Four-layer model

Fig. 6.3 Four layer model for the OFRR vapor sensor. OD ring resonator outer diameter / polymer thickness d ring resonator wall thickness , n2, n2, and are the refractive indices for the medium inside (air), polymer, silica ring resonator, and medium outside (air), respectively...

To model this, Duncan-Hewitt and Thompson [50] developed a four-layer model for a transverse-shear mode acoustic wave sensor with one face immersed in a liquid, comprised of a solid substrate (quartz/electrode) layer, an ordered surface-adjacent layer, a thin transition layer, and the bulk liquid layer. The ordered surface-adjacent layer was assumed to be more structured than the bulk, with a greater density and viscosity. For the transition layer, based on an expansion of the analysis of Tolstoi [3] and then Blake [12], the authors developed a model based on the nucleation of vacancies in the layer caused by shear stress in the liquid. The aim of this work was to explore the concept of graded surface and liquid properties, as well as their effect on observable boundary conditions. They calculated the hrst-order rate of deformation, as the product of the rate constant of densities and the concentration of vacancies in the liquid. 

The four layer model (Bowden et ah, 1980 Bousse and Meindle, 1986) also locates different adsorbing ions in different planes. It has been used to model adsorption of phosphate, citrate and selenite (Bowden et ah, 1980) and borate (Bloesch et al., 1987) on goethite and competitive adsorption of Ca and Cd on ferrihydrite (Cowan et al., 1991). 

The GSM makes it possible to compute the dynamics of industrial C02 distribution between the oceans, terrestrial biota, and the atmosphere. The GSM describes the World Ocean as a spatial four-layer model with due regard for water chemistry. Spatial heterogeneity of the World Ocean is represented by the structural... 

In the four layer model of the edl, proposed by Charmas et al. (Fig. 4), the separate planes are assumed for the adsorbing specifically ions (cation and anion) of the background electrolyte [63]. According to this, for the compact layer the separate capacity is assumed, concerned with the adsorbing... 

With respect to whole cell biosensors utilising dissolved oxygen probes, Liang et al. reported a four-layer model to describe the signals from an oxygen probe used to transduce the respiratory activity of mouse leukaemia tumour cells [13]. This work was carried out with a view to using the biosensor to study the dynamic responses to various drugs. Finite difference methods were used to solve the material balances between the inner... 

If these issues can be addressed, then integrated searching becomes a fairly straightforward technical issue. Wild (2006) introduced a four-layer model of future life science information storage and use that is scalable to large volumes of information and that tackles some of these points. The layers are, as follows, with the main connection point to the chemical researcher being in the fourth layer ... 

Other models differentiate the inner-sphere complexation of hydrogen and hydroxide ions, other cations and anions, the outer-sphere complexation of cations and anions, and a diffuse layer. This demands the application of the four-layer model. 

Other publications postulate specific adsorption between the surface and the /3-plane. For example Barrow and Bowden [69] interpreted adsorption of anions on goethite in terms of the mentioned above four layer model. The four layers are (in order of increasing distance from the surface) surface layer (H" and OH ions), the layer of specifically adsorbed anions, the first layer of inert electrolyte counterions (analogous to the /3-layer in TLM). and diffuse layer. This model requires an additional adjustable parameter, namely, the capacitance between the surface and the layer of specifically adsorbed anions. Barrow and Bowden report 2.99 F m for phosphate and 60,000 F m ( ) for silicate. The fit in the four layer model was substantially better than with simpler models for fluoride adsorption, but for other anions equally good fit could be obtained without introducing the additional electrostatic plane. In another paper of this series the capacitance of 3-5 F was used in model calculations of phosphate adsorption on aluminum and iron oxides [92]. Similar approach was used by Venema et al. [93] who applied the 1-pK model to interpret the Cd binding by goethite. The ions were assumed to... 

Figure 4.14. The four-layer model used for the calculations of the interfacial thickness, nj designates the refractive index, 0j the incidence angle, r. the Fresnel reflection coefficient, Rj the reflection coefficient in the incident plane and dj the thickness of the layer.

The most artificial aspect of this model, which is expressed in Eq. 3.55, is the monolayer approximation, and in fact it is unnecessary to require all layers below the top monolayer to have the bulk composition. Williams and Nason [25] presented a four-layer model in which the top four layers were allowed to have compositions different from the bulk, while the fifth and deeper layers had the bulk composition. The results of the derivation are four coupled equations relating the surface composition of the four layers to T, Q, and the crystal-structure parameters. 

Four-layer model [82] The morphology of the injection-molded bar of Ul-trax KR 4002 (all-aromatic TLCP from BASF) is composed of four distinct layers highly oriented skin layer, weakly oriented sub-skin layer, highly... 

Figure 8.20 Schematic of four-layer model of injection-molded LCP at low and high injection...

Chemical adsorption mechanisms that are based on chemical interactions between the metal complexes and the solid support. In this case, all the ionic species present in the liquid solution compete for the active sites at the solid surface. This type of adsorption is usually described by surface ionization models, such as the triple-layer model and its extended versions (e.g., four-layer model) [1]. 

Model h is the so-called four layer model, which, compared to the triple-layer model, introduces one supplementary layer. The major reason for this is that the electrolyte ions typically differ in size. It may be argued that the usually larger anion has to be placed further away from the surface than the more compact cation. The consequence of the additional layer is an additional capacitance value. Furthermore, constraints on electrolyte binding from experimental data, which indicate symmetrical electrolyte binding, become more complicated. This is because in addition to the stability constant for the formation of the outer-sphere complexes, the location of charge also affects the interaction of the ion with the surface. 

However, recently the fundamentals of ellipsometry have been questioned [77, 78]. The assumptions made in the four-layer model are maybe not close enough to the real situation. In the applied fitting procedure, the interface is considered as a uniform layer with a uniform refractive index. In reality, there is certainly a concentration gradient at the interface. This is a weak point of the method, but it is difficult to assess the error induced by this approximation. 

Fig. 9. (a) Z vs. wavelength before (solid curve) and after (dashed curve) adsorption ofhuman serum albumin in a 288-nm thick porous silicon layer. The measurements were done in a citrate-FlCl buffer (pH 4) at a protein concentration of 1 mg/ml. The angle of incidence was 68°. (b) Four-layer model of a porous silicon layer with human serum albumin (HAS) adsorbed in the pores. The voids are filled with buffer solution. The numbers to the left are the thicknesses of the sublayers. After Ref. 88. Reprinted with permission from Elsevier, Copyright 2000. 

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