Space charge models

To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic-aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy-Chapman theory [31,34]. 

Guo et al. " proposed that there exists a de-doping effect in nanometer-thick YSZ films, which results in a lower bulk conductivity in nanocrystalline YSZ (grain size 80 nm, thickness = 12 and 25 nm) than in the microcrystalline specimen. They predicted that the conductivity of nanostructured YSZ (e.g., <5 nm) will be even smaller, analyzing from a space charge model. Because XRD results were not provided, neither the crystallinity nor the existence of the second phase is known in YSZ films grown by Pulsed Laser Deposition (PLD). However, electrical measurements were carefully carried out in both dry and wet O2, and the overall conductivity in their YSZ films is lower than that of bulk YSZ (grain size > 15 pm) by a factor of 4 (figure 10.8). 

According to the space charge model (SC), when a solution is flowing in the porous structure under a pressure gradient, pore wall is reduced to the Stern-surface between the static and the mobile portions of solution. The pore radius equivalent to the Stern-surface is called hydrod5mamic radius Tk with... 

X.L.Wang, T. Tsuru, S.-I. Nakao and S. Kimura, Electrolyte transport through nanofiltration membranes by the Space Charge Model and the comparison with Teorell-Meyer-Sievers model. /. Membr. Sci., 103 (1995)117. 

The chapter begins with a review of space charge models, and how standard assumptions must be modified to address shrinkage in dimensions to the nanoscale. 

While the improvement of ionic conductivity via an insulating phase may appear counterintuitive, the concept was first discussed with respect to the space charge model by Wagner [53]. A thorough review and analysis of this effect was later presented by Maier [17]. The conductivity enhancement in systems such as LiI Al203... 

Tschdpe, A. (2001) Grain size-dependent electrical conductivity of polycrystalline cerium oxide. 11 Space charge model. Solid State Ionics, 139, 267-280. 

We have seen that the picture is always simple if the charge density is independent of the component potential. This then applies on account of Eq. (5.252) also for the enriched defect at x=0, in our example for 0. For mass action reasons, the concentration of the counterdefect (Vq) is also constant. However, electronic charge carriers — as minority species — are, as in the bulk case, appreciably dependent on the component potential. In our example Nh-,o = 1/4, while in the bulk Nh oo = 1/6-In such cases then, it is in fact possible within the framework of our simple core-space charge model to express Ck(x=s) and in simple cases C c(x=0) too in the form of the bulk relationship Eq. (5.150)... 

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