Diffuse double layer 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. 

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). 

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. 

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. 

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