Thermal conductivity of commodity polymers under high pressures

TL;DR

The study addresses thermal transport in amorphous polymers PMMA and PLA under high pressure, combining all-atom MD with a SCETM framework and a quantum-corrected minimum thermal conductivity approach based on the vibrational DOS. It shows κ increases with pressure, roughly following $\kappa = \kappa_1 + \kappa_2 \sqrt{P}$, and reveals that nonbonded energy transfer dominates under compression, increasing by about 5–6×, while bonded transfer grows more modestly. Quantum corrections improve agreement with experimental data at low to moderate pressures, validating the approach but revealing deviations at high pressure that point to force-field and density uncertainties and the limits of the local transport model. The work provides a multiscale, mechanistic understanding of pressure-enhanced thermal transport in polymers and informs design of thermal-management materials for extreme environments.

Abstract

Understanding the thermal conductivity of polymers under high-pressure conditions is essential for a range of applications, from aerospace and deep-sea engineering to common lubricants. However, the complex relationship between pressure, $P$, the thermal transport coefficient, $κ$, and polymer architecture poses substantial challenges to both experimental and theoretical investigations. In this work, we study the pressur-dependent thermal transport properties of a widely used commodity polymer -- poly(methyl methacrylate) (PMMA) -- using a combination of all-atom molecular dynamics simulations and semi-analytical approaches. While we report both classical and quantum-corrected estimates of $κ$, the latter approach reveals that as the pressure increases from 1 atm to 10 GPa, $κ$ rises by up to a factor of four -- from 0.21 W m$^{-1}$ K$^{-1}$ to 0.80 W m$^{-1}$ K$^{-1}$. To better understand the mechanisms behind this increase, we disentangle the contributions from bonded and nonbonded monomer interactions. Our analysis shows that nonbonded energy-transfer rates increase by a factor of six over the pressure range, while bonded interactions show a more modest increase -- about a factor of three. This observation further consolidates the fact that the nonbonded interactions play the dominant role in dictating the microscopic heat flow in polymers. These individual energy-transfer rates are also incorporated into a simplified heat diffusion model to predict $κ$. The results obtained from different approaches show internal consistency and align well with available experimental data. Additionally, some data for polylactic acid (PLA) are presented.

Figures (7)

• Figure 1: Time evolution of the kinetic temperature difference between hot and cold slabs, $\Delta T(t) = T_{\rm hot}(t) - T_{\rm cold}(t)$, for (left) poly(methyl methacrylate) (PMMA) and (right) polylactic acid (PLA). Results are shown for different pressures $P$. Solid lines represent exponential fits, from which the thermal conductivity $\kappa$ is extracted using Equation \ref{['eq:ate']}. Note that slightly larger fluctuations in the PLA data is because it consists of a smaller number of atoms within the simulation domain owing to its smaller monomer size.
• Figure 2: The main panel shown the classical estimate of the thermal transport coefficient $\kappa$ as a function of pressure $P$ for two polymers: poly(methyl methacrylate) (PMMA) and polylactic acid (PLA), at $T = 300$ K. The lines represent fits to the empirical relation $\kappa = \kappa_1 + \kappa_2 \sqrt {P}$. The inset shows the same data as the main panel but with $\kappa$ normalized by its value at $P = 1$ atm, i.e., $\kappa/\kappa_{\mathrm{(1~atm)}}$, for the respective PMMA and PLA simulations.
• Figure 3: Temperature profiles $\Delta T$ as a function of time during the relaxation of a central monomer initially heated to 1000 K. The data correspond to its first nearest bonded neighbors, shown for three different pressures $P$. Lines are included as visual guides. The data for 1 atm is taken from Ref. MM21mac.
• Figure 4: The relaxation rates $\alpha_p$ of the cosine-transformed temperature modes $\hat{T}_p(t)$ are plotted as a function of $4\sin^2\left(\pi p / 2N_{\ell}\right)$. The data correspond to poly(methyl methacrylate) (PMMA) at a temperature of $T = 300$ K, with representative results shown for three different applied pressures $P$. The dataset for ambient pressure (1 atm) is taken from Ref. MM21mac. The solid lines represent fits to the data using Equation \ref{['eq:alphap']}.
• Figure 5: The vibrational density of states $g(\nu)$ for poly(methyl methacrylate) (PMMA) at various pressures $P$, measured at a temperature of $T = 300$ K. The arrow indicates the direction of increasing $P$.