Graphene mechanics: I. Efficient first principles based Morse potential

Abstract

We present a computationally efficient pairwise potential for use in molecular dynamics simulations of large graphene or carbon nanotube systems, in particular, for those under mechanical deformation, and also for mixed systems including biomolecules. Based on the Morse potential, it is only slightly more complex and computationally expensive than a harmonic bond potential, allowing such large or mixed simulations to reach experimentally relevant time scales. By fitting to data obtained from quantum mechanics (QM) calculations to represent bond breaking in graphene patches, we obtain a dissociation energy of 805 kJ mol(-1) which reflects the steepness of the QM potential up to the inflection point. A distinctive feature of our potential is its truncation at the inflection point, allowing a realistic treatment of ruptured C-C bonds without relying on a bond order model. The results obtained from equilibrium MD simulations using our potential compare favorably with results obtained from experiments and from similar simulations with more complex and computationally expensive potentials.

Graphene mechanics: II. Atomic stress distribution during indentation until rupture

“…We employed MD simulations to study the deformation of finite graphene sheets of circular shape under spherical AFM indenters in vacuum, during which we recorded load-displacement profiles. The calculations were performed with GROMACS 18 4.5.3 using the truncated Morse potential 12 and LAMMPS 19 version 17Feb2012 using the AIREBO potential. 13 We noticed that the energy conservation was not maintained when the GROMACS calculations were performed in single precision for the larger graphene sheets.…”

“…We perform MD simulations closely mimicking the experiment, allowing us to directly compare the results. The indenter is modeled as a sphere built from discrete atoms; we use a first principles based Morse potential as presented in part I 12 and, for a small set of simulations, the AIREBO potential 13 to allow C-C bond breaking in graphene. All molecular systems are simulated at 300 K, unlike most other studies, which only slightly displaced C atoms from their equilibrium positions to add kinetic energy.…”

Examining the Mechanical Equilibrium of Microscopic Stresses in Molecular Simulations

“…We first consider a periodic graphene sheet with a Stone-Wales defect as a model system to compare the atomic virial and the IK stresses. The system is modeled with the force field described in [36] involving up to four-body interactions and simulated in a NVT ensemble at 300 K [23]. We compute microscopic stresses here and elsewhere in the Letter with a freely available implementation [7,37].F i g u r e1(a) highlights the fundamental features of each stress definition.…”

Degeneracy and coherent states of the two-dimensional Morse potential

“…This problem is similar to that of the particle in a square box, though, because the quantum numbers n, m take on only finitely many values, some solutions may be discarded. For instance (8,1) lie outside of the bound state parameter range and as such should not be included as degenerate contributions.…”

“…In physical contexts the two-dimensional Morse product eigenfunctions have been used as a basis for perturbative solutions to a triatomic molecular hamiltonian [2][3][4][5][6]. Throughout physics the Morse potential is used in a variety of applications including the study of graphene [7,8], spectroscopy [9,10], Bose-Einstein condensation [11], theories of interacting electrons [12], nuclear physics [13], supersymmetric quantum mechanics [14], and molecular dynamics [15]. Coherent states for the 1D Morse potential have been studied [16], and while there is literature on defining coherent states for systems with degenerate spectra [17], and coherent states for the 2D square well have been analysed [18], so far coherent states for the 2D Morse potential have not been explicitly defined.…”