Force barrier

Fig. 11. (A) Force normalised by radius as a function of surface separation between mica surfaces in 0.01 wt.% acetic acid solution (pH 3.8). The arrow indicates a jump from a force barrier into molecular contact. (B) Forces between mica surfaces coated with chitosan across 0.01 wt.% acetic acid solution (pH 3.8). Two sets of measurements are shown. Filled and open symbols represent the forces measured on approach and separation, respectively, after 24 h of adsorption. The crosses represent the forces measured at pH 3.8 after the cycle of exposing chitosan adsorption layers for solutions of increasing alkalinity and measuring forces at pH 4.9, 6.2 and 9.1. The solid lines represent theoretically calculated DLVO forces. Redrawn with permission from Ref. [132]. 1992, American Chemical Society.

The phenomenon of formation of a new NBF when a very small bubble is pressed into the solution/gas surface by buoyancy force, can be used for determining of positive line tension values only. The nascency and expansion of the new contact (NBF) between the bubble and the bulk gas phase are hindered by a force barrier due to the positive linear energy. The buoyancy force (necessary to overcome this force barrier) must be larger than a critical value which depends on the value of k. This principle has been realised in the critical bubble method developed by Platikanov et. al. [474]. The results obtained by this method for 0.05% aqueous solutions of NaDoS are presented in Fig. 3.100 [475]. 

For the two particles to come into close contact they would have to cross this energy barrier. Figure 49 shows a schematic drawing of the system. Curves A and B represent cases where the minima are separated by a maximum (energy barrier). Curve C represents a special case where the disappearance of the force barrier has taken place, and no energy barrier exists between the two minima. Derjaguin and Landau " derived the following criterion for the adhesion reaction to occur... 

Figure 9 Force normalized by radius measured between two hy-drophobized mica surfaces in crossed cylinder geometry across aqueous solutions of dodecylammonium chloride the surfactant concentration was 0.01 mM ( ), 0.1 mM ( ), and 1 mM (A), respectively. The arrows indicate inward jumps occurring when the force barrier has been overcome. (Redrawn from Ret 39, with permission.)...

At low surfactant concentrations it is observed that an attraction dominates at short separations. The attraction becomes important at separations below about 12 nm when the surfactant concentration is 0.01 mM, and below about 6 nm when the concentration is increased to 0.1 mM. Once the force barrier has been overcome the surfaces are pulled into direct contact between the hydrophobic surfaces at D = 0, demonstrating that the surfactants leave the gap between the surfaces. The solid surfaces have been flocculated. However, at higher surfactant concentrations (1 mM) the surfactants remain on the surfaces even when the separation between the surfaces is small. The force is now purely repulsive and the surfaces are prevented from flocculating. Emulsion droplets interacting in the same way would coalesce at low surfactant concentrations once they have come close enough to overcome the repulsive barrier, but remain stable at higher surfactant concentrations. Note, however, that the surfactant concentration needed to prevent coalescence of emulsion droplets cannot be accurately determined from surface-force measurements using solid surfaces. 

Schottky (1914) emission is governed by the Richardson-Schottky equation of thermal emission over the image-force barrier... 

By varying the electrolyte concentration, it is possible to make the force barrier disappear (see Fig. VI.3, curve 2) and thus cause the particles to stick together. The concentration at which the force barrier may disappear (threshold concentration) can be determined from the equation [184]... 

The experimental data demonstrate that, on the basis of the concept of a repulsive force barrier (see Fig. VI.3), the conditions for particle adhesion can be determined [187, 188]. 

Simmons treated tunneling and Schottky emission through very thin films with a double-image force barrier. With thin enough films the current depended on the work function of the positive electrode, as in Standley and Maissel s work. 

The forces of interaction (attraction and repulsion) depend not only on the properties of the bodies in contact and the layer separating these, but also on the external applied force. This force determines the thickness of the gap between the bodies. If the compressing force is no greater than Fj ax (height of the force barrier) the adhesive force will be relatively small and equal to F nin H the compressive force exceeds F the adhesive force will be equal to F nin ... 

By varying the electrolyte concentration, we may achieve the vanishing of the force barrier (see Fig. IV.7, curve 2), as a result of which adhesion of the particles takes place. The concentration above which the appearance of a force barrier is possible (threshold concentration) may be determined from the equation [188]... 

It was shown in Ref. 12 that Eq. (208) is also apphcable for higher coverage even if there is no specific force barrier. This is so because the B(, h) function approaches zero for —> which means that the steric barrier height —kT In 5(0, h) becomes much larger than the kT unit. As a result, the maximum contribution to the integral, Eq. (205), stems from the region close to the interface, where 5(0, h) = 5q(0), so... 

So far we have discussed only the wetting of particles for contact angles less than 90° (see Fig. 9) that is, we considered only particles that had initially been immersed into the liquid phase by at least 50% before further immersion by a positive line tension was considered. Yet particles do land on the surface from the air phase that is, for the expansion of the contact, a new interface with the corresponding contact line has to be formed. This formation of the new contact is hindered by a force barrier owing to the positive line tension (92). At the onset of the contact, when r is very small, o/r is large. 

As discussed in the previous section, self-assembled C12TAB, a cationic surfactant, provided stability to silica suspensions at high ionic strengths by introducing a strong repulsive force barrier [78,79]. This novel concept has... 

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