An A-B diblock copolymer is a single polymer chain made of two chemically distinct segments joined end to end. Because A and B repel each other (Flory-Huggins interaction χ) but are covalently bonded and cannot fully phase-separate at the macroscale, the melt instead microphase-separates into periodic nanoscale domains a few chain-lengths wide — the same mechanism used industrially in directed self-assembly for semiconductor nanolithography.
Free energy (Flory-Huggins / Leibler):
F/kT ∝ χN · f(1-f) + entropy of chain stretching
Order-disorder transition (symmetric, mean field):
(χN)_ODT ≈ 10.5
Equilibrium morphology (strong segregation, by A fraction f):
f ≈ 0.5 → lamellae (alternating stripes)
0.65 < f < 0.8 (or 0.2–0.35) → hexagonal cylinders
f < 0.2 or f > 0.8 → spheres on a triangular lattice
This 2D companion integrates the same Langevin dynamics for coarse-grained beads arranged into short chains, projected onto a plane. Bonded beads feel a harmonic spring; any two nearby beads feel a short-range soft (DPD-style) repulsion whose strength between unlike (A-B) beads is set by the χN slider — the larger it is relative to the ≈10.5 order-disorder threshold, the more strongly A and B beads are pushed apart even though their chains keep them tethered together, driving spontaneous domain formation. The f slider sets what fraction of each chain is A-type, which sets the natural curvature of the A-B interface and therefore which morphology the domains organize into. The order parameter tracks how far the local A-B contact statistics have drifted from a fully random (well-mixed) melt: 0% is disordered, values approaching 100% indicate sharply segregated domains.