Lattice Monte Carlo simulations of mixed surfactant systems and polymer surfactant systems.

Abstract

A lattice Monte Carlo Model is developed to examine mixed surfactant systems, or more specifically, (i) the non-ideal mixing behavior of binary surfactant solutions, (ii) the growth of large aggregates in binary surfactant solutions, and (iii) mixtures of polymer and surfactant in dilute aqueous solutions. Simulated critical micelle concentrations (CMC) of binary surfactant systems are compared with the predictions of both a molecular thermodynamic theory and a regular solution theory. The simulated CMC as a function of overall surfactant composition is in reasonable agreement with the theoretical models when a fitted value for the interaction parameter, beta, is used. The fitted value is in good agreement with a value estimated a priori from the lattice model for the surfactants with attractive head groups, but there are large discrepancies for the case of repulsive head groups. The discrepancies in the latter are caused by non-random mixing, i.e., segregation of the two-surfactants within each micelle. A novel simulation approach is developed to accelerate the formation of diffusion-limited large aggregates in an effort to examine the stable microstructures in the micelle-to-vesicle transition. Our simulation results indicate the evolution of microstructures exhibits four distinct morphologies; (i) initially, the amphiphile mixture aggregates into spherical micelles; (ii) as micelles collide they grow and eventually transition into rod-shaped aggregates; (iii) the rods grow into wormy, polymer-like micelles; (iv) finally the wormy micelles interconnect to form a network of disk-shaped aggregates. While unable to produce a vesicle on the small boxes to which our simulations are limited, these intermediate structures correspond quite well with those seen in experimental studies. From the investigation in polymer-surfactant systems, we are able to capture images of polymer-surfactant complexation that match generally accepted structure for these complexes. However, plots of the free monomer concentration versus the total surfactant concentration fail to show the expected behavior at the critical aggregation concentration (CAC), where polymer-bound micelles begin to form, and at the critical concentration for the formation of free micelles. This failure of the model can be traced to a combination of weak binding of micelles to polymers and large simulation errors, due to the finite box-size effects.