Filled polymer systems

Polymers, as well as elastomers, are reinforced by the addition of small filler particles. The performance of rubber compounds (e.g. strength, wear resistance, energy loss, and resilience) can be improved by loading the rubber with particulate fillers. Among the important characteristics of the fillers, several aspects can be successfully interrogated by AFM approaches. For instance, the particle and aggregate size, the morphology, and in some cases the surface characteristics of the filler can be assessed. 

In semicrystalline polymers, fillers may act as reinforcement, as well as nucle-ation agents. For example in PP, nanoscale silica fillers may nucleate the crystallization resulting in spherulites that show enrichment in particles in the center of the spherulite (Fig. 3.64). For a quantitative analysis of, e.g., filler sizes and filler size distributions, high resolution imaging is necessary and tip convolution effects [137-140] must be corrected for. The particles shown below are likely aggregates of filler particles considering the mean filler size of 7 nm [136]. 

---

The effect of aging and of process variables on the rheological properties of solid proplnts has been the subject of mechanical shear relaxation spectroscopy (Ref 4). The technique is of interest to such filled polymer systems generally in that anisotropy in the viscoelastic properties can be readily observed... 

For filled polymer systems with inorganic and powdery fillers, a rule of mixtures1 can be written as... 

Typically, titanate-treated inorganic fillers or reinforcements are hydrophobic, organophilic, and organofunctional and, therefore, exhibit enhanced dispersibility and bonding with the polymer matrix. When used in filled polymer systems, titanates claim to improve impact strength, exhibit lower viscosity, and enhance the maintenance of mechanical properties during aging. 

It is understandable that the properties of these multicomponent polymer systems are related to those of the homopolymers is a very complex way. In some case, e.g. in random copolymers and homogeneously filled polymer systems, additivity is found for certain properties. 

The activation energy of viscous flow will be decreased by an increase in filler loading and, therefore, the viscosity and modulus of filled polymer systems are less temperature dependent. On the other hand, filler loading has little effect on the activation energy of cure. 

The relationship between steady-shear viscosity and dynamic-shear viscosity is also a common fundamental rheological relationship to be examined. The Cox-Merz empirical rule (Cox, 1958) showed for most materials that the steady-shear-viscosity-shear-rate relationship was numerically identical to the dynamic-viscosity-frequency profile, or r] y ) = r] m). Subsequently, modified Cox-Merz rules have been developed for more complex systems (Gleissle and Hochstein, 2003, Doraiswamy et al., 1991). For example Doriswamy et al. (1991) have shown that a modified Cox-Merz relationship holds for filled polymer systems for which r](y ) = t] (yco), where y is the strain amplitude in dynamic shear. 

The complex viscosity can be related to the steady-shear viscosity rf) via the empirical Cox-Merz rule, which notes the equivalence of steady-shear and dynamic-shear viscosities at given shearing rates ri y) = rj (co). The Cox-Merz rule has been confirmed to apply at low rates by Sundstrom and Burkett (1981) for a diallyl phthalate resin and by Pahl and Hesekamp (1993) for a filled epoxy resin. Malkin and Kulichikin (1991) state that for highly filled polymer systems the validity of the Cox-Merz rule is doubtful due to the strain dependence at very low strains and that the material may partially fracture. However, Doraiswamy et al. (1991) discussed a modified Cox-Merz rule for suspensions and yield-stress fluids that equates the steady viscosity with the complex viscosity at a modified shear rate dependent on the strain, ri(y) = rj yrap3), where y i is the maximum strain. This equation has been utilised by Nguyen (1993) and Peters et al. (1993) for the chemorheology of highly filled epoxy-resin systems. 

The measurement of yield stress at low shear rates may be necessary for highly filled resins. Doraiswamy et al. (1991) developed the modified Cox-Merz rule and a viscosity model for concentrated suspensions and other materials that exhibit yield stresses. Barnes and Camali (1990) measured yield stress in a Carboxymethylcellulose (CMC) solution and a clay suspension via the use of a vane rheometer, which is treated as a cylindrical bob to monitor steady-shear stress as a function of shear rate. The effects of yield stresses on the rheology of filled polymer systems have been discussed in detail by Metzner (1985) and Malkin and Kulichikin (1991). The appearance of yield stresses in filled thermosets has not been studied extensively. A summary of yield-stress measurements is included in Table 4.6. 

A.V. Shenoy. Rheology of Filled Polymer Systems, Kluwer Academic Publishers, 1999, p. 339. 

The scaling described in Equation 2 indicates that the modulus is a strong function of the hybrid loading and is consistent with the data obtained for other filled polymer systems as well as the scaling observed for block copolymers with spherical microdomains. ... 

The rheology of most filled polymer systems and polymer blends can be described accurately enough by a relatively simple equation ... 

V.V. Korshak, LA. Gribova, A.P. Krasnov, et al. Study of surface layers during friction of filled polymer system based on polyphenylquinoxahne (PPQ). Soviet J. FYiction and Wear, 1981, Vol. 2, No. 2, pp. 22-25. 

In filled polymer systems, it has been observed that the effect of filler content on viscosity decreases as shear rate increases [14, 49]. In the case of nanocomposite flllers, this effect has been explained in terms of a detachment/reattachment mechanism [49]. With respect to the dimensions of the flllers, it has been observed that as the surface area of the filler increases so does the viscosity of the filled polymer melt [18, 48]. For particles with similar shapes, an increase in the surface area means a reduction in particle size. In this sense, nanoflllers are expected to significantly increase the viscosity of polymer melts in relation to flllers with sizes in the range of micrometers. An analysis of filler shape and other relevant aspects of polymer flllers can be found in the work by Shenoy [50]. 

Chin WC (2001) Computational rheology for pipeline and annular flow. Butttrw[Pg.284]

Applicability of equation (12.23) (with K = 1.21) to several filled polymer systems has been reported (Nicolais and Narkis, 1971). 

One of the most comprehensive comparisons of data for many filled polymer systems is given in the review by Holliday and Robinson (1973), which also provides additional expressions not discussed here. Several points are of special interest. First, equations such as Kerner s (1956a,h) and Wang and Kwei s (1969) agree reasonably well for spherical particles, while Turner s (1946) equation is better for systems in which fillers are fibrous or platelike. Second, fibers and fabrics induce the greatest deviation from additivity (see Figure 12.36). Finally, the behavior of polytetrafluoro-ethylene is strikingly anomalous. 

It has now been shown that recent studies of relaxation, sorptive, and diffusive behavior in many filled polymer systems amply confirm earlier observations of deviations from values predicted by simple additivity (Kumins, 1965). Such effects are not confined to high-surface-area fillers such as certain carbon blacks and fillers (typical reinforcing fillers for rubber) they are also observed frequently with low-surface-area fillers, such as pigments and even glass beads with average diameters in the range of tens of micrometers. 

The actual industrial practice is similar to that used in the filled polymer system and it is preferable to prepare the concentrate or master batch of the polymer with more nanomaterial than is required. This is subsequently incorporated into the base polymer with the required dose of nanomaterial. It should be noted that the final state of dispersion of nanomaterial in the polymer matrix ultimately depends on favourable thermodynamic factors, whichever technique is used to prepare it. 

The foregoing method can also be employed to determine the adhesion properties of other filled polymer systems. The procedures involved in this analytical method are summar ized as follows (1) Use proper experiments to obtain the contact angle measurements for both the filler and the polymer, (2) Plot the contact angle measurements as cos 9 versus An y and determine the critical surface... 

---