The influence of diffusion and chemical reaction on adsorption kinetics in binary surfactant systems

Abstract

A macroscopic transport theory of adsorption kinetics in binary surfactant systems has been developed, taking into account the influence of diffusion as well as bulk and surface chemical reaction. The chemical kinetics involve reaction of a surfactant (solute 1) with either the host liquid or another species present in large excess to form a second surfactant (solute 2), which is also reactive. When the chemical rate equations are “pseudo-first-order” in bulk and surface concentration of surfactant, and there are no energy barriers to adsorption, the transport equations describing subsurface dynamics can be solved analytically. However, when we assume a binary Langmuir-type adsorption isotherm relating surface and subsurface concentrations, we generate a set of coupled, non-linear integral equations which must be solved numerically. These solutions show that, because diffusion increases the surface concentration while chemical reaction ultimately decreases the total amount of surfactant in the system, the surface concentration exhibits a maximum value with time. The position of the maximum, the value of the surface concentration at maximum, as well as the shape of the surface concentration/time curve, are all shown to be sensitive, in varying degrees, to changes in diffusion, chemical reaction, and adsorption parameters. For example, increases in the dimensionless Damköhler number, which is a ratio of chemical reaction to diffusion rates, decrease both the time to maximum, as well as the surface concentration at maximum. The applicability and relevance of this work to situations of technological interest, such as the migration of reactive adhesion promoting species in polymeric resins, is also briefly discussed.