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 top-down 2D view 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 atoms jitter in place (real graphene is never perfectly flat — thermal phonons buckle it out-of-plane; here that shows as in-plane jitter) 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.