Measurement Of Effective Oxygen Diffusivity In Electrodes For Proton Exchange Membrane Fuel Cells

Zhiqiang Yu*, Robert N. Carter

*Corresponding author. Tel.: +1 585 624 6653; fax: +1 585 624 6680. E-mail addresses: [email protected], [email protected] (Z. Yu).

Abstract
This paper describes a novel method to measure directly effective diffusivity in electrodes as a function of temperature and relative humidity (RH) at conditions that are relevant for proton exchange membrane fuel cells (PEMFCs). The efficacy of this method to measure effective oxygen diffusivity (DeffO2) is demonstrated with measurements of a series of electrodes of varying the ionomer-to-carbon weight ratio (I/C ratio). The measured DeffO2 decreases sharply with increasing I/C ratio from 0.5 to 1.5 at the same RH, and reduces gradually with increasing RH from 0% to 100% at the same I/C ratio. The measured DeffO2 is considerably smaller than the calculated one using the Bruggeman correction, indicating the Bruggeman correction drastically underestimates the tortuosity with increasing I/C ratio in PEMFC electrodes.

1. Introduction
The heart of a PEMFC is a three-layer assembly comprised of a proton-conductive membrane sandwiched between anode and cathode electrodes. Electrodes typically contain Pt nanoparticles as catalyst, carbon black as support for Pt nanoparticles, and ionomer as proton (H+) conductor and binder. Electrodes must be sufficiently porous to transport gases and water vapor to carry out electrochemical reactions inside them. To improve the performance of PEMFCs, it is essential to identify and understand different voltage losses. The cell voltage (Ecell) of PEMFCs can be represented by the following equation [1]:

Ecell = Erev – nHOR – |nORR| – i · (Re– + RH+,mem + RH+,An + RH+,Ca) -ntx(gas),       (1)

where Erev is the thermodynamic potential, nHOR is the anode overpotential due to hydrogen oxidation reaction (HOR), nORR is the cathode overpotential due to oxygen reduction reaction (ORR), i is the applied current density, Re- is the electronic resistance, RH+,mem, RH+,An, and RH+,Ca are the proton resistances in the membrane, anode, and cathode, respectively, ntx(gas) is the gas-diffusion overpotential caused by the hydrogen and oxygen concentration gradients in the electrodes due to gas transport resistances. Except for ntx(gas), these voltage-loss terms can be adequately determined based on various electrochemical measurements [2–5]. ntx(gas) is often split into two components: a dry component that depends on the microstructure of the porous gas-diffusion media (GDL) and electrode layers that the gas must transport through, and a wet component that is a function of the operating condition combined with the ability of the cell’s components to reject liquid water. Clearly, the effective diffusivity of the electrode layer and its dependence on RH are important to fully characterize the gas transport resistance of PEMFCs.

To our knowledge, there is no reported method capable of directly measuring gas effective diffusivity of PEMFC electrodes under the conditions relevant to the PEMFC operating conditions. The Bruggeman correction which is commonly used to estimate gas effective diffusivity is reported to likely lead to overestimation for electrodes with low porosities [6,7]. While one can use traditional analysis techniques such as mercury intrusion porosimetry (MIP) and nitrogen adsorption with Barret–Joiner–Helenda (BJH) method to characterize the porosity of electrodes, these techniques are restricted to dry analysis conditions. Given that the ionomer in the electrode is highly hygroscopic and swells upon humidification, it is important to be able to characterize the electrode layer’s porosity under conditions more relevant to fuel cell operation. Additionally, the thickness and loading of the electrode layer (typically 10μm thick and 0.4mgPt cm-2, respectively) combine to make it difficult to use representative samples in traditional analysis techniques. The novel method described herein addresses these shortcomings by measuring the effective diffusivity in an electrode layer under conditions similar to those of an operating PEMFC and at a sample scale of 50cm². The efficacy of the developed method is demonstrated in measurements of oxygen effective diffusivity (DeffO2) in electrodes with a range of ionomer-to-carbon weight ratios (I/C ratio).

2. Measurement of DeffO2 inside electrodes
2.1. Method description
The measurement is based on oxygen “in-plane” diffusion in electrodes on a conventional PEMFC platform with 50cm² flow fields. Fig. 1 shows the schematic cross-section of the cell fixture for the DeffO2 measurements. The “in-plane” diffusion means that the diffusion direction is parallel to the electrode surface (the x direction in Fig. 1). In operating PEMFCs, oxygen is more likely to experience “though-plane” diffusion in electrodes, where the diffusion direction is perpendicular to the electrode plane (the y direction in Fig. 1). However, DeffO2 in porous PEMFC electrodes should be the same no matter oxygen is in either “in-plane” or “through-plane” diffusion. Fig. 1 shows the porous electrode film coated on ethylene tetrafluoroethylene (ETFE) is tested by mounting it between a flow field with three parallel gas channels and a blank flow field. Air flows through the two outer channels and nitrogen through the center channel. This arrangement results in oxygen diffusion from the air channel into the nitrogen channel via the porous electrode. Because the nitrogen channel is flanked on both sides by the air channels, the rate of oxygen diffusion is effectively doubled, thereby reducing the required length of flow channel to achieve a measurable oxygen concentration at the exhaust of the nitro
gen channel.

Fig. 1. Schematic cross-section of the cell fixture.
Fig. 1. Schematic cross-section of the cell fixture.

A gasket made of silicone rubber with the thickness of 250μm (Durometer 35A, McMaster-Carr) is used to seal the air and nitrogen channels under a load of 5.3 kN. The gasket is cut by laser to match the channels. The width of the gasket that seals the lands between the air and nitrogen channels are 2mmas shown in Fig. 1, allowing some tolerance for placement of the gasket to ensure that it is completely supported by the 3mm wide flow field lands. Placement of the gasket is important because the width of the gasket between the air and nitrogen channels defines the oxygen diffusion length used in the calculation of DeffO2.

Fig. 2 shows the plan-view of the flow field depicting the features of the air and nitrogen channels. Air and nitrogen co-flow through the flow field with a channel length of 19 cm. The oxygen concentration at the exhaust of the nitrogen channel is monitored by a self-heated oxygen sensor (model: LZA03-E1,NGKSpark Plugs, Michigan). The test is run with the two gas streams held at ambient pressure (101.3 kPa). The pressure drops in the air and nitrogen channels are calculated to be 21 and 17 Pa, respectively. The maximum pressure gradient between the air and nitrogen channel is only 4 Pa when both air and nitrogen are flowing. Even if a pressure gradient of 10 kPa exists between the air and nitrogen channels, the resulting oxygen bulk convection is calculated to account for less than 2.13% of the oxygen diffusion flux in the DeffO2 measurements for electrodes with I/C ratios of 0.5 and 1.0. Thus, the driving force for forced convective flow between the adjacent air and nitrogen channels is negligible, and the transport of oxygen from the air channels to the nitrogen channel is driven only by the oxygen concentration gradient. Because of the minimal pressure gradient between the external air channel and the ambient, it is assumed that there is no much oxygen in the air channel diffusing through the electrode to the ambient. Thus, oxygen can only diffuse from the air channels to the nitrogen channel though the porous electrode.

Fig. 2. Plan-view of the flow field.
Fig. 2. Plan-view of the flow field.

To measure the oxygen diffusion length accurately under the load, a piece of Fuji Prescale film for super low pressure (FujiFilm, Japan) is inserted between the electrode and the gasket and then compressed by the two flow fields. Under the compression, the Fuji Prescale film develops colorful strips due to the pressure exerted by the gasket between the air and nitrogen channels. The width of colorful strips on the pressure-paper reflects that the expansion of the 2mmwide gasket under a load of 5.3kN is negligible. Thus, the oxygen diffusion length is 2mm in the calculation of DeffO2.

2.2. Calculation of DeffO2
As described above, oxygen is designed to “in-plane” diffuse through a 2mm wide porous electrode due to the oxygen concentration gradient between the air channels and the nitrogen channel. Since the electrode thickness (10μm) is 200 times smaller than the oxygen diffusion length (2 mm), the oxygen concentration inside the electrode is assumed to be the same in the y direction in Fig. 1. In addition, the oxygen concentration inside the electrode which is under the air or nitrogen channel is assumed to be the same in the x direction in Fig. 1. Therefore, the oxygen transport in this study is simplified to an issue of oxygen diffusion due to the concentration gradient through a porous electrode which is 2mm wide, 10μm thick, and 19cm long.

Fig. 3 illustrates an oxygen mass balance over a segment of the nitrogen channel for developing the equation in the calculation of DeffO2. It is expressed as follows:

Q × (Cx+Δx – Cx) + 2Jy × Δx × δ= 0       (2)

where Q is the gas volumetric flow rate, Cx is the molar oxygen concentration in the nitrogen channel, Jy is the molar diffusion flux of oxygen from both air channels to the nitrogen channel,Δx is the length of the illustrated segment in Fig. 3, and δ is the thickness of the electrode. In the limit of Δx→0, Eq. (2) becomes:

(dCx / dx) = -(2Jyδ / Q).       (3)