Interactions between surfaces in the presence of nonadsorbing equilibrium polymers

The behaviour of a solution of equilibrium polymers (or living polymers) between two surfaces is studied using a Bethe-Guggenheim lattice model for molecules with orientation-dependent interactions. The average monomer concentration, the average length of the chains and the interaction between the surfaces are calculated as a function of the separation distance between the surfaces. When the gap is in full equilibrium with a homogeneous bulk solution, the equilibrium polymers cause a depletion attraction, which becomes stronger with increasing bulk monomer concentration. The range of the interaction passes through a maximum as a function of the concentration. In dilute solutions the range of the interaction increases and the strength decreases with increasing bonding energy, while above the overlap concentration the bonding energy is irrelevant. For restricted equilibrium between the gap and the bulk, when the amount of polymer in the gap is determined by the flow of fluid out of the gap upon compression, the interaction becomes repulsive. This repulsion becomes stronger with increasing concentration and depends only very weakly on the bonding energy. Two limiting cases for the fluid flow were considered: (i) perfect-slip conditions at the surfaces, resulting in a constant monomer concentration in the gap and (ii) no-slip conditions at the surfaces, resulting in a parabolic flow profile of solution out of the gap.