Complex Chiral Nanodendrimers and Graph-Property Relationships for Chiroptical Activity

Organic, polymeric, and inorganic nanomaterials with radially diverging dendritic segments are known for their unique optical, physical, chemical and biological properties. However, a methodology to quantitatively link their complex architecture to measurable properties is difficult due to characteristically large degree of structural disorder. Here, we address this fundamental and technological problem using dendrimer-shaped gold particles with distinct stochastic branching and intense chiroptical activity. Unlike typical molecular or nanostructured dendrites, gold nanodendrimers are two-dimensional with branches radially spreading within one plane. They are also chiral with mirror asymmetry propagating through multiple scales. In this work, we demonstrate how their complex architecture is quantitatively described by image-informed graph theory (GT) models accounting for both organized and disordered structural components of the nanodendrimers. Using finite-difference time-domain simulations, we then establish how the chiroptical behavior of computationally constructed particles change in the limit of having perfectly deterministic structures. To extend this to predicting chiroptical properties of experimental particles, we used GT to enumerate experimentally observed stochastic structural features which distort the chiroptical behavior of deterministic structures. With this, we develop a descriptor integrating topological and geometrical characteristics of particle graphs and provide accurate physics-based predictions of the non-linear and non-monotonic dependence between synthesis conditions and the optical asymmetry factor, making this the first case of bespoke GT parameters for complex nanostructure properties. Simplicity of the GT models capable of capturing the complexity of the particle organization and related light-matter interactions opens the way to the design of scalable nanostructures with multiple functions.