Each carbon atom in graphene is sp2-hybridized: it forms three strong, in-plane σ (sigma) bonds to its neighbours, locking every atom into a perfect hexagonal honeycomb. The fourth electron sits in a delocalized π (pi) orbital above and below the sheet — free to hop from atom to atom, which is why graphene conducts electricity far better than copper by weight. This simulation splits those two properties apart so you can drive each one independently.
conduction: v_drift ∝ field / (1 + defects + temp/T0) (phonon + defect scattering)
mechanical: bond breaks when (L_current − L_rest)/L_rest > ε_crit(defect-adjacency)
- Electric field — drives the cyan electrons along the π system in the +x direction; higher field means faster net drift.
- Temperature — makes the sheet ripple (real graphene is never perfectly flat — thermal phonons buckle it out-of-plane) and randomizes electron hops, lowering conductivity.
- Vacancy defects — removes carbon atoms outright. Missing atoms force electrons to detour around the hole (scattering centres) and locally weaken the σ-bond network around the vacancy.
- Tensile strain — stretches the whole sheet along x. Bonds redden as they near their breaking strain; bonds touching a vacancy fail at a much lower strain, since a missing atom concentrates stress on its neighbours — the same reason grain boundaries and holes are where real graphene sheets actually fracture first.
Pristine graphene's in-plane bonds give it a measured tensile strength around 130 GPa and a Young's modulus near 1 TPa — by weight, roughly 100–300× stronger than structural steel — while its unbroken π system gives it electron mobility far exceeding silicon. Real samples fall short of both numbers exactly because of the defects and ripples this simulation lets you dial in.