Donnan membrane potential

For the BOHLM systems (see Chapter 5) with water-immiscible carriers, the concentration gradient-driven solute-solvent complexation/ decomplexation interactions are the dominant driving forces. For the BAHLM systems, Donnan membrane potential [18-26, 32-36], osmotic pressure gradient [27, 37], and possibly pressure gradient [38-40], have to be added as driving forces. Therefore, the theory should take into account both diffusive and convective transport. 

The equilibrium conditions for homogeneous systems with membranes were first formulated in this form by Frederick G. Donnan in 1911. Hence, such equilibria are often called Donnan equilibria, and the membrane potentials associated with them are called Donnan potentials. Sometimes these terms are used as well for the equilibria arising at junctions between dissimilar solutions (Section 5.3). 

Cells of the type in Scheme 10 represent the simplest case of an ion-selective liquid cell its EMF is often called a membrane, or monoionic, potential [3]. The first term is too narrow due to the fact that the membrane potential corresponds to the behavior of a number of cells, including those of Schemes 8 to 11, and to the cells with solid membranes and with Donnan equilibrium. 

A Donnan membrane, i.e., a membrane impermeable to certain kinds of ions, which results in the occurrence of the Donnan potential. 

When the expressions (6.2.5) are substituted into the Henderson equation (2.5.34) A0l is obtained. Both contributions A0D are calculated from the Donnan equation. From Eq. (6.2.3) we obtain, for the membrane potential,... 

Due to the presence of interactions, the apparent redox potential of a redox couple inside a polyelectrolyte film can differ from that of the isolated redox couple in solution (i.e. the standard formal redox potential) [121]. In other words, the free energy required to oxidize a mole of redox sites in the film differs from that needed in solution. One particular case is when these interations have an origin in the presence of immobile electrostatically charged groups in the polymer phase. Under such conditions, there is a potential difference between this phase and the solution (reference electrode in the electrolyte), knovm as the Donnan or membrane potential that contributes to the apparent potential of the redox couple. The presence of the Donnan potential in redox polyelectrolyte systems was demonstrated for the first time by Anson [24, 122]. Considering only this contribution to peak position, we can vwite ... 

The action of so-called active transport, also known as ion pumps, facilitates larger Na" /K" gradients than those possible considering calculations of Donnan equilibria. For instance, the concentration of K+ in red blood cells equals 92 mM versus 10 mM in blood plasma. Calculation of the membrane potential using equation 5.11 would lead to a large negative potential ... 

Earlier, Gavach et al. studied the superselectivity of Nafion 125 sulfonate membranes in contact with aqueous NaCl solutions using the methods of zero-current membrane potential, electrolyte desorption kinetics into pure water, co-ion and counterion selfdiffusion fluxes, co-ion fluxes under a constant current, and membrane electrical conductance. Superselectivity refers to a condition where anion transport is very small relative to cation transport. The exclusion of the anions in these systems is much greater than that as predicted by simple Donnan equilibrium theory that involves the equality of chemical potentials of cations and anions across the membrane—electrolyte interface as well as the principle of electroneutrality. The results showed the importance of membrane swelling there is a loss of superselectivity, in that there is a decrease in the counterion/co-ion mobility, with greater swelling. 

The combined effects of electroneutrality and the Donnan equilibrium permits us to evaluate the distribution of simple ions across a semipermeable membrane. If electrodes reversible to either the M+ or the X ions were introduced to both sides of the membrane, there would be no potential difference between them the system is at equilibrium and the ion activity is the same in both compartments. However, if calomel reference electrodes are also introduced into each compartment in addition to the reversible electrodes, then a potential difference will be observed between the two reference electrodes. This potential, called the membrane potential, reflects the fact that the membrane must be polarized because of the macroions on one side. It might be noted that polarized membranes abound in living systems, but the polarization there is thought to be primarily due to differences in ionic mobilities for different solutes rather than the sort of mechanism that we have been discussing. We return to a more detailed discussion of the electrochemistry of colloidal systems in Chapter 11. 

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 concentration of all ions in the two surface layers in the membrane are considered to be given. These are related to those of the outer solution by a set of Donnan relations analogous to equation (24). Schlogl calculated the fluxes, the profiles of the concentrations in the membrane and the membrane potential. 

In order to obtain the membrane potential EM, the two Donnan potentials, which occur in the surface-layers membrane-solution, must be added to the diffusion potential. 

In order to obtain the membrane potential, any potential differences present in adhering liquid films must be taken into account, such in addition to the Donnan potentials. It should be observed that the splitting up of the membrane potential in diffusion potential, phase-boundary potentials and film potentials has met with opposition (49,121). 

Bi-Ionic Potentials (B.I.P s). If a membrane separates two salt solutions with two different counterions, but the same co-ion, the corresponding membrane potential is called bi-ionic potential. For the calculation of the B.I.P. this is split in a diffusion potential and two Donnan potentials. The diffusion potential can be calculated by proceeding from equation (37). 

Experiments with ion exchange membranes were described as early as 1890 by Ostwald [1], Work by Donnan [2] a few years later led to development of the concept of membrane potential and the phenomenon of Donnan exclusion. These early charged membranes were made from natural materials or chemically... 

F.G. Donnan, Theory of Membrane Equilibria and Membrane Potentials in the Presence of Non-dialyzing Electrolytes, Z. Elektrochem. 17, 572 (1911). 

This theory of an equilibrium of one species between each side of the membrane was formulated by Donnan in 1925 and from then until 1955, it reigned as the theory of membrane potentials. Its demise came when radiotracer measurements showed that all relevant ions (e.g., K+, Na+, and Cl ) permeated more than a dozen actual biological membranes, although each ion had a characteristic permeability coefficient in each membrane (Hodgkin and Keynes, 1953). 

Em, the corresponding liquid junction potential, is called the membrane potential or Donnan potential. Ideally Em changes in a Nernstian fashion with the activity of the ion in one of the phases, the activity in the other phase being held constant. This is the basis of the functioning of ion-selective electrodes (Chapter 13) and, to a good approximation, of biomembranes (Chapter 17). 

The double-layer model of the membrane consists of many particles (assume a diameter of 0.1 gm) that are impenetrable for solution and carry a surface charge. Electrical double layers exist around each particle, and because the dimensions of the membrane pores are of the same order as the double layers around the particles, double layers exist throughout the membrane pores. The potential measured by the underlying ISFET, with respect to the bulk potential, is on one hand determined by the mean pore potential, which is the net result of the contribution of all surface potentials of the charged particles, and on the other hand by the pH at the membrane-1 SFET interface. The measured ISFET response in equilibrium is therefore the same as that of an ISFET without a membrane, because the distribution of the protons between membrane and solution results in a pH difference, which compensates the mean membrane potential (this is the same mechanism as in the Donnan model). The relation between the surface charge on the particles a (C/cm2) and the surface potential jx of each particle is given by... 

For the interpretation of the parameters that influence the membrane potential a general three-segment model of Teorell [17], Meyer and Sievers [18] (TMS model) is often used (Figure 4). The membrane potential (Equation 1) is given by the potential of the (inner) reference solution (O ) minus the potential of the sample solution ([Pg.196]

FIGURE 28.3 Membrane potential E, contributions from the diffusion potential and the Donnan potential difference AiJ/y)on — / don / don functions of the density of memhrane-fixed charges N. The values of the parameters used in the calculation are the same as those in Fig. 28.2. The dashed line is the approximate result for E (Eq. (28.21)). As A—> CX3, ni tends to the Nemst potential for cations (59 mV in the present case). From Ref. [7]. 

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