DLVO theory deviations from

As is seen from the figure, at film thickness less than 20 nm, there is a maximum in the curve which indicates that either the theory about Ylei or flvw or both are not correct. Lyklema and Mysels [168] attributed this discrepancy to nei though their studies were performed at counterion concentration from 10 2 to 10 1 mol dm"3 the maximum in the figure corresponds to this concentration range at which the modem theory of the diffuse electric layer does not require considerable corrections of the classical DLVO-theory. There exist several other experimental facts that indicate deviation from the DLVO-theory at foam films of thicknesses less than 20 nm (see Section 3.4.1.3). 

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. 

Hence, the experimental isotherms of films from NaDoS cannot be explained with the DLVO-theory. The above analysis reveals that the reason for the deviations is not connected to the restrictions of the theory of molecular forces but to the theory of electrostatic interactions of double electric layers, especially at high surface charge and potential values. Another way to explain the deviations from the DLVO-theory is the expression of the structural interactions forces in spite of the fact that the scope of their actions appears to be very large. 

If we substitute the expression Eq. (2.4), for pa in Eq. (3.95), a relation about Cei cr as a function of the film radius r can be derived. Calculations from the latter yield a value of Cei,Cr about 5 times lower than the experimentally determined in the range of film radii studied. Probably this is caused by the properties of CBF that deviate considerably from the DLVO-theory (see Section 3.4.1.3). The improvement of DLVO-theory by introducing additional components of disjoining pressure will specify the Ceicr r) dependence. It should be bom in mind that in films of large areas the probability for transition from metastable to stable state is... 

These (pocr values should be regarded as conditional, especially for black films when their behaviour deviates from the DLVO-theory. Nevertheless, the direction in which (f cr changes (increase in (pocr with the rise of ionic strength) corresponds to the DLVO-theory. 

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. 

Given the appropriate potential energy diagrams from the DLVO theory, the stability ratio may be calculated by graphical or numerical integration and then compared with experimental values of W=kyk, the ratio of the experimental rate constants for rapid and slow flocculation. Such a comparison is a severe test of the applicability of theory to experiment, and the observed deviations, although often not appreciable, reflect the assumptions and approximations which are necessary in the calculation of the potential energy terms. An advanced treatment of these issues will be found in Russel et al.- . 

Rocculation kinetics can be readily measured for dilute dispersions, e.g. by particle counting (equation 6.7)), or from light-scattering data and recently by photon-correlation spectroscopy, and numerous experimental data for aqueous systems confirm that the DLVO theory is essentially correct although there are deviations in some of the fine detail. 

At separation distances of less than about 30 A, solvation forees and other effects of molecular structure sometimes eause large deviations from the predictions of DLVO theory. At very small separation distances, for instanee, oscillatory forces are sometimes observed that are evidently associated with the ease of paeking molecules between the two surfaees (Christenson et al., 1982 Israelach-vili, 1991 Ninham, 1980). At certain definite separation distanees, molecular... 

Let us consider in more details the coion expulsion model, also called reduced screening model [589], This model was developed to explain the strong short-range repulsion detected in foam films see Figure 4.38. It was found [589] that the excluded volume model [588] cannot explain the observed large deviations from the DLVO theory. Quantitative data interpretation was obtained by... 

More recent experimental data [4] show that considerable deviations from the conventional DLVO theory appear for short surface-to-surface distance hydration repulsion) and in the presence of bivalent and multivalent counterions ionic correlation force). Both effects can be interpreted as contributions to the double-layer interaction not accounted for in the DLVO theory see Sec. VLB. 

Effects of different physical origin are termed hydration forces in the literature see Ref. 317 for a review. For that reason, from the very beginning we specify that here we call hydration force the short-range monotonic repulsive force which appears as a deviation from the DLVO theory for short distances between two molecularly smooth electrically... 

At Cei>Cei cr the double layer repulsion is practically suppressed and this is manifested by the fact that the film thickness no longer changes with increasing Cel above Cei.cr (Figure 6.7). Under these conditions, flei = 0, and the experimental results cannot be explained in the framework of DLVO theory only. If one assumes that the only contribution to n is there are very large deviations from the experimental data. This directly implies that there is an additional repulsive contribution to the disjoining pressure, namely flsf... 

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