A multiscale model for kinetics of formation and disintegration of spherical micelles

Abstract

Dynamics of self-assembly and structural transitions in surfactant systems often involve a large span of length and time scales. A comprehensive understanding of these processes requires development of models connecting phenomena taking place on different scales. In this paper, we develop a multiscale model for formation and disintegration of spherical nonionic micelles. The study is performed under the assumption that the dominant mechanism of micelle formation (disintegration) is a stepwise addition (removal) of single monomers to (from) a surfactant aggregate. Different scales of these processes are investigated using a combination of coarse-grained molecular dynamics simulations, analytical and numerical solution of stochastic differential equations, and a numerical solution of kinetic equations. The removal of a surfactant from an aggregate is modeled by a Langevin equation for a single reaction coordinate, the distance between the centers of mass of the surfactant and the aggregate, with parameters obtained from a series of constrained molecular dynamics simulations. We demonstrate that the reverse process of addition of a surfactant molecule to an aggregate involves at least two additional degrees of freedom, orientation of the surfactant molecule and micellar microstructure. These additional degrees of freedom play an active role in the monomer addition process and neglecting their contribution leads to qualitative discrepancies in predicted surfactant addition rates. We propose a stochastic model for the monomer addition which takes the two additional degrees of freedom into account and extracts the model parameters from molecular dynamics simulations. The surfactant addition rates are determined from Brownian dynamics simulations of this model. The obtained addition and removal rates are then incorporated into the kinetic model of micellar formation and disintegration.

On the predictions and limitations of the Becker–Döring model for reaction kinetics in micellar surfactant solutions

“…It is, however, possible to calculate an equilibrium aggregate size distribution from knowledge of the chemical potential differences between monomers in different sized aggregates. This may be done via Molecular Dynamics (MD) simulations [13,16,25] or by Molecular Thermodynamics (MT) [26,27,30]. Either method predicts a distribution characterized by the following key features.…”

“…where ω is still defined by (25). The right-hand side of (40) is exponentially small unless ν and ω are asymptotically close to 1.…”

Modelling the interfacial behaviour of dilute light-switching surfactant solutions

“…However, even with commonly used CG approaches, pre-cmc calculations are strongly dependent on (i) the capability of the model to preserve the molecular character of surfactant-solvent interactions and, (ii) the adopted methodology. [30][31][32][33][34][35][36][37][38] However, in these simulations, the key limitation to performing a full-fledged simulation including the surfactant and the full amount of solvent molecules associated with these dilute conditions remains, even with the reduced resolution of the coarse grained models.…”

Kinetics of formation of bile salt micelles from coarse-grained Langevin dynamics simulations

“…For head-tail surfactants, simulations 47,59 suggest that addition and removal of a monomer from a micelle is well-described via a single reaction coordinate, the distance, r, between monomer and micelle. The removal process is activated, being associated with large free energy barriers (8k B T, including the contribution of the 2 ln(r) term 47 ).…”