Applications of self-consistent field theory in polymer systems

Abstract

The self-consistent field theory (SCFT) based upon coarse-grained model is especially suitable for investigating thermodynamic equilibrium morphology and the phase diagram of inhomogeneous polymer systems subjected to phase separation. The advantage of this model is that the details of the chain such as the architecture of the chain and the sequence of blocks can be considered. We present here an overview of SCFT approach and its applications in polymeric systems. In particular, we wish to focus on our group's achievements in applications of SCFT in such fields: simulation of microphase separation morphologies of multiblock copolymers with a complex molecular architecture, interactions between brush-coated sheets in a polymer matrix, mixtures of flexible polymers and small molecular liquid crystals at the interface, shapes of polymer-chain-anchored fluid vesicles, self-assembled morphologies of block copolymers in dilute solution, and so on. Finally, the further developments as well as the perspective applications of SCFT are discussed.

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

“…The SCF method is used to study fluctuations, pattern formation, and segregation in various kinds of polymer mixtures (see references [244][245][246][247] and references therein). In many works, the method is applied on a mixture of different types of homopolymers or block copolymers built of two types of monomers A and B.…”

Binary hairy nanoparticles: Recent progress in theory and simulations

“…Theoretical methods frequently involved in the research of binary polymer brushes include scaling arguments, self‐consistent mean field theory (SCFT), single chain in mean field (SCMF), and density functional theory (DFT) . Scaling theory is a powerful method in predicting the power law behavior that relates physical quantities (e.g., brush height and grafting density in a polymer brush).…”

An alternative derivation of orbital-free density functional theory

“…Using Hubbard-Stratonovich transformations, the partition function can be The Journal of Chemical Physics ARTICLE scitation.org/journal/jcp rephrased, without approximation, into a form involving a density function n(r) and a conjugate chemical potential field w(r), expressed using Kac-Feynman path integrals. [20][21][22][23] A mean field approximation then gives a partition function which, if classical correlations missing from the mean field are included in the exchangecorrelation term, can be considered exact. The term "exact" is used throughout this paper in the context of DFT, that is, expressions are exact if a "perfect" exchange-correlation function is known.…”

“…A free energy is readily obtained from the field theory transformed partition function through F = −kBT ln QN. The details of this process are widely available, [20][21][22][23] but for completeness, a summary is provided in Appendix A.…”