 Main
Multicomponent Diffusion of Interacting, Nonionic Micelles with Hydrophobic Solutes
 Alexander, Nathan
 Advisor(s): Dungan, Stephanie R.;
 Phillips, Ronald J.
Abstract
In this thesis, we examine diffusion in ternary, aqueous solutions of the nonionic surfactant decaethylene glycol monododecyl ether (C12E10) and a hydrophobic solute, either decane or limonene. In solution, the surfactant molecules selfassemble to form micelles swollen by hydrophobic solutes, with essentially no free hydrophobic solute or surfactant monomer in the surrounding solvent. The diffusive behavior of this system is very interesting in that surfactantsolute interactions are strong, and result in a highly nondiagonal diffusivity matrix [?], which depends in part on how strongly micelles grow with an increasing amount of solubilizate along the diffusion pathway. This behavior is distinct from that of colloidal dispersions comprised of polydisperse rigid hard particles, which are unable to reassemble on a molecular level to lower the system free energy as they diffuse. The goal of this work is to present experimental data and develop rigorous theoretical results that capture the influence of selfassembly on the ternary diffusion coefficient matrix [?], and on the time and static correlation functions that are commonly used to analyze light scattering data in these mixtures.
In Chapter 1, ternary diffusion coefficient matrices [?] and morphological parameters, such as the micelle aggregation number, hydrodynamic radius, and hydration index, were measured using the Taylor dispersion method and static and dynamic light scattering techniques, respectively, for C12E10/decane/water solutions. The matrix [?] for this system was found to be highly nondiagonal, and concentration dependent, over a broad domain of solute to surfactant molar ratios, and micelle volume fractions up to ? ≈ 0.25. Measurements for the average micelle radius and aggregation number indicate a weak dependence on the micelle volume fraction but a strong linear increase with the solutetosurfactant molar ratio. Furthermore, a theoretical model, based on Batchelor’s theory for gradient diffusion in dilute, polydisperse mixtures of interacting spheres is developed and effectively used to predict [?] with no adjustable parameters. In this model, a Poisson distribution of solute molecules among micelles was assumed with a onetoone correspondence between the number of solute to surfactant molecules distinguishing each micelle species.
In Chapter 2, experimental data for the ternary diffusion coefficient matrices [?] are presented for crowded ternary mixtures of C12E10 surfactant with either decane or limonene solute. Our theoretical model for [?], which was introduced in Chapter 1, is simplified by neglecting local polydispersity. Even though the model originates from dilute theory that incorporates pairwise hydrodynamic and thermodynamic interactions, the theoretical results were in surprisingly good agreement with experimental data for concentrated mixtures, with volume fractions up to ? ≈ 0.47. This agreement suggests that the effects of manyparticle hydrodynamic and thermodynamic interactions cancel, resulting in experimental and theoretical predictions that are nearly linear over the entire range of concentration. In addition, the theory predicts eigenvalues ?− and ?+ that correspond to longtime self and gradient diffusion coefficients, respectively, for monodisperse spheres, in reasonable agreement with experimental data.
The third and final chapter of this thesis involves the development of model equations for the Rayleigh ratio and the mode amplitudes of the normalized electric field autocorrelation function, which are commonly used to analyze time averaged and photon correlation spectroscopy data, respectively. These theoretical results were derived using thermodynamic fluctuation theory applied to crowded solutecontaining micellar solutions and microemulsions with negligible molecular species and polydispersity. This theory invokes nonequilibrium thermodynamics and enforces local equilibrium between molecular solute, surfactant, and the various micellar species, in order to support the influence of selfassembly on the light scattering functions for the first time. We find that micelle growth effects along the diffusion path in these mixtures, which were shown to drive strong multicomponent diffusion effects, expressed via the ternary diffusivity matrix [?], do not affect the scattering functions in the limit of zero local polydispersity. Hence, theoretical predictions for the Rayleigh ratio and the field autocorrelation function for ternary mixtures of solutecontaining, locally monodisperse micellar solutions are identical to those developed for binary mixtures of monodisperse, colloidal hard spheres. However, micelle growth effects are predicted to influence the thermodynamic driving forces and eigenmodes for diffusion. In support of our theoretical results, measurements for the Rayleigh ratio and the field autocorrelation function for ternary aqueous solutions of decaethylene glycol monododecyl ether (C12E10) with either decane or limonene solute were performed for several molar ratios and volume fractions up to ? ≈ 0.25, and for binary mixtures of C12E10/water up to ? ≈ 0.5. Excellent agreement between our light scattering theory and experimental data is achieved for low to moderate volume fractions (? < 0.3) and at higher concentration when our volume fraction calculations are corrected to account for micelle dehydration.
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