A pseudo-thermodynamic description of dispersion for nanocomposites

- An analogy between thermally dispersed colloids and processed nanocomposites is made using the virial expansion.
- The pseudo-second order virial coefficient is a useful parameter to quantify dispersion in nanocomposites.
- A close to linear dependence is found for the second virial coefficient with primary particle size.
- The filler mesh size and the filler percolation threshold are quantified with values verified by TEM.
- A potential function based on the virial approach can be used in coarse grain simulations of nanocomposite dispersion.

Dispersion in polymer nanocomposites is determined by the kinetics of mixing and chemical affinity. Compounds like reinforcing filler/elastomer blends display some similarity to colloidal solutions in that the filler particles are close to randomly dispersed through processing. It is attractive to apply a pseudo-thermodynamic approach taking advantage of this analogy between the kinetics of mixing for polymer compounds and thermally driven dispersion for colloids. In order to demonstrate this pseudo-thermodynamic approach, two polybutadienes and one polyisoprene were milled with three carbon blacks and two silicas. These samples were examined using small-angle x-ray scattering as a function of filler concentration to determine a pseudo-second order virial coefficient, A2, which is used as an indicator for compatibility of the filler and polymer. It is found that A2 follows the expected behavior with lower values for smaller primary particles indicating that smaller particles are more difficult to mix. A2 is analogous to the excluded volume and long-range interaction potential for non-equilibrated nanocomposites. The measured values of A2 can be used to specify repulsive interaction potentials for coarse grain DPD simulations of filler/elastomer systems. In addition, new methods to quantify the filler percolation threshold and filler mesh size as a function of filler concentration are obtained. The results represent a new approach to understanding and predicting dispersion in polymer nanocomposites based on a thermodynamic analogy.

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