ELECTROPHORESIS IN STRUCTURED COLLOIDS

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1 ELKIN 4 ELECTROPHORESIS IN STRUCTURE COLLOIS José M. Médez A. Cvestv Mexo I ollboto wt O. Aló-Wess ULA d J. J. Beel-Mstett Cvestv.

2 V µ E; µ 6πη

3 ε ζ ; ζ 3

4 ε ζ ζ 4

5 THE GENERATION OF ONE PARTICLE EFFECTIVE YNAMICS 5

6 Lgev euto dv dt ζ v p [ ] u δ ; t V E f d 6

7 7 Cotuty euto E p k V k k E d t t t E J J J J J β δ δ δ δ ' '; Fk s ppoxto ; e

8 Modfed Fk s ppoxto We pss to by wtg d by tkg. sted of 8

9 9 Geelzed Lgev euto t t dt t t dt t t t dt d f F E E v v v ' ' ' ' ' ζ ζ

10 Popetes of teest ; dt t T k B L S ζ ζ ζ ζ ; dt t ζ ζ µ Log-te self-dffuso oeffet: Eletopoet oblty:

11 Popetes of teest ot. d ~ / 6 π ζ ζ d ~ 6 π

12 MOEL SYSTEM AN STRUCTURE

13 3 Ptve odel PM: Oe-opoet odel OCM: < fo fo u ε 4 fo e e fo B T k u < ε π κ κ ε κ κ

14 4 Te stutue of outeos d slt os s obted fo OZ te PM d ebye-hükel ppoxto H It esults ; '; ' ' k d k V k p k k. ; ε β Θ ; e e e κ κ κ ε β κ ε β

15 Te stutue of optles s obted fo OZ ' ' d' te OCM ypeetted HNC V exp[ βu γ ] γ d Roges-Youg ppoxtos RY exp[ γ f ] exp[ βu ] γ f f exp[ α ]; α s obted by dedg χ RY RY PY fo α HNC fo α s well s fo opute sultos. T χ T v 5

16 6 EUILIBRIUM YNAMIC PROPERTIES SELF-IFFUSION COEFFICIENT [ ] / 3 / ~ π κ κ ε π B L S T k K K d

17 7 ELECTROLYTE EFFECTS / L S K 78. 3K..8 e Stokes Cl Stokes N ε T

18 8 STRUCTURE EFFECTS / ~ L S K d π 78. 3K..8 e Stokes Cl Stokes N ε T

19 9 NON-EUILIBRIUM YNAMIC PROPERTIES ELECTROPHORETIC MOBILITY [ ] 3 / 3 / ~ ~ 6 π κ κ ε π π µ µ B T k K K d K d

20 ELECTROLYTE EFFECTS E V V V V E E E E E V E 3 / K K µ µ

21 Te oblty ot be veted s f s oly syet slt s dded to te syste. µ µ K / L S 3 y 3 Stokes N Stokes Cl T 3K ε 78. e.8.

22 By ddg syet slt te ossove to te olous ego be eed two tes. Te veted oblty s t lest two odes of gtude slle t te ol oblty. e e Stokes Mg Stokes Cl T 3K ε

23 3 STRUCTURE EFFECTS E V E V E 3 / ~ ~ 6 K d K d π π µ µ

24 Te u of te oblty oves s futo of slt otet wt esg oo oetto. e ; T 3K; ε 78. Stokes Stokes.8;. N Cl ϕ 3 κ M. eggel T. Plbeg M. Hgebüle E. E. Me 4 R. Kuse C. Gf y R. Webe J. Collod Itefe S

25 Te oblty eses s te logt of te oetto of oos. Stokes Cl ε 78. T 3K Stokes N e.8. s 6 M M. Eves N. Gbow. Hessge y T. Plbeg Pys. Rev. E

26 6 Te oblty stutes wt te oos oetto. Its stuto vlue s two tes te fee ptle oblty. ~ ~ 6 d d π π µ µ >> 3 / ~ 6 K K d α α α α α α α π M. Eves N. Gbow. Hessge y T. Plbeg Pys. Rev. E M s

27 SOME CONCLUSIONS Te eletopoet oblty µ stutued ollodl suspesos s outed fo by exteso of te geelzed Lgev euto fols to o-eulbu sttoy poesses w s ble to ptue te oetto d eletolyte effets t te se level of despto. Te eletopoet oblty of oly oe oo s ot veted we te eletolyte s foed by syet slt. Wt syet slt te veso s possble depedg o te ge of te oo d o ts sze. By esg ϕ te veted bell gvg µ s futo of s beoes syet d ts u oves to lge vlues of s. Its ew posto s ougly gve by s [ oles/d 3 ] ϕ. It does ot deped o te ge of te oos. Fo teedte oettos we expet esg bevo of µ s futo of ϕ gog fo µ to µ s l ϕ. Fo gly stutued systes we get µµ ; te tspot veloty beoes extly two tes te tspot veloty dlute syste d ts sees to be uvesl bevo! 7

28 SOME REFERENCES Effetve teto potetls:. M. Med-Noyol d. A. Mue J. Ce. Pys P. Gozález-Mozuelos d M.. Cbl-Too J. Ce. Pys J. M. Médez-Alz d R. Kle Pys. Rev. E Stutue lultos:. J. M. Médez-Alz B. Aguo d R. Kle Lgu J. M. Médez-Alz M. Cávez-Páez B. Aguo d R. Kle Pys A Self-dffuso:. M. Med-Noyol Fdy suss. Ce. So A. Vz-Redó M. Med-Noyol H. Ruz-Estd d J. L. Auz-L Rev. Mex. Fís J. M. Médez-Alz d O. Aló.Wess Pys A Moblty:. O. Aló-Wess d R. M. Velso J. Ce. Pys M. Lozd-Cssou d E. Gozález-Tov J. Collod Itefe S J. M. Médez-Alz d O. Aló-Wess evelopets Mtetl d Expeetl Pyss Volue B: Sttstl Pyss d Beyod Kluwe Ade/Pleu Publses

ELECTROPHORESIS IN STRUCTURED COLLOIDS

ELECTROPHORESIS IN STRUCTURED COLLOIDS ELECTROPHORESIS IN STRUCTURE COLLOIS José M. Médez A. Civesv jedez@fis.ivesv.x p://www.fis.ivesv.x V µ E; µ 6πη ε ζ ; i i ζ i i 3 ε ζ ζ 4 THE GENERATION OF ONE PARTICLE EFFECTIVE YNAMICS 5 6 Lgevi euio