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 used at simulations on temperature-dependent <i>harmonic</i> and <i>anharmonic</i> 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 slot in explicitly <i>quantization effects</i> of the single-particle and many-particle energy levels of spatially confined phonons. The <i>harmonic</i> 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 the concept of <i>many-particle </i>vibrational density-of-states, introduced in 1995. Those characteristics define features of temperature-dependent <i>anharmonic</i> lattice capacities of 1D, 2D and 3D versions of the GSM in an essentially ‘non-perturbative’ manner. <i>Anisotropic</i> effects in 3D crystalline polymers are incorporated via evaluation of <i>anisotropic</i> 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 polyethylene and polypropylene, as well as with predictions of Tarasov’s Equations and those of the ‘three-band’ model.