Models for the prediction of the pressure-volume-temperature relationship and the diffusion coefficient in polymer melts
Abstract
A new equation of state has been developed to describe the pressure-volume-temperature (PVT) behavior of polymers. The polymer chain-of-rotators (PCOR) equation of state has been developed from a rotational partition function which describes the polymer molecule as a chain of rotators. By explicitly acknowledging the rotational contribution to the partition function, the lattice structure traditionally used in polymer equation of state is avoided, consistent with the lack of crystal-like structure in polymer melts. The rotational contributions to the partition function in the PCOR are balanced by the attraction of the molecular segments. The PCOR equation of state describes the specific volume of polymer melts to within 0.1% accuracy over wide ranges of temperatures and pressures. Three equation-of-state parameters are required to characterize a polymer. Correlations are developed for these parameters with the molecular structure of the repeating segment of the polymer molecules. Specifically, (i) the attractive force parameter, a, is correlated with the cohesive energy density; (ii) the excluded volume parameter, b, is correlated with the van der Waals volume; and (iii) the rotational degrees of freedom parameter, c, is correlated with the configurational entropy of the repeat unit. These correlations make possible the estimation of thermodynamic properties of polymers from the knowledge of their chemical structure. A model for describing the effect of temperature and solvent concentration on the self-diffusion coefficient has been developed. The model assumes the molecular mobility, and hence the diffusivity, depends upon the configurational entropy as suggested by Adam and Gibbs. Specifically, the logarithm of the diffusion coefficient is assumed to be proportional to I/TS$\sb{\rm c},$ where T is the absolute temperature and S$\sb{\rm c}$ is the configurational entropy determined as the integral of the configurational part of the heat capacity from the second order transition T$\sb2$ to T. The concentration and temperature dependence of the diffusion coefficient is accurately described by the configurational entropy model for a number of polymer-solvent systems. Methods for estimating the various parameters in the model from the chemical structure of the polymer and solvent have been developed. The configurational entropy model provides an alternative to the free volume model in describing the diffusion coefficient.
Degree
Ph.D.
Advisors
Chao, Purdue University.
Subject Area
Chemical engineering
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