Current-potential Relationship Research Articles

Revisiting the Butler-Volmer Electrode Kinetics: Separating the Anodic and Cathodic Current Components of a Quasi-Reversible Electrode Reaction in Staircase Voltammetry

A simple mathematical strategy is proposed to estimate anodic and cathodic current components in voltammetry by combining the basic mathematical model of a quasi-reversible electrode reaction at a conventional planar electrode with the Butler-Volmer electrode kinetics with a goal to simplify and facilitate the measurement of electrode kinetics. In spite of the fact that the separate anodic and cathodic current components are experimentally inaccessible parameters, it is demonstrated for the first time that they can be reliably estimated from the net (total) current over the whole potential interval of a common voltammetry, requiring only the current–potential relationship, without prior knowledge of any electrode kinetic parameter (i.e., the standard rate constant and the electron transfer coefficient). The mathematical procedure requires semi-integration of the current and previous knowledge of the formal potential of the studied redox couple. The theory predicts that very fast electrode processes, with an apparent electrochemical reversible behavior, are associated with anodic and cathodic current components the intensity of which is proportional to the standard rate constant. Thus, the proposed simple methodology provides a new perspective in analyzing voltammetric data and expands the accessible kinetic interval towards very fast electron transfer processes by means of simple voltammetry at macroscopic planar electrodes. The proposed methodology is experimentally illustrated with the electrode reaction of hexacyanoferrate(II) ion oxidation at platinum electrode.

Morphology and valence state evolution of Cu: Unraveling the impact on nitric oxide electroreduction

Ammonia (NH3) serves as a critical component in the fertilizer industry and fume gas denitrification. However, the conventional NH3 production process, namely the Haber-Bosch process, leads to considerable energy consumption and waste gas emissions. To address this, electrocatalytic nitric oxide reduction reaction (NORR) has emerged as a promising strategy to bridge NH3 consumption to NH3 production, harnessing renewable electricity for a sustainable future. Copper (Cu) stands out as a prominent electrocatalyst for NO reduction, given its exceptional NH3 yield and selectivity. However, a crucial aspect that remains insufficiently explored is the effects of morphology and valence states of Cu on the NORR performance. In this investigation, we synthesized CuO nanowires (CuO-NF) and Cu nanocubes (Cu-NF) as cathodes through an in situ growth method. Remarkably, CuO-NF exhibited an impressive NH3 yield of 0.50 ± 0.02 mg cm−2 h−1 at −0.6 V vs. reversible hydrogen electrode (RHE) with faradaic efficiency of 29.68% ± 1.35%, surpassing that of Cu-NF (0.17 ± 0.01 mg cm−2 h−1, 16.18% ± 1.40%). Throughout the electroreduction process, secondary cubes were generated on the CuO-NF surface, preserving their nanosheet cluster morphology, sustained by an abundant supply of subsurface oxygen (s-O) even after an extended duration of 10 h, until s-O depletion ensued. Conversely, Cu-NF exhibited inadequate s-O content, leading to rapid crystal collapse within the same timeframe. The distinctive current–potential relationship, akin to a volcano-type curve, was attributed to distinct NO hydrogenation mechanisms. Further Tafel analysis revealed the exchange current density (i0) and standard heterogeneous rate constant (k0) for CuO-NF, yielding 3.44 × 10−6 A cm−2 and 3.77 × 10−6 cm−2 s−1 when NORR was driven by overpotentials. These findings revealed the potential of CuO-NF for NO reduction and provided insights into the intricate interplay between crystal morphology, valence states, and electrochemical performance.

Determination of the electron temperature in a supersonic jet of a gas-discharge source from current measurements by an insulated probe system

The aim of this work is to substantiate the possibility of using the classical procedure for determining the electron temperature for diagnosing a supersonic jet of a collisionless plasma of a diatomic gas using the current-voltage characteristic of an insulated probe system. The probe system consists of a cylindrical probe and a reference electrode composed of several cylinders, all placed transversely in the plasma flow. The ratio of the current-collecting surface area of the reference electrode to the area of the probe is arbitrary and can be significantly less than required by the theory of a single probe. Based on a previously constructed mathematical model of current collection, which includes the calculation of the equilibrium potential of the reference electrode as a function of the probe bias voltage, a procedure is developed for determining the electron temperature by measuring the probe currents in a jet of a gas-discharge source of a laboratory dissociated plasma. An approximation of the floating potential of the insulated probe system in a strongly nonequilibrium plasma of a gas-discharge source jet is found, which allows one to determine the boundaries of the transition region of the current-voltage characteristic using a priori information on the plasma parameters. A formula is obtained for extrapolating the ion probe current vs. bias potential relationship into the transition region of the current-voltage characteristic. Within the framework of the adopted mathematical model of charged plasma particle collection, a numerical analysis of the method error of the electron temperature determination procedure is performed. Quantitative characteristics of the effect of the insulated probe system geometry on the method error are obtained. A numerical simulation of the effect of the probe current measurement errors showed that, within the framework of the adopted model, the accuracy of determining the electron temperature using the insulated probe system is comparable with the accuracy of measurements with a single cylindrical probe. The results obtained may be used in the diagnostics of a laboratory plasma of a gas-discharge source.

Simulation of the Electrochemical Response of Cobalt Hydroxide Electrodes for Energy Storage

Cyclic Voltammetry is an analysis method for characterizing the behaviors of electrochemically active materials by measuring current through defined potential sweeps. The current–potential relationship depends on key variables such concentration of electrolyte, electron-transfer rate, and the distance and time of species in relation to the electroactive surface of the material. A MATLAB® simulation was developed on a diffusion and kinetics basis, simulating the equations of Fick’s second law and Butler–Volmer, respectively, towards understanding the energy-storage mechanisms of cobalt hydroxide electrodes. The simulation was compared to a real cobalt hydroxide system, showing an accurate approximation to the experimentally obtained response and deviations possibly related to other physical/chemical processes influencing the involved species.

New radiolysis-driven matrix dissolution operational model based on stationary UO2 voltametric experiments

In the framework of research on direct deep disposal of spent nuclear fuel, a new α radiolysis-driven matrix dissolution model is proposed. This model is based on an experimental stationary voltametric curve established using a UO2 rotating disk electrode in a neutral pH non-complexing solution under reducing conditions. Kinetic and chemical speciation calculations give access to the equilibrium redox potential of a simulated Callovo-Oxfordian pore water solution containing α-radiolysis products, which is used in the experimentally obtained current-potential relationship to estimate the oxidative dissolution rate. Comparison of model results with literature data show good agreement with previously established α−activity threshold values.

Cross-platform dynamic goods recommendation system based on reinforcement learning and social networks

Aiming at the problems of cold start, gray sheep and sparsity of the traditional collaborative filtering recommendation system, this paper proposes a cross-platform dynamic goods recommendation system based on reinforcement learning and edge computing. First of all, this system models the current friendship relationship networks and potential friendship relationship networks, it also constructs two layers preference prediction models. Then, we consider the frequent change characteristic of social networks and shopping platforms, we design a dynamic reinforcement learning method and edge computing to learn the minimized entropy loss error. Finally, we finish the validation experiments based on the real datasets, the results show the proposed system realizes better link prediction accuracy, and using our proposed system can obtain an obvious increase in the accuracy compared to the existing of collaborative filtering recommendation systems.

Finite Element Modeling of SS316 Pit Stability, with Respect to Geometry Parameters, Under Atmospheric Conditions

Additive manufacturing (AM) of metals have become a promising fabrication method, due to the decreased waste from conventional manufacturing and the ability to create complex geometries [1]. However, the surface roughness of powder based additively manufactured structures appears porous, with complicated geometries that are a concern for localized corrosion. Knowing which defects are more susceptible than others, from a geometry perspective, will greatly aid mitigation strategies either in terms of AM process parameters or through post-build surface treatments. This study will explore how surface defects created on AM stainless steel parts impact local corrosion stability under atmospheric conditions.The stochastic nature of the pits initiating and repassivating, combined with the complexities of the AM defects and those of thin water layers, make for a very large parameter space to explore. In effect, the most important aspect of localized corrosion under these conditions is the determination of whether a pit will repassivate or grow, and if it grows, how large can it become. Many different parameters affect the pit stability, including the geometry of the cathode size, the anode (pit) size, details of the environment (solution composition, electrochemical potential), and the water layer thickness.It is known that the potential at a pit mouth must be more positive than in order to grow stably [2]. The repassivation potential therefore serves as one way to measure pit stability, while other parameters in the system are held constant. An additional pit stability criteria is the pit stability product, (i ⋅ x), from Galvele’s seminal work [3]. The maximum pit model [4] uses these criteria, parameters that define the thin electrolyte, and the current-potential relationship for the cathodic reaction(s) on the external surface to define the largest hemispherical pit for which the Conservation of Charge is met.Finite element modeling is used here to determine what combinations of geometric parameters associated with surface defects due to AM processing of SS316 lead to the stabilization of a pit or not. Pits of different dimensions, including hemispherical, rectangle, and disk shaped, are assessed as isolated pits. The model’s geometric complexity is then increased to better represent an additively manufactured surface with many pits of different shapes and sizes based on cross-sectional data from actual surfaces. A range of atmospheric conditions are investigated, including a range of relative humidity and salt loading density. The boundary conditions within the model represent the solution kinetics of both scenarios. The water layer and loading densities were varied, according to the equation proposed by Chen et al. [5].SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525. SAND2020-5408 A.[1] B. AlMangour and J. M. Yang, “Improving the surface quality and mechanical properties by shot-peening of 17-4 stainless steel fabricated by additive manufacturing,” Mater. Des., vol. 110, pp. 914–924, 2016.[2] J. Srinivasan, M. J. McGrath, and R. G. Kelly, “A High-Throughput Artificial Pit Technique to Measure Kinetic Parameters for Pitting Stability,” J. Electrochem. Soc., vol. 162, no. 14, pp. C725–C731, 2015.[3] J. R. Galvele, “Transport Processes and the Mechanism of Pitting of Metals,” J. Electrochem. Soc., vol. 123, no. 4, p. 464, 1976.[4] R. M. Katona, J. Carpenter, E. J. Schindelholz, and R. G. Kelly, “Prediction of Maximum Pit Sizes in Elevated Chloride Concentrations and Temperatures,” J. Electrochem. Soc., vol. 166, no. 11, pp. C3364–C3375, 2019.[5] Z. Y. Chen, F. Cui, and R. G. Kelly, “Calculations of the Cathodic Current Delivery Capacity and Stability of Crevice Corrosion under Atmospheric Environments,” J. Electrochem. Soc., pp. 360–368, 2008.

A New Method for Corrosion Current Measurement: the Dual-Electrochemical Cell (DEC)

This paper presents the “dual electrochemical cell” (DEC) method, a new technique that allows monitoring of corrosion current () in real time with a corrosion potential that may change with time. In this method, the of a metal corroding in a solution containing the oxidant of interest is measured in the 1st cell. This potential is then continuously applied in real time to a second cell using the same metal electrode in the same solution but free of the oxidant, and the current of the 2nd cell, which represents the of the 1st cell, is monitored. This setup allows direct measurement of without having to polarize the corroding electrode away from The advantages of DEC over conventional methods are that it does not require the corroding system to be at steady state, and avoids any ambiguities associated with the extrapolation of the measured current-potential relationship to extract The values obtained using the DEC method were compared with those obtained using conventional polarization techniques, using dissolved metal concentrations and surface analysis observations, and the results showed that the DEC method provides the most accurate measurement of

Analytical solutions of an isothermal two-dimensional model of a cathode flow channel in a proton exchange membrane fuel cell

Two key assumptions are usually made while deriving analytical solutions of coupled kinetics and transport equations in a single channel on the cathode plate of a proton exchange membrane fuel cell (PEMFC). These are: plug flow and uniform oxygen concentration along the depth of the channel. However these assumptions are not always valid under typical operating conditions of a PEMFC, and particularly so at high current density. In this article we relax these two assumptions and present approximate analytical solutions of the governing equations using the methodology of separation of variables followed by power series solution. Spatial profiles of oxygen concentration and current density were derived, which led to the final derivation of a comprehensive current-potential relationship (polarization curve) in the reaction-controlled regime of an operational PEMFC. We compare polarization curves predicted by the present model with predictions of the earlier analytical model and also with a complete 3D-simulation of the same flow geometry and operation conditions. The local profiles of oxygen concentration and the polarization curve predicted by the present model compare far better with the 3D simulations than the earlier analytical model. While this comparison highlights the importance of the effects of finite oxygen diffusion rate and velocity profile in the channel on the polarization curves, it also points to other important factors that affect the current-potential relation.

Kinetic Implications of the Presence of Intermolecular Interactions in the Response of Binary Self-Assembled Electroactive Monolayers.

Quantitative analysis of the influence of intermolecular interactions on the response of electroactive binary monolayers, incorporating the presence of electroinactive coadsorbed species and Marcus–Hush kinetic formalism, has been deduced as an extension of previous models. An expression for the current–potential relationship in terms of two global phenomenological interaction parameters and the apparent charge-transfer rate constant and formal potential has been obtained and applied to multipotential chronoamperometry for the analysis of intermolecular interaction effects on the kinetics of the charge transfer. Experimental verification of the theoretical framework has been performed with binary ferrocenylundecanethiol/decanethiol monolayers on gold and platinum substrates for different coverage degrees of the redox probe. The increase of the ferrocene coverage gives rise to a slowing down of the charge-transfer process through a decrease of the apparent rate constant above a 90% for gold and platinum electrodes when the surface coverage increases from 1–2 to 15–30%. Significant differences in the magnitude of intermolecular interactions and the symmetry degree of the charge-transfer process are observed between gold and platinum electrodes. Moreover, for high surface coverages of ferrocene, two different domains appear, from which it is possible to carry out a kinetic discrimination of the two responses. Values of the interaction and kinetic parameters have been obtained for the different monolayers under study, and the limit of applicability of this treatment is discussed.

Assessing the scalability of low conductivity substrates for photo-electrodes via modelling of resistive losses.

When scaling up photo-electrochemical processes to larger areas than conventionally studied in the laboratory, substrate performance must be taken into consideration and in this work, a methodology to assess this via an uncomplicated 2 dimensional model is outlined. It highlights that for F-doped SnO2 (FTO), which is ubiquitously used for metal oxide photoanodes, substrate performance becomes significant for moderately sized electrodes (5 cm) under no solar concentration for state of the art Fe2O3 thin films. It is demonstrated that when the process is intensified via solar concentration, current losses become quickly limiting. Methodologies to reduce the impact of substrate ohmic losses are discussed and a new strategy is proposed. Due to the nature of the photo-electrode current-potential relationship, operation at a higher potential where the photo-current saturates (before the dark current is observed) will lead to a minimum in current loss due to substrate performance. Crucially, this work outlines an additional challenge in scaling up photo-electrodes based on low conductivity substrates, and establishes that such challenges are not insurmountable.

Validation of Mixed Potential Theory Using Formic Acid and Ferric Ion As a Redox Couple

The present work explores the possibility of validating mixed potential theory using the redox reaction between formic acid with ferric sulphate (HCOOH + 2Fe3+ ⇋ CO2 + 2H+ + 2Fe2+) on platinum catalyst. It is hypothesized that the catalytic oxidation of formic acid by ferric sulphate can be viewed as two distinct electrochemical reactions proceeding simultaneously on the electrode, one being the electrochemical oxidation of formic acid and the other, electrochemical reduction of ferric ions. Moreover, for electroneutrality, the rate of oxidation of formic acid must match exactly with that of the reduction of ferric sulphate. The manifestation of this phenomenon is the unique electrode potential generally referred as the mixed potential. The value of the mixed potential can be determined easily by measuring the open circuit potential (OCP) of the electrode which is immersed in a solution containing both formic acid and ferric sulphate. Further, in the present work an attempt has been made to investigate the correlation between catalytic chemical reaction and the individual electrochemical halves in terms of conversion of ferric ions.The catalytic oxidation of formic acid by ferric sulphate was studied at rotating disk electrode on which platinum black catalyst was drop casted. The reaction was studied through open circuit potential (OCP) measurement (where no external electromotive force is applied) at different rotational rates of the electrode. The number of moles of ferric ions was determined spectroscopically over a period of five hours. It was observed that OCP increased with time due to decrease in the concentration of ferric ions. These experiments have been designated as chemical experiments. Simultaneously, the two electrochemical halves of the above redox reaction were studied independently at rotating disk electrode. Formic acid oxidation studies were performed through chronoamperometry and that of ferric ion reduction was studied via cyclic voltammetry technique. These sets of experiment are refereed as electrochemical experiments. From the electrochemical data obtained for reduction of ferric ions, key kinetic and transport parameter were determined and these were used further to model the current-voltage behavior for reduction of ferric ions to ferrous ions over time, assuming a first order reaction. Using this model in conjunction with OCP time data it was possible to predict the number of moles of ferric ion consumed as function of time during the OCP experiment. These predictions were compared with the number of moles of ferric ions actually consumed during OCP experiment. These comparisons were made at different rotation rates of the electrode and very good agreement between the measured and predicted values was observed at all rates of rotation. This validates the hypothesis that the kinetics of a catalytic chemical reaction can be obtained from the individual current potential relationship for the two electrochemical reactions.The present work suggests that catalytic chemical reactions follow an electron transfer mechanism. This approach would enable prediction of chemical kinetics for primarily catalytic reactions through few electrochemical parameters. Further, it opens up possibility of estimation of key electrochemical parameters for several catalytic systems and then the kinetics can be predicted by selecting the required parameters for corresponding oxidation as well as reduction reaction. Figure 1

Theory of unsupported, steady-state, Nernstian, three-ion, twin-electrode, voltammetry: the special case of dual concentration polarization

Steady-state voltammetry is easily attained in narrow cells. Here we develop an exact mathematical description of one of the simplest instances, in which a redox pair is present, but without supporting electrolyte. The Nernstian oxidation that depolarizes the anode is partnered at the nearby cathode by the converse reduction. The resulting voltammogram is sigmoidal in overall shape but, generally, no explicit analytic expression describes the current-potential relationship, or even the height of the limiting-current plateau. Such limiting currents arise either by exhaustive oxidation of one member of the redox pair at the anode or by exhaustive cathodic reduction of the other member. For a critical composition, which this study identifies, both exhaustions occur concurrently. The ionic strength plays a paramount role in unravelling the conditions during the experiment. Although no direct analytical application of this “closed” experiment suggests itself, there are implications of the theory for microgap cells and electroanalytical methods in “open” configurations, as well as separatory possibilities.

Hydrogen Permeation as a Tool for Quantitative Characterization of Oxygen Reduction Kinetics at Buried Metal-Coating Interfaces

The electrochemical stability of the buried metal-organic coating interface of painted metal is crucially governed by how effectively the oxygen reduction reaction at the interface is inhibited. As this interface is not directly accessible for study by conventional electrochemical techniques, a new non-destructive method has been developed wherein hydrogen permeation is used to quantitatively measure the oxygen reduction kinetics underneath the coatings. Presented here are results obtained with an adaptation of the Devanathan-Stachurski cell where the oxygen reduction reaction kinetics on the coated exit is probed by monitoring the dynamic electrochemical equilibrium potential established as a result of oxygen reduction and hydrogen oxidation reactions. From the hydrogen uptake on the entry side thus a full current-potential relationship curve (I (U)) can be constructed. First tested on non-coated Palladium, the results show very good concurrence of the oxygen reduction currents from the permeation experiments and that from standard cyclic-voltammetry (CV) measurements in buffered and non-buffered acidic electrolyte and under alkaline condition. Initial results obtained on coated samples are also presented.

Electrochemical Properties of Electrode Obtained by Cyclic Oxidation and Reduction of Ni Powder

The presented paper discusses a possibility of developing surface of nickel powder by cyclic oxidation (air) and reduction (H2) processes for their further use as electrode precursors, in electrochemical processes of hydrogen production. The studies of a samples surface were conducted with the use of SEM/EDX technique. The electrochemical properties of porous Ni electrodes were examined by potentiostatic method. The authors applied a rotating electrode during those tests. The current-potential relationship was obtained at 40ºC 1M KOH with Hg|HgO reference electrode, i.e. under conditions similar to the industrial process of hydrogen production.

Quantification of Transmembrane Currents during Action Potential Propagation in the Heart

The measurement, quantitative analysis, theory, and mathematical modeling of transmembrane potential and currents have been an integral part of the field of electrophysiology since its inception. Biophysical modeling of action potential propagation begins with detailed ionic current models for a patch of membrane within a distributed cable model. Voltage-clamp techniques have revolutionized clinical electrophysiology via the characterization of the transmembrane current gating variables; however, this kinetic information alone is insufficient to accurately represent propagation. Other factors, including channel density, membrane area, surface/volume ratio, axial conductivities, etc., are also crucial determinants of transmembrane currents in multicellular tissue but are extremely difficult to measure. Here, we provide, to our knowledge, a novel analytical approach to compute transmembrane currents directly from experimental data, which involves high-temporal (200 kHz) recordings of intra- and extracellular potential with glass microelectrodes from the epicardial surface of isolated rabbit hearts during propagation. We show for the first time, to our knowledge, that during stable planar propagation the biphasic total transmembrane current (Im) dipole density during depolarization was ∼0.25 ms in duration and asymmetric in amplitude (peak outward current was ∼95 μA/cm2 and peak inward current was ∼140 μA/cm2), and the peak inward ionic current (Iion) during depolarization was ∼260 μA/cm2 with duration of ∼1.0 ms. Simulations of stable propagation using the ionic current versus transmembrane potential relationship fit from the experimental data reproduced these values better than traditional ionic models. During ventricular fibrillation, peak Im was decreased by 50% and peak Iion was decreased by 70%. Our results provide, to our knowledge, novel quantitative information that complements voltage- and patch-clamp data.

Electrocatalyis for PEFCs: Oxygen Reduction on Nanoparticles and Extended Surfaces

ABSTRACTThis work makes an attempt to correlate experimentally observed Tafel slopes from the oxygen reduction reaction in both model rotating disk electrode and polymer electrolyte fuel cell measurements, respectively, with the kinetic description of a coverage dependent current-potential relationship. It is shown that the potential dependent OHadcoverage can be used as a descriptor of potential dependent Tafel slopes, pointing to the validity of underlying Temkin-Frumkin adsorption properties in combination with the Butler-Volmer approach.

A pH-controllable electrochemical molecule switch employing a new electrochemical measurement system as switching transducer

A new design concept of electrochemical pH-controllable molecular switch is presented by utilizing a new electrochemical measurement system as switching transducer. A pH sensor is connected in series between the terminal points of the working and counters electrodes of a potentisostat, and immersed in the solution together with a reference electrode, establishing a novel electrochemical measurement system. In this system, the variation of pH-controllable interface potential at the pH-sensing film/solution interface can be converted to current response when amperometry technique is employed. Based on this unique current–potential relationship, a pH-controllable switch is designed to monitor the protonation and deprotonation reaction of pH-sensing molecule. The current direction interchanges between positive and negative via pH control, illustrating a reversible conformation transition between protonated state and deprotionated state of molecule. The magnitude of current value represents the degree of protonation and deprotonation reaction of molecule. The strategy is successfully demonstrated with a remarkably reversible polyaniline-based pH-controllable switch, which confirms the feasibility of the novel electrochemical measurement system as switching transducer for designing electrochemical pH-controllable switches. This study may open up a potential avenue to construct the electrochemical pH-controllable switches.

The effect of the bioflavonoid quercetin on voltage-gated calcium channels in Periplaneta americana Df motoneuron

The effect of the natural bioflavonoid quercetin on voltage operated calcium channels was investigated in American cockroach (Periplaneta americana) fast depressor motoneuron (Df) using electrophysiological and pharmacological methods. For blockade of outward potassium currents, tetraethylammonium and cesium leakage from microelectrode tip was used. Under this condition and application of command potentials, current-potential relationship was obtained in the absence and presence of quercetin (10 µM). Meanwhile, frequency and amplitude of action potentials (calcium spikes) under current clamp were also determined. In the presence of quercetin, inward calcium current showed a significant increase (p<0.05-0.01) in the potential range of -40 to 0 mV as compared to vehicle. Meanwhile, the frequency of calcium spikes in the presence of quercetin significantly increased relative to vehicle (p<0.01) and quercetin did not significantly change their amplitude. On the other hand, it caused a significant reduction of afterhyperpolarization (AHP) (p<0.05). Quercetin also shifted the voltage dependence of the inactivation and activation curves to more negative potentials and caused a signicant increase in the slope of activation, which reflects a yield of more current for a given potential. Quercetin through augmentation of inward calcium currents (Ica, L), increasing frequency of calcium spikes, and reduction of AHP amplitude could increase excitability and firing of Df motoneurons and this may be of benefit in those brain diseases in which neuronal excitability is depressed. Key words: Quercetin, calcium channel, electrophysiology, Periplaneta americana.

Universal current–potential relationship for mass-transfer through Formal Graph approach

The Formal Graph theory, a new language able to model graphically instead of algebraically most of basic equations used in physics and chemistry, is applied to mass-transfer occurring in electrochemical reactions. The integral admittance used in electrodynamics is generalized to all domains where energy is defined. Associated with the concept of energy coupling, this leads to very simple relationships between variables and operators describing processes in a system containing several energy varieties. The paradox of two different forms for the electric capacitance, linear in electrostatics and exponential in electrified materials, is treated and understood. The concept of energetic path brings physical meaning into mathematical models by attributing to each link a role in the conservation or dissipation of the energy. Normal transient diffusion, featured by an exponent 1/2, conserves half of energy, while anomalous diffusion, featured by an exponent p different from 1/2, conserves only 100 p%. The principle of every electrochemical measurement is represented in a simple and clear way by associating two Formal Graphs. The use of a mass-transfer operator generalizing all kinds of mass-transfer (diffusion, convection, thin layer, etc.) and for all geometric situations, allows the characterization of unknown process without previous knowledge of an algebraic model.