Donnan potential drop

With the ion concentration so determined the current-voltage characteristic can be obtained by integrating the equation for the potential distribution. Again, as in the case of the electrolytic cell, some care must be exercised with respect to the boundary conditions. In particular, the total potential drop must equal that in the dialysate half-channel, plus that in the concentrate halfchannel, plus the Donnan potential drop across the membrane. The Donnan potential drop arises from the discontinuities in concentration at the boundaries of the membranes (in this case, the cation exchange membrane for the half-cell as considered). The origin and expression for the Donnan potential are the same as for the electrode concentration overpotential. For the cation exchange membrane the Donnan potential drop is... 

The same process of interfacial ion exchange determines the potential difference for other ion conductors, like membranes or SEs. The existence of this potential difference again leads to the formation of the EDL, but this time it is formed by excessive ionic charges in the surface layers of both solutions. Since this EDL is created by the ion transfer across the interface, without charge transport across the bulk media, the Donnan potential drop corresponding to the composition of the phases is established very rapidly. 

Building on initial work [47], the main focus of SECM in the study of ET at ITIES has been to identify and understand the potential-dependence of ET rates. In these studies, the potential drop across an ITIES has been controlled by varying the concentration of potential-determining ions in the two phases. The potential drop across an ITIES follows the Nernst-Donnan equation [74,75],... 

A terminological remark is due. An equilibrium between two media with different fixed charge density (e.g., an ion-exchanger in contact with an electrolyte solution) is occasionally termed the Donnan equilibrium. The corresponding potential drop between the bulks of the respective media is then termed the Donnan potential. By the same token, we speak of the local Donnan equilibrium and the local Donnan potential, referring, respectively, to the local equilibrium and the interface potential jump at the surface of discontinuity of the fixed charge density, considered in the framework of the LEN approximation. 

As far as the overall potential drop (E) is concerned, the contribution of solute polarization, namely the electric resistance (R ) and junction potential difference (TTj) across any boundary layer, may be neglected. On the contrary, the Donnan potential difference (Eu) in any cell pair, which behaves as a DC generator with inverted polarities with respect to those of the external DC generator (Figure 9), has to be accounted for as the solute concentration difference at both sides of the anionic and cationic membranes increases ... 

L and R represent the regions just inside a - membrane, in direct contact with - electrolyte. The - potential drop across the membrane consists of two - Donnan potentials associated with - ion exchange on the left and right side of the membrane and the - diffusion potential due to the concentration gradient within the - membrane. 

The total potential drop aeross the membrane is now estimated by adding the two Donnan potentials and the diffusion potential. The result is... 

An ion-selective electrode consists of a semipermeable membrane in contact with a reference solution on one side and the sample solution on the other. The membrane has to be selectively permeable to either a cation or an anion, but the penetration of the related counter ion must be restricted. Thus, charge sepeiration occurs at the interface leading to a potential difference (Donnan potential) which contains the analytically useful information. Within the membrane the diffusion of an ion is promoted by a concentration gradient, and when the mobilities of the cations and anions vary greatly, a diffusion potential is additionally developed by charge separation. The change in the membrane potential predominates, under well-deHned conditions (pH, ionic force, temperature), over changes in the overall cell potential due to concentration differences in the substance in question in the analyte. Hence, the cell potential is proportional to the potential drop over the ion-selective membrane. 

Brooks and coworkers [136,141] measured drop electrophoretic mobilities in ATPSs. They were surprised to discover that the sign of the droplet mobilities was opposite to that predicted from the phosphate partition and the Donnan potential. They also found mobility to be directly proportional to drop radius, which is a contradiction of standard colloid electrokinetic theory [144]. Levine [140] and Brooks et al. [141] hypothesized that a dipole potential at the phase boundary oriented in a way that reverses the potential gradient locally is responsible for the paradox of the sign of electrophoretic mobilities of ATPS droplets. 

The drop in Donnan potential is caused by the increased ratio of concentration of the peptide counterion, Cl , outside and inside the cell. 

As shown in Eqn. 26, the degree of oxidation or reduction of the electroactive coating is determined by the potential drop across the metal/polymer interface. Thus to describe the degree of charging of the system as a function of the electrode polarization E (relative to a reference electrode in the electrolyte), we must take into account the Donnan potential Disregarding short-range interactions of ionic... 

It is not a simple task to present precise pH and concentration dependence measurements, because changes in the pH and concentration of electrolyte refer to the solution phase, and thermodynamic relationships with respect to the film can only be obtained if an equilibrium exists between the film and solution phases. Constant ionic strength and constant pH should be maintained. Similarly, a liquid junction potential can distort observations. The formation of gas bubbles at extreme potential limits may cause ohmic drop and may also destroy the film. The pH values and ionic strength further assumes importance in light of experimental observations by Asturias et al. [73]. That polyaniline acts as an anion exchanger at pH 2 and 3 in its conductive state and its Donnan potential becomes... 

In the calculations in this section, in the spacer channel, we assnme a constant salt concentration, Csp. The membrane in front of the electrode is assumed to be 100% permselective, that is, only counter-ions can go through we also neglect a transport resistance within the membrane. In that case, the total potential drop from spacer across the manhrane (inclnding the two EDL Donnan edges of the membrane) to a point in the macropores located at the edge with the membrane is... 

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