# Mechanical durability characterization and modeling of ionomeric membranes.pdf

Mechanical durability characterization and modeling of ionomeric membranes Y. H. Lai 1 and D. A. Dillard 2 1 General Motors Corporation, Honeoye Falls, NY, USA 2 Virginia Tech, Blacksburg, VA, USA 1 INTRODUCTION One of the key challenges facing commercialization of pro- ton exchange membrane (PEM) fuel cells is the limited durability of the membrane electrode assembly (MEA). [1] In PEM fuel cells, the membranes serve to conduct pro- tons from the anode to the cathode, while preventing the crossover of reactant gases. The mechanical proper- ties of fuel cell membranes are generally very sensitive to temperature and the level of hydration. Many of the premature failures in PEM fuel cells are attributed to the crossover of reactant gases through microcracks (commonly referred to as “pinholes”) that develop in the membrane. The mechanism of microcrack formation in fuel cells is often complicated, although it is generally believed to be caused by physical degradation as the resulting mechanical stresses vary with humidity cycling and chemical degrada- tion as radicals attack the ionomer during fuel cell operation (see Highly durable PFSA membranes; Factors influ- encing ionomer degradation; Chemical and mechanical membrane degradation, Volume 5). [2] Since membranes are generally at least partially constrained in the fuel cell by the electrode, gas diffusion layers, and bipolar plates, expansion and contraction of the membrane from temper- ature/hydration change can induce mechanical stresses. As the fuel cell operating conditions fluctuate to meet changing power demands, the membrane experiences hydration and temperature fluctuations, effectively subjecting the mem- brane to hygrothermal fatigue loading. As in other engi- neering materials, fatigue, whether resulting from cyclic mechanical, thermal, or hygral loading, can lead to micro- scopic damage and eventual failure. Research on the mechanical durability of PEM fuel cells is of recent origin, as the bulk of prior research has rightly focused on optimizing the electrochemical performance required to develop viable energy sources. As fuel cell technology advances toward commercialization, however, many aspects related to mechanical integrity and durability remain to be explored. This article summarizes our recent efforts to characterize and model the stress and lifetime of PEMs subjected to the fuel cell environment. At the core of the current approach, we postulate that the hygrothermal fatigue stresses experienced by PEMs in fluctuating fuel cell environments can reduce the membrane strength over time, leading to physical membrane degradation and reduced fuel cell durability. This postulation is based on a series of in situ fuel cell tests of membranes conducted at General Motors, [3–5] which showed crossover leaks developing in membranes subjected to humidity cycling in the absence of electrochemical reaction. In Section 2, we present the humidity cycling test method, highlights of test results, and failure mode analyses using the postmortem micrographs of the membrane samples. Section 3 outlines the stress model, examples of the test methods, and representative results to characterize the membrane’s constitutive prop- erties. A parametric stress analysis of simulated humidity cycling using the membrane stress model is also discussed. To understand the membrane’s strength degradation from the cyclic loading, we have developed a biaxial strength test based on a pressurized blister test. In Section 4, we discuss Handbook of Fuel Cells – Fundamentals, Technology and Applications. Edited by Wolf Vielstich, Hubert A. Gasteiger, Arnold Lamm and Harumi Yokokawa. ? 2010 John Wiley B and J are the bulk and shear creep compliances; α and β are the linear coefficients of thermal and hygral expansion; δ ij is the Kronecker delta; s and s ij are the dilatational and deviatoric components of the applied stress σ; T is temperature; t and ξ are time; and λ is the water content of the membrane in terms of the number of water molecules per sulfonic acid (see Perfluorinated membranes, Volume 3). In principle, all of these constitutive properties can be time dependent, along with the diffusion process that affects the rates of moisture gain and loss. The bulk properties are difficult to determine for any material, and even more so for thin membranes. The time dependence of the coefficients of thermal and hygral expansion has not been investigated. Recognizing the engineering goal of predicting membrane stresses using finite element software or other computationally efficient algorithms, we have simplified the constitutive model. Assuming that a single viscoelastic constitutive property is sufficient (equivalent to assuming a constant Poisson’s ratio), that this Poisson’s ratio can be assumed to be 1/2 (considered to be a reasonable assumption for much of our analysis, where the operating conditions often exceed the moisture-depressed α transition of the membranes), that the expansion coefficients are time independent (as is often assumed even for viscoelastic materials), and that the thermal expansion is negligible (as is the case for these extremely hydrophilic membranes where the hygral strain is on the order of 20% for the humidity swings encountered in operating fuel cells), we have used: ε ij (σ,t,T,λ) = 3 2 integraldisplay t 0 D(t ? ξ)˙s ij (ξ) dξ + δ ij βDelta1λ (2) making use of the uniaxial creep compliance D.The uniaxial relaxation modulus E hasalsobeenused,andis compatible with the displacement-based formulations used in commercial finite element software such as ABAQUS ? (version 6.5, Dassault Syst`emes Simulia Corp): σ ij (σ,t,T,λ) = integraldisplay t 0 E(t ? ξ) d[ε ij (ξ) ? δ ij βDelta1λ] dξ dξ (3) ABAQUS ? is capable of taking either relaxation mod- ulus data or creep compliance data (which it converts to relaxation modulus) and developing Prony series expan- sions that represent the linear viscoelastic properties. Hygral expansion can be included by converting into the analogous thermal expansion form, or by writing user-defined material subroutines, UMATs, to represent the moisture response. Hygrothermal shift factors can be input to accurately model the reduced time parameter necessary to predict viscoelastic response under changing environmental conditions. If the spatial dependence of the resulting stress state is not needed, a simple spreadsheet can be developed using the efficient recursive relationship and the Prony series that represents the viscoelastic behavior, which converges easily and pro- vides a simple mechanism to explore the effects of temper- ature, water content, and operational parameters. [31] 3.2 Viscoelastic characterization of proton exchange membranes Linear viscoelastic properties of proton exchange mem- branes can be determined by dynamic mechanical analysis 6 Conductive membranes for low-temperature fuel cells 1 10 100 1000 ?4 ?3 ?2 ?1 0123456 Log time (s) Relaxation modulus (MPa) T ref = 70 °C Long-term validation test no. 1 Long-term validation test no. 2 RH ref = 30% RH Figure 4. The relaxation modulus master curve of Gore-Select ? 57 membrane referenced at 70 ? C and 30% RH. (DMA) as a function of frequency, providing the storage and loss moduli, E prime and E primeprime , along with tan δ = E primeprime /E prime . [32, 33] Relaxation and creep testing can be used to obtain the relax- ation modulus and creep compliance respectively. These tests also permit the determination of the onset and magni- tude of nonlinearity by constructing isochronal plots from data collected over a range of strains or stresses. [34] All of the above-mentioned linear viscoelastic properties may be converted to any of the others using exact or approxi- mate interrelationships, [35] providing options for test method used. There are advantages to each of the methods, but, for our purposes, stress relaxation testing has proven to be most convenient because the properties are directly used in the numerical models and because the strain control conditions mimic the mechanical strains imposed to offset hygrother- mal strains induced in constrained membranes. [36] In this section, representative results from relaxation test of Gore- Select ? 57 membrane are discussed. Experimental details and data analysis can be found in Ref. [36]. From the relaxation tests conducted by Patankar et al., [36] thermal and hygral shift factors (a T and a H respectively) were found to be functions of temperature and water content only, resulting in hygrothermal master curves by double-shifting the modulus data along the time axis to represent the constitutive properties of the membranes on many decades in time. The results from Patankar’s study suggest that the PEM material is hygrothermorheologically simple (HTRS) and, thus, the relaxation data so obtained can be shifted in several manners. Assuming that the total hygrothermal shift factor is the product of separable hygral and thermal shift factors, data collected can be first shifted for water content to form master curves at each of the test temperatures. After converting from RH to water content λ, the shifts required to produce the smooth master curves are recorded as the hygral shift factors at the respective temperatures. These hygral-shifted master curves at various temperatures are then shifted to form a final master curve that incorporates data from all of the temperatures and humidities, providing thermal shift factors in the process. The total hygrothermal shift factor, a TH , is then given by log a TH = log a T + log a H .The order of shifting can be switched, shifting for temperature before shifting for water content, with similar results. [36] Attempts to form a smooth master curve by freely shifting all data regardless of test conditions and simply noting the combined a TH in the process can also form similar master curve, although this method has generally proven to be less useful. Figure 4 illustrates a doubly shifted relaxation modulus master curve formed using the hygral followed by thermal shift method. Figure 5 shows the hygral and thermal shift factors. It should be noted that the water content in this plot was estimated using equation (4). The hygral shift factors are noted for each of the test temperatures. Within the temperature range most interesting to fuel cell operation from 60 to 90 ? C, the hygral shift factor appears to be relatively insensitive to temperature and shows good consistency across the range of temperatures of interest. Because the thermal shift follows hygral shift in this example, the thermal shift does not depend on the water content. Longer term data using different DMAs were collected in relaxation to validate the shifting procedure. They also suggest an equilibrium modulus of about 3 MPa. Results for two validation tests are superimposed on the master curve, and good agreement is seen, suggesting the validity of the method and usefulness of the results for stress modeling. 3.3 Coefficient of hygral expansion Water transport in PEMs has been an active area of research over the past 40 years. Three basic methods have been Mechanical durability characterization and modeling of ionomeric membranes 7 ?2 ?1.5 ?1 ?0.5 0 0.5 1 1.5 2 2.5 3 3.5 20 30 40 50 60 70 80 90 100 110 120 Temperature (°C) Temperature shift factor, log a T (a) ?2 ?1.5 ?1 ?0.5 0 0.5 1 0 5 10 15 20 25 Water content, λ Humidity shift factor, log a H 40 °C 50 °C 60 °C 70 °C 80 °C 90 °C 100 °C (b) Figure 5. The thermal and hygral shift factors of Gore-Select ? 57 membrane determined through the construction of the relaxation modulus master curve shown in Figure 4. (a) Thermal shift factor and (b) Hygral shift factor. used: mass uptake, nuclear magnetic resonance (NMR) relaxation, and permeation experiments. [37] Since water con- tent is treated as an independent variable within the current framework for viscoelastic stress model, there is a need for a convenient conversion between RH and water con- tent. Mittelsteadt (see Conductivity, permeability, and ohmic shorting of ionomeric membranes, Volume 5), [38] has shown that, in ionomers based on the –SO 3 Hmoi- ety, the hydration level in terms of nH 2 O/SO 3 H between 0 and 70% RH varies little regardless of EW or chemical backbone and is nearly identical to that of sulfuric acid. Springer et al. [39] used a third-order polynomial fit relating water uptake to water activity. Using an approach similar to Springer et al., Mittelsteadt accounted for the effect at higher temperatures by fitting with a second-order poly- nomial indexed to the reference temperature (30 ? C) and obtained a general equation for PFSA membranes: λ = bracketleftbigg 1 + 0.2325 × RH 2 parenleftbigg T ? 30 30 parenrightbiggbracketrightbigg × parenleftbig 14.22 × RH 3 ? 18.97 × RH 2 + 13.41 × RH parenrightbig (4) where T is the actual temperature in degrees Celsius and RH is in percentage (see Conductivity, permeability, and ohmic shorting of ionomeric membranes, Volume 5). The results obtained here match well with those of Thampan et al. [40] as well as those of Zawodinski et al. [41] Note that equation (4) has an applicable range of RH from 0 to 95% and temperature range from 25 to 95 ? C. In this article, equation (4) has been used to convert RH to λ. Compared to the water sorption and transport, the literature on the hygral expansion measurement is sparse. [4, 11, 18, 42, 43] Among the various techniques used in the literatures, the DMA method offers the most attractive option since the equipment, sample preparation, and test control are similar to those required in determining the viscoelastic properties of membrane materials. In this method, the DMA is nominally operated in creep mode at very small stress levels (0.01 MPa). The errors induced by creep at these small stress levels were estimated to be several orders of magnitude smaller than the hygral strains, and thus were deemed to be negligible. Figure 6 illustrates the result of a typical hygral expansion experiment of Gore- Select ? 57 membrane over a range of humidity levels at 80 ? C. The slope of the hygral strain plotted versus water content gave the coefficient of hygral expansion (CHE) of 0.005 (m/m) (H 2 O/SO 3 H) ?1 . 3.4 Parametric stress analysis of constrained membrane subjected to humidity cycling In this section, the stress response in a constrained mem- brane, Nafion ? NR-111, subjected to humidity cycling is demonstrated through a parametric study [18] with vari- ous humidity swings and hydration/dehydration rates using ABAQUS. The stress analysis is simplified by assuming that membrane hydrates and dehydrates uniformly through- out the membrane and that the membrane is biaxially constrained at the perimeter, which simulates the constraint imposed by the cell compression over the lands and by the electrode layers. The assumption of uniform hydra- tion throughout the membrane thickness is currently being investigated. It is fur