Interactive Lennard-Jones molecular dynamics simulation: observe phase transitions, crystallization, and gas-liquid-solid behavior by tuning temperature and interaction parameters
The Lennard-Jones potential V(r) = 4ε[(σ/r)¹² - (σ/r)⁶] models the interaction between neutral atoms or molecules. The r⁻¹² term represents short-range Pauli repulsion (electron cloud overlap), while the r⁻⁶ term describes long-range van der Waals attraction (induced dipole-dipole). Parameters: ε sets the potential well depth (interaction strength) and σ is the distance where V = 0 (effective atomic diameter). The equilibrium distance is r_min = 2^(1/6)σ ≈ 1.122σ, where V = -ε. The force is F(r) = -dV/dr = 24ε/r [2(σ/r)¹² - (σ/r)⁶]. This simple potential captures the essential physics of noble gases (Ar, Kr, Xe) and is the workhorse of molecular dynamics simulations, producing gas, liquid, and solid phases depending on temperature and density.
At low temperature (T* = kT/ε ≪ 1), particles settle into a hexagonal close-packed crystal lattice, minimizing potential energy. As temperature rises past the melting point (T* ≈ 0.7 at moderate density), thermal energy overcomes the lattice binding and particles flow freely — the liquid phase. At high temperature (T* > 2), particles move so fast that attraction barely matters — the gas phase with nearly free particle motion. The triple point occurs at T* ≈ 0.694 and the critical point at T* ≈ 1.326 for the LJ system. In 2D, the solid phase forms a triangular lattice (hexagonal packing). The simulation uses a Velocity Verlet integrator for time evolution and a Berendsen thermostat to control temperature, matching the approach used in real MD codes.
Materials science: MD simulations predict material properties (elastic constants, thermal conductivity, diffusion coefficients) from first principles. Nobel gas physics: The LJ potential accurately models Ar, Kr, Xe behavior — equation of state, viscosity, and phase diagrams agree with experiment. Protein folding: Coarse-grained models use LJ-like potentials for hydrophobic interactions driving protein collapse. Nanotechnology: MD simulations design nanoparticles, nanotubes, and surface coatings. Drug design: Molecular docking uses LJ potentials to score protein-ligand binding. Chemical engineering: Process simulation uses LJ-based equations of state. Soft matter: Colloids, polymers, and liquid crystals are modeled with extended LJ potentials. The 2013 Nobel Prize in Chemistry was awarded for developing multiscale MD methods combining quantum and classical approaches.
The main canvas shows a 2D molecular dynamics simulation of Lennard-Jones particles. Particles are colored by kinetic energy (blue=cold, red=hot). Lines between nearby particles indicate neighbors (distance < 1.5σ). Use Temperature to control the thermostat target — low T produces crystals, high T produces gas. Adjust ε to change interaction strength and σ for particle size. Start with the Crystal preset: particles form a hexagonal lattice. Slowly raise temperature to watch it melt into liquid. Switch to Gas to see fast-moving particles with minimal structure. The Freeze preset rapidly cools a random gas into a disordered solid (glass). Use Play/Pause/Step to control simulation. Toggle Neighbors to see nearest-neighbor connections, Velocities to see velocity arrows, and Potential Curve to view the V(r) function. The bottom canvas shows the LJ potential with a marker at the current average nearest-neighbor distance.