Toward the development of a quantitative tool for predicting dispersion of nanocomposites under non-equilibrium processing conditions

Developing process-structure relationships that predict the impact of the filler-matrix interfacial thermodynamics is crucial to nanocomposite design. This work focuses on developing quantitative relationships between the filler-matrix interfacial energy, the processing conditions, and the nanoparticle dispersion in polymer nanocomposites. We use a database of nanocomposites made of polypropylene, polystyrene, and poly(methyl methacrylate) with three different surface-modified silica nanoparticles under controlled processing conditions. The silica surface was modified with three different monofunctional silanes: octyldimethylmethoxysilane, chloropropyldimethylethoxysilane, and aminopropyldimethylethoxysilane. Three descriptors were used to establish the relationship between interfacial energy, processing conditions, and final nanoparticle dispersion. The ratio of the work of adhesion between filler and polymer to the work of adhesion between filler to filler (descriptor: \( W_{\text{PF}} /W_{\text{FF}} \)) and the mixing energy for the production of the nanocomposites (descriptor: E _γ ) are used to determine the final dispersion state of the nanoparticles. The dispersion state is described using a descriptor that characterizes the amount of interfacial area from TEM images (descriptor: \( \bar{I}_{\text{filler}} \)). In order to capture the descriptors accurately, the TEM images of the nanocomposites are binarized using a pixel-wise neighbor-dependent Niblack thresholding algorithm. The significance of the microstructural descriptors was ranked using supervised learning and the interfacial area emerged as the most significant descriptor for describing the nanoparticle dispersion. Our results show a stronger dependence of the final dispersion on the interfacial energy than the processing conditions. Nevertheless, for the final dispersion state, both descriptors have to be taken into account. We also introduce a matrix-dependent term to establish a quantitatively non-linear relationship between the processing and microstructure descriptors.