Quantitative study of fluctuation effects by fast lattice Monte Carlo simulations: Compression of grafted homopolymers

Abstract

Using fast lattice Monte Carlo (FLMC) simulations [Q. Wang, Soft Matter 5, 4564 (2009)] and the corresponding lattice self-consistent field (LSCF) calculations, we studied a model system of grafted homopolymers, in both the brush and mushroom regimes, in an explicit solvent compressed by an impenetrable surface. Direct comparisons between FLMC and LSCF results, both of which are based on the same Hamiltonian (thus without any parameter-fitting between them), unambiguously and quantitatively reveal the fluctuations/correlations neglected by the latter. We studied both the structure (including the canonical-ensemble averages of the height and the mean-square end-to-end distances of grafted polymers) and thermodynamics (including the ensemble-averaged reduced energy density and the related internal energy per chain, the differences in the Helmholtz free energy and entropy per chain from the uncompressed state, and the pressure due to compression) of the system. In particular, we generalized the method for calculating pressure in lattice Monte Carlo simulations proposed by Dickman [J. Chem. Phys. 87, 2246 (1987)], and combined it with the Wang-Landau-Optimized Ensemble sampling [S. Trebst, D. A. Huse, and M. Troyer, Phys. Rev. E 70, 046701 (2004)] to efficiently and accurately calculate the free energy difference and the pressure due to compression. While we mainly examined the effects of the degree of compression, the distance between the nearest-neighbor grafting points, the reduced number of chains grafted at each grafting point, and the system fluctuations/correlations in an athermal solvent, the θ-solvent is also considered in some cases.

Calculating pressure in polymer lattice simulations

“…To avoid the expensive numerical integration over the coupling parameter l, Jimenez and Rajagopalan combined this method with Bennet's acceptance-ratio method, 12 and we recently combined it with Wang-Landau -Optimized Ensemble (WL-OE) sampling 13 to estimate the density of states of N c and also replaced the rst-order backward nite difference in eqn (1) by the secondorder centered nite difference for higher accuracy. 14 nVT simulations avoid chain insertion/deletion and can therefore be used to calculate pressure at high f. When the RWM is used to calculate the bulk pressure P in nVT simulations, 10 however, the system is conned between two impenetrable surfaces and P n (L x ) ¼ P(f m ) is assumed, where f m is taken as the polymer volume fraction in the middle of the conned lm and has some statistical error due to the system uctuations (note that, at high f, a small variation in f leads to a large change in P; see Fig. 8).…”

Quantitative Study of Fluctuation Effects by Fast Lattice Monte Carlo Simulations. V. Incompressible Homopolymer Melts

“…This is the fifth paper in our series of study, − where fast lattice Monte Carlo (FLMC) simulations are directly compared with the corresponding polymer lattice field theories based on the same model system (Hamiltonian), thus without any parameter-fitting, to unambiguously and quantitatively reveal the effects of fluctuations and correlations either neglected or treated approximately in the theories. In the first paper in this series (referred to as Paper I hereafter), we studied a model system of compressible homopolymer melts (or equivalently, homopolymers in an implicit, good solvent).…”

Structural and phase transitions of one and two polymer mushrooms in poor solvent

“…Note that this 1/n scaling has also been found in our previous studies on the fluctuation effects in various systems using FLMC simulations. [2][3][4][5] To examine the fluctuation effects on CGT, Fig. 9 shows the distribution of α 2 at n/ρ 0 = 1/5 obtained from FLMC simulations at χ * CGT = 1.412 given by LSCF calculations.…”

“…6,7 It is also known that a polymer mushroom exhibits similar CGT. [8][9][10][11] In line with our previous work on grafted polymers, [3][4][5] here we consider CGT of a mushroom of flexible polymers grafted onto a planar, homogeneous, and neutral (non-selective) substrate, and immersed in an explicit and poor solvent. We use a coarse-grained lattice model with MOLS, and define a mushroom as a group of n chains each of N segments end-grafted at the same point onto a substrate.…”