Each monomer is a bead connected to its neighbours by stiff springs, and every bead is buffeted by random thermal kicks whose amplitude scales with temperature — overdamped Langevin dynamics, the same model used to simulate real polymer chains and DNA. Non-bonded beads interact through a Weeks–Chandler–Andersen repulsive core plus an attractive tail whose strength is set by solvent quality: in a good solvent the chain effectively repels itself and swells; at the theta point repulsion and attraction cancel and the chain behaves like an ideal random walk; in a poor solvent net attraction wins and the chain collapses into a compact globule.
Rg ≈ b · N^ν
ν ≈ 0.588 (good solvent, self-avoiding walk)
ν = 0.5 (theta point, ideal chain)
ν ≈ 0.33 (poor solvent, collapsed globule)
- Chain length N — number of monomer beads; longer chains take longer to equilibrate and show the scaling law more clearly.
- Temperature — amplitude of Brownian thermal motion; higher T fights the solvent-driven collapse and reswells a poor-solvent globule.
- Radius of gyration Rg — root-mean-square distance of every bead from the chain's centre of mass, the standard measure of coil size.
- Molecular-weight distribution — real polymerisations never produce chains of one exact length; the histogram shows a simulated batch following the classic most-probable (Flory) distribution, with Mn, Mw and PDI computed directly from the sampled chain lengths.
Real-world relevance: solvent-quality-driven coil-globule transitions govern how proteins fold, how DNA packs inside a cell, and how synthetic polymers are processed into fibres, films and gels — while a mixture's PDI determines whether a plastic behaves predictably or has a broad, hard-to-control range of mechanical properties.