Planar Films

Dewetting of macroscopic films is a process very frequently found in everyday fife for example, the film that covers a duck when it leaves a water pond, immediately dewets forming big droplets which fall by gravity. In that way, the duck looks dry and clean. 

The dynamics in this regime is known as nucleation dewetting and has been studied in different systems and configurations for relatively thick liquid films (from micrometers to hundreds of micrometers). 

Redon and coworkers were the first to study the dewetting process of macroscopic films deposited on planar and horizontal surfaces. They used different alkanes and poly (dimethylsiloxane) (PDMS) on sUanized silicon wafers. In all their studies, inertial effects were negligible against viscous ones. The film is extended on a circular surface and fixed in a perimetral wetting ring. Dewetting is initiated by producing a hole at the center of the film with a jet of ait. 

They observed that while the central dry zone increases, a bump is built up between the receding contact line and the liquid film the latter remains static and the receding contact line moves at constant dewetting velocity, V. They investigate the dependence of this velocity with the diffetent parameters of the system. The main results are that V4 does not depend on the film thickness (for h he) and that for viscous and non-polar liquids and small static contact angles (up to 50°) the dewetting capillary number Caj = i VdlV scales as the cube of (P while the prefactor varies weakly with the studied system. This result, that resembles Tanners law, was explainedby means of a simple hydrodynamic model that assumes a circular cross section for the bump and symmetrical dissipation at both of it ends. Following later observations of asymmetries in the bump s profile this last assumption was modified. 

Recent experimental results were obtained by CaUegari and coworkers using the same geometry and experimental procedure, but with highly polar liquids (water and glycerol) and PVC solid surfaces which display static contact angles up to 80° 

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The electrical characteristics of the SIKO are summarized below. The specific capacitance of the device shown in Fig. 10.20 is close to 4 pFV mnT3, and with smaller designs values of up to 20 pFV mnT3 are feasible. The range of manufacturable capacitance is not only a question of chip size but also of defect density of the ONO. Surprisingly, a defect density of porous structure, which is much smaller than the defect density of planar ONO layers, which is in the order of 0.1 cnT2. This low defect density can be understood if the defect density of planar films is assumed to be due to particles that do not penetrate into the pores. 

Next we consider similar problems as the growth or etching of sohd films, but now the solid is a sphere instead of a planar film. For growth or dissoluhon of a sphere with initial radius Rai the volume is F and d V = An dR, so that the number of moles of the solid B is... 

We describe this situation of a reacting film in Figure 9-12. The unreacted solid forms a planar film of thickness on an impermeable substrate, and the reacted layer Cs forms another film over B,. We shall assume that, as the reaction occurs, the total film thickness remains unchanged, so that, as the reaction proceeds, the position c moves from the substrate at x = 0 initially to the position X= q when the reaction has gone to completion. 

For a planar film of C with no reaction of A within the film, the steady-state flux of H is constant at all values of x so we solve the equation... 

Another important example of a solid transformation where growth requires diffusion through the product film is the transformation of solid spheres. The principles of this process are similar to those for planar films, but now the concentration profile is not linear, and the expression one obtains for the transformation and the solid conversion is more complex. 

Li et al. [189] assumed that a pair of deformable droplets has the shape of truncated sphere separated by a planar film and used the improved Carnahan-Starling equation to describe the repulsion term as ... 

Tinkham.M., Introduction to Superconductivity, McGraw-Hill, NY (1980). See also Glover, R., Critical Currents in Thin Planar Films, Rev. Mod. Phys. 36 299 (1964). 

To understand drainage we have to discuss the pressure inside the liquid films. At the contact line between liquid films, a channel is formed. This is called the Plateau border. Due to the small bending radius (rP in Fig. 12.18), there is a significant Laplace pressure difference between the inside of the compartment and the liquid phase. The pressure inside the liquid is significantly smaller than in the gas phase. As a result, liquid is sucked from the planar films into the Plateau s border. This is an important effect for the drainage of foams because the Plateau borders act as channels. Hydrodynamic flow in the planar films is a slow process [574], It is for this reason that viscosity has a drastic influence on the evolution of a foam. Once the liquid has reached a Plateau border the flow becomes much more efficient. The liquid then flows downwards driven by gravitation. 

However, there exists a way to employ the rigorous equations of continuum mechanics even for the cases, in which real phase boundaries cannot be exactly localized. This way is associated with the idea of hydrodynamic analogy between complex and simpler flow phenomena. More precisely, some particular similarities are meant between complex flow patterns encountered in industrial separations and geometrically simpler flows like planar films, cylindrical jets, spherical drops, etc., as well as their combinations (Kenig, 1997). These similarities are used in the hydrodynamic analogy approach by which the complex hydrodynamics established in a real column is replaced with an appropriate combination of simpler flow patterns. Such a replacement occurs on the basis of experimental observations which are very important for the successful... 

The calculations presented in this section show that the behavior of the black films can be understood in terms of the interaction energy between planar films. However, they cannot explain why, for the same electrolyte concentration, the transition from the common to the Newton black film occurs at various pressures (for example, for Ce = 10 3 mol/dm3,p = (2.5 4- 9.8) x 104 N/m2).2 In addition, the thickness at the transition apparently does not depend on the electrolyte concentration (while the Debye length A2 does) and is larger than the upper bound 3A2 (which is obtained, when only the double layer and van der Waals interactions are present, using the approach employed to derive eq 21). In the next section, it will be shown that by accounting for the thermal fluctuations of the interfeces one can provide answers to these questions. 

Now let us consider a planar film and perturb this planarity to a simple wave shape. Perturbations arise naturally in such systems, being caused by thermal fluctuations and/or during the oxidation process. The dynamics of the system can either ampfily the perturbation or cause its decay in time. The film will rupture when the perturbation is amplified. Of course, the perturbation increases the area of the free interface and hence increases the contribution to the free energy of the system due to the film-gas interfacial free energy. However, the perturbation displaces some molecules from distances nearer to the film substrate interface to greater distances (Fig. 5). 

In the Buerger145 precession camera (1944) the motions of the crystal and the planar film holder were mechanically coupled to provide a distortion-free... 

Let us first outline the theoretical background of the evaluation of both the charge and potential of two interacting diffuse electric layers. It is well known that the charge and potential distribution in the diffuse layer can be represented with a sufficient degree of accuracy using the Poisson-Boltzman (PB) approximation [e.g. 246]. For a planar film from aqueous symmetrical electrical electrolyte of valence z, the respective equation can be written in dimensionless form as... 

Based on the analysis of deformation of an idealised foam vertex, composed of six planar films, Stamenovich and Wilson obtained an expression for the shear modulus... 

Lastly, if the SiOj deposition is highly conformal, the regions between closely spaced metal lines may be filled without the production of gaps. If the film thickness is equal to half the space width, the space will fill completely and the comers of the film will join at the top of the space, thereby leaving a nearly planar film. Examples of CVD SiOj processes capable of the required high degree of conformality are ECR deposition and tetraethyl orthosilicate (TEOS) plasma CVD-enhanced. While this approach yields local planarization above closely spaced lines, the wide spaces between metal lines are not filled, and thus a sharp step is experienced at the edge of such spaces. Therefore, this approach is often coupled with SOG or resist etch-back processes or CMP.< >... 

The function of bacteriorhodopsin as a light-driven proton pump is well established from studies [14,70,83-85,323] of whole H. halobium cells, cell envelope vesicles prepared from the cells [78,324], and liposomes [17,18,135,191,325-327] as well as planar films [328-339] into which purple membrane was incorporated. In all of these cases light-dependent net translocation of protons across the membrane is observed, whose magnitude exceeds the number of bacteriorhodopsin molecules in the system by up to two orders of magnitude. 

The advantage of self-stop is the controllability of the post-planarization film thickness. In CMP case, thicker film than the initial step needs to be removed because of poor ability of CMP planarization. But the oxide removal rate has the within wafer and wafer to wafer non-uniformity. And these non-uniformity affects the post-CMP film thickness variation. On the other hand, the grinding has excellent planarization capability and self-stop phenomenon. The self-stop only remove the oxide on upper area and automatically stops oxide removal after the wafer surface becomes planar. So the grinding does not cause the oxide thickness variation and only the deposition cause the oxide thickness variation as shown in Fig.9. This controllability of postplanarization film thickness is very helpful for the semiconductor manufacturing. In ILD planarization, via-contact depth is not affected by planarization and this helps etch process and reliability of via-contacts. Actually the grinding oxide removal is thickness... 

Based on these observations, Wang and Caruso [237] have described an effective method for the fabrication of robust zeolitic membranes with three-dimensional interconnected macroporous (1.2 pm in diameter) stmctures from mesoporous silica spheres previously seeded with silicalite-1 nanoparticles subjected to a conventional hydrothermal treatment. Subsequently, the zeolite membrane modification via the layer-by-layer electrostatic assembly of polyelectrolytes and catalase on the 3D macroporous stmcture results in a biomacromolecule-functionalized macroporous zeolitic membrane bioreactor suitable for biocatalysts investigations. The enzyme-modified membranes exhibit enhanced reaction stability and also display enzyme activities (for H2O2 decomposition) three orders of magnitude higher than their nonporous planar film counterparts assembled on silica substrates. Therefore, the potential of such structures as bioreactors is enormous. 

One example of a practical application where polyelectrolytes are of crucial interest are immunoassays, where charged polymers are attached to surfaces and are then exposed to protein solution with the aim of loading of the polymer layer with a reproducible amount of these proteins. The protein-loaded particles or planar films thus obtained are in turn exposed to analyte solutions containing other proteins. If the proteins in the film match the proteins in solution, protein-protein complexes are formed, which are then visualized and/or quantified. In order to complete such a process successfully knowledge about the swelling of the polyelectrolyte layer in buffer solutions and the interaction of such a layer with proteins has to be established. Further questions, which are of great importance for such polyelectrolyte systems are the behavior of the monolayers in contact with common impurities present in contacting solutions especially traces of multivalent ions or tensides. 

Let us consider a planar film between the position coordinates r = Tq and r = r. Mass transfer between the two edges of the film occurs purely by molecular diffusion under steady-state conditions. The thickness of the film is — Tq. The equation of continuity... 

Equations 8.2.14-8.2.20, derived for the fluxes across a planar film, apply essentially unchanged for diffusion in cylindrical and spherical films. All that needs to be done is to use the appropriate definition of the characteristic length from Figure 8.3. The flux then calculated from Eqs. 8.2.14 or 8.2.15 would be that at the plane 77 = 0. 

For steady-state heat transfer within a planar film, the energy balance relation (Eq. 11.1.1) simplifies to... 

Depending upon the membrane geometry, film models can be of two types (a) Uniform flat sheet model, which assumes the membrane to be a planar film and (b) Spherical shell model in which an emulsion globule is characterized as a double shell with the membrane around a single internal phase droplet. Planar geometry models have been used [15-17]. Kremesec and Slattery considered the overall mass transfer resistance as a sum of the resistance through continuous, membrane, and internal phases [17]. 

The CF-SPT head has a simply stacked structure comprising planar films of magnetic, conductive and insulating materials, except for the connection part between the two coil windings. Therefore, the fabrication process of this head uses simpler... 

Several physically based expressions relating the thickness of adsorbed films to surface and liquid properties, geometry, and chemical potential have been developed (Iwamatsu Horii, 1996). The simplest case considered here is that of a liquid film adsorbed on a planar surface (Fig. 1-1 a) because of interfacial interactions induced by long-range molecular (van der Waals) forces only. The relationships between the disjoining pressure II(/i) and film thickness h for the planar film are given by (Derjaguin, et al., 1987 Iwamatsu Horii, 1996) ... 

Fig. 3.15. Drainage of a surfactant containing liquid between two oil droplets or air bubbles, a) -approach, b - planar film after dimple flow out, c - thermal fluctuations, d - equilibrium state, 2R - radius of the film, h -film thiclmess, according to Ivanov Dimitrov (1988)...

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