Pair Potential Research Articles

Assessment of regional water resource carrying capacity by the connection number of set pair analysis

In order to evaluate regional water resource carrying capacity, the subtraction set pair analysis is adopted to calculate the connection number, and an evaluation model of the regional water resource carrying capacity based on quadratic subtraction set pair potential is established. The model is applied to assess the water resource carrying capacity of 16 cities in Anhui province, China, 2015. The results show that the water resource carrying capacity was sever throughout the province in 2015. Specifically, the carrying capacity in southern part of An-hui province was better than that in the northern part. The main factor of water resource carrying status varied in different cities.

Phase behavior of binary mixtures of hollow and regular microgels.

Soft colloids are widely used to study glass transition, aging and jamming. A high size polydispersity is typically introduced in these systems to avoid crystal formation. Here, we use binary mixtures of hollow and regular microgels with comparable sizes to inhibit crystallization. The phase behavior of the mixture is probed as a function of the number fraction of hollow microgels and characterized by small-angle X-ray scattering. Molecular dynamic simulations are used to extract the particle-particle pair potential and obtain insight on their deformation. The results suggest that the high deformability of the hollow microgels offers an alternative route to maximize the entropy without crystal formation.

ROLE OF NANOSIZED ROTATIONAL VORTICES IN COLD DEFORMATION OF METALLIC GLASSES BY THE EXAMPLE OF ALLOY VIT105

The experimental data on the deformation of amorphous alloy Vit105 (Zr52.5Cu17.9Al10Ni14.6Ti5) and its molecular dynamics simulation gave birth to new ideas about the mechanism of plastic deformation of disordered structures. A special method of torsion under hydrostatic pressure allows forming a developed deformation relief on the surface of polished specimens. Inspection of the relief points to the formation of shear bands on the surface, which can merge or branch, freely intersect or be arrested by an obstacle, forming a delta of small shear bands. Simulations based on the Morse pair potential made it possible to obtain a two-dimensional amorphous structure and study its deformation at the atomic level. Under the applied load, material regions are displaced due to the appearance of atomic-scale vortices within the shear band creating free volume, which is a structural feature of amorphous materials. A vortex causes redistribution of stress fields, which, when added to external stresses, are capable of activating similar vortices in the neighboring regions of the material, both in the direction of the applied stresses and along the vortex axis. In the latter case, a vortex tube is formed, which acts by the tornado mechanism. Displacement occurs by the tube movement in the direction of the principle shear stresses, and a path on the specimen surface is made by the screw component of the tube. An increase in the number of vortex tubes and their interaction causes a deformation band. Though playing the role of dislocations, vortex tubes are independent of specific crystalline planes and can move in arbitrary directions. This explains the experimentally observed features of deformation of amorphous alloys.

Improved Initialization of Optimal Path Calculations Using Sequential Traversal over the Image-Dependent Pair Potential Surface.

In reaction path optimization, such as the calculation of a minimum energy path (MEP) between given reactant and product configurations of atoms, it is advantageous to start with an initial guess where the close proximity of atoms is avoided and bonds are not unnecessarily broken only to be reformed later. When the configurations of the atoms are described with Cartesian coordinates, a linear interpolation between the end points can be problematic, and a better option is provided by the so-called image dependent pair potential (IDPP) approach where interpolated pairwise distances are generated to form an objective function that can be used to construct an improved initial path. When started with a linear interpolation, this method can, however, still lead to unnecessary bond breaking in, for example, reactions in which a molecular subgroup undergoes significant rotation. In the method presented here, this problem is addressed by constructing the path gradually, introducing images sequentially starting from the vicinity of the end points while the distance between images in the central region is larger. The distribution of images is controlled by systematically scaling the tightness of springs acting between the images until the desired number of images is obtained, and they are evenly spaced. This procedure generates an initial path on the IDPP surface, a task that requires negligible computational effort, as no evaluation of the energy of the system is needed. The calculation of the MEP, typically using electronic structure calculations, is then subsequently carried out in a way that makes efficient use of parallel computing with the nudged elastic band method. Several examples of reactions are given where the linear interpolation IDPP (LI-IDPP) method yields problematic paths with unnecessary bond breaking in some of the intermediate images, while the sequential IDPP (S-IDPP) method yields paths that are significantly closer to realistic MEPs.

Approximate Gibbsian structure in strongly correlated point fields and generalized Gaussian zero ensembles

AbstractGibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many random fields with a strongly dependent spatial structure. In this work, we provide a very general framework for approximate Gibbsian structure for strongly correlated random point fields, including those with a highly singular spatial structure. These include processes that exhibit strong spatial rigidity, in particular, a certain one‐parameter family of analytic Gaussian zero point fields, namely the ‐GAFs, that are known to demonstrate a wide range of such spatial behavior. Our framework entails conditions that may be verified via finite particle approximations to the process, a phenomenon that we call an approximate Gibbs property. We show that these enable one to compare the spatial conditional measures in the infinite volume limit with Gibbs‐type densities supported on appropriate singular manifolds, a phenomenon we refer to as a generalized Gibbs property. Our work provides a general mechanism to rigorously understand the limiting behavior of spatial conditioning in strongly correlated point processes with growing system size. We demonstrate the scope and versatility of our approach by showing that a generalized Gibbs property holds with a logarithmic pair potential for the ‐GAFs for any value of . In this vein, we settle in the affirmative an open question regarding the existence of point processes with any specified level of rigidity. In particular, for the ‐GAF zero process, we establish the level of rigidity to be exactly , a fortiori demonstrating the phenomenon of spatial tolerance subject to the local conservation of moments. For such processes involving complex, many‐body interactions, our results imply that the local behavior of the random points still exhibits 2D Coulomb‐type repulsion in the short range. Our techniques can be leveraged to estimate the relative energies of configurations under local perturbations, with possible implications for dynamics and stochastic geometry on strongly correlated random point fields.

A cutoff-based method with charge-distribution-data driven pair potentials for efficiently estimating electrostatic interactions in molecular systems.

We introduce a simple cutoff-based method for precise electrostatic energy calculations in the molecular dynamics (MD) simulations of point-particle systems. Our method employs a theoretically derived smooth pair potential function to define electrostatic energy, offering stability and computational efficiency in MD simulations. Instead of imposing specific physical conditions, such as dielectric environments or charge neutrality, we focus on the relationship represented by a single summation formula of charge-weighted pair potentials. This approach allows an accurate energy approximation for each particle, enabling a straightforward error analysis. The resulting particle-dependent pair potential captures the charge distribution information, making it suitable for heterogeneous systems and ensuring an enhanced accuracy through distant information inclusion. Numerical investigations of the Madelung constants of crystalline systems validate the method's accuracy.

Particle-based simulations of electrophoretic deposition with adaptive physics models

This work represents an extension of mesoscale particle-based modeling of electrophoretic deposition (EPD), which has relied exclusively on pairwise interparticle interactions described by Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. With this standard treatment, particles continuously move and interact via excluded volume and electrostatic pair potentials under the influence of external fields throughout the EPD process. The physics imposed by DLVO theory may not be appropriate to describe all systems, considering the vast material, operational, and application space available to EPD. As such, we present three modifications to standard particle-based models, each rooted in the ability to dynamically change interparticle interactions as simulated deposition progresses. This approach allows simulations to capture charge transfer and/or irreversible adsorption based on tunable parameters. We evaluate and compare simulated deposits formed under new physical assumptions, demonstrating the range of systems that these adaptive physics models may capture.

Local gastronomy and wine geographical indications (GIs): Framework for identifying pairing potential

Associating local gastronomy with wines, i.e. enogastronomy, contributes to enhancing the identity and competitiveness of destinations. The main objective of this paper is to propose a framework for pairing potential, linking local gastronomy and geographical indication wines (GIs) involving multiple relationships, as in a meal. Most studies involving pairing focus solely on binary wine-product relationships, which do not adequately support the analysis of local gastronomic pairings within a meal. In such cases, wine becomes an integral part of a larger context and must harmonize with a multitude of sensory elements. The study was conducted in 3 IGs from Brazil. The framework is structured in three phases, in order to identify (1) local gastronomy highlights, (2) pairing potential and (3) ideal pairing. The pairing potential was based on an experts' panel using Delphi methodology, in two rounds. The best pairing were listed for each GI, considering local gastronomy and also suggestions of international gastronomy. The main contribution is a framework systematized to provide methodological support for pairing potential involving multiple relationships. This framework can be applied in other GIs for further studies and to support stakeholders in the development of new products and experiences.

Nonlocal Potentials and Crystalline Order in One and Two Dimensions

We revisit the seminal 1968 proof of the absence of crystalline order in two dimensions and analyze the importance played in the quantum theorem by the assumption of local pair potentials. We relax the assumption of local potentials and consider instead nonlocal pair potentials. We show that the 1/k2 -singularity that occurs in the Bogoliubov inequality, which leads to no crystalline order in two dimensions for local potentials and nonzero temperatures, does not occur for nonlocal potentials. Accordingly, crystalline order in one and two dimensions cannot be ruled out for nonlocal pair potentials at finite temperatures.

Amplitude modulation and surface wave generation in a complex plasma monolayer.

The response of a two-dimensional plasma crystal to an externally imposed initial perturbation has been explored using molecular dynamics (MD) simulations. A two-dimensional (2D) monolayer of micron-sized charged particles (dust) is formed in the plasma environment under certain conditions. The particles interacting via Yukawa pair potential are confined in the vertical (z[over ̂]) direction by an external parabolic confinement potential, which mimics the combined effect of gravity and the sheath electric field typically present in laboratory dusty plasma experiments. An external perturbation is introduced in the medium by displacing a small central region of particles in the vertical direction. The displaced particles start to oscillate in the vertical direction, and their dynamics get modulated through a parametric decay process generating beats. It has also been shown that the same motion is excited in the dynamics of unperturbed particles. A simple theoretical model is provided to understand the origin of the beat motions of particles. Additionally, in our simulations, concentric circular wavefronts propagating radially outward are observed on the surface of the monolayer. The physical mechanism and parametric dependence of the observed phenomena are discussed in detail. This research sheds light on the medium's ability to exhibit macroscopic softness, a pivotal characteristic of soft matter, while sustaining surface wave modes. Our findings are also relevant to other strongly coupled systems, such as colloids and classical one-component plasmas.

Scattering Problem of Three One-Dimensional Quantum Particles. Case of Repulsive Coulomb Pair Potentials at Large Distances

Scattering Problem of Three One-Dimensional Quantum Particles. Case of Repulsive Coulomb Pair Potentials at Large Distances

A central limit theorem for a classical gas

For a class of translation-invariant pair potentials ϕ in (mathbb{R}^{d},zlambda ) satisfying a stability and regularity condition, we choose z so small that the associated collection mathcal{ G}(phi,zlambda ) of Gibbs processes contains at least the stationary process G, which is a Gibbs process in the sense of DLR and is given by the limiting Gibbs process with empty boundary conditions. Using an abstract version of the method of cluster expansions and Dobrushin’s approach to the central limit theorem, we present a central limit theorem for the particle numbers of G.

Estimation of Two Component Activities of Binary Liquid Alloys by the Pair Potential Energy Containing a Polynomial of the Partial Radial Distribution Function

An investigation of partial radial distribution functions and atomic pair potentials within a system has established that the existing potential functions are rooted in the assumption of a static arrangement of atoms, overlooking their distribution and vibration. In this study, Hill’s proposed radial distribution function polynomials are applied for the pure gaseous state to a binary liquid alloy to derive the pair potential energy. The partial radial distribution functions of 36 binary liquid alloy from literatures were used to obtain the binary model parameters of four thermodynamic models for validation. Results show that the regular solution model (RSM) and molecular interaction volume model (MIVM) outperform other models when the asymmetric method calculates the partial radial distribution function. RSM demonstrates an average SD of 0.078 and an ARD of 32.2%. Similarly, MIVM exhibits an average SD of 0.095 and an average ARD of 32.2%. Wilson model yields an average SD of 0.124 and an average ARD of 226%. Nonrandom two-liquid (NRTL) model exhibits an average SD of 0.225 and an average ARD of 911%. On applying the partial radial distribution function symmetry method, MIVM and RSM outperform the other models, with an average SD of 0.143 and an average ARD of 165.9% for MIVM. RSM yields an average SD of 0.117 and an average ARD of 208.3%. Wilson model exhibits average values of 0.133 and 305.6% for SD and ARD, respectively. NRTL model shows an average SD of 0.200 and an average ARD of 771.8%. Based on this result, the influence of the symmetry degree on the thermodynamic model is explored by examining the symmetry degree as defined by the experimental activity curves of the two components.

Study of Andreev reflection in topological insulator-based ferromagnet/ [formula omitted] wave superconductor structures

The Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk theory are used to calculate the tunneling conductance and shot noise in topological insulator-based ferromagnet/ dx2−y2+idxy mixed wave superconductor (TI-based FM/ dx2−y2+idxy SC) junctions. The Andreev reflection is investigated by analyzing the conductance and shot noise. Results show that the Andreev reflection process strongly depend on the magnetic gap m in FM, the gate potential U applied to the electrode on top of SC, and the magnitude of the ratio of Δ1/Δ0 with Δ0(Δ1) the absolute of pair potential of dx2−y2(dxy) component. The specular Andreev reflection can be enhanced by m as well as U. The conventional Andreev retro-reflection, however, can be enhanced by U but be suppressed by m. Which of the two reflections dominates the tunneling phenomenon exists a turning point at m = EF where both the tunneling conductance and differential shot noise become zero. This can be used as a criterion for distinguishing between the specular Andreev reflection and the Andreev retro-reflection in thin film TI-based FM/ dx2−y2+idxy SC structures. In addition, the dx2−y2+idxy pairing symmetry as well as the magnitude of magnetic gap can be determined by the experiment of scanning tunnel spectroscopy.

Effect of the varying repulsive core of Gay–Berne pair potential on the structure and freezing transition in a two-dimensional system of soft ellipses

ABSTRACT We have investigated the effect of the strength of repulsive core of Gay–Berne (GB) ( n − 6 ) pair potential on the pair correlations and isotropic-nematic ( I − N ) freezing transition in a system of soft ellipses confined to a two-dimensional plane. The power n has been varied in the range 8 ≤ n ≤ 16 at an interval of two. Percus–Yevick (PY) integral equation theory (IET) has been solved to calculate the pair correlations of the isotropic fluid, which has been then used in the density functional theory to determine the isotropic-nematic transition parameters. The pair correlations obtained by PY theory have been compared with those obtained by NVT Monte-Carlo (MC) simulation. We observe a better agreement between PY and MC correlations at lower n -values of the interaction potential. An increase in the values of n results in more intricate structures manifested in both the radial distribution part and the higher order correlations. The I − N transition parameters are found to be sensitive to the value of the exponent n . The transition density is found to decrease, whereas the corresponding orientational order parameter is found to increase with the increase in n for a given temperature. At a given temperature, we observe a cut-off of n , below which the nematic does not stabilise. The smaller value of change in density at the transition indicates that the I − N transition is of weakly first order.

Parametrization of embedded-atom method potential for liquid lithium and lead-lithium eutectic alloy

Liquid lead-lithium eutectic remains as a promising candidate for various breeding-blanket designs in future nuclear-fusion technologies. The lack of a generalized theory of interatomic forces in the liquid state is reflected on the wide variety of proposed functional forms to describe interatomic interactions even in simple liquids. Computer simulations facilitate the study of liquid metal properties, due to mathematical and experimental challenges. A classical-MD EAM potential is parametrized using mechanical and non-mechanical (melting-point) properties to minimize the arbitrariness of functional forms, where the employed pair potential stems from the liquid-state theory to avoid the issue of the uniqueness of the potential. Enhanced performance is obtained for liquid density, energy, structure, diffusivity and shear viscosity of Li, and their temperature-dependencies. In a similar manner, reference experimental and ab initio MD data are used to parametrize a functional to describe Pb-Li pairwise interactions in liquid Pb-Li alloy, which is used with the derived EAM of liquid Li and a reference EAM of liquid Pb to investigate properties of liquid Pb-Li alloy. Enhanced transferability characteristics are obtained for low-in-lithium liquid Pb-Li melts, where Coulombic interactions are negligible. In specific, the exhibited behaviour of Li in liquid lead-lithium eutectic is consistent with findings from ab initio MD methods, and drastically different from predictions of previous C-MD studies which suggested a substantial segregation of Li atoms instead of dispersion. It is concluded that the functional form of the pair potential and its uniqueness influence both the pure liquid-metal properties and the validity of the potential transferability in multi-component systems, where a theoretical functional results in enhanced performance in pure and alloyed liquid systems.

Quantitative Diagnosis of Water Resources Carrying Capacity Obstacle Factors Based on Connection Number and TOPSIS in Huaibei Plain

To further quantitatively assess the water resources carrying capacity (WRCC) system and analyze and identify the regional water resources carrying state and the physical mechanism of the state change, WRCC and obstacle factor diagnosis were carried out. In this paper, we proposed the mobility matrix to determine the connection number components, considered the dynamic attributes of the difference degree coefficient, and calculated it using the semi-partial subtraction set pair potential and triangular fuzzy number, so as to construct the quantitative diagnosis method of regional WRCC obstacle factors based on the connection number and TOPSIS. The results applied to six cities in the Huaibei Plain showed that the WRCC fluctuated around grade 2 and was in a poor state, which was mainly due to the insufficient support force; the water resources carrying state of the six cities gradually improved from 2011 to 2018, but the state became worse in 2019, which was related to the low precipitation in that year, the reduction in water resources, and the high degree of water resource utilization. The WRCC of Fuyang and Huainan was worse than that of the other four cities; over the 9 years, the average grades of Fuyang and Huainan were 2.26 and 2.43, while those of Huainan, Bozhou, Suzhou, and Bengbu were 2.19, 2.12, 2.05, and 2.05, respectively. The key obstacles limiting the improvement in the WRCC of the Huaibei Plain were per capita water resources, annual water production modulus, per capita water supply, vegetation coverage ratio, utilization ratio of water resources, water consumption per 104 yuan value-added by industry, and population density. In time, the key obstacle factors in neighboring years generally tended to have similarity, and conversely appeared as a difference; in space, neighboring regions showed similarity and conversely presented as a difference. The results of this study can offer technical support and a decision-making basis for water resources management in the Huaibei Plain. The method constructed in this paper is extremely interpretive, easy to calculate, highly sensitive, and reliable in application results, which opens up a new perspective for the rational determination of the connection number and the difference degree coefficient and provides a new intelligent way to determine the state of a complex set pair system and its causal mechanism analysis and diagnosis of obstacle factors.

Visible light responsive AgBiS2 nanomaterials for photocatalytic applications in removal of antimicrobial compounds and bacterial pathogens: Possible electrochemical pathways

Potential synthesis of ternary chalcogenide nanocomposite to showcase a practical electronic pathway to improve photocatalytic efficiency was carried out. In the present study, AgBiS2 nanorod-shaped with remarkably visible-light absorption was prepared using solvothermal techniques. This material was employed in photocatalytic degradation of amoxicillin (AMX) under visible light irradiation. The results indicated more than 90% degradation of AMX under 60 min having a corresponding bandgap of ∼2.19 eV. In the verge of understanding the photogenerated separation of electron-hole pair, VB and CB potentials were calculated to be 2.06 eV and − 0.76 eV, proposing a possible pathway for the degradation study. The photogenerated intermediates were identified using LC-MS analysis and the mineralization was followed using TOC analysis. A scavenging experiment showed a potential reactive oxygen species involved in the oxidation of organics that proved effective in three consecutive trials.In addition, antibacterial and antibiofilm activity showcased fair efficiency of the material, especially the presence of Ag+ in AgBiS2 improves antimicrobial activity. In case of antibiofim activity, 4 × 107 CFU/mL were seen to be most effective for the biomass formation of the biofilms.

Nonadditivities of the Particle Sizes Hidden in Model Pair Potentials and Their Effects on Physical Adsorptions.

It is important to understand the mechanism of colloidal particle assembly near a substrate for development of drug delivery systems, micro-/nanorobots, batteries, heterogeneous catalysts, paints, and cosmetics. Understanding the mechanism is also important for crystallization of the colloidal particles and proteins. In this study, we calculated the physical adsorption of colloidal particles on a flat wall mainly using the integral equation theory, wherein small and large colloidal particles were employed. In the calculation system, like-charged electric double-layer potentials were used as pair potentials. In some cases, it was found that the small particles are more easily adsorbed. This result is unusual from the viewpoint of the Asakura-Oosawa theory, and we call it a "reversal phenomenon". Theoretical analysis revealed that the reversal phenomenon originates from the nonadditivities of the particle sizes. Using the knowledge obtained from this study, we invented a method to analyze the size nonadditivity hidden in model pair potentials. The method will be useful for confirmation of various simulation results regarding the adsorption and development of force fields for colloidal particles, proteins, and solutes.

Diagram for the Electrochemical Stability of Water

According to the electrochemical stability diagram of water (Fig. 1), Ox/Red pairs displace hydrogen and oxygen respectively, when equilibrium potentials E Ox/Red < E H+/H2 (line a ) and E Ox/Red > E O2/OH- (line b ). However, if this is theoretically possible, the fact is that only pairs with E Ox/Red > ~ +0.5 V SHE ( E o I2/I- = + 0.535 V SHE; E o NiO2/Ni(OH)2,OH- = + 0.49 V SHE) displace oxygen from alkaline solutions and only pairs with E Ox/Red < ~ +0.5 V SHE ( E o Cu/Cu2+ = +0.34 V SHE; E o Co/Co3+ = +0.4 V SHE) can displace hydrogen from acid solutions. There will be no displacement of oxygen by ions Cu2+ (Ox-form) and hydrogen by ions I- (Red-form) at the appropriate pH (Fig.1) [1,2].The reason for this is that Red-forms (I-ions) with E Red/Ox > ~+0.5 V SHE and Ox-forms (Cu2+, Co3+ ions) with E Red/Ox < ~+0.5 V SHE is already thermodynamically stable in solutions, their transitions to conjugated forms (I2, Cu) are not spontaneous. With the theoretical possibility of H2 displacement, ions I-will form acids (HI) with H+ ions. With the theoretical possibility of O2 displacement, ions Cu2+, Co3+ will form hydroxides (Cu(OH)2) with OH- ions. These reactions are more thermodynamically probable. Accordingly, electrodes displace either hydrogen or oxygen from water.Between pairs with low oxidizing and reducing activities, there should be a pair of zero activity, in which Ox + ne and Red-forms are chemically equilibrium (line c , Fig.1) [1-3]. Its average potential is E Red/Ox ~ +0.44 V SHE between E o I2/I- = + 0.535 V SHE and E o Cu/Cu2+ = +0.34 V SHE and E Red/Ox ~ +0.47 V SHE between nearest E o NiO2/Ni(OH)2,OH- = +0.49 V SHE and E o Ru/Ru3+ = +0.45 V SHE determined opposite activities [1,2].The intersection of line c with lines a (pH = -8; point d ) and b (pH=12.8; point e) should also correspond to zero activity of H+/H2 - and O2/OH- - electrodes (Fig.1). The differenceΔpH =12.8 – (-8) = 20.8 determines emf of H+/H2//O2/OH- element (20.8 x 0.0 59 = 1.227 V) [1]. The instability of metal ions reflects itself in the decomposition of hydroxides 2CuOH→ Cu2O + H2O; 2AuOH → Au2O +H2O. Unstable metal ions (Cu+, Te4+, Ag+, Au+) can polarize hydroxyl ions without the formation of the pair OH-/O2[2]. Indeed, the boundary at E Red/Ox ~+0.47 V SHE separates stable and unstable hydroxides (Table). Me/Men+ E o, V SHEHydroxide/Oxide Pb/Pb2+ -0.126 Pb(OH)2 Cu/Cu 2+ +0.34Cu(OH)2 Co/Co 3+ +0.4 (+0.46)Co(OH)3 Ru/Ru 2+ +0.45Ru(OH)2 Cu/Cu+ +0.52Cu2OTe/Te 4+ +0.568TeO2 Hg/Hg2 2+ +0.789Hg2OAg/Ag+ +0.799Ag2O Absolute values |-E H+/H2 | = |+E O2/OH- | = 1.227 V/ 2 = ~ 613.6 mV (10.4 x 59 mV) are equal at pH = 10.4 (line f , Fig.1), where 1.227 V is the distance between lines a and b (emf H2/H+//OH-/O2 element).Line f divides the horizontal distances (as g - i ) from pH = 0 to pH = 14 (14 x 59 mV= 826 mV) into parts 1227 mV / 2 = 613.6 mV ( g - h ) and 212.4 mV (3.6 pH x 59 mV; h - i ). Their ratio is 613.6 mV / 212.4 mV = ~ 2.89. Thus, presented613.6 mV = (212.4 mV + 0.89 x 212.4 mV) + 212.4 mV == 401.2 mV + 212.4 mV = 2.89 x 212.4 mV ==2.89 (ψ O2/OH-, pH=14 + ψ O2/OH-,pH=10.4)where ψ O2/OH-, pH=14 + ψ O2/OH-,pH=10.4 are the sum of external potential drops (not Galvani potentials) arising in half-reactions between oppositely charged particles in double-electrical layers on electrodes.Both sides are equal to 212.4 mV. Therefore, dividing 212.4 mV (left) / 2.89 = 73.5 mV should give the smallest actual component ψ O2/OH-,pH=14of equal 212.4 mV (right).Then, its second component ψ O2/OH-,pH=10.4 is 401.2 mV (left) / 2.89 =138.8 mV or 212.4 mV - 73.5 mV = 138.9 mV. Close ψ O2/OH-, pH=14 (14 - 12.8) x 59 mV = 70.8 mV and ψ O2/OH-, pH=10.4 - (12.8 - 10.4) x 59 mV =141.6 mV calculated relative to pH=12.8 (point e , Fig.1) [1].The potential of pairs of zero activity (line c , Fig.1) is calculated as E O2/OH-,pH=10.4 - ψ O2/OH-,pH=10.4 = 613.6 mV SHE - 138.8 mV = + 474.8 mV SHE. The potential drops ψ H +/H2,pH=0 = - 474.5 mV; ψ O2/OH-,pH=0 = + 752.4 mV and ψ H +/H2= ψ O2/OH- at pH = 2.4 are calculated (Fig.1).Reference1.A.I.Chernomorskii, Zh. Fiz. Khim., 51,924 (1977).2.A.I.Chernomorskii, Dokl. Akad.Nauk Uzb.SSR, 3,37(1989).3.A.I.Chernomorskii, Journal of The Electrochemical Society,2021,168,116514. Figure 1