Effective layer thickness

Considering the mutual relationships of the different parameters in equations (6) and (7) respectively, the effective layer thickness d, which is a measure for the "interaction strength" of the evanescent wave with the rare medium, could be increased by increasing the refractive index of the dense material and/or by choosing an angle of incidence close to the critical angle 0c>... 

Figure 3. Angular dependence of the effective layer thickness (dr) and the "penetration depth (d ) for parallel and perpendicular polarization of the incident light ( vacuum wavelength of the light n, = 1.51 n2 = 1.0).

Using this approach it is also possible to define and compute effective layer thicknesses and to find the distribution of chain elements touching the surface. The trend is that this distribution becomes more random with increasing temperature (not shown). Finally fig. 3.23 gives two snapshot configurations. 

Figure 3. A typical dependence of the chemical potential p, on the effective layer thickness (see the definition in the text). The inset is the enlarged high-density part of the picture.

A combined dependence of chemical potential on effective layer thickness h, defined ash = hath>d and h = dp/at h < d, is shown in Eig. 3. The dependence merges the sharp-interface formula (45) at h > d with the dependence p(p) given by Eq. (47) ath < d. The latter dependence allows for both dense and dilute precursor with densities approaching those of liquid and vapor. If the latter possibility is ignored, only the right-hand part of the picture, enlarged in the inset, is relevant. This part has qualitatively the same, albeit steeper, tent-like shape as in Eig. 2, allowing for equihbrium between a dense molecular precursor and bulk liquid at /Li = 0. Due to the steep dependence of the chemical potential on liquid density, the density depletion relative to p+ in the precursor at equilibrium with bulk fluid remains small even at moderate values of %. 

When two materials of differing refractive indices are extruded into a nanolayer structure that has an effective layer thickness of approximately 1/4 the wavelength of visible light, the material is effectively a ID visible photonic crystal. The nano-layer extrusion process is a continuous process that yields photonic crystals that are flexible sheets of a polymer. This is a great advantage since it can easily and rapidly produce photonic materials with a much larger size than typical photonic crystal fabrication techniques. 

Figure 7.S Effective layer thickness as a function of wavelength for various matrices. (Reprinted with permission from Siemens Review.)...

The data of Mewis et al. (39) and d Haene (40) for poly(methyl methacrylate) spheres stabilized by poly( 12-hydroxy stearic acid) and dispersi in decalin correlate reasonably well with results for hard spheres for low to moderate volume fractions, although the critical stress is somewhat smaller. For highly concentrated dispersions, however, packing constraints cause some interpenetration of the layers at rest and viscous forces at high shear rates drive the particles even closer together. Consequently, the effective layer thickness decreases with increasing 0 and Pe, the dimensionless shear rate. 

Viscometric determinations of this type tend to give quite high layer thicknesses of the order of several tens of nanometres. An example of this approach can be found in the work of Chibowski who studied the adsorption of polyacrylamide of different molecular weights on to the surface of titanium dioxide from aqueous solution [80]. He found effective layer thicknesses of 30-70 nm increasing with polymer molecular weight. The results obtained are, of course, influenced by the solvent. If possible, the measurements... 

For the polymer adsorbed on both sheets of mica, a parameter of interest was 2Lo, defined as the separation at which repulsion could just be detected, providing an effective layer thickness. Values of 2L plotted against molecular weight of the polystyrene chain are shown in Table 12.7 (71) see the arrows in Figure 12.24. The values follow the relationship... 

The values are the intermolecular potentials of the respective phase, and is the effective layer thickness. The variables have only positive values and they are symmetrical functions of the physical quantities of the corresponding phases. 

If the parameters defining the difference of the potentials and the effective layer thickness are, p q and respectively, the previous expression can be... 

On the basis of the above observation, Schultz and Asunmaa developed the following transport mechanism. They made an assumption that the low-density and the noncrystalUnc region of the polymer that fills the space between the circular cells is incorporated into the unit cell as its part. Those spaces (between the unit cells) were therefore assumed to be vacant. In reverse osmosis operation these vacant spaces are filled only with water, and this water is assumed to be more ordered than the ordinary water under strong influence from the polymeric material. This water flows by the viscous flow mechanism through channels that arc formed by connecting the vacant spaces. Suppose r is the effective radius of this pore (m), np is the number of the pore in a unit area (1/m ), p is the pressure drop across the membrane (Pa), 17 is the water viscosity (Pa s), L is the effective layer thickness (m), and r is the tortuosity factor (-), the volumetric... 

The effective layer thickness 1 is the characteristic decay length and resembles an average distance of the particles from the accumulation wall. It depends on the interaction of the particles and the field the stronger the interaction, the further the particles are compressed to the accumulation wall. 

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