Electric double layer composition

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. 

Cd + Bi alloy electrodes (1 to 99.5% Bi) have been prepared by Shuganova etal. by remelting alloy surfaces in a vacuum chamber (10-6 torr) evacuated many times and thereafter filled with very pure H2. C dispersion in H20 + KF has been reported to be no more than 5 to 7%. C at Emin has been found to be independent of alloy composition and time. The Emin, independent of the Bi content, is close to that ofpc-Cd. Only at a Bi content 95% has a remarkable shift of toward less negative E (i.e., toward o ) been observed. This has been explained by the existence of very large crystallites (10-4 to 10-3 cm) at the alloy surface. Each component has been assumed to have its own electrical double layer (independent electrode model262,263). The behavior of Cd + Bi alloys has been explained by the eutectic nature of this system and by the surface segregation of Cd.826,827... 

Various pc electrode models have been tested.827 Using the independent diffuse layer electrode model74,262 the value of E n = -0.88 V (SCE) can be simulated for Cd + Pb alloys with 63% Pb if bulk and surface compositions coincide. However, large deviations of calculated and experimental C,E curves are observed at a 0. Better correspondence between experimental and calculated C,E curves was obtained with the common diffuse-layer electrode model,262 if the Pb percentage in the solid phase is taken as 20%. However, the calculated C, at a Ois noticeably lower than the experimental one. It has been concluded that Pb is the surface-active component in Cd + Pb alloys, but there are noticeable deviations from electrical double-layer models for composite electrodes.827... 

Emersion has been shown to result in the retention of the double layer structure i.e, the structure including the outer Helmholtz layer. Thus, the electric double layer is characterised by the electrode potential, the surface charge on the metal and the chemical composition of the double layer itself. Surface resistivity measurements have shown that the surface charge is retained on emersion. In addition, the potential of the emersed electrode, , can be determined in the form of its work function, , since and represent the same quantity the electrochemical potential of the electrons in the metal. Figure 2.116 is from the work of Kotz et al. (1986) and shows the work function of a gold electrode emersed at various potentials from a perchloric acid solution the work function was determined from UVPES measurements. The linear plot, and the unit slope, are clear evidence that the potential drop across the double layer is retained before and after emersion. The chemical composition of the double layer can also be determined, using AES, and is consistent with the expected solvent and electrolyte. In practice, the double layer collapses unless (i) potentiostatic control is maintained up to the instant of emersion and (ii) no faradaic processes, such as 02 reduction, are allowed to occur after emersion. 

The central issue which has to be addressed in any comprehensive study of electrode-surface phenomena is the determination of an unambiguous correlation between interfacial composition, interfacial structure, and interfacial reactivity. This principal concern is of course identical to the goal of fundamental studies in heterogeneous catalysis at gas-solid interfaces. However, electrochemical systems are far more complicated since a full treatment of the electrode-solution interface must incorporate not only the compact (inner) layer but also the boundary (outer) layer of the electrical double-layer. The effect of the outer layer on electrode reactions has been neglected in most surface electrochemical studies but in certain situations, such as in conducting polymers and... 

In recent several years, super-capacitors are attracting more and more attention because of their high capacitance and potential applications in electronic devices. The performance of super-capacitors with MWCNTs deposited with conducting polymers as active materials is greatly enhanced compared to electric double-layer super-capacitors with CNTs due to the Faraday effect of the conducting polymer as shown in Fig. 9.18 (Valter et al., 2002). Besides those mentioned above, polymer/ CNT nanocomposites own many potential applications (Breuer and Sundararaj, 2004) in electrochemical actuation, wave absorption, electronic packaging, selfregulating heater, and PTC resistors, etc. The conductivity results for polymer/CNT composites are summarized in Table 9.1 (Biercuk et al., 2002). 

Figure 12. Voltage levels in the various sections of the unit cell of a battery, fuel cell, or electrochemical capacitor. The structure and composition of the electrical double layer differ at the anode and cathode.

The Helmholtz-von Smoluchowski equation indicates that under constant composition of the electrolyte solution, the EOF depends on the magnitude of the zeta potential, which is determined by various factors inhuencing the formation of the electric double layer, discussed above. Each of these factors depends on several variables, such as pH, specihc adsorption of ionic species in the compact region of the double layer, ionic strength, and temperature. 

Problems 2 and 3 are of direct relevance for an adequate understanding of concentration polarization at, respectively, composite heterogeneous and homogeneous permselective membranes. The main difference between these formulations is that in Problem 2, relevant for a composite heterogeneous membrane, the motion in a pore of the support is induced by the electro-osmotic slip due to the interaction of the applied electric field with the space charge of the electric double layer which is present already at equilibrium. 

When the solid is immersed directly in water, all these steps occur simultaneously. If the surface area is high, the development of the electrical double layer may lead to large changes in solution composition and pH. 

The composition of the insoluble compound (precipitate) obtained from the analyte must be known and stable. Poorly soluble substances may form colloidal suspensions (particle diameters from 10 7 to 10 4 cm). The formation of a colloidal suspension can be minimized or prevented by carrying out the precipitation from a dilute solution of the analyte, at a temperature close to the boiling point of water and with constant stirring. The relative supersaturation affects the particle size and is expressed as Q - S/S, where Q is the instantaneous concentration of the added species and S is the equilibrium solubility of the compound that precipitates. Particle size seems to be inversely proportional to relative supersaturation. The electric double layer formed during precipitation keeps the colloidal precipitate particles from coming into contact with each other, thus preventing further coagulation. 

Much work on these composite systems has to be done, For example, we have not considered yet the study of phenomena occurring at the surface of an electrified metal the version of PCM for ionic solutions [10] has been available for a longtime, but the modeling of the electric double layer has not been done yet (every new modeling requires considerable intellectual and computational efforts). 

The composition of this chapter is based on a well-known and well-understood model of the electrical double layer and therefore does not pretend to enhance overall understanding. It does, however, aim to answer the question of whether a useful mathematical technique exists that may allow for a numerical, if not analytical, description of the double layer for a surface of arbitrary shape and topography. It is fair to say that the colloid scientist ultimately seeks a quantitative description of the electrical double layer for whatever reason. The task then now faced is to uncover the most appropriate theoretical method of calculating the electrical double layer properties for a given nonideal situation. Here we suggest a few methods that may help in this respect. 

The structure electrical double layer at the silica-aqueous electrolyte interface was one of the earlier examined of the oxide systems. At the beginning the investigations were performed with application of electrokinetic methods next, with potentiometric titrations. The properties of this system were very important for flotation in mineral processing. Measurements proved that pHpZC and pHiep are equal to 3, but presence of some alkaline or acidic contaminants may change the position of these points on pH scale. Few examples, concerning edl parameters are shown in Table 3. Presented data concern a group of systems of different composition of the liquid phase and solid of a different origin. The latest measurements of this system takes into account the kinetics of the silica dissolution [152], and at zeta measurements, also the porosity of dispersed solid [155]. 

In order to determine a system thermodynamically, one has to specify some independent parameters (e.g. N, T, P or V) besides the composition of the system. The most common choice in MC simulation is to specify N, V and T resulting in the canonical ensemble, where the Helmholtz free energy A is the natural thermodynamical potential. However, MC calculations can be performed in any ensemble, where the suitable choice depends on the application. It is straightforward to apply the Metropolis MC algorithm to a simple electric double layer in the iVFT ensemble. It is however, not so efficient for polymers composed of more than a few tens of monomers. For long polymers other algorithms should be considered and the Pivot algorithm [21] offers an efficient alternative. MC simulations provide thermodynamic and structural information, but time-dependent properties are not accessible. If kinetic or time-dependent properties are of interest one has to use molecular dynamic or brownian dynamic simulations. 

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