Multiscale micromechanical modeling of polymer/clay nanocomposites and the effective clay particle

Abstract Polymer/clay nanocomposites have been observed to exhibit enhanced mechanical properties at low weight fractions (Wc) of clay. Continuum-based composite modeling reveals that the enhanced properties are strongly dependent on particular features of the second-phase ‘particles’; in particular, the particle volume fraction (fp), the particle aspect ratio (L/t), and the ratio of particle mechanical properties to those of the matrix. These important aspects of as-processed nanoclay composites require consistent and accurate definition. A multiscale modeling strategy is employed to account for the hierarchical morphology of the nanocomposite: at a lengthscale of thousands of microns, the structure is one of high aspect ratio particles within a matrix; at the lengthscale of microns, the clay particle structure is either (a) exfoliated clay sheets of nanometer level thickness or (b) stacks of parallel clay sheets separated from one another by interlayer galleries of nanometer level height, and the matrix, if semi-crystalline, consists of fine lamella, oriented with respect to the polymer/nanoclay interfaces. Here, quantitative structural parameters extracted from XRD patterns and TEM micrographs (the number of silicate sheets in a clay stack, N, and the silicate sheet layer spacing, d(001)) are used to determine geometric features of the as-processed clay ‘particles’, including L/t and the ratio of fp to Wc. These geometric features, together with estimates of silica lamina stiffness obtained from molecular dynamics simulations, provide a basis for modeling effective mechanical properties of the clay particle. In the case of the semi-crystalline matrices (e.g. nylon 6), the transcrystallization behavior induced by the nanoclay is taken into account by modeling a layer of matrix surrounding the particle to be highly textured and therefore mechanically anisotropic. Micromechanical models (numerical as well as analytical) based on the ‘effective clay particle’ were employed to calculate the overall elastic modulus of the amorphous and semi-crystalline polymer–clay nanocomposites and to compute their dependence on the matrix and clay properties as well as internal clay structural parameters. The proposed modeling technique captures the strong modulus enhancements observed in elastomer/clay nanocomposites as compared with the moderate enhancements observed in glassy and semi-crystalline polymer/clay nanocomposites. For the case where the matrix is semi-crystalline, the proposed approach captures the effect of transcrystallized matrix layers in terms of composite modulus enhancement, however, this effect is found to be surprisingly minor in comparison with the ‘composite’-level effects of stiff particles in a matrix. The elastic moduli for MXD6-clay and nylon 6-clay nanocomposites predicted by the micromechanical models are in excellent agreement with experimental data. When the nanocomposite experiences a morphological transition from intercalated to completely exfoliated, only a moderate increase in the overall composite modulus, as opposed to the expected abrupt jump, was predicted.