Composite polymer electrolytes model

Physical models of fuel cell operation contribute to the development of diagnoshc methods, the rational design of advanced materials, and the systematic ophmization of performance. The grand challenge is to understand relations of primary chemical structure of materials, composition of heterogeneous media, effective material properties, and performance. For polymer electrolyte membranes, the primary chemical structure refers to ionomer molecules, and the composition-dependent phenomena are mainly determined by the uptake and distribuhon of water. 

This review has highlighted the important effects that should be modeled. These include two-phase flow of liquid water and gas in the fuel-cell sandwich, a robust membrane model that accounts for the different membrane transport modes, nonisothermal effects, especially in the directions perpendicular to the sandwich, and multidimensional effects such as changing gas composition along the channel, among others. For any model, a balance must be struck between the complexity required to describe the physical reality and the additional costs of such complexity. In other words, while more complex models more accurately describe the physics of the transport processes, they are more computationally costly and may have so many unknown parameters that their results are not as meaningful. Hopefully, this review has shown and broken down for the reader the vast complexities of transport within polymer-electrolyte fuel cells and the various ways they have been and can be modeled. 

Figure 5.30. Schematic of the catalyst layer geometry and its composition, exhibiting the different functional parts, a A sketch of the layer, used to construct a continuous model, b A one-dimensional transmission-line equivalent circuit where the elementary unit with protonic resistivity Rp, the charge transfer resistivity Rch and the double-layer capacitance Cj are highlighted [34], (Reprinted from Journal of Electroanalytical Chemistry, 475, Eikerling M, Komyshev AA. Electrochemical impedance of the cathode catalyst layer in polymer electrolyte fuel cells, 107-23, 1999, with permission from Elsevier.)...

The fact which transport limitations prevails in the CCL depends on the composition. If it has insufficient porosity, but a well-developed network of polymer electrolyte, it will have severe gas transport limitations but good proton transport and the other way around. The macrohomogeneous model... 

Oleg Borodin works as a scientist at the Electrochemistry Branch of the Army Research Laboratory, Adelphi, MD since 2011. After obtained a Ph.D. degree in Chemical Engineering in 2000 he worked in the area of multiscale modeling of liquid, ionic liquid and polymer electrolytes for battery and double layer capacitor applications, modeling of energetic composite materials, polymers in solutions, and polymer nanocomposites. He coauthored more than a hundred publications and four book chapters. His modeling efforts focus on the scales from electronic to atomistic and mesoscale. 

This phenomenon has been studied by different combined electrochemical techniques such as -> spectroelec-trochemistry, radioactive -> tracer method, -> electrochemical quartz crystal microbalance, conductivity etc. by varying the experimental parameters, e.g., film thickness, the composition and concentration of the electrolyte solutions, the wait-time at different waiting potentials, and temperature [iii-x]. Several interpretations have been developed beside the ESCR model. The linear dependence of the anodic peak potential on the logarithm of the time of cathodic electrolysis (wait-time) -when the polymer in its reduced state is an insulator -has been interpreted by using the concept of electric percolation [ix]. Other effects have also been taken into account such as incomplete reduction [vii], slow sorp-tion/desorption of ions and solvent molecules [iii-vi], variation of the equilibrium constants of -+polarons and - bipolarons [viii], dimerization [xi], heterogeneous effects [xii], etc. 

When used in different kinds of electrochemical equipment the membranes are in contact with aqueous solutions of the low molecular weight electrolytes in which they swell. Moreover, a certain amount of the ambient solution penetrates the voids or pores in the membrane. So the swollen membrane is a multiphase system composed of an ion containing component appearing in a gel state, an inert partly crystalline polymer, and the electrolyte filling any voids or nonselec-tive domains, all of them in varying amounts. For such a system it is possible to calculate the approximate phase composition based on the conductivity and the multilayer electrochemical model. We presented such a model at the First Italian-Polish Seminar on Multi-component Polymeric Systems in 1979. 

When we choose a standard state, we are merely identifying a particular ideal solution on which to base an activity coefficient. The standard state may be real or hypothetical, so long as it is weU-defined and so long as a value for its fugacity can be obtained. Ultimately the choice of standard state is made for computational convenience normally this means either that reliable models for y, exist, or else that the value of Yi is close to unity over the states of interest. When neither of these conditions pertain, we should consider changing the standard state. In many situations the appropriate choice is one of the possibilities discussed in 10.2.1-10.2.3 however, when the mole fraction is not a convenient measure of composition, such as occurs for mixtures of electrolytes or of polymers, then other standard states may be preferred. 

The presence of an ion of this composition in solution was first deduced from the specific heats of aqueous acids, though the argument was based upon a rather artificial picture of water as a mixture of polymers. Supporting evidence comes from the thermodynamic properties of concentrated acid solutions. The rapid rise in the activity coefficients of electrolytes in concentrated solutions can be attributed largely to the removal of water by ionic hydration, with a consequent increase in the true mole fraction of the solute. A quantitative treatment in terms of a reasonable model " yields the mean hydration numbers of the ions, and a value close to 4 is found for the hydrogen ion. A similar deduction can be made from the indicator equilibria used in determining the acidity of concentrated... 

Usually, the starting point of model derivation is either a physical description along the channel or across the membrane electrode assembly (MEA). For HT-PEFCs, the interaction of product water and electrolyte deserves special attention. Water is produced on the cathode side of the fuel cell and will either be released to the gas phase or become adsorbed in the electrolyte. As can be derived from electrochemical impedance spectroscopy (EIS) measurements [14], water production and removal are not equally fast Water uptake of the membrane is very fast because the water production takes place inside the electrolyte, whereas the transport of water vapor to the gas channels is difiusion limited. It takes several minutes before a stationary state is reached for a single cell. The electrolyte, which consists of phosphoric add, water, and the membrane polymer, changes composition as a function of temperature and water content [15-18]. As a consequence, the proton conductivity changes as a function of current density [14, 19, 20). 

We extend the analysis and consider the entire ladder network in terms of distinct R and C circuit elements. The impedance x can be represented by a resistance Ri, which defined the resistance of counterions in the pore electrolyte. Furthermore the impedance element z, which is that of the solid polymer, is replaced by a Randles equivalent circuit (see Fig. 1.84), where there is a parallel arrangement of a resistor Rj. and a capacitor Q in series with a resistor Ra- Hence we see that the pore solution is modeled in terms of a simple resistor, whereas the solid polymer is a binary composite medium. TTie latter assumption can be justified as follows. From a macroscopic viewpoint (and this has been demonstrated experimentally), the electronic resistance of the polymer is due to two contributions the first, Ra, from regions of high structural order the second, R, from regions of low structural order. Hence Ra is smaller than R. From a microscopic point of view, the polymer may exhibit two fundamentally different types of conduction. As noted in... 

In this chapter we will firstly present a literature survey on vapour pressure, viscosity and conductivity properties of phosphoric acid with an emphasis on the temperature and composition range relevant for fuel cell applications. In a second part we want to elucidate the physico-chemical interactions of a protic electrolyte like phosphoric acid as a doping agent with polybenzimidazole-type polymer membranes. Literature data on m-PBI and AB-PBI as well as own measurements on Fumapem AM-55, a commercial PBI derivative, will be cOTisidered. On the basis of the observed doping behaviour a model describing the thermodynamics of the adsorption process is presented. 

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