Donnan, distribution

Winzor and coworkers have employed measurements of the Donnan distribution of small ions in dialysis equilibrium [14] to reinforce earlier evidence of charge-screening effects in polysaccharide anions [164,165]. These researchers used the absorption optical system of a Beckman XL-1 ultracentrifuge to monitor the distribution of ions in polysaccharide solutions... 

Comparison of the concentrations of either the cation or the anion in the two phases thus has potential for evaluating the polyanion valence provided that estimates of the mean ion activity coefficient (y ) are available. Furthermore, as realized by Svensson [165], expression of the Donnan distribution of small ions in this manner has two advantages in that (i) Eq. 31 applies to each type of small ion in situations where the supporting electrolyte is not restricted to single cationic and anionic species and (ii) multivalence of a small ion is also accommodated. 

Equation (38) gives an explanation for the curves reported in different salt solutions At high salt concentration the potential goes to zero and cq- approaches cq-, so that both terms diminish and the titration curve approaches that of a monofunctional acid. At low salt concentrations the potential is high and the Donnan distribution requires ccr >... 

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 ... 

To estimate the limiting value t (i) and to introduce the molal fixed charge concentration X, expressed in equivalents of univalent fixed anions per kg of water sorbed by the membrane, we have treated the ion concentrations in the membrane as being governed by a Donnan distribution. 

The ideal Donnan contribution, A /([ is a consequence of the Donnan distribution of diffusible ions. This phenomenon arises from a tendency to drive towards fulfilment of the condition of electrical neutrality in the solution (Tanford, 1961 Nagasawa and Takahashi, 1972), leading to the expression... 

As shown in Eqs. (3.9) and (3.10), the concentration of migrating cations is a squared function of the adsorbate concentration in the outer volume of the solution. The Donnan distribution is a source of serious error when determining M of ionic polysaccharides by membrane osmometry. Polyanions may be freed of cations and excess HsO+ by electrodialysis. 

Donnan distribution, leading to abnormally high tt, is a most serious source of error for Mn of polyanions measured by osmometry. The Donnan effect is allegedly overcome by very dilute concentrations that never exceed 25 g L 1 for the polyanion and i = 0.3 mol L-1 for the solvent (Wagner, 1949). A 25-g L-1 polysaccharide concentration is in the semidilute-to-concentrated domain, outside the theoretical dilution limit of osmometry where a power-law dependence of tt/c, on ct is expected. 

Equations (7.5)—(7.11) illustrate the effect of Donnan distribution on osmometry. Recalling Eq. (4.29) (,nVj = ntRT ), assuming an equivalent weight... 

Notwithstanding the problems associated with the Donnan distribution, a pectin Mn was obtained from e = 10-2 g mL-1 dispersion in 0.05-M sodium chloride and reported to have approximated Mn by reducing end-group analysis (Fishman et al., 1986). 

As pointed out already, since the inside of the cell is separated from the surrounding medium by a membrane with selective permeability, the potassium and chloride ions on both sides of the membrane are distributed according to Donnan distribution. The Donnan law states that the charges on both sides of the membrane are to be neutralized, and that the product of the diffusible ions on one side of the membrane equals the product of the diffusible ions on the other. In any cell, the diffusible cations (only potassium, since the membrane is virtually impermeable to sodium) traverse the membrane in order to neutralize the intracellular fixed negative charges (organic phosphates and carboxyl groups). 

Here X is known as the Donnan distribution coefficient, expressed by the membrane equilibrium condition in the presence of various ion types by... 

Fig. 59. Donnan distribution. The inner compartment contains a protein solution protein anions are neutralized by Na" " ions. In a, NaCl has been added to the outer compartment in b, Donnan equilibrium has been reached. It can be seen that the inner compartment contains more Na+ the outer one, more Cl . Inside, the osmotic pressure is higher.

The Donnan distribution does not result in osmotic equilibrium. The sum of diffusible ions is higher inside than outside and, consequently, the pressure inside must be higher. This is aggravated by the colloid-osmotic pressure of the macromolecules. The cell walls have to adjust to the rise of pressure if this is not possible, the cells burst. This is the case, for example, with erythrocytes if they become permeable to cations and become subject to the Donnan laws (osmotic hemolysis). 

Not only osmotic pressure and light scattering data confirmed this model but other thermodynamic measurements as well, such as enthalpy of dilution and Donnan distribution for polyelectrolyte gels, were in excellent agreement [7]. Electrical transport phenomena, moreover, could be very satisfactorily explained by the concept of two counter-ion populations, one condensed and one non-condensed, which depended upon the chain charge density. For example, the very precise conductance data of Eisenberg and Sachs [8] could be accounted for in terms of the osmotically determined 0p. 

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