Structural analysis of adsorbed chains using the Monte Carlo method

Abstract

By simulation of polymer chains using a computer a study has been made of different characteristics of macromolecules adsorbed on a plane surface. As a model we took a self intersecting chain on a simple cubic lattice. The first unit of the chain is constrained to an adsorbing surface, and when any other chain units get onto the surface an energy gain ϵ results. The analysis covered flexible chains where there is equiprobability of trans- and gauche-isomers, and also stiffer chains with a preferred trans-configuration. The amounts of units adsorbed at the surface were calculated as well as the length of adsorbed and loop-like segments, the adsorbing layer thickness, the chain lengths and the areas covered on the surface by polymers with varying degrees of polymerization for different ϵ values. It is shown that in the region of polymer-surface energies below a critical level the number of polymer-surface contacts is small, irrespective of the length of the chain, whereas with energy values exceeding the critical level the number of contacts increases linearly with increasing numbers of chain units. In addition there is a redistribution of trans- and gauche-isomers in adsorbed and nonadsorbed parts of the macromolecules. Rigidization of the polymer chain increases the number of units in contact with the surface, and there is a sharpening of the transition from the nonadsorbed to the adsorbed state. The calculated adsorptive layer thicknesses characterized by the mean height of a chain end over the adsorbing surface are large in the pre-critical region, and depend on the molecular weight of the polymer chain, while in the post-critical region, on the other hand, the layer thickness is not a function of the chain length, and is small. It was found that the root mean square radius of inertia for an entire chain 〈 R 2〉 is invariably proportional to MW, and varies relatively little with ϵ. At the same time the radius of inertia of the adsorbed part of a macromolecules is near zero in the region of low polymer-surface interaction energies, and approximates 〈 R 2〉 in cases where the energies exceed a critical level.