Free energy of a double

The total free energy of a double layer is the sum of an electrostatic free energy Fe, an entropic term due to the mobile ions Fent and a chemical free energy.6 The first one is given by... 

It is well known that Verwey and Overbeek and Derjaguin and Landau " " (DLVO) have given a quantitative treatment of the interaction of electrical double layers. According to them, the free energy of a double layer may be expressed as a difference between the surface energy G, of the system in its equilibrium state and the surface free energy G of a standard state in which no double layer is present ... 

To this end we shall consider, in the present chapter, the general problem of the free energy of a double layer system. 

As stated above, the free energy is the amount of work to be performed in building up, by some reversible and isothermal process, the double layers of the system. The formation of these double layers occurs spontaneously when the wall and the solution are brought into contact. Hence we can state, a priori, that the free energy of a double layer system must be a negatme quantity (work js gained by the formation). 

Fig. 18 Free energy profiles for the solvent extraction of copper, where L is Acorga P50. The profile shows the free energy of a site on the liquid/liquid interface. All higher-order rate constants are reduced to first-order rate constants by using the concentrations of reactants in either phase. The free energy lost in each cycle can be seen from the difference between 0 and the 10%, 50% and 80% extraction lines on the right of the diagram. The double-headed arrows indicate the rate-limiting free energy difference.

S. Fevine and A. Suddaby Simplified Forms for Free Energy of the Double-Layers of Two Plates in a Symmetrical Electrolyte. Proc. Phys. Soc. A 64, 287 (1951). 

In the DLVO framework, the free energy of a system of two overlapped double layers is composed of an electrostatic energy, an entropic contribution due to the ions in the double layer, and a chemical term, where applicable.4... 

The total interaction free energy of a film follows from a combination of electrical double layer and van der Waals-London interactions. 

Although this expression presents the basis of the free energy of the double layer, it is not truly expressive of the parameters that must be considered. According to Verwey and Overbeek and Ikeda, " the free energy of a system of reversible double layers is determined by the following ... 

Verwey and Overbeek formulated a second expression for the free energy of the double layer based on the Gouy-Chapman model. 

The determination of the free energy of a system of double layers may foUow a number of different ways. We shall here consider two methods. 

We already mention in 4 of Chapter III that this decrease of the double layer charge may well be considered to be the most important feature in the interaction of two double layers. It follows from equation (23) that the free energy of the double layer increases (becomes less negative) with decreasing charge. Now an increase of the free energy is equivalent to a repulsion between the plates, so this decrease of the charge is the primary cause of the repulsion between two double layers. This point is dealt with in more detail in Chapter V. 

In these two expressions, eq. (35) and eq. (36), we dispose of the necessary equations for the calculation of the variation of the free energy of the double layer system as a consequence of the interaction. 

In Chapter V we found that the repulsive potential V decreases with increasing distance according to a more or less exponential decay. At any rate the curve starts with a finite value oi Vfor zero distance (the free energy of the double... 

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