Rigidity percolation in dispersions with a structured viscoelastic matrix

This paper deals with rigidity percolation in composite materials consisting of a dispersion of mineral particles in a microstructured viscoelastic matrix. The viscoelastic matrix in this specific case is a hydrocarbon refinery residue. In a set of model random composites the mean interparticle surface-to-surface distance was controlled, changing particle volume fraction phi and particle number density independently. This was achieved by mixing two sets of monodisperse particles with widely differing radii (0.35 microm and 17.5 microm) with the matrix. A scaling exponent of 3.9 +/- 0.6 for the storage modulus G' vs phi- phi(c) was observed above a threshold phi(c) , in good agreement with theoretical values for rigidity percolation. It is found that at the rigidity-percolation threshold the pore structure, as characterized by the mean surface-to-surface distance for the filler, rather than the filler volume fraction, is similar for different types of composites. This behavior is explained from the internal structure of the viscoelastic matrix, which consists of fractal solid aggregates dissolved in a viscous medium; the effective radius of these aggregates and the mean surface-to-surface distance together determine whether or not the aggregates are capable of providing rigidity to the composite. The explanation is further supported by a qualitative comparison with effective-medium calculations. These indicate that the observed breakdown of time-temperature superposition near phi(c) is due to the appearance of a time scale characteristic for the mechanical interplay between the viscous binder phase and the purely elastic solid particles.