A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the molecular potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of singlewalled carbon nanotubes and the design of nanotube-based structural devices, the modeling technique has been applied to two independent examples: the determination of the effectivecontinuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalentcontinuum models. As a result, an effective thickness of the continuum model has been determined. The determined effective thickness is significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) with the strain energy of an equivalent-continuum plate subjected to cylindrical bending.

A continuum-based elastic micromechanics model is developed for silica nanoparticle/polyimide composites with various nanoparticle/polyimide interfacial treatments. The model incorporates the molecular structures of the nanoparticle, polyimide, and interfacial regions, which are determined using a molecular modeling method that involves coarse-grained and reversemapping techniques. The micromechanics model includes an effective interface between the polyimide and nanoparticle with properties and dimensions that are determined using the results of molecular dynamics simulations. It is shown that the model can be used to predict the elastic properties of silica nanoparticle/polyimide composites for a large range of nanoparticle radii, 10 Å to 10,000 Å. For silica nanoparticle radii above 1,000 Å, the predicted properties are equal to those predicted using the standard Mori-Tanaka micromechanical approach, which does not incorporate the molecular structure.It is also shown that the specific silica nanoparticle/polyimide interface conditions have a significant effect on the composite mechanical properties for nanoparticle radii below 1,000 Å.

Exposure to extended periods of sub-T g temperatures causes physical changes in the molecular structure of epoxy resins and epoxy-based materials to occur. These physical aging mechanisms include the reduction in free volume and changes to the molecular configuration. As a result, mechanical, thermodynamical, and physical properties are affected in ways that can compromise the reliability of epoxy-based engineering components and structures. In this review, the physical changes in the molecular structure of epoxies are described, and the influence of these changes on the bulk-level response is detailed. Specifically, the influence of physical aging on the quasistatic mechanical properties, viscoelasticity, fracture toughness, thermal expansion coefficient, volume relaxation, enthalpy relaxation, endothermic peak temperature, fictive temperature, and moisture/solvent absorption capability is reviewed. Also discussed are relationships between relaxation functions, crosslink density, composite reinforcement, and epoxy/copolymer blending and the physical aging response of epoxies. Finally, the concepts of thermal and mechanical rejuvenation are discussed.

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