Common black films

As it is well known, the contacts between drops (in emulsions), solid particles (in suspensions) and gas bubbles (in foams) are accomplished by films of different thickness. These films, as already discussed, can thin, reaching very small thickness. Observed under a microscope these films reflect very little light and appear black when their thickness is below 20 nm. Therefore, they can be called nano foam films. IUPAC nomenclature (1994) distinguishes two equilibrium states of black films common black films (CBF) and Newton black films (NBF). It will be shown that there is a pronounced transition between them, i.e. CBFs can transform into NBFs (or the reverse). The latter are bilayer formations without a free aqueous core between the two layers of surfactant molecules. Thus, the contact between droplets, particles and bubbles in disperse systems can be achieved by bilayers from amphiphile molecules. 

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. 

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.

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... 

Figure 5.15 shows an example of a disjoining pressure isotherm in which the steric force contributions have been superimposed on the classical DLVO force contributions. It can be seen that this creates two regions for meta-stable foam films. One region is the thick, common black film region, with film thicknesses of approximately 50 nm or so. The other region is the thin, Newton black film region, with film thicknesses of approximately 4 nm. While the common black films are mostly stabilized by electrostatic forces, the Newton black films are at least partly stabilized by the steric forces. 

M. Mandu, E. Ruckenstein Specific Ion Effects in Common Black Films The Role of the Thermal Undulation of Surfaces, LANGMUIR 20 (2004) 1775-1780. 

The recombination of surface charges with ions and the corresponding increase in repulsion also has consequences regarding the stability of common and Newton black films. However, in the latter case, the repulsive thermal undulations of the films also play a role [7.3]. As revealed by experiment and intuitively expected, an increase in temperature (which in turn increases the thermal undulations) decreases the stability of the films. In contrast, the insight provided by the traditional approach suggests that the increase in thermal undulations should lead to a larger Hel-frich repulsion, hence to a more stable system. However, the treatment of this repulsion by considering the membrane as composed of pieces of a suitable area implies that an increase in temperature decreases the area of the pieces, hence increases the probability of film rupture [7.3]. 

The effect of electrolyte concentration on the transition from common to Newton black films and the stability of both types of films are explained using a model in which the interaction energy for films with planar interfaces is obtained by adding to the classical DLVO forces the hydration force. The theory takes into account the reassociation of the charges of the interface with the counterions as the electrolyte concentration increases and their replacements by ion pairs. This affects both the double layer repulsion, because the charge on the interface is decreased, and the hydration repulsion, because the ion pair density is increased by increasing the ionic strength. The theory also accounts for the thermal fluctuations of the two interfaces. Each of the two interfaces is considered as formed of small planar surfaces with a Boltzmannian distribution of the interdistances across the liquid film. The area of the small planar surfaces is calculated on the basis of a harmonic approximation of the interaction potential. It is shown that the fluctuations decrease the stability of both kinds of black films. 

It is well-known that free films of water stabilized by surfactants can exist as somewhat thicker primary films, or common black films, and thinner secondary films, or Newton black films. The thickness of the former decreases sharply upon addition of electrolyte, and for this reason its stability was attributed to the balance between the electrostatic double-layer repulsion and the van der Waals attraction. A decrease in its stability leads either to film rupture or to an abrupt thinning to a Newton black film, which consists of two surfactant monolayers separated by a very thin layer ofwater. The thickness of the Newton black film is almost independent of the concentration of electrolyte this suggests that another repulsive force than the double layer is involved in its stability. This repulsion is the result of the structuring of water in the vicinity of the surface. Extensive experimental measurements of the separation distance between neutral lipid bilayers in water as a function of applied pressure1 indicated that the hydration force has an exponential behavior, with a decay length between 1.5 and 3 A, and a preexponential factor that varies in a rather large range. 

In the case of ionic surfactants (10 8 mol/dm8 sodium lauryl sulfate, NaLS), abrupt transitions from common black films to Newton black films were observed, for NaCl concentrations in the range 0.165—0.31 mol/dm8, by increasing the external pressure.2 The N ewton black films ruptured at a pressure of about 12 x 104 N/m2. 

II.G. Model Calculations. In what follows it will be shown that the general behavior discussed above is consistent with realistic calculations. An important parameter, which is however unknown, is the equilibrium constant of the association—dissociation equilibrium, Kv. The dissociation constant of the ion pair NaSQr was estimated to be Ku = 10 0 7 mol/dm3 = 0.1995 mol/dm3.11 Because of the repulsion among the headgroups on the interface, the dissociation constant is expected to be lower in the present case. In what follows, we will use Ku = 0.050 mol/dm3. For this value, the pressures at which the transitions from the common to the Newton black films occur are in agreement with the experiments of Exerowa et al.2... 

As noted in the previous section, to obtain a transition from the common to a Newton black film, the decay lengths of the hydration and double layer repulsions must be... 

The calculations presented in this section show that the behavior of the black films can be understood in terms of the interaction energy between planar films. However, they cannot explain why, for the same electrolyte concentration, the transition from the common to the Newton black film occurs at various pressures (for example, for Ce = 10 3 mol/dm3,p = (2.5 4- 9.8) x 104 N/m2).2 In addition, the thickness at the transition apparently does not depend on the electrolyte concentration (while the Debye length A2 does) and is larger than the upper bound 3A2 (which is obtained, when only the double layer and van der Waals interactions are present, using the approach employed to derive eq 21). In the next section, it will be shown that by accounting for the thermal fluctuations of the interfeces one can provide answers to these questions. 

III.B. The Role of Thermal Fluctuations on the Transition from Common Black Films to Newton Black Films. The method described in the previous section will be now applied to thin films with fluctuating interfaces, with the interaction energy calculated as in section II.G. For low values ofthe external pressure, the enthalpy has two metastable minima at Zk and 2c, and a stable one at 2 - 0 (the former two correspond to the Newton and to the common black films, respectively, and the latter implies the rupture of the film), separated by two maxima located at Z and 22 (see Figure 7a). At metastable equilibrium the distances between the surfaces are distributed between 21 and 22 for the Newton black film and between z2 and 2 —°° for the common black film. The stability of the metastable states depends on the chance for a small area S of the interface to reach the... 

Both minima of the enthalpy, while metastable, might have a relatively long lifetime, and a system prepared in one state (common black film or Newton black film) might remain in that state during the time of the experiment, if the potential barriers are sufficiently high. However, because of the thermal fluctuations, it is possible to have, for the same experimental conditions, a transition in a range of pressures, and this explains one of the experimental results of Exerowa et al.2... 

When both the Newton and the common black films have lifetimes exceeding the duration of the experiment in a domain of applied pressures, the common black film... 

In what follows, it will be considered that the lifetime of a metastable state exceeds the duration of experiment if the potential barrier for a small surface of area S, SAH, exceeds 3kT. For the first minimum in Figure 7a, the potential barrier is higher than 3kT for Kc > 20 x 10 19 J hence the Newton black films, once formed, remain stable in cases 4 and 5 during the experiment. In contrast, if the interfaces are more flexible (low Kc, cases 1,2, and 3), the probability for an individual small surface to reach the height which separates two minima is much higher. In this case, the metastable equilibrium of the Newton black film has a shorter lifetime while the film can either rupture or have a transition to a common black film, the second process has a higher chance. On the other hand, the common black films are more stable, because, while the minimum of the enthalpy is higher, the interfaces have more room to fluctuate. 

The increase of the applied pressure decreases the stability of the common black film and the probability for a transition from a Newton to a common black film but also increases the probability of the rupture of the Newton black films. Figure 7b plots the enthalpy and the ratios pn(2)/pn(2n) and pdz)lpdzc), for p = 6.2 x 104 N/m2 (Kc = 20 x 10 19 J). The common black film becomes unstable (and a transition to a Newton black films occurs), while the Newton black film has a longer lifetime. At even a higher pressure (Figure 7c, p = 1.6 x 105 N/m2, Kc = 20 x 1(T19 J) the Newton black film ruptures. 

The fluctuations increase the equilibrium thicknesses of the films (see Figures 5, 6a, and 7a), an effect which is particularly important for the common black films (see Figure 7a). This effect was found in the experiments of Exerowa et al.,2 who noted that the DLVO theory (for planar surfaces) predicts a too small repulsion and suggested that the hydration force (which has a shorter range) cannot account for the discrepancy. 

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