Self-Diffusion of Constituent Cationic Surfactants in Threadlike Micelles

Self-diffusion mechanisms of a surfactant molecule in entangled threadlike micelles formed from a mixture of cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) in aqueous solution (CTAB:NaSal/W) are discussed. The self-diffusion coefficient ( D self ) for the cetyltrimethylammonium (CTA + ) cation in the micelle was calculated on the basis of a phantom network model. Two formulations for the self-diffusion coefficient are derived for two separate regimes with respect to time and space. When the relaxation time (τ m ) for the micellar system is short, D self is represented as 〈ξ 2 〉{6τ m P ( L e,τ m )}, where 〈ξ 2 〉 is the mean square of the entanglement spacing which depends on the CTA + concentration and P ( L e,τ m ) is a probability for the CTA + cation to remain in the initial part of the threadlike micelle with the average contour length of L e between two entanglements. On the other hand, when τ m is long, D self is expressed as (2 Q /3)( D lat /2τ m ) 1/2, where Q and D lat are the persistence length of the threadlike micelle and the lateral diffusion coefficient of the CTA + cation along the micellar contour, respectively. D self values and activation energies determined experimentally by use of a forced Rayleigh scattering technique agree with those calculated based on the model.