Donnan exclusion coefficients

Note that the physicochemical mechanisms that enables us to perform the chromatographic bioseparations are not always adsorption-like but can involve ion exchange, ion exclusion, or size exclusion. Even if it is generally possible to fit experimental data with a mathematical function derived from the adsorption theory, it is strongly advisable to refer to the proper physicochemical process before modeling the separation. For instance, ion exchange can be modeled with selectivity coefficients (derived from the mass action law) that can be constant or not,18,19 ion-exclusion can be modeled thanks to theories based on the Donnan exclusion, etc. 

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. 

The self-diffusion coefficient for iodide ion was also measured at 25°C in the first sample of 1200 EW Nafion, before aging 04). The result, 9 10 8 cm2 sec"1, indicates that this anion is more mobile than cesium ion, but less than a sodium ion. This is also somewhat unusual. In general, co-ion diffusion coefficients are seen to be larger than those of counterions in ion exchangers, because no electrostatic attractions to the polymer phase exist. (The membrane concentration is only 5 x 10 3 mol L 1 though, reflecting the effects of Donnan exclusion processes (4 ).)... 

Because EY5 is equal to k the mass transfer coefficient, is strongly dete. There are two other effects that influences the performance of the process as well, i) osmotic flow and ii) less effective Donnan exclusion. Osmotic flow is inherently part of the process and can not be avoided. Since ions are transferred from one compartment to another an osmotic pressure difference is generated and this drives the osmotic transport of water from the diluate to the concentrated side. Secondly, in case of high ionic concentrations the Donnan exclusion becomes less effective. This effect and the less favoured energy consumption at high concentrations makes the process of electrodialysis mote competitive at relatively low concentrations. 

This will be true for any charged solute in the absence of any other interactions between the solute and the gel. Donnan exclusion theory Is well established and can directly relate the partition coefficient to the concentration of charges in the gel via equation (12). For 1 1 electrolytes in the absence of any specific interactions with the gel, equation (12) may be combined with equation (25) to yield ... 

The only restriction on this technique is that there must be no interactions between the gel and solute beyond Donnan exclusion. Since the partition coefficient is often affected by several factors, including molecular size, electric potential, and hydrophobic interactions [52], this can be a serious problem. Since the lack of... 

Mafe, S., Ramires, P., and Pellicer, J. Activity coefficients and Donnan coion exclusion in charged membranes with weak-acid fixed charge groups. J. Membr. Sci., 138, 269-277, 1998. 

Thus, the breakthrough curves of 0.1 N HCl shift from ca 1.5 column volumes in 5N LiCl to more than 8 column volumes in the concentrated (16 N) LiCl solution. A similar strong retention of HCl (because of the reduced activity coefficient of HCl ) was also characteristic of the ION solution of MgCl2. Yet, retention of HCl in amphoteric resins and anion exchangers contradicts the concept of ion exclusion according to which all strong electrolytes should be effectively excluded from absorption into ion-exchange resins, because of the Donnan equilibrium effect [117, 118]. 

In addition to a sample peak, some anomalous peaks often appear in chromatograms. when multicomponent eluent is used [ref. 71, 72]. Such an induced peak can be observed when polyelectrolyte is chromatographed using a simple electrolyte solution as eluent the first peak corresponds to polyelectrolyte and the second to an induced peak which has the elution volume exactly the same as that of the eluent salt [ref. 33, 45-48, 73-76]. This effect of polyelectrolytes in exclusion chromatography has been explained in terms of Donnan salt exclusion established on the gel [ref. 33, 45-48, 73-76] a polyelectrolyte is barred from the gel interior and thus promote the diffusion of the penetrable eluent coion into the inner volume of the gel, the gel matrix acting as a semipermeable membrane. The eluent coion thus excluded from the polyelectrolyte zone produces an induced peak. It has been reported that the area of the induced peak allows to calculate the Donnan salt exclusion parameter [ref. 33, 74] or the osmotic coefficient [ref. 46-48, 76] of the polyelectrolyte. 

Scatchard s equation (1946) is derived to explain Ai for proteins. The change in dimensions (e.g., mean-square end-to-end distance) is not of any concern in Scatchard s derivation. No model was assumed and no statistical mechanics was used. Scatchard successfully correlated the osmotic pressure with the distribution of diffusible solutes across a semipermeable membrane by manipulating the terms of activities of the components (such as protein, salt, and water) with changing composition of the solutions. The mathematical detail is simple but messy. According to Scatchard, the interactions involved in protein solutions are not limited to the exclusion of volume between the segments of macromolecules but also includes the Donnan effect and the binding of small ions to macro ions in a given system. For simplicity, let us consider a three-component system, and let 1 represent the solvent (or buffer), 2 the macromolecule (such as protein), and 3 a salt (e.g., NaCl). Scatchard derived an equation of the second vitial coefficient... 

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