Disjoining pressure between charged surfaces

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... 

A nice example of double layer effects occurs with the lamellar phases discussed in Section II. We already mentioned the beautiful experiments of Safinya et al.20 where the Helfrich undulation force was clearly demonstrated, using electrostatic interactions between the layers as a control parameter. Let us try to understand how the electrostatic interlayer forces have impact upon the undulation interaction Recall (Eqn. III.3) that the counterion distribution in the neighborhood of a single charged surface falls off as x 2 for x A. Since the counterions may be approximately considered as an ideal gas,the double layer contribution to the disjoining pressure between two lamellae separated by a distance, h, is roughly... 

Disjoining pressure was attributed in Ref 54 to the combined effect of van der Waals attraction and long-range electrostatic repulsion between similarly charged membrane surfaces. 

Note that the farther away the electric potential of the carbon surface is from the potential of zero charge point ( pzc) l e higher the disjoining pressure is. In principle, this may result in a systematic variation of the support pore size in Me/C catalysts with potential (similar to the electrocapillary curve [96,97]) and consequently the efficiency of metal particle blocking by the pore walls. Such behavior of porous carbons obviously can influence the measurements of the electrochemically active surface area and might be one of the reasons for the observed correlation between the apparent dispersion of Pt/C catalysts, measured by cyclic voltammetry, and pHpzc of the supports [95], whereas no noticeable difference in the particle size has been observed with HRTEM. Undoubtedly, this problem needs further investigation. 

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). 

When two charged surfaces approach each other at some point, the electric double layers start to overlap and a force, also called disjoining pressure, begins to act [13, 145]. This electrostatic double-layer force decays roughly exponentially. When the surface potentials of both surfaces are below approximately 25 to 50 mV, the force between a spherical tip and a flat sample can be approximated in an analytical form [146-149] ... 

Disjoining Pressure, Fig. 5 and 2 are electrical potentials of charged surfaces. and 2 are both negative, (a) The distance between two negatively charged surfaces, h, is bigger than the thickness of the Debye layers, R. Electrical double layers do not overlap and there is no electrostatic interaction between these surfaces, (b) The... 

Let us first consider the electrostatic (double-layer) interaction between two identical charged plane-parallel surfaces across a solution of a symmetrical Z Z electrolyte. If the separation between the two planes is very large, the number concentration of both counterions and coions would be equal to its btllk value, no, in the middle of the film. However, at finite separation, h, between the surfaces, the two electric double layers overlap and the counterion and coion concentrations in the middle of the film, nio and respectively, are no longer equal. As pointed out by Langmuir [311], the electrostatic disjoining pressure, Del, can be identified with the excess osmotic pressure in the middle of the film ... 

Equation 1.12 and Equation 1.13 show that the disjoining pressure does not vanish even in cases when only one of the two surfaces is charged (for example, = 0). The physical reason for this phenomenon is the deformation of the electrical double layer, if the distance between the surfaces is smaller than the Debye radius. 

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