A Gauss's law analysis of redox active adsorbates on semiconductor electrodes: The charging and faradaic currents are not independent.

A detailed framework for modeling and interpreting the data in totality from a cyclic voltammetric measurement of adsorbed redox monolayers on semiconductor electrodes has been developed. A three-layer model consisting of the semiconductor space-charge layer, a surface layer, and an electrolyte layer is presented that articulates the interplay between electrostatic, thermodynamic, and kinetic factors in the electrochemistry of a redox adsorbate on a semiconductor. Expressions are derived that describe the charging and faradaic current densities individually, and an algorithm is demonstrated that allows for the calculation of the total current density in a cyclic voltammetry measurement as a function of changes in the physical properties of the system (e.g., surface recombination, dielectric property of the surface layer, and electrolyte concentration). The most profound point from this analysis is that the faradaic and charging current densities can be coupled. That is, the common assumption that these contributions to the total current are always independent is not accurate. Their interrelation can influence the interpretation of the charge-transfer kinetics under certain experimental conditions. More generally, this work not only fills a long-standing knowledge gap in electrochemistry but also aids practitioners advancing energy conversion/storage strategies based on redox adsorbates on semiconductor electrodes.

A Description of the Faradaic Current in Cyclic Voltammetry of Adsorbed Redox Species on Semiconductor Electrodes.

A framework for interpreting the cyclic voltammetric responses from adsorbed redox monolayers on semiconductor electrodes has been developed. Expressions that describe quantitatively how the rates of the forward and back charge-transfer reactions impact the faradaic current density are presented. The primary insight is an explicit connection between the potential drops across the semiconductor space charge, surface, and electrolyte diffuse layers and the potential dependence of the reaction kinetics. Specifically, the evolution of the voltammetric shapes with experimental variables such as scan rate, standard potential of the redox adsorbate, and semiconductor surface energetics can now be interpreted for information on the operative charge-transfer rate constant and reaction energetics. This model is used to understand the complex dependence of the cathodic and anodic wave shapes for the first redox transition of an asymmetric viologen species adsorbed on n-Si(111). This system exhibited a heterogeneous rate constant of 0.24 s-1 and exhibited features consistent with an overwhelming majority of the applied potential dropping within the semiconductor space charge region. In total, experimentalists now have a visual key on how to interpret the faradaic current in voltammetric data for information on heterogeneous charge-transfer reactions between semiconductor electrodes and molecular adsorbates. The presented approach fills a long-standing knowledge gap in electrochemistry and aids practitioners interested in advancing photoelectrochemical energy conversion/storage strategies.

Beyond the Laviron Method: A New Mathematical Treatment for Analyzing the Faradaic Current in Reversible, Quasi-Reversible, and Irreversible Cyclic Voltammetry of Adsorbed Redox Species.

A new algorithm that describes the faradaic current for elementary redox reactions in the cyclic voltammetric responses of persistently adsorbed species on metal electrodes at any scan rate is presented. This work does not assume electrochemical reversibility and instead demonstrates a set of equations that encapsulate how the forward and back charge-transfer rate constants influence the data as a function of the experimental time scale. The method presented here is compared against other approaches that rely on either finite-difference calculations or that require numerical approximation of improper integrals (i.e., ±infinity as a bound). The method here demonstrates that the current-potential data can be described by incomplete gamma functions, whose two arguments capture the relevant kinetic variables. Following the notation for the Butler-Volmer model of charge transfer, exact solutions are presented for the cases of the charge-transfer coefficient, α, equal to 1 or 0. A related algorithm based on these results affords calculation of current-potential data for 0 < α < 1, allowing comprehensive analysis (i.e., point by point) of voltammetric data throughout the reversible, quasi-reversible, and irreversible regimes. Accordingly, this work represents an alternative to the method of Laviron, i.e., analyzing just the peak splitting values, for experimentalists to understand and interpret their voltammetric data in totality.

Direct Visualization of Trimerized States in 1T

Transition-metal dichalcogenides containing tellurium anions show remarkable charge-lattice modulated structures and prominent interlayer character. Using cryogenic scanning transmission electron microscopy (STEM), we map the atomic-scale structures of the high temperature (HT) and low temperature (LT) modulated phases in 1T^{'}-TaTe_{2}. At HT, we directly show in-plane metal distortions which form trimerized clusters and staggered, three-layer stacking. In the LT phase at 93 K, we visualize an additional trimerization of Ta sites and subtle distortions of Te sites by extracting structural information from contrast modulations in plan-view STEM data. Coupled with density functional theory calculations and image simulations, this approach opens the door for atomic-scale visualizations of low temperature phase transitions and complex displacements in a variety of layered systems.

The chain of chirality transfer in tellurium nanocrystals.

Despite persistent and extensive observations of crystals with chiral shapes, the mechanisms underlying their formation are not well understood. Although past studies suggest that chiral shapes can form because of crystallization in the presence of chiral additives, or because of an intrinsic tendency that stems from the crystal structure, there are many cases in which these explanations are not suitable or have not been tested. Here, an investigation of model tellurium nanocrystals provides insights into the chain of chirality transfer between crystal structure and shape. We show that this transfer is mediated by screw dislocations, and shape chirality is not an outcome of the chiral crystal structure or ligands.