Effect of Chain Conformation on the Free Energy of Dilute Polymer Solutions: Monte Carlo Simulations and Perturbation Theory for the Second Virial Coefficient of Lennard–Jones Chains

Abstract

The free energy of chain molecules in solution, and therefore polymer–solvent phase equilibria, is generally believed to be strongly connected to changes in chain conformation. In this paper, we employ Monte Carlo simulations to analyze this connection. Specifically, we calculate the osmotic second virial coefficient B₂ and several single-chain properties for 3-dimensional, off-lattice chains comprising up to 256 segments interacting by a Lennard-Jones potential of mean force. Our results indicate that (1) the temperature for single-chain collapse (T_θ), the Boyle temperature (T_B), and the upper critical solution temperature for polymer–solvent phase separation (T_c) asymptotically converge to the same value for long chains, consistent with Flory–Huggins mean-field predictions for polymers on a lattice. (2) The asymptotic scaling of the second virial coefficient with chain length in the poor solvent regime is exponential. (3) The emergence of the three scaling regimes for B₂ (i.e., the good solvent regime, theta solvent regime, and poor solvent regime), the scaling of B₂ with chain length in those regimes, and─to a lesser extent─the actual value of B₂, are unaffected by single-chain collapse. The third point suggests that the residual free energy of dilute polymer–solvent systems is insensitive to changes in chain conformation, implying a simplified route to developing thermodynamic models for describing polymer–solvent phase equilibria based on molecular models that do not exhibit single-chain collapse. Based on our simulation data and liquid-state perturbation theory, we develop an analytic model for the second virial coefficient of Lennard–Jones chains that might further benefit the development of such thermodynamic models.