Molecular Dynamics

The Molecular Dynamics Exploration shows the molecular dynamics of simple atoms and molecules in a two-dimensional system. The force between the atoms is weakly attractive at short distances, but strongly repulsive when they touch. Use the simulation to explore phases of matter, emergent behavior, irreversibility, and thermal effects at the nanoscale.

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The physics

Each atom in the simulation moves in response to the forces exerted by nearby atoms and the container walls, in accord with Newton’s laws of motion. The simulation code knows nothing about phase transformations or crystal structure or irreversibility, yet these high-level phenomena, and others, emerge from the microscopic physics.
The force between the atoms is calculated from the Lennard-Jones formula (truncated at a distance of 3 molecular diameters). This is a reasonably accurate model of the interactions between noble gas atoms.
The simulation approximates Newton’s laws using the Verlet algorithm with the indicated Time step Δt. Using too large a time step can make the simulation inaccurate and sometimes even unstable (see below).
The simulation uses a natural system of units, with the atomic diameter, the atomic mass, the depth of the Lennard-Jones potential, and Boltzmann’s constant all set equal to 1. For argon (for example), the unit of distance is 3.4 angstroms, the unit of mass is 40 atomic mass units, and the unit of energy is 0.012 electron-volts; the corresponding unit of time is then 2 picoseconds, the unit of velocity is 170 meters per second, and the unit of temperature is 140 kelvin.
The walls exert a linear (spring) force on the molecules, with a spring constant of 50 in natural units.
There’s an optional uniform downward force, controlled by the gravity parameter g that is available using the More button. The magnitude of this force, however, is not meant to be realistic. The numerical value should be small to avoid numerical instabiity. A value of g ~0.01 gives a good visualization with the default initialialization but it is orders of magnitude larger than 9.8 m/s². Earth’s gravitational constant is utterly negligible in the units used here (a little over 10⁻¹³ for argon).

Credits

The Molecular Dynamics Exploration was developed by Wolfgang Christian at Davidson College using the Easy Java/JavaScript Simulation (EjsS) modeling and authoring tool created by Francisco Esquembre. This EjsS simulation is based on a pure JavaScript + HTML 5 simulation developed by Daniel V. Schroeder, Physics Department, Weber State University. Schroeder's simulation is described in Interactive Molecular Dynamics article (pdf), published in the American Journal of Physics 83 (3), 210-218 (2015), arXiv:1502.06169 [physics.ed-ph].