Layer, compact diffusion

Combustion, 27 189, 190 reaction, sites for, 33 161-166 reaction scheme, 27 190, 196 Commercial isomerization, 6 197 CoMo catalysts, 40 181 See also Cobalt (nickel)-molybdenum-sulfide catalysts Compact-diffuse layer model, 30 224 Compensation behavior, 26 247-315 active surface, 26 253, 254 Arrhenius parameters, see Arrhenius parameters... 

An adsorbed layer of water molecules at the interface separates hydrated ions from the solid surface. The interfacial electric double layer can be represented by a condenser model comprising three distinct layers a diffuse charge layer in the ionic solution, a compact layer of adsorbed water molecules, and a diffuse charge layer in the solid as shown in Fig. 5-8. The interfacial excess charge on the... 

Fig. 5-8. Diffuse charge layer on the solution side of metal electrode M = electrode metal S = aqueous solution HL = compact layer (Helmholtz layer) DL = diffuse charge layer x distance from the outer Helmholtz plane (OHP).

Figure 5.8 Schematical illustration of the structure and distatic-charge-layer of colloidal particle of alkali silica sol. 3 compact layer A diffuse layer

Fig. 1. Schematic potential distribution across the compact diffuse layer (/> , metal potential i/im-p potential at the outer Helmholtz plane (OHP) tt>, electrolyte potential.

The potential distribution of Fig. 1 is typical of the compact-diffuse layer models (42-44). The potential varies almost linearly within the compact double layer, decaying exponentially within the diffuse layer. The thickness of the latter depends on the electrolyte ionic strength and becomes negligible in strong electrolytic solutions (42). This feature becomes important in electrocatalytic studies, since it is the potential difference (0 — < e) that can be measured or fixed experimentally versus a reference electrode, while reacting ions and molecules experience a potential difference ((j) —... 

Figure 3 The solid/aqueous solution interface and electrical double layer for a hydrolyzed oxide surface o, charge density V /, electrostatic potential +, cation anion, 0, surface c, compact layer d, diffuse layer.

Atomic Polarization Fields Ionic Fields Electric Dipole Fields The Helmholtz Planes Diffuse Double Layer Compact Double Layer Potential Transients Constant Current Constant Potential Faradaic Processes Non-Faradaic Ideal Polarizable... 

Figure 1.6 (a) Structure of the double layer at the electrode/solution interface. Note the highly ordered structure of the compact layer the diffuse layer is less ordered but is not the random arrangement of the solution away from the interface, (b) Potential field resulting from this model. 

The attack of most glasses in water and acid is diffusion controlled and the thickness of the porous layer formed on the glass surface consequently depends on the square root of the time. There is ample evidence that the diffusion of alkali ions and basic oxides is thermally activated, suggesting that diffusion occurs either through small pores or through a compact body. The reacted zone is porous and can be further modified by attack and dissolution, if alkali is still present, or by further polymerisation. Consolidation of the structure generally requires thermal treatment. 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

The total charge of the compact and diffuse layers equals (and is opposite in sign to) the net charge on the electrode side. The potential-distance profile across the double-... 

The capacitance of the double layer consists of combination of the capacitance of die compact layer in series with that of the diffuse layer. For two capacitors in series, the total capacitance is given by... 

The traditional treatment of a double layer at electrode-electrolyte interfaces is based on its separation into two series contributions the compact ( Helmholtz ) layer and the diffusive ( dif ) layer, so that the inverse capacitance is... 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

On the basis of this model, the overall differential capacity C for a system without specific adsorption, i.e. if the compact layer does not contain ions, is divided into two capacities in series, one corresponding to the compact layer Cc and the other to the diffuse layer Cd ... 

The diffuse layer is formed, as mentioned above, through the interaction of the electrostatic field produced by the charge of the electrode, or, for specific adsorption, by the charge of the ions in the compact layer. In rigorous formulation of the problem, the theory of the diffuse layer should consider ... 

The charge density on the electrode a(m) is mostly found from Eq. (4.2.24) or (4.2.26) or measured directly (see Section 4.4). The differential capacity of the compact layer Cc can be calculated from Eq. (4.3.1) for known values of C and Cd. It follows from experiments that the quantity Cc for surface inactive electrolytes is a function of the potential applied to the electrode, but is not a function of the concentration of the electrolyte. Thus, if the value of Cc is known for a single concentration, it can be used to calculate the total differential capacity C at an arbitrary concentration of the surface-inactive electrolyte and the calculated values can be compared with experiment. This comparison is a test of the validity of the diffuse layer theory. Figure 4.5 provides examples of theoretical and experimental capacity curves for the non-adsorbing electrolyte NaF. Even at a concentration of 0.916 mol dm-3, the Cd value is not sufficient to permit us to set C Cc. 

For semiconductor electrodes and also for the interface between two immiscible electrolyte solutions (ITIES), the greatest part of the potential difference between the two phases is represented by the potentials of the diffuse electric layers in the two phases (see Eq. 4.5.18). The rate of the charge transfer across the compact part of the double layer then depends very little on the overall potential difference. The potential dependence of the charge transfer rate is connected with the change in concentration of the transferred species at the boundary resulting from the potentials in the diffuse layers (Eq. 4.3.5), which, of course, depend on the overall potential difference between the two phases. In the case of simple ion transfer across ITIES, the process is very rapid being, in fact, a sort of diffusion accompanied with a resolvation in the recipient phase. 

The formation of a membrane potential is connected with the presence of an electrical double layer at the surface of the membrane. For a thick, compact membrane, an electrical double layer is formed at both interfaces. The electrical double layer at a porous membrane is formed primarily in the membrane pores (see Section 6.2). The electrical double layer at thin membranes is formed on both membrane surfaces. It is formed by fixed ions on the surface of the membrane and the diffuse layer in the electrolyte. 

The primary characteristic necessary for a liner, cover, or cutoff wall is low permeability, which essentially enables them to slow down the seepage or diffusion of chemicals. Clay is therefore the main material used to construct these containment systems. The thickness and chemical compatibility of containment systems are of concern in assessing the performance of a system. For example, clay liners are constructed as a simple liner that is 2 to 5 ft thick. In composite and double liners, the compacted clay layers are usually between 2 and 5 ft thick, depending on the characteristics of the underlying geology and the type of liner to be installed. Regulations specify that the clay used can only allow water to penetrate at a rate of less than 1.2 in./yr. However, the effectiveness of clay liners can be reduced by fractures induced by freeze-thaw cycles, drying out, and the presence of some chemicals. 

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