Comparison of nanocomposite dispersion and distribution for several melt mixers.

Breakup (dispersion) and distribution of nanoparticles are the chief hurdles towards taking advantage of nanoparticles in polymer nanocomposites for reinforcement, flame retardancy, conductivity, chromaticity, and other properties. Microscopy is often used to quantify mixing, but it has a limited field of view, does not average over bulk samples, and fails to address nano-particle hierarchical structures. Ultra-small-angle X-ray scattering (USAXS) can provide a macroscopic statistical average of nanoscale dispersion (breakup) and emergent hierar-chical structure, as well as the distribution on the nanoscale. This work compares several common mixer geometries for carbon black-polystyrene nanocomposites. Two twin-screw extruder geometries, typical for industrial processing of melt blends, are compared with a laboratory-scale single screw extruder and a Banbury mixer. It is found that for a given mixer, nanoscale distribution increases following a van der Waals function using accumulated strain as an analogue for temperature while macroscopic distribution/dispersion, using microscopy, does not follow this dependency. Breakup and aggregation in dispersive mixing follow expected behavior on the nanoscale. Across these drastically different mixing geometries an unexpected dependency is observed for nanoscale distributive mixing (both nano and macroscopic) as a function of accumulated strain that may reflect a transition from distributive turbulent to dispersive laminar mixing as the mixing gap is reduced.