Black film thickness

Figure 14. Typical FRAP data curves obtained with (a) 2 mM SDS in 2 mM sodium phosphate buffer, pH 7.0 containing 0.1 M NaCl and 14 /xM ODAF (b) FITC-BSA (0.5 mg/ml) in distilled water, pH 8.0, at an equilibrium film thickness of 83 nm (c) FITC-BSA (0.2 mg/ml) in 50 mM Na acetate buffer, pH 5.4 at an equilibrium common black film thickness of 14 nm.

This device was used in the study of the kinetics of common thin film thinning [16,106], in the determination of the critical thickness of rupture of macroscopic films having an area of about 1 cm2 as well as in the measurement of black film thickness [107]. In equilibrium films this technique does not give reliable results, since there are difficulties in the evaluation of the capillary pressure in the menisci. 

Fig. 3.51 shows the disjoining pressure isotherms at 21 O 3 mol dm 3 CaCl2. Comparatively thick films were formed at low pressures and their thickness decreased with increase in n. The transition CBF/NBF occurred in the pressure interval 510 3 to 610 3 Pa. The black film thickness did not change with further increase in pressure up to 4-10 4 Pa (not shown in Fig. 3.51). 

As it is known, the black film thickness h is a function of the electrolyte concentration (Fig. 3.62). Such a dependence has been studied in detail for microscopic foam films from sodium oleate solutions [14,73,96]. It has given the first quantitative evidence for the existence of the two types of black films. After a monotonous decrease in film thickness upon increasing electrolyte concentration up to 0.8 mol dm 3, a jump-like change in its thickness is observed (Fig. 3.62,a). An about twice thinner film is formed which does not change in thickness at a further increase in Cei. Thus Cei,cr was precisely determined and the concentration range in which the two types of black films are stable at a given temperature (21°C) was established. 

The films formed from potassium thiocyanate solutions behaved differently from those formed from sodium chloride solutions. At the lowest salt concentration examined, 4 X 10"4 mole/dm3, the film had a thickness of 975 A, clearly a first black film. With increasing salt concentration the film thickness decreased and reached 60 A at a thiocyanate concentration of 5 X 10 1 mole/dm3 it remained at this thickness as the salt concentration was increased to 1 mole/dm3. This corresponded to the second black film thickness obtained with the films in sodium chloride solutions, and in this state the films were quite stable. The considerably thicker films formed in the presence of the thiocyanate ion indicate a stronger double layer repulsion effect than with chloride and hence a stronger adsorption of the thiocyanate ion to the film surface. These re-... 

Newton black films (thickness 10 nm) and then rupture. However, when the nonionic surfactant (Tween 20 or Tween 60) is initially dissolved in the xylene drops and the jBlm is formed from the nonpreequilibrated phases, neither black film formation nor rupture is observed [489]. Instead, the films have a thickness above 100 nm, and one observes the formation of channels of larger thickness connecting the film periphery with the film center (Fig. 38b). One may observe that the liquid is circulating along the channels for a time period from several hours to several days. The phenomenon continues until the redistribution of the surfactant between the phases is accomplished. These observations can be interpreted in the following way. Because the surfactant concentration in the oil phase (the disperse phase) is higher than the equilibrium one, the surfactant molecules cross the... 

As a point of interest, it is possible to form very thin films or membranes in water, that is, to have the water-film-water system. Thus a solution of lipid can be stretched on an underwater wire frame and, on thinning, the film goes through a succession of interference colors and may end up as a black film of 60-90 A thickness [109]. The situation is reminiscent of soap films in air (see Section XIV-9) it also represents a potentially important modeling of biological membranes. A theoretical model has been discussed by Good [110]. 

Clear-bright and blue-bright chromium conversion colors are thin films (qv) and may be obtained from both Cr(III) and Cr(VI) conversion baths. The perceived colors are actually the result of interference phenomena. Iridescent yellows, browns, bron2es, oHve drabs, and blacks are only obtained from hexavalent conversion baths, and the colors are Hsted in the order of increasing film thickness. Generally, the thicker the film, the better the corrosion protection (see Eilmdepositiontechniques). 

Physical properties of Fullerene C q. It does not melt below 360°, and starts to sublime at 300° in vacuo. It is a mustard coloured solid that appears brown or black with increasing film thickness. It is soluble in common organic solvents, particularly aromatic hydrocarbons which give a beautiful magenta colour. Toluene solutions are purple in colour. Sol in (5mg/mL), but dissolves slowly. Crysts of C o are both needles and plates. 

Emissivity Table 15.5 shows the total heat emissivity of various aluminium surfaces, as a percentage of that of a black body. The figures have been recalculated from the data of Hase. The emissivity of anodised aluminium rises rapidly with film thickness up to 3 fim after which the rate of increase diminishes. 

Black-Ground Method. The relative scattering power is determined from the tristimulus values Y of the pigmented medium applied in various film thicknesses to black substrates. Compared with the gray paste method, the black-ground method has the advantage that it is not restricted to any particular test medium. Apparatus spectrophotometer or tristimulus colorimeter. 

A modem well-equipped color measurement laboratory can use the principle of spectral evaluation described above [1.38] to simulate this procedure with a computer. The thickness of the hiding film can then be calculated in advance from the reflectance curves of a single film on a black/white substrate at a known film thickness. 

Transparency. Transparency is expressed quantitatively as the transparency number. This is defined as the reciprocal of the increase in color difference AE b on a black substrate obtained on increasing the film thickness h of the pigmented medium. The transparency number has the unit mm ( = L/m2). It indicates the number of liters of pigmented medium needed to coat 1 m2 of a black substrate in order to obtain a color difference of AE%b = 1 relative to this substrate. In a simplified method the transparency number can be determined by evaluating one or two points on the straight part of the AE b(h) curve. A computer method is more exact, furthermore calculations can be made using the spectral principle of spectral evaluation (see above). For standards, see Table 1 ( Transparency ). 

Of these methods, the first can give accurate values of the mean film thickness only in the absence of surface waves. The fourth and fifth methods can be used only for the mean film thickness, while methods (2), (3), (6), (7), and (8) may be used for measuring either the local or mean film thicknesses. Black (B12) and Portalski (P4) have discussed the advantages and disadvantages of most of these measurement techniques, and Hewitt and Lovegrove (Hlla) have compared the film thickness values measured by three different methods. 

Black (B12), 1961 Discussion of various methods of measuring local film thicknesses. 

When two emulsion drops or foam bubbles approach each other, they hydrodynamically interact which generally results in the formation of a dimple [10,11]. After the dimple moves out, a thick lamella with parallel interfaces forms. If the continuous phase (i.e., the film phase) contains only surface active components at relatively low concentrations (not more than a few times their critical micellar concentration), the thick lamella thins on continually (see Fig. 6, left side). During continuous thinning, the film generally reaches a critical thickness where it either ruptures or black spots appear in it and then, by the expansion of these black spots, it transforms into a very thin film, which is either a common black (10-30 nm) or a Newton black film (5-10 nm). The thickness of the common black film depends on the capillary pressure and salt concentration [8]. This film drainage mechanism has been studied by several researchers [8,10-12] and it has been found that the classical DLVO theory of dispersion stability [13,14] can be qualitatively applied to it by taking into account the electrostatic, van der Waals and steric interactions between the film interfaces [8]. 

The observed equilibrium thickness represents the film dimensions where the attractive and repulsive forces within the film are balanced. This parameter is very dependent upon the ionic composition of the solution as a major stabilizing force arizes from the ionic double layer interactions between any charged adsorbed layers confining the film. Increasing the ionic strength can reduce the repulsion between layers and at a critical concentration can induce a transition from the primary or common black film to a secondary or Newton black film. These latter films are very thin and contain little or no free interlamellar liquid. Such a transition is observed with SDS films in 0.5 M NaCl and results in a film that is only 5 nm thick. The drainage properties of these films follows that described above but the first black spot spreads instantly and almost explosively to occupy the whole film. This latter process occurs in the millisecond timescale. 

Between the time a liquid film is first formed, until it thins to an equilibrium black film, the thickness can be measured by techniques based on the interference of light. For monochromatic light, the intensity of light, IR, reflected at angle 8 from a fluid film compared to the maximum intensity yielded by constructive interference, I0, enables the determination of the film thickness, t, as ... 

In foam stability, gas bubbles and the liquid films between them, would be stabilized by the repulsive forces created when two charged interfaces approach each other and their electric double layers overlap. The repulsive energy VR for the double layers at each interface in the thin film is still given by Eq. (5.1) where H is the film thickness. Here also, for extremely thin films, such as the Newton black films, Bom repulsion becomes important as an additional repulsive force. 

Figure 5.6 shows an example of a total interaction energy curve for a thin liquid film stabilized by the presence of ionic surfactant. It can be seen that either the attractive van der Waals forces or the repulsive electric double-layer forces can predominate at different film thicknesses. In the example shown, attractive forces dominate at large film thicknesses. As the thickness decreases the attraction increases but eventually the repulsive forces become significant so that a minimum in the curve may occur, this is called the secondary minimum and may be thought of as a thickness in which a meta-stable state exists, that of the common black film. As the... 

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