Donnan equilibrium potential

However, as soon as at the eluate-side H ions are replaced with an equivalent amount of Na or K ions, which elute, the then asymmetric cell acquires a potential that reflects the Donnan equilibrium potential on the basis of the ion mobilities concerned. Hence the potential change as a function of time represents the ionic chromatogram and the peaks concerned yield the alkali metal ion contents via calibration. 

Formerly, the membrane potential in biological cells was thought to be due to this Donnan equilibrium potential. Bernstein suggested that the resting membrane potential was determined by the ratio of potassium ion concentration inside and outside the cell. The relative impermeability of Na" across the cell membrane was observed by Boyle and Conway. The validity of the formula of the membrane potential for biological cells... 

The boundary potentials E and j are expressed by the Donnan equilibrium potentials which are... 

For biological membranes and polymer-resin membranes, which may contain charged groups within the membrane matrix, the above argument with regard to the contribution of the surface potential to the transmembrane potential may not be valid. In particular, when there are highly conductive ionic channels composed of lipoprotein molecular assemblies within the membrane (where channels may be mostly hydrophilic and probably main ionic transport pathways across the membranes), the observed transmembrane potential is a very complicated mixture of ion diffusion and Donnan equilibrium potentials. The idealized surface potential concept may not be a good approach to analyze such a transmembrane potential. 

Another approach, also based on thermodynamic equilibrium concepts, invokes the Donnan equilibrium potential, which for univalent ionic solutions separated by a membrane gives... 

Concentration of Electrolyte Myer and Sievers"" applied the Donnan equilibrium to charged membranes and developed a quantitative theory of membrane selectivity. They expressed this selectivity in terms of a selectivity constant, which they defined as the concentration of fixed ions attached to the polymer network. They determined the selectivity constant of a number of membranes by the measurement of diffusion potentials. Nasini etal and Kumins"" extended the measurements to paint and varnish films. 

At each phase boundary there exists a thermodynamic equilibrium between the membrane surface and the respective adjacent solution. The resulting thermodynamic equilibrium potential can then be treated like a Donnan-potential if interfering ions are excluded from the membrane phase59 6,). This means that the ion distributions and the potential difference across each interface can be expressed in thermodynamic terms. 

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefficients or distribution constants of the ions, 5 (M+) and B X ), are related to the extraction constant the... 

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 semi-permeable membrane, which is unequally permeable to different components and thus may show a potential difference across the membrane. In case (1), a diffusion potential occurs only if there is a difference in mobility between cation and anion. In case (2), we have to deal with the biologically important Donnan equilibrium e.g., a cell membrane may be permeable to small inorganic ions but impermeable to ions derived from high-molecular-weight proteins, so that across the membrane an osmotic pressure occurs in addition to a Donnan potential. The values concerned can be approximately calculated from the equations derived by Donnan35. In case (3), an intermediate situation, there is a combined effect of diffusion and the Donnan potential, so that its calculation becomes uncertain. 

This theory will be demonstrated on a membrane with fixed univalent negative charges, with a concentration in the membrane, cx. The pores of the membrane are filled with the same solvent as the solutions with which the membrane is in contact that contain the same uni-univalent electrolyte with concentrations cx and c2. Conditions at the membrane-solution interface are analogous to those described by the Donnan equilibrium theory, where the fixed ion X acts as a non-diffusible ion. The Donnan potentials A0D 4 = 0p — 0(1) and A0D 2 = 0(2) — 0q are established at both surfaces of the membranes (x = p and jc = q). A liquid junction potential, A0l = 0q — 0P, due to ion diffusion is formed within the membrane. Thus... 

The movement of solute across a semipermeable membrane depends upon the chemical concentration gradient and the electrical gradient. Movement occurs down the concentration gradient until a significant opposing electrical potential has developed. This prevents further movement of ions and the Gibbs-Donnan equilibrium is reached. This is electrochemical equilibrium and the potential difference across the cell is the equilibrium potential. It can be calculated using the Nemst equation. 

Donnan potential (ptrYS chem) The potential difference across a boundary between two electrolytic solutions in Donnan equilibrium. dan-on p3,ten-chol ... 

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. 

A related phenomenon occurs when the membrane in the above-mentioned experiment is permeable to the solvent and small ions but not to a macroion such as a polyelectrolyte or charged colloidal particles that may be present in a solution. The polyelectrolyte, prevented from moving to the other side, perturbs the concentration distributions of the small ions and gives rise to an ionic equilibrium (with attendant potential differences) that is different from what we would expect in the absence of the polyelectrolyte. The resulting equilibrium is known as the Donnan equilibrium (or, the Gibbs-Donnan equilibrium) and plays an important role in... 

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. 

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. 

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... 

We now consider a capsule which consists of liquid surrounded by a closed semi-permeable membrane (figure 2) details are provided in [3,4], Water and salt can pass through the membrane from side 1 (inside the capsule) to side 2 (outside), and vice versa, but large polymer molecules cannot. Trapped inside the capsule are n p polyelectrolyte molecules of valence zp and partial molar volume Tip. The resulting Donnan equilibrium is reviewed in [5, 6], Inside the capsule, electroneutrality requires zpn p + z+n + + Z-ri - = 0. We now assume the salt to be monovalent. At equilibrium there is a jump in electrical potential across the membrane inside the capsule x +xi- r X2+X2- x2 with x = (Q =F zpX p) where... 

It is therefore clear that the Donnan potential for equilibrium potentials (Section 2.11) cannot be used in (17.3), except in special circumstances, since there are various components in the total transmembrane potential. Donnan himself predicted that the phenomenon would be more complicated for ion transfer processes between living cells or tissue and the liquids that surround them9. This transmembrane potential is not, however, the only one that can occur in the membrane10. 

Adsorbed films between two immiscible liquids. The question of the meaning of the term pn in the surface layer has been raised by Crax-ford, Gatty, and Teorell,2 without, however, coming to any very clear decision. Danielli s estimate was a very rough one, based on the application of the Donnan equilibrium between the surface layer and the interior, and suffers from the difficulties always attending an attempt to consider concentrations in the surface layer in a similar way to concentrations in a bulk phase the surface layer is not homogeneous. pH is closely related to, and is determined by, the electrochemical potential (see Chap. VIII, pp. 304 ff.), and this depends on the electrostatic potential, which varies rapidly at different levels near to the surface it appears possible that the only satisfactory definition of pa in the surface may be one which varies rapidly at different depths. The question appears one which would repay... 

Sep. 5,1870, Colombo, Ceylon (British Empire), now Sri Lanka - Dec. 16,1956, Canterbury, Kent, UK). Donnan was a British chemist who greatly contributed to the development of colloid chemistry, physical chemistry, and electrochemistry [i—iii]. In different periods of his life, he was working with van t - Hoff, -> Ostwald, F. W., and Ramsay. In electrochemistry, he studied (1911) the electrical potential set-up at a semipermeable membrane between two electrolytes [iv], an effect of great importance in living cells [v], Donnan is mostly remembered for his theory of membrane equilibrium, known as - Donnan equilibrium. This equilibrium results in the formation of - Donnan potential across a membrane. 

Equation (6.148) is the well-known Donnan equilibrium of salt across a membrane in the presence of a polyelectrolyte, to which the membrane is permeable. It demonstrates the characteristic properties of the chemical potentials of neutral salts. 

Under the condition of electroneutrality, Eq. (10.1) describes the Donnan equilibrium across a membrane, which separates solutions containing nonpermeating ions. With the Donnan equilibrium, differences of pressure and electric potential will appear. If the nonpermeating components are electrically neutral, only the pressure difference occurs. 

Figure 4.1b is a typical illustration of the Donnan equilibrium [1], A membrane impermeable to macroions (P" ) but permeable to small ions (M+, X ) and solvent molecules (S) divides a solution into two regions. The situation is a common one in colloid science, and the fact that the equilibrium salt concentration in region II (the simple electrolyte solution), [X ]n, is greater than that in region I (the region occupied by the macroions), [X ]I( has been used in countless dialysis experiments. It is also well known [2] that equilibrium involves the establishment of not only a pressure difference but also an electrical potential difference across the membrane and that, in the simple case where the mobile ions behave as ideal solutes, the equilibrium condition is expressed as... 

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