Films thickness

Calculate the film thickness for the Marongoni instability shown in Fig. Xlll-2 using the relationship in Eq. XIIl-3, assuming that the interfacial tension is 20 mN/m. 

Here, x denotes film thickness and x is that corresponding to F . An equation similar to Eq. X-42 is given by Zorin et al. [188]. Also, film pressure may be estimated from potential changes [189]. Equation X-43 has been used to calculate contact angles in dilute electrolyte solutions on quartz results are in accord with DLVO theory (see Section VI-4B) [190]. Finally, the x term may be especially important in the case of liquid-liquid-solid systems [191]. 

Fig. XI-3. Ellipsometric film thickness as a function of number of layers of methyl 23-(trichlorosilyl)tricosanoate on silicon wafers (Ref. 33).

Volumes in mm (liquid) radii and film thicknesses in A area in m g . The remainder of the standard columns ([1] to [9]) may be built up from Tabic 3.2A an alternative table, based on regular intervals of r, may be built up from Table 3.2B. 

The problem of film flow is formulated on the assumption that the film thickness h is much smaller than the length 1 (in our case h/1 10 ). In Cartesian coordinates with transversal axis y and longitudinal one z we can write the equation for a film flow as follows  

This may be based on Eq. XVI-2 [232] or on related equations with film thickness given by some version of the Frenkel-Halsey-Hill equation (Eq. XVII-79) [233,234], 

In a study of tarnishing the parabolic law, Eq. VII-30, is obeyed, with kj = 0. The film thickness y, measured after a given constant elapsed time, is determined in a 

Figure Bl.26.14. Plot of A versus K, the imaginary part of the refractive index. (B) MEASUREMENT OF FILM THICKNESS AND OPTICAL PROPERTIES

It will be noted that the first suffix of Q j refers to the pore radius of the group, and the second to the film thickness. 

Smith [113] studied the adsorption of n-pentane on mercury, determining both the surface tension change and the ellipsometric film thickness as a function of the equilibrium pentane pressure. F could then be calculated from the Gibbs equation in the form of Eq. ni-106, and from t. The agreement was excellent. Ellipsometry has also been used to determine the surface compositions of solutions [114,115], as well polymer adsorption at the solution-air interface [116]. 

The first term on the right is the common inverse cube law, the second is taken to be the empirically more important form for moderate film thickness (and also conforms to the polarization model, Section XVII-7C), and the last term allows for structural perturbation in the adsorbed film relative to bulk liquid adsorbate. In effect, the vapor pressure of a thin multilayer film is taken to be P and to relax toward P as the film thickens. The equation has been useful in relating adsorption isotherms to contact angle behavior (see Section X-7). Roy and Halsey [73] have used a similar equation earlier, Halsey [74] allowed for surface heterogeneity by assuming a distribution of Uq values in Eq. XVII-79. Dubinin s equation (Eq. XVII-75) has been mentioned another variant has been used by Bonnetain and co-workers [7S]. 

The gas permeability constant is the amount of gas expressed in cubic centimeters passed in 1 s through a 1-cm area of film when the pressure across a film thickness of 1 cm is 1 cmHg and the temperature is 25°C. All tabulated values are multiplied by 10 and are in units of seconds" (centimeters of Hg) k Other temperatures are indicated by exponents and are expressed in degrees Celsius. 

Electrolyte adsorption on metals is important in electrochemistry [167,168]. One study reports the adsorption of various anions an Ag, Au, Rh, and Ni electrodes using ellipsometry. Adsorbed film thicknesses now also depend on applied potential. 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E  

The existence of a characteristic isotherm (or of a r-plot) gives a very important piece of information about the adsorption potential, at least for polar solids for which the observation holds. The direct implication is that film thickness f, or alternatively n/n is determined by P/I independent of the nature of the adsorbent. We can thus write 

A possible explanation of the hysteresis could be the non-equilibrium of the DNA hydration. In that case the value of hysteresis has to depend on the size of the experimental sample. However, such a dependence is not observed in the wide range of DNA film thicknesses (0.05-0.2 fmi) [14], [12]. Thus, hysteresis cannot be a macroscopic phenomenon and does reflect the molecular interaction of water and the biopolymer. 

This description is traditional, and some further comment is in order. The flat region of the type I isotherm has never been observed up to pressures approaching this type typically is observed in chemisorption, at pressures far below P. Types II and III approach the line asymptotically experimentally, such behavior is observed for adsorption on powdered samples, and the approach toward infinite film thickness is actually due to interparticle condensation [36] (see Section X-6B), although such behavior is expected even for adsorption on a flat surface if bulk liquid adsorbate wets the adsorbent. Types FV and V specifically refer to porous solids. There is a need to recognize at least the two additional isotherm types shown in Fig. XVII-8. These are two simple types possible for adsorption on a flat surface for the case where bulk liquid adsorbate rests on the adsorbent with a finite contact angle [37, 38]. 

Ultra-high vacuum (UHV) surface science methods allow preparation and characterization of perfectly clean, well ordered surfaces of single crystalline materials. By preparing pairs of such surfaces it is possible to fonn interfaces under highly controlled conditions. Furthennore, thin films of adsorbed species can be produced and characterized using a wide variety of methods. Surface science methods have been coupled with UHV measurements of macroscopic friction forces. Such measurements have demonstrated that adsorbate film thicknesses of a few monolayers are sufficient to lubricate metal surfaces [12, 181. 

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