The animation on our home page is a live molecular dynamics simulation running in your browser. Two particle species, A and B, interact through Lennard-Jones potentials. A single size parameter decides whether they assemble into compact clusters or linear chains.
Each pair interacts through a truncated Lennard-Jones potential:
U(r) = 4ε [ (σ/r)12 − (σ/r)6 ] for r < rc
| Pair | ε | σ | Cutoff rc | Character |
|---|---|---|---|---|
| A–B | 1.0 | 1.0 | 1.5 | Attractive (bonding) |
| A–A | 0.2 | adjustable, 0.8–2.0 (default 1.5) | 1.12σ | Purely repulsive |
| B–B | 0.2 | same as A–A | 1.12σ | Purely repulsive |
The A–B cutoff of 1.5 lies well beyond the potential minimum at 21/6σ ≈ 1.12, so unlike particles attract and form bonds. For like pairs the cutoff is fixed at 1.12σ, right at the potential minimum. That removes the attractive tail and leaves only a soft repulsive core. A and B therefore behave like two complementary building blocks: they want to bond to each other, and they push their own kind away.
Other settings: about 500 A and 500 B particles (300 + 300 on phones), number density 0.2, periodic boundaries, a Langevin thermostat at temperature T (adjustable, 0.02–0.5, default 0.2) and time step 0.004 in reduced LJ units. Particles start at random positions with no overlaps. Your cursor acts as a local heater: within about 7σ the bath temperature rises by up to 3.0, so you can melt the assemblies locally and watch them re-form.
The A–A / B–B size σ sets how many partners each particle can bond to, which is its coordination number.
When the A–A and B–B repulsion is short-ranged, several B particles can crowd around one A (and vice versa) at the A–B bond length without hitting each other. Coordination numbers of 3–4 or more are allowed, so particles condense into dense, highly coordinated A–B clusters.
When the like-pair repulsion is long-ranged, two B neighbors of the same A must stay far apart. With A–B bonds about 1.1 long, a third neighbor cannot fit once σ approaches about 1.9 (= √3 × 1.1), so the maximum coordination number is 2. The only structures that can grow are alternating …ABAB… linear chains, a minimal model of step-growth polymerization.
Between these limits you get branched networks and short oligomers. Raising the temperature breaks A–B bonds and shifts everything toward monomers and dimers.
The idea that simple two-body potentials can capture bonding, valence and polymerization underlies the minimalist reactive potentials developed in our group. In this "reactive Lennard-Jones" approach, short-range repulsion between like species limits valence, and the resulting chemistry is cheap enough to simulate polymerization and mechanics at large scale.