Polymer brushes in weakly interpenetrating regimes

We employ Molecular Dynamics (MD) simulations and develop new scaling laws to probe the behavior of semi-dilute polymer brushes in the weakly interpenetrating regime. This particular regime is characterized by the condition d$_{\mathrm{g}}$ being more than d$_{\mathrm{0}}$ but less than 2d$_{\mathrm{0}}$, where d$_{\mathrm{g}}$ is the gap between two opposing surfaces with grafted polymer brushes and d$_{\mathrm{0}}$ is the unperturbed brush height. Our results, showing excellent match between the MD simulation and scaling theory predictions, establish (a) unlike the classically studied case of strongly interpenetrating polymer brushes with d$_{\mathrm{g}}$ less than d$_{\mathrm{0}}$, here the brush height ($d)$, instead of being solely dictated by the interpenetration length, can be expressed in a power law form where $d$ scales as $N^{\chi }$ (where $N$ is the polymer size), (b) the exponent $\chi $ shows a monotonic increase with a decrease in the degree of interpenetration, (c) the interpenetration length shows a different scaling behavior as compared to the strongly interpenetrated case, and (d) the scaling behavior of the experimentally-witnessed variation of the compressive energy between the brushes can be reproduced.