Electrical double layer at equilibrium

The electrical double layer at BiDER/PrOH and BiDER/2-PrOH interfaces with the addition of various electrolytes (LiC104> Lil, LiSCN, KSCN) has been studied using impedance.691-693 The Emj was independent of cei and v. A weak dependence of C on v has been found at cucio4 < 0- 1 M and at a > -0.03 C m 2, and the equilibrium differential capacitance C o has been obtained by linear extrapolation of C vs. tu,/2 to co1/2 = 0. Parsons-Zobel plots at a = 0 are linear, with/pz = 1.01 0.01. The values of cf have been obtained according to Grahame and Soder-... 

E is the standard equilibrium potential, i. e. the potential corresponding to unit activity and RTF. The dissolution reaction leads to the development of an electrical double layer at the iron-solution interface. The potential difference of the Fe/Fe " half cell cannot be measured directly, but if the iron electrode is coupled with a reference electrode (usually the standard hydrogen electrode, SHE), a relative potential difference, E, can be measured. This potential is termed the single potential of the Fe/Fe electrode on the scale of the standard hydrogen couple H2/H, the standard potential of which is taken as zero. The value of the equilibrium potential of an electrochemical cell depends upon the concentrations of the species involved. 

Equation (1.35) is known as the Debye-Hiickel or Gui-Chapman equation for the equilibrium double layer potential. In terms of the original variable x (1.34), (1.35) suggest e1/2(r(j) is the correct scale of ip variation, that is, the correct scale for the thickness of the electric double layer. At the same time, it is observed from (1.32) that for N 1 the appropriate scale depends on N, shrinking to zero when N — oo (ipm — — oo). This illustrates the previously made statement concerning the meaningfulness of the presented interpretation of relectric potential

(—oo) — 0, < (oo) — —oo). 

Activation Processes. To be useful in battery applications reactions in list occur at a reasonable rate The rare or ability of battery electrodes to produce current is determined by the kinetic processes of electrode operations, not by thermodynamics, which describes the characteristics of reactions at equilibrium when the forward and reverse reaction rates are equal. Electrochemical reaction kinetics follow the same general considerations as those of bulk chemical reactions. Two differences are a potential drop that exists between the electrode and the solution because of the electrical double layer at the electrode interface, and the reaction that occurs at a two-dimensional interfaces rather than in three-dimensional space. 

In the following sections, the relationship between surface charge and electrokinetic phenomena is expounded in terms of classical theory. First, a few possible mechanisms and models for the development of charge at a surface in contact with an aqueous solution are described in order to form a basis for the formation of an electrical double-layer at an interface. Secondly, the electrical double-layer is discussed in terms of an equilibrium charge distribution and electrostatic potential near the interface. With an adequate description of the interface, the discussion turns to explication of electrokinetic phenomena according to the charge distribution in the electrical double-layer and the Navier-Stokes equation. A section then follows which describes common methods and experimental requirements for the measurement of electrokinetic phenomena. The discussion closes with a few examples of the use of measurement of the pH dependence of electroosmosis as an analytical characterization technique from this present author s own experience. The intention is to provide... 

Figure 6.14 presents the variation of equilibrium film thickness with NaCl concentration at three different INUTEC SPl concentrations ]10]. The general trend is similar in each case - a decrease in film thickness with increasing electrolyte concentration, reaching a break point in the heq(Cei) curve at a critical electrolyte concentration, Cei <-r Above that concentration the heq(Cei) dependency shows ordy a slow decrease with increasing Cel- The Cei cr value, at which almost constant h q is reached, is lower for Na2S04 solutions (10 moldm ) than with NaCl solutions (10 moldm" ). This behavior (decrease of a film thickness with electrolyte concentration) reflects the compression of the electrical double layer at higher Cei as described in the DLVO-theory [41, 42]. 

Two questions can be asked and will be examined in this section firstly, how does the electrical double layer at an electrode affect the photoemission process, and secondly, as one of the key aims of electrochemical experimentation is to clarify our understanding of the structure and function of the double layer, can photoemission studies assist with determining its role in heterogeneous equilibrium and dynamic processes Experiments have been performed from each of these viewpoints and these topics have been represented in detail elsewhere. ... 

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. 

Consider a system of two solvents in contact in which a single electrolyte BA is dissolved, consisting of univalent ions. A distribution equilibrium is established between the two solutions. Because, in general, the solvation energies of the anion and cation in the two phases are different so that the ion with a certain charge has a greater tendency to pass into the second phase than the ion of opposite charge, an electrical double layer appears at... 

The physical sense of the distribution potential can be demonstrated on the example of the distribution equilibrium of the salt of a hydrophilic cation and a hydrophobic anion between water (wt) and an organic solvent that is immiscible with water (org). After attaining distribution equilibrium the concentrations of the anion and the cation in each of the two phases are the same because of the electroneutraUty condition. However, at the phase boundary an electrical double layer is formed as a result of the greater tendency of the anions to pass from the aqueous phase into the organic phase, and of the cations to move in the opposite direction. This can be characterized quantita tively by quantities—and — AGJJ. ", for which... 

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