PEMFC contamination model: Foreign cation exchange with ionomer protons

doi:10.1016/j.jpowsour.2011.04.008

Journal of Power Sources

Volume 196, Issue 15, 1 August 2011, Pages 6274-6283

https://doi.org/10.1016/j.jpowsour.2011.04.008 Get rights and content

Abstract

A generic, transient fuel cell ohmic loss mathematical model was developed for the case of contaminants that ion exchange with ionomer protons. The model was derived using step changes in contaminant concentration, constant operating conditions and foreign cation transport via liquid water droplets. In addition, the effect of ionomer cations redistribution within the ionomer on thermodynamic, kinetic and mass transport losses and migration were neglected. Thus, a simpler, ideal, ohmic loss case is defined and is applicable to uncharged contaminant species and gas phase contaminants. The closed form solutions were validated using contamination data from a membrane exposed to NH₃. The model needs to be validated against contamination and recovery data sets including an NH₄⁺ contaminated membrane exposed to a water stream. A method is proposed to determine model parameters and relies on the prior knowledge of the initial ionomer resistivity. The model expands the number of previously derived cases. Most models in this inventory, derived with the assumption that the reactant is absent, lead to different dimensionless current vs. time behaviors similar to a fingerprint. These model characteristics facilitate contaminant mechanism identification. Separation between membrane and catalyst (electroinactive contaminant) contamination is conceivably possible using additional indicative cell resistance measurements. Contamination is predicted to be significantly more severe under low relative humidity conditions.

Highlights

► A fuel cell model was developed for cations that exchange with ionomer protons. ► Closed form solutions were validated using data from a membrane exposed to NH₃. ► The model expands an existing library facilitating mechanism identification. ► Contamination is predicted to be more severe under low relative humidity conditions.

Introduction

Proton exchange membrane fuel cells (PEMFCs), an alternative power source currently being developed [1], is sensitive to contaminants present in reactant streams and released from system components [2]. Generic models were developed to address the large number of existing and unidentified contaminants [3], [4], [5], [6]. Such models are useful to classify contaminants (mechanism identification), set tolerance limits and design experimental procedures for validation and extraction of model parameters. For instance, fuel cell testing with low contaminant concentrations requires significant time and resources because effects are small and not easily measured with certainty. A simple model for membrane contamination has not yet been derived and is needed to complete the existing library.

Several models have already been proposed showing that all types of performance losses take place within a contaminated PEMFC including thermodynamic, kinetic, ohmic and mass transport losses [7], [8], [9], [10], [11], [12], [13]. Experimental data support this statement [14]. However, in most model cases, the physics associated with the ion exchange process were not taken into account [7], [8], [9], [10], [11], [12]. Langmuir isotherms were recently used [13] but such an approach was discontinued to characterize ion exchangers [15] because it does not reproduce their behavior.

A simple transient PEMFC contamination model is derived using a similar approach as prior efforts [3], [4], [5], [6] with a focus on the membrane ion exchange with foreign cations. The approach considers first order effects, to maintain model generality and applicability to many different cations, and the derivation of an analytical solution, to simplify its use for predictions, validation and extraction of model parameters.

Section snippets

Model assumptions

Fig. 1a illustrates the path taken by a foreign cation X⁺ⁿ from the flow field channel to the ionomer exchange site. It is assumed that liquid water droplets maintain a steady flow and concentration of foreign cations originating from the environment or system components. Liquid water is not necessarily required to introduce foreign cations into the fuel cell. Particles containing soluble salts and entrained by the reactant flow provide a supply of foreign cations by dissolution in fuel cell

Model equations

An ion exchange model for diffusion control in the liquid phase (absence of migration and convection) was derived [15]. This model is reformulated here for the case of an ionomer sheet. Fick's first law for the proton flux is: $N = D_{l} \frac{c_{l, H^{+}} (d_{l}, t) - c_{l, H^{+}} (0, t)}{d_{l}}$

The membrane proton mass balance is: $\frac{d c_{i, H^{+}} (t) V}{d t} = - A N$

Reformulation of Eq. (6) in terms of concentrations leads to the following equilibrium condition at the liquid phase/ionomer phase interface: $c_{i, H^{+}} (t) = \frac{c_{i} α_{X^{+ n}}^{H^{+}} c_{l, H^{+}} (d_{l}, t)}{c_{l} + c_{l, H^{+}} (d_{l}, t) (α_{X^{+ n}}^{H^{+}} - 1)}$

Model validation

Two problems complicate model validation. In the first instance, ohmic loss measurements do not represent the actual ionomer conductivity [11]. During steady state operation, the inactive foreign cation flux is equal to zero. However, ohmic measurements performed with alternating currents or potentials affect all cations present in the ionomer. Therefore, the resulting measurement values include a contribution from foreign cations. If direct current or potential methods are used instead to

Conclusion

A PEMFC contamination model was derived for the case of a foreign cation displacing the ionomer proton. The model was derived by taking account of only key processes to obtain analytical solutions and facilitate a widespread implementation. Model validation indicates that the simplified approach derivation is accurate and represents a benchmark for a more complicated model that includes migration effects. Additional fuel cell validation data obtained at low and high current densities (cell

Acknowledgements

The author is indebted to the United States Department of Energy, Energy Efficiency and Renewable Energy for funding (National Renewable Energy Laboratory sub-contract ZGB-0-99180-01). The author also thanks Kitiya Hongsirikarn for providing data files used for model validation (Fig. 3, Fig. 6, Fig. 7, Fig. 8).

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PEMFC contamination model: Foreign cation exchange with ionomer protons

Abstract

Highlights

Introduction

Section snippets

Model assumptions

Model equations

Model validation

Conclusion

Acknowledgements

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J. Power Sources

J. Electroanal. Chem.

J. Electroanal. Chem.

J. Electroanal. Chem.

Electrochim. Acta

Int. J. Hydrogen Energy

J. Power Sources

J. Electroanal. Chem.

J. Power Sources

Electrochim. Acta

J. Electroanal. Chem.

J. Membr. Sci.

J. Electroanal. Chem.

Sep. Purif. Technol.

J. Power Sources

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J. Power Sources

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Electrochim. Acta

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