Graphene is a single sheet of carbon atoms bonded into a hexagonal honeycomb lattice. Its sp² covalent bonds make it about 200 times stronger than steel by weight, while its delocalized π-electrons travel almost unimpeded across defect-free regions, giving extremely high electron mobility.
2D Young's modulus E₂D ≈ 340 N/m (~1 TPa bulk-equivalent)
σ(strain) ≈ E₂D · ε − nonlinear softening near bond-breaking strain (~20–25%)
mobility μ(defects) ≈ μ₀ / (1 + k·defect_density) (impurity scattering)
- Applied strain — stretches the lattice; bonds elongate and, past roughly 20%, begin to fail, dropping retained tensile strength.
- Applied voltage — drives glowing electron particles through the lattice; higher voltage raises current for a given mobility.
- Defect density — vacancy/impurity sites that scatter electrons, lowering mobility and current, and slightly weakening the lattice.
- View mode — Mechanical view colors bonds by stress; Electrical view highlights electron flow paths and dims stress coloring.
These two properties combine in real applications such as flexible touchscreens, ultra-fast transistors, and lightweight structural composites that must stay both strong and conductive under strain.