Electrochemical diffusion potential

Goodings, J.M., Guo, J. and Laframboise, J.G. (2002) Electrochemical diffusion potential in a flame plasma theory and experiment. Electrochemistry Communications, 4, 363-369. 

If a diffusion potential occurs inside the membrane, the relation between mass transport and electrochemical potential gradient — as the driving force for the diffusion of ions — has to be examined in more detail. This can be done by three different approaches ... 

K+ ions in the presence of valinomycin do not distribute passively at electrochemical equilibrium rather, this represents a nonequilibrium state in which creates a diffusion potential following which protons move. 

It is, of course, not easy to make statements about the relative contributions of phase boundary and diffusion potentials. Since the electrochemical behavior of membranes is generally reflected by the total membrane potential, we did not try to differentiate in this respect. The models described in my report may, however, approximate the selectivity of certain membrane systems in the equilibrium domain even when assuming the absence of diffusion potentials. 

Figure 18.1—Electrochemical measurement string using an ion selective (or specific) electrode (ISEJ. The membrane potential varies with the concentration of the specific ion in solution. Other potentials are fixed by the construction of the electrode. The junction (diffusion) potential Ej has a low value and is generally constant. Measurement is typically conducted with an ionometer. Manufacturers also supply combined electrodes that include both electrodes (external and ion selective) in the same device. Commonly employed pH electrodes are of this type. The schematics of combined electrodes are much less clear due to the proximity of the membrane to other electrode components.

Consider an ionic material that contains a dilute concentration of positively charged ions that diffuse interstitially (interstitial diffusion is described in Section 8.1.4). D is the interdiffusivity of these ions in the absence of any field. As shown in Sections 2.2.2 and 2.2.3, if an electric field, E = —V, is applied, the diffusion potential will be the electrochemical potential given by Eq. 2.41. According to Eq. 2.21, the flux of charged interstitials is... 

Extensive studies have been carried out on the proton-translocating ATPase of mitochondrial, bacterial and chloroplast membranes. This enzyme can also function in reverse to exploit the electrochemical potential of protons built up by respiration for the synthesis of ATP from ADP and P .298 The synthesis of ATP can be effected by the application of external electrical pulses to the ATPase vesicles in suspension with submitochondrial particles, showing that the diffusion potential of the protons (ApH) is not used. The yield of ATP was linearly dependent on the number of pulses.299... 

The liquid junction is a practical necessity in most electrochemical measurements and in almost all potentiometric measurements. It is a site of the dreaded liquid junction (or diffusion) potential Ej. Because this potential is the result of the diffusion, which is a nonequilibrium process, any potentiometric measurement, which uses a liquid junction is a nonequilibrium measurement, by definition. The origin of Ej is explained in Fig. 6.5. 

Tabulated standard potentials — The - standard potential of various redox couples have been tabulated by using either the values obtained in electrochemical experiments or calculated from thermochemical data. The electrochemical determination of these values based on -> emf measurements is possible provided that -> diffusion potentials and thermo emf s are elimi-... 

Thus, the concentration of the diffusing species has the same value c at any t at f = 0 or for any r > 0 at x >. This is true for almost all electrochemical diffusion problems in which one switches on (at t = 0) the appropriate current or potential difference across the interface and thus sets up interfacial charge-transfer reactions which, by consuming or producing a species, provoke a diffusion flux of that species. 

When two electrolyte solutions at different concentrations are separated by an ion--permeable membrane, a potential difference is generally established between the two solutions. This potential difference, known as membrane potential, plays an important role in electrochemical phenomena observed in various biomembrane systems. In the stationary state, the membrane potential arises from both the diffusion potential [1,2] and the membrane boundary potential [3-6]. To calculate the membrane potential, one must simultaneously solve the Nernst-Planck equation and the Poisson equation. Analytic formulas for the membrane potential can be derived only if the electric held within the membrane is assumed to be constant [1,2]. In this chapter, we remove this constant held assumption and numerically solve the above-mentioned nonlinear equations to calculate the membrane potential [7]. 

The electrochromic shift of the carotenoids is usually calibrated with K-diffusion potential in the presence of valinomycin. One problem is that the shifts observed in respiring chromatophores (where the proton electrochemical potential is predominantly in the form of a membrane potential) are much larger than those induced by the calibrating diffusion potential, so that an extensive extrapolation is required. Thus, the carotenoids in illuminated chromatophores may indicate a membrane potential in excess of 300 mV, whereas the distribution of CNS, an electrically permeant anion, in the same system only indicates 140 mV [32]. The extent of this discrepancy, and the uncertainty as to whether the carotenoids see the bulk-phase potential, or only the local electrical field within the membrane, limits the confidence with which carotenoids may be used for quantitative as opposed to qualitative potential measurements. 

The thermal diffusion potential, td> arises if an electrochemical system is nonisothermal. This phenomenon is due to the heat transport of ionic species and can be taken into account if the individual ion entropy of transport, conductivity, and activity coefficients of the species of interest are known. Therefore, the thermal diffusion potential depends on the temperature, pressure, and composition of the electrolyte liquid junction. Also, td is a function of the temperature gradient and can be a substantial value from tens to hundreds of millivolts [19]. 

The mentioned thermodynamic prerequisite that the formal potential of the substrate redox system must be more positive than the formal potential of the catalyst redox system means that, in principle, reduction of S is easier compared to Cat , but that kinetic constraints essentially hinder this process at potentials where the catalyst is oxidized. Then, the direct reduction of S does not proceed electrochemically at potentials where Cat is reduced (or maybe even at no accessible potential at all) but only via homogeneons redox reaction (Equation (3.2)) with CaC". In this context, the regeneration of the catalyst leads to much steeper concentration profiles of the catalyst in the diffusion reaction layer that is, to a steeper concentration gradient that (see Chapter 1) means larger current. 

In general, the chemical potentials of the cation are not equal in a given solution and in the membrane. At equilibrium the electrochemical potentials of the cation must be equal in the two phases. As a result, a potential difference called the Donnan potential is established at each interface. Moreover, the concentration of the cation on the left-hand side of the membrane is not always the same as that on the right and the cation diffuses from the location of high concentration to the one where it is lower. The non-equilibrium diffusion process gives rises to a diffusion potential. 

Within this working range, the presence of a reactive sample will give rise to a cui-rent/potential (// ) curve (Fig. 4.3). This curve is unique for a particular sample/elu-ent/electrode combination. It is characterized by a half-wave potential and by a "diffusion current plateau. The half-wave potential (the potential half way up to the diffusion current plateau) is defined as the potential needed to induce electrolysis of the electroactive species. As the potential is increased, the electrolysis current also increases because more ions migrate to the electrode and become oxidized (or reduced). The electrolysis current eventually forms a plateau in the HE curve because, ultimately, the amount of current is limited by the rate of diffusion of ions to the electrode surface. In normal operation, the electrochemical detector potential is set at the smallest potential possible that is still on the diffusion current plateau. The detector should be on the plateau for consistent performance, but at the lowest potential to lessen the chance of side reactions. 

When there is an electrical potential gradient, including diffusion potential, the flux of z, Ji(e), is proportional to the gradient of the electrical potential, (dW/dx), the concentration, C and valence, zi of ion i and its electrochemical mobility w ... 

Fixed Charge Theory. As a result of combining the above two theories, a fixed charge membrane theory was developed by Teorell and Meyer and Sievers. The theory includes the equilibrium of the electrochemical potentials of ions at the membrane boundaries and the diffusion of ions in the membrane. Therefore, the total membrane potential E is composed of three separate potential differences Eo corresponds to the first transition region between the solution (o) and membrane phases, difl corresponds to the ion diffusion potential in the membrane, and corresponds to the other transition region between membrane and the solution (i) phases (see Figure 26B). Thus, the transmembrane potential is... 

The following rules were adopted by the International Union of Pure and Applied Chemistry (lUPAC) in Stockholm in 1953 to solve the question of the sigjis of electrode potential and to determine which substances should be considered as the reactants and which as products. Any electrochemical cell, according to this agreement, is written from left to right as follows (i) the material of one of the two electrodes, (ii) the solution in contact with one electrode, (iii) the solution in contact with the second electrode, and (iv) the material of the second electrode. In the written expression, the electrodes are separated from the solutions by a single bar, while the solutions are separated by a double bar, indicating that there is no diffusion potential between the solutions in the cell. 

The universal definition of the standard potential of a redox couple Red/Ox is as follows the standard potential is the value of emf of an electrochemical cell, in which diffusion potential and thermo-emf are eliminated. This cell consists of an electrode, on which the Red/Ox equilibria establish under standard conditions, and a SHE. 

Figure 3.2 Potential diagram of an electrochemical cell with a Cu working electrode with unknown Galvani potential difference connected to a reference electrode of constant Galvani potential difference. Changes of the unknown Galvani potential difference of the working electrode can he measured as difference of the inner potentials of the Cu electrode Cuj and the connecting Cu wire Cuj. The diffusion potential between electrolytes Elj and El 2 is neglected.

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