Macroionic phase

Mechanical work done on the macroionic phase is stored as electrostatic energy in that phase. So, in the system under consideration, the Gibbs, Helmholtz and electrostatic energies are related by... 

It is a misinterpretation of the concept of a phase to consider these two possible sites for a counterion as separate phases. This confuses a macroscopic property of a well-defined phase (a solid) in equilibrium with another well-defined phase (a homogeneous electrolyte solution) with an internal property of an inhomogeneous single phase, the macroionic (or colloidal or gel) phase. It divides the macroionic phase into two regions that have no physical counterpart. 

By definition, in a solution all ions belong to the same phase, even though counterions may cluster more or less diffusely around the macroions. When significant amounts of a simple 1 1 electrolyte (such as KCl) are added to a polyelectrolyte solution, dissociation of the polyelectrolyte macromolecule is repressed in an extreme case the polyelectrolyte may be salted out. An undissociated polyacid may be precipitated by generous addition of a simple acid such as HCl. 

For the purpose of our discussion, we designate the side of the membrane that contains the macroions as the a phase and the solution from which the macroions are withheld as the /3 phase. Equation (12) continues to describe the equilibrium condition applying it to component 3 leads to the following ... 

Another factor that we have not yet taken into account is the requirement that both sides of the membrane be electrically neutral. For the a phase, which contains the macroion, this condition is expressed by... 

A11 concentrations are in moles per kilogram of solvent. The a phase contains positive macroions. 

The electrospray process consists of feeding a liquid through a metal capillary which is maintained at a high electrical potential with respect to some nearby surface. As the liquid reaches the capillary tip, the liquid is dispersed into fine electrified droplets by the action of the electric field at the capillary tip. If the liquid is volatile, as the liquid evaporates the droplets shrink in size, become electrically unstable, and break down into smaller size droplets. This process has been experimentally demonstrated by Doyle, Moffett, and Vonnegut (10) and by Abbas and Latham (11). If the liquid contains macromolecules, after the solvent has evaporated completely the macromolecules are left as electrically charged particles in the gas phase, that is, as gaseous 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. 

As g can also be calculated in terms of the surface potential (see below), Nlic can be calculated as a function of 4>s. When Ade is known, the average number density of the deficit, nie, can be calculated from Equation 4.6 the position of the coulombic attraction theory minimum is connected to the average electrolyte concentration in the gel phase because it defines the average volume occupied per macroion. The number density of the deficit of negative ions in the gel phase is given by... 

To calculate k in the gel phase, we continue to adopt the simple procedure used above in calculating 5, that of assuming that neither the macroions nor the counterions contribute toward the screening length. Because k is then determined solely by the electrolyte concentration, it seems logical to choose... 

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. 

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. 

Firstly, the two phases considered by Ettelaie do not have the same chemical composition. One phase (the surface-adsorbed phase) contains the macroion, and the other phase (the solution) does not contain the macroion. The condition for thermal equilibrium in these circumstances has been clearly stated by Guggenheim... 

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