Single chain structure in thin polymer films: corrections to Flory’s and Silberberg’s hypotheses

Abstract

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