The properties of particulate-filled thermoplastics depend strongly and usually nonlinearly on composition. Models are needed for the prediction of properties in order to produce composites with desired characteristics. Relatively few models exist for the prediction of the effect of filler content on properties, and the majority of these are empirical equations.

Rheological Properties

The introduction of fillers or reinforcements changes practically all properties of the polymer including its rheological characteristics. Viscosity usually increases with

Fig. 17 SEM micrograph showing the fracture of a wood particle during the deformation of PP/wood composites. Good adhesion of the components was achieved by the use of functionalized PP

Fig. 18 Close correlation between the initiation stress of the dominating deformation process and the strength of the composite. Symbols: (?) rPP/wood, (O) hPP/wood, (Д) PLA/wood. Full symbols: poor adhesion, empty symbols: good adhesion filler content, while melt elasticity decreases at the same time (Faulkner and Schmidt 1977). These changes depend very much on the particle characteristics of the filler although unambiguous correlations are not known. Matrix/filler interactions lead to the formation of an interphase and have the same effect as increasing filler content (Stamhuis and Loppe 1982).

The composition dependence of rheological properties is modeled only in surprisingly few cases. Quite a few models are derived from Einstein’s equation, which predicts the composition dependence of the viscosity of suspensions containing spherical particles. The original equation is valid only at infinite dilution or at least at very small, 1-2%, concentrations (Jeffrey and Acrivos 1976), and in real composites, the equation must be modified. Usually, additional terms and parameters are introduced into the model most often in the form of a power series (Jeffrey and Acrivos 1976). The Mooney equation represents a more practical and useful approach which contains adjustable parameters accommodating both the effect of interaction and particle anisotropy (Jeffrey and Acrivos 1976), i.e.,

where n and n_{0} are the viscosity of the composite and the matrix, respectively, ф is the volume fraction of the filler, and k_{E} is an adjustable parameter related to the shape of the particles. ф^{тах} is the maximum amount of filler, which can be introduced into the composite, i.e., maximum packing fraction, and it is claimed to depend solely on the spatial arrangement of the particles. The study of PP/CaCO_{3} composites proved that interfacial interactions and the formation of a stiff interface influence its value more than spatial arrangement, and the maximum amount of filler which can be introduced into the polymer decreases with increasing specific surface area of the filler.