Coarse-grained simulations of rapid assembly kinetics for polystyrene-b-poly(ethylene oxide) copolymers in aqueous solutions.

We present a coarse-grained, implicit solvent model for polystyrene-b-poly(ethylene oxide) in aqueous solution and study its assembly kinetics using Brownian dynamics simulations. The polymer is modeled as a chain of freely jointed beads interacting through effective potentials. Coarse-grained force field parameters are determined by matching experimental thermodynamic quantities including radius of gyration, second virial coefficient, aggregation number, and critical micelle concentration. We investigate the influence of cooling rate (analogous to the rate of solvent quality change in rapid precipitations), polymer concentration, and friction coefficient on the assembly kinetics and compare simulation results to flash nanoprecipitation experiments. We find that assembly kinetics show a linear scaling relation with inverse friction coefficient when the friction coefficient is larger than 1. When the cooling time is less than the characteristic micellization time, stable kinetically arrested clusters are obtained; otherwise, close-to-equilibrium micelles are formed. The characteristic micellization time is estimated to be only 3-6 ms, in contrast to 30-40 ms previously determined in experiments. We suggest that previous experiments probed the formation of micellar clusters while simulations in this work studied the kinetics of a single micelle assembled from free polymer chains.