Membrane conductivity models

Macroscopic models can be classified into two broad categories (i) membrane conductivity models and (ii) mechanistic models, typically for fuel cell water management purposes. The latter usually require the use of a conductivity model, a fit to empirical data, or the assumption of constant conductivity (e.g. fully hydrated membrane at all times), and can be further classified into hydraulic models, in which a water transport is driven by a pressure gradient, and diffusion models, in which transport is driven by a gradient in water content. 

The effective conductivity of the membrane depends on its random heterogeneous morphology—namely, the size distribution and connectivity of fhe proton-bearing aqueous pafhways. On fhe basis of the cluster network model, a random network model of microporous PEMs was developed in Eikerling ef al. If included effecfs of varying connectivity of the pore network and of swelling of pores upon water uptake. The model was applied to exploring the dependence of membrane conductivity on water content and... 

One of the most important parts of the fuel cell is the electrolyte. For polymer-electrolyte fuel cells this electrolyte is a single-ion-conducting membrane. Specifically, it is a proton-conducting membrane. Although various membranes have been examined experimentally, most models focus on Nafion. Furthermore. it is usually necessary only to modify property values and not governing equations if one desires to model other membranes. The models presented and the discussion below focus on Nafion. 

The membrane conductivity was measured in HCl(aq) solutions of different concentrations and in 2 M HC1 + 0.2 M CuCl solution to model the catholyte and anolyte solutions in the electrolyser. All membranes were equilibrated in the same solutions for 20 hours before starting the measurements. Detailed characterisation data for a number of commercial anion exchange membranes are published elsewhere (Gong, 2009). The AHA membrane, which demonstrated the highest conductivity in HC1 (12.61 mS/cm) compared to other membranes with similar IEC and water uptake, was selected to prepare a membrane electrode assembly (MEA) and carry out electrolysis tests with this MEA. The ACM membrane with lower conductivity values was also chosen for the electrolysis tests due to its proton blocking properties and high Cl- selectivity. 

The membrane conductivity in Equation 19.4 can be estimated using the following three models [48] isostrain or parallel model... 

There is still a long way between the conductance of a single-pore and the macroscopic membrane conductivity. Water fractions in the membrane form tortuous pathways with ramified boundaries. Upon water uptake the system continuously evolves by the swelling of individual pores and the creation of new connections between pores. For modeling purposes, the highly interconnected porous structure may be subdivided into elementary segments resembling lamellae, cylinders, or spheres. 

The studies of elementary films formed in inverse emulsions and stabilized by different synthetic and natural surfactants revealed that the membrane electric conductivity experiences a sharp increase upon the addition of some biologically active surfactants. For instance, membrane conductivity may increase by five orders of magnitude when trace amounts of valinomycin antibiotic are introduced into the outer aqueous medium of lipid membrane. At the same time the membrane becomes permeable to potassium and hydrogen ions but impermeable to sodium ions. A sharp decrease in electric resistance of synthetic membranes is observed when proteins and enzymes with suitable substrates are introduced into them. By studying the properties of such membranes one may model important biological processes, e.g. the transfer of neural impulses. 

Figure 2A. Longer time scale (0-80 /is) electrical behavior, predicted by the same model that shows rupture and simple charging of an artificial planar bilayer membrane (16). The characteristic sigmoidal behavior of U(t) is predicted by the model (16), but the time scale is somewhat shorter than found in experiments (61). Each curve is labeled by the corresponding value of the injected charge Q. The curves for Q — 25 and 20 nC are the spikes at t — 0. The curve for Q = 15 nC shows that the membrane underwent REB at t = 2 pus, but the membrane recovered before it had time to discharge completely. The curve for Q = 10 nC shows rupture, whereas the curve for Q = 5 nC shows that the membrane conductance did not increase enough to discharge the...

Bamberg and Lauger [18] formulated a kinetic model assuming that the rate constants for formation and break up of the channel were voltage-dependent. This model predicted that the time constant for relaxation of the current should depend on the square root of the mean 0 V membrane conductance if the channel was a dimer. This dependence was found. 

A Numerical Analysis of the Conduction Process in a Membrane Cell Model, ... 

Often, as in Figure 4.3b, the conductivity is measured as a function of the activity of the solvent with which the membrane is equilibrated. In order to relate these measurements to the actual water content, one can use experimentally determined sorption isotherms as shown in Figure 4.4 for Nafion and a sulfonated polyaromatic membrane. The sorption isotherms will be revisited in more detail to discuss their critical role in membrane transport models [21]. 

The distinguishing feature of the classical diffusion model of Springer et al. [39] (hereafter SZG) is the consideration of variable conductivity. SZG relied on their own experimental data to determine model parameters, such as water sorption isotherms and membrane conductivity as a function of the water content. Alternative approaches include the use of concentrated solution theory to describe transport in the membrane [45], and invoking simplifying assumptions such as thin membrane with uniform hydration [46]. 

Conductivity is directly related to the transport of hydronium ions through the membrane, and is the best-documented transport property. In this section we reduce the BFM2 model, Eq. (4.22)) to a conductivity model. It should be emphasized that this conductivity model is derived here primarily as a tool to gain insight into the behaviour of the unknown transport coefficients and to specify the model constants. 

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