Electrochemical Thermodynamics Research Articles

Grand Canonical Rate Theory for Electrochemical and Electrocatalytic Systems I: General Formulation and Proton-coupled Electron Transfer Reactions

Electrochemical interfaces present a serious challenge for atomistic modelling. Electrochemical thermodynamics are naturally addressed within the grand canonical ensemble (GCE) but the lack of a fixed potential rate theory impedes fundamental understanding and computation of electrochemical rate constants. Herein, a generally valid electrochemical rate theory is developed by extending equilibrium canonical rate theory to the GCE. The extension provides a rigorous framework for addressing classical reactions, nuclear tunneling and other quantum effects, non-adiabaticity etc. from a single unified theoretical framework. The rate expressions can be parametrized directly with self-consistent GCE-DFT methods. These features enable a well-defined first principles route to addressing reaction barriers and prefactors (proton-coupled) electron transfer reactions at fixed potentials. Specific rate equations are derived for adiabatic classical transition state theory and adiabatic GCE empirical valence bond (GCE-EVB) theory resulting in a Marcus-like expression within GCE. From GCE-EVB general free energy relations for electrochemical systems are derived. The GCE-EVB theory is demonstrated by predicting the PCET rates and transition state geometries for the adiabatic Au-catalyzed acidic Volmer reaction using (constrained) GCE-DFT. The work herein provides the theoretical basis and practical computational approaches to electrochemical rates with numerous applications in physical and computational electrochemistry.

Rethinking Electrochemical Science and Engineering Education

Electrochemical Science and Engineering is a particularly challenging subject to teach at the undergraduate/graduate level. The students need a substantial background in the physics of electrostatics, fields, potentials, and electrical circuits, solution chemistry, thermodynamics, mass transport and kinetics. They must also be versed in the underlying mathematics of differential and integral calculus. A lack of knowledge or retention of any of the aforementioned prerequisite subject areas can pose significant barriers to advanced learning. A minority of the students at The University of New Mexico have had some prior training in electrochemical research from internships at UNM, and National and Defense laboratories. The performance of the student interns was largely superior to the students with no direct laboratory experience. These students were generally much more engaged at achieving a better understanding of the underlying science behind their laboratory work. A major goal of the School of Engineering at UNM is to improve the comprehension and retention of key fundamental concepts and skills in the aforementioned areas for all students in the chemical engineering field and provide more opportunities for “hands on” learning and skills development. The Department of Chemical and Biological Engineering (CBE) at the University of New Mexico is engaged in a program to revolutionize engineering education by launching FACETS: Formation of Accomplished Chemical Engineers for Transforming Society. FACETS will revolutionize CBE by: (1) introducing "CIRE" design challenges in the core curriculum that are Community-, Industry-, Research-, and/or Entrepreneurship-based; (2) conducting professional development institutes that will train and mentor faculty and graduate students; workshops will be led by experts from industry and national laboratories, from the learning sciences, from engineering education and multicultural studies, for example the directors of UNM Native American Studies and Chicano/a Studies, and (3) create a digital badging system that will help students take ownership of their competencies and develop engineering identities and enable faculty to monitor and assess student outcomes and to engage in research on their teaching. We believe that this comprehensive approach towards modular learning and digital validation will improve our teaching of Electrochemistry and Electrochemical Engineering and heighten our student’s understanding of the subject material. We have prepared core concept modules with supporting experimentation in the subject areas of: Types of Electrochemical Cells, Solution Theory, Electrostatics, Electrolytes, Ionic Transport, Charged Interfaces, Electrochemical Thermodynamics, Batteries, Fuel Cells, Electrolysis, Electrodeposition, Electroanalysis and Environmental Electrochemistry.

Modeling the Effect of the Operating Temperature on the Performance of a Zinc/Bromine Flow Battery

The zinc/bromine (Zn/Br2) flow battery is an attractive rechargeable system for energy storage because of its inherent chemical simplicity, high degree of electrochemical reversibility at the electrodes, good energy density, and abundant low-cost materials. Because the performance of a Zn/Br2 flow battery depends strongly on the operating temperature, it is important to develop a mathematical model to predict the performance of the battery as a function of the operating temperature in order to estimate such quantities as current efficiency and conversion per pass. This information can be used to design both of bench and production scale cells and to select the operating conditions for optimum performance. In this work, a method of modeling the dependence of the charge and discharge curves of a Zn/Br2 flow battery on its operating temperature is presented. This work adopts a simple modeling approach by considering Ohm’s law and charge conservation on the electrodes based on the simplified polarization characteristics of the electrodes. To accommodate the temperature dependence, the key modeling parameters are expressed as the functions of temperature based on the well-known principles of the Arrhenius equation of chemical kinetics and the Nernst equation of electrochemical thermodynamics. The model is validated by comparing the modeling results with the experimental measurements.

Preparation of Nano‐bismuth with Different Particle Sizes and the Size Dependent Electrochemical Thermodynamics

AbstractNano‐bismuth has excellent electrochemical properties. However, it is still unclear how the particle size of nano‐bismuth influences its electrochemical thermodynamic properties. In this paper, spherical bismuth nanoparticles with different particle sizes were prepared by solvothermal method; the electrode potentials, the temperature coefficients of the electrode potentials and the thermodynamic functions of reaction for nano‐bismuth electrodes with different particle sizes at different temperatures were determined; and the effects of particle size on the electrode potential, the temperature coefficient and the thermodynamic functions were discussed. The experimental results show that particle size of bismuth nanoparticles has a significant influences on the electrochemical thermodynamic properties. The standard electrode potential of the nano‐bismuth electrode with a diameter of 39.9 nm was 0.009 V lower than that of the ordinary standard electrode (0.308 V); the temperature coefficient of the electrode potential with a diameter of 39.9 nm was nearly double that of 85.9 nm. With the particle sizes decrease, the standard molar Gibbs energy of reaction, the standard molar enthalpy of reaction, the standard molar entropy of reaction, the molar reversible reaction heat and the temperature coefficient increase; and these quantities are linearly related to the reciprocal of the particle diameter.

Microvia Superfilling Process Control

Abstract Electrochemical thermodynamics is the foundation of the microvia fill process, whose model represents the mass conservation of species (copper ions and surfactants) in the condition of moving boundary. The shape of via changes due to the deposed metallic copper, whose growth depends on the blocking effect of surfactants, which in turn depends on the boundary curvature. The via filling process is controlled through the boundary by adjusting the electric current flowing through the bath system. Maximizing the current raises the via fill process speed but ends up in depletion of the copper ions at the bottom of via causing an incomplete via fill (poorly fabricated board). In this paper the problem is solved by adjusting the concentration of copper ions to a reference value near the panel surface of the plated board. The stabilizing control is proposed based on the developed via fill model. By applying the control, the via fill process can be sped up by ca. 20% and the via dimple minimized 5% without risking product output quality.

The microstructure and electrochemical properties of Mn-doped La-Y-Ni-based metal-hydride electrode materials

The structural characteristics and electrochemical performances of superlattice La5.42Y18.50Ni76.08-xMnx (x = 0, 2, 4, and 6) metal-hydride electrodes were investigated. La5.42Y18.50Ni76.08 alloy is composed of LaY2Ni9, Y2Ni7, and La2Ni7 phases, while the amount of AB3-type phase increases due to the increasing substitution amount of Ni by Mn. The mechanisms on the related electrochemical thermodynamics and kinetics were investigated systematically. Compared with La5.42Y18.50Ni76.08 alloy, the maximum discharge capacity of La5.42Y18.50Ni70.08Mn6 alloy increased from 275.2 mAh g−1 to 379.6 mAh g−1 and the discharge capacity after 30 cycles increased from 155.0 mAh g−1 to 281.1 mAh g−1, which contribute to the increase of the amount of AB3-type phase as well as the ameliorated structural stability through the substitution of Mn for Ni.

Size-dependent phase morphologies in LiFePO4 battery particles

Lithium iron phosphate (LiFePO4) is the prototypical two-phase battery material whose complex patterns of lithium ion intercalation provide a testing ground for theories of electrochemical thermodynamics. Using a depth-averaged (a-b plane) phase-field model of coherent phase separation driven by Faradaic reactions, we reconcile conflicting experimental observations of diamond-like phase patterns in micron-sized platelets with observations of surface-controlled patterns in nanoparticles. Elastic analysis predicts this morphological transition for particles whose a-axis dimension exceeds twice the bulk elastic stripe period. We also simulate a rich variety of non-equilibrium patterns, influenced by size-dependent spinodal points and electro-autocatalytic control of thermodynamic stability.

Influence of particle size on electrochemical thermodynamics of Nano-Au electrodes: Mechanism, factors, range and degree

There is a significant effect of particle size on electrochemical thermodynamics of nano-metal electrodes, it is still unclear, however, the mechanism, factors, range and degree of the effect. Herein, in theory, we derived the relations of the electrochemical thermodynamic quantities and the size of nanoparticles which constituted the nano-metal electrodes, discussed the mechanism and the influencing factors. Experimentally, nano-Au with different radii (0.9–37.4 nm) made as nano electrodes to research the size dependence of electrochemical thermodynamic quantities. Combining the results of theory and experiments, discussed the influencing regularities, range and degree. The regularities obtained from these experiments are consistent with the theoretical relations. The research results show that particle size has pronounced effect on electrochemical thermodynamic quantities. Both the Eo and the lnKo decrease with the particle size decreasing, while other electrochemical thermodynamic quantities increase. These effects should be attributed to partial molar surface area, surface tension and its temperature coefficient. Thereinto, partial molar surface area and surface tension are the major influencing factors for Eo, Ko, ΔrGm and ΔrHm, partial molar surface area and temperature coefficient of surface tension are for (∂E/∂T)p, ΔrSm and Qr,m. For Au nanoparticles, as the radius exceeds 10 nm, the major factor is partial molar surface area, there exist linear relationships between the electrochemical thermodynamic quantities and reciprocal of radius. However, as the radius is less than 10 nm, the effects of surface tension and its temperature coefficient gradually hold the main positon with the radii decreasing, respectively; as well as there are no linear relationships. Our research offer significant fundamental insight on the size-dependent electrochemical thermodynamics, and can greatly impact future exploration and application of nano-metal electrodes.

Development of Zinc-Air Batteries with Advanced Aqueous Electrolytes: A Model-Based Approach

Zinc-air batteries (ZABs) are promising candidates for next-generation electrochemical energy storage. They offer a high theoretical specific energy (1086 Wh∙kg-1) and energy density (6093 Wh∙l-1), are based on cheap and non-hazardous materials, and have superior operational safety characteristics. In fact, primary alkaline ZABs already have a long history in low-current industrial applications like hearing aids (1). But over time, the alkaline electrolyte reacts with CO2 to form carbonates, which reduces the ionic conductivity of the electrolyte and degrades the performance of the battery (2). Furthermore, metallic zinc can irreversibly passivate when discharged and may build dendrites when charged. We have developed continuum models based on principles of electrochemical thermodynamics and kinetics to simulate the performance of metal-air batteries (3, 4). Our models for ZABs introduce a new method for considering the thermodynamic stability of aqueous species in continuum simulations. By combining this approach with the basic aspects of electrochemical cell modeling (like mass transport in concentrated electrolytes, multi-phase flow in porous media, and concentration-dependent electrochemical reaction kinetics), we are able to investigate transient and spatially resolved changes in cell potential, electrolyte concentrations, and multi-phase volume fractions. Our investigation specifically considers ZABs with two different types of aqueous electrolytes: alkaline KOH and neutral ZnCl2-NH4Cl. For ZABs with alkaline KOH electrolytes, our simulations show that inhomogeneous Zn dissolution and ZnO precipitation cause the zinc electrode to change shape when cycled and lead to the local depletion of KOH, which induces type II (irreversible) ZnO passivation. Furthermore, the dissolution of CO2 in the electrolyte leads to a steady drop in cell potential over months of operation (2). In the neutral ZnCl2-NH4Cl electrolyte, the low OH- concentration limits the formation of carbonates, potentially extending the lifetime of the battery (5-7). However, in the near-neutral pH regime the stability of the aqueous zinc-ligand complexes shifts significantly with even small changes in concentration. This affects the ionic conductivity of the electrolyte, the composition of the final discharge product, and the pH stability. Our simulations show that under conditions reported in the literature, the pH may become strongly acidic, which affects the performance and stability of the bifunctional air catalyst (6-8). We investigate how the composition of the electrolyte and the architecture of the cell can be adjusted to maintain a stable, neutral pH over cycling. In this contribution, we highlight the physical and electrochemical processes which govern ZAB performance, and discuss how these processes can be managed to develop a rechargeable battery. This work is supported by the European Union Horizon 2020 project ZAS! (Zinc Air Secondary Batteries Based on Innovative Nanotechnology for Efficient Energy Storage).

The Size-Dependence of Electrochemical Thermodynamics of Metal Nanoparticles Electrodes in Theory and Experiment

Metal nanoparticles electrodes present great difference in electrochemical thermodynamics compared with corresponding bulk electrodes, which depends on the size of nanoparticles that construct the electrodes. However, it remains unclear about the influences of particle size on electrochemical thermodynamics of the electrodes. Herein, the size-dependence of electrochemical thermodynamic functions of metal nanoparticles electrodes was deduced theoretically. Experimentally, taking copper nanoparticles electrode as an example, the standard electrode potentials, the temperature coefficients, and the thermodynamic functions of electrode reaction were obtained by determining the electrode potentials of the electrodes constructed by copper nanoparticles with different sizes at different temperatures. Both the theoretical and the experimental results indicate that with the particle size of metal nanoparticles decreasing, the standard electrode potential and surface tension decreases, while the temperature coefficient, the molar reaction Gibbs energy, enthalpy and entropy increase. Moreover, all these physical quantities are linearly related with the reciprocal of particle radius when the radius exceeds 10 nm. Meanwhile, we also found that the influence regularities of particle size on electrochemical thermodynamic functions of metal nanoparticles electrodes are quite opposite to those of oxide nanoparticles electrodes, which is attributed to the nanoparticles being reactant or product in an electrode reaction.

New Foundations of Newman’s Theory for Solid Electrolytes: Thermodynamics and Transient Balances

Newman’s developments of electrochemical thermodynamics and transport phenomena are extended to account for changes in elastic or plastic deformation stress, as well as for varying pressure, temperature, and composition. The material, momentum, energy, and entropy balances from concentrated-solution transport theory are modified to include extended underpinning thermodynamic relationships. Various colligative properties describing electrolytic materials at equilibrium are identified through analysis of the Gibbs function, which also gives rise to state equations for volume, deformation strain, and entropy. A dynamical analysis on the continuum scale produces multiphysical versions of the equation of motion and the heat equation. The discussion concludes with a statement of the second law from the perspective of irreversible thermodynamics, providing a basis for the future development of transport constitutive laws for ion conductors with elastic, as well as viscous, character.

Analysis of Capacity Fade from Entropic Heat Coefficient of Li[NixCoyMnz]O2/Graphite Lithium Ion Battery

The entropic heat coefficient (i.e., dU/dT) of Li[NixCoyMnz]O2/graphite before and after cycle was determined using the electrochemical thermodynamics measurements (ETMs) tool. DU/dT could be attributed to the individual electrodes for this notable battery and associates with the Li-intercalated state. Lithium intercalation number in negative and positive electrode was calculated and compared for the battery before and after cycle, respectively. Results show that the trend of dU/dT with Li-intercalated state before and after cycle is basically consistent except for the initial and maximum state. DU/dT has the typical characteristics of stage structures of graphite. In particular, these changes is independent of the battery aging. Negative electrode has greater Li-intercalated depth loss than that of positive electrode after cycle, thus negative electrode is the dominant degradation factor of the battery.

Links between electrochemical thermodynamics and kinetics

Redox systems are considered when proceeding (a) in an electrochemical cell (heterogeneous reactions), and (b) in a single compartment (homogeneous reactions), also including the case of a solution in contact with solid phases. Special emphasis is given to the electrochemical systems. Starting from equilibrium states in the individual half-cells, the cell as a whole is (1) made to work spontaneously (batteries, fuel cells) and (2) forced to induce non-spontaneous transformations (electrolysis). Kinetics needs to be considered in both cases: phenomenological aspects and rigorous mathematic tools are intended to concur to draw the picture. Supplementary material is given in order to help visualise what the equations given express.

Heyrovsky – the inventor of polarography

The second Nobel Prize for electrochemistry was won by Heyrovsky in 1959 for an invention rather than a discovery (thefirstwaswonbyNernst in 1921 for electrochemical thermodynamics). In the previous decade, in the 1940s, chemical analysis was in relative infancy andmethods were needed for the measurement of elements at ppm levels and below, ions in solution, and distinctionmade between ions of differing valency states. This was important in a number of areas includingmedicinal chemistry, environmental and legal fields, andmetal finishing. Heyrovsky recognised this need but also the unique characteristics of mercury as an electrode metal. Mercury was noble and therefore could be tarnishfree. It was also liquid, thereby able to besmoothandflatanddissolveatoms ormoleculesdischargedon its surface into an infinitely dilute solution. This was the basis for a new analytical technique.

Sustainable generation of hydrogen using chemicals with regional oversupply – Feasibility of the electrolysis in acido-alkaline reactor

An integral part of the concept of sustainable development and a serious challenge to be addressed is the demanding and costly disposal of the hazardous waste chemicals and/or overproduced chemicals remaining after various production cycles in the chemical industry. For example, the recently reported overproduction of sulfuric acid in China can affect base metal production rates. In this context the consideration of new technologies that can avoid environmental damage or even introduce an economically feasible framework for the utilization of hazardous waste chemicals becomes appealing.In this work, adopting the fundamental aspects of electrochemical thermodynamics, for the first time the feasibility of efficient hydrogen production in an acido-alkaline electrochemical cell is analyzed. Generation of hydrogen, based on the utilization of low cost (“cost-free”) acids/bases whose world turnover is measured in tens and hundreds of megatons, and importantly, who suffer from regional overproduction, is proposed. The cell with two electrolytes separated by the cation transparent membrane is proven to be operational at significantly lower voltage than conventional water electrolysis cell, as long as cathodic reaction proceeds in acidic while anodic reaction proceeds in alkaline media. Significant electric energy saving, in comparison to conventional water electrolysis can be of high impact taking into consideration the general tendency of growing electricity price. While the economic justification of this particular concept has to be carefully examined considering the local conditions and technical implementation, acido-alkaline electrochemical cells are recognized as feasible and can have a distinct role for sustainable energy conversion and storage and waste utilization.

Effect of Particle Size on Electrode Potential and Thermodynamics of Nanoparticles Electrode in Theory and Experiment

The particle size of electrode materials has a significant influence on the standard electrode potential and the thermodynamic properties of electrode reactions. In this paper, the size-dependent electrochemical thermodynamics has been theoretically investigated and successfully deduced electrochemical thermodynamics equations for nanoparticles electrode. At the same time, the electrode potential and thermodynamical properties of Ag2O/Ag nanoparticles electrode constructed by the solid and spherical Ag2O nanoparticles with different sizes further testified that the particle size of nanoparticles has a significant effect on electrochemical thermodynamics. The results show that the electrode potential depends on that of the smallest nanoparticle in a nanoparticles electrode which consisted of different particle sizes of nano-Ag2O. When the size of Ag2O nanoparticles reduces, the standard electrode potentials and the equilibrium constants of the corresponding electrode reactions increase, and the temperature coefficient, the mole Gibbs energy change, the mole enthalpy change and the mole entropy change decrease. Moreover, these physical quantities are all linearly related with the reciprocal of average particle size (r > 10nm). The experimental regularities coincide with the theoretical equations.

Glucose contents in anaerobic ethanol stillage digestion manipulate thermodynamic driving force in between hydrogenophilic and acetoclastic methanogens

In disciplines related energy conversion, thermodynamics is the cornerstone for interpretation of process performance. It can provide the basis for the estimation of maximum convertible energy and spontaneity in novel, sustainable, anaerobic digestion processes. Here electrochemical thermodynamics is applied to the interpretation of glucose decomposition in anaerobic digestion of ethanol distillation residues (stillage) containing residual ethanol and ammonia. Under saturated conditions for biochemical mediators such as NAD+/NADH the microbial oxidations and reductions between hydrolytic fermentative bacteria, syntrophic acetogens and methanogens will always be close to or at the electrochemical equilibrium state through the mediator. The product distribution arising from the up-take of glucose is found to be sensitive to the electrochemical potential which is a measure of the thermodynamic driving force, ΔG and related to both ΔH and ΔS via the standard relationships. Glucose decomposition is strongly favorable and only weakly dependent on electrochemical potential in the range investigated. However the system showed overall ΔH<0, indicating the potential for significant exotherm but ΔS was also found to be less than zero, indicating that the forward reaction was not spontaneous. This work also finds that as the mole fraction of glucose, x, is increased up to x=0.001, the thermodynamic driving force for hydrogenophilic methanogenesis is dramatically decreased whilst that for acetoclastic methanogenesis is increased, and the thermodynamic “inhibition” of beta oxidation of volatile fatty acids is reduced. This may be interpreted as the diversion of the metabolic pathway from the conventional route ‘glucose–acetate–CH4/CO2’ towards glucose–butrate–proprionate–acetate–CH4/CO2.

Volt Equivalent diagrams as a means of displaying the electrochemical thermodynamics of the sulfur–water system

In this paper, we describe the use of Volt-Equivalent Diagrams (VEDs) to display the electrochemical thermodynamics of one of the most complicated chemical systems in nature; the S–H2O system, as it relates to the use of copper for the isolation of high level nuclear waste (HLNW) in granitic repositories in Sweden. The complexity stems from this element having oxidation states that vary from −2 to +8 including a multitude of fractional oxidation states. The volt equivalent describes the reactivity of a species and foretells the various chemical transformations that may occur between different sulfur-containing species in the system.

Phase transition in porous electrodes. III. For the case of a two component electrolyte

The electrochemical thermodynamics of electrolytes in porous electrodes is qualitatively different from that in the bulk with planar electrodes when the pore size is comparable to the size of the electrolyte ions. In this paper, we discuss the thermodynamics of a two component electrolyte in a porous electrode by using Monte Carlo simulation. We show that electrolyte ions are selectively adsorbed in porous electrodes and the relative concentration of the two components significantly changes as a function of the applied voltage and the pore size. This selectivity is observed not only for the counterions but also for the coions.

Phase transition in porous electrodes. II. Effect of asymmetry in the ion size

The electrochemical thermodynamics of electrolytes in porous electrodes is qualitatively different from that in the bulk with planar electrodes when the pore size is comparable to the size of the electrolyte ions. In this study, the effect of the ion size asymmetry on the thermodynamics in porous electrodes was studied by using Monte Carlo simulation. We used the electrolyte ions for which the size of the cations and that of anions is different. Due to the asymmetry in the ion size, the ionic structure and the way the surface charge is distributed on the electrode surfaces were found to be qualitatively different in the cathode and in the anode. In particular, for some ranges of applied voltage, the distribution of the surface charge induced on the electrode planes shows inhomogeneity, which is not intrinsic to the structure of the porous electrodes. The transition from the homogeneous to the inhomogeneous distribution of surface charge on changing the voltage is a second order phase transition.