Equilibrium Donnan

The DonnarP equilibrium is related to osmosis. However, it deals with eharged particles. Therefore, not the ehemieal potential, but rather the electrochemieal potential is the starting point to ealeulate the equilibrium. 

Electrocbemical systems consisting of two parts where one or more charged species is restricted to one part of the system by a semipermeable membrane were first investigated by Donnan in the early twentieth century. In such systems, the equilibrium condition for all solute species is that their electrochemical potentials are equal on both sides of the membrane  

From Equation (1) the relation for the activities of ionic solute species on both sides is 

---

There are two additional concepts which we can invoke to simplify Eq. (8.118) electroneutrality and a less familiar principle called Donnan equilibrium. Some relationships pertaining to these are developed below ... 

Donnan equilibrium arises from applying the phase equilibrium criterion to the indifferent electrolyte . From Eq. (8.13) this is /ia = +... 

This last result describes the Donnan equilibrium condition as it applies to the system under consideration. Like other ionic equilibrium expressions, it requires the equality of ion products in equilibrium solutions. 

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. 

When the Donnan equilibrium is operative the entry of ions into the membrane is restricted. Consequently as the concentration of ions in the solution increases the resistance of the membrane remains constant until the concentration of ions in the solution reaches that of the fixed ions attached to the polymer network. At this point their effect will be swamped and the movement of ions will be controlled by the concentration gradient. 

Films of a pentaerythritol alkyd, a tung oil phenolic and an epoxypolyamide pigmented with iron oxide in the range 5-7% p.v.c. were exposed to solutions of potassium chloride in the range 0.0001-2.0 m. It was found that in all cases the resistance of the films steadily decreased as the concentration of the electrolyte increased. Since the resistances of the films were at no time independent of the concentration of the electrolyte, it was concluded that the Donnan equilibrium was not operative and that the resistance of the films were controlled by the penetration of electrolyte moving under a concentration gradient. 

Membrane Efficiency The permselectivity of an ion-exchange membrane is the ratio of the transport of electric charge through the membrane by specific ions to the total transport of electrons. Membranes are not strictly semipermeable, for coions are not completely excluded, particularly at higher feed concentrations. For example, the Donnan equilibrium for a univalent salt in dilute solution is ... 

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. 

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. 

Overbeek, J. Th. G., The Donnan equilibrium, in Progress in Biophysics and Biophysical Chemistry, Vol. 6, Pergamon Press, London 1956. 

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... 

For homopolyelectrolyte, we first studied the ellipsometric measurement of the adsorption of sodium poly(acrylate) onto a platinum plate as a function of added sodium bromide concentration (5). We measured the effect of electrolyte on the thickness of the adsorbed layer and the adsorbances of the polyelectrolyte. It was assumed that the Donnan equilibrium existed between the adsorbed layer and the bulk phase. The thickness was larger and the adsorbance of the polyelectrolyte was lower for the lower salt concentration. However, the data on the molecular weight dependence of both the adsorbance and the thickness of the adsorbed polyelectrolyte have been lacking compared with the studies of adsorption of nonionic polymers onto metal surfaces (6-9). 

Since the components in the adsorbed polyelectrolyte layer are considered to be the same as the bulk phase with a three component system which consists of polyelectrolyte, simple salt, and water, we calculate the adsorbances of polyelectrolyte and salt by assuming the Donnan equilibrium between the bulk phase and the adsorbed polyelectrolyte layer, as described previously (5). 

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 distribution coefficient phys chem A coefficient In an expression giving the distribution, on two sides of a boundary between electroiyte solutions in Donnan equilibrium, of ions which can diffuse across the boundary. dan-on, dis-tro byu-shon, kO-o,fish-ont ... 

Donnan equilibrium phys chem The particular eq ul 11 bri u m set up when two coexisting phases are subject to the restriction that one or more of the ionic components cannot pass from one phase into the other commonly, this restriction is caused by a membrane which is permeable to the solvent and small ions but impermeable to colloidal ions or charged particles of colloidal size. Also known as Gibbs-Donnan equilibrium. dO-non e-kwo lib-re-om ... 

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. 

Assuming Donnan equilibrium with an external solution containing c concentration of an electrolyte Mv+Av, one may write... 

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... 

VIGNETTE III BIOPHYSICS AND PHYSIOLOGY Donnan Equilibrium and the Resting States of Nerve Cells... 

For our purpose here, we are interested in the following question How do the membranes maintain the ionic environments in the cell over long periods of time while simultaneously allowing transmembrane passage of the needed ions The mechanism that makes this possible is the so-called Donnan equilibrium we discuss the details of this equilibrium in this chapter, but a qualitative picture of the Donnan effect can be obtained with the help of a simplified model of a cell shown in Figure 3.1 (See, also, Section 3.5a.). 

---