Multiscale analysis of solution partitioning by randomly distributed electroactive sites: Relationship between Voronoi and diffusion cells tessellations

• Current tubes connecting each site to the bulk compete to partition the solution. • At short times jagged Voronoi Tessellation (VT) patterns dominate the competition. • At long times competition enforces equal-area Diffusion Cell Tessellation (DCT). • Ratio of DCT and VT areas varies as that of redox kinetics to diffusion length. Numerous important applications include active components, which are randomly dispersed on a carrier substrate and include catalytic single atoms, nanoparticles, clusters, etc. These arrays involve competing mass transport regimes to deliver reactants from bulk solutions to active sites while bypassing inactive areas. The non-symmetric distribution of active elements makes theoretical prediction of random array behaviour challenging and time-consuming. Voronoi tessellation (VT) is a useful formalism for efficient theoretical treatment of global performance of random arrays. However, it does not provide access to the activity of separate active elements. Rather, simulations show that the competition of transport flux lines related to each active site forces the solution to be partitioned, leading to dynamic time-dependent diffusion cell tessellations (DCT). Each tessellation type has different experimental significance for the characterization of random arrays, but cannot be confused with one another. This work sheds light on this problem by presenting a quantitative analysis of how a solution reacting at random arrays, consisting of bands or disks, becomes structured as a result of the interaction between the active site performance and the intensities of the transport fluxes. An illustration of how VT gradually transforms into DCT as the distance from the carrier substrate increases and the relationship between these two tessellations are provided.