Theoretical Analysis of Lattice Thermal Conductivity of Polystyrene at Low Temperature

Prakash Dubey

doi:10.71097/IJSAT.v17.i1.10049

Theoretical Analysis of Lattice Thermal Conductivity of Polystyrene at Low Temperature

Author(s)	Dr. Prakash Dubey
Country	India
Abstract	The thermal transport properties of amorphous polymers at cryogenic temperatures have attracted considerable attention due to their technological relevance and fundamental scientific importance. In the present work, a detailed theoretical analysis of the lattice thermal conductivity (K) of polystyrene (PS), an amorphous polymer, is carried out in the low temperature range of 0.1–4 K. Experimental studies on noncrystalline solids indicate that their thermal conductivity exhibits a characteristic temperature dependence, similar to that observed in inorganic glasses. At very low temperatures, K follows an approximate T^2dependence, followed by a gradual rise and the appearance of a plateau region at higher temperatures. The present analysis is based on the phenomenological approaches proposed by Klemens and Walton, further extended using the theoretical framework developed by Dubey for amorphous materials. The total lattice thermal conductivity is expressed as a sum of three contributions arising from boundary scattering, empty-space scattering, and high-frequency phonon processes. The phonon relaxation rates corresponding to these mechanisms are incorporated into a modified Debye-type integral formulation. The relative contributions of boundary-interacting phonons (K_BE) and empty-space-interacting phonons (K_EM) to the total thermal conductivity are evaluated as functions of temperature. The variation of phonon scattering relaxation rates with the dimensionless parameter xis also examined at fixed temperatures. The theoretical results demonstrate that boundary scattering dominates thermal transport at extremely low temperatures, while empty-space scattering becomes increasingly significant with rising temperature. The present model successfully explains the experimentally observed low-temperature behavior of lattice thermal conductivity in polystyrene and provides valuable insight into phonon transport mechanisms in amorphous polymers.
Keywords	Lattice thermal conductivity, Polystyrene, Low temperature physics, Amorphous polymers, Phonon scattering, Boundary effects.
Field	Physics
Published In	Volume 17, Issue 1, January-March 2026
Published On	2026-01-05
DOI	https://doi.org/10.71097/IJSAT.v17.i1.10049
Short DOI	https://doi.org/hbh5zr

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Theoretical Analysis of Lattice Thermal Conductivity of Polystyrene at Low Temperature

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