Solvent electrode bulk dielectric

For all kinds of transitions, the system tends to hesitate between order and disorder and is prone to exhibit thermodynamic fluctuations which reflect the search for a compromise between the simultaneous requirements for minimum energy and maximum entropy. As the conducting polymers are pseudo-one-dimensional/two-dimensional systems, the probability of thermodynamic fluctuation increases significantly, resulting in a decrease in the ordered phase. The basic concept is that all electrochemical reactions proceed by adsorption from solution. This amounts to the replacement of solvent molecules by substrate, a process which is simultaneously governed by solvent-electrode, solvent-solute and solute-electrode interactions. Water, which is the most common solvent, possesses a high dielectric constant and, as such, tends to reject at its bulk periphery all molecules with a low dielectric constant. 

The solvent also acts as a dielectric medium, which determines the field diji/dx and the energy of Interaction between charges. Now, the dielectric constant e depends on the inherent properties of the molecules (mainly their permanent dipole moment and polarizability) and on the structure of the solvent as a whole. Water is unique in this sense. It is highly associated in the liquid phase and so has a dielectric constant of 78 (at 25 C), which is much higher than that expected from the properties of the individual molecules. When it is adsorbed on the surface of an electrode, inside the compact double layer, the structure of bulk water is destroyed and the molecules are essentially immobilized... 

The simplest interpretation of the compact-layer capacitance is represented by the Helmholtz model of the slab filled with a dielectric continuum and located between a perfect conductor (metal surface) and the outer Helmholtz plane considered as the distance of the closest approach of surface-inactive ions. Experimental determination of its thickness, zh, may be based on Eq. (12). Moreover, its dielectric permittivity, h, is often considered as a constant across the whole compact layer. Then its value can be estimated from the values of the compact-layer capacitance, for example, it gives about 6 or 10 (depending on the choice of zh) for mercury-water interface, that is, a value that is much lower than the one in the bulk water, 80. This diminution was interpreted as a consequence of the dielectric saturation of the solvent in contact with the metal surface, its modified molecular structure or the effects of spatial inhomogeneity. The effective dielectric permittivity of the compact layer shows a complicated dependence on the electrode charge, which cannot be explained by the simple hypothesis of the saturation effects on one hand or by the unperturbed bulk-solvent nonlocal polarizability on the other hand. 

Here, kq = k /s where e is the dielectric constant of the bulk solvent and is the Debye length 9 stands for the Heaviside unit step function, which reflects here the distance of closest approach, I, of ions to the electrode [I is calculated from the edge of the metal skeleton). 

Equations (3.16) and (3.17) correspond to a simple model of a dielectric, homogeneous right up to the interface with the metal. On the basis of the properties of the double layer, it is usually assumed that a layer of solvent, having a permittivity much lower in value than in bulk, adjoins the electrode[222,223,230,231]. This effect was considered by Kharkats[232]. For an ion outside the dielectric layer, the value of Es is close to the value obtained with the help of (3.16) or (3.17). If, however, the ion is inside this layer. Eg has a considerably larger value. 

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