Donnan correction

Note that this treatment inherently takes into account the effect of the Donnan equilibrium. The osmotic coefficient obtained therefore is that of the polyelectrolyte with no further Donnan correction term being necessary. 

The measured colloid-osmotic pressure of proteins in salt or buffered solutions will be too high because of the unequal distribution of the small ions. This effect can be calculated in advance and taken into account as a so-called Donnan correction. These effects are larger the higher the net charge on the proteins at the isoelectric point, however, the Donnan effects disappear completely. 

Clearly, the results of osmotic pressure measurements on solutions of charged colloidal particles, such as proteins, will be invalid unless precautions are taken either to eliminate or to correct for this Donnan effect. Working at the isoelectric pH of the protein will eliminate the Donnan effect but will probably introduce new errors due to coagulation of the protein. Working with a moderately large salt concentration and a small protein concentration will make the... 

The work of Yaillant3 and Lewis 4 has shown that the colour changes cannot be quantitatively interpreted without considering that water plays a definite r61e in the reactions. It follows that if Donnan and Bassett s views on complex ion formation be correct, water is either produced or used up when cobalt chloride and chloride ion interact thus, for example, where the ion CoCl3 is assumed for simplicity ... 

Use of Eq. (18) permits identification of the log(y +/Yp,+ ) term as the one contributing most importantly to differences in affinity of pairs of univalent metal ions, M and N, for a cation-exchange resin. For example, for the equilibrium distribution of Li and Na ions between dilute solutions of Li and Na" " chloride (myQ + m jci = 0.010 m) and the much more highly concentrated Dowex-50 (8% cross-linked by weight with divinylbenzene) phase (niy, + iUnj, = 4.5 m) the p(Vy+ - Vjjj,+ )/2.3 RT and the 2 log(yyQ/y j(-i) term yield a small sum (< 0.04) while the value of log (Yu /Ynj,+ ) approaches 0.35 once correction for interaction between the two metal ions is made. Correlation between experiment and computation of the Gibbs-Donnan-based terms is strongly supportive of the model. 

The simple Donnan model has limitations that are comparable to those of the GC model. The assumption that d,D = 0 just outside the hypothetical membrane is reasonable as long as the particle size is much larger than For particle sizes that are of the order of the hypothetical membrane can be thought at about a distance from the particle surface to incorporate the diffuse layer ions in the Donnan phase [25]. Ultimately this leads to a value of Vd that is larger than the void volume inside the particles and an average Donnan potential that is somewhat lower than the potential without this correction. The magnitude of the differences will depend on... 

At low solute concentrations, there are discrepancies between the theoretical and experimental hues even after corrections. It may be explained by following. The values of distribution coefficients p and depend on many conditions including lEM and LMF capacities. At low metal concentrations, the Donnan exclusion is pronounced and lEM potential is much higher, so its contribution to the overall BAHLM transport kinetics is more considerable than at higher concentrations. But the metal concentrations data, used for calculation of the averaged sums of lEM and LMF potentials, are much higher. So, the calculating parameters obtained do not satisfy the real transport kinetics at low concentrations. 

By the systematic work on the complexation equilibrium analyses of both weak acidic and weak basic polyelectrolytes, the Gibbs-Donnan approach is validated to provide deep insights into the complexation behaviors of linear polymer ligands. This concept does not need any adjustable parameter it only uses the logic of phase separation of polyelectrolyte aqueous solutions. The electrostatic nonideality (polyelectrolytic effect) observed in the acid dissociation equilibria of a polyion can directly be used to correct for the electrostatic nonideality for metal complexation. The potentiometric titration technique with concurrent measurements of pH and pM is most suit-... 

FIGURE 4.9. Nemst plot of the variation of the composition of the poljrvinylferrocene layer with electrode potential. Arrows show the effect of correcting the applied potential for the Donnan potential. 

Our considerations qualitatively explain the results of Fig. 3.16 The dissolution of salt in addition to the polyelectrolyte suppresses the osmotic pressure contribution by the counter-ions and transforms the stiffened polyelectrol3de chain into a much more flexible quasi-neutral chain. In the absence of these polyelectrolyte characteristics, one recovers the behavior of neutral systems and, therefore, in the semidilute range the associated scaling law Eq. (3.41). Equation (3.136) correctly describes the general tendencies, but is not an accurate expression. First, in view of the complex structures in polyelectrolytes with shell formations and screening effects, equilibria have to be expressed in terms of activities rather than concentrations. Furthermore, the Donnan expression is not the only contribution to the second virial coefficient. There exists another part, AA2, which accounts as usually for excluded volume effects, the quality of the solvent and the peculiar ordering phenomena found in polyelectrolyte solutions. Therefore, in general, one has to write... 

Klaarenbeek has applied these ideas to the Donnan equilibrium using the model of flat double layers of the GouY-CHAPMAN-type, and obtained rather satisfactory results, which were in better agreement with the experimental data than the classical Donnan theory even when the latter has been corrected for activity coefficient. 

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