Nanoparticles in solution are characterized by colloidal thermodynamics such as the second virial coefficient and Debye charge screening. We have found that this approach can be adapted to kinetic mixing in Banbury mixers, twin screw and single screw extruders. An analogy is made between thermal dispersion and kinetic dispersion. This allows adaptation of the van der Waals model to describe nanoscale dispersion in terms of enthalpic interactions and excluded volume. Enthalpic interactions can be in the form of specific interactions that lead to correlated nanoparticles or mean field interactions that result in disordered particles. Specific Coulombic interactions display Debye screening that can result in a critical concentration where a transition between specific and mean field behavior is observed. In many situations, such as elastomer reinforcement, nano-scale dispersion is not optimal since agglomeration on the nano-scale can enable the formation of a network on macroscopic scales assocated with properties such as tear resistance.

Quantification of nano-dispersion in polymer nanocomposites: A thermodynamic analogy

ACS Spring 2022

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