K-Index: A Descriptor, Predictor, and Correlator of Complex Nanomorphology to Other Material Properties

Morphology is a qualitative property of nanostructured matter and is articulated by visual inspection of micrographs. For deterministic procedures that relate nanomorphology to synthetic conditions, it is necessary to express nano- and microstructures numerically. Selecting polyurea aerogels as a model system with demonstrated potential for rich nanomorphology and guided by a statistical design-of-experiments model, we prepared a large array of materials (208) with identical chemical composition but quite different nanostructures. By reflecting on SEM imaging, it was realized that our first preverbal impression about a nanostructure is related to its openness and texture; the former is quantified by porosity (Π), and the latter is oftentimes related to hydrophobicity, which, in turn, is quantified by the contact angle (θ) of water droplets resting on the material. Herewith, the θ-to-Π ratio is referred to as the K-index, and it was noticed that all polyurea samples of this study could be put in eight K-index groups with separate nanomorphologies ranging from caterpillar-like assemblies of nanoparticles, to thin nanofibers, to cocoon-like structures, to large bald microspheres. A first validation of the K-index as a morphology descriptor was based on compressing samples to different strains: it was observed that as the porosity decreases, the water-contact angle decreases proportionally, and thereby the K-index remains constant. The predictive power of the K-index was demonstrated with 20 polyurea aerogels prepared in 8 binary solvent systems. Subsequently, several material properties were correlated to nanomorphology through the K-index and that, in turn, provided insight about the root cause of the diversity of the nanostructure in polyurea aerogels. Finally, using response surface methodology, K-indexes and other material properties of practical interest were correlated to the monomer, water, and catalyst concentrations as well as the three Hansen solubility parameters of the sol. That enabled the synthesis of materials with up to six prescribed properties at a time, including nanomorphology, bulk density, BET surface area, elastic modulus, ultimate compressive strength, and thermal conductivity.