Interfacial model

Mechanisms of Sorption Processes. Kinetic studies are valuable for hypothesizing mechanisms of reactions in homogeneous solution, but the interpretation of kinetic data for sorption processes is more difficult. Recently it has been shown that the mechanisms of very fast adsorption reactions may be interpreted from the results of chemical relaxation studies (25-27). Yasunaga and Ikeda (Chapter 12) summarize recent studies that have utilized relaxation techniques to examine the adsorption of cations and anions on hydrous oxide and aluminosilicate surfaces. Hayes and Leckie (Chapter 7) present new interpretations for the mechanism of lead ion adsorption by goethite. In both papers it is concluded that the kinetic and equilibrium adsorption data are consistent with the rate relationships derived from an interfacial model in which metal ions are located nearer to the surface than adsorbed counterions. 

Nafion is characterized by its multi-phase structure (30). The interfacial model (31) includes three domains a Teflon-like hydrophobic fluorocarbon phase, an... 

Recalling that x is defined for the movement of a test charge from vacuum into the metal, and defining in the same way for movement of a test charge from solution into the metal, is a positive quantity at the PZC. As 0 increases from negative values to positive ones, becomes smaller. As a result, is a negative quantity. Its role in the overall picture of the electrical double layer is to introduce the polarizability of the metal s electronic cloud into the interfacial model. The net capacity of the inner layer with consideration of the metal is now... 

G. Frontiers of interfacial modeling References and notes for Chapter 7... 

A rough but instructive approximation for the temperature dependence of y(T) below Tg will be presented in Section 7.E. The new correlation for Ps will be developed, and its predictive use demonstrated, in Section 7.F. Finally, some new directions in research at the frontiers of interfacial modeling will be highlighted in Section 7.G. 

Figure 10-16. Interfacial model of mica surfaces covered with adsorbed monolayers of stearic acid.

This idea is a consequent transfer of the three-dimensional van der Waals equation into the interfacial model developed by Cassel and Huckel (cf. Appendix 2B.1). The advantages of Frumkin s position is a more realistic consideration of the real properties of a two-dimensional surface state of the adsorption layer of soluble surfactants. This equation is comparable to a real gas isotherm. This means that the surface molecular area of the adsorbed molecules are taken into consideration. Frumkin (1925) additionally introduced, on the basis of the van der Waals equation, the intermolecular interacting force of adsorbed molecules represented by a . 

This interfacial model (2-4, 6-8, 15, 16), first suggested by Stem (29), can be treated by extending the considerations of the last section. The Poisson-Boltzmann equation,... 

In the second class are interfacial models, in which it is assumed that essentially all the amphiphiles in the system are part of a monolayer or a bilayer. These models are restricted to... 

The two classes of models should be considered to be complementary descriptions of amphiphilic systems. Microscopic models can describe self-assembly and explicate the differences between weak and strong amphiphiles. Interfacial models describe very strong amphiphiles and emphasize their universal behavior. 

We have already mentioned in the Introduction that microemulsions containing long-chain amphiphiles can be described by interfacial models. These models are based on the curvature elasticity of the amphiphilic monolayer and thus contain as material parameters the bending rigidity and the saddle-splay modulus. These parameters have to be calculated from a more microscopic model. A somewhat similar problem occurs in the... 

The same conclusion was reached by Golubovic and LubenslQ [121], based on an interfacial model of lamellar phases. 

We want to mention parenthetically that the characteristic shape of the one-phase region of the lamellar phase in the Cio E5-water-octane phase diagram can also be understood from a calculation based on an interfacial model of membranes [174]. In this model, the undulation modes are responsible for the swelling of the lamellar phase a disordered phase (which is modeled as a dilute droplet phase for simplicity) competes with the symmetric lamellar phase in the lower part of the phase triangle. 

The joint use of the aforementioned adsorption-electrochemical and spectroscopic techniques, over a wide range of impregnation parameters, allows the predominant mode of interfacial deposition and the interface speciation/structure of the deposited precursor species to be approached, for each value of these parameters. The next step is to use this information, and eventually information drawn from quantum-mechanical calculations, in order to depict several tentative pictures for the interface, for a given set of impregnation parameters. These pictures should be tested quantitatively by applying the proper combination of a surface ionization/interfacial model. 

Another way to treat an ion-transfer reaction is to consider the reaction as an elementary jump across a thin interfacial layer, which we will call the reaction plane, but it may also be called inner layer or mixed-solvent layer depending on the interfacial model used. The interface (about 1 nm thick) comprises back-to-back diffuse layers. 

FIG. 7 The latent heat AQ per cubic centimeter of sample volume for the transition lam — Li is plotted as a function of ( )s at a fixed ratio < )o/< >w = 5.67. The squares are obtained from the calorimetric spectra, and the solid line is the prediction of Eq. (12) for the heat changes obtained from the interfacial model [29]. The inset shows the location of the sample compositions in the Gibbs phase triangle. 

Theoretical analysis can be used to estimate the possible ultrasonic response function for various frequency input waves as they interact with these three interfacial models. One method... 

N. R. Bernardino, A. 0. Parry, C. Rascon, and J. M. Romero-Enrique, Derivation of a non-local interfacial model for 3D wetting in an external field,/. Phys. Condens. Matter, 21,465105 (2009]. 

To achieve a more precise understanding of the swelling behavior of EAPs, multiple models incorporating microscale properties have been developed by many authors. These so-called mesoscale models are based on the principles of modem continuum mechanics. In the present review, modeling approaches based on porous media, mass transport, as well as an interfacial model are considered. 

Random disturbance interfacial model, in which the disturbed points are stochastic. 

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