Effects of Porous Carbon Morphology, Agglomerate Structure and Relative Humidity on Local Oxygen Transport Resistance

X-ray radiographs of a state-of-the-art alloy catalyst electrode (extracted from the cathode of a membrane-electrode assembly from a Toyota Mirai stack which was subjected to 300 h of use in on-road driving, refer to Ref. 30 for more details) were acquired using the Xradia nano XCT-S100 TXM at beam line 32-ID-C of the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). Employing a fly-scan technique, 1080 projection images were acquired over 180° rotations. The projection images were reconstructed into a 3D image sequence with ∼20-nm voxel size using Tomopy and Astra.^33,34

Following the procedure in Refs. 35, 36 the Cs⁺ exchanged sample was scanned in both absorption and Zernike phase contrast modes. The phase contrast mode resolves the overall morphology of the solid material (a mixture of C, Pt, ionomer and primary pores below resolution) while the absorption contrast images provide an intensity map of the high electron-density materials within the sample (i.e., Cs⁺ indicating the ion exchanged ionomer) as illustrated in Figs. 1a and 1b. The raw data in Fig. 1 shows a 5–6 μm thick electrode with some variations in thickness which might be associated with sample preparation. Absorption image shows high intensity spots (over 2-μm sizes) distributed throughout the electrode as highlighted by the green circles in Fig. 1b. These bright spots indicate the presence of large ionomer agglomerates in the electrode. It should be noted that the intensity map in Fig. 1b also includes the contribution from the catalyst particles (especially the large catalyst particles observed as small bright dots) but due to the small volume of the catalyst in comparison to ionomer, the signal from the catalyst particles are ignored.

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Figure 2a shows the in-plane (X, Y) and the through-thickness (Z) distribution of ionomer volume fraction (for 20 nm slices of data) which is correlated with the intensity in the absorption contrast images as described in Refs. 35, 36. The oscillations in all directions indicate the structural heterogeneity of the electrode. The high amplitude fluctuations can be attributed to the ionomer agglomerates illustrated in Fig. 1b. The ionomer volume fraction has a mean value of 0.26 and standard deviations of 0.015, 0.018 and 0.035 in X, Y and Z directions respectively. Overall, Fig. 2a indicates a graded ionomer distribution with more ionomer closer to the membrane and less ionomer closer to the diffusion media while there is no obvious trend in the in-plane directions. Nano-CT data is further quantified by segmenting the phase contrast image using open source Fiji software.³⁷ One can refer to Ref. 17 for more details of the segmentation procedure. Figure 2b presents the calculated solid size distribution based on the diameter of the largest sphere that can be inscribed in each solid voxel in the segmented phase contrast image. Such distributions calculated from nano-CT data were previously referred to sizes of agglomerates in Refs. 13, 17 by making analogy to the spherical agglomerate models.^11–14 Here, this quantity is referred as the solid size while the agglomerates are extracted with a different method which is discussed in the next section. The mean solid size for this electrode sample is 320 nm with a standard deviation of 166.5 nm. Figure 2c presents the so called shortest path tortuosity which is a mass transport related structural property. Shortest pathways in the pore phase between opposing surfaces of a 6 μm × 10 μm × 15 μm size sub-volume extracted from electrode are calculated in X, Y, Z directions using the algorithm described in^17,38 (see Fig. 2c). Shortest path tortuosity is obtained as a distribution by dividing the calculated path lengths with the actual distance between the start and target surfaces. Figure 2c shows that the pores are more tortuous in the through-thickness direction (Z direction) than in the in-plane directions (X-Y), thus highlighting the anisotropic electrode structure and transport properties.

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Recently, electron tomography has been used to quantify the 3D structures of porous carbon supports as well as the distribution of catalyst particles on the surface and in the interior pores of HSC.^20,39 This technique is quite powerful, however the analyzed structures are limited in integrity (i.e. it is not possible to visualize an agglomerate as it is situated inside the electrode) due to the destructive nature of sample preparation (e.g., cross-sectioning, microtoming, focused ion beam milling). While nondestructive nano-CT protects the integrity of the sample, it suffers from insufficient resolution. Previously, we demonstrated a numerical approach combining nano-CT images with statistical information from TEM, X-ray scattering and porosimetry techniques to generate detailed structures of electrode³² and 3D agglomerates of solid carbon¹⁷ defined as spheres inscribed to segmented nano-CT images (as described above). Here, we further extend this approach to study agglomerates of HSC support extracted from the connectivity of solid the phase in the segmented phase contrast image.

In order to identify the agglomerates within the nano-CT images, we employ a technique called watershed separation of binary image (available in Fiji³⁷), which is commonly used to separate touching objects. This technique finds centers of objects to be separated by repeatedly applying morphological erode operations. A map is constructed from the calculated distance between the center points and the edges of the objects. Using the distance map, objects are successively filled with the so-called water phase (starting from the center points) and identifying the borders of touching objects where water phases of different objects meet. Applying this technique to the segmented phase contrast data, 24359 different agglomerates of various shapes, sizes and compositions are extracted and labeled as different colors in Fig. 3a.

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The volume to surface area ratio was used to define an effective diameter for such random shapes in Ref. 36 but here we quantify agglomerate size by defining an equivalent diameter (d_A) of sphere that has the same volume as the non-spherical object. The average equivalent diameter is calculated as 358 nm (see the inset in Fig. 3b) while the average effective diameter is 86 nm. In agreement with our observations, the two-dimensional TEM images of the same electrode show large (∼1-μm length scale) and densely packed agglomerates isolated by secondary pores.³⁰ The aspect ratio (A_r) distribution in Fig. 3b illustrates that there is a wide variety of agglomerate shapes, ranging from long chain like structures (low A_r) to sphere like structures (high A_r) as illustrated in Fig. 3b. Most of these agglomerates are below 1000 nm equivalent diameter (see the inset in Fig. 3b) and exhibit a wider distribution of aspect ratios in comparison to large agglomerates (d_A > 1000 nm). In addition, majority of the agglomerates have aspect ratio exceeding 0.5 as shown in the inset in Fig. 3b.

The composition of these agglomerates (i.e., carbon volume fraction (ε_C)) is estimated from the ionomer volume fraction (ε_N) determined from the absorption contrast data following the procedure in Ref. 17. It is important to note that we assumed constant Pt/C weight ratio (f = 0.30) and primary pore volume fraction (ε_A = 0.08) for all agglomerates.

where V_A is the agglomerate volume, I is the intensity from absorption contrast data, and I_max is the intensity of the brightest voxel in the absorption image. Figure 3c presents the variation of agglomerate composition in the sample in terms of I/C. The mean I/C and standard deviation are calculated as 0.83 and 0.12 respectively (see the inset in Fig. 3c). The distribution of the agglomerate I/C shows a positive correlation with the equivalent agglomerate diameter as shown in Fig. 3c, highlighting the role played by ionomer in binding carbon and forming larger agglomerates.

The agglomerate shape and Cs⁺ intensity distribution extracted from 20-nm voxel size nano-CT images are mapped into 1-nm voxel size domains. The features missing in nano-CT images because of insufficient resolution (such as HSC clusters, catalyst particles and ionomer) are numerically reconstructed with 1-nm voxel resolution by using supplementary data. Initially, the body of the agglomerate is filled by clustering various size solid carbon particles (primary particle sizes from TEM and X-ray scattering data in Ref. 32) following the 2-step procedure in Refs. 17, 32 as illustrated in Fig. 4b. Unlike our previous works,^17,32 the interior pores of HSC supports are taken into account in this study by using the carbon pore size distribution and volume of pores per gram carbon as obtained from BET data by Park et al.¹⁰ Pores below 10-nm are assumed to be inside the support particles and the BET data is discretized into 2-nm bins. Looping over each solid carbon particle, pore seeds of different diameter are initiated on the surface and are grown toward the center of each support particle until the measured porosity is reached as shown in Fig. 3c. For simplicity in physical modelling, non-overlapping carbon pores are assumed which results in pores of different length and shape (see the details of HSC pores in Fig 3c). Based on the microscopy data from Refs. 10, 20, 75% of the Pt particles are distributed within the pores of HSC. We assume that the interior Pt particles are of the same size as the HSC pores and 20% of the Pt particle volume overlaps with the carbon wall base (so that the particle doesn't block transport inside the HSC pore). Searching the availability of the HSC pore wall voxels (i.e., interior Pt cannot overlap with each other and pores outside carbon), Pt particles are placed until the desired volume fraction is satisfied as shown in Fig. 4d (interior Pt shown in red color). The remaining 25% of the catalyst particles are distributed on the surface of carbon by using the size distribution data obtained from TEM analysis in Ref. 30 as illustrated by gold color in Fig. 4e. In the last step, ionomer is generated using Cs⁺ intensity (from the absorption contrast image) as ionomer distribution probability. Following the findings of electrochemical measurements,^19,21–23 ionomer is not allowed to intrude into the HSC pores. Ionomer seeds (single voxel ionomer) are placed on the exterior Pt and HSC surfaces and agglomerate outer boundary using a random number generator and a constant distribution probability (i.e., if generated random number is smaller than the ionomer distribution probability then voxel is assigned as ionomer). Searching the neighborhood of the existing ionomer voxels, ionomer is grown by comparing a random number generator with the ionomer distribution probability of the available neighborhood voxel. The ionomer growth step is successively repeated until the target volume fraction is reached as shown in Fig. 4f. It should be noted that primary pores are naturally formed in the agglomerates as a result of the reconstruction process.

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To study O₂ transport to the catalyst surfaces in agglomerates at different RH, we employ a pore scale model that accounts for mass transfer across multiple phases (i.e., gas, liquid, solid) which we described in Ref. 18 in more detail. The governing equation for the multiple-phase medium in terms of scaled O₂ concentration () and scaled diffusivity () is derived as following in Ref. 18:

where C_j is the O₂ concentration in medium j (i.e., primary pore, liquid water, ionomer), D_j is the diffusion coefficient of O₂ in medium j, and H_j is the Henry's law constant defined as the ratio of O₂ concentration in any medium j to O₂ concentration in gas phase¹⁸ (i.e., for primary pores H_g is unity). In this model, Pt and HSC in the agglomerates are regarded as impervious while transport is allowed in primary pore, liquid water and ionomer. Considering the primary pore length scale in agglomerates, both molecule-molecule (bulk diffusion, D_b) and molecule-wall (Knudsen diffusion, D_Kn) collisions are taken into consideration for calculation of O₂ diffusion coefficient in the gas phase.

where d_p is the pore diameter, and M is molecular weight. Liquid water is introduced in the system using the capillary condensation theory which states that the smaller the pore size, the lower the RH at which the condensation occurs.^31,40 In addition to perfect wetting surface assumption, RH is considered to be constant inside the agglomerates (small length scale). Accordingly the primary pores inclusive of the pores inside HSC are filled with liquid water if the following condition is satisfied:

where γ is the liquid-vapor surface tension, and V_m is the liquid water molar volume. All Pt surfaces in contact with liquid water or ionomer are assumed active. Thus water condensation plays a role in determining ECA and altering the transport properties (higher resistance in water filled pores). Transport associated parameters used in the model are tabulated in Table I.

Table I. Transport Parameters.

Temperature	T = 353 K
Pressure	P = 1 atm
O2 bulk diffusion coefficient in air	Db = 2.94 x 10− 5 m2.s− 1
O2 diffusion coefficient in ionomer 100% RH41
Henry' law constant for O2 in ionomer8	Hi = 0.09269
O2 diffusion coefficient in water	Dw = 2.04 x 10− 9 m2.s− 1
Henry' law constant for O2 in water42	Hw = 0.01760

For all the simulations performed in this study, we considered a limiting current scenario in which the active catalyst surfaces are assigned zero O₂ concentration (C_S = 0). Concentration at the agglomerate-secondary pore space boundary (C_A) is calculated from the experimentally measured limiting current (i_L) in units of A.m²-Pt.

where is the experimentally measured local O₂ transport resistance associated with nano-scale transport inside agglomerate. One can refer to Ref. 25 for experimental estimation of. In this study, the values of (presented in the next section) are determined based on our analysis of an extensive limiting current data set (not presented in this study).

Using the boundary conditions and transport scenario described above, we seek direct numerical solution of Eq. 4 on the 3D structured grid defining the connectivity of transport cells (7-point stencil) in the agglomerates. The computational domains include up to ∼ 250 million cells. To handle such large system of equations we used high performance computers at Laboratory Computer Resource Center (LCRC) of Argonne National Laboratory. The equations are discretized using second-order central difference scheme and arranged in a sparse form coefficient matrix. Equation systems are solved using 'hypre' preconditioner in PETSc⁴³ until residual (L² norm of numerical solution) drops below 10⁻¹⁴.

It is hypothesized that capillary condensation allows liquid water to form in pores below the saturation pressure and this water provides ion conducting paths to Pt particles in HSC pores. In support of this hypothesis, employing electrochemical characterization techniques such as CO stripping,^24,25 studies have demonstrated a strong dependence of catalyst utilization on RH. Figure 5a presents normalized electrochemically active area (NECA) at different RH as measured in Refs. 24, 25 and compares with the numerical result from porous HSC agglomerate reconstruction. The model predictions in Fig. 5a show similar trends as the experimental observations indicating that the reconstructed structure accurately reproduces the NECA-RH relationship. The inset in Fig. 5a shows the fraction of active catalyst particles at 100% RH depending on location (i.e., ∼25% of the active area is on the surface of the HSC support).

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The length scales of primary pores in between support particles are close to the HSC pore sizes. Transport restrictions due to condensation in HSC pores were discussed in literature^26,27 but possible limitations of capillary-condensed water in the primary pores (between support particles) were not taken into account in any studies to the best of authors' knowledge. Here, we consider condensation both in primary and C pores following the rule in Eq. 9. Figure 5b shows section view of an agglomerate (d_A = 300 nm, I/C = 0.8) indicating the degree of capillary condensation at different RH levels. At low RH (42%) capillary-condensed water is observed only in limited number of tiny pores inside HSC as shown in Fig. 5b. As RH increases most of the HSC pores become proton accessible (with water) and significant amount of primary pores get filled with condensed water leading to the flooded agglomerate at 100% RH.

We used experimental limiting current measurements to determine the RH dependence of O₂ diffusivity in ionomer (D_i). Accounting for capillary condensation effects, direct transport simulations were performed on the agglomerate shown in Fig. 5b and D_i was tuned to match the measured limiting current shown in the inset of Fig. 5c. Figure 5c compares the inferred RH dependence of D_i with the experimental data of Chen et al.⁴⁴ for 1000-nm ionomer films on SiO₂ substrate. The model shows a similar trend with data indicating that inferred RH dependence of D_i is realistic.

Figure 5d compares the modeled O₂ transport resistance () in the agglomerate with the values derived from the limiting current data. In the agglomerate, is calculated as follows:

where i_Pt is the current generated at each Pt surface, and A₀ is the total surface area of all Pt particles in the agglomerate at 100% RH (similarly the roughness factor at 100% RH was used for derived from the limiting current data). Additionally Fig. 5d presents calculated based on RH corrected A₀ which cancels the NECA-RH effect on . Under dry conditions (< 42% RH), the RH corrected is significantly different than indicating that low NECA (i.e., ∼25% NECA at 20% RH) is mainly responsible for extremely high resistance. Respectively minor contribution of reduced D_i (see Fig. 5c) to the elevated under dry conditions can be assessed by comparing the RH corrected between 42% and 20% RH (i.e., 10% reduction in D_i results in 2.4 s.cm⁻¹ higher RH corrected). Figure 5d shows that rapidly decreases until 64% RH and converges to ∼13 s.cm⁻¹ at 100% RH. Despite the ∼60% improvement in D_i (see Fig. 5c) from 42% RH to 100% RH, the RH corrected increases ∼40% due to transport limitations in the condensed water filled primary pores in agglomerate (see Fig. 5b).

In the previous sections, we demonstrated structural heterogeneity of the agglomerates in the electrode in terms of size (equivalent diameter) and shape (aspect ratio). Size and shape of ideal core-shell agglomerates (such as spherical or cylindrical) were shown to have significant impact on transport.^13,45,46 However, none of these studies account for porous structure of HSC, primary pores and catalyst particles which play critical role in local O₂ transport losses.¹⁸ Furthermore, the capillary condensation-RH effects were not considered in any of these agglomerate models. Depending on the realistic agglomerates and the transport model described above, here we examine the agglomerate size and shape effect on at limiting current conditions for different RH.

The O₂ transport model (calibrated with experimental data for 300-nm agglomerate) is applied to different size agglomerates (having A_r in range 0.77–0.83 and I/C of 0.8). Figure 6a presents at 42% and 100% RH. Under dry conditions (42% RH) the agglomerates show significantly higher than at 100% RH consistent with the observations in the previous section. Figure 6a highlights that strongly correlates with agglomerate size at 100% RH (primary pores are flooded as in Fig. 5b); the resistance increases approximately 52% from 200-nm to 500-nm agglomerate. As intuitively expected the larger the agglomerate diameter the longer the diffusion distance and the higher is the transport resistance. On the other hand, under dry conditions (42% RH) Fig. 6a shows similar for different size agglomerates. At 42% RH, becomes independent of agglomerate size because the primary pores in agglomerates remain dry (see Fig. 5b) and the majority of the transport resistance originates from the ionomer film over the outer Pt particles. Figure 6b shows the corresponding ionomer film thickness distribution over the outer catalyst particles which is calculated employing the shortest distance method explained in.¹⁷ Due to heterogeneity of the agglomerate composition (i.e. Cs⁺ intensity distribution) calculated film thicknesses range 2–35 nm in agglomerates. Thickness distribution appears to be very similar for different size agglomerates and does not indicate any correlation to agglomerate size. The average ionomer thickness for different agglomerates (see the inset Fig. 6b) correlates well with calculated at 42% RH pointing out that the agglomerate size– relation strongly relies on the accessibility of the primary pores in the agglomerates.

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Figure 7a shows two distinctive shapes of same volume agglomerates (d_A = 250 nm and I/C = 0.8). The low aspect ratio (A_r = 36) agglomerate resembles a long chain like structure whereas the high aspect ratio (A_r = 78) agglomerate looks closer to a sphere. Figure 7b presents the corresponding calculated for limiting current conditions at 42% and 100% RH. Agglomerate shape does not seem to play any roles in local O₂ transport losses at dry conditions (42% RH) as shown in Fig. 7b. Because correlates only with the ionomer film thickness at dry conditions due to accessible (low resistance) primary pores as explained above. On the other hand, agglomerate shape comes into play when the primary pores get filled with water at higher RH. Figure 7b shows approximately 30% rise in of the sphere like agglomerate at 100% RH in comparison to the low aspect ratio agglomerate. Figure 7c shows that reactant cannot reach the inner sections of the high A_r agglomerate whereas the core region of the low A_r agglomerate appears to be more accessible due to shorter diffusion length. Consequently, the catalyst particles located away from the agglomerate surface get utilized more in low A_r agglomerate which results in lower (in comparison to high A_r agglomerate).

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It is important to understand the transport to interior (inside HSC support pores) and exterior (on the surface of HSC) catalyst particles for more effective use of precious metal. For identical locations of carbon support, we performed a parametric study by changing the number fraction of the outer Pt particles (f_o) to evaluate the catalyst location effect on . Figure 8a shows the section views of two agglomerates with f_o = 0.25 (corresponding to HSC) and f_o = 1.00 (corresponding to solid carbon). Due to random distribution of Pt particles there are negligible differences between different f_o structures but the overall morphologies are quite similar as shown in Fig. 8a. Figure 8b presents calculated at 42% and 100% RH. As intuitively expected, higher f_o results in lower both for dry and flooded conditions. At 100% RH the difference between for f_o = 0.25 and f_o = 1.00 (∼ 4 s.cm⁻¹) approximately quantifies the effect of transport to interior catalyst particles (in water filled C pores) on . Figure 8b also shows the diminishing impact of RH on with increasing f_o.

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