Potential Donnan

The Donnan effect acts to exclude like-charged substrate ions from a charged surface region, and this exclusion, as well as the concentration of oppositely charged ions, can be expressed in terms of a Donnan potential pD. Thus for a film of positively charged surfactant ions S one can write... 

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. 

Finally some assumptions could not be verified as, e.g., the complete co-ion exclusion necessary for the treatment of the phase boundary potential as a Donnan potential, or the constant ion mobility through glass membranes with hydrated layers76). 

Ohshima, H Kondo, T, Electrophoretic Mobility and Donnan Potential of a Large Colloidal Particle with a Surface Charge Layer, Journal of Colloid and Interface Science 116, 305, 1987. O Neil, GA Torkelson, JM, Modeling Insight into the Diffusion-Limited Cause of the Gel Effect in Free Radical Polymerization, Macromolecules 32,411, 1999. 

FIG. 10 Nomalized unbalanced surface charge in a cylindrical pore with R = 5din the presence of an external potential The results, from left to right, are for original surface charge densities of —0.001, —0.005, —0.01, —0.02, —0.04, —0.05, —0.07123 C/m respectively. The x-intercepts are values of the corresponding equilibrium Donnan potentials. 

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). 

An ion-selective electrode contains a semipermeable membrane in contact with a reference solution on one side and a sample solution on the other side. The membrane will be permeable to either cations or anions and the transport of counter ions will be restricted by the membrane, and thus a separation of charge occurs at the interface. This is the Donnan potential (Fig. 5 a) and contains the analytically useful information. A concentration gradient will promote diffusion of ions within the membrane. If the ionic mobilities vary greatly, a charge separation occurs (Fig. 5 b) giving rise to what is called a diffusion potential. 

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

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. 

It can be readily seen that this procedure yields an equation whose left-hand side is the same as that for Eqs (6.1.6) and (6.1.7) and whose right-hand side is not equal to zero, but rather to v+(p — p2) or V-(pi — p2)-Equations (6.1.6) and (6.1.7) yield the Donnan potential A0D = A0M in the form... 

The Donnan potentials contain the individual ionic activities and cannot be measured by using a purely thermodynamic procedure. In the concentration range where the Debye-Hiickel limiting law is valid, the ionic activities can be replaced by the mean activities. 

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... 

Here, b is the distance between the nearest unit charges along the cylinder (b = 0.34nm for the ssDNA and b = 0.17nm for the dsDNA), (+) and (—) are related to cations and anions, respectively, and a = rss for the ssDNA and a rds for the dsDNA. The expressions (5) and (6) have been obtained using the equations for the electrostatic potential derived in [64, 65], where a linearization of the Poisson-Boltzmann equation near the Donnan potential in the hexagonal DNA cell was implemented. 

Ohshima, H. and Ohki, S. (1985). Donnan potential and surface-potential of a charged membrane, Biophys. J., 47, 673-678. 

Ohshima, H. and Kondo, T. (1987). Electrophoretic mobility and Donnan potential of a large colloidal particle with a surface-charge layer, J. Coll. Interf. Sci., 116, 305-311. 

Figure 2. Sodium and chloride uptake across an idealised freshwater-adapted gill epithelium (chloride cell), which has the typical characteristics of ion-transporting epithelia in eukaryotes. In the example, the abundance of fixed negative charges (muco-proteins) in the unstirred layer may generate a Donnan potential (mucus positive with respect to the water) which is a major part of the net transepithelial potential (serosal positive with respect to water). Mucus also contains carbonic anhydrase (CA) which facilitates dissipation of the [H+] and [HCO(] to CO2, thus maintaining the concentration gradients for these counter ions which partly contribute to Na+ import (secondary transport), whilst the main driving force is derived from the electrogenic sodium pump (see the text for details). Large arrow indicates water flow...

Donnan potential a voltage arising from the passive uneven distribution of diffusible ions, usually across a cell membrane, or between a mucus layer and simple saline solution. 

Freed of other restrictions, a mobile ion may be expected to diffuse down any concentration gradient that exists between porous solid and liquid. In the particular case of ion exchange, there is an additional requirement that the resin and liquid phases should remain electrically neutral. Any tendency for molecules to move in such a way as to disturb this neutrality will generate a large electrostatic potential opposing further movement, known as the Donnan potential. 

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 ... 

Figure 2.10 Scheme showingthe Donnan partition of mobile ions between the solution and a polymeric phase bearing an excess of negative charges. While positive ions are incorporated in the film to mantain electroneutrality, negative ions are excluded from it. This situation give rise to an interfacial potential (Donnan potential) at the interface. 

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]. 

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... 

The equilibrium (also known as the Donnan effect) established across a semipermeable membrane or the equivalent of such a membrane (such as a solid ion-exchanger) across which one or more charged substances, often a protein, cannot diffuse. Diffusible anions and cations are distributed on the two sides of the membrane, such that the sum of concentrations (in dilute solutions) of diffusible and nondiffusible anions on either side of the membrane equals the sum of concentrations of diffusible and nondiffusible cations. Thus, the diffusible ions will be asymmetrically distributed across the membrane and a Donnan potential develops. 

With some stationary phases at low pH values (<4) benzyl amine as benzyl ammonium ion can be excluded by a Donnan potential from the pores, when positive charges are present at the surface. These could have stemmed from the manufacturing process or could have been introduced on purpose to shield amines from interacting with silanols. With an increasing pH, the Donnan exclusion decreases and at pH >5 benzyl amine is retarded increasingly. An example of this effect with a modern RP with low silanophilic properties is demonstrated in Figure 2.22, where the elution peaks of benzyl amine are presented as a function of pH. With these stationary phases, basic analytes cannot be separated at low pH values. 

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