Can the Voigt Model be Directly Used for Determining the Modulus of Graphene in Laminate Thin Films?

Laminate thin-film composites that couple polymers with single-layer graphene (SLG) are lightweight and have shown superb electromechanical strength. The mechanical strengths of the composites can be described by elastic micromechanical models such as the Voigt mixing rule. However, the reinforcement behavior between polymer and SLG has raised questions about the validity of such models in laminate composites at the nanoscale. Herein, we have fabricated laminate thin films of poly(ether imide) and SLG (PEI/SLG) with varying volume fractions of SLG (phi(g)) as a model system to evaluate the effective reinforcement using the mixing rule. Linear regression analysis of the Young's modulus of the composite (E-c) versus phi(g) revealed an unexpectedly high-effective Young's modulus of large-area, polycrystalline SLG, E-g = 1.12 +/- 0.05 TPa. Further analysis of theoretical and experimental E-c using the Voigt-Poisson model showed a lower maximum value of E-g similar to 0.9 TPa for films with phi(g) >= 0.11 vol %. Our results show that an ideal mixing rule is followed only beyond a critical value of phi(g) for laminate thin-film composites, which explains the wide inconsistency of E-g reported in the literature. This knowledge will guide the fabrication of laminate polymer-graphene thin films with near-ideal mechanical reinforcement.