Bulk Modulus and Grüneisen Parameters for Linear Polymers

Abstract

Expressions are derived for the isothermal bulk modulus $B_T$ and Anderson–Grüneisen parameter $\delta$ for a simple two‐dimensional bundle‐of‐chains model where parallel nearest‐neighbor chains are assumed to interact with a simple separation‐dependent potential. Bulk modulus data for general linear polymers are examined and shown to be essentially temperature independent at constant volume in accord with the model. The theory is shown to predict quite accurately for reasonable assumed pair potentials both $B_T$ and $\delta$ of high‐density polyethylene and n‐paraffins with no adjustable parameters. The values of $\delta$ obtained for polyethylene from $B_T$ data are in excellent agreement with those reported from ultrasonic data. The analysis is also shown to provide a sensitive measure of the form of the effective chain pair potential near its minimum. Also, a close relationship between $\delta$ and the Grüneisen constant $\gamma$ is derived for this model.