A Ubiquitous Thermal Conductivity Formula for Liquids, Polymer Glass, and Amorphous Solids*

Abstract

The microscopic mechanism of thermal transport in liquids and amorphous solids has been an outstanding problem for a long time. There have been several approaches to explain the thermal conductivities in these systems, for example, Bridgman’s formula for simple liquids, the concept of the minimum thermal conductivity for amorphous solids, and the thermal resistance network model for amorphous polymers. Here, we present a ubiquitous formula to calculate the thermal conductivities of liquids and amorphous solids in a unified way, and compare it with previous ones. The calculated thermal conductivities using this formula without fitting parameters are in excellent agreement with the experimental data. Our formula not only provides a detailed microscopic mechanism of heat transfer in these systems, but also resolves the discrepancies between existing formulae and experimental data.

Thermal conductivity of amorphous polymers and its dependence on molecular weight

“…Note that the constant thermal conductivity found in all simulation studies for N ≥ N c is in direct contradiction with Hansen et al [11] results. These simulation results show good qualitative agreement with a recent model proposed by Xi et al [22] with a general expression for the thermal conductivity of amorphous materials ranging from liquids to polymer glasses (i.e., for amorphous solids λ is found to be dependent on M and for polymer glasses it is found to be independent). To describe the thermal conductivity of polymers, this model makes use of a Thermal Resistance Network that highlights the importance of the distance between entanglements in the path followed by energy carriers along the chains [22,23].…”

“…These simulation results show good qualitative agreement with a recent model proposed by Xi et al [22] with a general expression for the thermal conductivity of amorphous materials ranging from liquids to polymer glasses (i.e., for amorphous solids λ is found to be dependent on M and for polymer glasses it is found to be independent). To describe the thermal conductivity of polymers, this model makes use of a Thermal Resistance Network that highlights the importance of the distance between entanglements in the path followed by energy carriers along the chains [22,23]. This model has successfully reproduced the pressure and temperature dependence of λ in polymer solids and melts and qualitatively described anisotropy in oriented polymers.…”

Tuning network topology and vibrational mode localization to achieve ultralow thermal conductivity in amorphous chalcogenides

“…In this case, the calculation of assumes that P changes with respect to the mean coordination number of each composition. Following the model proposed by Xi et al 30 showing a power-law dependence between mean coordination number and thermal conductivity ( k ∝ < r m > 1/3 ), we normalize each coordination number with respect to pure Si, i.e., P = (< r m >/< >) 1/3 = (< >/< r Si >) 1/3 . Using this assumption, P changes from 1 for Si (< r S i > = 4) to ~0.8 for Te (< r T e > = 2).…”

Perspectives on Molecular-Level Understanding of Thermophysics of Liquids and Future Research Directions

“…If one takes d in the Horrocks and McLaughlin model as the speed of sound v, their formula also becomes similar to the Bridgman formula since n ¼ 1/d 2 , except that Horrocks and McLaughlin have an extra factor of 2 and used a specific heat of 3k B per molecule. More recently, Xi et al [99] extended this line of modeling and developed athermal conductivity expression, which they claimed is valid for both liquids and amorphous solids.…”