Electrically bulk concentration

The Nernst equation is of limited use at low absolute concentrations of the ions. At concentrations of 10 to 10 mol/L and the customary ratios between electrode surface area and electrolyte volume (SIV 10 cm ), the number of ions present in the electric double layer is comparable with that in the bulk electrolyte. Hence, EDL formation is associated with a change in bulk concentration, and the potential will no longer be the equilibrium potential with respect to the original concentration. Moreover, at these concentrations the exchange current densities are greatly reduced, and the potential is readily altered under the influence of extraneous effects. An absolute concentration of the potential-determining substances of 10 to 10 mol/L can be regarded as the limit of application of the Nernst equation. Such a limitation does not exist for low-equilibrium concentrations. 

At time t = 0 an electric current of constant strength begins to flow in the system. At this time the uniform initial concentration distribution is still not disturbed, and everywhere in the solution, even close to the electrode surface, the concentration is the same as the bulk concentration Cyj. Hence, the first boundary condition (for any value of jc) is given by... 

To reduce and overcome this concentration polarization, several techniques are available. For reactants soluble in the electrolyte, high bulk concentrations are used and also the electrolyte is circulated by pumping which uses a fraction of the electricity produced by the fuel cell and hence reduces the available power. For gaseous reactants, porous gas electrodes are used to achieve larger contact of the three phases, namely the gas, the liquid and the solid phases. There are different types of such electrode and two examples are shown in Figures 3a et 3b. 

The conditions (6.3.5a,b) merely state that at the outer edges of the filter the electrolyte concentrations are assumed fixed equal to the bulk concentrations in the vessels I and II. Conditions (6.3.5c,d) fix the electric potential and the pressure at the left I edge of the filter at zero reference level. Condition (6.3.5e) is just a combination of (6.1.1), (6.1.2) of 6.1, N is the average number of pores per unit cross-sectional area of the filter. 

In practical applications, where the maximum yield of a product or electricity in electrochemical energy conversion systems at the lowest energy cost is desirable, the rate of mass transport should be fast enough in order not to limit the overall rate of the process. For electroanalytical applications, such as polarography or gas sensors, on the other hand, the reaction must be limited by the transport of the reactant since the bulk concentration which is of interest is evaluated from the limiting con-vective-diffusional current. 

Now we assume that only electric work has to be done. We neglect for instance that the ion must displace other molecules. In addition, we assume that only a 1 1 salt is dissolved in the liquid. The electric work required to bring a charged cation to a place with potential -ip is W+ = etf). For an anion it is W = -ertp. The local anion and cation concentrations c and c+ are related with the local potential ij) by the Boltzmann factor c = c0 ee /fesT and c+ = co e e /kBT. Here, cq is the bulk concentration of the salt. The local charge density is... 

Equations (1.72)—(1.78) provide relationships between characteristic parameters of the interface (qM, qs, Cd, Cu and surface concentrations of ionic species) and macroscopic magnitudes such as the surface tension, the applied potential and the bulk concentration of electrolyte. However, they provide no information about the double-layer structure. Next, some theoretical models about the structural and geometrical description of the electrical double layer are discussed briefly. 

Z>xhase is the diffusion coefficient of the target ion in the different phases and m/ out bulk concentration in the inner/outer solution, A t m the electric potential difference across the interface corresponding to the /nth potential applied, and A t(/iformal potential of the ion transfer. 

Here zm denotes the valency of the counterions with the highest absolute charge. The function G is dependent upon the zeta potential of the particle as well as the bulk concentrations, valencies and diffusivities of the ions. The equilibrium electrical potential can be obtained using the Runge-Kutta method to solve the Poisson-Boltzmann equation numerically, and then the integral in Eq. (52) can be evaluated. 

Debye-Huckel parameter. (V2 Laplace operator, o -> permittivity of vacuum, er -> dielectric constant of the electrolyte solution, cf bulk concentrations of all ions i, zp charges of the ions i, f electric potential, k - Boltzmann constant, and T the absolute temperature). See also -5- Debye-Huckel theory. 

Here er is the relative -> permittivity (static dielectric constant) of the solution, 0 is the permittivity of free space, e is the unit charge on the electron (- elementary electric charge), 3 is the valence of the ionic species i, Ci is the bulk concentration of the adsorbing species i, k is the Boltzmann constant, T is the absolute temperature, and (V(a)) is the time-averaged value of the electric potential difference across the diffuse layer. The diffuse layer capacitance is (very roughly) of the order of 10 pF cm-2. The thickness of the diffuse layer is essentially the - Debye length Ld,... 

Consider a gel that carries a certain concentration c,-(r) of immobile negative charges and is immersed in an aqueous solution. The bulk solution carries monovalent mobile ions of concentration c+(r) and c (r). Away from the gel, the concentration of the salt ions achieves the bulk concentration, denoted c0. What is the difference in electrical potential (known as the Donnan potential) between the bulk solution and the interior of the gel [Hint assume that inside the gel the overall concentration of positive salt ion balances immobile gel charge concentration.]... 

Consider two parallel similar plates 1 and 2 of thickness d separated by a distance h immersed in a liquid containing N ionic species with valence zt and bulk concentration (number density) nf i=, 2,. . . , N). Without loss of generality, we may assume that plates 1 and 2 are positively charged. We take an x-axis perpendicular to the plates with its origin at the right surface of plate 1, as in Fig. 9.1. From the symmetry of the system we need consider only the region —oo < x < h/2. We assume that the electric potential i/ (x) outside the plate (—oo < x < —d and 0 < x < hl2) obeys the following one-dimensional planar Poisson-Boltzmann equation ... 

We first consider two interacting parallel similar plates 1 and 2 with constant surface potential at separation h in a symmetrical electrolyte solution of valence z and bulk concentration [13]. We assume that the surface potential ipo remains unchanged independent of h during interaction. We take an x-axis perpendicular to the plates with its origin 0 at the surface of plate 1 (Fig. 9.6). The Poisson-Boltzmann equation for the electric potential (which is a function of x only) relative to the... 

Composition. While the average environment of a molecule in solution is well represented by the bulk concentrations of the various constituents of a reaction mixture, the environment of a molecule bound to a heterogeneous interface may be strongly perturbed. The properties of the motionally restricted phase may dictate. rather large deviations in the local concentrations of ions, reactants, and other mobile species from their respective bulk concentrations. The most important examples of this have been demonstrated for electrode-solution interfaces where, for example, the pH in the electrical double layer may differ significantly from its value in the bulk solution and can change with applied potential (1). A similar, though less extreme,example involves the interface between aqueous solutions and hydrophobic polymers. 

GD-MS is of use for the direct determination of major, minor and trace bulk concentrations in electrically-conductive and semi-conductor solids down to concentrations of 1 ng/g. Because of the limited ablation (10-1000 nm/s), the analysis times especially when samples are inhomogeneous are long. It has been applied specifically to the characterization of materials such as Al, Cd, Ga, In, Si, Te, GaAs and CdTe. 

X is the concentration of the adsorbate A which is varied in order to study the effect of bulk concentration on the interfacial surface excess y is the concentration of the electrolyte whose activity is kept constant. The corresponding electrolyte concentration is kept reasonably high to provide electrical conductivity to the solution. For low values of x, the electrolyte concentration is constant. However, at higher concentrations of organic solute, the activity coefficient of the electrolyte varies with organic solute concentration. Thus, in general, the concentration of the electrolyte must also be varied in order to keep its activity constant. It is also important that the ions of the electrolyte not adsorb on the electrode to a significant extent. 

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