Keywords: nanocomposites, modeling, nanomechanics, micromechanics, homogenization, multifunctional.

Nanocomposite materials hold the power to revitalize and revolutionize the field of composite materials. Nanoscale quantities, of even common materials, can exhibit strikingly different material properties from their bulk counterparts; often displaying them at significantly lower volume fractions, and below established percolation thresholds of the included phase. If these properties can be accessed at the bulk scale, not only can materials be better tailored to suit various applications, but also the possibility of designing multi-functional materials expands exponentially.

Initial research efforts have focused on polymer nanocomposites because of the potential to tailor properties in addition to the mechanical, for example electrical conductivities; certainly flexible electronic materials have immediate applications. Predictive models of these materials, however, have largely focused on single physics applications, and are often limited to the effects of the random microstructures resulting from 'well-dispersed' phase. In order to motivate the fabrication of more complex materials with specific microstructural design that can enable this multi-physics technology, predictive and informative models are required.

Using the micromechanics model known as the generalized method of cells, effective mechanical properties are predicted for gold nanoparticles in a polymeric matrix at a low volume fraction, ~0.05, using a designed microstructure. The resulting composite is transversely isotropic and when the particles are aligned along a long axis, greater stiffness is observed in the axial direction. Particles are spaced ~3 rod diameters apart, in both the longitudinal and transverse directions. The model incorporates an interfacial region between the embedded nanoparticles and surrounding matrix. When the interface is included in the model this spacing is reduced to ~2 rod diameters. With these interfaces the microstructure initially percolates (interfaces touch), at a volume fraction of ~0.11.

Increasing the stiffness of the interface increases the effective axial and transverse elastic stiffnesses of the composite. The change in stiffness exhibits percolation type behaviour, reaching a maximum composite stiffness while interfacial stiffness is still significantly below the stiffness of the gold rods. Reducing the stiffness of the interface degrades the composite stiffness to a greater degree with similar changes of the order of magnitude of interfacial stiffness.

Electrical conductivity can be usefully modelled using the same model and underlying principles of homogenization. The effect of increasing interfacial conductivity is an increasing in effective composite conductivity. The effect of reducing interfacial conductivity again has a more significant effect, producing an insulating region around the metallic rods.

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