Electrochemical Potential Profiles Research Articles

Monte-Carlo Simulation Combined with Density Functional Theory to Investigate the Equilibrium Thermodynamics of Electrode Materials: Lithium Titanate As Model Compounds

Thermodynamics of the electrode materials is of interest in understanding their mechanism of electrochemical reactions, which should in turn contribute to designing and developing a new material for rechargeable batteries. While the recent development in the computational power has remarkably advanced the highly accurate electronic structure simulations, such as density functional theory (DFT), it is not always straightforward to extract from those theoretical studies certain insights that are “understood” or “interpreted” in simple terms. One also occasionally comes across the situation where the thermodynamics at the finite temperature T > 0 is beyond the general DFT considerations. Monte-Carlo simulation, on the other hand, tries to describe the physical process at the finite temperature in a simple (or an abstract) manner of which the meaning is clear to understand, although one has to worry if the simple model represents the reality.Dealing with lithium titanate (LiTi2O4 and Li4/3Ti5/3O4, LTO) as a model electrode material, we propose a method to describe its equilibrium thermodynamics based on the Monte-Carlo simulation (MC), for which the energetic parameters are determined by the density functional theory (DFT). The electrochemical potential profile is simulated by a simple topological model which consists only of three parameters representing the Li site energies; namely, the binding energy of the 8a site (ε8a), the difference in the site energy between the 8a and 16c sites (∆ε) and the repulsion between two Li atoms situated at the adjacent 8a and 16c sites (J).Parameter physics by the MC revealed that the term ∆ε plays a decisive role, with a collateral effect from J, for characterizing the thermodynamics of the material whereas the term ε8a determines the electrochemical potential at which the reaction takes place. For instance, if ∆ exceeds the thermal energy at the temperature under consideration, i.e., if ∆ε > 3kT, the first order phase transition takes place during which two phases coexist, resulting in a plateau region in the potential profile. On the other hand, if ∆ε < 3kT, the lithiation of LTO is viewed as a phenomenon above the critical point, above which the material is in a homogeneous uniphasic state.A multiple regression analysis of a set of the total energy of LiTi2O4 calculated by DFT allows us to determine these energetic terms. The MC simulation with the determined parameters well reproduces the shape and position of the experimental potential profile of LTO. Since the determined value, ∆ε/eV ~ 0.4, far exceeds the thermal energy at ambient temperature, the potential plateau of LTO is explained by the first-order phase transition as long as the equilibrium state is concerned. Unlike for LiTi2O4, we were unsuccessful in determining the parameters for Li4/3Ti5/3O4, for which the reason we will briefly address on site.In the paper, the outline of the methodology will be presented, of which the details are available in our recent publication.[1] Reference [1] H. Ozaki, K. Tada and T. Kiyobayashi, Phys. Chem. Chem. Phys., 21, 15551 (2019). Figure Caption Potential profile of LTO. Exp: Li4/3Ti5/3O4 experimentally determined by the galvanostatic intermittent titration test (GITT) during the Li extraction process at T/K = 303. Sim: Result of the grand canonical Monte-Carlo simulation at T/K = 300, for which the energetic parameters were determined by the DFT calculations based on LiTi2O4. The error bar placed in the middle of the potential plateau for the simulated result indicates twice the standard deviation (±2σ) estimated from the multiple regression analysis of the DFT total energy data set. The abscissa is scaled so as to fit the experimental data. Figure 1

Quasi-Fermi level splitting in nanoscale junctions from ab initio

The splitting of quasi-Fermi levels (QFLs) represents a key concept utilized to describe finite-bias operations of semiconductor devices, but its atomic-scale characterization remains a significant challenge. Herein, the nonequilibrium QFL or electrochemical potential profiles within single-molecule junctions obtained from the first-principles multispace constrained-search density-functional formalism are presented. Benchmarking the standard nonequilibrium Green's function calculation results, it is first established that algorithmically the notion of separate electrode-originated nonlocal QFLs should be maintained within the channel region during self-consistent finite-bias electronic structure calculations. For the insulating hexandithiolate junction, the QFL profiles exhibit discontinuities at the left and right electrode interfaces and across the molecule the accompanying electrostatic potential drops linearly and Landauer residual-resistivity dipoles are uniformly distributed. For the conducting hexatrienedithiolate junction, on the other hand, the electrode QFLs penetrate into the channel region and produce split QFLs. With the highest occupied molecular orbital entering the bias window and becoming a good transport channel, the split QFLs are accompanied by the nonlinear electrostatic potential drop and asymmetric Landauer residual-resistivity dipole formation. Our findings underscore the importance of the first-principles extraction of QFLs in nanoscale junctions and point to a future direction for the computational design of next-generation semiconductor devices.

Monte-Carlo simulation combined with density functional theory to investigate the equilibrium thermodynamics of electrode materials: lithium titanates as model compounds.

By using lithium titanate (LTO) as a model electrode material, the present study proposes a method to describe its equilibrium thermodynamics based on the Monte-Carlo simulation (MC), for which the energetic parameters are determined by the density functional theory (DFT). The electrochemical potential profile is simulated by a simple topological model which consists only of three parameters representing the Li site energies; namely, the potential energy of the 8a site (ε8a), the difference in the site energy between the 8a and 16c sites (Δε) and the repulsion between two Li atoms situated at the adjacent 8a and 16c sites (J). Parameter physics by the MC revealed that the term Δε plays a decisive role, with a collateral effect from J, for characterizing the shape of the potential profile whereas the term ε8a determines its position along the electrochemical potential. For instance, if Δε exceeds the thermal energy at the temperature under consideration, i.e., if Δε > 3kT, the first-order phase transition takes place during which two phases coexist, resulting in a plateau region in the potential profile. On the other hand, if Δε < 3kT, the lithiation of LTO is viewed as a phenomenon above the critical point, above which the material is in a homogeneous uniphasic state. A multiple regression analysis of a set of the total energy calculated by DFT allows us to determine these energetic terms. The MC simulation with the determined parameters well reproduces the shape and position of the experimental potential profile of LTO. Since the determined value, Δε/eV ∼ 0.4, far exceeds the thermal energy at ambient temperature, the potential plateau of LTO is explained by the first-order phase transition as long as the equilibrium state is concerned.

Turning optical switching properties of Mg-Y films in electrochemical process by tailoring composition

A series of Pd capped Mg-Y binary thin films have been prepared by direct current magnetron co-sputtering and their optical switching properties combined with electrochemical potential profiles have been investigated. The maximum optical transmittance of Mg-Y/Pd thin films in the hydrogenated state, are not positively related to the Mg-Y ratio. The phase composition and grain size of the thin films have been found to greatly affect the electrochromic properties of Mg-Y thin films. As long as Mg particles is present in the thin film, the optical transmittance remains low as these metallic Mg are hard to completely hydrogenated and maintain highly reflective state in charging process. Forming intermetallic (i.e. Mg24Y5, Mg2Y and MgY) in pristine thin films is crucial and favorable to achieve high optical transmittance in the hydrogenated state. In these samples containing intermetallic only, the in situ generated Mg domains have very small size and are surrounded by the YH2 domain. The YH2 domains provide fast H diffusion path, sufficient hydrogen source and nucleating agents, which, together with the small Mg domain size, results in complete hydrogenation of the thin films.

Simulating Ion Transport with the NP+LEMC Method. Applications to Ion Channels and Nanopores.

Abstract We describe a hybrid simulation technique that uses the Nernst-Planck (NP) transport equation to compute steady-state ionic flux in a non-equilibrium system and uses the Local Equilibrium Monte Carlo (LEMC) simulation technique to establish the statistical mechanical relation between the two crucial functions present in the NP equation: the concentration and the electrochemical potential profiles (Boda, D., Gillespie, D., J. Chem. Theor. Comput., 2012 8(3), 824–829). The LEMC method is an adaptation of the Grand Canonical Monte Carlo method to a non-equilibrium situation. We apply the resulting NP+LEMC method to ionic systems, where two reservoirs of electrolytes are separated by a membrane that allows the diffusion of ions through a nanopore. The nanopore can be natural (as the calcium selective Ryanodine Receptor ion channel) or synthetic (as a rectifying bipolar nanopore). We show results for these two systems and demonstrate the effectiveness of the NP+LEMC technique.

Multiscale modeling of a rectifying bipolar nanopore: Comparing Poisson-Nernst-Planck to Monte Carlo.

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolytemodel. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge,electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.

Understanding degradation of solid oxide electrolysis cells through modeling of electrochemical potential profiles

Establishing the spatial distribution of the various chemical and electrochemical potentials in an operating SOEC is critical as several degradation mechanisms are tightly connected to them, but at the same time very challenging to achieve experimentally. Such distributions are presented here on the basis of a two dimensional bi-layer electrolyte SOC model including for both electrodes a description of activation, concentration, and conversion losses. An extensive parametric study is reported to illustrate the influence of the electrode polarization resistances, the ionic and electronic conductivities in the electrolyte, the gas composition, temperature, and pressure on the current density distribution over the cell and the oxygen activity distribution within the electrolyte. The developed model is further used to simulate long-term durability experiments during different stages of operation, thereby helping to rationalize microstructural and chemical changes observed in post-mortem analysis. Finally, measures to mitigate degradation by changing conditions of operation, material or electrode properties or overall cell geometry are suggested.

A first principles scanning tunneling potentiometry study of an opaque graphene grain boundary in the ballistic transport regime

We report on a theoretical interpretation of scanning tunneling potentiometry (STP), formulated within the Keldysh non-equilibrium Greenʼs function description of quantum transport. By treating the probe tip as an electron point source/sink, it is shown that this approach provides an intuitive bridge between existing theoretical interpretations of scanning tunneling microscopy and STP. We illustrate this through ballistic transport simulations of the potential drop across an opaque graphene grain boundary, where atomistic features are predicted that might be imaged through high resolution STP measurements. The relationship between the electrochemical potential profile measured and the electrostatic potential drop across such a nanoscale defect is also explored in this model system.

Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations.

We propose a procedure to compute the steady-state transport of charged particles based on the Nernst-Planck (NP) equation of electrodiffusion. To close the NP equation and to establish a relation between the concentration and electrochemical potential profiles, we introduce the Local Equilibrium Monte Carlo (LEMC) method. In this method, Grand Canonical Monte Carlo simulations are performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solves the NP and flux continuity equations with LEMC is shown to converge quickly. This NP+LEMC technique can be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that are difficult for other particle simulation techniques.

Evaluation of oxide layers formed during the decarburisation of grain-oriented electrical steel using a Fourier transform infrared (FTIR) technique

Electrical steels are highly specialised, magnetically soft materials, used to form the cores that carry the magnetic flux in electrical machines such as motors, generators and transformers. During the production of GO electrical steel, the strip passes through a decarburisation furnace, which promotes the formation of a thin surface oxide layer consisting of predominantly fayalite (Fe 2SiO 4) and silica (SiO 2). During a subsequent high temperature anneal, this layer reacts with magnesia (MgO) to form a forsterite ‘glass film’ layer, which applies a tensile stress to the steel. This reduces the magnetic losses of the material on which the final product is routinely graded. Due to the effect that the oxide layer has on the quality of the final material, it would be beneficial to possess a technique that can rapidly assess its composition and/or morphology. This paper details the assessment of Fourier transform infrared (FTIR) and electrochemical potential (ECP) analysis, and a technique of combining the two. FTIR analysis of the decarburisation oxide layer exhibited evidence of just fayalite, with silica only being observed on the spectra following brief acid etching. To refine the etching process, samples were removed from the acid at various intervals based on the output of the ECP technique. It was established that there was a clear link between the position reached on the ECP profile and absorption bands observed on the corresponding FTIR spectra.

Measurement of fatty amine ethoxylate surfactants using electrochemiluminescence

Direct incorporation of fatty amine ethoxylate surfactants (trade names Ethomeen T/15 and Ethomeen T/25) into an electrochemiluminescence (ECL) reaction sequence is reported. A linear relationship between ECL intensity and concentration of surfactants exists using Ru(bpy) 3 2+ (bpy: 2,2′-bipyridine) as the light emitting molecule. Detection limits of 0.7 ppm (mg/l) and 0.9 ppm have been observed for Ethomeen T/15 in aqueous buffer and seawater, respectively. Detection limits of 1.1 ppm have been achieved for Ethomeen T/25. ECL intensity versus electrochemical potential profiles show that emission occurs at potentials corresponding to the oxidation of both Ethomeen and Ru(bpy) 3 2+. The ECL emission is also pH dependent, with maximum intensities observed at pH ∼8. These results parallel those observed when tri- n-propylamine is substituted for Ethomeen T/15 or T/25 and indicate a possible mechanism for ECL generation.

Application of miniaturized electrochemical probes to nonisothermal transport studies in α-Ag 2S

Using miniaturized ionic and electronic probes we measured the electrochemical potential profiles of cations (Ag +) and electrons (e′) in α-Ag 2S under the Soret stationary state conditions. From the measured potential profiles of those charge carriers the transported entropies of cations and electrons and the reduced heat of transport of the neutral Ag, Q Ag ∗ , could be obtained as functions of temperature (220–240 °C) and nonstoichiometry, δ (0.8 × 10 −3–1.7 × 10 −3). The heat of transport, Q Ag ∗ , increases as temperature increases and decreases slightly as the nonstoichiometry, δ, increases.

Quantum kinetic analysis of mesoscopic systems: Linear response

Numerical results are presented for R xx and R xy in a rectangular Hall geometry from B = 0 − 10T. At low fields we find the usual semiclassical results while at high fields both Shubnikov-de Haas oscillations and the quantum Hall effect are evident. Electrochemical potential profiles and current flow patterns are also discussed. The analysis is based on a linear response equation derived earlier from the Keldysh formalism. This equation assumes low temperatures and point-like phase-breaking scatterers. We also discuss how this equation is generalized to high temperatures and extended scatterers.

Voltage drop in mesoscopic systems: A numerical study using a quantum kinetic equation.

In this paper, we present a numerical method for evaluating the full Wigner function throughout a device by solving a steady-state quantum kinetic equation in two dimensions, in the linear-response regime. This method has two advantages over conventional treatments of mesoscopic devices. First, dissipative processes can be included within the device, thus allowing a smooth transition from the quantum to the semiclassical regime. Second, the contacts are treated in the same manner as in semiclassical device analysis. A short phase-breaking time can be used in the contact regions so that oscillations in the electron density due to interference effects die out quickly; this is particularly useful when obtaining self-consistent solutions with the Poisson equation. Any quantity of interest, such as electron density or current density per unit energy, can be computed throughout the entire device. We will first show that under low-bias, low-temperature conditions, the diagonal elements of the Wigner function can be used to define a local electrochemical potential (\ensuremath{\mu}) that lends insight into the internal transport physics. We show that separate electrochemical potentials ${\mathrm{\ensuremath{\mu}}}_{\mathit{L}}$ and ${\mathrm{\ensuremath{\mu}}}_{\mathit{R}}$ for left- and right-moving electrons show unphysical behavior when defined in a local sense. But sensible results are obtained when these potentials are defined in an average sense over regions the size of a de Broglie wavelength. We then examine the difficulties associated with measuring \ensuremath{\mu}, with numerical examples. Next, we use the local electrochemical potential profile to clarify the nature of the spreading resistance associated with the narrowing of a current lead. Finally, we show that the electrostatic potential (\ensuremath{\varphi}) can be viewed as a convolution of \ensuremath{\mu} with a screening function and present example computations of \ensuremath{\varphi}.

The metal centers of cytochrome c oxidase: Structure and function

Abstract Considerable progress has been made in recent years on the structure of the metal centers in cytochrome c oxidase. Most of these studies have naturally focused on the ligands of the metal center as they play a prominent role in electron transfer, oxygen reduction and possibly also energy conservation. The most unambiguous structural information on the ligands has emerged from EPR/ENDOR studies, particularly when these studies are undertaken in conjunction with isotopically substituted cytochrome c oxidases prepared by incorporating selectively isotopically substituted amino acids into the protein via biosynthetic procedures. These results will be reviewed. Good progress has also been made towards elucidating the mechanism of dioxygen reduction. Preliminary evidence for a mechanism involving both a peroxo and a ferryl intermediate will be presented. The possible structural differences at the dioxygen reduction site between the resting oxidized enzyme and the pulsed enzyme will also be discussed. While impressive progress has been made toward understanding the structure of the metal centers of cytochrome oxidase and their roles in dioxygen reduction, comparatively little is known about the mechanisms by which the free energy of this reaction is conserved in the form of a transmembrane electrochemical potential gradient. It appears likely that the protons consumed in the reduction of dioxygen to water are derived from the matrix side of the mitochondrial membrane. Since the electrons used in this reaction originate from the intermembrane space of the mitochondrion, a transmembrane electrochemical potential gradient will be generated. However, the spatial dispositions of the metal centers in the membrane profile (or along the transmembrane electrochemical potential profile) are not sufficiently known to allow one to pinpoint the electron transfer step(s) which will lead to energy conservation by this mechanism. The available data which bear upon this question will be discussed briefly and new experimental approaches will be suggested. Another means of conserving the available energy is pumping protons from the mitochondrial matrix to the intermembrane space. Evidence that the enzyme is, in fact, a proton pump will be reviewed, as will some of the current models for the mechanism of this pumping. The relative merits of each of the metal centers as the site of proton pumping will be considered. The implications of electron transfer rate theory for the mechanism of proton pumping and the positioning of the metal sites in the transmembrane electrochemical potential profile will be explored. It is suggested that CuA in the most suitable candidate for the proton pump; available evidence for this hypothesis will be presented. The cytochrome oxidase-catalyzed dioxygen reduction reaction will probably not release energy in uniform increments. Thus, it might be expected that some elctron-transfer steps will not lead to proton pumping, particularly under conditions of high membrane potential. This possibility has not been adequately appreciated by investigators who attempt to assign fixed proton/electron stoichiometrics to the cytochrome oxidase reaction. This question will be discussed with reference to available information on the thermodynamics of this reaction. Simple mechanisms by which the enzyme might adapt to a changing membrane potential will be described.

Kinetic study of bicarbonate reabsorption in proximal tubule of the rat.

Kinetic study of bicarbonate reabsorption in proximal tubule of the rat.