An Improved Form for the Electrostatic Interactions of Polyelectrolytes in Solution and its Implications for the Analysis of QELSS Experiments on Sodium Dodecyl Sulfate and Cetyl Trimethyl Ammonium Bromide Solutions

Abstract

The electrostatic interaction between two charged spheres in the presence of a screening electrolyte is calculated at the level of the linearized Debye-Hückel theory. The calculation is performed analytically as a multipole expansion by applying two-center spherical harmonic expansions and symbolic manipulation methods. I focus on charge-charge and charge-induced dipole interactions, calculated for two spheres of possibly unequal size. The former interaction is given to good approximation by the familiar Debye-Hückel form ~ q₁q₂exp[-k(R-2a)]/[(epsilon*r(1+ka)^2]. The new results are the charge-induced dipole interactions. Physically, these terms arise from two sources: (i) surface polarization charge at the surface of each sphere, and (ii) exclusion of the counterion cloud of each sphere from the volume occupied by the other sphere. With parameters appropriate for micelles, the charge-induced dipole interactions dominate the charge-charge interaction at small separations.
Quasi-elastic light scattering measurements of the diffusion of sodium dodecyl sulfate (SDS) and cetyl trimethyl ammonium bromide (CTAB) micelles in aqueous solutions, and the diffusion of mesoscopic optical probes through the same solutions, were carried out at 35°C and multiple solvent ionic strengths. Assuming a spherical micelle, I deduced the micelle radius, aggregation number, charge, and hydration from nonlinear least-squares fits to both probe and mutual diffusion data. For SDS micelles the charge that I find is lower than reported in the literature [Hayter, J. B.; Penfold, J. Colloid & Polymer Science 1983, 261, 1022; Triolo, R.; Caponetti, E.; Graziano, V. J. Phys. Chem. 1985, 89, 5743.] because I used an improved functional form of the micellar electrostatic interaction. I find a smaller aggregation number and a larger micellar hydration than literature values. My analysis of CTAB data implies extensive micellar growth, and failure of the spherical micelle assumption.