Structural emergence, correlations and quantification of dispersion for surface-modified, aggregated, fumed silica in polymer nanocomposites*

The dispersion of nanoparticles in viscous polymers is dictated by kinetics; particle interaction potential; and interfacial compatibility between the matrix and dispersed phases. An analogy can been made between thermally dispersed colloids and kinetically dispersed nanoparticles for cases where weak interactions exist between particles allowing for a mean field description under the Ginzburg criterion such as for surface-modified silica and carbon black nanocomposites. However, this approach fails for precipitated/fumed fillers with extensive surface charge which results in strong correlations. Dispersion in these systems is quantified using a pseudo-second virial coefficient and the resulting correlations are accounted through 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. The dependence of the amount of surface charge, concentration and dielectric nature of the polymer on the emergence of correlated structures is explored.