Critical thickness films

The above result was obtained with front-side illumination geometry. As one would intuitively expect, carrier collection is most efficient close to the rear contact. Indeed, marked differences have been observed for photoaction spectra with the two irradiation (i.e., through the electrolyte side vs. through the transparent rear contact) geometries for Ti02, CdS and CdSe nanocrystalline films [319, 342]. Obviously, the relative magnitudes of the excitation wavelength and the film thickness critically enter into this variant behavior. 

The film thickness critical for uniform oxidation depends on the temperature and increases with decreasing temperature, Figure 1.42. While oxygen diffusion plays no role in films or fibers, it does play a role in thicker parts [38]. 

Numerical solution of Eq. (51) was carried out for a nonlocal effective Hamiltonian as well as for the approximated local Hamiltonian obtained by applying a gradient expansion. It was demonstrated that the nonlocal effective Hamiltonian represents quite well the lateral variation of the film density distribution. The results obtained showed also that the film behavior on the inhomogeneous substrate depends crucially on the temperature regime. Note that the film exhibits different wetting temperatures on both parts of the surface. For chemical potential below the bulk coexistence value the film thickness on both parts of the surface tends to appropriate assymptotic values at x cx) and obeys the power law x. Such a behavior of the film thickness is a consequence of van der Waals tails. The above result is valid when both parts of the surface exhibit either continuous (critical) or first-order wetting. 

Thickness, critical, see Critical thickness film, determination, see Film thickness, determination variation of line intensity with, 153-158... 

The shapes of film thickness along A—in Fig. 8 are given in Fig. 9. With the decrease of speed, the curve of film thickness in the central region becomes flat. The thickness of the film in a cross section of the central region is about 24 nm for the mineral oil with a viscosity of 36 mPa-s (20°C). However, for the lubricant with a viscosity of 17.4 mPa s as in Fig. 10, the curve is quite crooked when the average thickness is about 24 nm, and the curve becomes flat at a thickness of about 14 nm. These indicate that the thinner the film is, the flatter the film in the central region will be. The thickness at which the shape of the film curve becomes flat is related to the critical film thickness where EHL transfers to TFL. The thicker the critical film is, the thicker will be the average film at which the film curve turns flat. 

The capacity of the ordered film for supporting loads is between that of the static film and that of the dynamic fluid film. The orientation property of the ordered layer gradually becomes weak with the distance apart from the metal surface. The transition occurs as the ordered film appears more important between the two solid surfaces. The thickness of the ordered film is related to the initial viscosity or molecular size of the lubricant, as shown in Fig. 13, so that we can generally write the critical film thickness as follows ... 

Fig. 13—Critical transition film thickness versus viscosity [2]. Load 4 N, Ball 2Q mm. Lubricant mineral oils.

Equation (7) indicates that the critical film thickness changes very slowly with an increase in initial viscosity when it is close to 26 nm. 

If a critical film thickness is not reached during film drainage, the drops separate from each other. Conversely, if the critical film thickness is reached, the film ruptures—as a result of van der Waals forces—and the drops coalesce. This generally occurs at thin spots, because van der Waals forces are inversely proportional to h (Verwey and Overbeek, 1948). The value of bent can be determined by setting the van der Waals forces equal to the driving force for film drainage, giving (Verwey and Overbeek, 1948)... 

For the vertical case, the denominator is never zero, and a critical film thickness does not exist. 

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