Monte Carlo Study of Coiling-Type Molecules. II. Statistical Thermodynamics

The statistical thermodynamics of coiling‐type polymer molecules has been studied by using non‐self‐intersecting random walks generated on a tetrahedral lattice by Monte Carlo methods with a high‐speed digital computer. By introducing a potential energy of interaction between nonbonded nearest neighbors, one can establish a partition function for the polymer chains so simulated. The changes in free energy, internal energy, and heat capacity are then calculated relative to those for molecules subject to no intramolecular interactions other than excluded volume. Empirical equations are developed for the significant thermodynamic quantities. In particular, it is found that for chains no longer than 120 links, the Helmholtz free energy is given by $$\text{ΔA/kT=(−0.4129+0.06275N)ξ}\exp \text{(−0.7378ξ),}$$ where N is the number of links in the chain and ξ=ε/kT if ε is the potential energy of interaction between nearest nonbonded neighbor pairs. Expressions for ΔE/kT and ΔC_v/kT are also derived, but their ranges of applicability are not as wide.