Numerical Monte Carlo Simulations to Evaluate the Influence That Spherical Nanoparticle Size and Arrangement Have on Interparticle Charge Transport across the Surface of Dye- and Cocatalyst-Modified Materials

Abstract

Mechanistic information underlying the function of illuminated mesoporous thin films of nanomaterials that contain distinct light-absorbing and electrocatalytic units can be gleaned from discrete-time random walk Monte Carlo simulations. These simulations bridge the length and time scales between individual electron-transfer events and ensemble behavior observed from bulk thin films. Most simulations are performed using models that simplify random mesoporous networks as isolated spherical nanoparticles. However, these simplifications may not provide sufficient detail to capture macroscopic experimental observations, especially when mesoporous nanomaterials consist of various geometries. Herein, we examine the role that the structure of the mesoporous thin film plays on the ability of photogenerated charges to accumulate on surface-confined redox-active electrocatalysts that require two redox events for turnover. We observe that the structure has a dramatic influence on the expected spectroscopic absorption anisotropy signal over time. We also observe that the yield for electrocatalyst turnover, as a function of the ratio of the electron-transfer time constant for self-exchange reactions and charge recombination time constant between the semiconducting mesoporous thin film and an oxidized/reduced surface-confined dye or electrocatalyst, is influenced by the total surface coverage of redox-active species. Structures consisting of spherical nanoparticles that are barely touching or partially necked are more effective at electrocatalytic turnover in the presence of vacant sites than discrete spherical nanoparticles or those that are arranged in a rodlike structure. Moreover, we show that the yield for electrocatalyst turnover is nearly independent of whether the simulations are performed on complex three-dimensional structures or simple two-dimensional planar grids. This discovery suggests that the added complexity of three-dimensional models may not be necessary to explain differences in electrocatalytic turnover yield in photoelectrochemical constructs containing surface-confined light-absorbing and electrocatalytic units.