The Role of Shape Commensurability in Chirality Transfer: Gold Nanoshape Solutes in a Discotic Nematic Liquid Crystal...

Chirality, as an inherently geometric concept, is well understood at most length scales and is a principal attribute of objects and figures. Quantitative models predicting the efficacy of chirality transmission across length scales have only recently begun to emerge. We provide further proof-of-concept data and calculations for a modus operandi for nanoshape solutes featuring a chiral ligand shell in an achiral discotic nematic (ND) liquid crystal solvent, demonstrating that chirality transfer can be understood through remarkably simple geometric considerations. This mechanism is based on the product of a pseudoscalar chirality indicator and a geometric shape compatibility factor based on the 2D isoperimetric quotients for nanoshape solutes and N_D molecule. The model is tested on an experimental set of precisely engineered gold nanoshapes, rods, prisms, and discs, that validates that shape commensurability between nanoscale solute and nematic solvent is a prerequisite for efficacious chirality transfer as determined by the helical twisting power of the nanoshapes in the induced chiral N_D* phase. Thus, we predict that libraries of calculated and in-parallel acquired experimental data among related nanoshapes and even small organic molecules pave the way for predictive calculations of chirality transfer in nanoscale, macromolecular, biological, and small-molecule systems.