Intermolecular Forces Simulation

Understanding the Lennard-Jones Potential

The curve shows how potential energy between two atoms varies with distance:

📏 Key Parameters

ε (epsilon): Energy scale - depth of potential well. Sets interaction strength and determines if substance is gas/liquid/solid. At equilibrium: U = -ε.

σ (sigma): Size scale - collision diameter where U = 0. Roughly the "effective atomic size" including electron clouds.

🔴 Short Distances (Repulsive Region)

When atoms get too close (r < 1.12σ), their electron clouds overlap, creating strong repulsive forces. Energy rises steeply - like trying to compress a spring.

🔵 Equilibrium Distance (Energy Minimum)

At r ≈ 1.12σ, attractive and repulsive forces balance perfectly. This is the most stable configuration with lowest energy (-1.0ε).

🟢 Large Distances (Attractive Region)

Beyond equilibrium, weak van der Waals forces try to pull atoms together. Energy slowly approaches zero as distance increases.

Real Examples: Argon (ε ≈ 1.67 kJ/mol, σ ≈ 3.4 Å), Water (ε ≈ 37 kJ/mol), Hydrogen (σ ≈ 2.9 Å). Larger ε = stronger attraction = higher melting points. Larger σ = bigger atoms = lower density.

Key Physics: The curve's shape comes from two competing effects - strong short-range repulsion (∝ r⁻¹²) and weaker long-range attraction (∝ r⁻⁶). This model explains why solids have preferred spacing between atoms and how they resist both compression and stretching.

Equilibrium

Distance Control

Distance (σ):

1.12

Current State

Energy: -1.00 ε

Force: 0.00 ε/σ

🔴 Repulsive forces

🔵 Equilibrium state

🟢 Attractive forces