The theory of polymer adsorption during polymerization reactions

Exact values are obtained for the grand canonical partition function of model chains absorbed at a surface. On a six-choice simple cubic lattice, chains are generated as function of the activity of chain bonds. The molecular weight distribution of adsorbed chains and of solution chains in equilibrium with them is obtained. It is shown that the average molecular weight of adsorbed chains is higher than that of solution chains. The difference is the more pronounced the flatter the chain is when adsorbed at the surface. When the activity of chain bond; increases the surface coverage increases, more segments occur in loops extending into the solution, and the average molecular weight of solution chains approaches that of adsorbed chains. The segment density in loops as function of distance from the surface is shown to be exponential, in agreement with previous results. If polymer adsorption is high and the concentration in solution is small, the number of segments in tails is amall. The dimensions of the adsorbed polymer chain are smaller than those in solution of the same molecular weight. It is suggested that if polymer adsorption during polycondensation reactions with bond interchanges is measured, the bothersome tirne effects, invariably observed, might be eliminated. In this manner a valid comparison between theoretical and experimental results might become feasible.