Using data science to locate nanoparticles in a polymer matrix composite

Structural polymers such as epoxy are commonly reinforced with nano-sized reinforcement particles to increase the toughness and thermo-mechanical properties. Although qualitative measurements can be made to examine particle distribution on a scratched or abraded nanocomposite surface, it is difficult to quantify the three-dimensional locations of the particles relative to the visible surface. In this investigation, we developed a method that combines experimental data obtained from atomic force microscopy (AFM), data science, and continuum micromechanics to discover the 3D position of ∼142 nm diameter nanosilica (NS) particles relative to an abraded surface. Finite element analysis was used to develop a training set of modulus values as a function of NS particle position relative to the surface of the polymer. Bayesian optimization was then used to determine the particle position(s) by minimizing the error between simulated and experimental modulus (AFM) contours. The algorithm can consistently predict particle positions within 3 nm of the actual known positions in synthetically created AFM data. We implemented the algorithm on experimental AFM data to create simulated modulus contours that partially reproduce key features present in an experimental modulus contour. This method provides a powerful tool to map spherical particle distribution in a 3D space, allowing better processing-structure-property understanding that can arise from resin chemistry variations, surface functionality, processing conditions, and nanofiller particle properties.