Enthalpy distributions and densities of states in linear polymers

Abstract

AbstractUsing polypropylene as an example, we applied a method we have recently developed to calculate the probability distribution of enthalpy from the temperature dependence of the heat capacity. The method involves the use of local temperature expansions of the heat capacity to calculate a set of moments of the enthalpy distribution. Using the maximum‐entropy method, one can then construct the enthalpy distribution for the system. The method is completely model free. The enthalpy distribution so obtained is the analogue of the Maxwell–Boltzmann distribution of kinetic energies for a gas, and like that function, tells one the distribution of enthalpies that an average unit in the polymer chain can have, a quantity that is crucial to understanding the chemical and physical properties of a polymer. Given the enthalpy distribution, one can then calculate the Gibbs free energy and the density of states that correspond to a particular value of enthalpy, thus giving one an expanded thermodynamics of the system in addition to the usual average quantities. We illustrate the fact that the Gibbs free‐energy distribution for this system scales as a simple function of temperature and that the density‐of ‐states function yields a simple empirical partition function for the system giving both the average thermodynamics and the distribution functions. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1513–1518, 2001