Constitutive Equations for the Elastic Behavior of Polymers Based Upon Molecular Parameters.
ROHM AND HAAS CO HUNTSVILLE AL REDSTONE RESEARCH LABS
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Using a free-energy approach introduced by Born and Huang in studying crystalline elasticity, molecular constitutive equations isothermal or adiabatic conditions were developed for elastic polymeric solids. The molecular model consists of non-spherical molecules which are dispersed throughout a random network of crosslinked chain molecules. The non-spherical molecules are assumed to possess an intramolecular separation potential involving the mean-square end-to-end chain distance and a torsional oscillation potential. These non-spherical molecules interact with each other and the network chains via physical physical entanglements and orientational-dependent secondary interactions. Explicit relationships for the number of such subchains were developed and depend upon the distribution, number functionality and chemical efficiency of the crosslink sites, and the functionality of the chain ends. The isothermal constitutive equations depend upon the statistical averages involving the various potentials and a strain function involving the three principal strains. The adiabatic equation is more complex and involves the statistical average, variance and covariances of the potential and kinetic energies, and the strain function. Simplifications of these constitutive equations are discussed for various types of polymers, and a numerical example involving the volumetric coefficient of thermal expansion is given. Author
- Elastomers and Rubber
- Atomic and Molecular Physics and Spectroscopy