Correlating Negative Thermal Expansion and Thermal Conductivity in Two-dimensional Carbon-based Materials

Negative thermal expansion (NTE) is a fascinating phenomenon where certain materials contract upon heating. The phonon transport properties of two-dimensional carbon-based allotropes are poorly understood in terms of their NTE properties. This work with a specific focus on carbon-based allotropes, explores the underlying mechanisms of the thermal conductivity (TC) and NTE of graphene, haeckelite, pentahexoctite, s-graphene, 6.6.12 and delta Graphynes (Gys). High TC is imperative for efficiently dissipating heat in electronic devices, whereas thermoelectric devices need to be thermally resistive with low TC. Delta-Gy shows highest NTE as well as lowest TC and vice versa is true for graphene. Graphene displays a lower degree of anisotropic TC, while s-graphene exhibits the highest level of anisotropic TC. The behaviour of their TC are understood on the basis of soft-phonon modes, phonon group velocity (vg), phonon lifetime (τ) and mean free path (MFP). The acoustic and optical phonon branches play a key role in determining both TC and NTE of the materials. Out-of-plane buckling of a two-dimensional materials can suppress heat conductivity by increasing the phonon scattering. Buckling is also shown to increase the NTE. A precise control on the pore sizes 5-7 (Haeckelite), 5-6-8 (Pentahexoctite), and 4-8 (s-graphene), 6-12-14 (6.6.12-Gy) and 6-14 (delta-Gy) can make a big impact on their soft unit modes. This investigation not only deepens our understanding of NTE and TC but also highlights the potential of future applications of carbon-based materials with controlled thermal expansion properties in nanotechnology, composites, and beyond.