Theoretical estimates of the temperature dependence of shear moduli in crystalline polymers

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Abstract
The shear moduli, C44 and C55, and the temperature dependence have been computed for the orthorhombic unit cell of paraffinic hydrocarbons. The computations were conducted by expressing the shear moduli in terms of intermolecular interactions formulated for infinitely long rows of H…H force centers. The interaction parameters used for the row formulation were shown to predict the correct equilibrium unit-cell dimensions. Temperature dependence was introduced by varying unit-cell dimensions according to reported thermal expansion data. These computations show that C44 decreases nearly linearly from 5×1010 dyn/cm2 at −263 °C to 3×1010 dyn/cm2 at 138 °C; C55 decreases nearly linearly from 2.4×1010 dyn/cm2 at 263 °C to 1×1010 dyn/cm2 at 138 °C. These results show that the decrease in the shear moduli resulting from changes in the intermolecular interaction field facilitates deformation at elevated temperatures. The decrease of the elastic constants with temperature further suggests that the equilibrium population of crystal defects increases more rapidly with temperature than a Boltzmann factor alone would predict.