Statistical Thermodynamics of the Lattice Model of a Polymer Molecule

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Abstract
Introduction of a potential energy of interaction between nonbonded neighbors of a lattice‐simulated random‐walk polymer enables us to study the thermodynamic properties of such a polymer. When the potential energy over a given range of intramolecular separations becomes infinitely large, the free energy and the entropy per unit step can be computed directly either from the attrition data using the Monte Carlo method of generating random walks, or from the exact numerical calculations for short chains. The transition to rodlike molecular configurations and the accompanying change in the free energy per unit step can be followed by gradually extending the range of the infinitely large intersegment interactions. Instead of using computational methods for estimating the free energy of a polymer with a hard‐core potential energy, one can approximate the free energy by limiting the intramolecular interactions to the nearest neighbors only. These interactions are limited to configurations separated by the smallest number of steps needed to bring two polymer segments within a specified range of a hard‐core potential energy. The free energy can be calculated analytically, using certain recurrence relations constructed for the number of permissible configurations. A comparison is made of the results obtained on the basis of nearest‐neighbor approximation to the more accurate data obtained from the numerical calculations.

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