Lab 06 — Molecular Dynamics

Thermal Motion & the States of Matter

A 2D molecular-dynamics sandbox: 70 particles moving under a Lennard-Jones interaction and weak gravity. The only force between them is a simple one — strong repulsion when they get too close, gentle attraction at arm’s length. The "atom" is not a specific substance but the generic LJ model; since it was historically calibrated to noble gases, the temperature axis is converted to Kelvin using argon’s ε/k_B = 119.8 K. It is a 2D toy, so read the Kelvin numbers as a rough guide. Cool the particles into a vibrating cluster (solid), warm them into a sloshing liquid, heat them into a gas that fills the box. The water glyph is decorative; real water’s hydrogen bonding is not modelled.

V(r) = 4\varepsilon\left[\left(\dfrac{\sigma}{r}\right)^{12} - \left(\dfrac{\sigma}{r}\right)^{6}\right] \qquad \left\langle \tfrac{1}{2}mv^{2} \right\rangle = k_{\mathrm{B}}T \ (\text{2D}) \qquad T\,V^{\gamma-1} = \mathrm{const} \;\; (\gamma = 2 \;\Rightarrow\; T\,V = \mathrm{const})

Temperature drives ice → water → steam. Park it on a boundary for coexistence

TemperatureT* = 0.50≈ 60 K

SLG

PhaseLiquid (water)

Solid, liquid and gas are not different substances — just different intensities of motion of the same particles. Park the slider on a boundary temperature (this model melts at T* ≈ 0.32 and boils at ≈ 1.0) and the two phases coexist. Switch to Adiabatic to cut the heat bath and compress the box from the top. With nowhere for the heat to go, the piston’s work turns straight into temperature, and in the gas phase T·V stays roughly constant. The exponent comes from degrees of freedom: this 2D monatomic gas has f = 2, so γ = 2 (a real 3D monatomic gas has γ = 5/3). The same adiabatic heating lets a diesel engine ignite fuel without a spark — and the same cooling, in rising air, makes clouds.