Quantifying the critical micelle concentration of nonionic and ionic surfactants by self-consistent field theory

Quantifying the critical micelle concentration (CMC) and understanding its relationship with both the intrinsic molecular structures and environmental conditions remains a great challenge because 1) models need to reflect detailed molecular structures and chemistry-specific interactions and 2) long-range electrostatic interactions need to be accurately treated to model ionic surfactants and capture their responses to a variety of salt effects. We propose to solve these challenges by developing a self-consistent field theory (SCFT) which is applicable to both nonionic and ionic surfactants. We perform calculations for the structure and free energy of individual micelles in a subvolume, where this information is then incorporated into the dilute solution thermodynamics for the study of CMC, micellar structure, and the kinetic pathway of micellization. The long-range electrostatic interactions are decoupled from the short-range van der Waals interactions and are explicitly treated in our theory. This enables us to study a variety of salt effects such as counterion binding, salt concentration dependence, and the specific ion effect.

We apply the theory to three types of commonly used surfactants: alkyl poly(oxyethylene) ether (C_mE_n), sodium dodecylsulfate (SDS), and sodium poly(oxyethylene) dodecylsulfate (SLES). We investigate the dependence of the micellar structure and CMC on both the intrinsic structure of the surfactants and the external salt effects such as the salt concentration and the specific-ion effect. We compare CMC predicted by our theory with experimental measurements reported in the literature.

For alkyl poly(oxyethylene) ether (C_mE_n) surfactants, we predict a wide range of CMC from 10^-6 to 10^-2M as the composition parameters m and n are adjusted. For the ionic sodium dodecylsulfate (SDS) surfactant, we show a decrease of the CMC as the salt concentration increases and capture both the specific cation effect and the specific anion effect. Furthermore, for sodium poly(oxyethylene) dodecylsulfate (SLES) surfactants, we find a non-monotonic dependence of both the CMC and micelle size on the number of oxyethylene groups. Our theoretical predictions of CMC are in quantitative agreement with experimental data reported in the literature for all three types of surfactants, demonstrating the effectiveness and versatility of our theory.