Spanning Network Gels from Nanoparticles and Graph Theoretical Analysis of Their Structure and Properties

Abstract

Gels self‐assembled from colloidal nanoparticles (NPs) translate the size‐dependent properties of nanostructures to materials with macroscale volumes. Large spanning networks of NP chains provide high interconnectivity within the material necessary for a wide range of properties from conductivity to viscoelasticity. However, a great challenge for nanoscale engineering of such gels lies in being able to accurately and quantitatively describe their complex non‐crystalline structure that combines order and disorder. The quantitative relationships between the mesoscale structural and material properties of nanostructured gels are currently unknown. Here, it is shown that lead telluride NPs spontaneously self‐assemble into a spanning network hydrogel. By applying graph theory (GT), a method for quantifying the complex structure of the NP gels is established using a topological descriptor of average nodal connectivity that is found to correlate with the gel's mechanical and charge transport properties. GT descriptions make possible the design of non‐crystalline porous materials from a variety of nanoscale components for photonics, catalysis, adsorption, and thermoelectrics.

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“…Thus, evaluating and quantifying complex architectures (e.g., PDZn) with aperiodic stochastic can efficiently guide the synthesis and regulation of the gas-sensing material. Graph theory (GT), a network theory, is a useful tool for quantitatively characterizing and comparing complex architectures. , By using a Python package of Structural GT, we performed GT analysis to convert SEM images of PDZn into a G (n, e) model, consisting of points (nodes, n) connected by lines (edges, e), toward comprehensively describing and comparing the percolating nanoscale networks. As shown in Figure c and Figure S3, there are clearly and visually porous structures in PDZn prepared in a 3 h reaction (i.e., PDZn-3 h) via GT analysis.…”

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“…80 By applying graph theory (GT) and fractal analysis, a method is developed to quantify these complex structures of the gels using a topological descriptor of average node connectivity that correlates with the mechanical and charge transport properties of the gels. 79…”

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