A Monte-Carlo and Self-Consistent Field calculations of encapsulated spherical polymer brushes

TL;DR

This study compares self-consistent field and Monte Carlo methods to analyze spherical polymer brushes in confined cavities, revealing insights into density profiles, pressure relationships, and the effects of curvature and compression.

Contribution

It introduces an extended Flory theory for highly compressed brushes and compares SCF and MC methods, highlighting their agreement and differences in modeling confined polymer systems.

Findings

SCF and MC methods show good agreement for free and softly compressed brushes.

An extended Flory theory accurately predicts behavior in highly compressed regimes.

Monomer volume fraction scales with cavity pressure, with different exponents from SCF and MC analyses.

Abstract

We present the results of extensive numerical self-consistent field (SCF) and 3-dimensional off-lattice Monte Carlo (MC) studies of a spherical brush confined into a spherical cavity. The monomer density profile and the cavity pressure have been measured in systems where curvature of the cavity has an important effect on the polymer brush conformation. A direct comparison between the SCF and MC methods reveals the SCF calculation to be a valuable alternative to MC simulations in the case of free and softly compressed brushes. In the case of strongly compressed systems we have proposed an extension of the Flory theory for polymer solutions, whose predictions are found to be in good agreement with the MC simulations and has the advantage of being computationally inexpensive. In the range of high compressions, we have found the monomer volume fraction $v$ to follow a scale relationship with the cavity pressure $P$, $P \sim v^\alpha$. SCF calculations give $\alpha=2.15 \pm 0.05$, close to {\em des Cloiseaux law ($\alpha=9/4$)}, whereas MC simulations lead to $\alpha=2.73 \pm 0.04$. We conclude that the higher value of $\alpha$ obtained with MC comes from the monomer density correlations not included in the SCF formalism.