The thermoelastic properties of monolayer covalent organic frameworks studied by machine-learning molecular dynamics

Two-dimensional (2D) covalent organic frameworks (COFs) are emerging as promising 2D polymeric materials with broad applications owing to their unique properties, among which the mechanical properties are quite important for various applications. However, the mechanical properties of 2D COFs have not been systematically studied yet. Herein, a machine-learned neuroevolution potential (NEP) was developed to study the elastic properties of two representative monolayer 2D COFs, namely COF-1 and COF-5. The trained NEP enables one to study the elastic properties of 2D COFs in realistic situations (e.g., finite size and temperature) and possesses greatly improved computational efficiency when compared with density functional theory calculations. With the aid of the obtained NEP, molecular dynamics (MD) simulations together with a strain-fluctuation method were employed to evaluate the elastic constants of the considered 2D COFs at different temperatures. The elastic constants of COF-1 and COF-5 monolayers were found to decrease with an increase in the temperature, though they were almost isotropic irrespective of the temperature. The thermally induced softening of 2D COFs below a critical temperature was observed, which is mainly attributed to their inherent ripple configurations at finite temperatures, while above the critical temperature, the damping effect of anharmonic vibrations became the dominant factor. Based on the proposed mechanisms, analytical models were developed for capturing the temperature dependence of elastic constants, which were found to agree with the MD simulation results well. This work provides an in-depth insight into the thermoelastic properties of monolayer COFs, which can guide the development of 2D COF materials with tailored mechanical behaviors for enhancing their performance in various applications.