A thermal model to describe kinetic dispersion in rubber nanocomposites: The effect of mixing time on dispersion

Nanocomposites can be produced by a variety of processes. A common method used in industry is to mix a viscous polymer such as an elastomer compound, with nanofillers in a Brabender mixer or in a calendar. Dispersion has been quantified using a mixing index, DR, that is based on micrographs of reinforced elastomers on the micron-scale. A recently developed technique based on X-ray scattering allows for an alternative nano-scale description of dispersion based on a thermal-dispersion model where an analogy is made between temperature for thermal dispersion and nanocomposite processing conditions such as mixing time, mixing geometry, and viscosity for kinetic dispersion. In this paper the impact of mixing time on dispersion is investigated taking advantage of the van der Waals equation to describe excluded volume and interaction energy in the dispersion. It is found that the thermal-dispersion analogy is well behaved and can determine the wetting time for nano-scale incorporation of filler into elastomer. The nano-scale excluded volume depends only on the filler type and the excess excluded volume seems to be sensitive to the bound rubber layer. The pseudo-interaction energy is strongly dependent on viscosity and polymer chemistry. The thermal-dispersion model offers a novel approach to understanding kinetic dispersion in nanocomposites.