Correlating negative thermal expansion and thermal conductivity in two-dimensional carbon-based materials†

Negative thermal expansion (NTE) is a fascinating phenomenon wherein certain materials contract upon heating. The phonon transport properties of two-dimensional carbon-based allotropes are not yet fully understood in terms of their NTE properties. This work with a specific focus on carbon-based allotropes investigates 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 the highest NTE as well as the 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 can be explained based on the soft-phonon modes, phonon group velocity (v_g), phonon lifetime (τ) and mean free path (MFP). The acoustic and optical phonon branches play a key role in determining both the TC and NTE of the materials. Out-of-plane buckling in two-dimensional materials reduces thermal conductivity by increasing the phonon scattering. Buckling has also been 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 significantly influence 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.