Donnan partition model

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 ... 

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. 

J. Schaep, C. Vandecasteele, A.W. Mohammad and W.R. Bowen, Evaluation of the salt retention of nanofiltration membranes using the Donnan and steric partitioning model, Sep. Sci. Technol., 34 (1999) 3009-3030. 

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. 

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. 

Transport through nanofiltration membranes is controlled primarily by electrostatic and steric interactions. The extended Nemst-Plank equation commonly is used with Donnan and steric partitioning to predict transport rates based on effective membrane charge density, pore radius, and thickness to porosity ratio [131-132]. Inclusion of solute-pore hydrodynamic interactions and a pore size distribution improves the predictive and correlative capabilities of the models [133]. 

Schaep, J., Vandecasteele, C., Mohammad, A.W., and Bowen, W.R., Analysis of the salt retention of nanofiltration membranes using the Donnan-steric partitioning pore model, Separ. Purif. Technol, 34 (15), 3009-3030, 1999. 

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