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A new approach to the problem of measuring the properties of micelles

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A new approach to the problem of measuring the properties of micelles

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Content A N EW APPROACH TO THE PROBLEM OF M EASURING- THE PROPERTIES O F MI3ELLES A D is s e r ta tio n P re se n te d to th e F acu lty of the (Graduate School U n iv e rsity of Southern C a lif o r n ia In P a r t i a l F u lfillm e n t of th e Requirem ents f o r th e Degree Doctor o f Philosophy by H orst Hbyer September, 1951 Ph 0 0. '52 t i U l This dissertation, written by ” _ " under the guidance of AiS— .Faculty Committee on Studies, and approved by all its members, has been presented to and accepted by the Council on Graduate Study and Research, in partial ful fillment of requirements for the degree of D O C T O R OF P H IL O S O P H Y Dean Committee on Studies i l l . TABLE OF CONTENTS CHAPTER PAGE I . INTRODUCTION.............................................................. 1 I I . THEORY OF ELECTROPHORESIS A N D DIFFUSION OF COLLOIDAL ELECTROLYTES . . • . . 17 I I I . ELECTROPHORETIC APPARATUS A N D EXPERIMENTAL R E S U L T S ............................................................................ 42 IV. M EASUREM ENT OF THE DIFFUSION COEFFICIENT OF COLLOIDAL ELECTROLYTES................................. 117 V. DISCUSSION..........................................................................138 Optimum Amount of Dye P assed Through Double Y C e ll ......................................................138 C o n cen tratio n Dependence of M obility . 141 Temperature Dependence of M o b ility . . 146 The Size and Charge of M ic e lle s . . . 147 The Types of M i c e l l e s ...............................................158 SU M M A R Y ........................................................161 APPENDIX .................................. 163 BIBLIOGRAPHY................................................................................... 165 i v . LIST OF TABLES TABLE PAGE I* E le c tro p h o re sis of Potassium L aurate S o lu tio n s. Experiment # 1 ..........................................49 I I . M igration o f Ascending Boundary . . . . . 50 I I I . M igration o f Descending Boundary . . . . 51 j i IV. A n aly sis of F ig u re s 2 to 14 . . . . . 59 j V. A nalysis o f F ig u res 2 to 14 . . . . . . 60 I VI. A n aly sis of F ig u re s 16 to 18 67 V II. M o b ilitie s in H o riz o n ta l T is e liu s C e ll 9*4$ Potassium L au rate . . . . . . . 71 V III. O p tic al D ensity v s. W avelength. Sudan Iv in 9.4$ P otassium L au rate . . . . . . 79 IX. T u rb id ity of Soap S o lu tio n s . . . . . . 81 X. T u rb id ity of S o lu tio n s . . . . . . . 83 j XI. M o b ility v s. Volume of Dye Passed Through Double Y C e l l ................................................................... 85 X II. O p tic a l D ensity v s . C on cen tratio n of Sudan IV 88 X III. E ffe c t of S o lu b iliz e d Dye . . . . . . 90 | XIV. S p e c tra l. Curve f o r O il B l a c k ......................................... 91 XV. M o b ilitie s o f Potassium L au rate S o lu tio n s . 98 XVa. M o b ilitie s of Potassium L au rate S o lu tio n s . 99 TABLE XVI. M o b ility of A erosol M A and A erosol O T XVIa. M o b ility o f A erosol O T and A erosol M A XVII. E ffe c t of A lte rn a tin g C urrent XVIII. P ro p e r tie s of D iffu sio n C e lls XIX. L ight S c a tte rin g of S u lfu r Sol * . • XX. S u lfu r Sol Stopped w ith Iodine XXI. S u lfu r Sol Stopped w ith Potassium Hydroxide XXII. “D if fu s io n ” o f Gold Sol . . . . . XXIII. Apparent D iffu s io n C onstant of Gold Sol XXIV. Charge on M ic e lle s ....................................... XXV. Charge on A erosol M A M icelle . . . . XXVI. Charge on Potassium L au rate M icelle . ; XXVII. Size o f M ic e lle s from B ra d y ^ D ata . ^OCVIII. Charge on A erosol M A M icelle from Brady fs ! D ata and D i f f u s i o n ...................................... PAGE 102 103 115 120 123 125 126 134 135 150 154 155 157 159 LIST OF FIGURES FIGURE PAGE I . T is e llu s C ell and E lectro d e V e s s e lls . . . 46 2 - 1 4 . T is e llu s Boundary . . . . . . 52- 58 15. M ic ro -T ise liu s A pparatus ................................. 62 16 - 18. Photographs of M ic ro -T ise liu s Boundary 64- 65 19. O peration of Gates .......................................... 68 19a. O peration o f Gates . . . . . . . . 69 20. E le c tro p h o re s is and E lectroosm osis in C a p i l l a r i e s .............................................................. 73 21. Double Y C e l l ............................................................ 75 22. P ercen t Dye Passed v s. M o b ility o f Potassium L a u r a t e ..................................................................... 86 23. O p tic a l D ensity v s . Dye C o n cen tratio n . . 89 24. M o b ility v s. C o n cen tratio n o f Potassium L a u r a t e ..................................................................... 100 25. M o b ility v s. C o n cen tratio n o f Aerosol M A . 101 26. Diaphragm C e ll ..................................................... 107 27. M o b ility in Diaphragm C ell a s Function of Time .. ... . .. . .. . 109 28. E ffe c t of C urrent Density on M o b ility . . 112 29. E ffe c t o f C urrent D ensity upon Dye P assed Through Diaphragm C e l l ..................................... 113 v i i . FIGURE PAGE 30. C a p illa ry A dapter f o r C e n trifu g e . . . . 128 31. O p tic al D ensity v s. Wavelength fo r Gold Sol 131 32. O p tic al D ensity v s. C o n cen tratio n o f Gold Sol 132 33. M obility and E quivalent C o n d u ctiv ity o f Potassium L au rate . . . . . . . . 144 34. M o b ility and E quivalent C o n ductivity of A erosol M A ............................................................... 145 CHAPTER I INTRODUCTION One o f th e c u rre n t problems of c o llo id a l chem istry involves th e e lu c id a tio n of the s tr u c tu r e of c o llo id a l e le c t r o l y t e s . C o llo id a l e l e c tr o ly te s , as o r ig in a lly d efin ed by McBain,1 a re H e l e c t r o l y t e s in which one o f th e io n s i s p a r t i a l l y o r wholly re p la c e d by conducting charged c o llo id a l p a r t i c l e s o r m i c e l l e s .1 1 These c o llo id a l e l e c t r o ly t e s have b o th t h e o r e t i c a l and p r a c t ic a l s ig n ific a n c e . On th e th e o r e tic a l sid e, one might be a b le to o b ta in from t h e i r study a concept o f the fo rc e s h o ld in g to g e th e r th e sin g le m olecules in th e asso c ia tio n complex. Furtherm ore, sin c e c o llo id a l e le c tr o ly te s may c a rry charges some te n or tw enty tim es th a t o f common e le c tr o ly te s , some c o n trib u tio n to th e th e o ry of e le c tr o ly t e s may develop from t h e i r stu d y . On th e p r a c t ic a l side one fin d s innum erable a p p li c a tio n s o f c o llo id a l e l e c t r o ly t e s In th e f i e l d s of te c h nology, biology and m edicine. McBain, J . Chem. S oc., 101, 2042 (1912); 105, 417, 957 (1914); 11S, 825 (1918). “ 2. The o rd in ary soaps are the b e st known members o f t h i s c la s s , and by them selves c o n s titu te a fam ily w ith hun dreds of members. The newer fam ily of s y n th e tic d e te rg e n ts f a r outnumber th e soaps and most of th e se a re a ls o to be c l a s s i f i e d as c o llo id a l e l e c t r o ly t e s . B ile s a l t s may a lso be c l a s s i f i e d as c o llo id a l e l e c t r o ly t e s sin ce they a re be lie v e d ^ to s o lu b iliz e f a t s by methods s im ila r to th o se shown by d e te rg e n ts . A study of c o llo id a l e l e c t r o l y t e s may also c o n tr i b u te toward a b e t t e r u n d erstan d in g of th e phenomenon o f em ulsion p o ly m e rizatio n , sin c e i t has been shown by Har kins^ th a t th e i n i t i a l lo cu s of th e p o ly m e rizatio n r e a c tio n i s th e monomer s o lu b iliz e d in th e c o llo id a l m ic e lle . The monomer th e n d if fu s e s to th e r e a c tio n s i t e and th e polymer grows u n t i l i t i s no lo n g e r s o lu b le in th e m icelle* The phenomenon of m ic e lle fo rm atio n i s th u s s u f f i c ie n tly g e n e ra l so th a t any c o n trib u tio n tow ards th e under stan d in g of t h i s e f f e c t would have re p e rc u ssio n s throughout many f i e l d s . That soap s o lu tio n s have unusual p r o p e r tie s has ^ Wieland and Sorge, Z, P h y s io l. Chem., 97, 1 (1916) 3 H arkins, J . Am. Chem. Soo., 69, 1428 (1947). / 3. been known f o r about f i f t y y e a rs and, during t h i s in te r v a l, many in v e s tig a to r s have devoted them selves to th e study of th e s e and s im ila r system s. The s tr u c t u r e o f such s o lu tio n s, however, has only begun to become evident during th e p ast te n or f i f t e e n y e a rs. C e rta in anomalous p r o p e r tie s of soap so lu tio n s were d isco v ered by K ra ft4 around th e tu r n of t h e c e n tu ry . He observed th a t th e m olecular w eights as c a lc u la te d from th e r i s e in th e b o ilin g p o in t o f th e s a l t s of f a t t y ac id s were much h ig h e r th a n th e th e o r e tic a l v a lu e s, th e discrepancy becoming apparent w ith th e nonylate s a l t . L a te r in v e s tig a - 5 6 tio n s , p a r t i c u l a r l y by McBain and h is coworkers, * estab lis h e d th a t o th e r p r o p e r tie s , among them c o n d u c tiv ity , osmotic p re s s u re , v is c o s ity and su rfa c e te n s io n showed abrupt changes at a c o n c e n tra tio n which has become known a s th e c r i t i c a l c o n c e n tra tio n fo r th e form ation of m ic e lle s, o r C M C f o r s h o rt. I t i s now w ell e s ta b lis h e d th a t in th e v ic in ity of th e C M C th e simple soap m olecules o r io n s aggregate in to * K ra ft, B e r., 29, 1328 (1898). C McBain, Dye and Johnson, J . Am. Chem. Soc., 61, 3210 (1939). ® McBain, P ro c. Roy. Soc., A170, 415 (1939). la r g e r p a r t i c l e s c a lle d m ic e lle s . The e lu c id a tio n of th e s tr u c tu r e and com position of th e s e m ic e lle s has been en gaging th e a tte n t io n o f a number o f in v e s tig a to r s . Mc- Bain^'®*^ has p o s tu la te d the e x iste n c e o f two ty p es of m ic e lle s . One o f th e s e he b e lie v e s to be a sm all sp h e ric a l aggregate o f 10 o r 12 f u l l y charged hydrated io n s which are la rg e ly re sp o n sib le f o r th e r e l a t i v e l y high c o n d u c tiv ity of th e soap s o lu tio n s . The second m ic e lle i s th e s o -c a lle d la m e lla r m ic e lle , a sandwich a f f a i r c o n s is tin g of two p a r a l l e l la y e r s of f a t t y a c id m olecules or ions w ith th e hydrocarbon p a rt of each la y e r o r ie n te d tow ards one an o th er. X-ray stu d ie s of soap solutions^-0-1-4 a re b ex i eved 7 McBain and Johnson, J . Am. Ghem. Soc., 88, 9-13 (1944). ~ 8 McBain, P roc. Roy. Soc., A176, 415 (1939). 8 McBain and Hoffman, J . Phys. C o ll. Chem., 53, 39 (1949). ^ Hess, K iessig and P h ilip p o f f, N aturw is., 26, 194 (1938). ^ Hess, P h ilip p o f f and K ie ssig , K olloid Z ., 88, 40 (1938). H arkins, Mattoon and C o rrln , J . C o ll. S c i., 1, 105 (1946). H arkins, M attoon and C o rrin , J . Am. Chan. Soc., 36, 220 (1946). H arkins, S te a rn and Mattoon, J . Chem. P hys., 13, 209 (1947). 5. to dem onstrate th e e x iste n c e of t h i s la m e lla r McBain mi c e lle and have a ls o been in te r p r e te d by some in v e s tig a to r s as supplying proof o f th e s o -c a lle d Hess m ic e lle , an aggre g a tio n of se v eral McBain m ic e lle s one above th e o th e r ^ Although th e exact q u a n titiv e i n te r p r e t a ti o n o f th e x -ra y d a ta is s t i l l in d is p u te , most in v e s tig a to r s b e lie v e th a t th e e x iste n c e of th e la m e lla r m ic e lle i s w ell e s ta b lis h e d . A sm all m in o rity , however, co n tin u es to oppose t h i s id e a . H a r t l e y , f o r example, has c o n s is te n tly t r i e d to ex p lain th e p r o p e r tie s of soap s o lu tio n s in term s o f a 17 1A sin g le sp h e ric a l m ic e lle . R ecently , 0 he has again p o in ted out th a t most of th e observed phenomena, in clu d in g th e x -ray d a ta , can be exp lain ed on th e b a s is o f th e spher ic a l m ic e lle alone. He assumes th a t the strong e le c tro s t a t i c re p u ls io n s between th e m ic e lle s cause them to a r range them selves in a th ree -d im en sio n a l clo se-p ack ed assem b ly . On t h i s b a s is he deduces th a t th e d is ta n c e s between th e c e n te rs of neighboring spheres i s given by 15 Davis and P h ilip p o f f, N ature, 164, 1087 (1949). H a rtle y , C o llie and Samis, T rans. F arad. Soc., 32, 795 (1936). 1 7 H artle y , N ature, 163, 767 (1949). 18 H artley , Ann. Report Chem. Soc., 45, 48 (1948). 6. 5 V 1/ 3 1 * 2 / 2 r where r i s th e rad iu s o f th e sp h e ric a l m ic e lle and V th e f r a c tio n o f th e t o t a l volume occupied by them. For con s ta n t r , 1 was found to vary according to th e observed- long spacing w ith in c re a sin g c o n c e n tra tio n . S o lu b iliz a tio n of hydrocarbons in the m ic e lle would in c re a se r and so in c re a se 1. T his is also in q u a l i t a t i v e agreement with th e x^-ray d a ta although no q u a n tita tiv e comparison was made. I t i s I n te r e s tin g th a t sh o rtly b efo re H artley*s papers r e f e r re d to above, C o rrin 19 p u b lish ed a r e in te r p r e - 13 t a t ion o f th e d ata of H arkins, M attoon and C o rrin , in which he shows th a t i t i s p o s s ib le to assume a r a d ia l d is t r i b u t i o n fu n c tio n f o r sp h e ric a l m ic e lle s which would y ie ld a th e o r e tic a l x-ray in te n s ity p a tte r n , which spacing i s s im ila r to th e ones he and h is coworkers a c tu a lly observed. He concluded th a t x -ra y evidence by i t s e l f is in c ap ab le of d ecid in g between th e s p h e ric a l and la m e lla r m ic e lle . No c l e a r p ic tu re has yet emerged as to th e charge on th e m ic e lle . Van R y s s e lb e rg h e ^ has attem pted to ana- 19 C o rrin , J . Chem. P h y s., 16, 844 (1948). 20 Van R ysselberghe, J . Phys. Chem., 43, 1048 (1939). ly z e th e a v a ila b le co n d u c tiv ity and d if f u s io n d a ta fo r la u ry l su lfo n ic a c id and has o b ta in ed v alu es f o r th e compo s i t i o n o f th e average m ic e lle which ranged from H Lag***^ in — 89 d i l u t e s o lu tio n to Hg3g L a in a °*6 Molar s o lu tio n of la u ry l s u lfo n ic a c id . R ecently McBain^* has used charged membranes.to estim ate th e charge of th e m ic e lle . He ob ta in e d an average m ic e lle charge o f 2.22 e le c tro n s w ith 0 .2 Molar la u r y l pyridinium c h lo rid e and 2.72 w ith m y r i s t y l t r i - methylammonium c h lo rid e . The procedure involved c a lib r a ti o n of th e r a t e o f r i s e of th e s o lu tio n in a c a p ill a r y due to th e osmotic p re ssu re of sin g ly and doubly charged ions, and th e assum ption th a t th e same r a te of r i s e would apply to m ic e lle s of s im ila r charge. The la c k of th e o r e tic a l J u s t i f i c a t i o n fo r th e method makes th e r e s u l t s l i t t l e more than e s tim a te s . A th e o r e t i c a l l y sounder approach to th e problem was made by Brady and S a lle y ,2^ working w ith A erosol O T and A erosol MA, They used ra d io a c tiv e sodium to measure th e s e lf - d if f u s io n c o e f f ic ie n ts of th e sodium ion in th e s e s o lu tio n s . Prom t h e i r r e s u l t s they were ab le to c a lc u la te McBain and C handler, J . Phys. C o ll. Chem., 53, 930 (1948). Brady and S a lle y , J . Am. Chem. Soc., 70, 914 (1948). 8. th e p erce n t of sodium io n bound to th e m ic e lle a f t e r mak ing a reaso n ab le assum ption as to the d if f u s io n co n stan t of th e A erosol m ic e lle . For A erosol O T they obtain ed 36$, a fig u re which compares w ell w ith 35$, which they estim ated from c o n d u c tiv ity measurements. T h e ir method i s in cap ab le of y ie ld in g an a b s o lu te value of th e charge u n le s s com bined w ith a second Independent se t of d a ta . R ecently K e rs ti G -ranath^ has com pleted an in v e s ti g a tio n of th e p r o p e r tie s o f potassium la u r a te and potassium m y ris ta te s o lu tio n s as a fu n c tio n of th e io n ic s tre n g th . A ll p r o p e r tie s in v e s tig a te d , d iffu s io n , sedim entation, sol v a tio n and a s s o c ia tio n , showed marked changes w ith io n ic s tre n g th . Again, however, i t was necessary to assume th a t th e c o n trib u tio n of th e sim ple io n s in th e so lu tio n had a n e g lig ib le e f f e c t on th e p r o p e r tie s m easured. The d if f u sion c o e f f ic ie n t, f o r example, v a rie d from 12 x ICT^ cm^/ sec. in a 1$ potassium la u r a te s o lu tio n w ith an io n ic s tre n g th of 0 .5 , to about 2 x 10~? fo r an io n ic s tre n g th of 2.0. T his change of d iffu s io n c o n stan t w ith io n ic s tre n g th may account f o r the discrepancy o f th e d iffu s io n v alu es of Lamm, who in 1 9 4 0 ^ found th e f r e e d if fu s io n ^ Oranath, Acta Chemlca Scand., 4, 103-125 (1950). Lamm and Hdgberg, K o llo id Z., 91, 10 (1940). 9. c o e f f ic ie n t of sodium la u r a te to be 18 x 1 CP7 above th e C M C while in 19422® he found a valu e of 9.9 x 10"? fo r th e potassium soap w ith the porous d is k d if f u s io n c e l l . An im portant f a c to r in flu e n c in g a l l th e previous work has been th e i n a b i l i t y o f th e experim enter to d i f f e r e n tia te between th e c o n trib u tio n of th e m ic e lle and th a t o f th e simple ions p re se n t in the soap so lu tio n . Such solu tio n s , as McBain, Void and V o ld ^ were th e f i r s t to empha siz e , a re r e v e r s ib le , therm odynam ically s ta b le s o lu tio n s . They p o in te d out th a t phase diagram s could be c o n s tru c te d f o r soap s o lu tio n s and th a t d if f e r e n t methods f o r determ in ing th e se diagram s, e .g ., a n a ly s is o f th e se p a ra te phases, v is u a l o b se rv a tio n of th e tem p eratu res and c o n c e n tra tio n s a t which phases appear and disap p ear, m icroscopic observa tio n , vapor p re s s u re and d ila to m e te r methods, a re a l l in com plete agreem ent. I t was also emphasized th a t th e e x te r nal p r o p e r tie s o f soap s o lu tio n s a re com pletely determ ined by th e tem p eratu re, p re s s u re and com position of th e system and independent of i t s previous h i s t o r y . Such a thermodynamic concept o f soap s o lu tio n s i s 25 Lamm, K o llo id Z., 98, 45 (1942). McBain, Void, and Void, J . Am. Chem. Soc., 60, 1866 (1938). 10. of fundam ental im portance, since i t r e q u ire s th a t th e re must always be an eq u ilib riu m between th e sim ple soap mole c u le s o r ions and th e c o llo id a l m ic e lle . These sim ple io n s w ill th e re fo re c o n trib u te to the observed p ro p e rty u n le s s a sp e c ia l e f fe c t i s made to i s o l a t e and observe some prop e rty c h a r a c te r i s tic o f th e m ic e lle . I t i s my b e l i e f th a t such a p ro p e rty i s to be found in th e phenomenon of solu b i l i z a t i o n . The phenomenon o f s o lu b iliz a tio n o f dyes and hydro carbons in soap s o lu tio n s has been e x te n siv e ly stu d ied , p a r t i c u l a r l y by McBain, ^ “^ l, K o lth o ff, 3 2 ,33 H arkins, 34 and McBain, Fr o n tie r s in C o llo id Chem., Vol. 8. 28 McBain and OfConner, J . Am. Chem. Soc., 62, 2855 (1940). 29 McBain, M e r r ill and Vinograd, J . Am. Chem. Soc., 63, 679 (1941). 30 McBain and M e r r ill, J . Phys. Chem., 46, 10 (1943). ^ McBain and R ichard, Ind. Eng. Chem., 32, 642 (1946). 32 K olthoff and S tr ic k s , J . Phys. C o ll. Chem., 53, 915 (1949). 33 K olthoff and S tric k s , J . Phys. C o ll. Chem., 53, 424 (1949). 34 H arkins, J . Chem. P h y s., 15, 406 (1948). 35 Klevens. This e f f e c t may he d esc rib e d as the a b i l i t y of d e te rg e n t s o lu tio n s to ta k e up m a te ria l which would o th e r wise be in s o lu b le . I t d i f f e r s from e m u ls ific a tio n , how ever, in th a t the m a te ria l i s ta k en up in a thermodynamic a l l y r e v e r s ib le manner. Thus McBain^® has shown th a t s o lu b iliz a tio n in v o lv es th e spontaneous fo rm atio n of th e r - modynamically s ta b le c o llo id a l p a r t i c l e s of an o th erw ise in s o lu b le m a te r ia l. In th e case o f in s o lu b le dyes, th e r a te a t which s o lu b i liz a tio n e q u ilib riu m was e s ta b lis h e d seemed to depend upon th e s lig h t s o lu b i lity of th e o rg an ic dyes. Thus Orange OT, Sudan £ } and Sudan I re q u ired roughly 12- 16 hours f o r estab lish m e n t o f eq u ilib riu m , but th e much l e s s so lu b le Yellow A B re q u ire d fo u r days under comparable c o n d itio n s. A pparently th e dye f i r s t d is s o lv e s as simple m olecules which a re th e n in c o rp o rate d in to th e m ic e lle . McBain a lso measured th e s o lu b iliz a tio n o f Orange O T in s o lu tio n s o f potassium s a l t s of th e d if f e r e n t f a t t y a c id s . His r e s u l t s a re in te rp r e te d by him as proof th a t th e amount o f dye s o lu b iliz e d by a homologous s e r ie s of soaps cannot be explained by assuming tr u e s o lu tio n of th e 35 Klevens, J . Am. O il Chem., S ept. (1949). 12. dye in th e hydrocarbon p a r t of th e soap. Thus, in th e t r a n s i t i o n from C-8 to C-14 soaps, th e re is a tw elve fo ld in c re a se in th e amount of dye s o lu b iliz e d f o r le s s th an a two fo ld in c re a se in chain le n g th . McBain has in te r p r e te d h is r e s u l t s as in d ic a tin g th a t th e dye is in c o rp o ra te d be tween th e hydrocarbon la y e r s in a manner s im ila r to th a t which has been e s ta b lis h e d fo r s o lu b iliz a tio n of in so lu b le hydrocarbons. Vetter^® has c r i t i c i z e d McBain*s in te r p r e ta tio n , arguing t h a t th e e f f e c t iv e p a r a f f in ic n atu re o f th e spheri c a l m ic e lle would decrease w ith d is ta n c e from th e c e n te r. He th e re fo re a r b i t r a r i l y d ec reases th e ch ain le n g th of th e soap by th r e e carbon atoms and, cubing th e r e s u ltin g le n g th , fin d s th e r e s u l t to be in approxim ately th e same r a tio as th e amounts s o lu b iliz e d . T his, V e tte r b e lie v e s , i s e v i dence fo r th e sp h e ric a l m ic e lle . I t should perhaps be emphasized th a t th e above d i s - cusion, as w ell as th e work to .b e d escrib ed , a p p lie s to w ater in s o lu b le dyes. Water so lu b le dyes such as p in acy - a n o lc h lo rid e and a c rid in e a re also s o lu b iliz e d by soap s o lu tio n s b u t, in th e se cases, as Harkins* and Klevens* V e tte r, J . Phys. C o ll. Chem., 51, 262 (1947). 13. re se a rc h e s in d ic a te , th e dye i s probably bound to o r near th e su rfa c e o f th e m ic e lle by e l e c t r o s t a t i c fo rc e s . By means of th e phenomenon of dye s o lu b iliz a tio n , i t becomes p o ssib le to ta g th e m ic e lle d ir e c tly and to f o l io w th e p ro g re ss of th e m ic e lle independently of th e behav io r of th e in d iv id u a l soap m olecules. R a d io ac tiv e t r a c e r tag g in g of th e soap m ic e lle , as w ith carbon 14, would not be s a tis f a c to r y since th e eq u ilib riu m between m ic e lle and in d iv id u a l soap m olecules would ra p id ly d i s t r i b u t e th e tagged m olecules among m ic e lle s and in d iv id u a l soap mole c u le s . Any measurements th e n performed on th e system could only re v e a l p r o p e r tie s o f th e m icelle-m o lecu le m ixture. With dye s o lu b iliz a tio n i t becomes p o s s ib le to observe p r o p e r tie s c h a r a c t e r i s t i c of th e d y e-m icelle complex. The in te n s e c o lo r of th e dye s o lu tio n p erm its th e u se of a minute q u a n tity of dye, so th a t the a c tu a l c o n trib u tio n of th e dye m olecule to th e observed p ro p e rty can be assumed to be n e g lig ib le . Thus 100 ml. o f a 5$ potassium la u r a te s o lu tio n s o lu b iliz e s about 2 o r 3 m illig ram s of Sudan IV so th a t th e re are more th a n 2,000 potassium la u r a te mole c u le s fo r every m olecule of dye, o r, assuming a m olecular weight o f 40,000 f o r th e m ic e lle , th e re a re about 120 mi c e l l e s f o r each dye m olecule. To th e b e s t of our knowledge th e re i s only one paper 14. d ea lin g w ith th e p h y sic a l p r o p e r tie s of dye-soap so lu tio n s . T his, by Dean and V inograd,37 concerned i t s e l f w ith the d if fu s io n c o n s ta n ts o f Aerosol O T of d if f e r e n t co n cen tra t io n s bo th w ith and w ithout dye, but d id not e x p lo it the f u l l power of th e method. In s te a d of reg ard in g th e d if f u sion as a t r a c e r d iffu s io n , they m is in te rp re te d t h e i r d ata and s ta te th a t th e tru e d if f u s io n c o e f f ic ie n t o f th e mi c e l l e i s th e d iffe re n c e between th e observed d iffu s io n c o e ff ic ie n t of dye when no A erosol i s moving and when dye i s moving co u n ter to the A erosol. The use of th e d y e -tra c e r technique o u tlin e d above p erm its a d i r e c t d e te rm in a tio n of th e e le c tro p h o re tic m o b ility of th e m ic e lle . This d a ta can th en be combined w ith o th e r in fo rm atio n about th e same system, as f o r ex ample, th e d iffu s io n c o n s ta n t, o r th e p ercen tag e of th e t o t a l sm all ions which a re bound to th e m ic e lle , and so one can o b ta in an e stim a te of th e siz e and charge of th e m ic elle as i s done in C hapter V. A c tu a lly , of course, th e scope o f th e method i s much g r e a te r th a n i t s development, as in t h i s d is s e r ta ti o n , to th e d e te rm in a tio n of th e e le c tfo p h o re tic m o b ility o f 37 Dean and Vinograd, J . Phys. Chem., 46, 1001 (1942). 15. th e m ic e lle . Thus, f o r example, some work i s re p o rte d in C hapter IV on th e d if f u s io n o f dye-tagged m ic e lle s . T his, as i s shown in Chapter V, p ro v id es in fo rm atio n a s to th e f r i c t i o n a l c o e f f ic ie n t of th e tagged m ic e lle which can be combined w ith th e m o b ility d a ta to o b ta in th e charge on th e m ic e lle . Again, th e d if fu s io n d a ta may be used to c a l c u la te th e ra d iu s o f th e m ic elle, assuming th e l a t t e r to be s p h e ric a l. Or th e m o b ility d a ta may be combined w ith Brad3''*s^ d a ta on th e p ercen tag e of bound c a tio n s to c a lc u l a t e an eq u iv alen t sp h e ric a l ra d iu s and a charge. Perhaps th e b e s t method of u t i l i z i n g th e s e d a ta would seem to be to use th e m o b ility and d iffu s io n d a ta to c a lc u la te a charge, assuming only th a t th e f r i c t i o n a l r e s is ta n c e to d if fu s io n is th e same a s th e f r i c t i o n a l r e s is ta n c e to th e e le c tro p h o re tic m ig ratio n , and th e n combine t h i s r e s u lt w ith B rady1s d a ta to o b ta in a m olecular weight of th e mi c e l l e . These v a rio u s a sp e c ts of th e problem w ill be d i s cussed in d e t a i l in C hapter V. In a d d itio n to e le c tro p h o r e s is and d if fu s io n meas urem ents, i t i s also p o s s ib le to su b je ct th e tagged mi c e lle s to a c e n tr if u g a l f i e l d and so determ ine a m olecular weight o r a f r i c t i o n a l c o e f f ic ie n t. However, in th e ab sence o f p ro p er equipment, i t was p o s s ib le only to observe th a t, in a McBain-Ford u ltr a c e n tr if u g e , sedim entation of 16. th e m ic e lle d id occur in a c e n tr if u g a l f i e l d . An ex ten sio n of th e method along th e s e l i n e s i s h ig h ly d e s ira b le in view of th e i n a b i l i t y of th e x -ra y evidence to e s ta b li s h th e shape of th e m ic e lle . A knowledge o f the f r i c t i o n a l f a c t o r of th e m ic e lle would s e t t l e t h i s q u e stio n . T h is th e s is , however, i s p r in c ip a lly concerned w ith th e e le c tro p h o re s is of soap s o lu tio n s , th e th e o ry of which fo llo w s in th e next c h a p te r. Follow ing th e d isc u ssio n of th e th e o ry in Chap t e r I I , th e experim ental p a rt of th e e le c tro p h o re s is and d iffu s io n i s d isc u sse d in C hapters I I I and IV, r e s p e c tiv e ly . C hapter V c o n ta in s a d isc u ssio n of th e r e s u l t s which were o b ta in ed . c h a p t e r I I THEORY OF ELECTROPHORESIS A N D DIFFUSION OF COLLOIDAL ELECTROLYTES The c l a s s i c a l th eo ry o f e le c tro p h o r e s is i s due to H e lm h o ltz ^ and Smoluchowsky*^ who based t h e i r a n a ly s is on th e assum ption of Helmholtz th a t th e p o te n tia l d i f f e r ence e x is tin g between th e p a r t i c l e and the s o lu tio n i s due to a th in and r ig id e l e c t r i c double la y e r se p a ra tin g th e p a r t i c l e and so lu tio n , G o u y ,^ however, p o in te d out th a t th e therm al a g ita tio n of th e solvent m olecules must re n d e r th e e l e c t r i c double la y e r d if fu s e and so extend th e double la y e r much f u r th e r in to th e liq u id th a n Helm holtz and 41 Smoluchowsky had o r ig in a l ly su sp ected . Debye and Huckel su p p lied a b ro ad er and sounder b a s is th a n e a r l i e r work when th e y in tro d u ce d th e concept o f th e io n ic atmosphere as an i n t e g r a l and necessary p a r t of th e environment of charged p a r t i c l e s in s o lu tio n . 36 Helmholtz, Wied. Ann., 7, 337 (1879). 39 Smoluchowsky, Krakauer A nz., 183 (1903). 40 Gouy, J . P h y s., 9, 457 (1910). 4^ Debye and Huckel, Physik. Z., 24, 185, 305 (1923). A sim p lifie d concept of e l e c t r i c m o b ility may be developed by co n sid erin g an is o la te d charged p a r t i c l e in th e absence of o th e r charged ions, as might be th e case a t i n f i n i t e d i l u t i o n in th e case of an aqueous medium. Assume th a t th e p a r t i c l e has a charge q and t h a t a poten t i a l g ra d ie n t X i s a p p lie d to th e s o lu tio n . Then the fo rc e a c tin g on the p a r t i c l e i s However, th e motion o f th e p a r t i c l e i s opposed by th e v is cous fo rc e s c re a te d a s i t moves through th e liq u id so th a t th e viscous fo rc e i s where v i s th e v e lo c ity of th e p a r t i c l e and f th e f r i c tio n a l c o e f f ic ie n t. At eq u ilib riu m Fe s Fv and th e mo b i l i t y u i s given by Assuming th a t th e p a r t i c l e i s sp h e ric a l and th a t one may use S to k es' law to c a lc u la te f , such th a t (4) f - 6 7Tnr where n i s th e v is c o s ity of th e so lv e n t and r th e ra d iu s of th e p a r t i c l e . Thus ( i) F g s qX ( 2) v (5) 19. C onventionally th e m o b ility of c o llo id a l p a r t i c l e s has g e n e ra lly been expressed in term s of th e p o te n tia l, 5 , o f a sphere w ith charge q in a medium of d i e l e c t r i c con sta n t £> . Thus (6) t = -SL 3 Sir so th a t equation (5) becomes (7) u « 6rrn Equation (7) i s known as H uckelfs eq u atio n . The co rresponding Smoluchowsky eq uation f o r p a r t i c l e s w ith a ra d iu s much la r g e r th an th e th ic k n e s s o f th e double la y e r may be re a d ily d e riv e d by co n sid e rin g th e p a r t i c l e as a p a r a l l e l p la te condenser whose p la te s a re sep arate d by l/K , th e th ic k n e s s o f th e double layer, and which have a charge a" p e r u n it a re a . Again eq u atin g th e e l e c t r i c a l d riv in g fo rc e to th e f r i c t i o n a l fo rc e , we have (8) X a - » n dv/dx a n vK where ndv/dx i s th e f r i c t i o n a l fo rc e due to v is c o s ity , v th e v e lo c ity of th e p a r t i c l e , and l/K th e th ic k n e s s of th e double la y e r. The charge d e n s ity ,0 “ , i s given by th e ex p ressio n (9 ) o-. Equation (8) may th e r e f o r e be r e w r itte n as The d if fe re n c e in th e num erical f a c to r s o f H uckel1g and Smo lu chow sk y 1 s equation has been th e source of consid e ra b le d isc u ssio n and experim ent. H e n r y 4 ^ was th e f i r s t to p o in t out th a t im p lic it assum ptions by Huckel and Smol- uchowsky as to th e th ic k n e ss of th e double la y e r were re s p o n s ib le f o r th e d iscrepancy. He also c i t e s th e e x p e ri mental evidence of d if f e r e n t in v e s tig a to r s which convin c in g ly shows th a t f o r th e la rg e c o llo id a l p a r t i c l e s (g re a te r th a n 10~5 cm.) stu d ie d Smoluchowsky1s eq u atio n is v a lid . In g en e ra l, however, c s ta b le c o llo id a l p a r t i c l e s have d ia m eters sm aller than th e minimum re q u ire d by Smol uchowsky f s equation. Henry h as co n sid ered th e se in term ed i a te cases and shown th a t in g e n e ra l th e m o b ility may be expressed as (11) U » f (Kr) where f(K r) i s a fu n c tio n o f th e p ro d u ct o f the p a r t i c l e ra d iu s r and th e Debye-Huckel f a c to r K. At h ig h v a lu e s of Kr, f(K r) approaches u n ity w hile f o r low v alu es of Ka, as would occur a t i n f i n i t e d ilu t io n , f(Ka) has th e value Henry, P ro c. Royal Soc., 153, 106 (1931) 21. o f 2/3 so th a t H uckel1s equation i s a p p lic a b le . A pparently e x tra p o la tio n of th e experim ental m o b ility v alu es to i n f i n i t e d ilu t io n would th en perm it th e a p p lic a tio n o f Huckel*s eq u atio n . C o llo id a l e l e c t r o ly t e s , however, are found only in conducting medium, so i t becomes necessary to c o n sid e r th e p o s s ib le changes in equation (11) which might r e s u l t . In a conducting medium th e p o te n tia l o f a sphere i s no lo n g e r g iv en by (6) but in ste a d i s lowered due to th e form ation o f an io n ic atmosphere a r is in g from th e accumu- la tio n of charged p a r t i c l e s o f o p p o site sig n n ear th e su r face o f th e sphere. Assuming th a t th e double la y e r has a th ic k n e ss 1/K, and th e sphere c re a te d by th e double la y e r has a charge -q , th en th e t o t a l p o te n tia l becomes Again we n o tic e th a t e x tra p o la tin g to I n f i n i t e d ilu tio n where Kr approaches zero and f(K r) approaches 2/3, equa tio n (13) becomes H u ck el's eq u a tio n . E quation (13) might have been d eriv ed in a more rig o ro u s manner by in tro d u c in g th e Debye-Huckel concept * a * .^ 1 n — Q ~ J>r JSTr.* T/K) E quation (11) now becomes q f ( Kr) I*rnr~ Tl + Kr) 2 2 . o f th e Ion atm osphere. The equation, however, i s th en ob ta in e d w ith much g r e a te r e f f o r t hut w ith p erhaps a c le a r e r conception of th e n a tu re of th e d if f u s e double la y e r. The concept developed in th e preceding pages i s , however, ade quate f o r our purposes. I t rem ains to d isc u ss th e two o th e r f a c t o r s a f f e c tin g th e motion o f e l e c t r o l y t e s in solu tio n and to show th a t a t i n f i n i t e d ilu t io n th e s e too may be ignored and th a t th e Huckel equ atio n i s th en a p p lic a b le . These two e f f e c t s , f i r s t d isc u sse d by Debye and Huckel, a r i s e from th e gegenions which a re d is tr ib u te d around th e c e n tr a l ion and c o n s titu te i t s ion atm osphere. These gegenions im part a charge to the la y e r of so lv e n t c lo se to ' the su rfa ce o f th e p a r t i c l e . T his charge is of o p p o site sign to th e charge of th e c e n tr a l ion. The a p p li c a tio n of the p o te n tia l f i e l d has two e f f e c ts upon th e gegenions. F i r s t th e re is th e s o - c a lle d e le c tro p h o re tic e f f e c t due to th e m ig ratio n o f th e ion atm osphere in an o p p o site d ir e c tio n , and second, th e re i s th e r e la x a tio n e f f e c t which a r is e s from th e i n a b i l i t y of th e ion atm osphere to a d ju st i t s e l f immediately to th e motion o f th e c e n tr a l io n . The c e n tr a l ion, under th e in flu e n c e of th e fo rc e F, moves w ith a v e lo c ity equal approxim ately to (14) v - Fw 23. where w i s th e m o b ility of th e c e n tr a l ion. Upon th e a p p li c a tio n of t h i s fo rce, th e ion moves away from i t s ion a t mosphere but w ill s t i l l drag the atmosphere w ith i t due to th e e l e c t r o s t a t i c f o rc e s . L e ttin g t equal th e tim e of re la x a tio n o f th e io n ic atmosphere, th e c e n tr a l ion w ill be ahead o f t h i s atmosphere by a d ista n c e (15) v t - Fwt C a llin g th e th ic k n e ss o f th e ion atmosphere d - 1/K, where 1/K i s th e average ra d iu s of th e Debye io n ic atmosphere, th e r a tio o f v t to 1/K which equals FtKw w ill measure th e r e l a t i v e dissymmetry o f th e atm osphere. An approxim ate e stim a te of th e r e ta r d a tio n fo rc e due to t h i s dissymmetry is o b tain ed by m u ltip ly in g th e dissymmetry by th e t o t a l fo rc e between th e ion and i t s atm osphere, g iv in g (16) A F B _ # KFtw 43 But th e r e la x a tio n tim e i s shown by Harned and Owen to be given by th e ex p ressio n (17) t - ----- K%T so th a t eq u atio n (15) becomes Harned and Owen, P h y sic a l Chem istry of E le c tro l y t i c S o lu tio n , 1950, pp. 63-65, p . 76. 24. (18) * F e 2 KF jc T E r An estim a te of th e e le c tro p h o re tic e ffe c t is r e a d ily made by assuming th a t th e c e n tr a l ion o f charge q i s sur rounded by an ion atmosphere of charge - q . A fo rc e of -Xq w ill th u s a c t on th e ion atmosphere and move i t , w ith th e liq u id co n tain in g th e atmosphere, in a d ir e c tio n oppo s i t e to t h a t o f the c e n tr a l ion. In o th e r words, th e c e n tr a l io n must move a g a in st a co u n te r c u r r e n t. Assuming th a t th e e n t ir e charge of th e ion atmosphere i s lo c a te d in a s p h e ric a l s h e ll a t a d is ta n c e 1/K from th e central ion and th a t S to k es 1 law i s a p p lic a b le to th e motion o f th e sp h e ric a l atmosphere, one o b ta in s f o r th e v e lo c ity of th e ion atmosphere The net v e lo c ity o f th e c e n tr a l ion can be o b tain ed from (IB) and (19). In th e absence o f th e atmosphere, th e ion would t r a v e l w ith a v e lo c ity Fw. The io n atmosphere in tro d u c e s th e r e ta rd in g fo rc e A F of equation (18) so th a t th e net v e lo c ity becomes ( 2 0 ) v - ( F - ^ F ) w — Av (19) AV - ^ a g o r (20a) V 25. where the q u a n tity K i s d efin ed by th e Debye-Huckel equa tio n ( 2 1 ) K 2 = ± * £ r £ n lZ 2i and where e i s the e le c tro n ic charge, JD th e d i e l e c t r i c c o n sta n t, th e c o n c e n tra tio n o f th e i - t h ion and z^ i t s charge. Since both th e r e la x a tio n term and th e e le c tr o p h o re tic term depend upon th e f i r s t power of K, they are th e re fo r e p ro p o rtio n a l to th e square root of th e concentra tio n . H a rtle y 4 4 has considered th e a p p l i c a b i l i t y of th e Debye-Huckel th eo ry to c o llo id a l e l e c t r o l y t e s and fin d s th a t t h i s approach should giv e the v a r ia tio n o f m o b ility w ith c o n c e n tra tio n w ith in 3 o r 4 p e rc e n t. Equation (20a) a t zero c o n c e n tra tio n reduces to equation (3) (3) u s qw - q /f which, assuming a s p h e ric a l p a r t i c l e again becomes th e Huckel equ atio n (7) u - -jftjf 6 1 pn The above a n a ly s is has dem onstrated t h a t , i f i t i s p o s s ib le to e x tra p o la te the m o b ility of th e c o llo id a l elec- 4 4 H artley , T rans. Farad. Soc., 31, 31 (1935) 26. t r o l y t e to i n f i n i t e ' d ilu tio n , then th e Huckel equation may he used to c a lc u la te th e z e ta p o te n tia l o f th e p a r t i c l e . Then, assuming th a t th e ra d iu s of th e sp h e ric a l p a r t i c l e i s known, th e charge of th e p a r t i c l e may he c a lcu la te d from th e z e ta p o te n tia l assuming th a t th e d i e l e c t r i c co n stan t of th e so lv en t in th e v i c i n i t y of th e p a r t i c l e i s th a t of th e hulk so lv e n t. I t i s p o s s ib le , however, to c a l c u la te t h i s charge w ithout any assum ptions as to th e siz e o r shape o f th e m ic elle and independent of th e n a tu re of th e d i e l e c t r i c co n stan t in th e v i c i n i t y of th e m ic e lle . A ll th a t i s needed i s a knowledge of th e d if f u s io n c o e f f i c ie n t o f th e m ic e lle . In dem onstrating th e above statem ent we s h a ll fo llo w th e same procedure as was used f o r th e e le c tro p h o re s is . F i r s t th e case o f th e uncharged p a r t i c l e w ill he co nsidered, th e n th a t o f th e c o l lo lc a l ion alone, and f i n a l l y th e c o l lo id a l e l e c t r o ly t e in th e presence o f o th e r io n s. The b a sic eq u atio n which we s h a ll use in estim a tin g th e siz e and th e f r i c t i o n a l c o e f f ic ie n t of th e m ic e lle i s one due to E in s te in and S u th erlan d , namely ( 2 2 ) D . SE where D i s th e measured d if fu s io n c o e f f ic ie n t, R the gas c o n sta n t, T th e ab so lu te tem p eratu re, N Avogadro*s number 27. and f th e f r i c t i o n a l r e s is ta n c e th e m ic e lle experiences upon p assin g through th e medium. According to S to k e s 1 law f becomes, fo r s p h e ric a l p a r t i c l e s , (23) f s 6 /r n r where n i s th e v is c o s ity of th e medium and r th e ra d iu s of th e sphere. Making t h i s s u b s titu tio n we get ( 9 4 .1 p\ B S D W P ~ SfFESr? The d e riv a tio n o f equation ( 2 2 ) given by G-lasstone^ 5 i s based upon th e assum ption th a t th e k in e tic th eo ry of gases may be ap p lied to suspended p a r t i c l e s . C onsider a c y lin d e r w ith a c r o s s - s e c tio n a l a re a of 1 sq. cm. co n tain in g b suspended p a r t i c l e s , i . e . , m ic e lle s, p e r u n it volume a t a g iv en p la n e, and b - db p a r t i c l e s a t a given d is ta n c e dx from th e f i r s t p la n e. \ > 4— 4* — * ^ C lasstone, Textbook of P hysical C hem istry, 1940, p. 254. 28. Assuming th a t th e k in e tic theory o f gases may be a p p lie d to th e suspended p a r t i c l e s , th en th e p re s s u re due to t h e i r impacts at th e f i r s t plane i s given by (25) p - i mbc^ 3 where m i s th e mass o f th e p a r t i c l e and o^ i s th e mean square speed of th e in stan ta n eo u s Brownian movement. At a d ista n c e dx to th e r ig h t i t i s (26) p - dp - rn(b-db) Thus (27) dp - -g mc^db The fo rc e F a c tin g on a single p a r t i c l e i s , in t h i s case where we co n sid er u n it c ro s s s e c tio n area, equal to th e p re ssu re g ra d ie n t |j£ d iv id e d by n, th e number of p ar t i c l e s . T herefore Now th e average v e lo c ity which a p a r t i c l e w ill acq u ire when i t i s acted on by a fo rc e F i s lim ite d by th e f r i c tio n a l r e s is ta n c e f of th e medium, o r (29) v « F T herefore C onverting to moles p er u n it volume, we o b ta in th a t th e q u a n tity d if f u s in g in u n it tim e, 2 ^, i s vb mc^ db T “ s 3fN * cB c (31) - S2 The d if f u s io n c o e f f ic ie n t D i s d efin e d as th e q u a n tity of m a te ria l d if fu s in g a c ro s s a 1 om^ a re a when th e co n cen tra tio n g ra d ie n t ^ * s u n i t y • Thus i t follow s t h a t (32) D = Now th e k in e tic energy of a suspended p a r t i c l e i s (33) | - | kj. T herefore ( te ) D - *1 - | | Equation (34) has been used to determ ine Avogadro*s number. Values in th e neighborhood of 6 x 1 0 ^ have been o b tain ed f o r p a r t i c l e s o f gamboge, c o llo id a l gold, and c o llo id a l selenium .4® Although such agreement seems to len d 4 6 Svedberg, C o llo id a l C hem istry, 1924, p. 94. 30. support to th e v a l i d i t y of eq uation (33), th e agreement was probably a c c id e n ta l, due to th e presence of small amounts o f sin p le io n s . C o llo id a l e l e c t r o l y t e s , as w ill be shown below, need not obey equation (34) u n le s s c e r ta in o th e r c o n d itio n s a re f u l f i l l e d . H a rtle y 4^ f i r s t recognized th a t th e tr u e d riv in g fo rc e cau sin g d if fu s io n is th e g ra d ie n t of th e chem ical p o te n tia l o f th e d if f u s in g substance. T his concept, as H artley shows, p erm its th e d e riv a tio n of th e necessary equations f o r the d if fu s io n o f c o llo id a l e l e c t r o ly t e s in a rig o ro u s manner. The d if fu s io n o f c o llo id a l e l e c t r o ly t e s , o r fo r th a t m a tte r any charged c o llo id , cannot be d iscu ssed w ith out a c o n s id e ra tio n of th e e l e c t r i c a l fo rc e s which are involved. In th e absence of o th e r e l e c t r o ly t e s th e c o l lo id a l e l e c tr o ly te i s p u lle d ahead by th e e l e c t r i c a l poten t i a l c re a te d by th e d if fe re n c e in th e r a te of d if f u s io n of th e c o llo id a l ion and th e simple io n . The a d d itio n o f a second e le c tr o ly te reduces t h i s p o te n tia l, and th e d if f u sio n c o e f f ic ie n t o f th e c o llo id a l ion drops as more of th e second e l e c t r o ly t e i s added, u n t i l e v e n tu a lly th e c o llo id a l 4 7 H artle y , P h il. Mag., 12, 473 (1931). 31. ion d if f u s e s independently of th e o th e r ions and th e Ein s te in S u th erlan d equation w ill he a p p lic a b le . These con c e p ts w ill now be developed m athem atically follow ing in p r in c ip le th e method of H a rtle y , 4 * 7 , 4 8 but w ith some s a c r i f i c e of th e rig o r employed by him. As alread y m entioned, in a d d itio n to the g ra d ie n t of chem ical p o te n tia l, <)/*/j x, a g ra d ie n t of e l e c t r i c p o te n tia l, c )s/c )x , i s e s ta b lis h e d when ions having d i f f e r ent m o b ilitie s a re d if fu s in g . The v e lo c ity im parted to th e c o llo id a l ion by th e s e fo rc e s i s ( 3 5 ) T„ _ . u T f c + 4 1 v ' 0 ~ c I J I T + TTx where u 0 i s th e m o b ility of th e c o llo id a l ion. Since th e chemical p o te n tia l i s g iv en by th e ex p ressio n (36) =yC*Q t ln a 0 where R, T and JT a re th e gas c o n sta n t, tem perature and Faraday co n stan t re s p e c tiv e ly , ac th e a c t i v i t y in equiva le n ts p e r u n it volume, and qQ th e charge of th e c o llo id a l ion* S u b s titu tin g (36) in (35) g iv e s 40 H a rtle y and Robinson, P roc. Roy. Soc., A134, 20 (1 9 3 2 ). A s im ila r eq u ation may be w r itte n fo r th e g e g en io n s < « r l * « , 5 1 Observing th a t th e a c t i v i t y i s expressed as an eq u iv alen t c o n c e n tra tio n and th a t th e re fo re art - a and t h a t th e v e- c - g lo c i t y vG must equal v , i t i s p o s s ib le to e lim in a te th e p o te n tia l g ra d ie n t from equations (37) and (38) and ob ta in , a f t e r making th e s u b s t itu ti o n a - o(,c, where i s th e a c t i v i t y c o e f f ic ie n t and c th e eq u iv alen t c o n c e n tra tio n (39) S — Cv — — 22. ,°. - U & . ( i - r i- .) ( j . J i n p < \ ^ c r o+ ug o ns WfT where S i s th e q u a n tity of so lu te tra n s p o rte d through u n it area in u n i t tim e and u > th e m o b ility in cm .^ /v o lt-sec* But F ic k 's law o f d if f u s io n s t a t e s th a t (40) S = - D 4 ^ o) x so th a t th e r e l a t i o n between th e d if fu s io n c o e f f ic ie n ts and m o b ilitie s o f th e ions is g iv en by (41) D = S ..-°U S.. ■ fi . I n i fl 1 JT u 0 t + - I n o J ^ For u n i-v a le n t e l e c t r o ly t e s a t i n f i n i t e d ilu tio n , 35. equation (41) reduces to N e rn s t's 4 9 equation (eq u atio n 42) (42) D a 2RT ucug ~7* ui Equation (41) was f i r s t d erived by H a s k e ll^ who, however, co n sid ered osmotic p re s s u re as th e d riv in g fo rc e and whose equation lacked th e a c t i v i t y c o e f f ic ie n t term . N eglecting th e v a r ia tio n of a c t i v i t y c o e f f ic ie n t w ith c o n c e n tra tio n , eq u atio n (41) may be w ritte n E quation (43) c u rio u sly enough p r e d ic ts much h ig h e r d if fu s io n c o e f f ic ie n ts f o r c o llo id a l e l e c t r o ly t e s than have a c tu a lly been observed. Thus, a n tic ip a tin g d a ta f o r potassium la u r a te to be p re se n te d l a t e r in t h i s t h e s i s , th e m o b ility o f th e potassium la u r a te m ic e lle i s approxim ately 4 x 1CT4 cm.^ / v o l t - s e c . and n0 is approxim ately 10. Using 8 . 1 x 1 0 “*4 as th e m o b ility o f th e potassium ion, th e d i f fu sio n c o e f f ic ie n t i s c a lc u la te d to be D = 7 ,5 x 10~ 6 cm .^/sec. The value re p o rte d by Lamm^ 5 i s D - 9 .9 x 1 0 ~ 7 cm.2/s e c 5 0 H askell, Phys. Rev., 27, 145 (1908). 34 The low er r a te of d if f u s io n o f the c o llo id a l io n which is a c tu a lly observed i s undoubtedly due to presence of th e simple potassium and la u r a te ions, p re s e n t as a consequence of th e thermodynamic e q u ilib riu m between sim ple m olecules and m ic e lle s . This can be shown in a p e r f e c tly g eneral manner by co n sid erin g th e e ffe c t o f adding a second e le c tr o ly te , w ith io n ic m o b ilitie s ua and u^ to th e c o llo id a l e le c t r o ly t e . I n i t i a l l y th e only fo rc e s a c tin g on th e s e ions w ill be th e e l e c t r i c a l fo rc e s set up by th e d iffu s io n of th e c o llo id a l ion and i t s gegenions. The r a te s o f tr a n s f e r of th e s e two added ions in e q u iv a le n ts p er cm. p e r sec. w ill be where c* r e f e r s to th e c o n c e n tra tio n of th e second e le c t r o l y t e . Furtherm ore, th e re r e s u l t s from th e c o n d itio n of e l e c t r i c a l n e u t r a lity In a d d itio n F ic k 's equation f o r th e d iffu s io n o f th e c o l lo id a l e l e c t r o ly t e must be w ritte n (44) S a and (45) (46) s a f ap = 8b ♦ s 0 (47) S0 = - D Equation (38) may be r e w r itte n s _ -U gR T £ c , „ r t 3 E S = " q ^ r eT E *' g 3~S © w hile eq uation (37) may be r e w r itte n as (49) S„ - - UcRT J o _ u 0 J E 0 - qc9 " Uo° -gic S u b s titu tin g (44), (45) and (48) in to equation (46), one o b ta in s = f ub + u, (50) S„ s |(u ^ + ua ) o ' + cu( e) E < j O J x " qg^ - x Equations (49) and (50) may be solved sim ultaneously to give (51) S - j f o T (us/ % - UqA o ) 1 0 - y r % 9 x l 0 u c + Ug + ( u b 4 . 5 ^ c T / c J and comparing w ith (47) th e re is o b tain ed th e d if fu s io n c o e f f ic ie n t of th e c o llo id a l e l e c t r o ly t e in th e presence of o th e r ions as (52) , = g ^ f n . a , ' , . . . I r qo L u0 + ug * lub + V 0 ’/ 0 J Equation (52) was f i r s t d e riv e d by H artley and th e above d e riv a tio n i s e s s e n ti a ll y h i s . For c ’ - 0, equ atio n (52) reduces to (43), w hile fo r c 1)^ c, i t becomes RTu0 36. Equation (53) shows th a t in th e presence of a hig h c o n c e n tra tio n of a second e le c t r o ly t e , the c o llo id a l e le c t r o l y t e moves independently o f the o th e r ions in so lu tio n a t a r a te determ ined so le ly hy i t s own m o b ility . S u b sti tu tin g th e p revious v alu es o f n. and u in to equation (53) c c g iv es a d if f u s io n co n sta n t of D - 10.3 x 1 0 “ 7 cm.2A o l t - s e c . in b e t t e r agreement w ith th e experim ental value th a n was obtained w ith equation (43). I t remains to show th a t the E in ste in -S u th e rla n d d if fu s io n eq uation i s a p p lic a b le to c o llo id a l .e le c tr o ly te s . The m o b ilitie s o f th e c o llo id a l io n and i t s gegenions may be expressed by (34a) u ' c - q0 / f Q ( 3 4 b) u ' g = y ?g where th e q*s are the charges and f* s th e f r i c t i o n a l re sis ta n c e , and u ' i s th e m o b ility in a b s o lu te u n i t s . Sub s t i t u t i n g th e se eq u atio n s in (43) g iv e s the g e n e ra liz e d E in s te in equation fo r a c o llo id a l ion gqc cqg which, i f th e ion i s s p h e ric a l and Stokes * law i s a p p lic ab le , may be w ritte n 37. (55a) D - RT go + qg - eirnN q0 r g + qgr 0 R T Equation (55a) was f i r s t d eriv e d by Svedberg and l a t e r by H artley but seems somehow to have been fo rg o tte n . The lim itin g E in s te in d if f u s io n eq u atio n f o r e lec tr o l y t e s in th e p resence o f an excess o f second e le c tr o ly te may be o b ta in ed by s u b s titu tin g eq u atio n (54a) in to th e lim itin g d if fu s io n equation (53), g iv in g (56) - fP o r ( 56a) Dq - which i s id e n tic a l w ith th e g e n e ra lly accep ted form o f th e E in s te in eq u atio n . I t should be p o in te d out th a t applying th e generally accepted form of th e E in s te in equ atio n to c o llo id a l io n s in th e absence of any second swamping e l e c t r o ly t e in tr o duces an e rro r which i s co n sid erab ly g r e a te r th a n any e rro r due to th e d e te rm in a tio n of th e d if fu s io n c o e f f ic ie n t of th e c o llo id a l ion. U sing th e v alu es n - 10, n r 1, c g - r - 21 %, r - 1 .3 fi, we have as th e r a tio of equations ^ © (55a) and (56a) 0 * < * c> r c ^ ^ fr- - a * 6 * 8 0 Tqc^g + ^gr a^ 5 1 Svedberg, K olloid Z ., 36, 62 (1925). 38. B efore concluding t h i s th e o r e tic a l se c tio n , i t re mains to c o n sid er whether o r not th e c o n c e n tra tio n o f simple ions in eq u ilib riu m w ith th e c o llo id a l m ic e lle i s s u f f ic ie n t to ensure th a t th e E in ste in -S u th e rla n d equation i s obeyed. I t w ill be assumed t h a t t h i s eq u ilib riu m con c e n tr a tio n of simple io n s i s given a t a l l c o n c e n tra tio n s by th e c o n c e n tra tio n of simple io n s e x is tin g at th e CMC. For potassium la u r a te , the C M C o ccu rs a t about 0.026 /Y w hile a 9# so lu tio n , th e h ig h e st c o n c e n tra te used in our e le c tro p h o re tic m o b ility d eterm in atio n , is s li g h tly le s s th a n 0.38 N. Assuming th a t th e re a re about 170 m olecules p e r m ic e lle and th a t te n of th e se are io n ized , th e equiva le n t c o n c e n tra tio n of th e m ic e lle s i s about ■ ! ? . C .1 P.), n V to o r 0.021 N. Assuming th e m o b ility of th e la u r a te ion to be approxim ately 4 x 10“4 , of th e potassium ion 8.1 x 1 0 “4 , and of th e m ic e lle to be 4 x 10*"^, we o b ta in th e value of 3 .8 fo r th e b ra c k e tte d term of equation (52), im plying th a t th e measured d if f u s io n c o e f f ic ie n t w ill be almost fo u r tim es la r g e r than th e lim itin g v alu e. Normal ly , however, 4 mol p e rc e n t o f potassium hydroxide measured on the soap i s added to th e potassium la u r a te so lu tio n to prevent h y d ro ly s is . Furtherm ore th e d iffu s io n measurement may be perform ed a t c o n c e n tra tio n s s li g h tly above th e CM C, 39. say 2$ by weight o r about 0.083 N. The b ra c k e tte d term th en drops to 1 . 1 2 , reducing th e d if f u s io n c o e f f ic ie n t to w ith in 1 2 $ of th e th e o r e tic a l lim itin g v alu e. The above d isc u ssio n has dem onstrated th a t th e Ein s te in d if f u s io n eq u atio n can only be ap p lie d to c o llo id a l e l e c t r o ly t e s under s p e c ia l c o n d itio n s which provide f o r a s u f f ic ie n t c o n c e n tra tio n o f swamping e le c tr o ly te , so th a t th e m o b ility of th e c o llo id a l ion i s u n in flu en c ed by th e p resence o f i t s gegenions. U n fo rtu n a tely , i t has also developed th a t th e p resence o f sim ple ions in e q u ilib riu m w ith th e c o llo id a l e l e c t r o ly t e i s in s u f f ic ie n t to p rovide t h i s n ecessary swamping e f f e c t and th e d if fu s io n c o e f f i c ie n t may be too la rg e by a f a c t o r of 2 o r 3. A ddition of sm all amounts of a second e l e c t r o ly t e , e .g ., potassium hydroxide, s u f f ic ie n t to prevent h y d ro ly sis may reduce th e e r r o r to 1 2 $ but la r g e r amounts of e l e c t r o ly t e should be avoided, sin ce they undoubtedly a f f e c t th e s ta te of aggre g a tio n of th e m ic e lle . G-ranath2 3 has shown th a t la rg e changes in th e p h y sic al p r o p e r tie s o f th e m ic e lle of p o ta s sium m y rls ta te and potassium la u r a te occur w ith in c re a sin g s a l t c o n c e n tra tio n . The E in s te in d if fu s io n equation cannot th e re fo re be a p p lie d t o p u b lish ed d if f u s io n c o e f f ic ie n ts of c o llo id a l e l e c t r o ly t e s w ith any deg ree of confidence u n le s s th e experim ental c o n d itio n s a re also a v a ila b le . The technique o f dye ta g g in g of th e m ic elle d is cussed in C hapter I may, however, he used to e lim in a te th e u n c e rta in ty in th e d if fu s io n c o e f f ic ie n t a r is in g from th e presence of th e gegenions. I f , f o r example, th e so lu tio n s on th e o p p o site sid e s of th e d if fu s io n membrane a re iden t i c a l except f o r th e p resence of a small amount o f dye s o lu b iliz e d in the m ic e lle on one sid e of the membrane, th en th e only d riv in g fo rc e causing d if f u s io n is the chem ic a l p o te n tia l of the tagged m ic e lle , sin ce th e gegenions a re alread y uniform ly d is t r ib u t e d throughout th e system. The e l e c t r i c a l p o te n tia l term a r is in g from th e need fo r e l e c t r i c a l n e u t r a lity has now been elim in a ted . The r a t e of t r a n s f e r of th e c o llo id a l ion i s then given by And com parison w ith Ficfc!s eq u atio n (57) g iv es again equa t i o n (55) w hile u sin g th e eq u atio n (54a) we o b ta in ag ain th e E in s te in equation (56) RTuc (57) 4 1 . The above d is c u s s io n shows th a t d if f u s io n v alu es obtained by m ic e lle tag g in g tech n iq u es may be d i r e c t l y used to c a l c u la te th e f r i c t i o n a l c o e f f ic ie n t o f the m ic e lle . F u rth e r more, i t has a lso been shown th a t in s u f f i c ie n tly d ilu t e so lu tio n s th e e le c tro p h o re tic m o b ility is given by th e quo t i e n t of th e m ic elle charge and i t s f r i c t i o n a l c o e ffic ie n t in th e same so lu tio n . The theory of th e e le c tro p h o re tic m o b ility and d if fu s io n of c o llo id a l e le c t r o ly t e s has th e r e fo re been developed, and the method of o b ta in in g th e mi c e l l e charge from measurement of th e s e q u a n titie s has been In d ic a te d . I t should perhaps be p o in te d out th a t, h i s t o r i c a l l y , charges on c o llo id a l p a r t i c l e s have not g e n e ra lly been determ ined by a com bination of d if f u s io n and e le c tro p h o re s is but by th e l a t t e r alo n e, u sin g equations (7), (10), o r (13), and making some assum ption as to the. siz e of th e p a r t i c l e . An ex ten siv e d isc u ssio n o f th e se o th e r methods and t h e i r a p p lic a tio n to s p e c if ic systems i s to be found in th e ch a p ter on e le c tro p h o re s is in A lexander and Johnson’s book. 52 Alexander and Johnson, C o llo id S cience, 1949. CHAPTER I I I ELECTROPHORETIC APPARATUS A N D EXPERIMENTAL RESULT S The co n v en tio n al methods f o r determ ining m o b ility may be d iv id ed in to a n a ly tic a l and moving boundary methods. In th e a n a ly tic a l methods th e change in c o n c e n tra tio n o f th e ion i s determ ined a f t e r the passage o f a known amount of c u rren t through a boundary. The boundary may be formed by an e le c tro d e as in th e H itto r f method, or by another 53 s o lu tio n as in H a rtle y 1s method. Moving boundary meth ods, such as th a t ex te n siv e ly developed by T is e liu s , Mc- Innes and Longsworth, measure d i r e c t l y th e r a te of motion in a known p o te n tia l g r a d ie n t. T ra c e rs, in s p it e of th e fa c t th a t they o f f e r some advantages, do not seem to have been used except by Brady, ^ whc used ra d io -is o to p e s in th e development o f h is “a n a ly tic a l boundary” method. The use o f t r a c e r s in e le c tro p h o re s is p erm its th e measurement of th e movement of a boundary between two s o lu tio n s having id e n tic a l composi- 53 H artle y , T rans. Farad. Soc., 30, 648 (1934). 5 4 Bracly, J . Am. Chem. S oc., 70, 91X (1948). 4 3 . tio n and th u s e lim in a te s a l l boundary anom alies stemming from changes of com position a t th e boundary. In a d d itio n , t r a c e r e le c tro p h o re s is a lso p erm its th e la b e lin g of a com ponent o f th e s o lu tio n which i s not otherw ise a c c e s s ib le to a n a ly s is . By u sin g dyes as t r a c e r s , i t i s p o s s ib le to observe v is u a lly th e behavior of the tagged s o lu tio n and to fo llo w i t s motion in th e a p p a ra tu s. However, th e u se of t r a c e r s in e le c tro p h o re s is c r e a te s a d i f f i c u l t y a l l o f i t s own. The d en sity d iffe re n c e s which, along w ith m obil i t y d iffe re n c e s , s t a b i l i z e th e boundaries in th e u su al tech n iq u es, are now e lim in a te d and, u n le s s a p p ro p ria te p re ca u tio n s a re taken, co nvection and e le ctro o sm o sis soon render measurements im p o ssib le. The use of r a d io a c tiv e t r a c e r s h elp s in determ ining th e p r o p e r tie s of soap s o lu tio n s , as has been shown by Brady and S a l l e y , ^ but does not h elp in s e p a ra tin g th e p r o p e r tie s of m ic e lle s from th o se of th e sim ple ions w ith which th e m ic e lle s a re in e q u ilib riu m . W ater-in so lu b le dyes which are s o lu b iliz e d by th e m ic e lle , on th e o th e r hand, a c t as a tr a c e r which ta g s th e m ic e lle alo n e since th e only way in which th e dye may move i s by r id in g in a m ic e lle . With a dye such as Sudan IV, th e re a re more than 5 , 0 0 0 dye m olecules in sid e m ic e lle s f o r every one which is in t r u e so lu tio n in th e w ater. The motion o f 4 4 . th e l a t t e r th u s makes a n e g lig ib le c o n trib u tio n to th e t o t a l m otion. Since, under most c o n d itio n s, th e re is on th e average le s s than one dye molecule per m ic e lle , and since th e dye is of th e ord er of 1 $ by weight o f the t o t a l m ic e lle , i t i s lik e ly t h a t th e dye a c ts as a tr u e t r a c e r and does not ap p rec iab ly modify th e p r o p e r tie s o f th e mi c e l l e . The f i r s t attem pt to observe th e e le c tro p h o re tic m o b ility of th e m ic e lle was performed on a p ie c e of f i l t e r paper s a tu ra te d w ith potassium la u r a te s o lu tio n and held between two e le c tro d e s to which te n v o lts d .c . were ap p lie d . A drop o f th e same soap s o lu tio n but c o n ta in in g s o lu b iliz e d dye was p la c e d n ea r th e c e n te r o f th e paper and th e c o lo r observed to m igrate tow ards th e anode. This q u a l i t a t i v e o b se rv a tio n prompted a second, more q u a n tita t i v e atte m p t. The second attem pt to measure th e e le c tro p h o re tic m o b ility of a dye ta g g ed m icelle was perform ed in a con v e n tio n a l T is e liu s a p p a ra tu s o p e ra tin g a t 2°0. and made a v a ila b le to us through th e kindness of Dr. E. Jameson. The system stu d ie d was a 5$ potassium la u r a te s o lu tio n co n tain in g about 0.002$ of Sudan I V . ^ The h e a rt of th e 55 Hoyer and Mysels, J . Phys. G o ll. Chem., 54 , 966 (1950). 4 5 . T is e liu s ap p aratu s i s i l l u s t r a t e d in F igure 1. Here A and A* are th e h alv es o f th e e le c tro p h o re s is c e l l s , B and B 1 th e e le c tro d e v e sse ls, and E and E 1 th e s i l v e r - s i l v e r c h lo rid e e le c tro d e s . The l e t t e r a in d ic a te s th e o p tic a lly f l a t windows of the c e l l while c, d and e in d ic a te th e shear p la n e s in which th e components o f th e c e l l move and ♦ where th e boundaries a re formed. In usin g th e ap p aratu s th e e le c tro d e s E and E 1 were com pletely covered w ith sa tu ra te d potassium c h lo rid e . The rem ainder of th e a p p a ra tu s was th e n f i l l e d w ith th e 5$ potassium la u r a te s o lu tio n except f o r th e h a lf c e ll A 1 and th e base p la te below A*. The rig h t h a lf o f A1 was f i l l e d w ith th e 5fo potassium la u r a te s o lu tio n w hile th e l e f t h a lf co n tain ed 5% potassium la u r a te s o lu tio n tagged with a few m illig ram s of Sudan IV p e r l i t e r o f s o lu tio n . The base p la te co n tain e d the same la b e le d soap s o lu tio n . O rig in a lly th e se c tio n A 1 was s li g h tly d isp la c e d tow ards th e l e f t so th a t th e la b e le d and u n la b ele d s o lu tio n s were sep arated . A fte r tem perature eq u ilib riu m was e s ta b lis h e d , th e hydro s t a t i c p re s s u re s were equated by means o f th e two stopcocks and a p ie c e of connecting tu b in g . Then, a t th e s t a r t of th e experim ent, th e s e c tio n A1 was pushed into th e p o s itio n shown in F ig u re 1 and a p o te n tia l ap p lie d to th e e le c tro d e s . From a knowledge o f th e observed r a t e o f m ig ratio n , u, o f 4 6 . 4 7 . th e boundary, th e c ro s s se c tio n area, A, of th e c e l l , th e s p e c ific c o n d u c tiv ity , k, of th e soap so lu tio n and th e c u r re n t, i , p a ssin g th rough th e c e l l , one may c a lc u la te th e e le c tro p h o re tic m o b ility of th e m icelle from th e equation (1) U In our experiment an unexpected e f f e c t was observed upon applying th e p o t e n t i a l . The boundary, in s te a d of r e maining f l a t and m ig ratin g at a uniform r a te , soon acq u ired an in c re a s in g ly p a ra b o lic shape and remained in t h i s shape as i t m igrated th ro u g h th e c e l l . T his e f f e c t is presumably due to th e electro o sm o sis of th e liq u id due to th e ze ta p o te n tia l a t the in te r f a c e between th e g la s s w a lls and th e s o lu tio n . T his e f f e c t is commonly observed with th e m icro e le c tro p h o re s is ap p aratu s but not w ith th e T is e liu s , since th e d en sity d iffe re n c e s norm ally e x is tin g a c ro ss th e boun dary prevent th e e f f e c t . In our case th e re i s no d e n sity d iffe re n c e acro ss th e boundary and e le c tro o sm o sis may occur. For a re c ta n g u la r c e ll in which b o th electro o sm o sis and e le c tro p h o re s is occur, the tr u e e le c tro p h o re tic v elo c ity may be observed a t a d ista n c e from th e w alls of 2 1 . 1 $ of th e t o t a l w idth. Since we were unprepared fo r th e e f f e c t in t h i s f i r s t experiment we observed th e apex of th e p a ra b o la . The e rr o r due to t h i s is probably of the o rd e r o f 50io sin ce th e sid e s o f th e parab o la also m ig rate in th e 48. f i e l d . Table 1 l i s t s the re le v a n t d a ta . A second experim ent was th e n planned f o r th e same system but w ith p ro v isio n s f o r v is u a l o b se rv a tio n of th e p a ra b o lic boundary a t 21.1$ from the w a ll. In a d d itio n , % p re v is io n was made f o r photographic o b se rv a tio n o f th e boundary. However, i t again proved im possible to make th e p ro p er v is u a l o b se rv a tio n s due to the speed of th e boundary and in ste a d th e p o s itio n s of th e peak had to be oserved. These a re re p o rte d in T ables 2 and 3. The d a ta provided by the photographs, however, (F igures 2 to 14) proved s a t i s fa c to ry fo r a n a ly tic a l tre a tm e n t. The p ro p er p o s itio n of th e boundary could be observed and from t h i s th e r a te of m igration of the d y e -a ic e lle complex was c a lc u la te d . For some unknown reaso n th e ascending boundary in th e photograph was le s s d i s t i n c t th a n the descending boundary and seemed to move f a s t e r . In analyzing the d ata, b o th boundaries were, however, used and the r e s u ltin g m o b ilitie s averaged. A ll photographs were ta k en a t te n minute i n te r v a ls except f o r th e in te rv a l between F igures 8 and 9 which was twenty m inutes. In Table 5 th e r e is l i s t e d th e charge on the potassium la u r a te m ic e lle . A n tic ip a tin g th e r e s u l t s of th e next ch ap ter, t h i s value was tak en from th e d iffu s io n c o e f f ic ie n t of th e potassium la u r a te m ic e lle run a t 2 °C. u sing dye t r a c e r te ch n iq u e . Assuming, as d isc u sse d in TABLE I ELECTROPHORESIS- OF POTASSIUM LAURATE'SOLUTIONS EXPERIMENT #1 Time of m ig ratio n 127 minutes D istance tra v e le d 5 .5 7 cm C urrent 0 .0 1 amp Area of c e l l 0.76 cm 2 S p e c ific c o n d u c tiv ity 6.85 x ■ 10~& mhos M obility of m ic e lle 2 .3 x -,~ 1 0 - 4 cm ^/volt Temperature 2° c 4 9 . sec 5 0 . TABLE I I MIGRATION OF ASCENDING B O U N D A RY - Time R e f e r e n t P o s itio n Bom dary P o s itio n (cm) (cm) 8:00 0.4466 1.0022 8-08 : 0.4177 1.8956 8 :18 0.4156 1.5812 8 :28 . 0.4142 1.8402 8-58 7. . 0.4153 2.3162 8 *48 ■ ' ’ 2.6306 8*58 0,4236 ’ \ " , 3.0096 9:08 '*6^4257 ‘"’{v 3.2567 9 : 1 8 ' • . 0,4253 ' 3.6085 ■ ■ ■ • i 1 k . £ * * : « ! .< .'is * * • •' ,v; •. . - r i - -v ' 9:28 0.4268 , 3.7995 9 ;38 0.4273 4.1263 9 :48. - -0 .4232 V - “v V £..$423 4 1 ' Time 8 ;19 8 : 89 8 :39 8 j 49 8 ; 59 9 : 09 9;19 9 S 29 9:59 9:49 5 1 . TABLE I I I MIGRATION OF DESCENDING BO U N D A RY ■ Boundary: p o s itio n 0,3828 4.5082 0.3762 3.9726 0.3682 5.7453 Q.g762 ; \h . 3.7331 0.3798 3.5331 0 .3 8 1 2 ' ‘ 3.3041 0 43936 i : . 5.0737. 7 ■ . ' ' 7,. ■ , ; * 0.3924 : r.. 2.8426 . 0.5871 2.6201 0.3767 ’ 2.2892 52. "Ti s g Iihs / -# F / p w r « J * T ls e /|M 5 B o n tc /jr F i g u r e T i s e h u s & out h c/d F* I g m r G 4 v.' T i s * I m s y 53. 4 F* t f u r e 7 *7"/5' & / / « $ 3 o < 4 h d d > y V % . • 55. F l* Hr e f T t i e / t l i S 3 *>'<"'/*>■ V / u f V F t g u r e. ^ T ( 5 e / < « 5 * -ry 53. F r y u r e 7"/3 & / / C f ? $ 6 * * J Q .T T y TABLE IV ANALYSIS O F FIGURES 2 TO 14 F ig u re No, Descending Boundary Ascending Boundary D istance Hate Distance. Hate 2 0,19 0 . 0 0 ------ 3 0,59 0.040 0.26 0.026 4 0,87 0.034 0.49 0.025 5 1 . 0 2 0.028 1 . 0 1 0.034 6 1,41 0.031 1.35 0.034 7 1.51 0.026 1 . 8 8 0.038 8 1 . 8 8 0.028 2.44 0.041 9 2.13 0.024 3.05 0.038 1 0 2 . 2 1 0.023 3.22 0.036 1 1 2.48 0.023 o . o Q 0.036 1 2 2.93 0.025 3.95 0.036 15 0 . < £ < 4 0.025 4.35 0.035 14 5.46 0.025 4.83 0.037 Average 0.027 0.036 Conversion f a c t i o n from photograph to a c tu a l c e l l is TABLE V ANALYSIS OF FIGURES 2 TO 14 5 / POTASSIUM LAURATE Average v e lo c ity C urrent Area of c e l l S p e c ific co n d u c tiv ity M o b ility of m ic e lle U nit n eg a tiv e charges per m ic e lle Temperature 3*78 x 10-4 cm2/s e c 0 * 0 1 amp 0.76 cm 6*99 x 1 0 - 3 mhos 2 , 0 x 1 0 ~ 4 cm2/ v o l t 12 2 ° C 61. C hapters I and I I , th a t th e f r i c t i o n a l r e s is ta n c e to d i f fu sio n is th e same as th e f r i c t i o n a l re s is ta n c e to e le c tr o p h o re tic m ig ratio n at i n f i n i t e d ilu tio n , then th e charge may r e a d ily be c a lc u la te d from th e equation <2 ) q = j j £ u The low tem p eratu re of th e conventional T is e liu s ap p aratu s which i s so advantageous when vorking with pro te in s in tro d u c e s g re a t lim ita tio n s f o r a s s o c ia tio n c o llo id s which, in g e n e ra l, a re q u ite in s o lu b le at th is tem p eratu re. An o p e ra tin g tem perature o f 25°C. would be h ig h ly d e s ira b le sin ce many o th e r p r o p e r tie s of th e s e c o llo id s a re known a t t h i s tem p eratu re. At t h i s h ig h e r tem perature i t is no lon ger p o s s ib le to use the T is e liu s ap p a ra tu s, sin ce at 25°C. th e d e n s ity of w ater v a r ie s g r e a tly with te m p eratu re. The unavoidable h e a tin g e f f e c t s accompanying th e passage of th e c u rren t th ro u g h th e c e l l would produce convection c u r re n ts and make any d eterm in atio n im possible in th e absence of d e n sity d iffe re n c e s to s t a b i l i z e th e boundary. Since, how ever, th e boundary in our system i s not due to any d e n s ity d iffe re n c e , i t i s p o s s ib le to use a h o riz o n ta l type of c e l l . The apparatus of F igure 15 was th e re fo r e co n stru c te d u sin g p a r ts of a co n v en tio n al m ic ro -T ise liu s a p p a ra tu s. The h e a rt of th e app aratu s of F igure 15 i s th e m ic ro -T is e liu s s e c tio n (A) which i s f re e to s li d e up and w □ g FIGURE 15 MICRO TISELIUS APPARATUS 63. down between th e sid e arms (B ). The side arms a re connected to the e le c tro d e vessels (C) through a 3-way stopcock (D) by means of th e b a ll jo in t (E ). The e le c tro d e v e s se l con ta in s a s i l v e r - s i l v e r c h lo rid e e le c tro d e (F) immersed in a s a tu ra te d s o lu tio n o f potassium c h lo rid e which reaches to stopcocks D. The stopcocks (G -) serv e to f lu s h out th e e le c tro d e v e s s e ls \/\hile stopcocks (H) and (I) a re used in f i l l i n g and flu s h in g th e T is e liu s c e l l . In use, the ap p aratu s involved f i l l i n g th e lower compartment of th e T is e liu s c e l l (A-l) w ith soap p lu s dye by means o f stopcocks (I) and the rem ainder of th e appara tu s , up to stopcock D, w ith soap s o lu tio n o f th e same con c e n tr a tio n . The s e c tio n (A) was then pushed downward u n t i l a lig n e d as in F igure 15 and th e e l e c t r i c a l c i r c u i t c lo se d . The p ro g re ss of th e boundary may be follow ed v isu a l l y w ith a c a lib r a te d tr a v e lin g m icroscope or photographic a l ly . Due to the co m p licatin g f a c to r of electro o sm o sis which in tro d u c e s a p a ra b o lic shape to th e boundary, both methods a re r a th e r in a c c u ra te . However, F ig u res 16 to 18 a re photographs of th e boundary at one and two minute i n t e r v a ls f o r d if f e r e n t experim ents. The arrows in d ic a te th e p o s itio n of th e t i p o f th e boundary. From th e se photographs i t can r e a d ily be understood '■ — ----------- / — v 0 ce K s 7 y ^ & T*© ^* vb P*7*cvo 'T 'is ^ ltu s & oct+t(/d 65. why any a n a ly s is of t h i s data would be su b ject to c o n sid e r ab le error* Not only is th e re an u n c e rta in ty as to th e boundary between the tagged and untagged s o lu tio n s , but th e re i s also a sim ila r u n c e rta in ty as to th e so lu tio n -w a ll boundary. In a d d itio n , th e sm allness of th e d ista n c e which th e dye t r a v e l s make any a c cu rate measurement d i f f i c u l t . However, an attem pt was made to c a lc u la te th e e le c tro p h o r- e t ic m o b ility of the potassium la u r a te m ic elle in 5.4$ potassium la u r a te s o lu tio n by m easuring th e a re a swept out by th e dye s o lu tio n . The values o b ta in ed are ta b u la te d in T abl e 6 • The widespread in th e c a lc u la te d m o b ilitie s promp te d a search f o r a more p re c is e method of detet*mining th e m o b ilitie s . An obvious method would be to remove th e so lu tio n from th e T is e liu s c e l l and determ ine th e change in th e dye c o n c e n tra tio n due to the passage o f the c u rre n t. I t was thought th a t t h i s could be accom plished by th e in tro d u c tio n of fo u r re c ta n g u la r, s lo t te d g a te s, two between each sid e arm (B) and th e T is e liu s c e l l (A) . The mode of o p eratio n of th e g a te s i s i l l u s t r a t e d in F igure 19. In 19-1 th e T is e liu s c e l l i s shown w ith th e lower compartment f i l l e d with dye h e ld in p la c e by two g a te s . In 19-2 th e T is e liu s c e l l and th e side arms a re in p la c e and the g a te s are being flu sh e d out with soap s o lu tio n . The g ates a re then moved TABLE VI AMISS IS OF FIGURES 16 TO 18 5 .4 $ POTASSIUM LAURATE F ig u re Ho. M o b ility o m ^ /v o lt-seo 16 4 .3 x 1 0 -4 17 7 .5 x 10-4 5 .0 x IQ"4 Average 5 .6 x 1 0 -4 r ^ * 5 > tfit »< » f / t l-il a « l i nl 19-3 ■ v . w r € I ^ ^ c o n t i n t i e d y 70. downward as in 19-3 and c u rre n t passed through th e appara tu s . A fte r a s u f f i c ie n tly long p e rio d of tim e th e u n its a re again se p a ra te d as in 19-4 and th e d ilu te d dye s o lu tio n removed from th e lower compartment of the T is e liu s c e l l . C o nsiderable experim ental d i f f i c u l t y was experienced in removing th e dye s o lu tio n from th e c e l l . In a d d itio n a p p re c ia b le amounts of grease always seemed to become sus pended in th e s o lu tio n . Five v alu es obtained w ith a 9 .4 $ potassium la u r a te s o lu tio n a re , however, l i s t e d in T able 7. Again th e r e i s a wide spread in the c a lc u la te d v a lu e s. The m o b ility i s c a lc u la te d from th e eq u atio n ( ,) u = ( 0 . - W * V * where C0 and C a re the i n i t i a l and f i n a l co n c e n tra tio n s of th e dye as measured in th e Beckmann spectrophotom eter, V is th e volume o f th e compartment, k th e s p e c ific conductiv i t y of th e s o lu tio n , i th e c u rre n t p assin g th ro u g h the c e l l fo r a tim e t . Equation (3) may be r e a d ily d eriv ed since by d e f in i tio n th e m o b ility i s d efin ed as th e v e lo c ity , ^ caused by a p o te n tia l g rad ie n t E/1, o r (4) u B 1 7 1 But the p o te n tia l g ra d ie n t may be expressed in term s of th e TABLE ¥ 1 1 MOBILITIES IN HORIZONTAL TISELIUS CELL 9*4^ POT AS S IM LAURATE Experiment No. M obility em ^/volt-see 1 1.39 x 10 "*4 2 1.33 x 10~ 4 3 1.32 x 10 ” 4 4 2.53 x 1Q~ 4 5 2 . 1 1 x 1 0 ~ 4 Average 1 .8 x 10~ 4 72 a re a A of th e c e l l , th e sp e c ific c o n d u c tiv ity K o f th e so lu tio n , and the c u rre n t, i , p assed through th e c e l l , so th a t (5) u » IAK i The product vA equals th e volume swept out as th e boundary moves through the c e l l , and t h i s volume in tu r n i s th e prod u c t of th e volume, v, o f th e c e l l and the change in concen t r a t i o n , C0 - C, caused by th e e le c tro p h o re s is . S u b s titu t ing th e se v alu es in (5) gives equation (3 ). T his a n a ly tic a l method is dependent upon the condi tio n th a t th e z e ta p o te n tia l o f th e g la s s in te r f a c e i s le s s th an th a t o f th e tagged m ic e lle . C onsider f o r example Fig u re 20A i l l u s t r a t i n g th e flow w ith in th e c e l l . The v e r t i c a l d o tte d li n e s re p re s e n t th e f,g a t e s tt of th e ap p aratu s and th e p a ra b o lic d o tte d lin e s the flow of th e so lv en t which was i n i t i a l l y at the g a te . T his so lv en t moves to the l e f t ac ro ss th e boundary and to th e r ig h t in th e c e n te r of th e channel. The tagged m ic e lle , on th e o th e r hand, moves to th e rig h t a t a l l le v e ls but more ra p id ly in th e c e n te r. A ll of our so lu tio n s have shown t h i s type of behavior. I t is im portant to observe th a t, alth o u g h th e re 3s an e le c tr o - osmotic flow of w ater, th e re is no net tr a n s p o r t of w ater acro ss any boundary. I s o la tio n o f th e c e n tr a l compartment 7 3. 74. by low ering the g a te s w ill th u s perm it d eterm in atio n o f th e dye which has been c a r r ie d out of th e c e n tr a l compartment by th e e le c tro p h o re tic movement o f th e m ic e lle . Were th e z e ta p o te n tia l of th e g la s s to be g r e a te r th a n th a t of th e m ic e lle , an a n a ly tic a l method could s t i l l be used but would re q u ire th e a n a ly s is of two com partments. R e fe rrin g to F igure 20B, and l e t t i n g A be th e amount of dye c a rr ie d to th e l e f t of B by th e electro o sm o tic flow of th e w ater, th e n an equal amount, A, o f untagged m ic e lle is s im ila rly c a rr ie d to the l e f t of B 1. Hence th e observed change in th e amount of dye between B and B 1 i s a c tu a lly la rg e r by 2A than th e change due to th e m o b ility of the m ic e lle a lo n e. Although th e th e o ry of th e above m ic ro -T ise liu s ap p aratu s seems stra ig h tfo rw a rd , the a c tu a l m anipulation of th e ap p aratu s proved to be unexpectedly d i f f i c u l t . The ap p aratu s of F igure 21 was th e re fo r e c o n s tru c te d and found to be s a tis f a c to r y . In t h i s fig u re , stopcocks D and D 1 and th e b a ll j o i n t s E and E* are id e n tic a l w ith stopcocks 0 and O1 and th e b a l l jo in t s E and E* of F ig u re 15. The U tu b es and double Y of F igure 21 re p la c e th e m itro - T is e liu s p a r ts of F igure 15. E le c tro p h o re sis of the tag g ed m ic e lle now occurs in th e 3 mm. c a p illa r y between stopcocks B and B 1. The d is ta n c e between th e s e stopcocks i s 30 cm., providing V 3 / F i g u r e 21 Open Tube Cell [Ooufi/* Y Cell] 76. a volume of 3.167 cm.^ Tills Is ju s t s u f f ic ie n t to f i l l a standard 1 cm. a b s o rp tio n c e ll f o r th e Beckmann sp e c tro - photomet e r . Using t h i s ap p a ra tu s re q u ire d th a t th e c a p illa r y between B and B' be f i l l e d w ith th e la b e le d soap so lu tio n and th e rem ainder o f th e ap p aratu s to stopcocks D and D* w ith th e u n la b ele d soap s o lu tio n . Below th e stopcocks D th e r e was ag ain p la c e d the s a tu ra te d potassium c h lo rid e s o lu tio n . The U tu b e s, U and U*, and stopcocks, A and A1, served to c a tc h and remove any a i r bubbles caught in th e ap p aratu s as x?ell as to ensure th a t none of th e d en ser potassium c h lo rid e s o lu tio n would e n te r the c a p i l l a r y . One of th e stopcocks A i s norm ally kept open during th e run so th a t any le a k s which might develop q u ick ly become apparent and th e experiment stopped. Before t h i s p re c a u tio n was taken, wide v a r ia tio n was observed in th e measured m o b ili t i e s due to unobserved le a k s . A fter th e run th e stopcocks A, A1, B and B 1 a re opened and the soap so lu tio n between A and B, and A 1 and Bf d rain ed through P and P 1. The double Y c e l l is then removed, th e sid e arms washed w ith water and acetone, and then d rie d . The stopcocks B and B* a re then tu rn e d so th a t the tagged so lu tio n between them can flow in to th e arms 0 and O' of th e c e l l . G-entle rock ing soon p ro v id es good mixing of the co lo re d soap so lu tio n 77. w ith th e undyed s o lu tio n which m ig rated in under the in flu en ce of th e e l e c t r i c f i e l d . T his mixed so lu tio n is then drawn o f f and analyzed f o r dye co n ten t in th e Beckmann spectrophotom eter. Most of th e r e s u l t s to he p resen ted l a t e r were obtained w ith t h i s a p p a ra tu s. In a c tu a l o p e ra tio n i t was found th a t two f a c to r s tended to decrease th e accuracy of the method. I t was once again d isco v ered th a t soap s o lu tio n s a re good d is p e rs in g agents f o r g re a se . Every la b o ra to ry stopcock grease a v a il a b le was ev alu ated in an attem pt to f in d one which would not d is p e rs e in to the soap so lu tio n . F in a lly standard s ilic o n stopcock g rease from th e Dow Chemical Company was s e le c te d as most s a tis f a c to r y . While t h i s g re a se would s t i l l d is p e rs e to some e x ten t, i t d id show a much b e t t e r behavior than any o f th e s ix o th e r ty p e s t e s t e d . The stopcock g re a se would d isp e rs e in th e soap solu t i o n and impart a c e r t a i n clo u d in ess or t u r b i d i t y to i t , w ith a r e s u ltin g in c re a se in th e o p tic a l d e n s ity of th e so lu tio n . This was c o rre c te d fo r by s h if tin g to a new w avelength a t which th e o p tic a l d e n s ity o f th e dye was s lig h t and u sin g th e observed d e n s ity , tim es 1 .4 , as a c o rre c tio n to be ap p lied to the o p tic a l d en sity o f th e so lu tio n at the ab so rp tio n maxima. The f a c to r 1.4 is an ex p erim en tally determ ined 78, q u a n tity o b tain ed by measuring th e change in tu r b i d i t y of the g rease d isp e rse d in th e soap so lu tio n as a fu n c tio n of w avelength. This d a ta i s ta b u la te d in Tables 8 and 9 and, in the range of 400 to 620 m , th e d a ta show th a t the r a t i o of th e wavelengths i f 1.4 tim es th e in v e rse r a t i o of th e t u r b i d i t i e s . Upon f i r s t thought one might have expec te d the tu r b i d i t y to vary as in d ic a te d by th e R ayleigh equat i o n ^ ( 6 ) I - co n stan t f — — |y \ x where I i s th e in te n s ity of s c a tte r e d lig h t a t a d ista n c e x from a p a r t i c l e of volume v, and w here^ i s the wave le n g th of th e in c id e n t l i g h t . Were t h i s eq uation to hold, then th e t u r b i d i t y should vary in v e rse ly as th e fo u rth power of the w avelength. The d a ta in T ables 8 and 9 show th a t t h i s is not th e case, th a t th e tu r b id ity a c tu a lly v a rie s in v e rse ly as the f i r s t power of the w avelength. The a c tu a l ab so rp tio n maxima of Sudan IV is a t 528 m/U . At 625 th e o p tic a l d e n s ity of th e dye i s alm ost zero so th a t th e observed d e n s ity is due to th e d isp e rse d g rease p a r t i c l e s . T his o p tic a l d e n s ity a t 625 m y tiis th e re fo r e m u ltip lie d by 1.4 and th e product su b tra c te d from the o p tic a l d e n sity a t 528 m^t* Table 10 l i s t s th e t u r b i d i t i e s a c tu a lly measured 79. TABLE V III OPTICAL DM SITVVS. W A V ELEN G TH SUDAN IV W 9 .4 $ POTASSIUM LAURATE W avelength O p tic a l 1 (m ) 350 0.702 300 0.783 370 0 .720 M& 0^63 8 § m 0V597 400 0.568 ' -,410 0.523 420 0.482 430 0.448 440 0.425 450 0;417 400 0 .4 3 1 470 0.481 400 0*551 490 0.642 500 0.737 510 0*830 520 0* §06 530 0 .9 5 5 540 0.903 80. Wavelength (m ) 550 560 570 580 590 600 310 620 TABLE V III (continued) O p tic a l D ensity 0.8 5 8 0 .7 8 4 0 .6 0 2 0.37 6 0 .1 8 3 0.09 0 0 .0 5 3 0 .0 3 0 wave, (m 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 81. TABLE IX TUBBIDITM O F SOAP SOLUTIONS D ensity Turbid S o lu tio n Minus D ensity C lear Solu t io n 0 .0 4 8 0 .0 4 9 0 .0 4 9 0 .0 4 9 0.05 1 0 .0 5 3 0 .0 5 3 0 .0 5 3 0.052 0 .0 5 0 0 .0 4 8 0.046 0 .0 4 3 0 .0 4 1 0.03 8 0 .0 3 7 0 .0 3 6 0 .0 3 7 0 .0 3 7 D ensity Clear Solu tio n 0 .3 2 1 0.3 3 8 0 .3 8 9 0.^63 0.552 0 .6 4 1 0.739 0 .7 9 6 0 .8 2 2 82. Wavelength (m ) ■540 550 560 570 580 H Q '"' £On 610 620 625 TIB IS IX (continued) D ensity Turbid S o lu tio n Minus D ensity Clear Solu tio n n.035 0 . 0o3 0 .035 0 .0 6 1 ".027 n #r\p< ± n 0QPA n.^P3 0.02? 0 .0 2 3 D ensity Clear Solu tio n 0 .796 0.^59 0 .6 7 1 0 .5 1 5 0.300 0.128 0.(U8 0 .0 1 8 0.006 0 .0 0 4 83. TABLE X TUKBIDITI O F SOLUTIONS S tandard Dye Sample A fte r Standard Sample S o lu tio n E le c tro p h o r e s is 0 .0 1 2 0.010 0 .0 0 2 0 .0 1 7 0 .0 0 8 O.Q 08 0 .0 1 1 0 .0 1 7 - 0 .0 0 7 0.006 0 .015 - 0 .0 0 9 0 .0 0 7 0 .0 1 3 - 0 .0 0 8 0 .0 0 8 0 .0 1 6 - 0.007 G.QG8 0 .0 3 2 - 0 .0 2 5 0 .0 0 8 0 .0 1 3 - 0.006 0.0 0 7 0 .0 0 9 - 0 .0 0 2 0 .0 0 7 - 0 .0 0 1 0 .0 0 8 j .010 0.010 0.000 0 .0 1 0 0 .0 0 8 0 .0 0 3 0.02 7 0 .0 0 8 0 .0 2 1 0 .0 2 9 0.012 0 .0 2 0 0 .0 3 2 0 .0 2 3 0 .0 0 8 0 .0 0 3 0.000 to o o * o 1 0 .0 0 1 0 .0 0 1 - 0 .0 0 1 0 .0 0 8 - 0 .0 0 3 0 .0 1 1 0 .0 0 9 0 .0 0 2 0 .0 0 8 0 . O il Average 0 .0 1 0 Average 0 .0 0 8 Average 84. on twenty s o lu tio n s run in the double Y c e l l . One may conclude from, the d ata in t h i s ta b le th a t, u n le s s an appre c ia b le amount of dye i s p erm itted to p ass out of the tube, th e tu r b id ity c o rre c tio n may in tro d u ce c o n sid e ra b le uncer ta i n t y in th e measured o p tic a l d e n s ity . W e have found th a t a 40 to 60 p e rc e n t change in o p tic a l d e n sity g iv e s th e most rep ro d u cib le r e s u l t s . This is i l l u s t r a t e d in Table 11 and F igure 22, which shows the observed m o b ilitie s f o r d i f f e r ent volumes of dye p assed through th e c e l l . The d o tte d l i n e s of F ig u re 22 re p re se n t the range o f inaccuracy of th e measured m o b ility due to an average tu r b id it y c o rre c tio n as estim a ted from Table 10. I f only 10$ of th e dye i s p e rm itte d to pass from th e c e l l , then i t i s seen from F igure 22 th a t an e r r o r of 19$ may r e s u lt in th e measured m o b ility . At th e r i g h t hand end of th e graph, th a t is , at high p erce n tag e o f dye passed from th e c e l l , a new source of e r r o r appears sin ce some of th e untagged so lu tio n which e n tered the c e l l under th e in flu e n c e of th e e l e c t r i c f i e l d may leave th e c e l l and so le a d to low m o b ility . Temperature v a r ia tio n s w ith in th e la b o ra to ry during th e th r e e to fo u r hour e le c tro p h o re s is experiment a lso pro duced in a c c u ra c ie s in th e m o b ilitie s . These tem perature f lu c tu a tio n s would produce changes in th e d e n sity of so lu tio n being stu d ied . T his in tu rn r e s u lte d in a d is p la c e - 85. MOBILITY % Dye passed 1 4 .1 1 6 .8 1 8 .3 3 3 .5 3 4 .6 3 6 .1 4 7 .9 4 9 .3 5 0 .3 5 8 .3 7 2 .6 100 TABLE X I VERSUS VOLUM E DYE PASSED THROUGH DOUBLE Y CELL M o b ility x IQ4 cm^/sec v o lt 3 .6 0 3 .6 9 3 .9 7 3 .6 2 3 .7 6 3 .5 4 3 .5 5 3 .4 4 3 .5 8 3 .4 9 3 .4 4 2 .9 4 x/0 4.0 p C T O -QO r ~ r o 3.0 2.0 /o o 5 0 ' • F i g u r e 2 2 P e t c e t j t D y e P a s s c - J 87. ment of liq u i d through th e c a p ill a r y tube and out o f stop cock A. E rro rs of as much as 10# in th e m o b ility could be produced by such tem p eratu re f lu c tu a tio n s . The s itu a tio n was rem edied by the c o n s tru c tio n of an a i r ’therm ostat through th e co o lin g c o il of which a con tin u a l flow of r e f r ig e r a te d w ater c ir c u la te d . Temperature re g u la tio n was m aintained a t 25.0°C. to w ith in about 0.05°C by means o f a s p ir a l r e g u la to r in s e r ie s w ith a h ea tin g elem ent. An e s s e n tia l fe a tu re of th e th erm o stat was an a i r blower which, by means of a system of b a f f l e s , provided fo r p ro p er mixing of warm and cold a i r and i t s c ir c u la tio n through the th e rm o s ta t. I t was, of c o u rse , necessary to e s ta b lis h th a t th e o p tic a l d e n s ity of our dye so lu tio n , Sudan IV, In potassium la u ra te , was a lin e a r fu n c tio n o ft he dye c o n c e n tra tio n . T his is c le a r ly shown in Table 12 and F igure 23. I t was s t i l l necessary , however, to e s ta b lis h th a t the m o b ility did not depend upon th e p a r tic u la r dye used. W e th e re fo re made two runs in which O il Black rep la ced th e Sudan IV. These r e s u l t s are l i s t e d in Table 13. The average of 3.51 x 10~^ shows good agreement with th e 3.52 x 1 0 ~^ obtained f o r th e same so lu tio n w ith Sudan 14. The r e l a t i v e l y f l a t s p e c tr a l curve of O il Black shown in Table 14 made a t u r b id ity c o rre c tio n im possible, so th a t th e a c tu a l agreement 88 . TABLE X I I OPTICAL DEHSITY VERSUS COHCMTRATION O F SU D A 2T IV O p tical D ensity % of S a tu ra te d Dye S o lu tio n 1 .9 0 4 100 1 .7 5 3 90 1 .5 2 9 80 1.3 3 2 70 1 .1 8 3 60 0.963 50 0 .7 7 8 40 0 .5 8 2 30 0 .4 1 6 20 0.196 10 0 .0 0 0 0 Optical D ensity f.2 U O a lo 20 10 fo 7° 9° Dye Conceptntt** ( 0/o of S ztvrKtfoh) F~ i g ui i-e 2 ^ Optic&l Density vs. Dye Cohceritv^t TABIE X I I I EFFECT 0F SOLUBILIZED E O 5.0$ POTASSIUM LAURATE Dye Used Average M obility cm2/ v o l t sec Sudan IV 3.52 x 10~4 O il B lack 3.51 x 10-4 9 1. TABLE XIV SPECTRAL CURVE fOR OIL BLACK Wavelength O p tic a l D ensity (m ) 320 503 330 387 340 298 350 264 360 255 370 263 380 273 390 289 400 299 410 304 420 308 430 306 440 318 450 341 460 395 470 4 51 480 502 490 563 500 605 510 607 520 605 92. T&BLE XIV ( c o n t i n u e d ) Wavelength (m ) 550 540 550 560 570 580 590 600 610 620 O p tic a l D ensity 598 528 598 517 277 253 070 207 190 173 may not be a s good as T able 13 in d ic a te s . A p p lic a tio n of th e average tu r b id it y c o rr e c tio n as found in T able 10 would cause th e m o b ility of th e potassium la u r a te w ith O il Black to d i f f e r by p lu s o r minus 2$ from th e above value. Using our double Y c e l l , we have measured th e m obil i t i e s of potassium la u r a te and A erosol M A s o lu tio n s as a fu n c tio n o f c o n c e n tra tio n . A t y p ic a l experiment w ill be d e sc rib e d w ith the a id of F ig u re 21. The s il v e r e le c tro d e s F and F* are f i r s t coated with s il v e r c h lo rid e by making them th e anodes in an e le c tr o ly te of s a tu ra te d potassium c h lo rid e and u sin g a s i l v e r cathode, A c u rre n t of 2 to 3 m illiam peres fo r 12 to 18 hours was g e n e ra lly used. One such co a tin g g e n e ra lly s u ffic e d fo r th re e o r four experim ents. T his in te r v a l was f i n a l l y s tre tc h e d to an in d e f in ite ly long p erio d by th e simple expediency of re v e rsin g th e e le c tro d e s a f t e r each succes siv e experim ent. Compartment C was th en f i l l e d with s a tu ra te d p o ta s sium c h lo rid e s o lu tio n and th e e le c tro d e s placed in to p o s i t io n . A fte r tem perature eq u ilib riu m was e s ta b lis h e d , gen e r a lly a t 25°C., stopcocks D, D1, G - and G r* were clo se d . The 3 mm. c a p illa r y was th e n f i l l e d with th e dye-tagged soap s o lu tio n by p la c in g the so lu tio n in co n tact w ith open ing P; opening stopcocks B, B 1 and A1 so th a t when a 94. s lig h t vacuum was a p p lie d at A*, th e dye tagged so lu tio n would move in to the c a p ill a r y . Any dye which passed sto p cock B1 and en te re d compartment 0* was c a r e f u lly washed out with successive p o rtio n s of th e untagged soap s o lu tio n . The untagged soap so lu tio n was then in tro d u ced in to th e rem ainder of th e ap p aratu s by again applying a s lig h t vacuum at stopcocks A and p u llin g th e so lu tio n through opening P u n t i l i t mounted in to th e space above th e sto p cock. T his procedure was rep eated at opening P* and sto p cock A*. The ap p aratu s was then p la ced in to th e a i r th erm o stat w ith stopcocks A and A * open, stopcocks D and D* tu rn ed so th a t th e soap s o lu tio n and potassium c h lo rid e s o lu tio n made c o n ta c t, but the dye s o lu tio n in th e c a p il la r y is o la te d by stopcocks B and B '. The motion of th e meniscus above stopcock A could be watched w ith a tr a v e lin g te le sc o p e and when t h i s menis cus became s ta tio n a ry th e ap p aratu s had come to tem perature e q u ilib riu m . Stopcock A* was then clo sed by A l e f t open. The motion of the m eniscus above A then served as an in d i c a to r fo r any le a k s p re se n t in the system. The dye so lu tio n was then brought into co n tact w ith th e soap s o lu tio n by tu rn in g stopcocks B and B 1, and a p o te n tia l of about 50 to 70 v o lts ap p lied to th e e le c tro d e s . This p o te n tia l was o b tain ed from a f u l l wave r e c t i f i e r borrowed from P ro fe s s o r C. S. Copeland. T his p o te n tia l when t e s t e d on an o s c illo s c o p e gave only an alm ost imper c e p tib le r ip p le . A ctu a lly , of co u rse, i t was much e a s ie r and more a c c u ra te to measure th e c u rre n t flow ing through th e c i r c u i t than th e p o te n tia l which was a p p lie d to th e e le c tro d e s . This c u rre n t was c a lc u la te d from th e p o te n tia l drop a c ro ss a stan d ard Leeds and Northrup re s is ta n c e box in s e r ie s w ith th e e le c tro p h o re s is c e l l . The p o te n tia l drop was measured w ith the a id o f a standard p o te n tio m e ter c i r c u i t and was recorded a t fix e d in te r v a ls , g e n e ra lly o f 10 minute d u ra tio n . The r e s u l t i n g v a lu e s were averaged a t th e end o f th e experiment and, i f th e r e c t i f i e r had e x p e ri enced a p r io r warming p erio d of about two h o u rs, norm ally showed le s s th a n 1$ average d e v ia tio n from th e average v alu e. A recording galvanom eter o c c a sio n a lly used in ste a d of th e p o te n tio m e ter co u ld d e te c t no short range f lu c tu a tio n s in th e c u r re n t. A fte r about 50$ of th e dye had moved out of the cap i l l a r y , th e c u rre n t was shut o ff and th e tim e f o r th e dura tio n of th e experiment was reco rd ed . Stopcock A would then be clo sed and stopcock B and B1 tu rn e d so th a t th e soap so lu tio n could be d rain ed from th e U tu b e s upon reopening stopcocks A and A*. A fte r d ra in in g t h i s s o lu tio n , th e 96. c a p illa r y would be disconnected from th e rem ainder of th e ap c a ra tu s at th e b a l l socket j o i n t s E and E 1, and th e open s e c tio n s c a re fu lly washed and then d rie d . Stopcocks B and B‘ would then be tu rn e d so th a t th e dye s o lu tio n remaining in th e c a p illa r y would flow in to compartments 0 and 0* and th en , by g e n tle rooking, w ell mixed w ith th e soap so lu tio n , which had d isp la c e d th e dye s o lu tio n . This mixed s o lu tio n was th en d ra in e d in to a weighing b o t t l e and sealed u n t i l i t s o p tic a l d e n sity could be meas u red on a Beckmann M 0d el D U q u a rtz spectrophotom eter a t 528 m y i A - * Normally two s e ts of th r e e measurements were taken. F i r s t th e stan d ard dye s o lu tio n was compared a g a in st th e undyed soap so lu tio n and then a g a in st th e sample removed from th e c a p illa r y a f t e r e le c tro p h o re s is . As a check a - g a in s t th e second measurement, th e sample a f t e r e le c tro p h o r e s is was also compared w ith th e undyed soap s o lu tio n . Measurement 1 minus measurement 3 should g iv e th e same v a l ue as was determ ined by measurement 2, but w ith a s li g h tly low er accuracy. A fte r th e se th re e measurements were taken, th e wavelength was s h if te d to a new value, 625 m^e* when Sudan IV was th e s o lu b iliz e d dye, and th e above measurements were re p e a te d once o r tw ice and th e r e s u l t s averaged. The agreement of th e two o r th re e measurements was g e n e ra lly b e t t e r th an 1$. From th e knowledge of c u rre n t, tim e, cap i l l a r y volume, o p tic a l d e n sity , and s p e c ific c o n d u c tiv ity o f the soap s o lu tio n , th e m o b ility could he c a lc u la te d w ith th e a id of equation (3)• The d a ta fo r potassium la u r a te are shown in Tables 15 and 15a and in F ig u re 24. In F igure 24 th e s o lid lin e i s th e p lo t of m o b ility ag a in st soap c o n c e n tra tio n , w hile th e d o tte d lin e is th e p lo t a g a in st the square root of the c o n c e n tra tio n . The same type of d a ta is p lo tte d fo r A erosol M A in F ig u re 25 and ta b u la te d , along w ith one p o in t f o r A erosol OT, in T ables 16 and 16a. There are two fe a tu re s of F ig u res 23 and 24 which deserve comment. F i r s t i s th e f a c t th a t th e m o b ility of th e m ic e lle d ec re ase s w ith con c e n tr a tio n . The eq u iv ale n t c o n d u c tiv itie s of soap so lu tio n s o fte n show a s lig h t in c re a se w ith c o n c e n tra tio n above th e c r i t i c a l c o n c e n tra tio n . Our work i s evidence f o r the be l i e f th a t t h i s in c re a se is due to an enhanced m o b ility of th e gegenions as o r ig in a l ly suggested to H artley by Dav i e s 56 and d iscu ssed in C hapter V of t h i s t h e s i s , and prob- 7 f t 9 ably not, as suggested by McBain 9 > due to an in c re ase in. th e number of io n ic m ic e lle s . T ables 15 and 16 include, b e s id e s th e m o b ility d ata, 56 H artley , K olloid Z., 88, 33 (1939). 98. TABLE XV MOBILITIES O F POTASSIUM LAURATE SOLUTION C oncentration S p e c ific Conductance M o b ility (* ) c m ^ /v o l1 X 10^ : s e c 2 .0 6 .0 7 X 10-5 3 .8 0 4 - 2 5 .5 3 .8 6 X H O 1 ca 3 .6 5 4 - 2 5 .0 1 4 .4 7 X l o - 3 3 .5 5 + 4 7 .0 1 9 .9 5 X 10-S 3 .3 0 + 2 9 .4 2 4 .4 0 X ic r3 3 .1 5 + 2 99. TABLE XVa MOBILITY OF POTASSIUM MUEATE SOLUTION C o n c e n tr a tio n Time C u rre n t O p t i c a l D e n s ity ct J O s e c . m a . S ta n d a rd D if f e r e n c e 2 .0 5 ,0 0 0 , 4 .3 2 7 .3 6 9 ,1 6 1 2 .0 8 ,2 0 0 2 .6 9 7 .3 7 9 .166 S . 5 9 ,0 5 0 5 .2 0 0 .6 9 5 .3 8 0 r ? r* o .5 7 ,2 1 0 5 .1 7 1 .7 1 0 .3 0 8 0 .5 7 ,2 5 0 5 .2 2 7 .696 .312 5 .0 1 1 ,9 0 5 5 .2 5 6 .7 5 0 .3 6 2 5 .0 1 0 ,9 0 0 5 .1 9 9 .7 5 0 .5 3 4 7 .0 1 6 ,0 7 1 5 .4 5 5 .8 9 0 .4 0 5 7 .0 1 3 ,4 6 0 5 .4 4 1 .8 9 1 .5 4 3 9 .4 4 7 ,0 0 0 2 .2 8 0 1 .6 6 0 .7 3 0 9 .4 2 1 ,8 0 0 5 .3 9 6 1 .6 4 4 .7 8 4 9 .4 4 7 ,6 0 0 2 .5 3 0 1 .6 3 5 .7 9 0 Mlo bility vfo* ' 4.6" *.S" £ 6 “ zr 3.1' ?.» F i g Mre ^ 4 M o b ility V S - C oh c e n i V a i / o * P o t 2i*s t * * * • + Z.a«*-df^ h -5 o o / £ * 3 4 5 - * 7 e ? . / f re e c r o s s - s e c tio n in th e diaphragm and a v e lo c ity of 1 c m ./h r. in th e la r g e chan n e ls , i . e . , 3 x 10~4 c m ./s e c .). On th e o th e r hand, f o r th e average ion having a low d if fu s io n c o n s ta n t, D, such as 10“ ^ cm .^/sec. corresponding to m olecular weight of about 10^, th e time t necessary to c ro ss a channel having a diam eter of 10 m icrons (which i s more than th e average pore ra d iu s in "medium" f r i t t e d g la ss) is , according to E i n s t e i n 's equation, (V) t s I * ss i i i ° - 3 1 . 5 sec. Thus th e channel i s cro sse d b e fo re th e motion a t the f a s t e s t le v e l amounts to 10 m icrons. For p a r t i c l e s having a 106. m olecular weight o f th e o rd e r of 10,000, th e tim e and spread a re reduced by a f a c to r of 10. In view of th is b a sic soundness of B rady’s method, we c o n s tru c te d th e ap p aratu s shown in F igure 26. This s in te re d g la s s type of c e l l i s used very much as th e cap i l l a r y c e l l w ith the follow ing im portant ex cep tio n s. The s in te re d g la s s d isk s were always kept moist w ith d i s t i l l e d w ater when not in use, sin ce i t was fe a re d th a t any soap s o lu tio n l e f t in th e c e l l a f t e r an experiment might dry and th u s plug up th e minute c a p i l l a r i e s . The dye so lu tio n was kept between th e s in te re d g la s s plugs and was in tr o duced in to t h i s space by means of a hypodermic syringe, p re c a u tio n s being tak en th a t no dye would e n te r th e bore of th e stopcocks between the two d is k s . The dye is confined between th e two f r i t t e d g la s s diaphragms and can be r e a d ily removed fo r a n a ly s is . A glass enclosed iro n w ire was o r ig in a lly designed to s t i r up the so lu tio n a t th e end of th e experim ent, so th a t a rep resen t a t i v e sample is withdrawn. The c e l l was diamond-shaped so th a t should minor d e n sity d iffe re n c e s cause s t r a t i f i c a tio n , th e y would not bring e n te rin g so lu tio n in co n tact w ith th e e x it diaphragm. In use i t was found, however, th a t th e in c re ase d r e s is ta n c e a t th e diaphragm produced lo c a l h e a tin g w ith r e s u ltin g convection c u r r e n ts , some o f Z C Ce // 108. which a re c le a r ly v is i b le as the c le a r so lu tio n formed a t one of th e diaphragms, r i s e s and then descends from the top of th e 'c e l l . The r e s u l t s seemed to show (as Brady has also noticed) a decreasing m o b ility as th e experiment was ex tended due to th e f a c t th a t th e convection c u rre n t tended to c a rry untagged m ic e lle s from th e entran ce diaphragm to th e e x it one in an u n c o n tro lle d manner. However, a t th e tim e th e se experim ents were perform ed, we d id not p o ssess th e r e l i a b l e m o b ility measurement of th e double Y c e l l which averaged to 3 .5 x 1CT4 cm.2 p e r v o lt sec. W e th e re fo re overlooked th e now obvious f a c t th a t in a p lo t o f m o b ility v ersu s tim e in an a n a ly tic a l boundary method, th e m o b ility s t a r t s much above th e p ro p er v alu e. This is shown in F ig u re 27 where th e s o lid and d o tte d lin e re p re s e n ts m o b ili t i e s o b tain ed w ith continuous s t i r r i n g and w ithout s t i r r i n g re s p e c tiv e ly . The equation f o r th e l a t t e r case can be shown to be (8) u « 2 ^ 0 |( V H K i lQg where V i s th e volume of th e c e l l , K th e s p e c if ic conduc t i v i t y of th e so lu tio n , i th e c u rre n t passed in tim e t and C0 and C th e i n i t i a l and f in a l dye c o n c e n tra tio n in th e c e l l . Equation (8) may be derived by co n sid erin g th a t Mo b'lht X /o<" 4.0 r / ^ M r e 2 7 Mobility ih Dtd pKrao*M C«/f a$ FHnctfoH ^ o-F Ti*,e § 1 1 0 . the change in c o n c e n tra tio n , dc, of th e c e l l i s th e quo t i e n t o f th e c o n c e n tra tio n tim es th e change in volume, dV, of th e dye d iv id ed by th e volume, V, of th e c e l l . That i s (9) dc - - £51 V But since th e change in volume of th e dye is th e product of th e a re a o f the c e l l by the change in v e lo c ity , dv, of the dye during th e time d t, (1 0 ) do = - oAdv a t Now equation (4) g iv es th e r e la tio n s h ip between v e lo c ity , m o b ility , u, and p o te n tia l g ra d ie n t so th a t ( 1 0 ) becomes (11) do oAudE/dl jpr s -------- -------- o r (12) dc oAul I f ~ ~ TOT where 1 i s th e cu rren t and K th e s p e c ific c o n d u c tiv ity of th e s o lu tio n . Equation (12) may now be re w ritte n (13) & C u i ^ q" “ s y'jr d t I n te g r a tin g eq uation (13) and re a rra n g in g we g et equation (8). F ig u re 27 c le a r ly shows th a t th e m o b ility of th e s t i r r e d s o lu tio n i s approaching a lim it of about 3.5 x 1 0 ~ 4 w hile th e u n s tir r e d s o lu tio n i s approaching a lower 1 1 1 . value, probably 3.3 x 10~4 . I t i s b e lie v e d th a t th e d i f f e r ence between th e s t i r r e d and u n s ti r r e d v alu es i s due to th e h e a tin g o f th e s o lu tio n caused by the c u rre n t p assin g through i t , a b e l i e f f i r s t form ulated when i t was observed th a t th e so lu tio n w ith in th e c e l l was a degree o r two above room tem p eratu re. T his su spicion was checked by measuring th e m o b ility a t d if f e r e n t c u rren t d e n s itie s f o r a fix e d tim e, 11,000 seconds to be exact. The d a ta a re shown g ra p h ic a lly in F igure 28 and show th e r i s e in m o b ility a t te n d in g th e in c re a se in c u r r e n t. The a b s o lu te v alues by them selves are u n c e rta in , sin ce th e s ig n ific a n c e of th e tu r b i d i t y c o rre c tio n was not a p p re c ia te d a t the tim e of th e s e measurements. A f u r th e r t e s t of t h i s h y p o th e s is is shown in F ig u re 29. Experiments were run a t very short tim e in te r v a ls p a ssin g approxim ately 1 .9 , 4 .4 , and 8.0 m illiam peres thro u g h th e s o lu tio n in th e s in te re d g la s s c e l l . E x trap o l a tin g to zero tim e we found th a t th e hig h er c u rre n t d e n si t i e s caused movement of dye from th e c e l l even a t zero tim e. T his o b se rv a tio n can only be in te rp r e te d as an e f f e c t of th e g r e a te r heat produced by th e hig h c u rre n t d e n s itie s . This h e a tin g e ffe c t caused expansion of th e liq u i d and pro duced some mass flow th ro u g h the c e l l . A f u r th e r check was provided by applying an a l t e r - Nobilit 112 0 * o n- sr O ^ J r o a I** st ♦* K t* C est N r\ 4 oo o N < > V O « J £ o K o C * X L V L 3 L 3 O f« \ n ? '<N ~ si **e o s: o 0 u % ® r* o S - o - P u I p f p n r o O c * 0 0 O V «y p L I ! 3 u N *i u i *N • ft K J s ^ c x , N* - Do - V D V * O "X ft V * « k « > 0 s V J L 3 ll 0 * > & S - * 3 o « * t. c o G * -f- c weight m a te ria l re q u irin g a d if f u s io n tim e s im ila r to th a t of th e soap so lu tio n . The only such substances a v a ila b le are th e p ro te in s and th e se , i t was decided, would be too li a b l e to b a c te r io lo g ic a l ac tio n during th e th r e e weeks of th e experim ent. A second a l t e r n a t i v e i s to p rep are a sta b le , m onodispersed so l w ith a diam eter of 1 0 0 - 2 0 0 % and to measure i t s apparent r a te of d if f u s io n both w ith and without s t i r r i n g . La Mer*s monodispersed s u lfu r so ls seemed id e a lly su ite d f o r th e s e purposed. Not only i s th e th e o ry of t h e i r p re p a ra tio n w ell understood, but th e experim ental procedure f o r t h e i r p re p a ra tio n is s t r a i g h t f o r w a r d . 63 &&&!_ tio n , La Mer has d e sc rib e d th e se s o ls as "q u ite sta b le " , a r a th e r ambiguous term which we chose to in te r p r e t fav o r ably. The procedure o f La Mer and Johnson was used. Ten ml. of 0 .1 sodium th i o s u l f a t e and 10 ml. o f 0 .2 HC1 were added to 950 ml. of d i s t i l l e d w ater a t 25°. A fte r b rin g - La Mer and Barnes, J . C o ll. S c i., 1, 71 (1946). ^ La Mer and Johnson, J . Am. Chem. Soc., 69, 1184 (1947). La Mer, J . Phys. C o ll. Chem., 52, 65 (1948). 1 2 2 . ing the volume to 1 l i t e r th e f la s k was th erm o stat te d . In a few hours a Tyndal beam was ap p aren t, and th e growth of th e s u lfu r p a r t i c l e s was stopped by adding s u f f ic ie n t 0.01 N io d in e so lu tio n to n e u tr a liz e 80$ of th e u nreacted t h i o s u l f a t e . This s u lf u r sol was then p la ced in to th e upper compartment of th e d iffu s io n c e l l s w ith d i s t i l l e d w ater beneath. Two o f th e c e l l s were r o ta te d and two r e mained s ta tio n a ry . A fte r seven days a stro n g Tyndal e f f e c t was observed in both chambers o f a l l four d if f u s io n c e l l s and th e liq u id removed fo r an e stim a tio n of th e con cen tra t i o n of th e s u lfu r sol in each compartment. I t immediately became apparent th a t agglom eration of th e s u lfu r so l had occurred sin c e v i s i b l e th re a d lik e p a r t i c l e s were observed f lo a ti n g in a l l of th e samples. The o r ig in a l s o lu tio n was th en rechecked by l i g h t s c a tte r in g and the c o a g u la tio n con firm ed. The d a ta i s l i s t e d in Table 19. P erso n al c o rre spondence w ith P ro fe ss o r La Mer confirm ed th a t th e sta b i l i t y of th e s u lfu r p a r t i c l e did not extend over a p erio d of more than se v e ra l h o u rs. I t was thought th a t perhaps the s u lfu r p a r t i c l e could be s ta b ili z e d by the a d d itio n of v ario u s d e te rg e n ts . In th e case of th o se d e te rg e n ts whose C M C was known, th e f i n a l c o n c e n tra tio n o f d e te rg e n t was 1/4 of th e CMC. For th e o th e r d e te rg e n ts, a f in a l c o n c e n tra tio n of 2 .5 x 10~ 4 TABLE XIX LIGHT SCATTERING G F SULFUR SOL S o lu tio n F i l t e r s 90° s c a tte r in g o r ig in a l 1 , 2 & 4 91.0 a f t e r 7 days 2 & 4 22.0 s c a tte rin g 51.0 91. 124. m o l e s / l i t e r was used. A c o n c e n tra tio n below th e O M C was d e s ire d so th a t no s o lu b iliz a tio n would occur. S everal samples of n o n -d isp ersed s u lf u r sol were prepared according to La Mer*s procedure. A fte r !§■ hours, each sample was d iv id ed in to two p a r t s and th e r e a c tio n stopped, one w ith iodine, the o th e r w ith potassium hydrox id e. These samples were f u r th e r subdivided and to each a d if f e r e n t d e te rg e n t was added. These d e te rg e n ts, w ith the r e s u l t s o b tain ed on l i g h t s c a tte r in g , are l i s t e d in T ables 20 and 21. The v alu es G qqo/ ^ qo i s th e r a tio o f th e g a l vanometer reading f o r th e 90° beam and the u n s c a tte re d 0° beam, and i s to be co n sid ered as a fu n c tio n of the p a r t i c l e s iz e . A la rg e r a tio im p lies a la rg e p a r t i c l e s iz e . I t was apparent from our r e s u l t s th a t none o f the chem icals te s te d could be said to have s ta b ili z e d th e s u lfu r s o ls . I t was next decided to t r y gold so ls as a c a lib r a tio n stan d ard . When p ro p e rly p rep ared , th e se have been observed to be s ta b le f o r months. They do, however, la c k th e m onodispersity d e s ira b le f o r d if fu s io n work. Some u ltr a c e n tr if u g e work by N ic h o ls ^ and Svedberg and R in d e ^ 6 4 N ichols, P hysics, 1, 254 (1931). Svedberg and Rinde, J . Am. Chem. Soc., 46, 267? (1924). TABLE XX SULFUR SOL STOPPED .W ITH IODINE G9q/ G0 D etergent none potassium la u r a te A erosol O T sodium naph th a le n e s u l fo n a te sanomerse sodium ben zene s u l fo n a te 0 hours 0.138 3.18 0.471 6 .35 1.96 19 hours 0.100 3.02 0.490 4.65 2.66 6 6 hours 0.078 Bad F lo e . 0.526 3 .3 6 S lig h t Floe 2.44 1.22 0.712 1 2 6 . D etergent Hone Potassium la u r a te Sodium ben zene s u l fo n a te Sanomerse Sodium nap - th a le n e su lfo n a te A erosol O T C etyl p y rid - inum bromide TABLE XXI SULFUR SOL STOPPED WITH KOH G9 0 °/Gn° 0 hours 0.126 3.61 0.16 1.40 5.10 0.20 14.5 19 hours 0.169 3.51 0.14 1.82 5.18 0.23 48 . 6 6 6 hours 0.097 B ad Flo c 0.11 2.09 3.26 0.30 Bad F loe., 1 2 ? . has shown th a t in the case of the M n u c le a r gold s o l 1 1 th e d is t r i b u t i o n of p a r t i c l e siz e s i s q u ite lim ite d . From d a ta given by N ichols, i t is estim ated th a t 80$ o f th e n u clear gold so ls have a ra d iu s between 2 and 4 m illim ic ro n s w ith no d e t e c t ib le amount having a ra d iu s above 5 m illim ic ro n s. The n u c le a r gold so l was p rep ared from a u ric acid and phosphorus by v a rio u s m o d ific a tio n s of th e method em ployed by Svedberg and R inde . 6 5 The procedure found,most s a tis f a c to r y was to make 2.5 ml. o f 0.01 N a u ric acid and 5 ml. of 0 .1 N potassium carb o n ate, d ilu t in g to 100 m l., and then adding 0 . 1 0 ml. of a s a tu ra te d so lu tio n of phos phorus in e th a n o l. A fte r th e development of th e red gold so l c o lo r, oxygen was bubbled through the s o lu tio n to o x i d iz e any rem aining phosphorus. The samples were then exam ined fo r a Tyndal beam and those which showed one were re je c te d . S edim entation measurements in c a p i l l a r i e s made w ith a m odified Ivan S o rv a ll angle c e n trifu g e as d e sc rib e d below showed th a t th e p a r t i c l e s had a ra d iu s below 1 0 m. The h o ld e r f o r th e c a p i l l a r i e s is shown in F igure 30 and when in use, r e s t s in the space norm ally reserv ed f o r the c e n tr ifu g e tu b e s. The procedure used to estim ate th e siz e of th e gold p a r t i c l e s i s as fo llo w s. The c a p i l l a r i e s , about the diam eter of an o rd in ary m elting p o in t c a p illa r y but only one c e n tim e te r long, a re sicle F io u i - e . ^ 0 o o o Ca.pi ll o r C e h t ri f u j e 129. f i l l e d w ith th e s o lu tio n co n tain in g the gold so l and placed in th e h o le s in the base of the a d a p te r. The c e n trifu g e is then s ta r t e d and i t s speed determ ined by a sp e c ia l s tr o b oscope lamp. The c a p i l l a r i e s are removed and examined a f t e r a given i n t e r v a l . I f th e so lu tio n s t i l l appears uniform , f r e s h samples are c e n trifu g e d f o r a longer in te r v a l and the p ro c e ss rep eated u n t i l i t becomes ap p aren t, upon examining th e c a p i l l a r i e s , th a t sedim entation has o c c u rre d . In most ca se s i t proved im possible to observe th e a c tu a l s e t t l i n g o f a boundary, but the f in a l s t a t e of gold p a r t i c l e s con c e n tr a te d in th e low er p o rtio n o f the c a p illa r y would sooner o r l a t e r become ev id en t. Knowing the tim e, t , o f c e n trifu g in g a t an angular v e lo c ity of w, th e p a r t i c l e weight may be c a lc u la te d from th e sedim entation equation (3) dx 2 rs ( P - Pw ) w^x wmrnmgm r—& ■ n ■ ■■ i m T g in i w i n .............................. m... . cF E - 9f\ where dx i s the d ista n c e th e gold so l has s e t t l e d in tim e d t, r th e average ra d iu s of the c o llo id a l p a r t i c l e s , f p th e d e n s ity of the p a r t i c l e , ^ ^ th e d e n s ity o f the w ater, and h th e v is c o s ity of th e w ater. Since o p tic a l measurements on the Beckmann sp e ctro photom eter were to be used to determ ine th e c o n c e n tra tio n changes o f th e gold so l during the d iffu s io n p ro cess, i t 130. was necessary to e s ta b lis h th e sp e c tra l curve and the ef f e c t of c o n c e n tra tio n on o p tic a l d e n s ity f o r the gold sol used. T his d a ta is su p p lied g ra p h ic a lly in F ig u res 31 and 32. F ig u re 32 c le a r ly shows th a t the s o lu tio n does not show ary d e v ia tio n from B e e r's Law. The gold so ls were then p la ced in the upper compart ment of the s in te re d g la s s d if fu s io n c e l l and p e rm itte d to d iffu s e and sediment in to the low er compartment c o n tain in g doubly d i s t i l l e d d e a e ra te d w ater. A fte r th e appearance of gold sol in the lower compartment, i t waw flu sh e d and r e f i l l e d with th e doubly d i s t i l l e d w ater. Two of th e c e l l s were r o ta te d a t about 60 r.p .m . w hile th e o th e r two were s ta tio n a r y . The d iffu s io n experim ent was conducted in a co n stan t tem perature b ath a t 25.0°C. For sh o rt p e rio d s of tim e, g e n e ra lly two o r th re e hours, the tem perature of t h i s b a th could be m aintained co n stan t to 1 or 2 thousandths of a degree C en tig rad e. For the lo n g e r in te r v a ls o f two o r th re e weeks re q u ire d f o r the d iffu s io n experim ent, i t is u n lik e ly th a t tem perature c o n tro l was b e t t e r than 2 o r 3 hundredths of a degree. A fte r about th re e weeks in th e tem perature bat®h, the d iffu s io n c e l l s were removed and th e s o lu tio n s analyzed f o r changes in gold sol c o n c e n tra tio n . The d if fu s io n experim ent was then rep eated , but t h i s tim e 1 3 1 . f r r ?zr W ave length in *yu Opt/s.*.I D e u r i t y v s . \a / * \ s * (e.h ft A -foyr Gold Sol O p t i c *1 D ensity ' at T X f 4h JfO AO fro GO f Q t> O F f f u r e 'S Z Optical D ensity v s . C o h cen tr a .t/o t \ of G o id Sol 133. th e second set of c e l l s were ro tated * while th e f i r s t p a ir were s ta tio n a r y . The r e s u l t s a re ta b u la te d in T ables 22 and 23. The conclusion i s in escap ab le th a t more m a te ria l i s tra n s p o rte d through th e membrane during s t i r r i n g than under s ta tio n a ry c o n d itio n s. Furtherm ore, Table 23 shows th a t th e d iffe re n c e between th e sta tio n a ry and r o ta ti n g c e lls amounts to 2i tim es th e th e o r e tic a l d if fu s io n c o e f f ic ie n t of th e g o ld so ls , assuming a 1 0 0 8 ra d iu s and th a t the d if f u s io n i s given by th e E in s te in equation (A\ n _ HT W ^ F n rH These r e s u l t s c le a r ly in d ic a te th a t th e re i s tr a n s p o r t of gold so l through the s in te re d g la s s d isk by some means o th e r than d if fu s io n o r sedim entation. I t m ight p o ssib ly be argued th a t s t i r r i n g removes stagnant la y e r s and so sh o rten s the le n g th o f th e d if fu s io n p ath , but th e obser v a tio n th a t the d iffe re n c e between th e s t i r r e d and s ta tio n ary c e l l s i s 2 § tim es th e th e o r e tic a l d if f u s io n co n stan t e lim in a te s t h i s p o s s i b i l i t y . Due to the u n c e rta in ty of th e d if fu s io n r e s u l t s , i t was decided to make a ju d ic io u s se le c tio n of th e p u b lish ed d if fu s io n c o n sta n ts of potassium la u r a te , Aerosol O T and A erosol M A in in te r p r e tin g th e m o b ility r e s u l t s . 134. TABLE XXII "DIFFUSION" O F GOLD SOL 11 Number C o n cen tratio n in R a tio O p tic a l D ensity bottom, to p bottom I S 0.475 0.077 0.162 I R 0.270 0.059 .216 I I S 0.472 0.085 0.176 I I R 0.242 0.074 0.306 I I I S 0.255 0.052 0.804 I I I R 0.47C 0.140 0.306 IV S 0.25S 0.047 0.181 IV R 0.530 0.118 0.223 R atio R/S 1.35 1.74 1.50 1.23 TABLE XXIII APPARENT nDIFFUSION CONSTANTS” OF GOLD SOL Average of R o tatin g C ells 0.18+3 cm^/day Average of S ta tio n a ry C e lls O .IS il cm^/day T h e o re tic a l 0.0S cm^/day R o tatin g - S ta tio n a ry Values 0.05 cm^/day 136. While the d if fe re n c e o f 0.05 cm.^ p e r day between th e “d if f u s io n c o n s ta n t 1 1 f o r the r o ta tio n and s ta tio n a ry c e l l s i s cause fo r co n sid e ra b le thought when working w ith high m olecular weight m a te ria l, i t need not cause any d i f f i c u l t i e s when f a s t e r d iffu s in g lew m olecular weight m ater i a l s are stu d ied . Potassium c h lo rid e , fo r example, has a d if fu s io n co n stan t o f about 1.60 cm.^ p er day. The 0.05 cm.^ p e r day i s ju s t 3$ of the d iffu s io n condbant o f the potassium c h lo rid e . Furtherm ore, since the amount of ma t e r i a l tra n s p o rte d through the diaphragm by th e se “non d if f u s io n 1 1 mechanisms may depend upon the d u ra tio n of the experim ent, the a c tu a l e rr o r may be much sm aller than 3$, sin ce a d if f u s io n experim ent w ith potassium c h lo rid e re q u ire s about two days, and th a t w ith the gold s o l re q u ire d two to th re e weeks. CHAPTER V DISCUSSION O ptimum Amount o f Dye Passed Through Double Y C e ll. As in d ic a te d in C hapter I I I , th e most rep ro d u cib le v alu es w ith th e double Y e le c tro p h o re s is c e l l l i e in th e range from 35 to 60$ dye tra n s p a te d from th e c e l l . At the lower end of th is range the inaccuracy of m easuring small changes in c o n c e n tra tio n , upon which i s superimposed a r e l a t i v e l y la rg e tu r b id it y c o rre c tio n , is undoubtedly th e source of t h i s in accu racy . At th e h ig h e r c o n c e n tra tio n s some o f th e untagged soap so lu tio n which en tered th e c e l l under th e in flu e n c e of th e e l e c t r i c f i e l d le a v e s the c e l l w ith th e tagged s o lu tio n . T h e o re tic a lly , th e flow l i n e s of the l i q u i d through th e c y lin d r ic a l c a p ill a r y should be a p a ra b o lo id o f re v o lu tio n , the s ta tio n a r y le v e l of which i s a t 0.707 tim es th e ra d iu s from a x is . Furtherm ore, were th e ends of th e p a ra b o la to remain fix ed , none o f th e un tagged m ic e lle s should leav e th e c e l l u n t i l 50$ of th e tagged m ic e lle s have l e f t . C onsider, fo r example, the electro o sm o tic flow which r e s u l t s from th e a p p lic a tio n o f th e e l e c t r i c f i e l d . This flow of w ater r e s u l t s in a p re ssu re d iffe re n c e a t the ends of the tu b e . The p re ssu re d iffe re n c e , in tu rn , a c ts 1 3 8 . on th e ends of th e c y lin d r ic a l p o rtio n of th e f l u i d and is ju s t "balanced by th e shearing s tr e s s e s on th e c y lin d r i c a l su rfa ce caused by th e v is c o s ity and i s th e re fo re p ro p o r tio n a l to th e r a te of change of v e lo c ity with ra d iu s . I f v i s the v e lo c ity of th e w ater, p th e p re ssu re d iffe re n c e , L the le n g th of a tube of ra d iu s R, and n th e v is c o s ity , (X) 2irrL n = T" and in te g ra tin g ( 2 ) v - _ |_ * £ + c The c o n sta n t of in te g ra tio n , c, can b e e v a lu a te d by s e ttin g r m R where (3) v in which V a electro o sm o tic m o b ility of th e w ater and E th e a p p lie d p o t e n t i a l . Equation (2) then becomes (4) v = (r 2 _ r2) + VE Now the t o t a l volume o f liq u id tr a n s p o rte d i s zero f o r our clo sed system so th a t (5) - - r gfifrvdr s 0 o r VE PR2 w Z ~ ~ 8nC 1 3 9 . S u b s titu tin g in e q u a tio n (4) g i v e s * - A: [ -2 - # ] showing th a t th e flow lin e s are c e r ta in ly p a ra b o lic . The above d e r iv a tio n fo llo w s c lo se ly th a t of Smith and L is s e .6 6 The volume o f t h i s p a ra b o la can be r e la te d to the circu m scrib ed c y lin d e r by means c f th e volume form ula6 7 (s) v p a /^ r r y 2 ax p S u b s titu tin g y s 2ax, th e g e n e ra l form of a p arab o la, and in te g r a tin g from x s 0 to x « b g iv e s (9) V p s T T ab 2 The volume of th e circum scribed c y lin d e r i s ( 10) v c - ( i t y 2^ (11) V0 s 2<JTab2 - 2Vp showing th a t untagged m ic e lle s w ill begin to le a v e th e c e l l a f t e r 5O jo of th e tagged m ic e lle s have m igrated o u t of th e tu b e . A ctu a lly th e re are two f a c to r s a t work which tend to keep untagged m ic e lle s in th e c e l l f o r lo n g e r p e rio d s 6 6 Smith and L isse , J . Phys. Chem., 40, 399 (1934). 6 7 G ra n v ille , Smith and Langley, Elements of D if f e r e n t i a l and In te g r a l C alcu lu s, (1934), p . 265. 140. of tim e. F i r s t th e re i s the o b se rv a tio n th a t th e ends of th e p arab o la do not rem ain fix e d in the v i c i n i t y of th e stop-cock but a c tu a lly m igrate through th e tu b e . T his i s in te rp r e te d as in d ic a tin g a g r e a t e r z e ta p o te n tia l f o r th e m ic e lle th a n fo r th e g la s s , so th a t th e d y e-m icelle complex moves f a s t e r towards th e anode than i t i s pushed towards th e cathode by th e electro o sm o sis of th e w ate r. The second f a c to r i s th a t of d iffu s io n , which te n d s to remove th e tagged m ic e lle from th e w all of th e c s,p illa ry and in to th e f a s t e r moving i n t e r i o r o f th e l iq u i d . A com plete d isc u s sio n o f t h i s e ff e c t i s d i f f i c u l t , but i t may be p o in ted out th a t a th re e hour p erio d of e le c tro p h o r e s is i s , on th e a v e ra g e ,s u f f ic ie n t to move a tagged m ic elle from th e w all to th e c e n te r of a c a p ill a r y w ith a one m illim e te r ra d iu s, o r conversely, to move an untagged m ic e lle a t th e c e n te r to the w all. T his fo llo w s re a d ily from the E in s te in d i f fu sio n equ atio n i f we assume D - 0.04 cm.2/day as th e d if fu s io n c o n sta n t of th e m ic e lle . Then X2 = (0.04) s 0.01 o r x - 0 . 1 cm. T his l a t t e r e ff e c t ten d s to ren d er th e o u tlin e s of th e p arab o la q u ite d if f u s e and, in f a c t , a f t e r some 40 or 60 141. m inutes one observes a more o r l e s s broad bond m ig ratin g down th e c a p ill a r y . As alre ad y d isc u sse d in C hapter I I I , i t i s ju s t t h i s l a t t e r e ffe c t which makes B rad y 's analy t i c a l boundary method such a neat way of m easuring e le c tr o p h o r e tic m o b ilitie s . Concertration Dependence o f M o b ility . A s ig n if ic a n t f e a tu r e of our work which was not e n tir e ly unexpected i s th a t th e m o b ility of th e m ic e lle s o f A erosol M A and potassium la u r a te d ecrease lin e a r ly w ith th e square ro o t of th e c o n c e n tra tio n . This beh av io r i s q u ite r e a d ily seen in F ig u re 25 f o r A erosol M A. In F ig u re 24, th e v a r ia tio n o f th e m o b ility of th e potassium la u r a te m ic e lle w ith c o n c e n tra tio n gives alm ost, but not q u ite , as s tr a ig h t a l i n e as the v a r ia tio n with the square ro o t of th e c o n c e n tra tio n . This behavior i s commonly observed w ith simple ions where i t i s known as K ohlrausch's d ilu t io n law. I t has not been expected f o r c o llo id a l io n s, since th e se could conceivably change t h e i r charge w ith c o n c e n tra tio n due to flO changes in th e deg ree of a s s o c ia tio n . Onsageruo p o in ts ^ Onsager, Ann. N.Y. Acad. S c i., 46, 241 (1945). 142. out th a t i t should be p o s s ib le to p re d ic t the charge of th e ion from the slope of th e lin e a t i n f i n i t e d ilu t io n and from i t s lim itin g m o b ility . In our case th e s itu a tio n i s somewhat more d i f f i c u l t since the a c tu a l c o n c e n tra tio n of th e m ic e lle i s unknown, although i t i s presumably some f r a c tio n of th e c o n c e n tra tio n of th e sim ple m olecule or ions. Furtherm ore even though th e re may be, say, six te e n n eg ativ e charges on th e Aerosol M A m ic e lle , t h i s does not n e c e s s a rily imply th a t the e l e c t r o s t a t i c f i e l d about the m ic e lle i s s im ila r to th a t o f an o rd in a ry ion o f m olecular dim ensions and o f th e same charge. Indeed, ?;ork by McBain and S e a r l e s , i n v o l v i n g th e e f f e c t of m ixtures o f d e te r g en ts and s a lt s o lu tio n s on c o n d u c tiv ity , was in te rp r e te d by them as im plying th a t the charges, being spread over th e su rface o f th e m ic e lle , a re a c tu a lly too f a r ap a rt to e x e rt a m utual in flu e n c e . Hence th e e f f e c t s upon th e io n ic stre n g th o f m ic e lle s o lu tio n s was s im ila r to th o se of u n i- *70 u n iv a le n t e l e c t r o ly t e s . Work by E rikson and L in g a fe lte r, in which they ap p lied B ronsted*s c r i t i c a l complex theory to th e problem by studying th e r a te of re a c tio n of brom oacetal 69 McBain and S e a rle s, J . Phys. Chem., 40, 493 (1936). 170 E rikson and L in g a fe lte r, J , C o ll. S c i., 4, 591 (1949). 143. and th i o s u l f a t e in s o lu tio n s of sodium d o d ecan esu lfate, in d ic a te d a 2.9 f o ld in c re a se in the io n ic s tre n g th of sod ium dodecanesulfonate s o lu tio n s in going from th e c r i t i c a l c o n c e n tra tio n a t 0.0075 M to a 0.020 M s o lu tio n . For a 1:1 e l e c tr o ly te th e in c re a se in th e io n ic s tre n g th should be in th e same r a t i o a s the c o n c e n tra tio n s o r 2 . 7 . M cBain^ con cept i s th e re fo re a good f i r s t approxim ation. The in a b i l i t y to estim a te th e m ic e lle charge from th e slope of th e m o b ility v ersu s th e square ro o t of th e c o n c e n tra tio n i s not too d isa p p o in tin g since o th e r means, some alre ad y d iscu ssed and some to be d isc u sse d l a t e r , ex i s t f o r estim a tin g t h i s q u a n tity and since th e li n e a r v a r i a tio n of th e se two q u a n titie s i s by i t s e l f in te r e s ti n g . The eq u iv alen t conductance above th e c r i t i c a l con c e n tr a tio n does not show t h i s same l in e a r d ecrease but r a th e r le v e ls o f f and o f te n even shows a maximum when p l o t te d a g a in st th e c o n c e n tra tio n o r square root of th e concen t r a t i o n . T his behavior i s in d ic a te d in F ig u res 32 and 33, in which bo th m o b ility of th e m ic e lle and th e eq u iv ale n t c o n c e n tra tio n of the s o lu tio n i s p lo tte d a g a in s t the square ro o t o f th e c o n c e n tra tio n . Although th e re a re in s u f f ic ie n t p o in ts f o r a r e l i a b l e graph, the le v e ll in g - o f f of th e equiv a le n t conductance i s q u ite marked w ith good in d ic a tio n of a r i s e in the case of th e potassium la u r a te . Our work *6 -7o F If U r e Sjjr Mobility -and .Equivalent Conductivity of P o t a s s i u m L au rate W L *16 X * O fr\ob[ l/tu o’f h\ / e e / / e O . C S y . R ° * t o f hf o rry\ * f t f y R<& « r t ? * Equivalent Conductivity and Mobility o f A erosol MA 146. shows th a t t h i s e f f e c t cannot be explained by an in c re ase d m o b ility of th e c o llo id a l e l e c t r o l y t e . Davies5 6 has sug g ested th a t th e c o llo id a l ions and t h e i r io n ic atm ospheres form reg io n s w ith in which th e co n d u c tiv ity i s g r e a te r than i t is in th e s o l u b i l i t y between them, th a t i s , beyond th e io n ic atm ospheres. In creasin g th e c o n c e n tra tio n w i l l de crea se th e s e p a ra tio n and so in c re a s e th e m o b ility of th e geg en io n s. Temperature Dependence of M o b ility . Another in te r e s tin g f e a tu re of our work i s th e im p l i c a t i o n ly in g in th e valu es of th e e le c tro p h o r e tic m obil i t i e s of th e potassium la u r a te m ic e lle a t 2°C. and a t 25°C. These, from Tables 2, 5 and 14, were found to be 2 .0 x 10~ 4 and 3.6 x 10”4 cm .^/v o lt s e c ., r e s p e c tiv e ly , a r a t i o of 1 . 8 . providing th a t no changes i n s o lv a tio n , shape or charge of th e m ic e lle occurs i n th e tem perature range con sid e re d , th e two m o b ilitie s should be in th e r a t i o n-^/no where n r e f e r s t o th e v is c o s ity of th e w ater a t th e two tem p eratu res T^ and Tg. Taking l i t e r a t u r e values of th e v i s c o s i t i e s a t 2° and 25°C. as 1.674 and 0.895 c e n tip o is e , t h i s r a t i o i s 1 .8 7 , i n good agreement w ith th e experim ent 147. a l l y determ ined value of 1 .8 . The im p lic a tio n would seem to he th a t the n atu re o f the m ic e lle does not change ra d ic a l l y over t h i s tem perature, u n le s s , of co u rse, th e changes which do occur a re m utually com pensating. The S ize and Charge of M ic e lle s. The assignm ent o f a s p e c if ic siz e and charge to th e m ic e lle in e v ita b ly in v o lv es a s e t of assum ptions. The a s sumption to be e x p l i c i t l y made in th e a p p lic a tio n o f the experim ental r e s u l t s i s th a t the d riv in g fo rc e f o r d if f u sio n is , in th e presence of s u f f i c ie n t swamping e l e c t r o ly t e o r when u sin g tr a c e r d if fu s io n , s im ila r in kind to the fo rc e causing e le c tro p h o r e tic m ig ratio n and d i f f e r s from i t only in m agnitude. This concept im p lies th a t the f r i c t i o n a l co e f f i c i e n t s which an ion ex p erien ces in i t s motion through a so lu tio n are the same in d iffu s io n and e le c tro p h o re s is when measured under the p ro p er c o n d itio n s, as d isc u sse d in Chap t e r I I . T h is id e n tity o f the f r i c t i o n a l c o e f f ic ie n ts is e x p l i c i t l y assumed in th e w ell known N ernst equ atio n fo r 71 th e d if fu s io n of a u n i-u n iv a le n t ion, in H a r t l e y ^ exten sion of th e Nernst eq u atio n 4* * * and in th e Debye-Huckel- Onsager th e o ry of c o n d u c tiv ity .4^ N ernst, T h eo retlsch e Chemie, 1926, 15th E d itio n , p . 431. 148. Making, the above assum ption, i t i s p o s s ib le to c a l c u la te a charge on th e m ic e lle using experim ental v alues of the d if fu s io n c o n sta n t and the e le c tro p h o r e tic m o b ility . The necessary eq u atio n s have been given in C hapter I I . T olm an^ has d eriv e d th e id e n tic a l equation in a somewhat d if f e r e n t manner. This equation, (1 2 ) u - ^ where u i s th e e le c tro p h o re tic m o b ility , q th e charge, D th e d if fu s io n c o e f f ic ie n t, k Boltzmannf s c o n sta n t, and T th e tem perature, involves no assum ption o th e r than th a t th e motion o f the f l u i d around the p a r t i c l e i s stream lin ed . No assum ption i s made as to th e s iz e o r shape of th e p ar t i c l e . U nless, however, the c o n d itio n s d isc u sse d in Chap t e r I I are r e a liz e d , the in te r p r e t a ti o n of the charge q i s open to some q u e stio n . The necessary c o n d itio n s re q u ire th a t th e m o b ility be measured a t o r e x tra p o la te d to in f in i t e d ilu tio n , in o rd e r th a t H u c k e l^ equation be s a t i s f i e d and th a t the d iffu s io n c o e f f ic ie n t be measured e ith e r in th e presence of s u f f i c ie n t swamping e l e c t r o ly t e o r be a s e lf d if f u s io n c o e f f ic ie n t measured, e .g ., by tr a c e r te ch n iq u es. Tolman, S t a t i s t i c a l M echanics, 1926, p. 231. 149. Dean and V in o g ra d ^ have measured th e d if f u s io n con s ta n t of dye-tagged A erosol OT using th e McBain-Northrup type of c e l l . As d iscu ssed in C hapter I, however, t h e i r d a ta were m is in te rp re te d by them and th e proper value of 0*060 cm*2/day o r 7.0 x 10“ ^ cm .^ /sec . fo r a 0*5 to 1 .0 $ so lu tio n se le c te d fo r our c a lc u la tio n . V e tte r has meas ured th e d if f u s io n c o e f f ic ie n t of A erosol M A in a 0.257 N sodium c h lo rid e s o lu tio n using a f r e e d iffu s io n method* He found a v alu e of 13*8 x 1 CT7 cm .^/sec. in th e range of 1*5 to 2.25$ A erosol M A * Lamm^ has used the McBain-Northrup type of c e l l to measure th e d if f u s io n c o e f f ic ie n t of p o ta s sium l s u r a t e in a s o lu tio n 0*1 N in KOH and 1 N in KOI a t 20°0. Above th e c r i t i c a l c o n c e n tra tio n he observed a value of 9*9 x 10“^ cm .^/sec* These v a lu e s, w ith th e correspond ing m o b ilitie s a t approxim ately th e same co n cen tratio n an d th e charges c a lc u la te d from t h i s d a ta by means o f eq u atio n (12), a re l i s t e d in Table 24. The g r e a te s t source o f e r r o r in th e above c a lc u la te d charges would seem to l i e in the v a lu e s of th e d iffu s io n c o n s ta n ts . F i r s t , th e re i s th e e r r o r alread y d iscu ssed in th e preceding ch a p te r, a r is in g out o f th e n e c e s s ity of c a l ib r a tin g th e McBain-Northrup c e l l w ith low m olecular weight m a te ria l and assuming th a t the c a l i b r a t i o n a ls o a p p lie s when hig h m olecular weight substances are used* 1 5 0 TABLE XXIV S o lu tio n C oncentration M o b ility D iffu sio n Charges p cm / v o l t 4 Coef• sec x 1 0 " Potassium la u r a te 2 .'058 3.80 9.9 9,9 3.5$ 3,. 6 5. 9.9 9.5 5.058 3.55 9.9 9.2 7.0$ 0 «30 9.9 8 . 6 9.4$ 3.14 9.9 8 . 2 A erosol 0T Q.0287U 4.46 7.0 16.4 A erosol M A 0.096 N 3.28 ■ 13.8 6 . 1 0.186 H 2.78 13.8 5.2 0.43 U 2.08 13.8 C O 151. Secondly, th e re i s the need of determ ining th e d i f fu sio n c o e f f ic ie n t in th e presence of s u f f i c ie n t swamping e l e c t r o ly t e . V ickers and Lamm seem to have s a t i s f i e d t h i s requirem ent, but theamount of swamping e l e c t r o l y t e which they employed was much more than re q u ire d and may a c tu a lly have caused in creased ag gregation o f th e m ic e lle s . Gran- ath^^ has determ ined th e d if f u s io n c o e f f ic ie n t of p o ta s sium m y ris ta te and la u r a te as a fu n c tio n o f s a l t concentra tio n and observed a more th an fo u r f o ld change in m o b ility when th e s a lt so lu tio n was changed from one 0 .4 molar in potassium bromide and 0 * 1 molar in potassium carbonate to one which was 1 * 6 m olar in potassium bromide and 0 . 1 molar in potassium ca rb o n ate. T his la rg e decrease in d if fu s io n c o n stan t can only be in te r p r e te d a s due to in c re a se d aggre g a tio n o f th e m ic e lle s . The t h i r d and perhaps th e g r e a t e s t source c f e rro r l i e s in th e thermodynamic eq u ilib riu m e x is tin g between th e soap m olecules and th e m ic e lle . This e q u ilib riu m p erm its th e f a s t e r d if fu s in g soap m olecule to leave th e m ic elle, p e n e tra te the g la s s membrane, and th e re reform in to mi c e l l e s . In e f f e c t, th e m ic e lle a c ts as a r e s e r v o ir o f soap m olecules. Some of th e m ic e lle s which appear to have mi g ra te d through th e membrane may a c tu a lly have been formed from th e f a s t e r d if fu s in g soap m olecules which, once they had p e n e tra te d th e membrane, re e s ta b lis h e d eq u ilib riu m w ith th e new s o lu tio n in which they found them selves. The use of dye t r a c e r tech n iq u e e lim in a te s t h i s d i f f i c u l t y , sin ce th e only way in which th e w ater in so lu b le dye can p e n e tra te th e membrane i s by rid in g in a m ic e lle . The change in dye c o n c e n tra tio n i s th e n a measure of th e m ic e lle s which have p e n e tra te d th e membrane, and i s not in fluenced by th e thermodynamic e q u ilib riu m between m olecules and m ic e lle s . For t h i s reason, th e d a ta of Dean and Vino- grad a re probably th e most r e l i a b l e of the s e le c te d v a lu e s . In view of th e d i f f i c u l t i e s d isc u sse d above and in C hapter IV, and th e absence o f s p e c if ic d eterm in atio n s on th e exact systems stu d ied by e le c tro p h o re s is , th e p u b lish ed v alu es must be used but w ith th e understanding th a t la rg e e r ro rs may have been introduced by so doing. In time the c a lc u la tio n s may be rep ea ted when a more r e l i a b l e method of measuring d if f u s io n c o n s ta n ts i s a v a ila b le . Equation (12) i s independent of any assum ption as to th e shape o f th e m ic e lle . I t i s also p o s s ib le to use th e m o b ility d a ta and th e assum ption o f a sp h e ric a l m icelle to c a lc u la te a charge by means of Henry*s equ atio n (equation 13 of C hapter I I ) . This procedure involves se v eral new assum ptions. Thus i t i s necessary to determ ine both IC and 153. f(K r). The Debye-Huckel term K was estim a ted by means of equation (21) of C hapter I I using McBainfs a s s u m p tio n ^ th a t th e io n ic s tre n g th o f soap so lu tio n s is s im ila r to th a t of a u n i-u n iv a le n t e l e c t r o ly t e . The ra d iu s , r, could be c a lc u lte d from th e d if f u s io n measurements of V e tte rs and ofDean and Vinograd by means of E in s te in 1 s d iffu s io n equa tio n , and by assuming S to k e s 1 law (equation 24 of Chapter I I ) . Knowing K and r , i t i s p o s s ib le to e stim a te f(K r) from th e curve provided by Henryk® and th e n the charge could be c a lc u la te d from equation (13) of C hapter I I . This was done f o r A erosol M A and potassium la u r a te , and th e re s u l t s ta b u la te d in T ables 25 and 26. I t i s rem arkable th a t t h i s more cumbersome procedure w ith i t s dubious assum ptions agrees so w ell w ith th e char ges as c a lc u la te d by eq u atio n (1 2 ) w ithout a l l th e se e x tra assum ptions. U nless th e e rro rs which were intro d u ced by th e assum ptions are m utually com pensating, th e agreement by th e two methods seems to suggest th a t, in th e c o n c e n tra tio n I’ange stu d ie d , th e concepts of a sp h e ric a l m ic e lle i s not to o f a r from th e t r u t h . Brady has measured th e s e lf - d if f u s io n c o e f f ic ie n ts of th e f r e e c a tio n s in A erosol M A and A erosol OT so lu tio n s u sin g ra d io a c tiv e sodium, and from h is r e s u l t s has calcu la te d the percentage of sodium io n s bound to th e m ic e lle . 154. TABLE. X X V CHARGE O H AEROSOL M A MICELLE C oncentration Hr 1 + Kr f (Kr) Charge per m ic e lle 0.096N 0,0562 1,04 0.667 5.8 0 .186N 0.0506 1.05 0.667 4 .9 0.46H 0.0795 1.08 0.667 5.9 155. TABLE XXVI CHARGES O N POTASSIUM LAUBATE MICELLE i t r a t l o n Kr I + Xr f (Kr) Charge per m ic e lle Z.Qfo 0.0454 1.045 0.667 9.1 3 .5$ 0.0600 1.060 0.667 3.8 5 .0 % 0.0719 1.072 0.667 8.7 7 .0% 0.0847 1.085 0.667 8 .1 .9.4# 0.0985 1.099 0.667 7.9 156. His c a lc u la tio n I s based upon th e equation (13) D 0 - D* C1 - Dm C« where D , th e measured net d if fu s io n constant of th e sodium ion, Df th e d if fu s io n co n stan t of th e f r e e sodium ion, D m th e d iffu s io n co n stan t of th e m ic e lle , and where 0 , 0 1 and Cf l a re th e t o t a l , f r e e sodium ion and bound sodium c o n c e n tra tio n . I t i s , of co u rse, p o s s ib le to combine our value of th e t o t a l charge w ith Brady*s p ercen tag e of io n iz e d mole c u le s in th e m ic e lle to o b ta in an estim a te o f th e number o f m olecules p er m ic e lle . T his c a lc u la tio n i s again indepen dent of any assum ption as to the shape of th e m ic e lle , but does assume th a t th e charge as measured by Brady i s th e same as th e charge which c o n trib u te s to th e m o b ility of th e mi c e l l e . I f Brady*s equation c o r r e c tly d e fin e d th e system, then th e m o b ility at i n f i n i t e d i l u t i o n should g iv e the same charge as does Brady*s experim ent. In Table £7 a re tab u la te d th e m olecular w eights of th e Aerosol O T and Aerosol M A m ic e lle s o b tain ed from our m ic e lle charge as ta b u la te d in Table 24 and Brady*s d a ta of th e percen tag e of sodium ions bound to the m ic e lle . The valu es of th e number of m olecules p e r m icelle as c a lc u la te d from th e s e d a ta are much sm aller than one might expect, p a r tic u la r ly in view 157. A erosol 0.Q287H O T 0..096N M A f° TABLE XXVII SIZE O F MICELLE Ionized Charges M olecules /m i- M olecular c e lie H eight 33$ 16,4 20 8,900 64$ 6,1 9 .5 3,700 158. o f th e very marked s o lu b iliz in g power of th e s e d e te rg e n ts . Undoubtedly p a r t of t h e e rro r a r is e s in th e u n c e rta in ty in th e v alu e of th e d if f u s io n c o e f f ic ie n t, but a much g r e a te r source of e rro r must be in th e f a c t th a t the charge which Brady measured i s not the same as th e charge which is ob ta in e d from th e m o b ility measurements a t f i n i t e concentra ti o n s . I f one knows the m olecular weight of th e m ic elle, then B rady1s d a ta of th e p ercen tag e o f charged m olecules in th e m ic e lle may be used to c a lc u la te th e charge on th e m ic e lle . Assuming th a t th e m ic e lle i s s p h e ric a l with a ra d iu s o f 17.3 % and t h a t th e d e n s ity o f the m ic e lle i s approxim ately 1.0 (see V e tte r ) then the m olecular weight of th e m ic e lle is approxim ately 13,000. This m olecular w eight, tim es th e p erce n tag e f ig u re s re p o rte d by Brady, g iv e s th e charge on th e m ic e lle . These f ig u r e s are rep o r te d in Table 28 and a r e seen t o be more th an fo u r tim es th o se as c a lc u la te d by th e two methods p re v io u sly d isc u sse d . The Types of M ic e lle s. In concluding t h i s ch a p ter i t i s d e s ira b le to d is cuss b r ie f ly any co itrlb u tio n t h is work may have in reg ard to th e d isp u te over th e ty p e s of m ic e lle s . McBain, as d iscu ssed in the f i r s t ch a p ter, b e lie v e s th a t two ty p e s e x is t, one a small h ig h ly charged m ic e lle , and th e second 159. TABLE XXVIII CHARGE O N AEROSOL M A MICELLE FROM BRACT'S DATA Aim DIFFUSION C o n cen tratio n Charge per m ic e lle 0.096N 27 0.186N 24 0.46N 16 160. a la r g e r la m e lla r m ic e lle . Presumably, although McBain does not so s ta te , both ty p e s are capable of s o lu b iliz in g dyes and hydrocarbons, sin ce th e phenomenon of s o lu b iliz a tio n appears when m ic e lle s are form ed. In our e le c tro p h o re s is experim ents we have never observed th e form ation of more than one boundary. F u rth e r more, although q u a n tita tiv e measurements of th e r a t e o f spreading of the boundary could not be made, th e spreading seemed t o be due only t o d if f u s io n . These o b serv atio n s, seem to imply th a t e ith e r : (1) Only one type of s o lu b iliz in g m ic e lle e x is ts ; o r (2) I f two o r more ty p es o f s o lu b iliz in g m ic e lle s e x is t then they a re in such ra p id eq u ilib riu m th a t in an e le c tro p h o re s is experim ent they a c t as one e n t ity . The above co n clu sio n s suggest th a t, as f a r as our measurements are concerned, we can d e te c t only one type of s o lu b iliz in g m ic e lle . Whether one must conclude from t h is th a t only one type e x is ts is a m a tte r of in d iv id u a l p r e f e r ence and background. SU M M A R Y A tr a d e r te ch n iq u e has been developed f o r measuring th e p r o p e r tie s of soap m ic e lle s . This tech n iq u e u t i l i z e s th e phenomena of dye s o lu b iliz a tio n to ta g th e m ic e lle . In t h i s way th e p r o p e r tie s of th e m ic e lle may be stu d ied independently of th e p r o p e r tie s o f th e soap io n s w ith which th e m ic e lle s a re in eq u ilib riu m . The method is developed p a r t i c u l a r l y towards th e d eterm in atio n of th e e le c tro p h o re tic m o b ility of th e m ic e lle . The th eo ry of e le c tro p h o re s is and d if fu s io n i s d is cussed i n d e t a i l . I t is shown th a t th e charge o f th e mi c e l l e may be c a lc u la te d from th e e le c tro p h o r e tic m o b ility a t i n f i n i t e d ilu tio n and from th e s e lf - d if f u s io n c o e f f i c ie n t of th e m ic e lle . Two methods are developed fo r measuring e le c tr o p h o re tic m o b ility by t r a c e r te ch n iq u e. The double Y c e l l i s e s s e n tia lly a H itto r f method, while th e diaphragm c e l l i s a m o d ific a tio n o f B rady1s a n a ly tic a l boundary method. M o b ilitie s o b tain ed by th e two c e l l s a re in reasonably good agreement w ith one an o th er. The e le c tro p h o re tic m o b ilitie s o f th e m ic e lle s of potassium la u r a te and A erosol M A were determ ined over a c o n c e n tra tio n range and th a t o f A erosol O T a t one p a r tic u 162. l a r c o n c e n tra tio n . The d a ta which were o b tain ed are d is cussed in r e l a t i o n to th e s iz e and charge o f th e m ic e lle . APPENDIX A CHEMICALS USED T hepotassiua la u r a te used in a l l our experim ents was made from Eastman Kodak la u r io a c id #933, and ca rb o n a te f r e e potassium hydroxide. The c a rb o n a te -fre e potassium hydroxide was p rep ared by h ea tin g 50 grams ofBaker*s C.P. grade ofpotassium hydroxide w ith 400 ml. of a b so lu te ethan o l. A fte r most o f th e s o lid had d isso lv ed , th e so lu tio n was f i l t e r e d through a s in te r e d g la s s funnel in to 2 0 0 ml. of p re v io u sly b o ile d and cooled d i s t i l l e d w ater and th en made up to about 1 l i t e r . The s o lu tio n was th e n b o ile d , and th e w ater re p le n ish e d as necessary, u n t i l th e odor o f ethanol could no lo n g er be d e te c te d . The eq u iv alen t weight o f th e la u r ic a c id was ob ta in e d by a procedure given in N ied e ra l, Organic Q uantita tiv e M ic ro a n a ly sis, 1942, p. 6 6 , involving a t i t r a t i o n of the la u r ic a c id w ith K O H in 50$ e th a n o l. The equivalent weight was found to be 200.2. The t h e o r e t i c a l v a lu e f o r pure la u r ic acid i s 200.31. The c a p ill a r y m eltin g p o in t of th e la u r ic a c id was found to be between 43.3 and 43.8°C. The l i t e r a t u r e ^ valu e is 43.6°C. 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Asset Metadata

Creator Hoyer, Horst (author)

Core Title A new approach to the problem of measuring the properties of micelles

School Graduate School

Degree Doctor of Philosophy

Degree Program Biochemistry

Degree Conferral Date 1951-09

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry, biochemistry,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor [illegible] (committee chair), [illegible] (committee member), Vold, Robert D. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c17-15825

Unique identifier UC11347653

Identifier DP21756.pdf (filename),usctheses-c17-15825 (legacy record id)

Legacy Identifier DP21756.pdf

Dmrecord 15825

Document Type Dissertation

Rights Hoyer, Horst

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA