Modulus filler concentration

Interesting aspects of the effect of fillers on the relaxation behavior were noted in (158) illustrated by experiments with segmented polyurethanes. In this case the presence of segregations of blocks of different chemical stmcture, typical for blodc-copolymers, causes the appearance in such systems of selective interactions with blocks of different nature, and brings about a complex effect on the temperamre curves of the viscoelastic characteristics, as well as on the modulus-filler concentration curve. 

The model for a filled system is different. The filler is, as before, represented by a cube with side a. The cube is coated with a polymer film of thickness d it is assumed that d is independent of the filler concentration. The filler modulus is much higher than that of the d-thick coat. A third layer of thickness c overlies the previous one and simulates the polymeric matrix. The characteristics of the layers d and c are prescribed as before, and the calculation is carried out in two steps at first, the characteristics of the filler (a) - interphase (d) system are calculated then this system is treated as an integral whole and, again, as part of the two component system (filler + interphase) — matrix. From geometric... 

Figure I. Reinforcement of silicone gums by carbon blacks (including nonrreinforcmg NR), silica powder (both surface-treated T and untreated NT), and titanium dioxide. The increase in modulus per unit dose and filler concentration depends on filler particle size.

The influence of clay and modified clay on the physical properties of the CR vulcanizates at 5 phr filler concentration is given in Table 5. As is obvious, the modulus values (stresses at 100%, 200% and 300% elongation) increase in all cases after filler loading. Again, the extent of improvement depends on the nature of the nanofillers. In the case of unmodified clay, the increase in 100% and 300% modulus is more with LDH, whereas MMT shows similar enhancement as that observed with... 

In the framework of the approximation given by the rigidity condition, a simple power law relation can be derived for the dependency of the small strain modulus G 0 of the composite on filler concentration . It is obtained,... 

By analyzing the compositional dependent relaxation time, the stress-strain relationships of polymer composites are determined as a function of the filler concentration and strain rate. As the volume fraction of filler increases, both the effective elastic modulus and yield stress increases. However, the system becomes more brittle at the same time. 

This leads us to the conclusion that a percolation structure appears inappropriate for the modeling of filler networks in elastomers. Consequently, we will consider an alternative network structure in the next section that refers to a space-filling configuration of kinetically aggregated filler clusters. In particular, this model will be shown to be in agreement with experimental results concerning the effect of filler concentration on the storage modulus. 

Equation (70) predicts a power law behavior G cp3-5 for the elastic modulus. Thereby, the exponent (3 + d ) / (3 - df) 3.5 reflects the characteristic structure of the fractal heterogeneity of the filler network, i.e., the CCA-clusters. The predicted power law behavior at higher filler concentrations is confirmed by the experimental results shown in Fig. 15, where the small strain storage modulus of a variety of carbon black filled rubbers is plotted against carbon black loading in a double logarithmic manner. It also agrees with older experimental data obtained by Payne [1] as shown in [63,64]. 

Then, one obtains the following power law-dependency of the elastic modulus G on filler concentration cp, particle size d, and layer thickness A ... 

Materials filled with rigid particles follow closely the predicted growth in elastic modulus as filler concentration increases. Many examples can be found in the... 

Figure 19.14. Bulk modulus of dental composite vs. filler concentration. [Adapted, by pennission, from Jones D W, Rizkalla A S, J. Biomedical Materials Research (Applied Biomaterials), 33, No.2, 1996, 89-100.]...

The filler effects on the chemoviscosity of thermosetting resins have not been studied extensively, but are vital to understanding the rheology of filled thermosets. For example, the effects of filler concentration on viscosity can be used in process control to monitor batch-to-batch variations or to provide essential information for research into alternative filler/resin batches. Ng and Manas-Zloczower (1993) examined an epoxy-resin system with silica filler and established that the elastic modulus of the resin can be expressed in terms of... 

---