Donnan ratio

Equation (3.7) describes the equality of the chemical potentials of the mobile ions on both sides of the gel boundary expressed through the Donnan ratio KD and the ion charges z, Eq. (3.8) concerns the dissociation equilibrium of ionizable (carboxyl) groups of the network a is the degree of dissociation, eg is the concentration of the hydrogen ions in the gel Eq. (3.9) represents the gel electroneutrality condition. 

When a layer of protein molecules is in thermodynamical equilibrium with a solution with a certain pH and ion concentration, the ions in the solution and in the protein layer will be distributed according to the Donnan ratio (the ratio of the ion activities in the two phases). As a results, there will exist an electrical potential difference between the protein layer and the bulk solution, which is known as the Donnan potential. 

When there are multivalent ions in the system, the Donnan ratio is generally written as ... 

Equilibrium is assumed to prevail here at the boundaries of the membrane (e.g., the membrane is assumed to be thick or else it is a very thin film having a low ionic conductance so that the main resistance to the ionic fluxes is localized in the membrane proper and the equilibrium on the surfaces has enough time to be practically established) so that the boundary potential may be expressed by the Donnan ratios for the ions, and these ratios are determined from the fixed charge density in the membrane and the surrounding electrolyte concentrations. The diffusion potential, Eam, has a somewhat complicated expression. With the conditions of electroneutrality, zero electrical current, and a quasi-stationary state for each ion species, the expression for E m is... 

Membrane Efficiency The permselectivity of an ion-exchange membrane is the ratio of the transport of electric charge through the membrane by specific ions to the total transport of electrons. Membranes are not strictly semipermeable, for coions are not completely excluded, particularly at higher feed concentrations. For example, the Donnan eqmlibrium for a univalent salt in dilute solution is ... 

Figure 1 shows a set of calculated potential profiles for different electrolyte concentrations. For each curve, the asymptotic value on the left is ij/D, while the intercept with ordinates is i//Dm. For large c, the profile approaches the step functionality of the pure Donnan model. Note that for low potentials, the ratio... 

Manipulation of the Donnan potential in random polymer-modified electrodes can also be achieved. In the case of cast redox polyelectrolyte-modified electrodes one can control ion permselectivity by mixing the redox polymer with an oppositely charged polyelectrolyte in an appropriate ratio before film casting [123]. The same strategy can be followed in electropolymerized films by mixing the electroactive monomer with one of opposite charge [124]. 

C. Ende have shown that lithium chloride has a tendency to polymerize when dissolved in alcohol and other organic solvents H. C. Jones and co-workers have also shown that there is a tendency to form complexes between the lithium salt and the organic solvent while E. W. Washburn and E. W. Mclnnes calculate that in a JN-aq. soln. of lithium chloride, each mol. of the solute is hydrated with 18 mols. of the solvent. F. G. Donnan and W. E. Garner have studied the distribution ratio of lithium chloride between amyl alcohol and water. [LiCl]Am h[LiCl]Aq =0-0273. 

In these experiments respiring mitochondria are observed to take up the K+ or Rb+ to give a high ratio of K+ inside to that outside and consequently a negative Em. There are problems inherent in the method. The introduction of a high concentration of ion perturbs the membrane potential, and there are uncertainties concerning the contribution of the Donnan equilibrium (Eq. 8-5) to the observed ion distribution.184... 

The membrane perm-selectivity (y.m) is defined as the ratio between the actual and theoretical transfer of counterions through any IEM. It can be simply determined as the percentage ratio between the experimental and theoretical Donnan potential differences as measured using a test system consisting of two cells provided with calomel electrodes and filled with well-mixed standardized aqueous solutions of KC1 (at 0.1 and 0.5 kmol/m3), kept at 25 °C, and separated by the IEM sample under testing. 

For Eq. (26) only ftee metal ion is assumed to enter the cation exchanger phase. This assumption is acceptable only when Donnan invasion of negatively charged species is sufficiently low. VC th the two distribution ratios made available from a common equilibrating solution their ratio is examined to provide the following alternate path to species identification ... 

This equation indicates that the ApK term defined at a specified a value reflects the fi%e H -ion concentration ratio between the Donnan phase and the bulk solution phase. 

In such experiments the initial free H ion contained by the initial solution contacted with the cation exchanger must displace Na ion in the resin phase until equilibrium is reached. At this point the ratio of Na and H activity ratios in the resin and solution phases, i.e., the Donnan potential term, are equal. Once this process begins the increasing presence of H ion in the resin phase leads to the ion-ti sfer process described in Eq. (20) and nonequivalence of ion transfer is the hilse impression. 

---