Double layer structure model

Figure 4. a) Model for the double-layer structure on Pt(lll) as viewed both normal to (111) plane and parallel to the (111) plane at the potential 0TOin. The potential 0ro n is defined in the voltammetry curve in b). 

The presence of the diffuse layer determines the shape of the capacitance-potential curves. For a majority of systems, models describing the double-layer structure are oversimplified because of taking into account only the charge of ions and neglecting their specific nature. Recently, these problems have been analyzed using new theories such as the modified Poisson-Boltzmann equation, later developed by Lamper-ski. The double-layer capacitanties calculated from these equations are... 

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. 

What is dear from this introduction is that the journey into the area of metal deposition from ionic liquids has tantalizing benefits. It is also dear that we have only just begun to scratch the surface of this topic. Our models for the physical properties of these novel fluids are only in an early state of devdopment and considerably more work is required to understand issues such as mass transport, spedation and double layer structure. Nudeation and growth mechanisms in ionic liquids will be considerably more complex than in their aqueous counterparts but the potential to adjust mass transport, composition and spedation independently for numerous metal ions opens the opportunity to deposit new metals, alloys and composite materials which have hitherto been outside the grasp of electroplaters. 

The only models that exist for double layer structure in ionic liquids suggest a Helmholz layer at the electrode/solution interface [103, 104], If the reduction potential is below the point of zero charge (pzc) then this would result in a layer of cations approximately 5 A thick across which most of the potential would be dropped, making it difficult to reduce an anionic metal complex. Hence, the double layer models must be incorrect. 

The concept of double layer structure is far from being well established and evaluated. The models presented above give emphasis to electrostatic considerations. Chemical models have been developed that consider the electronic distribution of the atoms in the electrode, which is related to their work function. This was only possible after experimental... 

Various theories have been proposed to describe and interpret the adsorption of metal ions at hydrous oxide interfaces (10). Most models have stressed either the double layer structure and ion-solvent interactions (11, 12, 13) or surface coordination reactions with amphoteric functional groups (14, 15, 16). Recently Davis (17) and Davis and Leckie (18, 19)... 

Our approach combined concepts from models which emphasize specific chemical interactions of solutes with oxide surfaces O, and those with well-defined electrical double layer structure (, 10). Since the model and computational procedure... 

Liposomes, Vesicles and Cast Films - Supramolecular Assemblies Based on Lipid Bilayers Amphiphilic molecules or lipid molecules sometimes form double-layer structures. This structure is called a bilayer structure, and it can be used to model a cell membrane. 

The relationship between electrophoretic mobility and zeta potential depends on the model of the electrochemical double-layer structure used. 

Fig. 2. Double layer structure water dipole model (44).

Expression (V.25), referred to as the Helmholtz-Smoluchowski equation, relates the rate of relative phase displacement to some potential difference, Acp, within the electrical double layer. In order to understand the nature of this quantity, let us examine in detail the mutual phase displacement due to the external electric field acting parallel to the surface, taking into account the electrical double layer structure. Let us assume that the solid phase surface is stationary. Figure V-7 shows the distributions of the potential, cp(x ) (line 1), the rate of displacement of the liquid layers relative to the surface in the Helmholtz model, u(x) (line 1/), and the true distribution of the potential in the double layer (curve 2). 

Spohr describes in detail the use of computer simulations in modeling the metal/ electrolyte interface, which is currently one of the main routes towards a microscopic understanding of the properties of aqueous solutions near a charged surface. After an extensive discussion of the relevant interaction potentials, results for the metal/water interface and for electrolytes containing non-specifically and specifically adsorbing ions, are presented. Ion density profiles and hydration numbers as a function of distance from the electrode surface reveal amazing details about the double layer structure. In turn, the influence of these phenomena on electrode kinetics is briefly addressed for simple interfacial reactions. 

Models for Double-Layer Structure 547 The total charge per unit volume in any lamina is then... 

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