Near-second-order transition in confined living-polymer solutions

We analyze a near-second-order transition occurring in solutions of living polymers confined by two parallel surfaces in equilibrium with a reservoir solution. The molecular self-consistent field theory in the regime of weak adsorption or depletion is mapped to phenomenological Landau theory, where the order parameter is the average degree of polymerization or, equivalently, the normalized chain-end concentration. The distance between two surfaces at which the transition occurs scales as ℓ(c)(2)|c| where ℓ(c) is the correlation length of the polymer solution in the reservoir and c(-1) is de Gennes adsorption length. In the second half of the paper we focus on experimentally observable features. The predicted transition can be detected experimentally by probing the living-polymer mediated disjoining potential between surfaces by means of, e.g., colloidal probe atomic force microscopy. To facilitate experimental investigations we derive simple explicit expressions for the disjoining potential for several regimes. By comparison with full numerical calculations it was verified that these are quite accurate.