Plate macroions

The situation illustrated in Figure 4. la has by now become familiar. It depicts a gel composed of a parallel stack of plate macroions with a well-defined interplate spacing (in the colloidal range 10 to 100 nm) in equilibrium with a supernatant fluid. Let us think of the boundary of the gel as an effective membrane enclosing the macroions, transforming the picture into Figure 4.1b. This chapter is concerned with the calculation of the distribution of salt between the gel (I) and supernatant fluid (II) in the two-phase region of colloid stability. 

FIGURE 4.1 Schematic illustration of the phenomenon (a) a swollen n-butylammonium vermiculite gel and (b) the components present in the two phases, the gel (I) and supernatant fluid (II). The dotted line represents an effective membrane enclosing the plate macroions Pn. The symbols M+, X , and S stand for univalent counterions (n-butylammonium ions), univalent co-ions (chloride ions) and solvent (water) molecules, respectively. 

The n-butylammonium vermiculite system is an example of a three-component system of a monodisperse colloid, electrolyte and solvent. There are four constituents in the macroionic solution — the negatively charged clay plates, n-butylammonium ions (counterions), chloride ions (co-ions), and water — but these may not vary independently because they are subject to the restriction that... 

As far as I am aware, independent experimental evidence for the values of the surface potential and salt fractionation factor have not been obtained for any system other than the n-butylammonium vermiculite gels. For this isolated system, the predicted values of 5 from the Donnan equilibrium and the new equilibrium based on the coulombic attraction theory, namely 4.0 and 2.8, respectively, are definitely distinguished by the experimental results. It would be highly desirable to obtain further tests of our prediction for 5 in systems of interacting plate macroions, both in clay science and lamellar surfactant phases. 

The Exact Mean Field Theory Solution for Plate Macroions... 

Before setting out on the exact mean field theory solution to the one-dimensional colloid problem, I wish to emphasize that the existence of the reversible phase transition in the n-butylammonium vermiculite system provides decisive evidence in favor of our model. The calculations presented in this chapter are deeply rooted in their agreement with the experimental facts on the best-studied system of plate macroions, the n-butylammonium vermiculite system [3], We now proceed to construct the exact mean field theory solution to the problem in terms of adiabatic pah-potentials of both the Helmholtz and Gibbs free energies. It is the one-dimensional nature of the problem that renders the exact solution possible. 

So, what are we to make of the story that emerges from Chapters 1 to 8 The central result that emerged from Chapter 8 is that in a model clay system, the naked clay particle (of a thickness of about 10 A) is covered by two ordered layers of water molecules on each side, followed by a layer of counterions and another layer of partially ordered water molecules, to produce a dressed clay particle of a thickness of about 35 A. Within this dressed macroion, short-range molecular forces are dominant. We can interpret these as giving rise to an effective clay plate thickness of about 35 A in a swollen clay. 

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