Anisotropic and isotropic elasticity and thermal transport in monolayer C$_{24}$ networks from machine-learning molecular dynamics

TL;DR

This work develops a high-fidelity neuroevolution potential, NEP-C$_{24}$, to describe both quasi-hexagonal and quasi-tetragonal C$_{24}$ monolayers. Using this potential, it reveals that bond topology controls pronounced in-plane elastic anisotropy in qHP and near-isotropy in qTP, and that lattice thermal conductivity is dominated by low-frequency acoustic phonons with strong directional dependence. Spectral analyses and real-space heat-flow maps show heat transport occurs primarily through robust inter-fullerene covalent bonds, linking bonding motifs to phonon-mediated heat conduction. The results highlight a direct structure–property relationship that can guide the design of fullerene-based 2D materials with tunable mechanical and thermal characteristics, and demonstrate a general, extendable framework for modeling complex covalent networks. The approach enables predictive exploration of defects, edges, and nanoribbon widths in fullerene networks for targeted thermal management and sensing applications.

Abstract

Two-dimensional fullerene networks have recently attracted increasing interest due to their diverse bonding topologies and mechanically robust architectures. In this work, we develop an accurate machine-learned potential NEP-C$_{24}$ for both the quasi-hexagonal phase (qHP) and the quasi-tetragonal phase (qTP) C$_{24}$ monolayers, based on the neuroevolution potential (NEP) framework. Using this NEP-C$_{24}$ model, we systematically investigate the elastic and thermal transport properties. Compared with C$_{60}$ monolayers, both C$_{24}$ phases exhibit markedly enhanced stiffness, arising from the combination of reduced molecular size and increased density of covalent bonds. The qTP C$_{24}$ monolayer shows nearly isotropic elastic properties and thermal conductivities along its two principal axes owing to its four-fold symmetry, whereas the chain-like, misaligned bonding topology of the qHP C$_{24}$ monolayer leads to pronounced in-plane anisotropy. Homogeneous nonequilibrium molecular dynamics and spectral decomposition analyses reveal that low-frequency ($<5$ THz) acoustic phonons dominate heat transport, with directional variations in phonon group velocity and mean free path governing the anisotropic response in qHP C$_{24}$. Real-space heat flow visualizations further show that, in these fullerene networks, phonon transport is dominated by strong inter-fullerene covalent bonds rather than weak van der Waals interactions. These findings establish a direct link between intermolecular bonding topology and phonon-mediated heat transport, providing guidance for the rational design of fullerene-based two-dimensional materials with tunable mechanical and thermal properties.

Figures (9)

• Figure 1: Top and side views of the optimized crystal structures of (a) and (b) C$_{24}$ monolayers. The structures are visualized using OVITO Stukowski2009msme.
• Figure 2: (a) Evolution of the individual components of the loss function for the training and testing datasets as a function of generation. (b–d) Comparison of (b) energy, (c) virial, and (d) force predicted by -C$_{24}$ with reference data for both training and testing datasets. (e,f) Comparison of the forces obtained from (e) -Carbon and (f) Tersoff potentials with reference data for the testing dataset.
• Figure 3: (a,c) and (b,d) of (a,b) and (c,d) C$_{24}$ monolayer, obtained from the -$\rm C_{24}$- and -based simulations at 300 K. - simulations were performed for 10 ps using cells containing 48 atoms () and 24 atoms (), while -MD simulations were performed for 10 ns using systems containing 31,920 atoms () and 38,400 atoms ().
• Figure 4: Phonon dispersions of (a) and (b) C$_{24}$ monolayers calculated using -C$_{24}$ and . The DFT results are consistent with those reported in Ref. wu2025jacs
• Figure 5: Orientation-dependent (a) Young’s modulus $E(\theta)$, (b) shear modulus $G(\theta)$, and (c) Poisson’s ratio $\nu(\theta)$ of monolayer and from and calculations, where the dashed lines represent results and the solid lines represent results.