Coions, defined

Since there is normally adsorption of counterion, the exclusion of electrolytes has been conventionally defined based on the exclusion of the coion. The exclusion coefficient is de-fmed as... 

If, however, a carrier-mediated transport membrane containing charged species — in the form of either mobile ions or fixed sites — were placed between two electrolytic mixtures, significant Donnan effects could be expected. For example, consider a membrane in which the carrier is a counterion to the permeant. The permeant would be expected to be preferentially included in the membrane phase. If significant inclusion were to occur, the use of simple first-kind boundary conditions would be inappropriate and could lead to underestimation of flux. On the other hand, if the permeant and carrier were coions, the permeant could be excluded and failure to account for exclusion could lead to overprediction of flux. Further complications would arise if the complex were charged or if other charged species were present, since the net charge density inside the membrane defines Donnan equilibrium conditions. 

The first issue is to define the innermost layer. For this, a distance from the rod is chosen which contains many counterions but virtually no coions. A distance of roughly 11.5 A from the rod axis turned out to be quite suitable. This is about a third ion diameter farther out than the distance of closest approach. To avoid difficulties with remaining coions, only the counterions within this distance are taken into account in what follows. In a second step, the coordinates of those ions are radially projected onto the surface of the cylinder of closest approach, and this surface is then rolled out to a flat plane see Figure 23 for an illustration of this procedure. Finally, the two-dimensional pair correlation function g(r) of these projected points is computed. 

Let us first make a rough estimate of the thickness by assuming that there are no positive ions (coions) present. Then the electric potential from the Poisson equation (Eqs. 3.4.5 and 3.4.7) is defined by... 

As usual, the subscript V denotes equilibrium values is the age of the interface, which is defined as the period of time between the minimum pressure (bubble formation) and the maximum pressure (bubble detachment) in the case of MBPM A, is a dimensionless parameter A = 1 for immobile interfaces in the case of MBPM, A is an apparatus constant that can be determined by calibration experiments [57] as mentioned earlier, and C2 are the bulk concentrations of surfactant ions and counterions, respectively y is the activity coefficient D f[ is an effective diffusivity that depends on the diffusivities and bulk concentrations of surfactant ions, counterions, and inorganic coions = >eff( i 2> 3> ioo> 2oo> The latter dependence is described by explicit formulas... 

As already mentioned, the electrostatic component of disjoining pressure can be defined as the excess osmotic pressure in the film midplane with respect to the bulk solution, see Equation 4.189. Hence, if all coions are expelled from the film, the expression for the disjoining pressure acquires the form [589] ... 

---