Partitioning, Donnan

Figure 2.10 Scheme showingthe Donnan partition of mobile ions between the solution and a polymeric phase bearing an excess of negative charges. While positive ions are incorporated in the film to mantain electroneutrality, negative ions are excluded from it. This situation give rise to an interfacial potential (Donnan potential) at the interface. 

One of the main assumptions of the Donnan partition model is that two well-defined phases (polymer and solution) exist and the electrostatic potential presents a sharp transition between them. This approximation is fulfilled when the typical decay length of the electrostatic potential (Debye length) is much shorter than the film thickness. The other limiting situation is that where all the redox sites are located in a plane and thus the Debye length is larger than the film thickness. This situation can be described by the surface potential model ... 

Hydrogels are crosslinked polymer networks with entrapped solvent. In the case of hydrogels containing polyectrolytes, in addition to solvent, ions and salt can be found in the gel as determined by the Donnan partition. This arises from the exclusion of ions of the same charge that sets a membrane potential at the gel/external electrolyte interface. 

From a survey of the literature in chemically modified electrodes [13], one can identify simple phenomenological models that have been very successful for the analysis of a particular aspect of the experimental data. Such models are, for instance, the Donnan partition model [24, 122], the Laviron [158], Albery [159] and Anson models [127] to account for the nonideal peak width, the Smith and White model for the interfacial potential distribution [129], and so on. Most of these models contain one or more adjustable parameters that give some partial information about the system. For example, the lateral interaction model proposed by Anson [127] provides a value for the lateral interactions between oxidized and reduced sites, but does not explain the origin of the interactions, neither does it predict how they depend on the experimental conditions or the polymer structure. In addition, none of these models provide information on the interfacial structure. 

Finally a more comprehensive model for simulating the Ru /Fe system was solved using finite-element methods. This model takes into account mass transport due to diffusion and migration, electron transfer due to electron hopping, homogeneous chemical reaction in the membrane, heterogeneous reactions, double-layer charging, and Donnan partition equilibrium between the membrane and diffusion layer. 

A second potential player is Ca, which is generated by the marble reaction [112]. This species should also accumulate with time. It also may affect the membrane s swelling properties as a result of favorable Donnan partitioning and reduction in Donnan osmotic pressure. The dynamics and effect of Ca have not... 

Unlike the pellicular packings used for ion exchange, the packings used in ion exclusion are derived from totally sulphonated polymeric materials. Separation is dependent upon three different mechanisms Donnan exclusion, steric exclusion and adsorption/partitioning. 

Separation is dependent on three different mechanims Donnan exclusion, steric exclusion, and adsorption/partitioning. Donnan exclusion causes strong acids to elute in the void volume of the column. Weak acids that are partially ionized in the eluent are not subject to the Donnan exclusion and can penetrate into the pores of the packing. Separation is achieved through differences in acid strength, size, and hydrophobicity. The major advantage of ion exclusion is the ability to handle samples that contain both strong and weak acids. 

This may work well if the process involves only electrically neutral species. However, when ions are discriminated on the basis of size, the partitioning process is affected by the Donnan potential. This potential, which we discuss more fully in Chapter 6, develops at the membrane/electrolyte interface. Another possibility is to discriminate on the basis of charge, as shown in Fig. 7.10 (see Chapter 7). Again, a porous barrier membrane is used, although here it would contain fixed, electrically charged moieties. When placed in front of the transducer, it rejects the like-charged species by electrostatic repulsion. In other words, it is a form of ion exchange membrane. 

The Donnan membrane cell was made of Plexiglas, partitioned into two chambers, as shown in Figure 34.8 with dimensions L = 30 cm, W=1 cm, and //=40 cm. Fixed volumes of feed (WTR) and recovery (acid) solutions were used for every mn ... 

Ion exclusion is the term that describes the mechanism by which ion-exchange resins are used for the fractionation of neutral and ionic species. Ionic compounds are rejected by the resin, due to Donnan exclusion, and they are eluted in the void volume of the column. Nonionic or weakly ionic substances penetrate into the pores of the packing, they are retained and, thus, separation is achieved, as they partition between the liquid inside and outside the resin particles. 

Note that the sodium ion concentrations in the two compartments are quite different in this last case, as are the hydroxyl ion concentrations. This is the Gibbs-Donnan equilibrium effect. The fact that each ion partitions unevenly between the two compartments results in a contribution to the osmotic pressure from the ions in addition to that which results... 

UF and RO models may all apply to some extent to NF. Charge, however, appears to play a more important role than for other pressure driven membrane processes. The Extended-Nemst Planck Equation (equation (3.28)) is a means of describing NF behaviour. The extended Nernst Planck equation, proposed by Deen et al. (1980), includes the Donnan expression, which describes the partitioning of solutes between solution and membrane. The model can be used to calculate an effective pore size (which does not necessarily mean that pores exist), and to determine thickness and effective charge of the membrane. This information can then be used to predict the separation of mixtures (Bowen and Mukhtar (1996)). No assumptions regarding membrane morphology ate required (Peeters (1997)). The terms represent transport due to diffusion, electric field gradient and convection respectively. Jsi is the flux of an ion i, Di,i> is the ion diffusivity in the membane, R the gas constant, F the Faraday constant, y the electrical potential and Ki,c the convective hindrance factor in the membrane. 

Brooks and coworkers [136,141] measured drop electrophoretic mobilities in ATPSs. They were surprised to discover that the sign of the droplet mobilities was opposite to that predicted from the phosphate partition and the Donnan potential. They also found mobility to be directly proportional to drop radius, which is a contradiction of standard colloid electrokinetic theory [144]. Levine [140] and Brooks et al. [141] hypothesized that a dipole potential at the phase boundary oriented in a way that reverses the potential gradient locally is responsible for the paradox of the sign of electrophoretic mobilities of ATPS droplets. 

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