Relationship between macroscopic and microscopic models of surfactant adsorption dynamics at fluid interfaces

In a companion preceding paper, we presented an experimental investigation into the adsorption dynamics of a diblock copolymer surfactant to a polymer/polymer interface and found them to be well-described by a microscopic model of diffusion in a potential generated using self-consistent field theory. We compare the predictions of the microscopic approach with a macroscopic (adsorption-diffusion) model and demonstrate the equivalence of the two models when the free-energy well underlying surfactant adsorption is flanked by barriers that are significantly larger than thermal energy (kT). However, when the energy barriers are nonexistent, as is the case for the experimental system of interest, a finite interfacial width must be introduced into the classical model to obtain physically meaningful results (i.e., nonnegative desorption rates). Surprisingly, we find that the predictions of the macroscopic finite interfacial width model with no adjustable parameters are in excellent agreement with experimental data presented in the companion paper even though the latter was obtained with molecular resolution. This agreement provides insight into aspects of the free-energy landscape that determine surfactant transport.