Equilibrium films

Data for equilibrium film pressures on mercury are from Ref. 11. 

Spreading velocities v are on the order of 15-30 cm/sec on water [39], and v for a homologous series tends to vary linearly with the equilibrium film pressure, it", although in the case of alcohols a minimum seemed to be required for v to be appreciable. Also, as illustrated in Fig. IV-3, substrate water is entrained to some depth (0.5 mm in the case of oleic acid), a compensating counterflow being present at greater depths [40]. Related to this is the observation that v tends to vary inversely with substrate viscosity [41-43]. An analysis of the stress-strain situation led to the equation... 

A surfactant for evaporation control has an equilibrium film pressure of 15 dyn/cm. Assume a water surface and 25°C and calculate the distance traveled by the spreading film in 8 sec. 

A thin film of hydrocarbon spread on a horizontal surface of quartz will experience a negative dispersion interaction. Treating these as 1 = quartz, 2 = n-decane, 3 = vacuum, determine the Hamaker constant A123 for the interaction. Balance the negative dispersion force (nonretarded) against the gravitational force to find the equilibrium film thickness. 

Figure 18 shows the dependence of the activation barrier for film nucleation on the electrode potential. The activation barrier, which at the equilibrium film-formation potential E, depends only on the surface tension and electric field, is seen to decrease with increasing anodic potential, and an overpotential of a few tenths of a volt is required for the activation energy to decrease to the order of kBT. However, for some metals such as iron,30,31 in the passivation process metal dissolution takes place simultaneously with film formation, and kinetic factors such as the rate of metal dissolution and the accumulation of ions in the diffusion layer of the electrolyte on the metal surface have to be taken into account, requiring a more refined treatment. 

P — dimensionless equilibrium film thickness, defined in Equation A4... 

Equilibrium film thickness, 12 6-7 Equilibrium moisture content, 9 97, 107-109... 

Experimental dependence of equilibrium film thickness and characteristic buildup time in laminar and turbulent flow. 

What is equilibrium film pressure What is its physical signi ficance ... 

It is important to remember the significance of irv. It refers specifically to the equilibrium between two surface states. There is a danger of confusing ttv with the equilibrium spreading pressure ire, introduced in Chapter 6. The latter is the pressure of the equilibrium film that exists in the presence of excess bulk material on the surface. It is the equilibrium spreading pressure that is involved in the modification of Young s equation (Equation (6.49)), for which a bulk phase is present on the substrate. For tetradecanol at 15°C, the equilibrium spreading pressure is about 4.5 10 2 N m so ire and irv are very different from one another. 

Emulsions and foams are two other areas in which dynamic and equilibrium film properties play a considerable role. Emulsions are colloidal dispersions in which two immiscible liquids constitute the dispersed and continuous phases. Water is almost always one of the liquids, and amphipathic molecules are usually present as emulsifying agents, components that impart some degree of durability to the preparation. Although we have focused attention on the air-water surface in this chapter, amphipathic molecules behave similarly at oil-water interfaces as well. By their adsorption, such molecules lower the interfacial tension and increase the interfacial viscosity. Emulsifying agents may also be ionic compounds, in which case they impart a charge to the surface, which in turn establishes an ion atmosphere of counterions in the adjacent aqueous phase. These concepts affect the formation and stability of emulsions in various ways ... 

The equilibrium film thickness (h) is calculated using the expression ... 

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.

The foam stability of /3-cas foams progressively decreased with added Tween 20. In contrast, there was a very sharp transition in equilibrium film thickness at R = 0.5. Surprisingly, surface diffusion of /3-cas was not detected at any R value in these films. This was unexpected since it has been reported that adsorbed layers of /3-cas are characterized by a very low surface viscosity [3], signifying that protein-protein interactions in /3-cas films are very weak. We had expected to observe surface diffusion either in the films stabilized by... 

Figure 10.4 shows the results of some measurements on aqueous sodium oleate films. The sensitivity of the equilibrium film thickness to added electrolyte reflects qualitatively the expected positive contribution of electric double layer repulsion to the disjoining pressure. However, this sensitivity to added electrolyte is much less than that predicted from electric double layer theory and at high electrolyte concentration an equilibrium film thickness of c. 12 nm is attained which is almost independent of the magnitude of the disjoining pressure. To account for this observation, Deryagin and Titijevskaya have postulated the existence of hydration layers... 

If the balance of van der Waals attraction, electric double layer repulsion, capillary pressure, structure propagation, etc., favours an equilibrium film thickness, random fluctuations in film thickness will, in any case, tend to be neutralised. 

Theoretical considerations by Clarke and co-workers (Clarke, 1987 Clarke etal., 1993) show that an equilibrium film thickness arises from the competition between attractive dispersion forces determined by the dielectric properties of the grains and repulsive disjoining forces which can be steric forces and/ or double-layer forces. Wetting will occur when the solid-solid boundary energy, yb, is less than that of the wetted boundary, 2y, where y is the liquid-solid interfacial energy (Clarke, 1985), provided that there is a suitable source of liquid, for example as a consequence of liquid-phase sintering at high temperatures. 

Clarke (1987) examined the form of Eq. (17.1) for the situation where n, D = nADS = nHB = 0, in which case the repulsive force per unit area enabling an equilibrium film thickness to arise is simply Ilsx. Subsequently, Clarke etal. (1993) examined the situation where nx D 0, nADS = nHB = 0 for zero and finite values of nsx, concluding that it is only under certain restricted conditions that it is plausible for an electrical double-layer force to contribute significantly to the total repulsive force. 

The trend which arises from a consideration of Eq. (17.2) is that the lower the value of the Hamaker constant, A, the higher the equilibrium film thickness (Clarke, 1987). Striking confirmation experimentally of such a trend has come from work in which the local Hamaker constants in silicon nitride ceramics have been determined from spatially resolved-valence electron energy-loss spectroscopy (French et al 1998). Conversely, if A is too large, then there will be no thickness Z for which Eq. (17.2) is satisfied. 

HRTEM observations of three differently misoriented interphase boundaries between hexagonal boron nitride (h-BN) and 3C silicon carbide (3C SiC) grains showing an orientation dependence on equilibrium film thickness. In (a) and (b) the (0001) of the highly anisotropic b-BN are parallel to the interface, whereas in (c) they make an angle of 68° with the interphase boundary (reprinted from Ultramicroscopy, Knowles KM and Turan S, The dependence of equilibrium film thickness on grain orientation at interphase boundaries in ceramic-ceramic composites, 83(3/4) 245-259 (2000) with kind permission of Elsevier Science). 

Effect of intergranular film composition on equilibrium film thickness... 

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