Disjoining pressure electrostatic component

Films of a relatively smaller initial thickness ( 500 nm) can be formed from aqueous electrolyte solutions at low concentrations. They can be also produced either in the absence of a surfactant or in its presence at low concentrations, as long as there acts the electrostatic component of disjoining pressure [53,73],... 

The simplest explanation of film rupture involves reaching a thermodynamically unstable state [20]. A typical example of thermodynamically unstable systems are foam films in which the disjoining pressure obeys Hamaker s relation. Such are films from some aqueous surfactant solutions containing sufficient amount of an electrolyte to suppress the electrostatic component of disjoining pressure as well as films from non-aqueous solutions (aniline, chlorobenzene) [e.g. 80],... 

The DLVO-theory considers only the molecular van der Waals and electrostatic interactions. A complete analysis of the theory can be found in several monographs [e.g. 3-6] where original and summarised data about the different components of disjoining pressure in thin liquid films, including in foam films are compiled. 

According to DLVO-theory the disjoining pressure in thick films is considered as a sum of the electrostatic and van der Waals component... 

An approximated expression of the electrostatic component of disjoining pressure can be derived from Eq. (3.71) at small values of [Pg.126]

The results obtained indicate that at (po]Cr only NBF form. These studies prove that the barrier in the TT(/i) isotherm, impeding the transition of one film type to another, is mainly determined by the electrostatic component of disjoining pressure, Tlf(. It should not be forgotten that if there exist other components of disjoining pressure, this estimation is no more valid. A CBF/NBF transition could not even be realised if there is another positive component, such as steric one in polymer films. 

The analysis of the above techniques (Section 3.4.2.2) developed to estimate the conditions under which stable CBF and NBF exist, and reveals the equilibrium character of the transition between them and the particular features of the two types of black films. Furthermore the difference between the techniques of investigation as well as the difference between their intrinsic characteristics proves to be a valuable source of information of these thinnest liquid formations. The transition theory of microscopic films evidences the existence of metastable black films. Due to the deformation of the diffuse electric layer of the CBF, the electrostatic component of disjoining pressure 1 L( appears and when it becomes equal to the capillary pressure plus Ylvw, the film is in equilibrium (in the case of DLVO-forces). As it is shown in Section 3.4.2.3, CBF exhibit several deviations from the DLVO-theory. The experimentally obtained value of ntheoretically calculated. This is valid also for the experimental dependence CeiiCr(r). Systematic divergences from the DLVO-theory are found also for the h(CeiXr) dependence of NaDoS microscopic films at thickness less than 20 nm. 

The fact that the disjoining pressure in NBF does not contain an electrostatic component as well as the lack of a free aqueous core in the film structure allows to use the bilayer lattice model to explain the stability of NBF. This model accounts for the interaction between first neighbour molecules (see Section 3.4.4). 

At higher electrolyte concentrations in the NaDoS solution, e.g. 0.35 mol dm-3 (curve 2, Fig. 3.77), formation of black spots is observed at higher surfactant concentrations which correspond to closer packing of the adsorption layer. Probably with the increase in electrolyte concentration the stabilizing ability of the electrostatic component of disjoining pressure decreases. 

With respect to the molecular interactions the simplest asymmetric films are these from saturated hydrocarbons on a water surface. Electrostatic interaction is absent in them (or is negligible). Hence, of all possible interactions only the van der Waals molecular attraction forces (molecular component of disjoining pressure) can be considered in the explanation of the stability of these films. For films of thickness less than 15-20 nm, the retardation effect can be neglected and the disjoining pressure can be expressed with Eq. (3.76) where n = 3. When Hamaker s constants are negative the condition of stability is fulfilled within the whole range of thicknesses. 

Another point of view concerning foam stability appeared in relation to the development of the general theory of stability of colloid systems (DLVO-theory). It has already been noted that this theory was verified for the first time with foam films [35]. This gave rise to the concept of foam stabilisation on the account of the electrostatic component of disjoining pressure [e.g. 24, 32, 36],... 

It follows from these data that the electrostatic component of disjoining pressure cannot alone provide the formation of a stable (long-living) foam. It is necessary to account for other positive components of n and the different conditions under which the films exist in the foam. 

In practice, the disjoining pressure II(/i) must be taken into account only for films of thickness 1CT9 < h < 10 7m. The disjoining pressure comprises some components of different physical nature [383] Van der Waals attraction, electrostatic repulsion, steric elastic interaction, etc. The approximation formulas for these components in various regions of h acquire different forms [116, 122, 383],... 

The molecular component of the disjoining pressure, IIm(/i), is negative (repulsive). It is caused by the London-van der Waals dispersion forces. The ion-electrostatic component, IIe(/i), is positive (attractive). It arises from overlapping of double layers at the surface of charge-dipole interaction. At last, the structural component, IIs(/i), is also positive (attractive). It arises from the short-range elastic interaction of closed adsorption layers. 

The disjoining pressure is a sum of several components (just as with soil water potential). The major components of the n(A)-isotherm in porous media are molecular, nm(h) electrostatic, ne(A) structural, ITS(A) and adsorptive IIa(A) ... 

VII.4. Electrostatic Component of Disjoining Pressure and its Role in Colloid Stability. Principles of DLVO Theory... 

In the case of a more strict approach to evaluation of change in energy with decreasing distance between charged surfaces, the expression for electrostatic component of disjoining pressure has to be written as... 

The above relationship for electrostatic component of disjoining pressure has the following meaning the first term, in agreement with eq. (III.20), represents the osmotic pressure of ions in the center of a gap, while the second term is the osmotic pressure in the bulk of dispersion medium. One may thus say that the electrostatic component of disjoining pressure equals to the difference in osmotic pressure between the gap and the bulk, that forces the dispersion medium to flow into the gap between surfaces causing a disjoining action. For small values of (p(h/2) the expansion of hyperbolic cosine into series as cosh (y) 1 + A (y)2 readily yields eq. (V1I.21). 

Thus, the properties of diffuse part of electrical double layer determine the dependence of electrostatic component of disjoining pressure on the thickness of film [15], The screening of the charged surface with a layer of counterions results in a sharp decrease of the electrostatic component of disjoining pressure with a corresponding increase in film thickness. For the surface bearing low charge, when... 

Fig. VII-9. The electrostatic component of disjoining pressure, FIel, as a function of surface potential, (p0...

The electrostatic components of disjoining pressure and free energy of interaction in the film, given by eqs. (VII.21) and (VII.22), are positive, i.e. represent repulsion. These quantities may be compared with corresponding molecular components that are negative and describe attraction. This allows one to analyze according to the DLVO theory the stability of thin films, and consequently of disperse systems stabilized by adsorption layers. Carrying out summation of eqs. (VII.21) and (VII.22) with expressions (VII.9) and (VII. 10) one obtains ... 

The nature of stability of disperse systems with solid dispersed phase and liquid continuous phase against coagulation is determined by phase composition, particle size and particle concentration. The stability of hydrosols at low electrolyte concentrations is usually related to the electrostatic component of disjoining pressure (Chapter VII), arising from the overlapping diffuse parts of electrical double layers. 

Surface forces also include electrostatic interaction forces arising from the overlap of the double layers (DL) of a particle and a bubble, which usually have equal charges (Huddleston Smith 1975), i.e., the electrostatic component of the disjoining pressure of an interlayer between them (Derjaguin 1934), which may be positive. In the case of large particles, the positive disjoining pressure of the double layer is overcome by an inertia impact on the bubble surface. The small particles do not undergo such an impact the approach occurs in an inertialess way and can be hampered by electrostatic repulsion (second peculiarity). 

In recharging the bubble surface, the depth of the potential well formed beyond the limits of the barrier of non-electrostatic repulsion forces is insufficient to ensure the contactless flotation of large particles. Therefore, in the presence of the non-electrostatic component of the disjoining pressure recharging can cause the contactless flotation only if the particles are sufficiently small. 

Two techniques decrease the possibility of particle detachment. One consists of the use of reagents which decrease the non-electrostatic component of the disjoining pressure. The second technique consists of choosing bubble size and hydrodynamic regime so as to decrease detachment forces. 

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