A theoretical model is presented to describe the effect of particle clustering on the elastic modulus of composite gelled systems. In this model, particle clusters are described as regions with an increased volume fraction of the dispersed particles and with a firmness that is determined by the volume fraction of the particles in the cluster. The firmness of the composite gel is then calculated on the basis of the volume fraction and firmness of these clusters, which are treated as cluster particles. In this way, the Kerner equation (including compressibility, but neglecting the particle surface) and the Palierne equation (including the particle surface, but neglecting compressibility), both corrected for particle crowding at high volume fractions of the dispersed particles by the method of Lewis and Nielsen, are extended to describe the effect of particle clustering. It is demonstrated that, even in the absence of discrete bonds between the particles, clustering considerably amplifies the effect of the dispersed phase on the elastic modulus of the composite gel. This amplifying effect increases for higher volume fractions of the dispersed particles.
- particulate-filled composites
- shear modulus