established in the case of the model surfactant AM Br

Transcription

1 Topic 279 Sufactants and Miceles; Ionics An intense debate concens the stuctue of micelles, paticulaly those fomed by ionic sufactants such as SDS and CTAB. It seems geneally ageed that micelles ae essentially spheical in shape. The pola head goups ( e.g. N Me 3 ) ae at the suface of each micelle, having stong inteactions with the suounding solvent. In close poximity in the Sten laye ae counteions (e.g. bomide ions in the case of CTAB); the aggegation numbe n descibes the numbe of cations which fom each micelle. The total chage on the micelle is detemined the aggegation numbe and a quantity β, the latte being the faction of chage of aggegated ions foming the micelle neutalised by the micelle bound counte ions. The emaining faction of counte ions exists as fee ions in aqueous solution. Both n and β ae chaacteistic of a given sufactant system, and ae obtained fom analysis of expeimental data [1. The popeties of ionic sufactants have been extensively studied [2-14. Hee we examine fou themodynamic desciptions of these systems. Ionic Sufactant:1:1 salt: Phase Equilibium: Dy Neutal Micelle We conside a dilute aqueous solution of an ionic sufactant; e.g. AM B. As moe sufactant is added a tace amount of micelles appea in the solution when the concentation of sufactant just exceeds the cmc. The tace amount of sufactant is pesent as micelles constituting a micella phase. At defined T and p, the following uilibium is established in the case of the model sufactant AM B ; AM B ( aq) AM B ( mic) (a) Then, [ AM B ( aq) = [ AM B ( mic) (b) We assume that the micelles cay no chage. The chemical potential of the sufactant in aqueous solution is elated to the cmc using the following uation whee y is the mean ionic activity coefficient. We set [ AM B ( mic) ual to the chemical potential of the sufactant in the pue micella state, [ AM B ( mic).

2 ( AM B ; aq; c scale) 2 R T ln( cmc y / c ) = ( AM B ; micella phase) (c) Hee ( AM B ; aq; c scale) is the chemical potential of the salt AM B - in aqueous solution at unit concentation whee the popeties of the salt ae ideal. Thus y descibes the ole of ion-ion inteactions in the solution having salt concentation cmc. Because the model states that thee is only a tace amount of micelles in the system, we do not take account of salt-micelle inteactions. Then mic G = (micella phase; AM B ) (AM B ;aq;c scale) (d) Hence, mic G ( aq; c scale) = 2 R T ln( cmc y / c ) (e) If the salt concentation in the aqueous solution at the cmc is quite low, a useful assumption sets y ual to unity. Then, mic G ( aq; c scale) = 2 R T ln( cmc/ c ) (f) The latte uation leads to the calculation of the standad incease in Gibbs enegy when one mole of salt AM B - passes fom the ideal solution, concentation 1 mol dm -3 to the micella phase. Thee is a modest poblem with the latte uation which can aise conceptual poblems. As nomally stated the cmc fo a given salt is expessed using the unit mol dm -3 so that c = 1 mol dm 3. This means that when cmc > 1 mol dm -3, mic G ( aq; c scale) is positive. Fo solutes whee cmc < 1 mol dm -3, the deived quantity is negative. Anothe appoach expesses the cmc using the mole factions, cmx such that uation (c) is witten as follows. (AM B ;aq; x scale) 2 R T ln(cmx f ) = (AM B ;micella phase) (g) Hee ( AM B ; aq; x scale) is the chemical potential of the salt AM B in an ideal solution whee the (asymmetic) activity coefficient f = 1. and cmx = 1.. By definition lim it[x(am B ) f 1. at all T and p. } The = analogue of uation (f) takes the following fom. mic G ( aq; x scale) = 2 R T ln( cmx) (h)

3 Because cmx is always less than unity, mic G ( aq; x scale) is always negative. It is impotant in these calculations to note the definitions of efeence and standad states fo solutes and micelles othewise false conclusions can be dawn [14. The analysis poceeds to use the Gibbs- Helmholtz uation. Hence, (i) 2 mic H (aq; x scale) = 2 R T { ln(cmx) / T} p The tem { ln( cmx)/ T} p is conveniently obtained by expessing the dependence of cmx on tempeatue using the following polynomial. 2 ln( cmx) = a a T a T Equation (h) is staightfowad, the stoichiometic facto 2 emeging fom the fact that each mole of salt AM B - poduces on complete dissociation 2 moles of ions. A key assumption in this analysis is that the micelles cay no electic chage. In othe wods a micelle is fomed by n moles of cation AM, n moles of counte ions B - being bound within the Sten laye such that the chage on each micelle is zeo. This model is a little unealistic. Ionic Sufactant: 1:1 salt: Phase Equilibium: Dy Chaged Micelle A cationic sufactant AM B - in aqueous solution foms micelles when n cations come togethe to fom a micella phase. Beaing in mind that n might be geate than 2, the idea that thee exists mico-phases of macocations in a system with an electic chage at least 2 is not attactive. In pactice the chage is patially neutalised by bomide ions in the Sten laye. The quantity β efes to the faction of counte ions bound to cations. Thus the fomal chage numbe on each micelle is [ n ( 1β ). In the model developed hee we epesent the fomation of the mico-phase compising the micelles as follows whee n is the numbe of cation monomes which cluste, the emaining bomide ions being pesent in the aqueous solution (phase). nam ( aq) n ( 1 β β) B ( aq) (k) n ( 1β) [ nam n - ( mic) n ( 1β) B ( aq) We e-expess this uilibium in tems of uilibium chemical potentials fo a system at fixed T and p. (j)

4 n (AM n (1 β β) (B (l) - n (1β) = {[nam n ;micelle} n (1 β) (B We define the chemical potential of the micelle micophase which contains 1 mole of AM. This is a key extathemodynamic step. We also descibe the micelle as a pue phase. {[AM - (1β) = ;micelle} {[nam n - n (1β ) ;micelle}/ n (m) Hence, (AM = {[AM (B - (1β) ;micelle} (1 β) (B (n) O, (AM B 1 = {[AM - (1β) ;micelle} (1 β) (B (o) The tem 1 ( AM B ; aq) is the uilibium chemical potential of a 1:1 salt in solution at the cmc. The tem (B is the uilibium chemical potential of the bomide ion in the solution at the cmc of the sufactant. In any event the system is electically neutal. (AM B = {[AM 1 By definition, 2 R T ln[cmc y(am B ) / c - (1β) (1 β) { ;micelle} (B R T ln[cmc y(b ) / c } (p) mic G = {[AM (1 β) - (1β) ;micelle} (B (AM B 1 (q) Assuming both yamb ( ) and y ( B ) ae unity, G = 2 R T ln[ cmc/ c ( 1β ) R T ln[ cmc/ c () mic o mic G = ( 1 β ) R T ln[ cmc/ c (s) The latte uation closely esembles that fo non-ionic sufactants fo which β is unity. Fo ionic sufactants it is not justified to assume that β is also unity. Ionic Sufactant: 1:1 salt: Dy Chaged Micelle:Mixed Salt Solutions As moe ionic sufactant is added to a solution having the concentation of sufactant ual to the cmc, so the solution inceasingly esembles a mixed salt solution, simple salt, chaged micelles and counte ions. Analysis of

5 the popeties of such solutions was descibed by Buchfield and Woolley [2-5. We might develop the analysis fom uation (k). An advantage of witing the uation in this fom stems fom the obsevation that both sides of the uation descibe an electically neutal system. Woolley and co-- wokes [4,5 pefe a fom which emoves a contibution n ( 1β ) B ( aq) fom each side of uation (k). nam aq n B n aq nam ( ( ) ( ) [ β) β n - 1 ( aq) (t) Nevetheless one might ague that uation (k) does have the meit in compaing two salts wheeas uation (t) descibes the links between thee ions. In tems of uation (k), thee ae two salts in solution. (I) AM B - whee ν ν ν 1/ ν ν ν ν 2 = 1, ν = 1, ν = 2,Q = ( ν ν ) = 1, y = y y,o y = y y But (AM B ) = (AM B ) 2 R T ln(c(am B ) y (AM B ) / c ) (u) n (II) Fo the micella salt, [ nam ( 1β n ) n (1- β)b - - ν = 1, ν = n ( 1 β), and ν = n ( 1 β) 1 and Q n β n β = [ 1 { n ( 1β )} with y = y y n ( 1 β) 1 ( 1 ) ( 1 ) 1 1 n ( 1β) Then, ( mic. salt) = ( mic. salt) [n (1- β) 1 R T ln[ Q c( mic. salt) y / c (v) At uilibium, n ( AM B ; aq) = ( mic. salt ; aq) (w) Hence, G = R T ln(k ) = (mic.salt) n (AM B ) (x) mic.salt The total concentation of salt ctot in the system is given by uation (y). ctot( AM B ; system) = n c(ch ag ed micelles) c(am B ; aq) (y) The analysis makes no explicit efeence to a cmc. Instead the micella system is descibed as a mixed salt solution. Application of these uations uies caeful compute based cuve fitting fo multi-paametic uations. The latte include uations elating mean ionic activity coefficients fo salts to the composition of a given solution. A shielding facto δ was use by Buchfield and Woolley to educe the impact of micella chage of the cationic micelles on calculated ionic stength [2.

6 Thus the effective chage on the cationic micelles was witten as n ( 1β) δ whee δ is appox..5. Ionic Sufactant: Mass Action Model In geneal tems the uilibium between sufactant monomes Z, counte anions X - and micelles M can be epesented by the following uation. ( n m) nz ( aq) mx ( aq) M ( aq) Then in tems of the mass action model, the concentation uilibium constant, K ( n m) n m = [ M /{[ Z [ X } c (z) (za) 1 By definition, mic G =( n) R T ln( K c ) (zb) Then, 1 ( n m) mic G /( R T) = ( n) ln[ M ln[ Z ( m/ n) ln[ X (zc) Footnotes [1 N. M. van Os, J. R. Haak and L. A. M. Rupet, Physico Chemical Popeties of Selected Anionic, Cationic and Non-ionic Sufactants, Elsevie, Amstedam [2 T. E. Buchfield, and E. M. Woolley, J. Phys. Chem.,1984,88,2149. [3 T. E. Buchfield and E. M. Woolley, in Sufactants in Solution, ed. K. L. Mittal and P. Bothoel, Plenum Pess, New Yok, 1987, volume 4, 69. [4 E. M. Woolley and T. E. Buchfield, J. Phys. Chem.,1984,88,2155. [5 T. E. Buchfield and E.M.Wooley, Fluid Phase Equilib., 1985,2,27. [6 D. F.Evans, M. Allen, B.W. Ninham and A. Fouda, J. Solution Chem.,1984,13,87. [7 D. G. Ache, J. Solution Chem.,1986,15,727 [8 (a) L. Espada, M. N. Jones and G. Pilche, J.Chem. Themodyn., 197, 2,1, 333; and efeences theein. (b) M. N. Jones, G. Pilche and L.Espada, J. Chem.Themodyn,.,197,2,333 [9 M. J. Blandame, P. M. Cullis, L. G. Soldi and M. C. S. Subha, J. Them. Anal.,1996,46,1583. [1 R. Zana, Langmui, 1996,12,128.

7 [11 M. J. Blandame, K. Bijma, J. B. F. N. Engbets, P. M. Cullis, P. M. Last, K. D. Ilam and L. G. Soldi, J. Chem.Soc. Faaday Tans.,1997,93,1579; and efeences theein. [12 M. J. Blandame, W. Posthumnus, J. B. F. N. Engbets and K. Bijma, J. Mol. Liq., 1997, 73-74,91. [13 R. DeLisi, E. Fiscao, S. Milioto, E. Pelizetti and P. Savaino, J. Solution Chem.,199,19, 247. [14 M. J. Blandame, P. M. Cullis, L. G. Soldi, J. B. F. N. Engbets, A. Kacpeska, N. M. van Os and M. C. S. Subha, Adv. Colloid Inteface Sci.,1995,58,171. [15 Fo futhe efeences concening the Sten Laye, see N. J. Buuma, P. Seena, M. J. Blandame and J. B. F. N. Engbets, J. Og. Chem., 24, 69, 3899.