Rheological properties

The introduction of fillers or reinforcements changes practically all properties of the polymer including its rheo-logical characteristics. Viscosity usually increases with filler content, while melt elasticity decreases at the same time [104]. These changes depend very much on the particle characteristics of the filler. Matrix/filler interactions lead to the formation of an interphase and have the same effect as increasing filler content [71]. Viscosity increases consider-ably with decreasing particle size and increasing surface en-ergy, which can create processing problems and lead to the deterioration of mechanical properties as well as aesthetics.

The effect can be compensated by non-reactive coating which results in the decrease of interactions. Occasionally viscos-ity might also decrease at small filler loadings as an effect

of preferential adsorption of large molecular weight fraction or due to decreasing interaction upon non-reactive treatment.

Einstein's equation is often used for the modeling of viscosity. The original model is valid only at infinite dilu-tion, or at least at very small, 1-2 %, concentrations [105]

and it is useless in real composites. Frequently additional terms and parameters are introduced into the model, most often in the form of a power series [105], showing the non-linear composition dependence mentioned above. The Mooney equation represents a more practical and useful approach which contains adjustable parameters accommodating both the effect of inter-actions and particle anisotropy [105], i.e.

(10)

where  and 0 are the viscosity of the composite and the matrix, respectively,  the volume fraction of the filler, while kE is an adjustable parameter related to the shape of the particles. fmax is the maximum amount of filler, which can be introduced into the composite, i.e. maximum packing frac-tion, and it is claimed to depend solely on the spatial ar-rangement of the particles. The study of PP/CaCO3 composites proved that interfacial interactions and the formation of a stiff interface influences its value more than spatial ar-rangement and the maximum amount of filler which can be in-troduced into the polymer decreases with increasing specific surface area of the filler.

max

8.2. Stiffness

Modulus is one of the basic properties of composites and the goal of using particulate fillers is often to increase it.

Stiffness invariably increases with increasing filler content;

the incorporation of the stiff and strong fillers or fibers, usually with large surface energy, always results in increas-ing modulus. Decreased stiffness is the result of erroneous measurement, or in the case of very large particles debonding may also lead to decreasing Young's modulus. Stiffness in-creases exponentially with filler content. A linear correla-tion or an increase with decreasing slope indicate structural effects, usually aggregation or the changing orientation of anisotropic particles. Filler anisotropy results in stronger reinforcement, but only if the particles are orientated in the direction of the load. Perpendicular orientation leads to much smaller increase in stiffness.

Modulus is not only the most frequently measured, but also the most often modeled composite property. A large number of models exist which predict the composition dependence of stiffness or give at least some bounds for its value. The abundance of models is relatively easy to explain: modulus is determined at very low deformations thus the theory of linear viscoelasticity can be used in model equations. The large number of accessible data also helps both the development and the verification of models. Model equations developed for het-erogeneous polymer systems can be classified in different

ways. Apart from completely empirical correlations, the models can be categorized into four groups: i) phenomenological equa-tions, ii) bounds, iii) elf-consistent models and iv) semi empirical models. Although self-consistent models are more rigorous, they very often fail to predict correctly the com-position dependence of composite modulus, thus additional, adjustable parameters are introduced in order to improve their performance. The most often applied semi empirical model is the Nielsen (also called Lewis-Nielsen or modified Kerner) equation [106] matrix and the filler, respectively, m is the Poisson’s ratio of the matrix and f is filler content. The equation contains two structure related or adjustable parameters (A, ). The two parameters, however, are not very well defined. A can be related to filler anisotropy, through the relation A = kE-1, where kE is Einstein's coefficient, but the relation has not

f

been thoroughly investigated and verified.  depends on max-imum packing fraction. fmax is related to anisotropy, but it is influenced also by the formation of an interphase which was not taken into consideration in the original treatment [106].

Its experimental determination is difficult.

The model is quite frequently used in all kinds of par-ticulate filled composites for the prediction of the composi-tion dependence of modulus. In some cases merely the existence of a good fit is established, in others conclusions are drawn from the results about the structure of the composite. How-ever, the attention must be called here to some problems of the application of these equations or any other theoretical model. The uncertainty of input parameters might bias the results considerably. Maximum packing fraction influences pre-dicted moduli especially strongly, but its value is usually not known. On the other hand, the model is very useful for the estimation of the amount of embedded filler in polymer/elas-tomer/filler composites, but otherwise its value is limited.

8.3. Properties measured at large deformations, tensile