Swelling and Residual Bond Orientations of Polymer Model Gels: The Entanglement-Free Limit

We investigate the swelling of polymer model networks prepared at different polymer volume fractions and in solvents of different quality. We extend the existing theory to describe residual bond orientations (the vector and the tensor order parameters) for theta, good, and athermal solvents and put these relations in context with modulus at preparation conditions and the equilibrium degree of swelling. We find good agreement with the assumption of affine swelling for the weakly entangled networks of our study. The same scaling relations (up to numerical coefficients) are obtained for the vector order parameter, m, and the tensor order parameter, S, as a function of the preparation conditions, network structure, the equilibrium degree of swelling, Q, and the modulus at swelling equilibrium, G. We obtain m ∝ Q^–2 and G ∝ m^3/2 for swelling in theta solvents and m ∝ Q^–1.08 with G ∝ m^2.14 in the good-solvent regime, in both cases independent of preparation conditions. Modulus and residual bond orientation are related by G ∝ φ₀m and G ∝ φ₀^1.23m as a function of the preparation polymer volume fraction φ₀ for theta solvents and good solvents, respectively. Computer simulations and experimental data for the good-solvent regime show good agreement with the predictions.