A simple theoretical model for the bulk properties of nanocomposite materials.

Nanocomposites may be produced simply by combining two materials in such a manner as to produce domains of nanometric scale in the resulting composite [1]. True nanocomposites are distinct from simple mixtures in that they exhibit material properties that do not vary monotonically in proportion to the ratio of the constituent materials - throughout this paper this behavior will be labeled as a "nano effect". It is widely supposed that "nano effects" are produced by interactions that occur at the interface of the nanometric domains [2]. In typical polymer-nanofiller systems, it is proposed that these interactions act to modify the material properties in a region of the polymer matrix near to the surface of the nanoparticle fillers. We shall refer to this volume of modified material as the interphase. A simple theoretical model is presented which links the interphase volume (and the nature of the material within that volume) with the externally measured properties of the nanocomposite. An equation for the probability that inserting an additional nanoparticle will increase the interphase volume is defined. This equation is applied in a Monte Carlo type calculation to evaluate the interphase volume as a function of filler loading. The resulting properties of the nanocomposite are calculated simply by combining the material properties of the constituents (nanoparticle, matrix and interphase) in the appropriate volume ratios. The strength of this approach is that its simplicity both minimises the number of free-parameters and ensures wide applicability. In this work the model is fitted to measured values of permittivity in nanodielectrics, however, the same approach may readily be applied to a range of other material properties. Statistical calculations are provided that demonstrate the generality of this result. Analysis of the model parameters is shown and provides insight into the extent and type of modification that occurs within the interphase.