Macromolecules, Vol.39, No.6, 2364-2372, 2006
Confinement of equilibrium polymers: A field-theoretic model and mean-field solution
We develop a field-theoretic model for equilibrium polymers in good solvent. Using the Gaussian chain model, we present a derivation in the grand canonical ensemble in which the parameters are the monomer chemical potential mu(M), the excluded volume parameter u(0), and the energy decrease for forming a bond 2h. Only the quantity Gamma, which is proportional to u(0)e(-2h), matters in determining the mean-field solution. For a bulk system, the homogeneous mean-field solution gives an exponential polymer length distribution with a characteristic length that decreases with increasing Gamma. Moreover, the extent of polymer overlap in a semi-dilute solution decreases with increasing density in the mean-field approximation. We study the inhomogeneous properties of equilibrium polymers confined between two parallel repulsive plates with numerical self-consistent field theory. The polymer length distribution is exponential for all L, the dimensionless distance between the plates. For small L, the characteristic polymer length of the exponential distribution scales as L-2, which is ideal equilibrium polymer behavior. For any fixed L, the characteristic length approaches the bulk characteristic length as Gamma increases. We also find that alpha, the ratio of the volume-averaged confined density to the bulk density, decreases monotonically with decreasing F and L. As u(0) -> 0, our data converge to previous analytic results for ideal equilibrium polymers.