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Effect of gas-diffusion electrode material heterogeneity on the structural integrity of polymer electrolyte fuel cell
Energy 35 (2010) 5241e5249
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Energy journal homepage: www.elsevier.com/locate/energy
Effect of gas-diffusion electrode material heterogeneity on the structural integrity of polymer electrolyte fuel cell K.K. Poornesh a, Chongdu Cho a, *, Do-Young Kim b, Yongsug Tak b a b
IASME Laboratory, Department of Mechanical Engineering, Inha University, 253 Yonghyun-dong, Nam-gu, Incheo, South Korea Materials and Electro-Chemistry Laboratory, Department of Chemical Engineering, Inha University, Incheon, South Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 April 2010 Accepted 24 July 2010 Available online 9 September 2010
In polymer electrolyte fuel cell (PEFC), gas-diffusion electrode (GDE) plays very significant role in force transmission from bipolar plate to the membrane. This paper investigates the effects of material heterogeneities of gas-diffusion electrode layer (gas-diffusion layer (GDL) and catalyst layer (CL)) on the assembly stress levels of single PEFC stack. In addition, we adopt a force transfer mechanism in a single fuel cell stack based on material heterogeneities of GDL and CL to understand the limitations and advantages associated with it through numerical analyses. Nanoscale heterogeneities in GDE are effectively implemented in the simulation cases along with the membrane swelling. Influence of presence or absence of CL interlayer in the numerical environment is found to have significant impact on the adjacent layers as well as interfaces. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Polymer electrolyte fuel cell (PEFC) Catalyst layer Gas-diffusion layer Swelling Structural integrity Heterogeneity
1. Introduction Over the past decade, significant progress has been achieved in terms of power density and electro-chemical functioning targets of PEFC; however, issues regarding lifetime and performance decay persist to make a negative impact on its commercialization. The power density of PEFC largely depends on the coupled electrochemical and electro-mechanical optimal functioning of the MEA (membrane electrode assembly). However, only few significant advances have been achieved in understanding the mechanical principles of gas-diffusion electrode (GDE; GDL and CL) materials. This is because CLs are complex and heterogeneous whereas GDLs are mechanically non-conventional carbonecarbon composites [1]. Hence, material response of GDE is largely assumed to respond similar to a dense solid with the elastic properties of GDL. Durability of GDL is primarily affected by non-uniform distribution of stack pressure, which decreases the gas-diffusion with optimal flexural stiffness capacity leading to porosity loss [2e8]. Carbon fiber breakage and deterioration of hydrophobic coatings in GDL as reported by Lin et al. [6] and Bazylak et al. [7] is bound to accelerate due to the compressed loading conditions. In general, GDLs will be in a compressed as well as tensile state of loading due to the geometrical design of bipolar plate (BPP) flow fields. Thus,
* Corresponding author. Tel.: þ82 32 860 7321; fax: þ82 32 868 1716. E-mail address: [email protected] (C. Cho). 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.07.041
cyclic loadings caused from the cell operating conditions may have a lethal effect on the reliability of GDLs that is realized in terms of carbon fiber (CF) breakage. The nanomechanical investigation of TeflonÒ coated CF by Poornesh et al. [1] reveals the heterogeneity marked by ductile to brittle phase material transition that explains rupturing and breaking of CFs as observed in practical cases. Thus, force transfer characteristics of heterogeneous GDL realized under numerical environment will be very different from that of homogeneous counterpart. On the other hand, optimal functioning of CLs in an operating fuel cell is largely limited by the electro-chemical and chemicomechanical degradation [9e14]. This is characterized by delamination from the membrane, layer cracking, catalyst ripening, particle migration, ionomer dissolution and agglomeration of Pt particles [9e12]. The CLs of fuel cell are heterogeneous and are marked by the 3-phase material interactions (Pt/Carbon particles contained by the ionomer matrix) separated by voids. The presence of nafion ionomer induces a ductile phase in CLs. Thus, constitutive response of CLs may play a vital role in understanding the mechanical degradation. Recent nanoscale investigation [15] on thin Pt/Carbon CL (w3 mm) has explored the effect of gradation of Pt concentration on the elastic modulus as well as the hardness. It appears that the heterogeneity in mechanical properties is due to the heterogeneity of its constituents’, although it is not well established for relatively thick CLs (w10 mm). Further, durability is directly influenced by the degradation mechanism that is different for each cell layer of MEA (e.g., on a mechanical perspective,
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membrane, CL, and GDL differ due to their respective material responses of polymer, ductile, and brittle materials). Hence, it is expected that the estimation of interfacial stress transfer mechanisms near major interfaces (GDL/CL and CL/membrane) may become tedious task and hence it is convenient to use numerical methods to understand the mechanisms behind the stress transfer between layers. Thus, ideal structural integrity design of fuel cell system takes into account the end-to-end load transfer mechanism. However, it is unlikely that most of the assembly techniques available today give special concentration to MEA, especially CL, since its contribution to the whole assembly is assumed less or there is no much literature available on the mechanical principles of CL. Further, a high efficient theoretical assembly design is generally independent of fuel cell operating conditions [16]. Thus, even if complete structural failure of MEA takes place, it has insignificant contribution on the theoretical assembly design of the whole cell. Therefore, it is believed that the ideal clamp loading condition for structural integrity of PEM fuel cell is independent of structural integrity of MEA as it fails to address the failure mechanisms involved. Hence, it is convenient to investigate the structural response of MEA, separately. This article is largely classified into two parts. In the first part, mechanical properties of CL are extracted via instrumented indentation and analyzed for material heterogeneity. In the second, numerical investigation is performed on the structural integrity of MEA to understand the influence of material heterogeneities of GDE components on the structural integrity, especially under the membrane swelling.
2. Materials and methods 2.1. Experimental: CL preparation and mechanical property extraction A 20wt% Pt/Carbon CL of nearly w10 mm thickness is subjected to nanoindentation test to extract the mechanical properties. Catalysts prepared by precipitation method are mixed with the ionomer and isopropanol mixture to form catalyst ink. Ink is then carefully painted over GDL via spray technique. For mechanical characterization, samples Pt/Carbon CL) of 0.5 cm2 were carefully cut and subjected to indentation testing. Nano indenter G200 (MTS corp.) with Berkovich diamond indenter tip was used for our experimental investigations. Samples were mounted on sample disk, which was initially heated using heating element to appropriate temperature in order to bond the sample and disk using small amount of crystalbond. The important indentation contactderived characteristics of elastic or elastic-plastic materials are hardness and modulus. There is vast number of literature available on the application of this method to characterize the properties of size or small volume dependent materials and some of these can be found elsewhere [17e24]. The obtained values of load and displacement as a function of depth or time are used to calculate hardness and elastic modulus. It is also possible to establish a relation between contact stiffness and displacement and from this, material under investigation can be classified as a heterogeneous or homogeneous one. Alternatively, this study uses continuous stiffness measurement (CSM) technique to extract the contact stiffness of CL. This is accomplished
Fig. 1. (a) Schematic of PEM single stack cell showing the cell components. (b) Unit cell model used in the numerical analyses. (c) Mechanical property heterogeneity in MEA components as a function of depth.
K.K. Poornesh et al. / Energy 35 (2010) 5241e5249 Table 1 Mechanical properties of PEM fuel cell layers used in numerical simulation. Properties
Value
Source
Membrane (NafionÒ112) Density (kg/m3) Modulus (MPa) Dry 90% humidity Yield strength (MPa) Dry 30a ¼ 0; 0.05 90% humidity 30a ¼ 0; 0.05
2000 197 121 6.76; 7.16 4.2; 5.11
[26] [26] [26] [26] [26]
Gas diffusion layer (GDL) Density (kg/m3) Modulus (MPa) Poisson’s ratio
400 10,000 0.25
[27] [27] [27]
Heterogeneous carbon fiber (CF) Modulus Poisson’s ratio
Table 3 0.18
Table 3
Catalyst layer (Pt/Carbon) Density (kg/m3) Modulus (MPa) Yield strengthb (MPa) Poisson’s ratio
3000 Eq. (1) wH/3 0.18
Assumed
Bipolar plate (BPP) (steel) Density (kg/m3) Modulus (MPa) Poisson’s ratio
7750 209,000 0.25
[25] [25] [25]
a b
30 implies strain rate.
Effect of nanoporosity on the mechanical properties are assumed insignificant at this stage and hence the yield strength of CL is estimated as H/3.
by imposing a harmonic force to the nominally increasing load. Calculation procedure of contact stiffness (S) along with the determination of dynamic response of the indentation system is discussed in Appendix 1. 2.2. Model description 2.2.1. Unit cell model and layer properties Fig. 1a shows the schematic representation of single stack cell of PEM fuel cell including end plates. This model is used in extracting the unit cell model as shown in Fig. 1b. Present model considers CL as a separate layer as well as geometrical heterogeneities of both CL and GDL as discussed in Fig. 1c. Only left side of the unit cell (Fig. 1b) is taken for numerical analyses. Unshaded area of unit cell is used to describe the property mapping as in Fig. 1(c). Bottom edge of the model is fixed and right edge (dotted line) is allowed to displace only in Y-direction. Geometrical dimensions of MEA along with BPP are shown in Fig. 1b. Axisymmetric FE modeling is preferred here and hence the left side of model is taken as the axisymmetric line. All the parts are assigned with the 4-node bilinear axisymmetric quadrilateral elements (CAX4R) available in the ABAQUS element library [25]. BPP is assigned with high strength steel material. For membrane swelling as well as GDE material heterogeneities, user subroutines (UEXPAN and UFIELD, respectively) are written and all the models are solved in ABAQUS 6.7 commercial package. At this stage, only isotropic swelling strain is considered and is estimated in Appendix 2. Membrane and CL is modeled as the elasticeplastic material, and GDL (or CF) as well as BPP is modeled according to their elastic response. Material properties of all cell layers are listed
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in Table 1. Since carbon fiber of GDL is assumed to possess elastic behavior, its modulus response is listed in equation form by referring to the values of previous investigation [1] as in Table 2 (generalized form is shown in Fig. 1c). Material heterogeneities of CLs are characterized by variation in mechanical properties and are experimentally verified in Section 3. 2.2.2. Force transfer mechanism in MEA under material heterogeneities Factors affecting single stack integrity are analyzed by taking CL as an interlayer between GDL and membrane. Structural integrity principle near MEA under nanoscale as described in Fig. 1c is explored by assuming an increasing material gradation (material heterogeneity) in CL toward the membrane. This means, mechanical properties of CL near GDL/CL interface is less than CL/ membrane interface. Nanoscale heterogeneities in CF are found to vary unusually due to the hydrophobic coating on the carbon fiber [1], which is generalized to follow a particular path. In addition, mechanical properties of membrane are assumed homogeneous throughout the thickness. On the continuum scale, it appears that the properties described in Fig. 1c are decreasing linearly towards membrane, making the membrane susceptible for damage. However, at the nano level under the material heterogeneities, variation of properties is better understood by further exploring MEA interfaces. It is possible to observe the interfacial stress transfer mechanism and can accordingly be categorized into four possible load transfer zones. The CF/ CL zone numbered, ‘F1’, is characterized by a sudden fall in the mechanical properties and is hence capable of developing local stress concentrations near the interfacial line that may ultimately be realized in terms of surface cracks in CL. The CL/membrane interface zone numbered, ‘F2’, is quite a complex zone in terms of force transmission and damage evolution as opposed to the CF/CL interface. This is because, the CL/membrane interface can be analyzed under different cell conditions such as dry, hygrothermal load, cyclic load, and their respective modes of failure (elasticplastic and viscous). All in general there are two-force transfer mechanisms that can quickly be analyzed, i.e., the effect of external clamping load and the swelling force from the membrane. Under no swelling, damage initiated in the CF/CL interface hardly causes any propagation in cracks that is proportional to the material gradation direction in CL. However, think of a situation where there is no material gradation in CL and is then described as a homogeneous material. Now assume the amount of electro-chemical degradation of CL that might result in lining up of CL constituents (carbon black or Pt) near the CL/membrane interface. On a mechanical perspective, this mechanism leads to increasing resistance (this equals to increase in the layer stiffness) for penetration in CL as viewed from GDL. Hence, it is concluded that the mechanical properties of CL near CF/CL are very different from CL/membrane interface and this is generalized to follow a path described in Fig. 1c and is represented as ‘Y(F1)’. This will make CL play an ideal role in mitigating the damage propagation. On the other hand, when swelling of membrane is considered, CL’s role is reversed. Swelling force from the membrane now acts against the clamping load but in the direction of reaction force and is represented as ‘Y(F2)’ shown in
Table 2 Heterogeneity in elastic modulus of TeflonÒ coated carbon fiber [1]. Properties
Heterogeneous values estimated for nearly half the diameter (z3.5 mm) of carbon fiber thickness (d)
Modulus (GPa)
d ¼ f
0/0:35 mm0E ¼ 5:49 expðd=54:73Þ þ 3:67 0:75/3:5 mm0E ¼ 4:5 expðd=568:6Þ þ 0:84
d values in the above relations must be substituted in ‘nm’ scale.
Equation number
Average modulus
(7)
2.1
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Fig. 3. Modulus and hardness response of CL as a function of indentation depth up to 2 mm.
stage, we assume that effect of humidity has no influence on the variation in CL’s mechanical properties. Fig. 2. Combined SEMeEDS cross-section analysis of Pt/Carbon CL to measure the constituent concentrations. (First and second inset figures numbered as ‘1’ and ‘2’ shows the surface of CL and TEM image of Pt catalysts distributed on carbon base, respectively.)
Fig. 1d. This means, evolution of damage resulted from the CL/ membrane interfacial local stress concentrations might propagate more catastrophically. 2.2.3. Simulation cases Finite element analysis (FEA) is performed for unit cell model to investigate the effect of material heterogeneities and membrane swelling, and to underline the stress transfer mechanism. FEA is performed under different modeling conditions and are described under what follows: 1. Conventional modeling e This condition represents a conventional method of modeling where CL is assumed to have bonded to GDL with the mechanical properties same as GDL. Here, material heterogeneities of GDL are neglected. In brief, CL is neglected and elastic properties are assigned for GDL elements. 2. Hetero CL e This refers to the heterogeneous CL where the mechanical properties are varied according to the experimental results. Further, in this case GDL is not modeled as heterogeneous layer. If the instrumented indentation results show heterogeneity in CLs then it is modeled accordingly in the numerical environment. 3. Hetero GDE e This refers to the heterogeneous GDE where each of GDL and CL are modeled as a heterogeneous layer. GDL is modeled as a series of carbon fibers (CFs) stacked to form one complete layer and each of CF (diameter z 7 mm) is assigned with the heterogeneous mechanical properties (GDL is primarily a carbonecarbon composite where matrix volume fraction is very less compared to CF volume fraction). Present modeling of GDL is a simplified model that neglects the random alignments of CFs as well as interconnecting matrix volume fraction (matrix volume fraction is significantly less compared to fiber volume fraction). 4. Swelling e This refers to the 90% RH introduced in the membrane. GDE is modeled as a heterogeneous layer. At this
Simulations are performed under above-mentioned cases for three important reasons. Firstly, in order to highlight the strategic advantages and shortcomings of heterogeneous CL interlayer on the integrity of interfacial as well as adjacent layers. Secondly, in order to estimate the effect of layer mechanical property heterogeneities on the assembly stress levels. Lastly, to characterize the effect of external loading and swelling effects on stress transfer capabilities of individual layers’ influence on the structural integrity. 3. Results and discussion 3.1. Physical characterization Fig. 2 shows SEM cross-section image along with the EDS line analysis for Pt concentration in Pt/Carbon. Heterogeneity in Pt content is clearly observed throughout the CL. Surface morphology
Fig. 4. Contact stiffness plot as a function of indentation depth. Overall response has a linear relationship, except some inter-mediate nonlinearities occurring due to the constituent distribution as observed in Fig. 2.
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of the CLs taken by SEM as well as TEM images of Pt catalyst distribution on supporting blocks can be observed in the inset figures. Inhomogeneous distribution of Pt particles (average particle size estimated to be around 4 mm) on the carbon support particle is observed in case of Pt/Carbon catalyst. 3.2. Mechanical characterization Figs. 3 and 4 shows the mechanical response of Pt/Carbon CL. Modulus and hardness response of CL as function of indentation depth is shown in Fig. 3. It is observed from the plot that the properties exponentially decay as a function of depth and beyond
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w750 nm of indentation depth properties appear to fall plateau and gradually decreases.This effective response of CL obtained from the indentation results are analyzed as follows: a) Plateau of properties beyond some indentation depth indicates that CL responds similar to that of porous foams. Since CL is a nanoporous material, it is likely that properties plateau due to the crushing and plastic densification of CL constituents near the indented zone. This is realized in the form of inter-mediate nonlinearities of contact stiffness response as shown in Fig. 4. b) Overall contact stiffness response of CL as shown in Fig. 4 describes the linear relation with the indenter depth except
Fig. 5. (a) In-plane stress distribution in MEA under (1) heterogeneous GDE and no swelling (2) no CL and swelling (3) heterogeneous CL and swelling (4) heterogeneous GDE and swelling. (b) Out-of-plane stress distribution in MEA under (1) heterogeneous GDE and no swelling (2) no CL and swelling (3) heterogeneous CL and swelling (4) heterogeneous GDE and swelling.
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the inter-mediate nonlinearities. Thus, the gradation of Pt or carbon particles in CL has insignificant effect on the mechanical properties, which is contrary to ultra-thin CLs where the properties are sensitive to Pt and carbon particle distribution [15]. c) However, heterogeneity of particle distributions as observed from the EDS analyses are realized in the form of gradual decrease in the modulus, beyond the plateau area. Thus, the combined effect of plateau of properties and the gradual decrease beyond the plateau region may become tedious task to interpret in numerical simulations. To avoid this ambiguity, CL’s response can be classified as heterogeneous and homogeneous based on continuously varying mechanical properties (heterogeneity caused from the Pt or carbon particle inhomogeneous distribution) and comparing to the porous foams (homogeneous properties extracted from the plateau region of the indentation response), respectively. This study takes into only the heterogeneity of CL. 3.3. Numerical analyses Numerical model is solved under four different cases as mentioned in Section 2. For the heterogeneous CL, experimentally obtained modulus and hardness are fitted to standard equations for the convenient use in numerical programming. Modulus E(GPa) is given as follows (from Fig. 3):
E ¼ 0:417= 1 þ 5:8 104 d
(1)
where d is the CL thickness and varies from 0.4 to 12 mm. Due to the high surface roughness of CL, indentation results for the initial
displacement up to 350 nm are not given. It is noted that the experimentally extracted properties are only up to 2 mm of CL thickness, but then by following the nature of the curve, values can be extrapolated to obtain the Eq. (1). Similarly, hardness H (GPa) is given as in Eq. (2):
H ¼ 7:85 expðd=62:7Þ þ 0:01
(2)
When the CL is modeled as heterogeneous, it is assumed that nanoporosity has no effect on the variation in mechanical properties. Hence, the yield strength of CL can be equated to experimental hardness as H/3. On the other hand, for homogeneous CL, this relation may not hold well as we attribute the plateau of properties to the porosity of CL; that is, for homogeneous CL the yield strength is just equal to hardness. Stress transfer characteristics of PEM fuel cell layers finds their importance in ideal stack design and mechanical durability. Major importance in this study is given to the heterogeneous thin CL interlayer between the GDL and membrane. 3.3.1. In-plane and out-of-plane stresses In the following, significance of plotting in-plane and out-ofplane stresses are explored. Integrity principle discussed in Section 2.2 is incorporated to FE model to study the effect of material heterogeneities. Fig. 5a shows the contour plot of in-plane stress distribution in the MEA under different modeling cases. Top contour plot shows the in-plane stress distribution under no swelling where GDE is modeled as a heterogeneous layer. Negative stresses observed here are due to the compressive nature of the loading under the BPP land area (see Fig. 1b). Rest of the simulation cases considers the swelling of membrane. However, there is no significant difference between the second and third contour plots, which could underline the importance of CL. Hence, influence of
Fig. 6. Von-mises stress variation studied along (a) middle plane of MEA (b) right end of the model (c) left end of the model.
K.K. Poornesh et al. / Energy 35 (2010) 5241e5249
presence of CL in the simulation model is currently unclear from Fig. 5a. On the other hand, stresses appear to have been distributed for the swelling under heterogeneous GDE case (fourth contour plot) which is conversely true for two of the above models. There can be no significant conclusion drawn other than this, hence outof-plane stresses are plotted as shown in Fig. 5b. The contours plots of Fig. 5b exactly represent the force transfer mechanism involved and under no swelling (first plot in Fig. 5b), there is a direct one-way force transfer, which is opposed only by the reaction forces acted upon by external clamp loading. Further, CL avoids direct stress transfer from GDL to membrane. In the subsequent plots, swelling of membrane is assumed and notably there is a build-up of negative stresses in the membrane. Moreover, this is where the importance of CL comes into play. Inability of membrane to transfer the stress through an inappropriate interface leads to stress concentrations near GDL/membrane interface and is explored in the second contour plot of Fig. 5b, where CL is neglected and GDL is modeled as a homogeneous layer. When the CL is introduced between homogeneous GDL and membrane (third plot of Fig. 5b), stress in the membrane decreases, however, no significant changes occur in GDL. Nevertheless, when the GDL is modeled as a heterogeneous layer, significant reduction in stress concentration is observed as shown in the fourth plot of Fig. 5b. Modeling strategies presented in this article can further be applied to study the MEA response under cyclic loadings and the results may significantly differ from homogeneous modeling to the heterogeneous modeling of GDE.
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the swelling effect) until the GDL is stiff enough to oppose the swelling force. This stress near CL/membrane interface caused due to effective force transfer mechanism (effective load transfer ¼ external load e (swelling force þ reaction force)) tries to create a rippling effect on the subsequent GDL layer and is visualized just near GDL/CL interface. However, heterogeneous CFs tries to mitigate this effect and therefore stress levels are maintained as in other cases. Moreover, upon many hygrothermal loadings, this effect may intensify and then damage propagation can be catastrophic under their respective mode of failure. As detailed earlier, influence of effective load transfer can be realized from Fig. 6c, where the effect of swelling leads to lowering of stress levels in GDE and the reverse is true for membrane. This observation is consistent with the contour plots of Fig. 5b (Section 3.3.1). This is studied directly under the BPP land area on the left side of the model. The difference in modeling strategies is clearly understood from the large variation in stress levels under hetero CL and hetero GDE cases. The stress levels are directly related to the individual layer’s mechanical properties and structural integrity of PEM fuel cell. From the above analyses, it is understood that the stress variations differ significantly under various modeling (homogeneous and heterogeneous) and cell conditions in a particular or various vicinity of MEA. This means, damage evolution in any cell layer is directly related to the amount of ‘local’ stress concentrations and their modes of failure, upon which the damage propagation or mitigation is dependent on the nanoscale heterogeneity of the cell layers. 4. Conclusion
3.3.2. Mises stress and the effect of material heterogeneities Fig. 6a shows the variation in mises stress (equivalent stress) levels in the MEA under different simulation cases investigated directly under the edge of the BPP land area. It is noted that the role of CL can be better understood while stress transfer takes place from GDL to membrane under no CL (conventional modeling of PEFC) and rest of the cases. When CL is assumed to possess the same material properties as that of GDL, there are sudden drops in stress level indicating no damage-mitigating factor and this would ultimately result in failure of interfacial layers. However, that is not a realistic analysis of the practical situation. Hence, when the heterogeneous CL is considered, there is an obvious prevention of sudden stress fall from GDL to membrane, characterized by a low elevated stress from CF/CL interface to CL/membrane interface. This acts as a damage resistant zone for any damage occurred and propagated from GDL/CL interface under no swelling in the membrane. In the next simulation case, heterogeneous GDE is considered and that exactly shows the variation in stress levels which is considered to be near equivalent to real situation. As can be seen from the Fig. 6a wavy natured stress patterns are just an outcome of stress transfer from an individual CF to its adjacent one. This highly indicates that any type of damage accumulation within GDL or force or reaction force or swelling force transfer from the adjacent layer is quickly responded by the individual CFs. Further, upon modeling a heterogeneous GDE it is found that the stress levels are higher than in any other case except the swelling case. The effect of swelling on the membrane as well as GDE can be observed and is characterized by the increased stress levels in MEA, especially, near interfaces. Fig. 6b shows the stress variation in MEA studied under right side of the model, and is clearly characterized by a peak near the CL/ membrane interface except for ‘hetero CL’ case. (From here onwards, analysis result under ‘no CL’ case is not discussed, as it is considered unrealistic.) Under the membrane swelling, a remarkable stress peak appears and is due to restrained location of CL interlayer that initially tries to follow the GDL (under BPP channel area, GDL is subjected to tensile loading which is now increased by
Material design principles for PEFC must be investigated for inventing and implementing new cell materials, as the performance and durability of the whole cell is a function of ideal structural integrity. This article stresses on the importance of CL’s role in stress transfer characteristics and hence in damage propagation or mitigation. Absence and presence of CL and its material heterogeneities in a simulation model guarantee a reliable estimation of stress transfer mechanism of the whole cell. In addition, GDL is also modeled as a simplified heterogeneous layer and is observed to play a major role in stress redistribution as opposed to homogeneous model. More importantly, membrane swelling is found to reduce the stress levels in GDE at some particular location of MEA that can well be explained from the ‘equivalent force transfer mechanism’, although it is not the same under every other vicinity of MEA because of the geometrical shape of BPP. The nanoscale based property mapping is presented and applied to simulation model to identify the advantages and disadvantages of interlayer CL. Experimental combined numerical approach presented here emphasizes on the heterogeneous CLs that can be seen as a thin interlayer between GDL and membrane. Its investigation on the role as an ‘interlayer’ is further influenced by the external clamp loading and the membrane swelling pressure. Acknowledgement This work was supported by Inha University. Appendix A. Continuous stiffness measurement (CSM) A schematic of a nanoindenter system using a three-plate capacitor for displacement sensing is shown in Fig. 7. The tip is mounted directly onto the middle plate of the capacitor and a load is applied to move the tip into the sample. Load and displacement are monitored continuously during the indentation process, resulting in a load-displacement curve. The basics of CSM involves a harmonic oscillations combined with the
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tanF ¼ uD= K mu2
(9)
These equations can be solved to obtain K and D. Finally, the stiffness and damping of the contact are given as follows:
1 1 S ¼ F 0 cosF Ks mu2 Kf
(10)
Ds u ¼ ðFo =z0 Þsinf Di u
(11)
z0
While performing the test u is set. The displacement amplitude (z0), phase angle (F), and excitation amplitude (F0) are measured and by knowing the machine parameters Kf, Ks, m, Di one can calculate the S and Dsu.
Fig. 7. Schematic illustration of the indentation instrument.
increasing nominal load. This principle is simplified in Fig. 8 based on the first principles of vibrations or differential equations. Thus, force summation on the mass yields the following equation:
m€z þ Dz_ þ Kz ¼ FðtÞ
(3)
Where K is the equivalent stiffness given by as follows:
K ¼
S1 þ Kf1 þ Ks
(4)
Further, equivalent damping is given by,
D ¼ Di þ Ds
(5)
Let us have exciting force function as,
FðtÞ ¼ F0 eiut
(6)
Then, we have a particular solution for the resulting displacement in the form of Eq. (7):
zðtÞ ¼ z0 eiðutFÞ
(7)
This means, displacement oscillates at the same force frequency (u) but lags behind a phase angle of F. Substituting the particular solution (Eq. (7)) to the Eq. (3), and equating the magnitudes we have:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 2 0 K mu2 þðuDÞ2 : : ¼ z0
(8)
Appendix B. Swelling induced volumetric strain in membrane Assume isotropic elasto-plastic response of the membrane at room temperature. Let the membrane be subjected to humidification (relative humidity (RH) of 90%). Since nafionÒ membrane is highly sensitive to hygroscopic environment (effect of temperature is neglected as CL properties are extracted at atmospheric conditions), total strain (3T) in membrane is represented as follows:
ð3T Þij ¼ ð3e Þij þ 3p ij þð3h Þij
(12)
where, 3e, 3p, and 3h is the elastic, plastic and hygroscopic (swelling) strain, respectively. For isotropic case, swelling strain can be modified ((3h)ij ¼ 3h dij; dij is the Kronecker delta) to follow uniform swelling in all axial directions ((3h)x ¼ (3h)y ¼ (3h)z). The volumetric swelling strain of the membrane is then defined in terms of product of all axial swelling strains (lateral and vertical swelling strains) and is given as following:
3vol ¼
change in volume ¼ ð1 þ 3h Þ3 1 original volume
(13)
At 90% humidity and 25 C temperature, swelling strain of the membrane is reported to be around 0.06 [26]. Hence, volumetric swelling strain of the membrane at this condition is calculated to be around 0.174.
Fig. 8. Harmonic oscillator models.
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[13] Lee G, Lee H, Kwon D. Interfacial characterization of catalyst coating on electrolyte polymer through microscratch analysis in DMFC. Electrochimica Acta 2007;52:4215e21, http://dx.doi.org/10.1016/j.electacta.2006.11.047. [14] Kundu S, Fowler MW, Simon LC, Grot S. Morphological features (defects) in fuel cell membrane electrode assemblies. Journal of Power Sources 2006;157:650e6, http://dx.doi.org/10.1016/j.jpowsour.2005.12.027. [15] Poornesh KK, Cho CD, Lee GB, Tak YS. Gradation of mechanical properties in gas-diffusion electrode, part 1: influence of nano-scale heterogeneity in catalyst layer on interfacial strength between catalyst layer and membrane. Journal of Power Sources 2010;195:2709e17, http://dx.doi.org/10.1016/j. jpowsour.2009.11.101. [16] Lin P, Zhou P, Wu CW. A high efficient assembly technique for large PEMFC stacks part I. theory. Journal of Power Sources 2010;194:381e90, http://dx. doi.org/10.1016/j.jpowsour.2009.04.068. [17] Feng G, Nix WD, Yoon Y, Lee CJ. A study of the mechanical properties of nanowires using nanoindentation. Journal of Applied Physics 2006;99:074304, http://adsabs.harvard.edu/cgi-bin/nphabs_connect? fforward¼http://dx.doi.org/10.1063/1.2189020. [18] Li X, Gao H, Murphy CJ, Caswell KK. Nanoindentation of silver nanowires. Nano Letters 2003;3:1495e8, http://dx.doi.org/10.1021/nl034525b. [19] Tan EPS, Lim CT. Nanoindentation study of nanofibers. Applied Physics Letters 2005;87:123106, http://link.aip.org/link/APPLAB/v87/i12/p123106/s1. [20] Logothetidis S, Kassavetis S, Charitidis C, Panayiotatos Y, Laskarakis A. Nanoindentation studies of dual-layer amorphous carbon films. Carbon 2004;42:1133e6, http://dx.doi.org/10.1016/j.carbon.2003.12.054. [21] Lucas M, Mai W, Yang R, Wang ZL, Riedo E. Aspect ratio dependence of the elastic properties of ZnO nanobelts. Nano Letters 2007;7:1314e7, http://dx. doi.org/10.1021/nl070310g. [22] Oyen ML. Nanoindentation hardness of mineralized tissues. Journal of Biomechanics 2006;39:2699e702, http://dx.doi.org/10.1016/j.jbiomech.2005. 09.011. [23] Ebenstien DM, Pruitt LA. Nanoindentation of biological materials. Nanotoday 2006;1:26e33, http://dx.doi.org/10.1016/S1748-0132(06)70077-9. [24] Li X, Bhushan B. Development of continuous stiffness measurement for composite magnetic tapes. Scripta Materialia 2000;42:929e35, http://dx.doi. org/10.1016/S1359-6462(00)00316-X. [25] ABAQUS. Analysis user’s manual. Hibbitt, Karlsson & Sorensen, Inc.; 2007. [26] Kusoglu A, Karlsson AM, Santare MH, Cleghorn S, Johnson WB. Mechanical response of fuel cell membranes subjected to a hygro-thermal cycle. Journal of Power Sources 2006;161:987e96, http://dx.doi.org/10.1016/j.jpowsour.2006. 05.020. [27] Product information of Toray Industries, Inc.; 2003.
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Effect of gas-diffusion electrode material heterogeneity on the structural integrity of polymer electrolyte fuel cell K.K. Poornesh a, Chongdu Cho a, *, Do-Young Kim b, Yongsug Tak b a b
IASME Laboratory, Department of Mechanical Engineering, Inha University, 253 Yonghyun-dong, Nam-gu, Incheo, South Korea Materials and Electro-Chemistry Laboratory, Department of Chemical Engineering, Inha University, Incheon, South Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 April 2010 Accepted 24 July 2010 Available online 9 September 2010
In polymer electrolyte fuel cell (PEFC), gas-diffusion electrode (GDE) plays very significant role in force transmission from bipolar plate to the membrane. This paper investigates the effects of material heterogeneities of gas-diffusion electrode layer (gas-diffusion layer (GDL) and catalyst layer (CL)) on the assembly stress levels of single PEFC stack. In addition, we adopt a force transfer mechanism in a single fuel cell stack based on material heterogeneities of GDL and CL to understand the limitations and advantages associated with it through numerical analyses. Nanoscale heterogeneities in GDE are effectively implemented in the simulation cases along with the membrane swelling. Influence of presence or absence of CL interlayer in the numerical environment is found to have significant impact on the adjacent layers as well as interfaces. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Polymer electrolyte fuel cell (PEFC) Catalyst layer Gas-diffusion layer Swelling Structural integrity Heterogeneity
1. Introduction Over the past decade, significant progress has been achieved in terms of power density and electro-chemical functioning targets of PEFC; however, issues regarding lifetime and performance decay persist to make a negative impact on its commercialization. The power density of PEFC largely depends on the coupled electrochemical and electro-mechanical optimal functioning of the MEA (membrane electrode assembly). However, only few significant advances have been achieved in understanding the mechanical principles of gas-diffusion electrode (GDE; GDL and CL) materials. This is because CLs are complex and heterogeneous whereas GDLs are mechanically non-conventional carbonecarbon composites [1]. Hence, material response of GDE is largely assumed to respond similar to a dense solid with the elastic properties of GDL. Durability of GDL is primarily affected by non-uniform distribution of stack pressure, which decreases the gas-diffusion with optimal flexural stiffness capacity leading to porosity loss [2e8]. Carbon fiber breakage and deterioration of hydrophobic coatings in GDL as reported by Lin et al. [6] and Bazylak et al. [7] is bound to accelerate due to the compressed loading conditions. In general, GDLs will be in a compressed as well as tensile state of loading due to the geometrical design of bipolar plate (BPP) flow fields. Thus,
* Corresponding author. Tel.: þ82 32 860 7321; fax: þ82 32 868 1716. E-mail address: [email protected] (C. Cho). 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.07.041
cyclic loadings caused from the cell operating conditions may have a lethal effect on the reliability of GDLs that is realized in terms of carbon fiber (CF) breakage. The nanomechanical investigation of TeflonÒ coated CF by Poornesh et al. [1] reveals the heterogeneity marked by ductile to brittle phase material transition that explains rupturing and breaking of CFs as observed in practical cases. Thus, force transfer characteristics of heterogeneous GDL realized under numerical environment will be very different from that of homogeneous counterpart. On the other hand, optimal functioning of CLs in an operating fuel cell is largely limited by the electro-chemical and chemicomechanical degradation [9e14]. This is characterized by delamination from the membrane, layer cracking, catalyst ripening, particle migration, ionomer dissolution and agglomeration of Pt particles [9e12]. The CLs of fuel cell are heterogeneous and are marked by the 3-phase material interactions (Pt/Carbon particles contained by the ionomer matrix) separated by voids. The presence of nafion ionomer induces a ductile phase in CLs. Thus, constitutive response of CLs may play a vital role in understanding the mechanical degradation. Recent nanoscale investigation [15] on thin Pt/Carbon CL (w3 mm) has explored the effect of gradation of Pt concentration on the elastic modulus as well as the hardness. It appears that the heterogeneity in mechanical properties is due to the heterogeneity of its constituents’, although it is not well established for relatively thick CLs (w10 mm). Further, durability is directly influenced by the degradation mechanism that is different for each cell layer of MEA (e.g., on a mechanical perspective,
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membrane, CL, and GDL differ due to their respective material responses of polymer, ductile, and brittle materials). Hence, it is expected that the estimation of interfacial stress transfer mechanisms near major interfaces (GDL/CL and CL/membrane) may become tedious task and hence it is convenient to use numerical methods to understand the mechanisms behind the stress transfer between layers. Thus, ideal structural integrity design of fuel cell system takes into account the end-to-end load transfer mechanism. However, it is unlikely that most of the assembly techniques available today give special concentration to MEA, especially CL, since its contribution to the whole assembly is assumed less or there is no much literature available on the mechanical principles of CL. Further, a high efficient theoretical assembly design is generally independent of fuel cell operating conditions [16]. Thus, even if complete structural failure of MEA takes place, it has insignificant contribution on the theoretical assembly design of the whole cell. Therefore, it is believed that the ideal clamp loading condition for structural integrity of PEM fuel cell is independent of structural integrity of MEA as it fails to address the failure mechanisms involved. Hence, it is convenient to investigate the structural response of MEA, separately. This article is largely classified into two parts. In the first part, mechanical properties of CL are extracted via instrumented indentation and analyzed for material heterogeneity. In the second, numerical investigation is performed on the structural integrity of MEA to understand the influence of material heterogeneities of GDE components on the structural integrity, especially under the membrane swelling.
2. Materials and methods 2.1. Experimental: CL preparation and mechanical property extraction A 20wt% Pt/Carbon CL of nearly w10 mm thickness is subjected to nanoindentation test to extract the mechanical properties. Catalysts prepared by precipitation method are mixed with the ionomer and isopropanol mixture to form catalyst ink. Ink is then carefully painted over GDL via spray technique. For mechanical characterization, samples Pt/Carbon CL) of 0.5 cm2 were carefully cut and subjected to indentation testing. Nano indenter G200 (MTS corp.) with Berkovich diamond indenter tip was used for our experimental investigations. Samples were mounted on sample disk, which was initially heated using heating element to appropriate temperature in order to bond the sample and disk using small amount of crystalbond. The important indentation contactderived characteristics of elastic or elastic-plastic materials are hardness and modulus. There is vast number of literature available on the application of this method to characterize the properties of size or small volume dependent materials and some of these can be found elsewhere [17e24]. The obtained values of load and displacement as a function of depth or time are used to calculate hardness and elastic modulus. It is also possible to establish a relation between contact stiffness and displacement and from this, material under investigation can be classified as a heterogeneous or homogeneous one. Alternatively, this study uses continuous stiffness measurement (CSM) technique to extract the contact stiffness of CL. This is accomplished
Fig. 1. (a) Schematic of PEM single stack cell showing the cell components. (b) Unit cell model used in the numerical analyses. (c) Mechanical property heterogeneity in MEA components as a function of depth.
K.K. Poornesh et al. / Energy 35 (2010) 5241e5249 Table 1 Mechanical properties of PEM fuel cell layers used in numerical simulation. Properties
Value
Source
Membrane (NafionÒ112) Density (kg/m3) Modulus (MPa) Dry 90% humidity Yield strength (MPa) Dry 30a ¼ 0; 0.05 90% humidity 30a ¼ 0; 0.05
2000 197 121 6.76; 7.16 4.2; 5.11
[26] [26] [26] [26] [26]
Gas diffusion layer (GDL) Density (kg/m3) Modulus (MPa) Poisson’s ratio
400 10,000 0.25
[27] [27] [27]
Heterogeneous carbon fiber (CF) Modulus Poisson’s ratio
Table 3 0.18
Table 3
Catalyst layer (Pt/Carbon) Density (kg/m3) Modulus (MPa) Yield strengthb (MPa) Poisson’s ratio
3000 Eq. (1) wH/3 0.18
Assumed
Bipolar plate (BPP) (steel) Density (kg/m3) Modulus (MPa) Poisson’s ratio
7750 209,000 0.25
[25] [25] [25]
a b
30 implies strain rate.
Effect of nanoporosity on the mechanical properties are assumed insignificant at this stage and hence the yield strength of CL is estimated as H/3.
by imposing a harmonic force to the nominally increasing load. Calculation procedure of contact stiffness (S) along with the determination of dynamic response of the indentation system is discussed in Appendix 1. 2.2. Model description 2.2.1. Unit cell model and layer properties Fig. 1a shows the schematic representation of single stack cell of PEM fuel cell including end plates. This model is used in extracting the unit cell model as shown in Fig. 1b. Present model considers CL as a separate layer as well as geometrical heterogeneities of both CL and GDL as discussed in Fig. 1c. Only left side of the unit cell (Fig. 1b) is taken for numerical analyses. Unshaded area of unit cell is used to describe the property mapping as in Fig. 1(c). Bottom edge of the model is fixed and right edge (dotted line) is allowed to displace only in Y-direction. Geometrical dimensions of MEA along with BPP are shown in Fig. 1b. Axisymmetric FE modeling is preferred here and hence the left side of model is taken as the axisymmetric line. All the parts are assigned with the 4-node bilinear axisymmetric quadrilateral elements (CAX4R) available in the ABAQUS element library [25]. BPP is assigned with high strength steel material. For membrane swelling as well as GDE material heterogeneities, user subroutines (UEXPAN and UFIELD, respectively) are written and all the models are solved in ABAQUS 6.7 commercial package. At this stage, only isotropic swelling strain is considered and is estimated in Appendix 2. Membrane and CL is modeled as the elasticeplastic material, and GDL (or CF) as well as BPP is modeled according to their elastic response. Material properties of all cell layers are listed
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in Table 1. Since carbon fiber of GDL is assumed to possess elastic behavior, its modulus response is listed in equation form by referring to the values of previous investigation [1] as in Table 2 (generalized form is shown in Fig. 1c). Material heterogeneities of CLs are characterized by variation in mechanical properties and are experimentally verified in Section 3. 2.2.2. Force transfer mechanism in MEA under material heterogeneities Factors affecting single stack integrity are analyzed by taking CL as an interlayer between GDL and membrane. Structural integrity principle near MEA under nanoscale as described in Fig. 1c is explored by assuming an increasing material gradation (material heterogeneity) in CL toward the membrane. This means, mechanical properties of CL near GDL/CL interface is less than CL/ membrane interface. Nanoscale heterogeneities in CF are found to vary unusually due to the hydrophobic coating on the carbon fiber [1], which is generalized to follow a particular path. In addition, mechanical properties of membrane are assumed homogeneous throughout the thickness. On the continuum scale, it appears that the properties described in Fig. 1c are decreasing linearly towards membrane, making the membrane susceptible for damage. However, at the nano level under the material heterogeneities, variation of properties is better understood by further exploring MEA interfaces. It is possible to observe the interfacial stress transfer mechanism and can accordingly be categorized into four possible load transfer zones. The CF/ CL zone numbered, ‘F1’, is characterized by a sudden fall in the mechanical properties and is hence capable of developing local stress concentrations near the interfacial line that may ultimately be realized in terms of surface cracks in CL. The CL/membrane interface zone numbered, ‘F2’, is quite a complex zone in terms of force transmission and damage evolution as opposed to the CF/CL interface. This is because, the CL/membrane interface can be analyzed under different cell conditions such as dry, hygrothermal load, cyclic load, and their respective modes of failure (elasticplastic and viscous). All in general there are two-force transfer mechanisms that can quickly be analyzed, i.e., the effect of external clamping load and the swelling force from the membrane. Under no swelling, damage initiated in the CF/CL interface hardly causes any propagation in cracks that is proportional to the material gradation direction in CL. However, think of a situation where there is no material gradation in CL and is then described as a homogeneous material. Now assume the amount of electro-chemical degradation of CL that might result in lining up of CL constituents (carbon black or Pt) near the CL/membrane interface. On a mechanical perspective, this mechanism leads to increasing resistance (this equals to increase in the layer stiffness) for penetration in CL as viewed from GDL. Hence, it is concluded that the mechanical properties of CL near CF/CL are very different from CL/membrane interface and this is generalized to follow a path described in Fig. 1c and is represented as ‘Y(F1)’. This will make CL play an ideal role in mitigating the damage propagation. On the other hand, when swelling of membrane is considered, CL’s role is reversed. Swelling force from the membrane now acts against the clamping load but in the direction of reaction force and is represented as ‘Y(F2)’ shown in
Table 2 Heterogeneity in elastic modulus of TeflonÒ coated carbon fiber [1]. Properties
Heterogeneous values estimated for nearly half the diameter (z3.5 mm) of carbon fiber thickness (d)
Modulus (GPa)
d ¼ f
0/0:35 mm0E ¼ 5:49 expðd=54:73Þ þ 3:67 0:75/3:5 mm0E ¼ 4:5 expðd=568:6Þ þ 0:84
d values in the above relations must be substituted in ‘nm’ scale.
Equation number
Average modulus
(7)
2.1
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Fig. 3. Modulus and hardness response of CL as a function of indentation depth up to 2 mm.
stage, we assume that effect of humidity has no influence on the variation in CL’s mechanical properties. Fig. 2. Combined SEMeEDS cross-section analysis of Pt/Carbon CL to measure the constituent concentrations. (First and second inset figures numbered as ‘1’ and ‘2’ shows the surface of CL and TEM image of Pt catalysts distributed on carbon base, respectively.)
Fig. 1d. This means, evolution of damage resulted from the CL/ membrane interfacial local stress concentrations might propagate more catastrophically. 2.2.3. Simulation cases Finite element analysis (FEA) is performed for unit cell model to investigate the effect of material heterogeneities and membrane swelling, and to underline the stress transfer mechanism. FEA is performed under different modeling conditions and are described under what follows: 1. Conventional modeling e This condition represents a conventional method of modeling where CL is assumed to have bonded to GDL with the mechanical properties same as GDL. Here, material heterogeneities of GDL are neglected. In brief, CL is neglected and elastic properties are assigned for GDL elements. 2. Hetero CL e This refers to the heterogeneous CL where the mechanical properties are varied according to the experimental results. Further, in this case GDL is not modeled as heterogeneous layer. If the instrumented indentation results show heterogeneity in CLs then it is modeled accordingly in the numerical environment. 3. Hetero GDE e This refers to the heterogeneous GDE where each of GDL and CL are modeled as a heterogeneous layer. GDL is modeled as a series of carbon fibers (CFs) stacked to form one complete layer and each of CF (diameter z 7 mm) is assigned with the heterogeneous mechanical properties (GDL is primarily a carbonecarbon composite where matrix volume fraction is very less compared to CF volume fraction). Present modeling of GDL is a simplified model that neglects the random alignments of CFs as well as interconnecting matrix volume fraction (matrix volume fraction is significantly less compared to fiber volume fraction). 4. Swelling e This refers to the 90% RH introduced in the membrane. GDE is modeled as a heterogeneous layer. At this
Simulations are performed under above-mentioned cases for three important reasons. Firstly, in order to highlight the strategic advantages and shortcomings of heterogeneous CL interlayer on the integrity of interfacial as well as adjacent layers. Secondly, in order to estimate the effect of layer mechanical property heterogeneities on the assembly stress levels. Lastly, to characterize the effect of external loading and swelling effects on stress transfer capabilities of individual layers’ influence on the structural integrity. 3. Results and discussion 3.1. Physical characterization Fig. 2 shows SEM cross-section image along with the EDS line analysis for Pt concentration in Pt/Carbon. Heterogeneity in Pt content is clearly observed throughout the CL. Surface morphology
Fig. 4. Contact stiffness plot as a function of indentation depth. Overall response has a linear relationship, except some inter-mediate nonlinearities occurring due to the constituent distribution as observed in Fig. 2.
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of the CLs taken by SEM as well as TEM images of Pt catalyst distribution on supporting blocks can be observed in the inset figures. Inhomogeneous distribution of Pt particles (average particle size estimated to be around 4 mm) on the carbon support particle is observed in case of Pt/Carbon catalyst. 3.2. Mechanical characterization Figs. 3 and 4 shows the mechanical response of Pt/Carbon CL. Modulus and hardness response of CL as function of indentation depth is shown in Fig. 3. It is observed from the plot that the properties exponentially decay as a function of depth and beyond
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w750 nm of indentation depth properties appear to fall plateau and gradually decreases.This effective response of CL obtained from the indentation results are analyzed as follows: a) Plateau of properties beyond some indentation depth indicates that CL responds similar to that of porous foams. Since CL is a nanoporous material, it is likely that properties plateau due to the crushing and plastic densification of CL constituents near the indented zone. This is realized in the form of inter-mediate nonlinearities of contact stiffness response as shown in Fig. 4. b) Overall contact stiffness response of CL as shown in Fig. 4 describes the linear relation with the indenter depth except
Fig. 5. (a) In-plane stress distribution in MEA under (1) heterogeneous GDE and no swelling (2) no CL and swelling (3) heterogeneous CL and swelling (4) heterogeneous GDE and swelling. (b) Out-of-plane stress distribution in MEA under (1) heterogeneous GDE and no swelling (2) no CL and swelling (3) heterogeneous CL and swelling (4) heterogeneous GDE and swelling.
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the inter-mediate nonlinearities. Thus, the gradation of Pt or carbon particles in CL has insignificant effect on the mechanical properties, which is contrary to ultra-thin CLs where the properties are sensitive to Pt and carbon particle distribution [15]. c) However, heterogeneity of particle distributions as observed from the EDS analyses are realized in the form of gradual decrease in the modulus, beyond the plateau area. Thus, the combined effect of plateau of properties and the gradual decrease beyond the plateau region may become tedious task to interpret in numerical simulations. To avoid this ambiguity, CL’s response can be classified as heterogeneous and homogeneous based on continuously varying mechanical properties (heterogeneity caused from the Pt or carbon particle inhomogeneous distribution) and comparing to the porous foams (homogeneous properties extracted from the plateau region of the indentation response), respectively. This study takes into only the heterogeneity of CL. 3.3. Numerical analyses Numerical model is solved under four different cases as mentioned in Section 2. For the heterogeneous CL, experimentally obtained modulus and hardness are fitted to standard equations for the convenient use in numerical programming. Modulus E(GPa) is given as follows (from Fig. 3):
E ¼ 0:417= 1 þ 5:8 104 d
(1)
where d is the CL thickness and varies from 0.4 to 12 mm. Due to the high surface roughness of CL, indentation results for the initial
displacement up to 350 nm are not given. It is noted that the experimentally extracted properties are only up to 2 mm of CL thickness, but then by following the nature of the curve, values can be extrapolated to obtain the Eq. (1). Similarly, hardness H (GPa) is given as in Eq. (2):
H ¼ 7:85 expðd=62:7Þ þ 0:01
(2)
When the CL is modeled as heterogeneous, it is assumed that nanoporosity has no effect on the variation in mechanical properties. Hence, the yield strength of CL can be equated to experimental hardness as H/3. On the other hand, for homogeneous CL, this relation may not hold well as we attribute the plateau of properties to the porosity of CL; that is, for homogeneous CL the yield strength is just equal to hardness. Stress transfer characteristics of PEM fuel cell layers finds their importance in ideal stack design and mechanical durability. Major importance in this study is given to the heterogeneous thin CL interlayer between the GDL and membrane. 3.3.1. In-plane and out-of-plane stresses In the following, significance of plotting in-plane and out-ofplane stresses are explored. Integrity principle discussed in Section 2.2 is incorporated to FE model to study the effect of material heterogeneities. Fig. 5a shows the contour plot of in-plane stress distribution in the MEA under different modeling cases. Top contour plot shows the in-plane stress distribution under no swelling where GDE is modeled as a heterogeneous layer. Negative stresses observed here are due to the compressive nature of the loading under the BPP land area (see Fig. 1b). Rest of the simulation cases considers the swelling of membrane. However, there is no significant difference between the second and third contour plots, which could underline the importance of CL. Hence, influence of
Fig. 6. Von-mises stress variation studied along (a) middle plane of MEA (b) right end of the model (c) left end of the model.
K.K. Poornesh et al. / Energy 35 (2010) 5241e5249
presence of CL in the simulation model is currently unclear from Fig. 5a. On the other hand, stresses appear to have been distributed for the swelling under heterogeneous GDE case (fourth contour plot) which is conversely true for two of the above models. There can be no significant conclusion drawn other than this, hence outof-plane stresses are plotted as shown in Fig. 5b. The contours plots of Fig. 5b exactly represent the force transfer mechanism involved and under no swelling (first plot in Fig. 5b), there is a direct one-way force transfer, which is opposed only by the reaction forces acted upon by external clamp loading. Further, CL avoids direct stress transfer from GDL to membrane. In the subsequent plots, swelling of membrane is assumed and notably there is a build-up of negative stresses in the membrane. Moreover, this is where the importance of CL comes into play. Inability of membrane to transfer the stress through an inappropriate interface leads to stress concentrations near GDL/membrane interface and is explored in the second contour plot of Fig. 5b, where CL is neglected and GDL is modeled as a homogeneous layer. When the CL is introduced between homogeneous GDL and membrane (third plot of Fig. 5b), stress in the membrane decreases, however, no significant changes occur in GDL. Nevertheless, when the GDL is modeled as a heterogeneous layer, significant reduction in stress concentration is observed as shown in the fourth plot of Fig. 5b. Modeling strategies presented in this article can further be applied to study the MEA response under cyclic loadings and the results may significantly differ from homogeneous modeling to the heterogeneous modeling of GDE.
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the swelling effect) until the GDL is stiff enough to oppose the swelling force. This stress near CL/membrane interface caused due to effective force transfer mechanism (effective load transfer ¼ external load e (swelling force þ reaction force)) tries to create a rippling effect on the subsequent GDL layer and is visualized just near GDL/CL interface. However, heterogeneous CFs tries to mitigate this effect and therefore stress levels are maintained as in other cases. Moreover, upon many hygrothermal loadings, this effect may intensify and then damage propagation can be catastrophic under their respective mode of failure. As detailed earlier, influence of effective load transfer can be realized from Fig. 6c, where the effect of swelling leads to lowering of stress levels in GDE and the reverse is true for membrane. This observation is consistent with the contour plots of Fig. 5b (Section 3.3.1). This is studied directly under the BPP land area on the left side of the model. The difference in modeling strategies is clearly understood from the large variation in stress levels under hetero CL and hetero GDE cases. The stress levels are directly related to the individual layer’s mechanical properties and structural integrity of PEM fuel cell. From the above analyses, it is understood that the stress variations differ significantly under various modeling (homogeneous and heterogeneous) and cell conditions in a particular or various vicinity of MEA. This means, damage evolution in any cell layer is directly related to the amount of ‘local’ stress concentrations and their modes of failure, upon which the damage propagation or mitigation is dependent on the nanoscale heterogeneity of the cell layers. 4. Conclusion
3.3.2. Mises stress and the effect of material heterogeneities Fig. 6a shows the variation in mises stress (equivalent stress) levels in the MEA under different simulation cases investigated directly under the edge of the BPP land area. It is noted that the role of CL can be better understood while stress transfer takes place from GDL to membrane under no CL (conventional modeling of PEFC) and rest of the cases. When CL is assumed to possess the same material properties as that of GDL, there are sudden drops in stress level indicating no damage-mitigating factor and this would ultimately result in failure of interfacial layers. However, that is not a realistic analysis of the practical situation. Hence, when the heterogeneous CL is considered, there is an obvious prevention of sudden stress fall from GDL to membrane, characterized by a low elevated stress from CF/CL interface to CL/membrane interface. This acts as a damage resistant zone for any damage occurred and propagated from GDL/CL interface under no swelling in the membrane. In the next simulation case, heterogeneous GDE is considered and that exactly shows the variation in stress levels which is considered to be near equivalent to real situation. As can be seen from the Fig. 6a wavy natured stress patterns are just an outcome of stress transfer from an individual CF to its adjacent one. This highly indicates that any type of damage accumulation within GDL or force or reaction force or swelling force transfer from the adjacent layer is quickly responded by the individual CFs. Further, upon modeling a heterogeneous GDE it is found that the stress levels are higher than in any other case except the swelling case. The effect of swelling on the membrane as well as GDE can be observed and is characterized by the increased stress levels in MEA, especially, near interfaces. Fig. 6b shows the stress variation in MEA studied under right side of the model, and is clearly characterized by a peak near the CL/ membrane interface except for ‘hetero CL’ case. (From here onwards, analysis result under ‘no CL’ case is not discussed, as it is considered unrealistic.) Under the membrane swelling, a remarkable stress peak appears and is due to restrained location of CL interlayer that initially tries to follow the GDL (under BPP channel area, GDL is subjected to tensile loading which is now increased by
Material design principles for PEFC must be investigated for inventing and implementing new cell materials, as the performance and durability of the whole cell is a function of ideal structural integrity. This article stresses on the importance of CL’s role in stress transfer characteristics and hence in damage propagation or mitigation. Absence and presence of CL and its material heterogeneities in a simulation model guarantee a reliable estimation of stress transfer mechanism of the whole cell. In addition, GDL is also modeled as a simplified heterogeneous layer and is observed to play a major role in stress redistribution as opposed to homogeneous model. More importantly, membrane swelling is found to reduce the stress levels in GDE at some particular location of MEA that can well be explained from the ‘equivalent force transfer mechanism’, although it is not the same under every other vicinity of MEA because of the geometrical shape of BPP. The nanoscale based property mapping is presented and applied to simulation model to identify the advantages and disadvantages of interlayer CL. Experimental combined numerical approach presented here emphasizes on the heterogeneous CLs that can be seen as a thin interlayer between GDL and membrane. Its investigation on the role as an ‘interlayer’ is further influenced by the external clamp loading and the membrane swelling pressure. Acknowledgement This work was supported by Inha University. Appendix A. Continuous stiffness measurement (CSM) A schematic of a nanoindenter system using a three-plate capacitor for displacement sensing is shown in Fig. 7. The tip is mounted directly onto the middle plate of the capacitor and a load is applied to move the tip into the sample. Load and displacement are monitored continuously during the indentation process, resulting in a load-displacement curve. The basics of CSM involves a harmonic oscillations combined with the
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tanF ¼ uD= K mu2
(9)
These equations can be solved to obtain K and D. Finally, the stiffness and damping of the contact are given as follows:
1 1 S ¼ F 0 cosF Ks mu2 Kf
(10)
Ds u ¼ ðFo =z0 Þsinf Di u
(11)
z0
While performing the test u is set. The displacement amplitude (z0), phase angle (F), and excitation amplitude (F0) are measured and by knowing the machine parameters Kf, Ks, m, Di one can calculate the S and Dsu.
Fig. 7. Schematic illustration of the indentation instrument.
increasing nominal load. This principle is simplified in Fig. 8 based on the first principles of vibrations or differential equations. Thus, force summation on the mass yields the following equation:
m€z þ Dz_ þ Kz ¼ FðtÞ
(3)
Where K is the equivalent stiffness given by as follows:
K ¼
S1 þ Kf1 þ Ks
(4)
Further, equivalent damping is given by,
D ¼ Di þ Ds
(5)
Let us have exciting force function as,
FðtÞ ¼ F0 eiut
(6)
Then, we have a particular solution for the resulting displacement in the form of Eq. (7):
zðtÞ ¼ z0 eiðutFÞ
(7)
This means, displacement oscillates at the same force frequency (u) but lags behind a phase angle of F. Substituting the particular solution (Eq. (7)) to the Eq. (3), and equating the magnitudes we have:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F 2 0 K mu2 þðuDÞ2 : : ¼ z0
(8)
Appendix B. Swelling induced volumetric strain in membrane Assume isotropic elasto-plastic response of the membrane at room temperature. Let the membrane be subjected to humidification (relative humidity (RH) of 90%). Since nafionÒ membrane is highly sensitive to hygroscopic environment (effect of temperature is neglected as CL properties are extracted at atmospheric conditions), total strain (3T) in membrane is represented as follows:
ð3T Þij ¼ ð3e Þij þ 3p ij þð3h Þij
(12)
where, 3e, 3p, and 3h is the elastic, plastic and hygroscopic (swelling) strain, respectively. For isotropic case, swelling strain can be modified ((3h)ij ¼ 3h dij; dij is the Kronecker delta) to follow uniform swelling in all axial directions ((3h)x ¼ (3h)y ¼ (3h)z). The volumetric swelling strain of the membrane is then defined in terms of product of all axial swelling strains (lateral and vertical swelling strains) and is given as following:
3vol ¼
change in volume ¼ ð1 þ 3h Þ3 1 original volume
(13)
At 90% humidity and 25 C temperature, swelling strain of the membrane is reported to be around 0.06 [26]. Hence, volumetric swelling strain of the membrane at this condition is calculated to be around 0.174.
Fig. 8. Harmonic oscillator models.
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