DVLO theory

The development of the thermodynamics of thin films is related to the problem of stability of disperse systems. An important contribution to its solving are the works of the Russian scientists Derjaguin and Landau [1] and the Dutch scientists Verwey and Overbeek [2], known today as the DVLO theory. According to their concept the particular state of the thin liquid films is due to the change in the potential energy of molecular interaction in the film and the deformation of the diffuse electric layers. The thermodynamic characteristic of a state of the liquid in the thin film, as shown in Section 3.1, appears to be the dependence of disjoining pressure on film thickness, the n(/t) isotherm. The thermodynamic properties of... 

A number of works are dedicated to the experimental verification of DVLO theory to foam films. As shown above, the disjoining pressure is given as a sum of ne/ and nvw, i.e. 

The method of equilibrium foam film employs the experimental measurement of the equilibrium thickness and from the DVLO theory it is possible to determine (po and, respectively, the surface charge at the solution/air interface. This is a very valuable possibility since an equilibrium potential can be evaluated and all complications occurring at kinetic measurements, are avoided. The equilibrium values of (fo are important in the interpretation of electrostatic forces in thin liquid films, along with the other surface forces, acting in them. 

This foam film with a smaller equilibrium thickness hi is called Newton black film (NBF). Its point of equilibrium is situated on the rising left hand side of the isotherm and, alike the preceding minimum, is not described by the DLVO-theory. In Section 3.3 it was shown that the departure from the DVLO-theory begins to be expressed in the experimentally obtained fl(/i) isotherms at film thickness below 20 nm [254]. There are many other experimental data on black foam films [e.g. 18,96,201,202,253,254] which also indicate a deviation of the 1T(/i) isotherm from DLVO-theory that cannot be explained even if the various corrections reflecting the theory refinements are accounted for [e.g. 148,166,171,172,221,255-259]. One of the divergences from the DVLO-theory is the discrepancy between experimental and theoretical data about the interaction energy in black films. 

Another option to reach an agreement between theoretical and experimental isotherms is provided by the assumption that the shift observed is due to structural interactions in the film which determines the structural component of disjoining pressure ns, [5,312], In that context it is interesting to estimate the function ln(nexp - ITiheor) on h, presented in Fig. 3.60. It is plotted at different NaCl concentrations under the assumption that at constant ( -potential and at Cei = 10 4 and 10 3 mol dm 3, the DVLO-theory is conformed with. 

Independently Deryagin and Landau [1941] and Verwey and Overbeek [1948] developed a theory, usually referred to as the DVLO theory, to explain the complex interactions when electrostatic double layer systems are in contact. On... 

According to the classic DVLO theory (from the names Deriagin, Landau, Ver-wey and Overbeck) the stability of colloidal suspension is determined by the equilibrium between the van der Waals attraction forces (VJ and the electrostatic repulsion, occurring between the electric double layers ( F ). The changes of these forces vs the distance between the colloid particles is shown in Fig. 5.16. The repulsion forces are directly proportional to the product of charges of both particles and decreases with the second power of the distance between them as follows ... 

Electrical Double Layer Repulsion. Double layer interaction theory has been extensively investigated independraitly by Deryagin and Landau, and Verwey and Overbeek, DVLO theory. There are many reviews on the application of DVLO theory to colloids [Shaw, 1989]. One expression for the repulsive energy between two small spheres is ... 

Figure 8.3 Schematic diagram of the variation of free energy with particle separation according to DVLO theory. The net energy is given by the sum of the double layer repul-...

Matijevi6 (51) has discussed the applicability of the DVLO theory to various inorganic sols. In the case of silica sols, the nature of the electrolyte is of major importance. Cations vary so enormously in their adsorption and formation of stable complexes with the silica surface that the theory is of little practical value. The same conclusion was reached by Webb, Bhatnagar, and Williams in regard to colloidal TiO, (52). 

The formation of clusters is an important phenomenon, as it modifies the size and density of particulate entities. We summarize here the main results from the theory of interparticular forces, called the DVLO theory by way of reference to its contributors (Deryaguin, Vervey, Landau, and Overbeck). A detailed presentation of this theory is outside the scope of the present book, as such presentation requires substantial theoretical developments. This theory helps one to understand why particles are likely to form clirsters in specific conditions. It is not, however, a predictive model of clirster formation, able to provide their number, size, and density. 

The DVLO theory effectively enables us to determine whether particles are liable to form clusters. The most delicate variable to access is the surface electrical potential, or equivalently the negative snrface charge of particles. Still, this theory does not suffice to predict whether the particles will actually form flocculates under... 

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