Guoy-Chapman model

The above definition of the symmetric surface excess and the classical Guoy-Chapman model of the diffuse double layer are combined to show that the surface excess cannot be considered a surface concentration in the presence of an ionized monolayer on an impenetrable solid/liquid interface. 

Ions are considered to be held at the charged surface in a dijfuse double layer (the Guoy-Chapman model) in which the concentration of cations falls, and that of anions increases, with distance from the surface. In a reflnement of this, the Stern model introduces a layer of cations held directly on the surface of the soil component (Figure 13). Small cations, or dehydrated ions having lost their water of hydration, can sit at the surface and form a strong coulombic bond. This allows for the specificity described above. 

One of the first attempts at modeling SOFCs with KMC simulations was reported by Modak and Lusk [32]. In their study, their model was restricted to capture the behavior of the electrolyte, YSZ, as a function of the open-circuit voltage, and comparisons were made with analytical predictions (Guoy-Chapman model). The paper focused on the oxygen concentration distribution within the electrolyte at the TPB, the voltage profile across the electrolyte, and the electric field within the electrolyte. Furthermore, the influences of the temperature and relative permittivity of the electrolyte on these features were captured. In order to accelerate the convergence of the simulations and to facilitate comparison with analytic models, a one-dimensional (1-D) model was implemented, and the cathode and anode structures and reactions were completely neglected. 

The calculations were based on the Guoy-Chapman model for an electric double layer at the interface, a modified Stem model for the inner layer, and experimental input data for predicting the most likely cation-anion arrangement at the surface as shown below in Figure 7.15. The surface potential values 0 were measured and derived for the three ionic liquids mentioned above that had prositive values in the order of [BMIM][Bp4] > [BMIM][DCA] > [BMIM][MS] with potentials of 0.42, 0.37, and 0.14 V respectively. These surface potential values confirm that ionic liquids have a high charge density and different behavior at the interface versus the isotropically distributed molecules in the bulk. The surface potential at the interface includes ions in the Stern layer as well as the dipole contributions. The ion composition of the outer diffuse layer is assumed to give electroneutrality. 

Figure 19.7. The dependence of zeta potential on charge and electrolyte concentration for a 1 1 electrolyte according to the Guoy-Chapman model of the interface (Figure 19.1) and classical electrokinetic theory...

The double layer model of Helmholtz assumes fixed layer of charges on the electrode and the outer Helmholtz plane. This model has been modified by Guoy-Chapman analysis, which assumes that the ions of charge opposite of the charge on the electrode distribute themselves in a diffuse manner as shown in Figure 1.15. 

The micellar charge was also corroborated by the Guoy—Chapman diffused, double-layer model. At equilibrium, the surface charge of the micelle alters the ionic composition of the interface with respect to the bulk concentration. The difference between the actual proton concentration on the interface and the one measured at the bulk by pH electrode is observed as a pK shift of the indicator and is related with the Gouy-Chapman potential (Goldstein, 1972). 

Explain in your own words the differences between the Helmholtz, Guoy-Chapman, and Stem models of (he double layer. 

The potential arises from the difference in surface charges on the two sides of the two leaflets. A popular theory often employed is the Guoy-Chapman theory, which is based on a continuum model description of the solvent and employs the Poisson-Boltzmann equation. 

To study the ion diffusion within solid oxide electrolytes, Krishnamurthy et al. performed DFT calculations and KMC simulations of oxygen diffu-sivity in a YSZ electrolyte. Also, Modak and Lusk simulated the open-circuit voltage of a one-dimensional YSZ electrolyte model and then compared the predicted voltages and concentration profiles with an analytical Guoy-Chapman solution. Within the KMC model, many properties were predicted including the oxygen concentration distribution, the voltage profile, the local electric field, and the effects of the temperature and the relative permittivity. 

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