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Unified theoretical framework for thermal expansion engineering in multilayer 2D materials
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DOI：10.1016/j.eml.2026.102474.png)
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Abstract
En 中文
Two-dimensional (2D) materials exhibit diverse thermal expansion coefficients (TECs) spanning from negative to positive values, yet a unified theoretical framework connecting TECs to geometrical and interfacial factors remains elusive. Herein, we develop a statistical mechanics model to predict the TECs of multilayer 2D materials by incorporating the effects of layer number, lateral size, and substrate interaction. The total TEC is decomposed into positive bond-anharmonicity and negative fluctuation-induced contributions, with the latter governed by a dimensionless parameter coupling bending rigidity, interlayer shear, and substrate constraint. The theory predicts logarithmic size dependence for freestanding monolayers, progressive suppression of negative thermal expansion with increasing layer number, and substrate-mediated transitions from negative to positive thermal expansion. These predictions are validated by molecular dynamics simulations. Phase diagrams constructed in the parameter space of size, thickness, and substrate interaction delineate the boundaries between thermal expansion regimes. This theoretical framework offers predictive guidelines for engineering thermal expansion of 2D materials.
Keywords:
thermal expansion
2D materials
statistical mechanics
substrate interaction
phase diagrams
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