Watch molecules interact via the Lennard-Jones potential to form solids, liquids, and gases. Add or remove heat to drive phase transitions.
Learning Goals
Describe a molecular model for solids, liquids, and gases.
Extend this model to phase changes.
Describe how heating or cooling changes molecular behavior.
Describe how changing volume affects temperature, pressure, and state.
Interpret graphs of interatomic potential.
Describe how forces relate to the interaction potential.
Describe the physical meaning of ε and σ in the Lennard-Jones potential.
The Lennard-Jones Potential
V(r) = 4ε[(σ/r)¹² − (σ/r)&sup6;]
ε = well depth (bond strength). Higher ε → harder to separate molecules → higher boiling point.
σ = particle diameter. Where V(r) crosses zero.
r < σ: strong repulsion (particles can’t overlap)
r ≈ 1.12σ: equilibrium (minimum energy)
r > 2.5σ: effectively zero (cutoff)
Try These
Solid preset: Particles vibrate in place. Notice the lattice structure and bonds between neighbours.
Melt It preset: Gentle heat turns a solid into a liquid. Watch the lattice break apart and particles begin to flow.
Boil It preset: More heat turns a liquid into a gas. Particles fly free and fill the container.
Cool it down: Drag the heater left (“❄ Cool”) to remove energy. Watch gas condense, then freeze.
Compare Neon vs Water: Both are at similar temperatures, but neon is a gas while water stays liquid. Why? Water’s ε (bond strength) is 4× higher.
Compress: Drag the lid down or lower the volume slider. Pressure rises as you crowd molecules together.
Pump molecules: Drag the pump handle down to inject 3 molecules per stroke. More molecules = more pressure.
Make it explode! Use “Build Pressure” preset, then pump + heat + compress. If pressure stays high for 1 second, the lid blows off! This is why pressure vessels need relief valves.
Return lid: After an explosion, click the yellow “Return Lid” button. Escaped molecules are removed.