Self-assembly of coarse-grained ionic surfactants accelerated by graphics processing units

Due to the relatively long time scales inherent to ionic surfactant self-assembly (>μs), an aggressive computational approach is needed to obtain converged data on micellar solutions. This work presents a study of micellization using a coarse-grained (CG) model of aqueous ionic surfactants in replicated molecular dynamics (MD) simulations run on graphics processing unit hardware. The performance of our implementation of the CG model with electrostatics into the HOOMD-Blue GPU-accelerated MD software package is comparable to that of a modest sized cluster running a highly optimized parallel CPU code. From 0.36 ms of cumulative trajectory data, we are able to predict equilibrium thermodynamic and morphological properties of ionic surfactant micellar solutions. Estimating the critical micelle concentrations (CMC) from the free monomer (ρ ₁) and premicellar concentrations obtained from simulations of sodium hexyl sulfate (S6S, CMC of 460 ± 6 mM) at high (1 M) concentration, a value in good agreement with experimental results is obtained; however, the same method applied to simulations of sodium nonyl sulfate (S9S, ρ ₁ of 2.4 ± 0.01 mM) and sodium dodecyl sulfate (SDS, ρ ₁ of 0.02 ± 0.01 mM) at the same total concentration systematically underestimates the CMCs. An alternative method for calculating the CMC is presented, where the free monomer concentration computed from high concentration CG-MD data is used as the input to a simple theoretical model which can be used to extrapolate to a more accurate prediction of the CMC. Better agreement between the empirical and predicted CMC is obtained from this theory for S9S (28.7 ± 0.3 mM) and SDS (3.32 ± 0.04 mM), though the CMC for S6S is slightly underestimated (304 ± 3 mM). We also present statistically converged morphological data, including aggregation number distributions and the principal components of the gyration tensor. This data suggest a transition from spherical micelles to rod-like at a specific aggregation number, which increases with increasing hydrocarbon length.