Electrical double layer dependence

The above discussions illustrate that the interactions between overlapping electrical double layers depend on a number of considerations, such as the magnitude of the surface potential, the thickness of the double layer, and the type of electrolyte, among others. Moreover, the expressions that have been obtained here (and others that are available in the literature) depend on additional conditions that are determined by the approximations made in deriving the expressions. 

The orientation of the exposed crystal face affects 0 because the strength of the electric double layer depends on the density of positive ion cores which in turn will vary... 

The treatment may be made more detailed by supposing that the rate-determining step is actually from species O in the OHP (at potential relative to the solution) to species R similarly located. The effect is to make fi dependent on the value of 2 and hence on any changes in the electrical double layer. This type of analysis has permitted some detailed interpretations to be made of kinetic schemes for electrode reactions and also connects that subject to the general one of this chapter. 

On the electrode side of the double layer the excess charges are concentrated in the plane of the surface of the electronic conductor. On the electrolyte side of the double layer the charge distribution is quite complex. The potential drop occurs over several atomic dimensions and depends on the specific reactivity and atomic stmcture of the electrode surface and the electrolyte composition. The electrical double layer strongly influences the rate and pathway of electrode reactions. The reader is referred to several excellent discussions of the electrical double layer at the electrode—solution interface (26-28). 

Electrically, the electrical double layer may be viewed as a capacitor with the charges separated by a distance of the order of molecular dimensions. The measured capacitance ranges from about two to several hundred microfarads per square centimeter depending on the stmcture of the double layer, the potential, and the composition of the electrode materials. Figure 4 illustrates the behavior of the capacitance and potential for a mercury electrode where the double layer capacitance is about 16 p.F/cm when cations occupy the OHP and about 38 p.F/cm when anions occupy the IHP. The behavior of other electrode materials is judged to be similar. 

In some cases, e.g., the Hg/NaF q interface, Q is charge dependent but concentration independent. Then it is said that there is no specific ionic adsorption. In order to interpret the charge dependence of Q a standard explanation consists in assuming that Q is related to the existence of a solvent monolayer in contact with the wall [16]. From a theoretical point of view this monolayer is postulated as a subsystem coupled with the metal and the solution via electrostatic and non-electrostatic interactions. The specific shape of Q versus a results from the competition between these interactions and the interactions between solvent molecules in the mono-layer. This description of the electrical double layer has been revisited by... 

If a bar of zinc is dipped into a solution of zinc sulphate, the former acquires a negative, the latter a positive charge, and a difference of potential is established at the boundary the magnitude of which depends on the concentration of the solution. There is in fact an electrical double layer produced, which is formed of negative charges on the metal (which has lost ions into the solution) ... 

For an ideally polarizable electrode, q has a unique value for a given set of conditions.1 For a nonpolarizable electrode, q does not have a unique value. It depends on the choice of the set of chemical potentials as independent variables1 and does not coincide with the physical charge residing at the interface. This can be easily understood if one considers that q measures the electric charge that must be supplied to the electrode as its surface area is increased by a unit at a constant potential." Clearly, with a nonpolarizable interface, only part of the charge exchanged between the phases remains localized at the interface to form the electrical double layer. 

The interaction between two double layers was first considered by Voropaeva et a/.145 These concepts were used to measure the friction between two solids in solution. Friction is proportional to the downward thrust of the upper body upon the lower. However, if their contact is mediated by the electrical double layer associated with each interface, an electric repulsion term diminishes the downward thrust and therefore the net friction. The latter will thus depend on the charge in the diffuse layer. Since this effect is minimum at Eam0, friction will be maximum, and the potential at which this occurs marks the minimum charge on the electrode. 

In the second group of models, the pc surface consists only of very small crystallites with a linear parameter y, whose sizes are comparable with the electrical double-layer parameters, i.e., with the effective Debye screening length in the bulk of the diffuse layer near the face j.262,263 In the case of such electrodes, inner layers at different monocrystalline areas are considered to be independent, but the diffuse layer is common for the entire surface of a pc electrode and depends on the average charge density <7pc = R ZjOjOj [Fig. 10(b)]. The capacitance Cj al is obtained by the equation... 

The electrical double-layer structure and fractal geometry of a pc-Ag electrode have been tested by Se vasty an ov et al.272 They found that the geometrical roughness of electrochemically polished pc-Ag electrodes is not very high (/pz 1.5 to 1.25), but the dependence of Chtr curves on cej, as well as on/pz, is remarkable (C, =30 to 80 fi cm-2 if/pz =1.5 to 1.0). 

The temperature dependence of the electrical double-layer parameters has been determined for real393,398 as well as quasi-perfect Ag planes.382,394 For quasi-perfect Ag electrodes, the value of 3 ffa0/9rhas been found to be higher for Ag(100) than for Ag(lll), and so it was concluded that Ag(lll) is more hydrophilic than Ag(100). For real surfaces,382,385,386 dEff=0/BT increases in the order (110) < (100) <(111). The same order of planes has been observed for Au 446-448 BEa /BT linearly increases as AX (interfacial parameter) decreases, i.e., as the hydrophilicity of Ag and Au electrodes decreases.15 32 393 397 398 446 48... 

The dependence of the electrical double-layer parameters of pc-Cd on temperature (0 to 85 °C) has been studied647,648 in H2O + KF solutions. The Emin depends slightly on T, the temperature coefficient BEmiri/dT being 0.15 mV K"1. C,-at cr < -0.09 C m 2has been found to decrease as the temperature increases. C, rises if a decreases and at a = 0 the inner-layer temperature coefficient BCt/BT is equal to 0.05 8//F cm-2 K 1. It has been pointed out that the intersection point of Ch a curves at various temperatures lies at a less negative a than the charge at which the C a curves have the minimum value. The same is the case with pc-Pb electrodes,649 but for Hg/H20 the opposite is observed.305... 

The temperature dependence of the electrical double-layer parameters has been studied for Cd(OOOl).662 The positive value of dEa=0/dT (0.33 0.03 mV K-1) is taken to indicate that the H20 dipoles are oriented with their negative end toward the metal surface.121,663 The value of 9Ea=0/dT increases in the order Ag(l 11) < Ag(100) < Cd(0001), which is explained in terms of enhanced disorientation of physically adsorbed H20 dipoles in the same order.662... 

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-... 

In the region of a very good correspondence has been found between experimental and calculated C,E curves and this has been taken to indicate that the electrical double-layer structure conforms to the GCSG theory. Comparison of the ChE curves for Hg/TMU and Fe/TMU shows that the dependence of Cf on E is less pronounced for an Fe electrode than for Hg/TMU, and the values of Cf for Fe are remarkably lower than for Hg. The same is the case for Fe/DMF, DMAA, MPF, and HMPA interfaces.732-736... 

The electrical double-layer structure of a Pt/DMSO interface has been investigated using the potentiostatic pulse method.805 The value of C at E = const, as well as the potential of the diffuse layer minimum, have been found to depend on time, and this has been explained by the chemisorption of DMSO dipoles on the Pt surface, whose strength depends on time. Eg=Q has been found11 at E = -0.64 V (SCE in H2O). 

Anodically polished and then cathodically reduced Cd + Pb alloys have been studied by impedance in aqueous electrolyte solutions (NaF, KF, NaC104, NaN02, NaN03).827 For an alloy with 2% Pb at cNap 0.03 M, Emfo = -0.88 V (SCE) and depends on cNaF, which has been explained by weak specific adsorption of F" anions. Surface activity increases in the sequence F" < CIO4 < N02. The Parsons-Zobel plot at E is linear, with /pz = 1.33 and CT° = 0.31 F m"2. Since the electrical double-layer parameters are closer to those for pc-Pb than for pc-Cd, it has been concluded that Pb is the surface-active component in Cd + Pb alloys827 (Pb has a lower interfacial tension in the liquid state). 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

Equation 46 suggests that, maintaining pi constant, q, must depend linearly on if only a first-order electroviscous effect exists, and an increase in the electrolyte concentration implies a decrease in the thickness, 1/k, of the electrical double layer. 

Surface forces measurement is a unique tool for surface characterization. It can directly monitor the distance (D) dependence of surface properties, which is difficult to obtain by other techniques. One of the simplest examples is the case of the electric double-layer force. The repulsion observed between charged surfaces describes the counterion distribution in the vicinity of surfaces and is known as the electric double-layer force (repulsion). In a similar manner, we should be able to study various, more complex surface phenomena and obtain new insight into them. Indeed, based on observation by surface forces measurement and Fourier transform infrared (FTIR) spectroscopy, we have found the formation of a novel molecular architecture, an alcohol macrocluster, at the solid-liquid interface. 

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