Quantification of dispersion for weakly and strongly correlated fillers in polymer nanocomposites*

The dispersion of nanoparticles in viscous polymers is dictated by kinetics; interaction potentials between particles; and interfacial compatibility between the matrix and dispersed phases. An analogy has been made between thermally dispersed colloids and kinetically dispersed nanoparticles for cases where only weak interactions exist between particles allowing for a mean field description under the Ginzburg criterion such as for carbon black dispersed in polybutadiene. For these cases the pseudo- second virial coefficient can be used to quantify the quality of dispersion. However, this approach fails for nanoparticles with surface charges or other specific interactions that display strong correlations such as precipitated silica in styrene-butadiene rubber. Here, these strongly correlated systems are investigated in the context of the mean-field systems in order to gain a comparative description of dispersion using the network mesh size and a derived virial coefficient. In the proposed approach, the correlations in nanoaggregates are described by a combined semi-empirical function based on the Born-Green theory and a distribution function that accounts for the non-uniform accumulated strain in nanocomposites.