Studying Amphiphilic Self-assembly with Soft Coarse-Grained Models

Abstract

Highly coarse-grained models for investigating the self-assembly of lipids and copolymer materials are discussed. Soft interactions between segments that represent many atoms naturally arise in the course of systematic coarse-graining, and they are necessary for modeling fluctuation effects whose strengths is dictated by a large invariant degree of polymerization. The soft non-bonded interactions of the coarse-grained models are related to the excess free-energy functional of an equivalent field-theoretic description. The connection between the particle-based model and the field-theoretic description helps to identify the physical significance of the model interactions. Non-bonded interactions, which describe the complex phase behavior of compressible mixtures or include local fluid-like packing effects of the coarse-grained segments, can be systematically constructed based on liquid-state theory or classical density functional theory. Details of the computational implementation and limitations of soft coarse-grained models are discussed. Two computational techniques-field-theoretic force-matching and umbrella sampling-are devised for computing a free-energy functional from a particle-based description. They can be employed to (i) derive the non-bonded free-energy functional of a soft coarse-grained model from a more detailed computational model or to (ii) derive a field-theoretic description from a particle-based model. Moreover, different strategies for accurately calculating free energies of self-assembled systems are described and selected applications presented.

Mechanics of membrane fusion/pore formation

“…However, the chemical potential, (r) ≡ (ıF[m]/ım(r)), can be obtained by field-theoretic umbrella sampling (Müller, 2009(Müller, , 2011Müller and de Pablo, 2013). To this end, one augments the interactions of the particle model by an additional Hamiltonian of the form…”

Kinetics of directed self-assembly of block copolymers on chemically patterned substrates

“…In this manuscript we use a soft, coarse-grained polymer model [22,23] that is able to describe the kinetics of structure formation on the pertinent time and length scales. Then we discuss the kinetics of structure formation for pattern replication, i.e., when there is a one-to-one correspondence between the chemical guiding pattern and copolymer structure, and for two-fold density multiplication.…”

“…On the length scale of such a highly coarse-grained segment, the macromolecule already adopts its random-walk like statistics and the distances are Gaussian distributed. Therefore we use a discretized Edwards Hamiltonian to model the connectivity along the polymer backbone [22,24,23]…”

Phase diagrams of block copolymer melts by dissipative particle dynamics simulations

“…In the field of block copolymers, this general tendency stimulated two lines of research. First of them implies developing hybrid techniques [10][11][12][13] that involve the concept of a self-consistent field into the calculation of interactions in the ensemble of particles. In that way, the evaluation of interchain interactions becomes a considerably less time-consuming procedure.…”