Quantitative Compensation of Edge Effects for Particle Sizing in Stochastic Electrochemical Collision Experiments

Stochastic electrochemistry has emerged as an important area of fundamental electrochemistry over the past decade. Understanding electrochemical processes on the nanoscale is critical for the development of sensors and single-molecule electrochemical methods. In addition, collisions of insulating particles with ultramicroelectrodes (UMEs) can be used to estimate the particle size by analyzing the current step generated when an insulating particle blocks a portion of the electrode surface. However, accurate particle-size determination is hindered by the edge effect, whereby the diffusional flux is greater at the edge of the UME than at its center, leading to inaccuracies in blocking collision data analysis. In this study, we present an analytical treatment of edge effects for the estimation of polymeric particle size using current-step measurements obtained from stochastic electrochemical experiments at UMEs. Initially, we identify the conditions under which edge effects begin to significantly impact the particle-size estimation. By varying the UME size while using two fixed sizes of polystyrene (PS) beads, we established the conditions under which edge effects influence the current response associated with stochastic collision events. We then combine numerical simulations with experimental data to determine a semiempirical correction factor that accounts for the edge effect and improves the accuracy of particle-size determination. Finally, we evaluate the applicability and limitations of this semiempirical edge-flux correction factor across a range of UME and PS bead sizes. Our results demonstrate that the proposed correction significantly reduces the error in particle-size estimation, expanding the utility of stochastic electrochemistry for quantitative particle characterization.