Verwey-Niessen theory

The basic system consists of two immiscible solvents, each of which contains a salt that is badly solvable in the other solvent. When a potential difference is applied between the two solutions, opposing space charge layers form on both sides of the interface and give rise to a capacity. The simplest model consists of two diffuse double layers back to back, which are described by the GC theory - in the context of liquid-liquid interfaces this model is known as the Verwey-Niessen theory [76]. 

The Verwey-Niessen model gives a reasonable first approximation, but at a closer glance significant deviations are observed even at low ionic concentrations, where this theory is expected to hold. Surprisingly, at low (<10 M) concentrations the experimental capacity is often higher than that predicted by Verwey-Niessen theory - this is just the opposite to the behavior of metal-solution interfaces, where the capacity is always ioiver than the GC value. 

The concept of capillary wave explains the increase of the interfacial capacity beyond the Verwey-Niessen limit, and thus helps in understanding the structure of the interface. A quantitative interpretation of experimental data within this model is, however, difficult since there are other causes for the deviations from Verwey-Niessen theory besides the surface roughness. 

In 2005, an interesting critical summary of the current knowledge on capacitance measurements and potential distribution, together with a new model, was published by Monroe et al. [64]. In this work, the good old Verwey-Niessen theory was extended to allow ionic penetration at the interface. With this adaptation, several features could be accounted for, such as asymmetry and shifts of the capacitance minimnm, that could not be described by the classical Gouy-Chapman or Verwey-Niessen theories. Gibbs energies of ion transfer were used as input parameters to describe ionic penetration into the mixed-solvent interfacial layer, and experimental data were successfully reproduced. 

The Gouy-Chapman theory for metal-solution interfaces predicts interfacial capacities which are too high for more concentrated electrolyte solutions. It has therefore been amended by introducing an ion-free layer, the so-called Helmholtz layer, in contract with the metal surface. Although the resulting model has been somewhat discredited [30], it has been transferred to liquid-liquid interfaces [31] by postulating a double layer of solvent molecules into which the ions cannot penetrate (see Fig. 17) this is known as the modified Verwey-Niessen model. Since the interfacial capacity of liquid-liquid interfaces is... 

These deviations were first explained by the presence of a compact, ion-free layer at the interface this is known as the modified Verwey-Niessen model. Obviously, the presence of an ion-free layer can only reduce the capacity, so the theory had to be modified further. For a few systems a consistent interpretation of the experimental capacity was achieved [78-80] by combining this model with the soolled modified Poisson-Boltzmann (MPB) theory [81], which attempts to correct the GC theory by accounting for the finite size of the ions and for image effects, while the solvent is still treated as a dielectric continuum. The combined model has an adjustable parameter, so it is difficult to judge whether the agreement with experimental data is significant. The existence... 

Verwey and Niessen first described the EDLat ITIES as two noninteracting diffuse layers, one at each side of the interface [9]. Both solvents were assumed to be structureless media with macroscopic dielectric permittivities, and potential distribution in the EDL was defined by Gouy-Chapman theory. 

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