Finite volume method for self-consistent field theory of polymers: Material conservation and application

Single chain in mean field simulation of flexible and semiflexible polymers: comparison with discrete chain self-consistent field theory

Single chain in mean field (SCMF) simulation is a theoretical framework performing Monte Carlo moves of explicit polymer chains under quasi-instantaneously updated external fields which were originally imported from the self-consistent field theory (SCFT). Even though functional-based hybrid simulations are often used to compare the results of SCFT and MC simulation, the adoption of a finite number of coarse-grained segments makes direct comparison rather difficult. In this study, we perform SCMF simulation of block copolymers using various chain models and quantitatively compare it with discrete chain SCFT (DCSCFT) which finds the mean field solution of polymers with a finite number of segments. By comparing free energy and natural period of the symmetric block copolymer lamellar phase, we systematically show that DCSCFT serves as an intermediate step between SCMF simulation and SCFT. In addition, by adopting angle dependent bond potential, we perform SCMF simulation of semiflexible polymers using bead-spring and freely jointed chain models. As the chain stiffness increases, the lamellar phase tends to align perpendicular to the surfaces when confined between two neutral walls. We also investigate the effects of fluctuation and chain stiffness on the distribution of chain ends. The tendency of chain end segregation towards the surfaces turns out to increase as the chain stiffness increases for both homopolymer and block copolymer systems.

Numerical implementation of pseudo-spectral method in self-consistent mean field theory for discrete polymer chains

In the standard self-consistent field theory (SCFT), a polymer chain is modeled as an infinitely flexible Gaussian chain, and the partition function is calculated by solving a differential equation in the form of a modified diffusion equation. The Gaussian chain assumption makes the standard SCFT inappropriate for modeling of short polymers, and the discrete chain SCFT in which the partition function is obtained through recursive integrals has recently been suggested as an alternative method. However, the shape of the partition function integral makes this method much slower than the standard SCFT when calculated in the real space. In this paper, we implement the pseudospectral method for the discrete chain SCFT adopting the bead-spring or freely jointed chain (FJC) model, and a few issues such as the accurate discretization of the FJC bond function are settled in this process. With the adoption of the pseudospectral method, our calculation becomes as fast as that of the standard SCFT. The integral equation introduces a new boundary condition, the neutral boundary, which is not available in the standard SCFT solving the differential equation. This interesting physical situation is combined with the finite-range interaction model for the study of symmetric block copolymers within thin films. We find that the surface-perpendicular block copolymer lamellar phase becomes preferable to the surface-parallel one when both the top and bottom surfaces are neutral.

Interactions between brush-grafted nanoparticles within chemically identical homopolymers: the effect of brush polydispersity

We systematically examined the polymer-mediated interparticle interactions between polymer-grafted nanoparticles (NPs) within chemically identical homopolymer matrices through experimental and computational efforts. In experiments, we prepared thermally stable gold NPs grafted with polystyrene (PS) or poly(methyl methacrylate) (PMMA), and they were mixed with corresponding homopolymers. The nanocomposites are well dispersed when the molecular weight ratio of free to grafted polymers, α, is small. For α above 10, NPs are partially aggregated or clumped within the polymer matrix. Such aggregation of NPs at large α has been understood as an autophobic dewetting behavior of free homopolymers on brushes. In order to theoretically investigate this phenomenon, we calculated two particle interaction using self-consistent field theory (SCFT) with our newly developed numerical scheme, adopting two-dimensional finite volume method (FVM) and multi-coordinate-system (MCS) scheme which makes use of the reflection symmetry between the two NPs. By calculating the polymer density profile and interparticle potential, we identified the effects of several parameters such as brush thickness, particle radius, α, brush chain polydispersity, and chain end mobility. It was found that increasing α is the most efficient method for promoting autophobic dewetting phenomenon, and the attraction keeps increasing up to α = 20. At small α values, high polydispersity in brush may completely nullify the autophobic dewetting, while at intermediate α values, its effect is still significant in that the interparticle attractions are heavily reduced. Our calculation also revealed that the grafting type is not a significant factor affecting the NP aggregation behavior. The simulation result qualitatively agrees with the dispersion/aggregation transition of NPs found in our experiments.