Reaction efficiency of diffusion-controlled processes on finite, aperiodic planar lattices – III: Supramolecular architectures

Supramolecular architectures provide a reproducible template on which surficial processes can be studied. We consider the irreversible reaction A + B → C where B is a stationary reaction center and A is a coreactant diffusing on a finite, discretized d = 2 dimensional surface of a supramolecular assembly. A lattice-statistical model is developed to quantify how the reaction efficiency changes when the template is planar, Euler characteristic Ω = 0, or wrapped on the surface of a d = 3 host, Ω = 2. We find that for aperiodic or regular surfaces of finite spatial extent, dispersed Ω = 2 assemblies better optimize surficial reactions than Ω = 0 planar hosts.