A Chemical Model for the Dispersion of Fillers in a Polymeric Matrix

Abstract

1135I n the polymer industry, particulate fillers are often used to improve material properties and to reduce cost. The interest in developing such composites is therefore to widen the range of applications of the polymer. The quality of filler dispersion affects the properties of the finished product. Large agglomerates tend to form a flaw, which causes failure. The size reduction of particles depends upon the nature of the fillers (i.e size, shape, structure, cohesivity, etc.) as the intensity and duration of the applied hydrodynamic stress. Understanding the mechanism of agglomerate dispersion can be useful in improving mixing equipment.There are mainly two mechanisms by which the agglomerate size reduction occurs. Parker et al. (1972) proposed the occurrence of two distinct breakage mechanisms in turbulent conditions (agitation): large scale splitting into a few fragments (breakup process); and fine particle detachment on the periphery of the agglomerates (erosion process). Kao and Mason (1975) and Powell and Mason (1982), by systematic visualization in a well-defined flow field generated by a four-roll apparatus, observed only the erosion mechanism of the flocs model (cohesionless clusters of spherical particles). In that work, the erosion rate did not depend on the magnitude of the applied shear rate; the size reduction rather depended upon total deformation. Quigley (1977), also using a four-roller apparatus, observed that the internal structure of cohesive agglomerates (ferric hydroxide) suspended in water-sucrose affected the rupture mechanism. Agglomerates with greater initial sphericity were observed to undergo only micro-particle erosion at its extremities, without splitting. Agglomerates that were not as irregular underwent gross splitting and the resultant fragments continuously lost fine particle through erosion. Rwei et al. (1990) and (1992), by shearing carbon black agglomerates in simple shear flow (cone and plate rheometer) within low viscosity polymers (PDMS) and high viscosity polymeric melts (PS and PE), confirmed the same mechanisms of rupture and erosion. These authors pointed out that rupture characteristically starts at a shear stress higher than that for erosion. Either in erosion or in the rupture process, shear stresses developed in the polymer must exceed some critical value higher than the interparticle agglomerate forces.The work differs from others (e.g. Pandya, 1982Pandya, , 1981 regarding the agglomeration, breakup and erosion as an infinite series of chemical reactions or, alternatively, as an evolution of the size of one particle subjected to mean-field type interactions with others. The latter framework provides a new method of solving numerically the balance equation.Most dispersion models of cohesive agglomerates found in the literature focus on the prediction of size of a single agglomerate by an erosion mechanism process or the prediction of a homogeneous size of a population of agglomerates undergoing the break-up process. In fact, size distribution affects strongly phys...

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