Film secondary minimum

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... 

With this size of latex particle it becomes possibfe to make direct observations on particles over a perind of time and record them with a high-speed camera. Using this technique Cornell et al (1975)) discovered that particles in an associated unit could be quite mobile. It was observed that as well as some particles leaving the aggregated unit as single particles and returning to the disperse phase there was a continued rearrangement of the particles. This was also observed with floccules at salt concentrations well above the ccc. These observations clearly support the contention that association can occur in a secondary minimum and that in this situation a liquid film is maintained between the particles. 

Several investigations were carried out to study the above transitions from CF to common black film, and finally to Newton black film. For sodium dodecyl sulphate, the common black films have thicknesses ranging from 200 nm in very dilute systems to about 5.4 nm. The thickness depends heavily on the electrolyte concentration, while the stability may be considered to be caused by the secondary minimum in the energy distance curve. In cases where the film thins further and overcomes the primary energy maximum, it will fall into the primary minimum potential energy sink where very thin Newton black films are produced. The transition from common black films to Newton black films occurs at a critical electrolyte concentration which depends on the type of surfactant... 

Typical curves corresponding to eqs. (VII.23) and (VII.24) are shown in Fig.VII-10. The appearance of the so-called secondary minimum at film thickness h 1/k is related to the fact that electrostatic repulsion decreases with distance faster than the molecular attraction. Molecular interaction also prevails at low film thickness change in the sign of derivatives causes a maximum to appear in the II (h) and A curves. One has to remember... 

Black Film Fluid films yield interference colors in reflected white light that are characteristic of their thickness. At a thickness of about 0.1 /xm, the films appear white and are termed silver films. At reduced thicknesses, they first become grey and then black (black films). Among thin equilibrium (black) films, one may distinguish those that correspond to a primary minimum in interaction energy, typically at about 5-nm thickness (Newton black films) from those that correspond to a secondary minimum, typically at about 30-nm thickness (common black films). 

In distinction from macroemulsions, where the kinetic stability is the manifestation of droplet-droplet hydrodynamic interaction and droplet deformation, in miniemulsions the kinetic stability is the manifestation of the interplay between surface forces and Brownian movement (23). As the molecular forces of attraction decrease linearly with decreasing droplet dimension, namely, approximately 10 times at the transition from macroemulsions to miniemulsions, the potential minimum of droplet-droplet interaction (secondary minimum) decreases, and for miniemulsions this depth can be evaluated as 1—5 kT (12, 37). At this low energy. Brownian movement causes droplet doublet disaggregation after a short time (the doublet fragmentation time,7j). If this time is shorter than the lifetime of the thin film, rapid decrease in the total droplet concentration (t.d.c.) is prevented (restricted by the coalescence time, r ), i.e., stability is achieved due to this kinetic mechanism (23). 

It is noteworthy that low concentrations of an ionic surfactant can increase emulsion stability as a result of the simultaneous manifestation of three mechanisms. First, the depth of the secondary potential minimum decreases owing to the electrostatic repulsion that is accompanied by a xj decrease. Second, the transition from the secondary minimum through an electrostatic barrier and into the primary minimum extends the coalescence time. Third, the time of true coalescence, i.e., the time necessary for thin-film rupture increases because of electrostatic repulsion as well (27, 63). 

Later, the relevance of the van der Waals forces in foam films was realized and it was suggested that the black films correspond to a secondary minimum. However, the DLVO theory could not adequately describe... 

Thus a = 4.6° at the secondary minimum and a = 11.0° at the primary one. These values also seem to be reasonable and close to those experimentally observed. It is seen from Figure 10.5 that the trajectory of the transition between the two minima is complex compared to the case of solid particles, where no deformation is present. The film radius decreases almost to a zero value in the transition region, which is due to the fact that repulsive interactions do not favour formation of a plane parallel film. The exact trajectory could be important if one is interested in the kinetics of the process. We recall that the whole consideration is based on the idealised, truncated spherical shape of the interacting droplets. A more realistic approach is to solve the Laplace equations for the droplet surfaces. This, however, would lead to much greater computational difficulties without changing qualitatively and in many cases even quantitatively the main results and conclusions (see also below). 

G. Tolnai, A. Agod, M. Kabai-Faix, A. L. Kovacs, J. J. Ramsden, and Z. Horvolgyi, Evidence for secondary minimum flocculation of Stober silica nanoparticles at the air-water interface Film balance investigations and computer simulations, /. Phys. Chem. B, 107,11109, 2003. 

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