A Monte Carlo lattice study of living polymers in a confined geometry

We investigate the changes in the average chain length of a solution of semi-flexible living polymers between two hard repulsive walls as the width of the slit, D, is varied. Two different Monte Carlo models, that of the 'slithering snake' and of the 'independent monomer states' are employed in order to simulate a polydisperse system of chain molecules confined in a gap which is either closed (with fixed total density), or open and in contact with an external reservoir. It appears that the mean chain length L in a state of equilibrium polymerization depends essentially on the geometry constraints for sufficiently small D. We find that in the case of an open slit the mean length L(D) decreases with D --> 0 for flexible chains whereas it grows if the chains are sufficiently stiff. As the width of a closed gap D is decreased, in a three-dimensional gap L(D) gradually decreases for-absolutely flexible chains whereas for semi-rigid chains it goes through a minimum at D = 2 and then grows again for D = 1. In two dimensions, in a closed strip the average chain length L(D) for both flexible and rigid macromolecules goes through a sharp minimum and then grows steeply in compliance with a predicted divergence far semi-rigid polymers as D --> 0. We attribute the observed discrepancies of our numeric experiments with some recent analytic predictions to the ordering effect of container walls on the polymer solution when chain stiffness and excluded volume interactions are taken into account.