Donnan potential difference

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. 

By referring to Figure 9, in any cell pair the presence of an anionic and a cationic membrane gives rise to four boundary layers and thus to four junction potentials differences ( ja,k ar d jc,k) and two Donnan potential differences ( Da and k )c). their mathematical expressions being given in Table IV. 

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 ... 

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]. 

Ad is the Nernst-Donnan potential difference between the nonaqueous fraction and the aqueous solution of RE2 with the common ion A+ ... 

With different concentrations on each side, such membranes generate an osmotic pressure difference. With different ionic concentration also an electrical potential difference is generated. This is called the Donnan potential difference,... 

A more simplified model was presented in Ref. 10, where the membrane was assumed to be perfectly permselective toward the counter-ion, and the salt concentration in the macropores of the electrode assumed to be unvarying in time. A basic element in the modeling of the membranes in MCDI is that in the membrane the cation concentration is different from the anion concentration, with the difference compensated by the fixed membrane charge density, X. Except for this difference, the same ion transport model can be used as in free solution (Nemst-Planck equation), thus, with ions moving under the influence of a concentration gradient and because of an electrical field (electromigration). At the edges of the membranes, a Donnan potential difference develops between the outside solution and inside the membrane. For more information on MCDI, see Section 15.4.3, where a porous electrode is modeled which has an ideally permselective membrane layer in front. 

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. 

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. 

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 ... 

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 ... 

At equilibrium there is a zero free-energy change, AG=0, that takes place between compartments separated by a membrane, with the free-energy change being dependent on the difference in concentration of various ions and the electrical potential difference that exists across the membrane. The relationships among sodium, potassium, and chloride ions, pH, and electrolytic potential have become known as Donnan equilibria. The concentrations and electrolytic potentials are related by the following equation ... 

When a constant ionic strength of the test solution is maintained and the reference electrode liquid bridge is filled with a solution of a salt whose cation and anion have similar mobilities (for example solutions of KCl, KNO3 and NH4NO3), the liquid-junction potential is reasonably constant (cf. p. 24-5). However, problems may be encountered in measurements on suspensions (for example in blood or in soil extracts). The potential difference measured in the suspension may be very different from that obtained in the supernatant or in the filtrate. This phenomenon is called the suspension (Pallmann) effect [110] The appearance of the Pallmann effect depends on the position of the reference electrode, but not on that of ISE [65] (i.e. there is a difference between the potentials obtained with the reference electrode in the suspension and in the supernatant). This effect has not been satisfactorily explained it may be caused by the formation of an anomalous liquid-junction or Donnan potential. It... 

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. 

This potential difference is called Donnan potential and is given by ... 

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). 

Even for this simplest of all situations we had to make a fairly drastic assumption of high concentration of NaCl, in order to get from (6.11) to (6.13). The situation is considerably more complicated when different multivalent ions are present in the solution, although the basic argument is the same. In biological fluids, such as whole blood, the value of the Donnan potential across the dialysis membrane can be tens of millivolts. (In the above derivation of the Donnan potential, concentrations instead of activities have been used for purely historical reasons.)... 

MATHEMATICAL EXPRESSIONS OF THE JUNCTIONS ( ja t AND lir,M) AND DONNAN ( Da AND POTENTIAL DIFFERENCES FOR A GENERIC ANIONIC... 

CD is the Donnan capacitance, which tells us about the amount of charge in the pores accumulated by the potential difference between ED and E, the potential in the pores. When only counterion is present, CD will be given by... 

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. 

Donnan potential — is the - Galvani potential difference between two solutions separated by an -> ion-exchange membrane in the absence of any current flowing through the membrane. This potential originates from the different distribution of cations and anions on both sides of the semipermeable membrane. See also - potential. 

Consider a gel that carries a certain concentration c,-(r) of immobile negative charges and is immersed in an aqueous solution. The bulk solution carries monovalent mobile ions of concentration c+(r) and c (r). Away from the gel, the concentration of the salt ions achieves the bulk concentration, denoted c0. What is the difference in electrical potential (known as the Donnan potential) between the bulk solution and the interior of the gel [Hint assume that inside the gel the overall concentration of positive salt ion balances immobile gel charge concentration.]... 

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