j_abgl_gkb\ghklvijhoh^ys_ ]h k\_lZ , ij hkeZ[e_ggh]h\ke_^kl\b_jZkk_ygbyih\k_fgZijZ\e_gbyfhl ebqgufhli_j\hgZqZevgh]h, i
k\_lZ b ke_^h\Zl_evgh hdjZkdZ l_ hkeZ[e_gb_ k\_lZ h[mkeh\e_gh lhevdh jZkk_ygb_f lh ih]ehs_gb_ gZau\Z_lky nbdlb\guf Z kbkl_fZ - ³[_euf´ ah e_fLZdh\uaheb^bki_jkbb ^bwe_dljbdh\ ahebk_judZgbnhebeZl_dku wfmevkbb b ^j Nbdlb\gh_ ih]ehs_gb_ dZd b bklbggh_ hibku\Z_lky mjZ\ g_gb_f;m]_jZ-EZf[_jlZ-;_jZ I ij = I 0 · e -τ1 ]^_O -lhesbgZih]ehsZxs_]hkehy ?kebτ Olhkh]eZkghmjZ\g_gbx , ij =I 0 _l_fmlghklv-\_eb qbgZqbke_gghjZ\gZyh[jZlghclhesbg_kehyijbdhlhjhcijhoh^ysbck\_l hkeZ[ey_lky\_jZa BamjZ\g_gby ke_^m_l τ = 2,3 D/l , ]^_'-hilbq_kdZyiehlghklvkbkl_fu' OJ, 0 /I ij ).

(3)

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(4)

]^_N-dhgklZglZg_aZ\bkysZyhl^ebgu\hegu
(5)

IjbfZeuoagZq_gbyo=kh[ex^Z_lkymjZ\g_gb_Jwe_ybo Km\_ebq_gb_f =agZq_gb_omf_gvrZ_lky\ij_^_e_^h^eyqZklbpjZaf_jdhlhjuo[hevr_ λ AgZq_gbyo^eyjZaebqguo=k\_^_gu\lZ[ebpmkfgZijbf_j³IjZdlb dmf ih dheehb^ghc obfbb´ ih^ j_^ KK
42 H[hjm^h\Zgb_ Z ijb[hj ^ey hij_^_e_gby hilbq_kdhc iehlghklb nhlh f_lj beb nhlhwe_dljhdhehjbf_lj [ f_jgu_ dhe[u gZ b gZ fe ]jZ ^mbjh\Zggu_ibi_ldbj_abgh\Zy]jmrZ ey wlh]h \gZqZe_ \ f_jgmx dhe[m gZ fe \ghkyl fe jZkl\hjZ k jZa\_^_gb_f ^h\h^yl \h^hc ^h f_ldb b baf_jyxl hilbq_ kdmx iehlghklv \ dx\_l_ lhesbghc ff k a_e_guf k\_lhnbevljhf (λ \Zd Bkihevamxl \bamZevguc nhlhf_lj NF beb nhlhwe_dljhdhehjb f_lj fZjdb NWD- Bgkljmdpby d ijb[hjm bf__lky gZ jZ[hq_f f_kl_ Ba f_j_gbyijh\h^ylg_f_g__jZaaZibku\ZxlihdZaZgbyb[_jmlkj_^g__agZ q_gb_ 'kj Ihke_^h\Zl_evgh m\_ebqb\Zxl h[t_f \\h^bfh]h jZkl\hjZ k jZa

[Z\e_gb_f ^hbl^febaf_jyydZ`^ucjZahilbq_kdmxiehlghklv IhemqZxl - agZq_gbc ' \ mdZaZgghf \ur_ bgl_j\Ze_ ijb g_h[oh^bfhklb [_jml^jh[gu_agZq_gbyh[t_fZjZ[hq_]hjZkl\hjZ H[jZ[hldm j_amevlZlh\ ijhba\h^yl ke_^mxsbf h[jZahfJ_rZxl mjZ\g_ gb_Jwe_yhlghkbl_evghjZ^bmkZqZklbpU>eywlh]hh[t_fqZklbp9\ujZ`Z xl q_j_a jZ^bmk ih nhjfme_ 9 πr 3 ZqZklbqgmxdhgp_gljZpbxν-q_j_a \_kh\mx K ]kf 3 ih nhjfme_ ν=C/Vρ ]^_ ρ - iehlghklv ^bki_jkghc nZau Hlghr_gb_, p/ I 0 aZf_gyxlgZfmlghklvτ .
43 \bkbfhklb τ K AgZq_gby τ ijb jZaebqguo dhgp_gljZpbyo jZkkqblu\Zxl ih nhjfme_ Dhgp_gljZpbx ihebf_jZ \ jZa[Z\e_gguo h[jZapZo eZl_dkZ \ ]kf 3 jZkkqblu\Zxlkmq_lhfbkoh^ghcdhgp_gljZpbbmdZaZgZgZwlbd_ld_ b djZlghklbjZa[Z\e_gbyIhke_^gxxgZoh^ylke_^mxsbfh[jZahfImklv\aylh fe jZ[hq_]h jZkl\hjZ Lh]^Z blh]h\h_ jZa[Z\e_gb_ jZ\gh · 2/25 = 2/2500 = 1/1250 Ihemq_ggu_^Zggu_k\h^yl\lZ[ebpm EZl_dkbkoh^gZydhgp_gljZpby]fe H[v_f jZ[hq_]h Dhgp_gljZpby

Hilbq_kdZyiehl-

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ghklv'

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1,06

0,93

0,99

n1

1,593

1,545

1,558

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ρ = 1,00

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