Planar double layers, interaction free

Since the equations of state of the system are summarized by the curves in Figure 2, all interesting thermodynamic properties of the interface will have a simple representation in such a diagram. We shall consider the free energy of formation of a single charged surface and the interaction free energy due to the overlap of two identical planar double layers. 

The interaction free energy per unit area between two planar double layers V(L) is just the difference between the change in free energy per unit area in charging up two surfaces at a distance L apart and that at infinite separation... 

In this Appendix, equations will be derived for the double layer interaction between two charged, planar surfaces in an electrolyte-free system. W e assume that the potential ip(x) obeys the Poisson—Boltzmann equation... 

The present approach reduces to the traditional ones within their range of application (imaginary charging processes for double layer interactions between systems of arbitrary shape and interactions either at constant surface potential or at constant surface charge density, and the procedure based on Langmuir equation for interactions between planar, parallel plates and arbitrary surface conditions). It can be, however, employed to calculate the interaction free energy between systems of arbitrary shape and any surface conditions, for which the traditional approaches cannot be used. 

The purpose of this article is to present a model and to calculate on its basis the metastable equilibrium thicknesses of the film as a function of the applied pressure. In section II, the interaction energy of the film was calculated, assuming planar interfaces free of thermal fluctuations. The double layer interaction was calculated by accounting for the charge recombination at the surface with increasing electrolyte concentration. An approximate... 

In the earlier paper, the free energy of activation for the rate process in which a vesicle approached the synaptic membrane was treated as an electrostatic interaction between a positive point charge and the field of the membrane. It would be more appropriate to consider the interaction between two diffuse double layers. Such a problem was considered in detail by Verwey and Overbeek, who obtained the following expression for the potential energy per unit area between two planar double layers having identical surface potentials and separated by a distance d ... 

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