On Quantitative Evaluations on Harmonic and Anharmonic Lattice Thermal Capacity of Polymers

So-called ‘Generalized Skettrup Model(s)’ (GSMs) of different (1D, 2D, 3D) spatial dimensionalities are implemented at quantitative evaluations on temperature-dependent harmonic and anharmonic fractions of lattice thermal capacity of polyethylene and polypropylene with crystalline and/or amorphous atomic structures of limited spatial extents. Basic equations of the GSM take into account explicitly quantization effects of the single-particle and many-particle energy levels of spatially confined (within the 1D, 2D and/or 3D structural fragments of polymers) conventional longitudinal acoustic (LA), transverse acoustic (TA), and optical phonons. The harmonic lattice thermal capacity of 1D and 3D polymers is evaluated entirely based on single-particle (fundamental) states of the confined LA, TA and optical phonons. Statistical characteristics of many-particle states of the LA and TA phonons are obtained based on concept of many-particle vibrational density-of-states, introduced by the author of this article in 1995. Those characteristics define features of temperature-dependent anharmonic lattice capacities of 1D, 2D and 3D versions of the GSM in an essentially ‘non-perturbative’ manner. Anisotropic effects in 3D crystalline polymers are taken into account via evaluation of anisotropic sound velocities of conventional thermal waves, confined within 3D crystalline fragments of those polymers. Such evaluations have been carried out quantitatively for orthorhombic 3D polyethylene via implementation of the Christoffel Matrix formalism. Simulated temperature-dependent lattice thermal capacities are compared with their experimental counterpart for the polyethylene and polypropylene as well as with predictions of the Tarasov’s Equations and those of the ‘three-band’ model.