Lattice Thermal Conductivity of Polyethylene Molecular Crystals from First-Principles Including Nuclear Quantum Effects

Molecular crystals such as polyethylene are of intense interest as flexible thermal conductors, yet their intrinsic upper limits of thermal conductivity remain unknown. Here, we report a study of the vibrational properties and lattice thermal conductivity of a polyethylene molecular crystal using an ab initio approach that rigorously incorporates nuclear quantum motion and finite temperature effects. We obtain a thermal conductivity along the chain direction of around $160\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at room temperature, providing a firm upper bound for the thermal conductivity of this molecular crystal. Furthermore, we show that the inclusion of quantum nuclear effects significantly impacts the thermal conductivity by altering the phase space for three-phonon scattering. Our computational approach paves the way for ab initio studies and computational material discovery of molecular solids free of any adjustable parameters.

Figure 1

(a) Enclosed in the box is a unit cell of bulk crystalline polyethylene, containing two molecular chains, projected onto the $yz$ plane where the $x$ coordinate is along the chain. (b) A 3D representation of the bulk crystalline polyethylene. The polyethylene crystal is formed from long parallel polymer chains and stabilizes in the base-centered orthorhombic crystal structure, confirmed by x-ray and neutron scattering measurements [44, 45, 46]. (c) Spectral function along the chain direction at 25 K compared with experimental data for the longitudinal [42] and transverse [43] acoustic modes. Inset: Longitudinal optical and acoustic modes are close in frequency above 5 THz.

Figure 2

(a) Calculated thermal conductivity of a polyethylene molecular crystal along the chain direction as a function of the temperature including nuclear quantum effects (red line) and assuming classical statistics (yellow line). Inset: Thermal conductivity, normal to the chain direction. (b) Total spectral thermal conductivity and spectral conductivity decomposed into acoustic and semioptical modes at room temperature. The contribution of the optical modes above 20 THz to the thermal conductivity is negligible. In the frequency region between 8 and 16 THz, the longitudinal acoustic and optical modes carry the most heat. (c) Cumulative thermal conductivity as a function of the mean free path. Most heat is conducted by longitudinal modes with comparable mean free paths that are less than $1\mu \mathrm{m}$. The mean free paths of semioptical and transverse acoustic modes do not exceed 100 nm.

Figure 3

(a) Radial distribution function at room temperature. Atomic probability distribution (b) with and (c) without nuclear quantum effects. Zero-point motion increases the thermal displacements for all atoms but particularly for the hydrogen atoms.

Figure 4

Spectral function versus wave vector magnitude $\mathbf{q}$ using (a) quantum mechanics and (b) classical statistics. (c) Total and site-projected phonon density of states. Filled regions correspond to the hydrogen contribution to the total density of states (solid and dashed lines). In the quantum case, hydrogen participates in 20% of the motions in the low-frequency region, while with classical statistics the fraction is less than 8%.