Theoretical Models And Numerical Simulations Of Electrochemical Interfaces And Process At Nanoscale

Recent performance breakthroughs in various electrochemistry-based technologies have been largely relying on electrode nanosization and/or nanostructurization. They offer great opportunities to improve the electrochemical energy conversion efficiency and electrochemical detection sensitivity analysis, as well as to study electrochemical structures and processes with high spatial and temporal resolution. However, the nanosization leads to various possible nanosize effects and confinement effects in the electrochemical interface of nanoelectrodes. In the meantime, the effect of the ion size and the edge effects for nanometer electrodes due to these nanosize effects may significantly affect the interface structure and the electrode process. Therefore, some approximations and assumptions adopted in the conventional electrochemical theory become invalid. The nanometer-wide thin-layer cells and the nanoscale electrodes with various geometries are addressed theoretically in the thesis using the finite-element simulations, for the purpose of study the particularity of the electric double layer structure and the electrode process as well as the limitations of the conventional theories in describing these issues. The main results are summarized as follows:1. Electron-transfer kinetics and electric double layer effects in nanometer-wide thin-layer cellsThe confinement effects in nanometer-wide thin-layer cells holds great promise in ultrasensitive voltammetric detection and in probing fast heterogeneous electron-transfer kinetics due to the significantly improvement of the mass transport, which also cause the voltammetric behaviors controlled by the electron-transfer kinetics even at very high overpotentials. So the approximation of a linear relationship between the ET activation free energy and the electrode potential (E) of the classic Butler-Volmer (BV) theory would be problematic, and the treatment that only the electronic states at the Fermi level of electrode are involved in an ET reaction in the BV and Marcus-Hush (MH) models would also be not reasonable. The voltammetric responses in nanometer-wide thin-layer cells, obtained by using the Butler-Volmer and Marcus-Hush models and that predicted by the Marcus-Hush-Chidsey (MHC) based on the density of states (DOS) overlap between electrodes and redox agents, are compared systematically. The effect of the gap width between the electrodes (L), the standard rate constant (k0) and reorganization energy (A) for the electron-transfer reactions, the charges of the redox moieties (z) and the electric-double-layer (EDL) effects are considered.The results indicate that more pronounced deviation between voltammetric responses based on the BV and MH kinetic models and that deviate from those predicted by the more realistic MHC model occurs as L,k0and λ are smaller. For one-electron reactions with a typical k0of1cm/s and λ of100kJ/mol, the BV model may become inappropriate as L is reduced below50nm, whereas this limitation occurs for L<400nm for reactions with0.1cm/s k0. The classic MH model gives very similar prediction of voltammetric responses to that predicted by the MHC model for L<10nm. Therefore, the mathematically complex integration in the MHC formalism may be replaced by the quadratic MH equation for ET rate constants in treating the voltammetric responses of thin layer cells larger than10nm gap distances.The ET kinetics and mass transport dynamics in nanometer-wide thin-layer cells can be affected by the EDL structure due to the dimension comparability of the gap width between the electrodes with the EDL. The EDL effect would be more apparent as L. k0and λ, are smaller, and as z is larger. The EDL effect could not be ignored for L<50nm for reactions with1cm/s k0. In general, an inhibition of limiting current by the EDL effect could occur. According to the half-wave potential (E1/2) vs γ(=k0L/2D) relation, the fast ET kinetics analysis indicates that the deviation of the apparent rate constant k0a is higher than the real k0.2. Steric effects in the electrolyte phase for sphere nanoelectrodeThe classical Poisson-Boltzmann (PB) theory, which describe point-like ions in a mean-field approximation, break down when the crowding ions becomes significant, and steric repulsion potentially become important in the nanoscale electrode interface. The equilibrium EDL structure in the sphere nanoelectrode interface are obtained by using the classical PB theory and the modified PB model considering the effects of the ion size. The sphere nanoelectrode kinetics in the presence of the effects of the special EDL structure due to the steric effects are studied by combining the Poisson equation with the modified Nernst-Planck (NP) equation based on the Bikerman’ model.The results show that the formation of the saturated layer of counter ions in the interface in relatively high electrode potentials (E), large electrolyte concentration (cMN) and large solvated ion size (rion).And its effects on the electrode kinetics depends on the electrode radius (r0), the ET kinetic constant (k0) and the charge of the redox species (z). The steric effects of the EDL structure could be apparent even in the very dilute electrolyte solutions in the sphere nanoelectrode interface for an electrode radius of10nm and rion of0.4nm or larger. And it results in the weakness of the conventional Nernst-Planck (NP) model which describe point-like ions. The steric effects could not be ignored even on the low electrode potentails for rion of1nm. While the steric effects on the voltammetric responses can be neglected and the classic NP theory can be valid for a very small rion (0.1nm) and r0>100nm.3. Edge effects for nanoscale planar electrodesThe contribution of the mass transport of the electrode edge (non-Cottrell diffusion) and the ET kinetics to the total reaction current could not be omitted for the nanoscale planar electrodes. And the edge effects depend on the geometry and size of an electrode. The voltammetric responses on the the disk-, triangle-and square-like nanoscale electrodes are compared.The results show that the non-Cottrell diffusion and the deviation of the current on the nanoscale planar electrodes with the same surface area could be more pronounced with the smaller electrode scale. The limiting current on the nanoscale planar electrodes with the same area follows a trend of disk nanoelectrode<triangular nanoelectrode <rectangular nanoelectrode. Moreover, the applicability of the band electrode model in the voltammetry analysis is break down for the relative smaller aspect ratio of the rectangle nanoelectrods.