Grüneisen constant and thermal properties of crystalline and glassy polymers

Abstract

AbstractPolymer crystals are characterized by strong anisotropy of binding forces among units, i.e., the intrachain force constant f is much larger than the interchain force constant g. The anisotropic lattice is reduced to an isotropic one, in which each lattice point represents N* units (segment) along the chain axis of the anisotropic lattice [N = 2(f/g)1/2]. Vibrational modes of the reduced lattice correspond to interchain modes of the original lattice, i.e., modes whose frequencies are governed by interchain potential. Anharmonicity of crystalline force field is assumed to be related predominantly with interchain force alone. Thermodynamic and transport equations for a simple lattice are applied to the reduced, isotropic lattice, and numerical results are obtained for high‐density polyethylene. The Grüneisen constant γ was obtained from the pressure dependence of sound velocity. The heat capacity of the reduced lattice, Cinter (interchain specific heat), was calculated from Grüneisen's equation, α = γβCinter (where α = thermal expansion coefficient, β = compressibility), and the mass of a segment m* was estimated from Dulong‐Petit's equation, Cinter = 3ρk/m* (where ρ = density, k = Boltzmann constant). The value of m* is consistent with N* from force constants, m* = N*m (where m = mass of a unit in the original lattice). m*θ3 (where θ denotes the Debye temperature of the reduced lattice) is calculated from low temperature specific heat. The value of m* calculated from m*θ3 and θ from other sources agrees with that from the estimate by Dulong‐Petit's equation. The high‐temperature thermal conductivity K was calculated through Leibfried‐Schloemann's equation by employing γ and m*θ3 as estimated as described above; satisfactory agreement was obtained with experiment. Poly(methyl methacrylate) and polystyrene were also studied by similar methods.