A new model for electrochemical kinetics in nanoscale systems

Understanding the speed at which electrochemical reactions occur can provide scientific insight for various processes ranging from biochemical reactions to charge storage in capacitors and batteries. However, to date, many of the theoretical and experimental analyses of electrochemical reaction speed- such as those in the widely used Butler-Volmer formulations are based on classical thermodynamics and adapt 19th century-based Arrhenius theory. In these cases, the charge transfer rate is assumed to constantly increase with applied voltage. While complementary theories consider the influence of the configurational rearrangements in the electrolyte and energy level occupancy, none have related the kinetics to the specific arrangement of the electrons in the material constituting the electrode. The latter aspect is very important for nanoscale materials where the bulk is but a small part of the whole.

Recently, a team of engineers at UC San Diego led by professor of mechanical engineering Prab Bandaru and involving Ph.D. students Hidenori Yamada and Rajaram Narayanan, probed in detail, both theoretically and experimentally, the specific characteristics of a nanostructured material with respect to its effect on charge transfer. They demonstrated that in a one-dimensional nanotube, the electrons are confined to a line, while in two-dimensional graphene, the electrons are confined to a plane. Based on these findings, the researchers expect that the restriction on electron motion hinders charge transfer and electrochemical kinetics. On the other hand, the reduced electron scattering could enhance the kinetics. The team resolved these issues by taking advantage of the specific arrangement of the electrons in the nanostructure. They applied their theories to explain the experimental variation of the electrochemical rate constant of single layer graphene.

(a) Atomic force microscopy image of a section of the single layer graphene (SLG) sample transferred onto a p-Si/SiO₂ substrate. The wrinkles on the sample surface corresponding to the line scan (white line) are displayed in the lower left inset. The Raman spectrum of the transferred SLG is indicated in the top right inset. (b) Schematic of the three-electrode droplet electrochemical cell (actual experimental arrangement shown in the top right inset). The SLG working electrode (WE), Pt wire counter electrode (CE) and a reference (REF) saturated calomel electrode are indicated.

The researchers detailed their findings in a recent issue of the Journal of Physical Chemistry Letters. 

The team discovered that the charge transfer rate may either increase, decrease or remain constant, and that such variation is sensitive to the orientation as well as the relevant dimensionality of the nanostructure. As charge transfer per unit time determines the electrical current that may be obtained from a given electrode, the UC San Diego study provides a firm rationale for the use of nanostructures in charge storage electrodes, with applications encompassing solid state battery-related systems, wearable sensors, etc., where electrical current modulations would impact energy and power delivery.

A plot of the charge transfer related electrochemical rate constant (k) normalized to the k_η=0V as a function of the applied voltage (η), considered with respect to the redox potential. The experimental data is a poor fit with the theoretical fits expected from conventional Butler-Volmer (B-V) kinetics as well as three-dimensional Marcus-Hush-Chidsey (MHC) kinetics, but could be fit well through a dimensionality dependent electrochemical model proposed by a team of engineers at UC San Diego.

Paper: Dimensionality-Dependent Electrochemical Kinetics at the Single-Layer Graphene–Electrolyte Interface, R. Narayanan, H. Yamada, B.C. Marin, A. Zaretski, and P.R. Bandaru, J. Phys. Chem. Lett., 2017, 8 (17), pp 4004–4008.