Molecular Simulation of Surfactant Self-assembly: From Mesoscale to Multi-scale Modeling.
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Fully atomistic computer simulations of surfactant self-assembly are extremely challenging because of the different length scales and the associated different times scales, implying large system sizes and tediously long simulations. To overcome this, the uninteresting degrees of freedom at the atomistic level can be integrated out leading to a meso-scale model, which can span the required length and time scales with less computational burden. We use such a meso-scale model to study surfactant self-assembly and how alcohols affect this self-assembly behavior in supercritical carbon dioxide. Here the surfactants and alcohols are represented as a chain of beads where each bead represents a set of atoms. This model is implemented into lattice Monte Carlo simulations. We show that short chain alcohols act as cosurfactants by concentrating in the surfactant layer of the aggregates, strongly decreasing micellar size and increasing the number of aggregates. In contrast long chain alcohols act as cosolvents by concentrating more in the solvent and increasing the micellar size. We then focus on systematically constructing a meso-scale model that preserves the important aspects of the atomistic model, while spanning these different length and time scales. The process of constructing this meso-scale model from the corresponding atomistic model is called coarse-graining. We first explore the rigorous coarse-graining technique in which we match the partition function of the atomistic model with that of the meso-scale model. Such a rigorous procedure has the advantage that it leads to the reproduction of all the structural and thermodynamic properties of the atomistic model in the meso-scale model. We develop a procedure to calculate the rigorous 1, 2... N-body effective interactions using Widom's particle insertion method. We implement this rigorous procedure for a binary Ar⁄Kr system, where the degrees of freedom of Ar are integrated out. We observed that the structure at the pair level is well reproduced by the effective system using only effective pair potentials and ignoring all higher multi-body contributions. However, we observe deviations in the pressure for higher densities. These latter deviations are attributed to the neglect of three- and higher multi-body interactions. For complex systems, we explore coarse-graining techniques that match the correlation functions between the atomistic and the meso-scale models. We apply this coarse-graining procedure for a system of ethanol molecules in water. In the coarse-grained model each ethanol molecule is represented by one spherical bead and the water is coarse grained out completely. We show that the potential of mean force works well as an effective potential only for low concentrations (8wt%), an integral equation approach with hypernetted chain closure approximation works well up to quite high surfactant concentrations (50 wt%), while an iterative Boltzmann scheme works very well for even the highest concentrations studied (70wt%).
coarse-graining, cosolvent, supercritical, alcohol, co2, cosurfactant, multi-scale, simulation, modeling, surfactant, self-assembly, effective potential