Theory of surface forces

The development of the theory of surface forces by Derjaguin, Churaev, and Muller (353) made it possible to carry out quantitative estimations of wetting in relation to the properties of the solid support (hydrophilic or hydrophobic surface of SiC>2, in particular) as well as of the effect of the interaction between the wetting substances and the surface. 

Thin liquid films can be formed between two coUiding emulsion droplets or between the bubbles in foam. Formation of thin films accompanies the particle-particle and particle-wall interactions in colloids. From a mathematical viewpoint, a film is thin when its thickness is much smaller than its lateral dimension. From a physical viewpoint, a liquid film formed between two macroscopic phases is thin when the energy of interaction between the two phases across the film is not negligible. The specific forces causing the interactions in a thin liquid film are called surface forces. Repulsive surface forces stabilize thin films and dispersions, whereas attractive surface forces cause film rupture and coagulation. This section is devoted to the macroscopic (hydrostatic and thermodynamic) theory of thin films, while the molecular theory of surface forces is reviewed in Section 4.4. 

Rayleigh, Lord (1890), On the theory of surface forces. Philosophical Magazine 30, 285-298. 

In this section, we review the molecular theory of surface forces with special attention to the effect of surfactant adsorption and surfactant micelles on the interactions in the thin liquid films and between the particles in dispersions. 

It is beyond the scope of this review to cover in depth either valence theory or the theory of intermolecular forces and I shall only attempt to deal with some general principles of both which appear to be important for an understanding of potential energy surfaces. Before dealing separately with weak and strong interactions, there is one point they have in common and that is the increasing computational effect that is required as the number of internal coordinates increases. 

The molecular theory of surface tension was dealt with by Laplace (1749-1827). But, as a result of the clarification of the nature, of intermolecular forces by quantum mechanics and of the more recent developments in the study of molecular distribution in liquids, the nature and value of surface tension have been better understood from a molecular viewpoint. Surface tension is closely associated with a sudden, but continuous change in the density from the value for bulk liquid to the value for die gaseous state in traversing the surface. See Fig. 2. As a result of this inhomogeneity, the stress across a strip parallel to the boundary—pu per unit area—is different from that across a strip perpendicular to die boundary—pr per unit area. This is in contrast with die case of homogeneous fluid in which the stress across any elementary plane has the same value regardless of the direction of die plane,... 

In general, a minimum of the energy surface corresponds to a set of stationary vibrational states of the molecular system. The position of the energy minimum is commonly called the equilibrium geometry Re. Analogously, we denote the expectation values for the molecular geometries in the vibrational states 0,1,2,... by R0, Rx, R2, etc. In most cases Ro is very close to Re. There are also exceptions to this correspondence which are important in the theory of intermolecular forces. We distinguish several cases ... 

The precise direct measurement of surface forces is a subject of current interest, since it provides sufficiently reliable distinction of the forces, along with the elucidation of their mutual influence, their dependence on the distance between the interacting surfaces in systems of different composition, temperature, etc. All this enables a more critical application of the theories (old and new) of the known surface forces. On the other hand, the direct measurement of surface forces stimulate theoretical analyses. 

The main trends of the study of surface forces in foam films are briefly outlined here and the results obtained will be successively discussed in the next Sections. Furthermore, some earlier considerations will be commented, for instance, the first quantitative experimental verification of the DLVO-theory with the aid of foam films, since these results form the base of the further achievements in measurement and interpretation of surface forces and their role in the stability of foam 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. 

The CBF/NBF transition has already been considered in Section 3.4.1 with respect to the experimental n(/i) isotherms of disjoining pressure obtained with the Thin Liquid Film-Pressure Balance Technique. Theoretical concepts and comparison with the DLVO- and contemporary theories describing surface forces acting in this range of film thicknesses have also been discussed. 

As a second model potential we shall briefly discuss the PES for the water dimer. Analytical potentials developed from ab initio calculations have been available since the mid seventies, when Clementi and collaborators proposed their MCY potential [49], More recent calculations by dementi s group led to the development of the NCC surface, which also included many-body induction effects (see below) [50]. Both potentials were fitted to the total energy and therefore their individual energy components are not faithfully represented. For the purposes of the present discussion we will focus on another ab initio potential, which was designed primarily with the interaction energy components in mind by Millot and Stone [51]. This PES was obtained by applying the same philosophy as in the case of ArCC>2, i.e., both the template and calibration originate from the quantum chemical calculations, and are rooted in the perturbation theory of intermolecular forces. 

Leikin S, Kornyshev AA. Theory of hydration forces. Nonlocal electrostatic interaction of neutral surfaces. J. Chem. Phys. 1990 92 6890-6898. 

Specific coimter-ion effects are critical to biological function, in determining forces between individual sub-units of macromolecules and in the consequent shapes they take up. How much these effects can be attributed to physics and how much to specific chemistry can only be revealed by a reanalysis of all data in the light of the new theories of molecular forces. Until that reanalysis is done, present experimental inferences on binding surface potential and charge remain phenomenological curve fitting. 

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