A triple-layer, planar coordinate model for describing counter -ion association to micelles

Ching-Chieh Lin, Purdue University

Abstract

A planar triple layer model describing ion association to micelles composed of the anionic surfactant dodecylsulfate (DS–) was developed and evaluated. The governing Poisson-Boltzmann equation was solved ( i) analytically, and (ii) with a numerical shooting method. The second solution was developed to confirm the accuracy of the first, and because the analytical solution is only valid for symmetrical electrolytes. The latter solution is applicable also to multiple valence counter-ion systems. Because the absolute value of the electrical potential at the micelle surface is so large, the classical Debye-Hückle approximation is invalid and was not made. To evaluate the resulting algorithms, they were incorporated into an overall speciation model that describes surfactant and metal ion equilibria in aqueous solutions, and includes an equation that describes DS– micelle-monomer phase distribution: [special characters omitted] where [DS–]w is the DS– surfactant monomer concentration in the aqueous phase, and also equal to the critical micelle concentration (cmc), e is the elementary charge (1.602 × 10–19 C), Ψs is the Stern layer potential, and k T is the product of Boltzmann's constant and absolute temperature. The Stem layer thickness (λ s), and the Y-intercept of the cmc-electrical potential relationship (K1) were calculated by minimizing residuals between experimental and calculated cmc values over a range of experimental aqueous Na+ concentrations. For sodium dodecylsulfate in NaCl solutions, the analytical model and numerical model provided essentially the same result, the same optimum λ s, and K1 values, and accurate cmc predictions. For this system, λs = 1 Å, and K1 = –4.51. For sodium dodecylsulfate in MgCl2, NaCl electrolyte solutions, the numerical model provided increasing trend of optimum λs for increasing [Mg+2], (λs increases as 10.0, 11.0, 12.0 Å for [Mg+2]w increasing as 0.2, 0.5, 1.0 mM) with optimum K1 as –4.29, –4.22, –4.16 respectively. For sodium dodecylsulfate in AlCl 3, NaCl electrolyte solutions, the numerical model gave similar trend as that in MgCl2, NaCl solutions, while the optimum λ s is 11.0 Å, and optimum K1 is –4. 1. The average errors between the experimental cmc data and the optimal model results are 5.78 %, 3.56 %, 3.11 %, 4.14 %, and 4.62 % for pure NaCl, 0.2 mM, 0.5 mM, 1.0 mM MgCl2 - NaCl and 0.2 mM AlCl 3 - NaCl electrolyte systems solutions, respectively.

Degree

Ph.D.

Advisors

Jafvert, Purdue University.

Subject Area

Environmental engineering|Environmental science|Chemical engineering

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