Equality of diffusion-limited chronoamperometric currents to equal area spherical and cubic nanoparticles on a supporting electrode surface

Abstract

We computationally investigate the chronoamperometric current response of spherical and cubic particles on a supporting insulating surface. By using the method of finite differences and random walk simulations, we can show that both systems exhibit identical responses on all time scales if their exposed surface areas are equal. This result enables a simple and computationally efficient method to treat certain spherical geometries in random walk based noise investigations.

Single Co3O4 Nanocubes Electrocatalyzing the Oxygen Evolution Reaction: Nano-Impact Insights into Intrinsic Activity and Support Effects

“…This steady-state current can be calculated according to well-established equations if the correct reactant bulk concentration and diffusion coefficient are considered [ 24 ]. The diffusion limited currents towards cubic NPs on a surface were estimated from random walk simulations [ 25 ] and for free cubic particles from finite difference simulations [ 26 ]. To our knowledge, however, there is not yet an equation describing diffusional steady-state currents for impacting cubic particles at hand.…”

Destructive nano-impacts: What information can be extracted from spike shapes?

“…The surface concentration hence equals the saturation concentration at any time, leading to a temporal evolution of j lim,sol , which is exclusively determined by the diffusive mass transport of released ions away from the particle. Due to the small size of the particle and the fast mass transport facilitated by radial diffusion, the time that is required to reach the steady state will be of the order of hundreds of nanoseconds [21]. Transients between the kinetically-limited and the diffusion-limited case will hence be beyond the bandwidth of the potentiostat and can not be resolved experimentally.…”

“…without changing the structure of c. We may hence rescale the concentration values employed in the above solution (21) as well as in the boundary conditions by multiplication with a factor s ∈ R. Furthermore, since the diffusion equation solely comprises derivatives of c, all concentrations may be offset by a constant value c 0 ∈ R:…”

Nanoparticles in sensing applications: on what timescale do analyte species adsorb on the particle surface?

“…This assumption is supported by a previous study, in which we investigated the chronoamperometric response of differently shaped nanoparticles on a supporting surface in the diffusion limited case, and found that different shapes may lead to equal chronograms. 17…”

“…Due to the small size of nanoparticles, the diffusion eld around a nanoparticle quickly reaches a steady state as soon as the nanoparticle is exposed to adsorbing molecules in the surrounding solution. Since the time that is required to reach this state is typically of the order of a few 100 ns for particles featuring a diameter below 20 nm, 17 we can approximate q(t) in eqn ( 9) by using the assumption that the system instantaneously reaches the diffusional steady state in the derivation of q(t). For this reason, we rst determine the steady-state ux to a spherical electrode: we calculate the ux of molecules to the surface for the long-term limit (t / N) and nd that the timedependent term (pDt) À0.5 vanishes in eqn ( 4).…”