Statistical thermodynamics of equilibrium polymers at interfaces

The behavior of a solution of equilibrium polymers (or living polymers) at an interface is studied, using a Bethe-Guggenheim lattice model for molecules with orientation dependent interactions. The density profile of polymers and the chain length distribution are calculated. For equilibrium polymers at a nonadsorbing surface it is found that the depletion layer thickness has a maximum. In dilute solutions it is proportional to the average radius of gyration of the polymers, which increases with increasing concentration. Above the overlap concentration it corresponds to the bulk correlation length, which decreases with increasing concentration. Furthermore, it is found that the surface region is predominantly occupied by the shorter chains. Both in dilute solutions and in a melt of equilibrium polymers, a very simple relation is found between the surface excess of a component and the chain length