Single chain structure in thin polymer films: Corrections to Flory's and Silberberg's hypotheses

TL;DR

This study uses Monte Carlo simulations to analyze how ultrathin polymer films deviate from classical theories, revealing logarithmic divergence in chain size and power-law decay in bond correlations, with implications for experimental interpretations.

Contribution

It provides the first detailed simulation-based analysis of chain conformations in ultrathin films, extending beyond Flory's and Silberberg's hypotheses with new quantitative insights.

Findings

Logarithmic divergence of chain size parallel to walls in ultrathin films.

Bond-bond correlation function decreases as a power law with exponent 1.

Deviations from classical scattering models increase as film thickness decreases.

Abstract

Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond-fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, $H$, is smaller than the excluded volume screening length (blob size), $\xi$, the chain size parallel to the walls diverges logarithmically, $R^2/2N \approx b^2 + c \log(N)$ with $c \sim 1/H$. The corresponding bond-bond correlation function decreases like a power law, $C(s) = d/s^{\omega}$ with $s$ being the curvilinear distance between bonds and $\omega=1$. % Upon increasing the film thickness, $H$, we find -- in contrast to Flory's hypothesis -- the bulk exponent $\omega=3/2$ and, more importantly, an {\em decreasing} $d(H)$ that gives direct evidence for an {\em enhanced} self-interaction of chain segments reflected at the walls. Systematic deviations from the Kratky plateau as a function of $H$ are found for the single chain form factor parallel to the walls in agreement with the {\em non-monotonous} behaviour predicted by theory. This structure in the Kratky plateau might give rise to an erroneous estimation of the chain extension from scattering experiments. For large $H$ the deviations are linear with the wave vector, $q$, but are very weak. In contrast, for ultrathin films, $H<\xi$, very strong corrections are found (albeit logarithmic in $q$) suggesting a possible experimental verification of our results.