ABSTRACT Quantifying nanoparticle dispersion remains a central challenge in the development of polymer nanodielectrics, where electrical and dielectric properties are strongly governed by the three‐dimensional (3D) dispersion state of inorganic fillers. This study is aiming to establish a new quantitative framework that enables direct inference of the 3D dispersion state—expressed as the cluster size—from experimentally accessible two‐dimensional (2D) transmission electron microscopy (TEM) images. The framework integrates TEM image analysis, 3D numerical modelling, and machine‐learning regression, thereby linking 2D morphological descriptors to a physically interpretable 3D dispersion parameter. TEM images of three kinds of epoxy nanocomposites with different filler sizes and dispersion conditions were processed to extract particle contours, Feret maximum diameters, and inter‐particle distance distributions, from which a normalised full width at half maximum (FWHM) was obtained as a 2D descriptor of spatial heterogeneity. To clarify the physical origin of this descriptor, a 3D Thomas‐cluster model was constructed to generate particle configurations with controlled dispersion states and filler contents. Cross‐sectional slices extracted from the simulated structures reproduced the experimentally observed relationship between the normalised distance‐distribution width and the underlying 3D dispersion state, represented by the cluster size parameter. Using these simulation‐derived datasets, a LightGBM regression model was trained to predict the 3D dispersion state directly from two TEM‐extracted features: the normalised FWHM and the filler content. The model successfully inferred the relative dispersion states of the experimental samples, demonstrating that these 2D descriptors contain sufficient information to estimate the underlying 3D organization of nanoparticles. The proposed framework provides a physically grounded, data‐driven methodology for quantitative dispersion assessment and establishes cluster size as a robust, transferable metric for describing nanoparticle dispersion in polymer nanodielectrics.
Umemoto et al. (Thu,) studied this question.