Diffuse double layer, model electrochemical interface

Figure 2. Three models of the electrochemical interface (a) the Helmholtz fixed (rigid) double layer, 1879 (b) the Gouy-Chapman diffuse double layer 1910-1913 (c)the Stern double layer, 1924, being a combination of the Helmholtz and the Gouy-Chapman concepts.

Another difference between an electrochemical reaction and a catalytic reaction is that a so-called electrical double layer will form as the appearance of electrostatic potential gradient in the interface of electrolyte solution and electrode (conductor). Graham summarized in more detail the electrical double layer in 1947. He considered that this electrostatic potential, i.e. the double layer potential, is different from the electrode potential. He also discussed and observed in detail the double layer potential of Hg-electrode-water solution system. He found that it could not observe such potential when electrode reaction occurred while the ideal polarization happened in a wide range of electrode potential if there was no electrode reaction. Hg is a liquid and it is thus easy to observe its surface tension and calculate the relationship between surface tension and double layer potential. Therefore, its structure is clearer. The structure of electrical double layer is composed of Helmholz layer and diffusion layer. The Helmohloz face is located between Helmholz layer and diffusion layer. The external of Helmohloz face is diffusion double layer. The model of Helmholz electrical double layer corresponds to simple parallel-plate capacitor. According to its equation, it can quantitatively describe the structure of diffusion double layer. 

A similar approach to the boundary condition for the potential at the metal-solution interface has been applied by Biesheuvel et al., in consideration of diffuse charge effects in galvanic cells, desalination by porous electrodes, and transient response of electrochemical cells (Biesheuvel and Bazant, 2010 Biesheuvel et al., 2009 van Soestbergen et al., 2010). However, their treatment neglected the explicit effect of In principle, the PNP model could be modified to incorporate size-dependent and spatially varying dielectric constants in nanopores, as well as ion saturation effects at the interface. However, in a heuristic fashion, such variations could be accounted for in the Helmholtz capacitance of the Stern double layer model. 

Figure 5.11. (a) Electrical equivalent circuit model used to represent an electrochemical interface undergoing corrosion in the absence of diffusion control. Rp is the polarization resistance, Cpi is the double layer capacitance, Rp is the polarization resistance, and R, is the solution resistance [15]. (b) Electrical equivalent circuit model when diffusion control applies W is the Warburg impedance [13]. 

The typical IL system could be considered as a solvent-free system, in which it can simplify the EIS analysis significantly which spurs its wide use in the characterization of the IL-electrode interface. However, due to low mobility of ions in an IL and multiple molecular interactions present in an IL, more time is needed to reach to a steady state of IL-electrode interface structure and arrangement, when a potential is applied. Furthermore, the electron-transfer process in ILs is different from that in traditional solvents containing electrolytes. Thus, the interfacial structures of IL are more complex than other systems. Even the electrode geometry could affect the EIS results of IL systems. It is noted that the bulk ILs could not be simply described by a resistor (R ) as in classic electrochemical systems. And the electrode double layer in IL electrolyte couldn t be simply depicted as a capacitor. So the Randle equivalent circuit is not sufficient to describe an IL system. Significant efforts have been made to illustrate the properties of diffusion layer and the bulk ILs with equivalent circuits. However, currently there is no general equivalent circuit model to describe the interface of an IL system. 

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