Diffusional impacts of nanoparticles on microdisc and microwire electrodes: The limit of detection and first passage statistics

•We study nanoparticle impacts on microdisc- and wire electrodes.•Expressions for the average number of events are derived.•The variance and the first passage time are calculated.•First passage times are used to estimate the lower limit of detection.•The advantages of wire electrodes in ultra-dilute solutions are discussed.

We derive approximate expressions for the average number of diffusive impacts/hits of nanoparticles on microdisc and microwire electrodes for the case where the impact leads to the loss of the nanoparticles from solution either via irreversible adsorption or complete electro-dissolution. The theory can also be applied to sub-micrometre size electrodes (nano-electrodes). The resulting equations can be utilised to analyse the number of impacts and its variance in the ‘nano-impact’ experiment. We also provide analytical expressions for the first passage time of an impact for dilute nanoparticle solutions in the continuum limit of Fickian diffusion. The expressions for the first passage times are used to estimate the lower limit of detection in ultra-dilute nanoparticle solutions for typical nano-impact experiments, and show the advantage of using microwire electrodes in ultra-dilute solutions or solutions containing larger nano-particles.