Coion exclusion

In both cases the deviations from the EVM predictions are in the direction of too high SN values ( incomplete coion exclusion ). In terms of Eqs. (37) and (38) these deviations become evident in practice at low Cs (high a)109). This is so, incidentally, only because Eqs. (37) (38 a) are unsuitable for putting into evidence the corresponding discrepancies at high Cs (low a), as has been emphasized recently U0). Even so, a considerable number of other factors can and has been invoked to account for departures from Eqs. (37) and (38) without abandoning the EVM, including limi-... 

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. 

The ability of ion-exchanger membranes to act as a separation wall, along with the chemical and electrochemical properties of the ion exchangers, provides manifold opportunities toward selective separation and movement of ions. The principal phenomenon in any ion-exchanger membrane is Donnan coion exclusion. Consider an ion-exchanger membrane that separates two solutions containing ions (both cation and anion) of different concentration. If the ions were without any charge, these concentration differences... 

In experiments at trace level or very low loading of one ion, the isotope dilution procedure is not required. All that is necessary is that the exchangeable ions on the solid be those of the salt present in macro concentration. The computation of results, which followed that conventionally used in the determination of distribution coefficients, ignores possible effects of colon exclusion from water in the clay pack it is implicitly assumed that the water in the pack has the same coion concentration as the supernatant solution. It is possible that coion exclusion has an effect which may be significant on distribution coefficients (particularly when they are low) and on capacities computed from the results. We shall discuss this interference later in connection with the capacities measured by displacement of both cations and anions from the clay pack and associated water. Coion exclusion has been further discussed in references 1 and 7 (see also 8, 9, and 10). 

We conclude that there is no reason to assume a variation of capacity with Na(I)/Ca(II) ratio. It also appears that there is appreciable coion exclusion. However, the present results do not allow determination of relative exclusion in water between clay particles and intralayer water within particles, if such a distinction is justified at all. Any anion-exchange capacity present would result in higher cation-exchange capacities. These unresolved questions introduce some uncertainty in the values of K/V inferred from our results, and from literature values measured by similar procedures. 

Several models that depart partially or totally from DLVO have been proposed. One such model is the Spitzer dissociative electrical double layer theory (Spitzer 1984, 2003 and references therein). It essentially uses the linearized PB equation (which is consistent with Maxwellian electromagnetism) along with a coion exclusion boundary, which prevents ions of the same charge as the surface becomes too close in practice, this avoids negative concentrations, which will be predicted by the linear PB theory. It also includes a double layer association parameter a, which gives the fractions of counterions that are associated to the surface forming the Stern layer (Spitzer 1992). This theory, however, has not been further developed. 

This complicated set of nonlinear equations (due to the migration term in Eqn. 48) was solved for cases where a system has a predominance of ionic concentrations and for the opposite limiting case of strong coion exclusion from the In the former case... 

Referring to Section XI-6B, the effect of the exclusion of coions (ions of like charge to that of the interface) results in an increase in solution concentration from rq to Rq. Since the solution must remain electrically neutral, this means that the counterions (ions of charge opposite to that of the interface) must also increase in concentration from Ro to Rq. Yet Fig. V-1 shows the counterions to be positively adsorbed. Should not their concentration therefore decrease on adding the adsorbent to the solution Explain. 

RPM model, but theories for the SPM model electrolyte inside a nanopore have not been reported. It is noticed that everywhere in the pore, the concentration of counterion is higher than the bulk concentration, also predicted by the PB solution. However, neutrality is assumed in the PB solution but is violated in the single-ion GCMC simulation, since the simulation result of the counterion in the RPM model is everywhere below the PB result. There is exclusion of coion, for its concentration is below the bulk value throughout the pore. Only the solvent profile in the SPM model has the bulk value in the center of the pore. 

Since there is normally adsorption of counterion, the exclusion of electrolytes has been conventionally defined based on the exclusion of the coion. The exclusion coefficient is de-fmed as... 

If, however, a carrier-mediated transport membrane containing charged species — in the form of either mobile ions or fixed sites — were placed between two electrolytic mixtures, significant Donnan effects could be expected. For example, consider a membrane in which the carrier is a counterion to the permeant. The permeant would be expected to be preferentially included in the membrane phase. If significant inclusion were to occur, the use of simple first-kind boundary conditions would be inappropriate and could lead to underestimation of flux. On the other hand, if the permeant and carrier were coions, the permeant could be excluded and failure to account for exclusion could lead to overprediction of flux. Further complications would arise if the complex were charged or if other charged species were present, since the net charge density inside the membrane defines Donnan equilibrium conditions. 

Charged UF membranes reject low concentrations of salts primarily by the Donnan exclusion mechanism. Because the fixed charged groups on the membrane skin reject ionic solutes via repulsion of coions, the rejection would be expected to depend on solute type and coion charge. Obviously, divalent and tri-valent ions are rejected better than monovalent ions. Highly hydrated ions are rejected better than poorly hydrated ions. 

C9 expressed in equivalents/ke of solid, and if exclusion of coion X is essentially complete,... 

The eluent counterion and coion effects contribute the distribution coefficient of sample ion in the opposite direction. In general, the greater the of the eluent anion, the greater the of the sample cation is (counterion effect), while that of the sample anion is smaller (coion effect). Similar counterion and coion effects are also exhibited by the eluent cation. This background electrolyte effect, which appears to be essentially independent of the type of gel materials, suggests that the distribution of ionic solutes between the internal gel phase and the external liquid phase is governed by a mechanism which does not involve the steric exclusion effect as a main factor. 

Based on the concept mentioned above, Shibukawa et al. [ref. 31] have proposed a new model regarding the distribution of ionic solutes in practical exclusion chromatography, where the distribution of sample ion is assumed to be dependent not only on its own physicochemical properties but also on those of the counterion and coion in the eluent. The background eluent ion effect on the distribution coefficients of ionic solutes on neutral hydrophilic gels can be understood on the basis of the ion partition model presented. If there is not any specific interaction such as complex formation between the sample ion s (hereafter sample ion is represented by cation, but, of course, the expressions... 

The effect of sample concentration on the chromatographic behaviour of ionic solutes on Sephadex G-10 can be qualitatively described by means of the partition isotherms derived on the basis of the ion partition model proposed by Shibukawa et al. [ref. 69] (see Sec. 2.2.1). The overall partition isotherms are anticipated to be represented as shown in Fig. 9 from the analogy with typical ion-exchange isotherms [ref. 70], if the partition isotherm of process (A) is linear. It is thus predicted that, in the system where the contribution of the steric exclusion effect can be neglected, the difference in the affinity for the internal gel phase between sample ion, s , and coion Y , that is, the equilibrium constant of ion-exahange process (B), K, determines the sample concentration dependence of the elution behaviour of sample ion in the following manner. When > 1, the elution volume or the distribution coefficient of sample ion decreases and the elution profile is more skewed with sharp leading... 

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. 

In their paper concerning electrolyte effects in aqueous exclusion chromatography of inorganic salts, Neddermeyer and Rogers [ref. 12] rationalized the phenomena observed by invoking the existence of a Donnan diffusion [ref. 78], involving an internal volume of the gel penetrable to some, but not all, ionic solutes in solution. The peak of the eluent salt was attributed to the Donnan exclusion effect, on the assumption that the sample ion and the eluent coion were able to penetrate into the gel interior to different degrees. 

However, these interpretations in terms of the Donnan salt exclusion effect seem to be still open to discussion, because the difference in elution volume between small inorganic ions, such as chloride and nitrate ions, on tightly crosslinked hydrophilic gels cannot be attributed to their size differences, and furthermore, the eluent salt peak can also be produced by the injection of the sample ion which elutes slower than the eluent coion [ref. 16, 23, 26]. 

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