Sandwich-layer model

Fig. 5.16. Imaging polymer morphology by spin-diffusion contrast on a sample of electrically aged polyethylene, (a) Sample for electrical aging in needle-plate geometry and region cut out for spin diffusion imaging with one-dimensional spatial resolution, (b) Spatially resolved distribution of the domain sizes derived from fitting theoretical diffusion curves of a sandwich layer model to the experimental data. Pronounced changes in the thickness for crystalline, interfacial and amorphous layers are obtained [58].

The model here consists of a medium 3 (refractive index n3 e.g., glass), a sandwiched layer of thickness t (n2 e.g, polymer, metal, lipid, or more of... 

Fig. 12.1 Main structural models of graphene-metal oxide hybrids, (a) Anchored model oxide particles are anchored to the graphene surface, (b) Encapsulated model oxide particles are encapsulated by graphene, (c) Sandwich-like model graphene is sandwiched between the metal oxide layers, (d) Layered model a structure composed of alternating layers of oxide nanoparticles and graphene, (e) Mixed model graphene and oxide particles are mechanically mixed and graphene sheets form a conductive network among the oxide particles. Red metal oxide Blue graphene. Reprinted with permission from [41]. Copyright 2012, Elsevier B.V.

Mass and energy transport occur throughout all of the various sandwich layers. These processes, along with electrochemical kinetics, are key in describing how fuel cells function. In this section, thermal transport is not considered, and all of the models discussed are isothermal and at steady state. Some other assumptions include local equilibrium, well-mixed gas channels, and ideal-gas behavior. The section is outlined as follows. First, the general fundamental equations are presented. This is followed by an examination of the various models for the fuel-cell sandwich in terms of the layers shown in Figure 5. Finally, the interplay between the various layers and the results of sandwich models are discussed. 

Almost all of the models assume local thermal equilibrium between the various phases. The exceptions are the models of Beming et al., ° who use a heat-transfer coefficient to relate the gas temperature to the solid temperature. While this approach may be slightly more accurate, assuming a valid heat-transfer coefficient is known, it is not necessarily needed. Because of the intimate contact between the gas, liquid, and solid phases within the small pores of the various fuel-cell sandwich layers, assuming that all of the phases have the same temperature as each other at each point in the fuel cell is valid. Doing this eliminates the phase dependences in the above equations and allows for a single thermal energy equation to be written. 

Corkill et al. [56] have used for the first time the infrared spectroscopy for foam films. The measurement of the adsorption of the infrared light provides information about the water content in the foam films which is of major significance for the black foam films. These studies involved the use of dispersion type instruments. In order to obtain measurable values of adsorption, the infrared light is passed through a series of vertical films (up to 10) formed in a cylindrical tube acting as a frame. Additional information about the film structure the authors derived from the correlation between the optical infrared transmission data and the film reflectance measurements. Here a three-layer model of the film structure consisting of an aqueous core sandwiched between two adsorption layers is assumed (see Section 2.1.3). 

On the contrary the plateau values for the two copolymers are very different. Since the higher copolymer gives thicker films a surface force component of steric origin may be evoked. However, the thickness hK is an effective parameter which is too crude. As a reasonable compromise between physical relevance and tractability, the three-layer model is adopted. Within the three-layer model the foam film is viewed as a symmetric sandwich structure [159] two adsorption layers symmetrically confine an aqueous core (Fig. 3.34). 

Figure 7-11. Impedance models of a sandwich-layer system model A without defects, model B with defects in the outer layer Lj model C with defects in the outer Lj and the inner layer L2.

The schematic model of the film deposited by the technique is shown in Figure 45. A single-stranded DNA layer is sandwiched between two aliphatic amine monolayers. Thus, the technique can be useful for our objectives, for it allows depisition of single-stranded DNA on practically any substrate and does not demand a large quantity of DNA, since only one monolayer will be deposited. Nevertheless, there is a question of whether DNA in such a structure will hybridize. In fact, the film contains a single-stfanded DNA monolayer between two amine monolayers, and it is questionable whether the upper amine monolayer will prevent hybridization with complementary DNA stfands. 

Figure 7.2 Danielli-Davson membrane model. A layer of protein was thought to sandwich a lipid bilayer.

The first membrane model to be widely accepted was that proposed by Danielli and Davson in 1935 [528]. On the basis of the observation that proteins could be adsorbed to oil droplets obtained from mackerel eggs and other research, the two scientists at University College in London proposed the sandwich of lipids model (Fig. 7.2), where a bilayer is covered on both sides by a layer of protein. The model underwent revisions over the years, as more was learned from electron microscopic and X-ray diffraction studies. It was eventually replaced in the 1970s by the current model of the membrane, known as the fluid mosaic model, proposed by Singer and Nicolson [529,530]. In the new model (Fig. 7.3), the lipid bilayer was retained, but the proteins were proposed to be globular and to freely float within the lipid bilayer, some spanning the entire bilayer. 

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