Dynamics of a Grafted Chain into a Rubber Network: A Monte Carlo Study (minor grammatical changes)

Abstract

The dynamics of a single chain tethered to an interface and in contact with a cross-linked network is examined numerically. When the network is put in contact with the tethered chain, the chain moves with dynamics that are highly constrained due to entanglements. When the surface is repulsive, the chain runs straight along the surface and then forms a plume in the network that starts at a distance of order $\sim\!N^{1/2}$ from the graft point. For short times, the chain length in the gel increases algebraically as a function of time, in most cases as $\sim\!t^{1/2}$. The plume configuration is highly metastable and on a much longer time scale the point of entry into the network decreases to zero. This is similar to the relaxation of the arm of a star polymer in a cross-linked network. The above findings are in agreement with the analytical predictions of O'Connor and McLeish. The effects of a chemical disparity between the grafted chain, the network, and the substrate are investigated. Topological constraints are placed in the interface to determine their effects on the dynamics. Chains tethered at both ends are also studied and show a transition in behavior as a function of the thickness of the interface. Above a critical thickness chain does not penetrate.