# Characterizing PEM fuel cell catalyst layer properties from high resolution three-dimensional digital images, part I: A numerical procedure for the ionomer distribution reconstruction

Mohamed Ahmed-Maloum, Thomas David, Laure Guetaz, Arnaud Morin, Joël Pauchet, Michel Quintard, Marc Prat

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Mohamed Ahmed-Maloum, Thomas David, Laure Guetaz, Arnaud Morin, Joël Pauchet, et al.. Characterizing PEM fuel cell catalyst layer properties from high resolution three-dimensional digital images, part I: A numerical procedure for the ionomer distribution reconstruction. International Journal of Hydrogen Energy, 2024, 80, pp.39-56. 10.1016/j.ijhydene.2024.07.097. hal-04955002

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Submitted on 23 Oct 2025

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# Characterizing PEM fuel cell catalyst layer properties from high resolution three-dimensional digital images, Part I: A numerical procedure for the ionomer distribution reconstruction

Mohamed Ahmed-Maloumª, Thomas Davidᵇ, Laure Guetazᵇ, Arnaud Morinᵇ, Joël Pauchetᵇ,

Michel Quintardª, Marc Pratª

ªInstitut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS –
Toulouse, France

ᵇUniv. Grenoble Alpes, CEA, LITEN, 38000, Grenoble, France

**Abstract:**

In this work, a numerical approach is presented to reconstruct the ionomer three-dimensional distribution in the microstructure of the cathode catalyst layer (CCL) of a polymer electrolyte membrane fuel cell (PEMFC) from a 3D segmented image of the CCL obtained by focused ion beam-scanning electron microscopy (FIB-SEM). Three forms of ionomer are distinguished: the ionomer filaments, the coating ionomer and the inter-carbon grains ionomer. The ionomer filaments are identified by applying a filtering procedure to the size distribution in the segmented solid phase obtained via a maximum sphere inscription algorithm. The coating ionomer is reconstructed via a filtering procedure of the curvature distribution computed over the interface between the two segmented phases from the consideration that concave regions are preferential ionomer accumulation zones during the drying step of the CCL fabrication procedure. This procedure of coating controlled by the local curvature is applied until a desired value of coverage is reached. In a last step, catalyst nanoparticles, also not visible in the FIB-SEM image, are reconstructed in the image.

Keywords: Ionomer, Pt/C, Coverage, I/C, CCL, PEMFC
# 1. Introduction

Polymer Electrolyte Membrane Fuel Cells (PEMFC) have emerged as an alternative power source to combustion engines and batteries. However, improvements in terms of durability, performance and cost effectiveness are still necessary [1]. A PEM fuel cell is an assembly of various layers among which the cathode catalyst layer (CCL) is of central importance since this is the place of the oxygen reduction reaction (ORR), which is the most limiting reaction. A CCL is a complex layer in which carbon black, Pt nanoparticles and ionomer are combined to form a nano-porous material in which electrons, protons, water and oxygen are transported. To optimize the use of the costly platinum in the CCL and more generally the CCL performances, it is crucial to better understand and reduce as much as possible the different resistances that limit the efficiency of the various transport processes occurring in the CCL. In particular, this concerns the ionomer which is a pathway for the ionic and gaseous reactants toward the platinum catalyst surfaces and acts also as a binder for the platinum loaded carbon particles. As a result of the CCL fabrication process from a dispersion of the above ingredients in a solvent [2], the carbon particles form agglomerates in the CCL [3-4]. A low coverage of the carbon agglomerates by the ionomer or a poor connectivity of the ionomer in the CCL is detrimental to the performance [5]. The ionic transport is affected, as well as the wettability properties of the CCL and thus the impact of liquid water in the CCL [6]. Moreover, the local accumulation of ionomer introduces an additional gas diffusion resistance [2]. Therefore, it is essential to understand the ionomer distribution in the CCL, the latter being considered as the most structurally complex component of the CCL [7, 8].

Knowledge about the ionomer distribution in the CCL has significantly evolved over the years. In some earlier modelling studies, the pore space in the CCL is assumed completely filled with the ionomer [9, 10]. However, experimental studies [11, 12] carried out at about the same time indicated that this assumption was questionable. Since these pioneering studies, several experimental works have been developed to better understand the structure of the CCL and the distribution of the ionomer in the CCL. It is now well established that the ionomer does not fully fill the pores in the CCL. Investigations based on cryogenic scanning electron microscopy (cryo-SEM) shows that the ionomer structure in the catalytic layer depends on the water/alcohol ratio (W/A) in the solvent [13, 14], i.e. on the composition of the ink. The ink refers to the colloidal dispersion used to fabricate the CCL [2]. For a high W/A ratio, more ionomer is free in the solvent, while for a low W/A ratio, the free ionomer fraction is lesser. Free ionomer refers to ionomer not in the coating of the Pt/C particles.
Thus, as discussed in [13, 15, 16], not all the ionomer present in the ink ends as ionomer coating the Pt/C phase. Information about free ionomer is also reported in [17, 18, 19], where it is also concluded that only a fraction of the ionomer initially present in the ink is coated on the Pt/C support. The remaining of the ionomer is deposited on the surfaces onto which the CCL is in contact during the fabrication process [2] or remains in the catalyst layer. The values of the corresponding fractions are not well known and depend on the carbon type and ionomer carbon weight ratio (denoted by I/C). In [17], it is reported based on electron tomography analysis that between 60 to 76% of the ionomer is in the coating, depending on the ionomer-carbon ratio. In [20], where the investigation is based on nano-scale resolution X-ray computed tomography, it is considered that only 50% of the ionomer is in the coating of the carbon support. Both studies concern the case of Vulcan XC72 carbon black. The study in [21] for porous Ketjen Black using Cryo-electron tomography analysis shows that the segmented ionomer quantity depends on the ink preparation process. Also, the studies in [13] or [22] emphasize the importance of ionomer coverage on the electrocatalyst as a key parameter governing the properties of the catalyst layer, where the coverage is the surface fraction of the Pt/C phase surface coated with ionomer. This is in contrast with several numerical studies where, as mentioned later in the article, a full coverage is considered. The fact that the coverage is generally significantly less than 100% has been confirmed by other studies. The value of the coverage depends on the catalyst support [23]. For instance, a coverage of 75% on Ketjen Black is reported in [20] for an I/C ratio of 0.6 while values of 50 % and 80 % on Vulcan black are reported in [17] for an I/C ratio of 0.2 and 0.5 respectively. Even for higher I/C ratios the coverage is significantly less than 100 % (0.76 for the I/C ratio of 1.2 in [21] for example based on cryo-electron tomography). The carbon particle agglomeration process also depends on the W/A ratio. Larger agglomerates are formed at high (W/A) ratio whereas the carbon agglomerates are smaller in the opposite case [13]. Contrary to an assumption often made in numerical models (some of them are briefly discussed below), the experimental studies have also shown that the thickness of the ionomer coating on the carbon surface is not uniform. In [17], the ionomer film thickness is reported to vary between 5 nm and 15 nm with an average thickness of about 7 nm. Similar values are reported in [24] from AFM measurements. In [20], the average film thickness is found to vary with the I/C ratio and a wider distribution with thicknesses as high as 30 nm or lower than 5 nm is reported. In [21], the film thickness on the Pt/C phase surface varies between about 2 nm and 20 nm with an asymmetric distribution skewed to the left, i.e. with a majority of thickness data in the range [2-6 nm]. Values as low as 2 to 3 nm are also reported in [25]
from an analysis of small-angle neutron scattering profiles.

In addition to experimental characterizations, another type of approach consists in studying CCL properties or the transport phenomena occurring in a CCL by reconstructing the CCL microstructure via computational reconstruction methods [26]. In [27], the CCL is reconstructed by placing randomly carbon spheres of a given radius in the computational domain. An ionomer film coats the spheres. The ionomer film thickness is uniform and the coverage is 100%. Thus, there is no fraction of carbon particle surface in direct contact with the gas phase in the pore space. A similar assumption regarding the ionomer distribution is made in [28] where a reconstruction method based on a different technique for distributing the spherical particles in the computational domain is presented. Here again the ionomer is present as a film of uniform thickness covering all the carbon particle external surface. As mentioned above, considering an ionomer film uniform thickness and a full coverage is not consistent with the experimental observations. In more recent studies, i.e. [29, 30, 31, 32], a procedure for generating a coating of variable thickness and partial coverage is implemented. However, information on the obtained film thickness distribution and coverage in the reconstructed CCL images is not provided. In [33], the coverage can be varied but the ionomer forms a film of uniform thickness.

The method presented in [28] is used in a more recent study [34] where all the ionomer corresponding to a given I/C ratio is distributed in voxels adjacent to the solid phase (the spherical particles). The voxels adjacent to more solid voxels are filled with ionomer preferentially. This can be regarded as a preferential filling of the concave zones at the Pt/C phase surface as discussed later in the article. As a result, the ionomer film on the carbon particles is not of uniform thickness. However, no information on the resulting film thickness distribution is provided.

A different reconstruction method is used in [35] and also in [36]. The interesting idea is to perform the reconstruction by mimicking the CCL experimental fabrication procedure [2]. However, it can be noted that the size of 200 nm x 100 nm x 100 nm of the reconstructed sample in [35] is quite small compared to the CCL thickness (6 µm in the case of the CCL considered in the present study). The fabrication process seems also very roughly mimicked. For instance, the drying step, which is a key step in the CCL fabrication process [2], is not at all considered. Also, the image of the reconstructed structure seems to indicate a full coverage and a too large presence of ionomer in the pores. However, it can be noted that the ionomer is not distributed as a thin film uniformly covering the surface of the Pt/C structure, which is more realistic than the uniform film thickness assumption considered in [27, 28] for
instance. In [36], simulations are performed over a significantly larger and thus presumably
more representative reconstructed sample of size 4000 nm x 500 nm x 500 nm with a voxel
size of 5 nm. However, as discussed later in the present paper, such a resolution is too low
compared to the expected ionomer film thickness, which can be as low as about 2 nm [25].

The idea of mimicking the fabrication process to reconstruct the CCL is also present in a
series of works where various assumptions regarding the ionomer distribution are considered
[4, 37-40]. In [5], the CCL is reconstructed by first generating aggregates of spherical carbon
particles. Then these aggregates are positioned in the computational domain to form the
CCL. Regarding the ionomer, two cases are distinguished: the case of a uniform coating of
the Pt/carbon phase by the ionomer and the case of a non-uniform coating. The latter is
related to the drying step in the CCL fabrication process [2]. It is argued that the ionomer
adheres to the Pt/carbon phase with a certain curvature resulting from the impact of capillary
effects during the drying step. It is thus considered that the ionomer coating structure can be
reproduced by a curvature model. However, no information on the corresponding curvature-
based ionomer distribution algorithm is given. Nevertheless, the study shows that the CCL
effective transport properties are sensitive to the assumptions made to reconstruct the
ionomer in the CCL. These two options (coating with uniform thickness or coating with
uniform curvature) are also considered in [37, 38] where the impact of the two options on the
gas diffusion performance [37] and the ionomer conductivity [38] is further investigated. An
attempt for modelling the drying step is proposed in [38] using the same concept as in [5, 37]
of agglomerate packing made of particle aggregates. However, the impact of drying on the
ionomer distribution is not considered and an ionomer film with a constant thickness is
assumed. The curvature-based ionomer distribution model is used again in [39] in a
simulation study of Ketjen Black aggregates. Simulations at the scale of the CCL with
consideration of the electro-chemical reaction are presented in [40] with again two options
for the coating ionomer, uniform thickness or uniform curvature. The simulations show that
the results depend on the ionomer adhesion model.

Although simulations on numerically reconstructed microstructures can be insightful, study
of a porous material combining imagery techniques and pore scale numerical simulations has
become a widely used approach, referred to as Digital Rock Physics in reservoir engineering
[41]. This type of approach is expected to allow consideration of more representative
microstructures of the considered materials and is also used to study the PEMFC porous
components, e.g. [42] and references therein. The approach is often based on the use of high-
resolution X-ray Computed Tomography (XRCT). However, for a nanoporous material such
as a CCL, focused ion beam-scanning electron microscopy (FIB-SEM) [43] is an attractive
option since the voxel resolution can be only a few nanometers (5 nm in the present study).
Both techniques, i.e. XRCT and FIB-SEM, are used to study PEMFC porous components
and can actually be combined as in the case of the GDL as the difference in pore size
between the microporous layer and the fibrous diffusion medium is significant [42]. In the
present study, FIB-SEM is used to obtain a digital image of the considered CCL. FIB-SEM
has been used in previous studies on CCL. In [32, 44], it is reported that the ionomer cannot
be distinguished from the carbon particle agglomerates. In [44], a thin ionomer film of
uniform thickness is coated numerically to introduce the ionomer in the digital image.
However, it is not perfectly clear whether the ionomer is coated on the segmented solid
phase, thus in the pores, or within the segmented solid phase, i.e. along its surface but inside.
It is likely that the second option is chosen. In this approach the ionomer film thickness is
based on the ratio between the average agglomerate size and the ionomer film thickness
reported in the literature. It can be noted that the resolution of 10 nm in the FIB-SEM milling
is large compared to the expected minimum value of ionomer thin film (about 2 nm
according to [25]). A higher resolution of 5 nm is used in [45]. The ionomer film thickness is
uniform and four CCL structures are obtained and compared by considering four different
values of the film thickness, namely zero, 5nm, 10 nm or 15 nm. In [46], a slice thickness of
20 nm is considered, which is again large compared to the expected ionomer film thickness.
However, no attempt is made to reconstruct the ionomer distribution in the FIB-SEM image.
This is also the case in [47] where Cryo FIB-SEM with a slice resolution of 6 nm is used to
study the oxygen diffusivity from numerical simulations on the FIB-SEM image. In [48],
where additional references on FIB-SEM in relation with catalyst layers can be found, the
FIB-SEM image is obtained with a resolution of 2 nm. The segmented solid phase in the
FIB-SEM image is assimilated to the Pt/C phase. An ionomer film of uniform thickness (~8
nm) is then distributed along the surface of the segmented solid phase. The ionomer voxels
are therefore selected in the segmented pore space and not in the segmented solid phase.
Also, it can be noted that the simulations presented in [48] are performed over small sub-
volumes (100 x100 x 100 nm³) of the imaged CCL. In [32], the FIB-SEM layer spacing is 4
nm. The ionomer is considered to be in the segmented "solid" phase together with the
platinum and the carbon particles. Although the method used to reconstruct these three
components in the solid phase can lead to partial ionomer coverage and variable ionomer
coating film thickness, the coverage is not used as a parameter and information on the
coating film thickness is not provided.
From this review of the literature, four main conclusions emerged. Firstly, the ionomer morphological distribution, i.e. its spatial distribution within the CCL microstructure, is a key factor for understanding the transport phenomena in the CCL and to optimize its performance from numerical simulations at pore scale. Secondly, the ionomer is often distributed in the reconstructed CCLs, either from imaging techniques or numerical reconstruction techniques, under the form of an ionomer thin film of uniform thickness. This type of assumption is questionable and a more realistic ionomer distribution is highly desirable. Thirdly, the ionomer cannot be distinguished in the FIB-SEM images from the platinum and carbon. Fourthly, the coverage is an important parameter to characterize the ionomer distribution in the CCL.

As a result, the objective of the present work is to propose a numerical approach to reconstruct the ionomer distribution in a CCL microstructure three-dimensional image obtained by FIB-SEM. The assumption of uniform coating ionomer film thickness is not considered and a coating of variable thickness is obtained. As in some of the above-mentioned works, namely [5, 37-40], the ionomer distribution is considered to depend on curvature. However, contrary to [5, 37-40] where the curvature of the ionomer is assumed to be constant, the curvature considered in the present work is the local curvature of the interface between the void and the solid surface in the FIB-SEM image, which is not constant but varies from one place to the other over the considered interface. As in [5, 37-40], the motivation for considering the local curvature as a parameter controlling in part the coating ionomer distribution is related to the drying step in the CCL fabrication process [2]. Drying is controlled in part by capillary effects [49] leading to the formation of curved liquid-gas interfaces. The resulting invasion process by the gas phase is hierarchical with preferential invasion of the bigger pores. Then it is considered that the suspension during this invasion process tends to be trapped by capillarity in the concave regions at the surface of the Pt/C phase and that ionomer preferentially deposit in these concave regions as the result of evaporation of the dispersion trapped in these cavities. The final result is that the more concave the surface cavity, the more ionomer is deposited. These qualitative considerations thus introduce a correlation between the local curvature of the solid phase surface and the ionomer presence and the coating ionomer local thickness, which thus varies depending on the local curvature. Also, contrary to several previous works on CCL microstructure reconstruction, the ionomer is not considered to be present only as coating ionomer. In addition to coating ionomer, a fraction of the ionomer is considered to be present as filaments partially occupying the pores. This type of ionomer structures can be observed in TEM image
as reported in the present article and also in [21] or [50]. Also, as evidenced by the
experimental studies and contrary to the assumption considered in some numerically
reconstructed CCL, the coverage of the carbon support by the ionomer is not full and can
vary depending on the considered I/C ratio. The coverage is therefore an important parameter
in the presented reconstruction method.

Finally, as regards the methodological aspects, the presented CCL reconstruction method can
be regarded as hybrid [51] since it combines an imagery technique (FIB-SEM) with a
numerical reconstruction approach to reconstruct in the image an element, the ionomer,
which cannot be directly seen in the FIB-SEM segmented image.

The paper is organized as follows. The imaging of the CCL via FIB-SEM and TEM is briefly
presented in Section 2. Section 3 provides information on the pore size distribution and size
distribution in the solid phase. In Section 4, arguments leading to the conclusion that the
ionomer is not deteriorated by the FIB but should be considered as part of the segmented
solid phase are presented. Section 5 is the main part of the article with a presentation of the
ionomer reconstruction algorithm and illustrations of the obtained ionomer distribution. A
method for distributing the platinum particle in the reconstructed CCL is presented in Section
6. A discussion is proposed in Section 7. Section 8 consists of the main conclusions of the
study.

## 2. CCL FIB-SEM image and insights from transmission electronic microscopy (TEM)

The studied cathode electrode was prepared using TEC10E50E catalyst from Tanaka that is
50 wt % loading of Pt deposited on high-specific area carbon (HSAC), and Nafion D2020 as
the electrode ionomer. The Pt loading of the electrode is 0.2 mg Pt cm⁻² and the
ionomer/carbon ratio is 0.8.

### 2.1 FIB-SEM

3D FIB-SEM data was acquired on a Zeiss Crossbeam 550. A volume of 10.95 µm by 13.25 µm by 5.24 µm was imaged with pixel size of 5 nm and inter-slices distance of 5 nm too, resulting in cubic voxels of 5 nm³. The FIB milling was done at 30kV with a current of 700pA, and electron column was operated at 1.2 kV and 1 nA. Images from backscattered and secondary detectors were acquired simultaneously.

Image processing before segmentation included slice-to-slice alignment, homogenization of
contrast/brightness in all three directions, correction of curtaining effect and resampling in z
direction to correct for non-homogeneous inter-slice distances during milling and imaging.
These steps were done thanks to homemade python scripts based on usual image processing
python libraries (e.g. numpy, scikit-image...). Segmentation was done thanks to machine
learning based on random forest classifier with ilastik software [52] using the 'pixel
classification' workflow. The annotation and training phase was done on a sub-volume of
200x200x200 pixels. The obtained segmented 3D image is shown in Fig.1a.

<figure><img src="image_1.png" /><figcaption>a)</figcaption></figure>

<figure><img src="image_2.png" /></figure>
b)

**Fig.1 - (a) CCL segmented microstructure from FIB-SEM image with segmented solid phase in light gray and secondary pore space (void) in black. (b) FIB-SEM image sample of 250 x 250 x 250 nm³ with solid phase in grey and void in white**

As illustrated in Fig.1a, the segmentation leads to distinguish two phases referred to as the void and “solid” phases, respectively. Dropping the quotation marks from now on, the solid phase consists of carbon grains, platinum, ionomer and possibly tiny pores. As discussed in [6], the pore size distribution in the CCL is classically described in terms of primary pores inside the carbon particles (1-10 nm in radius) and secondary pores (10-100 nm in radius) between the carbon particles. Thus, the void phase in Fig.1 is considered as corresponding to the secondary pores. The volume fraction of the void phase in the image in Fig.1a is 0.55. This volume fraction, denoted by $ε$, is referred to as the CCL macro-porosity whereas the porosity in the carbon grains, denoted by $ε_m$, corresponding to the primary pores is referred to as the micro-porosity in the present article. The primary pores are not visible in the FIB-SEM image. Also, due to the lack of contrast in SEM images between the ionomer and the other components, the ionomer distribution remains unknown. Reconstructing the ionomer in the image and especially the ionomer coating is the major objective of the present article. The ionomer coating is defined as the ionomer forming a coating at the interface between the void and the solid phase in the FIB-SEM segmented image (Fig.1b), i.e. at the secondary pore wall. As discussed below, the ionomer possibly coating the carbon grains inside the solid phase is not considered as belonging to the ionomer coating, which again is restricted to the FIB-SEM void-solid phase interface.

The value of 0.55 for the CCL macro-porosity is comparable to the measurements reported in [54] but greater than the value of 0.4 reported in [46], both for a Vulcan black CCL. It is slightly lower than the values of 0.57-0.59 reported in [55] for graphitized Ketjen Black (I/C = 1,) and comparable to the values reported in [56] for the same carbon support as in our CCL (~ 0.55 for a I/C ratio of 1). It is shown in [56] that the final porosity depends on the conditions in the drying step of the fabrication process. Thus, some variability in the final porosity can be expected from one CCL to the other even for the same composition of the ink.

## 2.2 Transmission Electron Microscopy (TEM)

In order to get insights into the distribution of the ionomer in the CCL, high resolution
images of small regions in the CCL were obtained by high resolution transmission electron microscopy (HRTEM). For these experiments, thin MEA cross-sections were cut by cryo-ultramicrotomy as described in [48]. The HRTEM observations was performed on a FEI-Titan ultimate microscope equipped with both image and probe correctors and operating at 200kV.

As illustrated in Fig.2, HRTEM images show three different structures of ionomer. The first one is referred to as ionomer filaments (Fig.2a). The ionomer filaments partially occupy the void space and form protrusions on the surface of the Pt-carbon phase. The second one corresponds to ionomer coating the secondary pore walls. This type of ionomer structure is illustrated in Fig.2b and is referred to as coating ionomer film. As also illustrated in Fig.2b, the coating ionomer tends to accumulate in the concave regions (referred to as cavities in Fig.2) of the void / Pt-carbon phase interface. This point will be considered further in the modelling section (Section 5).

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>(c)</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig.2 -HRTEM images of different CCL areas where the ionomer is clearly visible together with carbon phase and Pt nanoparticles (darker spots); (a) example of ionomer filament, (b) coating ionomer. In (b) the detectable limit between the ionomer and the carbon phase surface is indicated by a yellow line. (c) image of ionomer confined between carbon particles.</figcaption></figure>

The third type of ionomer structures is illustrated in Fig.2c. It corresponds to ionomer inside the FIB-SEM segmented solid phase and not at the interface between the segmented solid phase and the void phase. It is discussed further later in the paper.

### 3. Size distributions in void and solid phases

The Maximum Sphere Inscription (MSI) algorithm available in the image analysis toolbox Porespy [57] was used to characterize the size distributions in the void and solid phases in the segmented image.

This algorithm gives for each voxel, the diameter of the maximum sphere inscribed either in the solid phase or the void phase to which the considered voxel belongs. Therefore, application of the algorithm to each voxel in the solid phase gives a distribution of inscribed sphere diameters, which is referred to as the size distribution in the solid phase. Similarly, application of the algorithm to each voxel in the void phase gives a distribution of inscribed sphere diameters, which is referred to as the (secondary) pore size distribution.

Figure 3b shows the size distribution in the solid phase, with a dominant value of 45 nm, which is larger than the expected average size of a carbon particle known to be around 30 nm [2, 21]. The obtained larger value is regarded as an additional indication that ionomer is
present inside the segmented solid phase. However, this larger size could be due in part to the
arrangement of carbon particles in aggregates. It is reported in previous studies [38, 39, 58]
that the aggregates are typically formed by only two or three particles on average, which is
consistent with the dominant value of 45 nm observed here.

The obtained pore size distribution is shown in Figure 3a. As can be seen, the pore diameters vary between 15 and 200 nm with an average value around 60 nm. This result agrees with previous studies [5, 59] and is consistent with the typical sizes of secondary pores in previous works, [6] and references therein. The local macro-porosity in the segmented image is computed over cubic averaging volumes paving the image. The obtained distribution of local macro-porosity is shown in Fig.3c as a function of the cubic averaging volume size. For the cubic averaging volume of 1500 nm, the local porosity varies only by ±7% from one cubic volume to the other. This indicates that a representative elementary volume (R.E.V.) can be identified as regards the porosity. This is in contrast with the case of the micro-porous layer (MPL) reported in [42], for which a R.E.V. could not be identified.

<figure><img src="image_6.png" /><figcaption>a)</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>b)</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>c)</figcaption></figure>
Fig.3 - (a) Secondary Pore Size Distribution (PSD) obtained with the maximum inscribed sphere algorithm in the void phase. (b) Size Distribution (SSD) obtained with the maximum inscribed sphere algorithm in the solid phase. (c) Local porosity distribution over the full segmented image as a function of the averaging volume size.

4. FIB-SEM image porosity

The objective in this section is to confirm that the ionomer is still present in the solid phase segmented from the FIB-SEM image acquisition procedure since the question may arise as to whether the FIB milling deteriorates the ionomer. To this end, the thickness of the CCL is expressed from the CCL composition and its macro-porosity as described below. The thickness is first expressed as:

$$l = \frac{m_t}{\rho_t} \qquad (1)$$

where $m_t$ is the CCL mass per unit surface area and $\rho_t$ is the CCL apparent density.

The mass $m_t$ can be expressed as

$$m_t = m_{Pt} + \frac{(1-Pt/C)}{Pt/C} m_{Pt} + I/C \frac{(1-Pt/C)}{Pt/C} m_{Pt} \qquad (2)$$

where $m_{Pt}$ (mg/cm²) is the platinum loading (0.2 mg/cm² for the considered CCL), $Pt/C$ is the platinum / carbon weight ratio (defined as the mass of platinum over the sum of the mass of carbon and platinum), $I/C$ is the ionomer - carbon ratio (defined as the mass of ionomer per unit mass of carbon). The CCL apparent density can be expressed as:

$$\rho_t = \varepsilon \rho_{air} + (1 - \varepsilon)(\phi_I \rho_I + \phi_C \rho_C + \phi_{Pt} \rho_{Pt}) \qquad (3)$$

where $\phi_I$, $\phi_C$ and $\phi_{Pt}$ are the volume fractions of ionomer, carbon and platinum relative to the volume of the solid phase respectively, $\rho_I$ is the ionomer density (2 g/ cm³), and $\rho_{Pt}$ is the platinum density (21.45 g/cm³). In Eq.(3), $\rho_C$ is the carbon apparent density. The latter is less than the carbon density since the carbon particles are porous and can be expressed as $\rho_C = (1 - \varepsilon_m) \rho_{Cm}$, where $\varepsilon_m$ is the micro-porosity, i.e. the porosity of the carbon particles, and $\rho_{Cm}$ is the density of non-porous carbon (1.8 g/cm³).

The volume fractions can be expressed as a function of the apparent carbon density $\rho_C$, the ionomer carbon ratio $I/C$ and the platinum carbon ratio $Pt/C$ as:

$$\phi_I = \frac{I/C \frac{\rho_C}{\rho_I}}{1 + I/C \frac{\rho_C}{\rho_I} + \frac{Pt/C}{(1-Pt/C)\rho_{Pt}}} \qquad (4)$$

$$\phi_C = \frac{1}{1 + I/C \frac{\rho_C}{\rho_I} + \frac{Pt/C}{(1-Pt/C)\rho_{Pt}}} \qquad (5)$$
$$ \phi_{Pt} = \frac{\frac{Pt/C}{(1-Pt/C)\rho_{Pt}}}{1 + I/C \frac{\rho_{C}}{\rho_{I}} + \frac{Pt/C}{(1-Pt/C)\rho_{Pt}}} \quad (6) $$

For the values of the I/C ratio (0.8) and Pt/C ratio (0.462) of the considered CCL, using the above equations leads to the results shown in Fig.4a, where the CCL thickness computed from Eq.(1) is plotted as a function of the CCL macro-porosity and carbon particle porosity. The latter cannot be determined from the FIB-SEM image and is considered here as a parameter. For the measured CCL thickness of 6 µm, the results shown in Fig.4a indicate that the CCL macro-porosity should be between 50% and 60%, depending on the value of the carbon micro-porosity. This is in good agreement with the value of the macro-porosity of 0.55 determined from the segmented image (Fig.1a). Furthermore, it can be seen that the macro-porosity of 0.55 is obtained for a micro-porosity $\epsilon_m$ of about 0.25 in Fig.4a. This value is in quite good agreement with the value reported in the literature for the HSA carbon particles. This value is obtained for Ketjen Black carbon from N₂ adsorption measurement in [59]. The same value is considered in [60]. In [25], a liquid water fraction of 23% is quantified inside the carbon particles. This fraction can be assimilated to the micro-porosity. The conclusion is therefore that the FIB milling does not deteriorate the ionomer. This conclusion is also supported by the following consideration. The macro-porosity without ionomer, denoted by $\epsilon'_{a,5}$ can be expressed from the macro-porosity with ionomer as $\epsilon' = \epsilon + \phi_I(1-\epsilon)$. From the latter equation, the CCL porosity without ionomer should be between 65% and 76%, which is a high value compared to the value of 0.55 obtained from the segmented image. In conclusion, all this confirms that the FIB-SEM image segmented solid phase includes the platinum loaded carbon particles and the ionomer. Also, it can be seen from Fig.4b that the platinum volume fraction in the solid phase is negligible compared to the carbon and ionomer volume fractions.

<figure><img src="image_9.png" /></figure>

a)

<figure><img src="image_10.png" /></figure>

b)

Carbon grain micro-porosity $\epsilon_m$
**Fig.4** - (a) Computed CCL thickness as a function of macro-porosity for various values of carbon particle micro-porosity; (b) Computed solid phase fractions as a function of carbon particle micro-porosity.

The next step is to identify the ionomer in the FIB-SEM image segmented solid phase.

**5. Ionomer filaments, coating ionomer film, inter carbon grain ionomer**

A step-by-step algorithm is developed to identify the ionomer in the FIB-SEM image segmented solid phase. The algorithm relies on the observations made on the TEM images presented in section 2.2 (Fig.2). As indicated in section 2.2, the TEM images (Fig.2) suggest to distinguish the ionomer filaments (Fig.2a), the coating ionomer films (Fig.2b) and the inter-carbon grain ionomer (Fig.2c). The former, i.e. the filaments, correspond to protrusions of ionomer in the void space from the void-solid interface. Also, as exemplified in Fig.2b, it is considered that the coating ionomer tends to accumulate in the concave regions of the void -solid interface.

**5.1 Ionomer filaments**

The algorithm proceeds by first identifying the ionomer filaments. To this end, the results obtained from the Maximum Sphere Inscription (MSI) algorithm applied to the segmented solid phase are used. As discussed in Section 3 and illustrated in Figs. 3b and 5a, application of the MSI algorithm to the segmented solid phase gives an inscribed sphere diameter distribution in the range [10 nm – 90 nm] with an average size of 45 nm. The latter is greater than the expected mean size of carbon particles (30 nm) [20], which, as mentioned in Section 3, is regarded as an additional indication that some ionomer is inside the segmented solid phase.

Ionomer filaments are detected from the MSI distribution considering that the ionomer filaments are smaller than carbon particles. To this end, an upper thresholding size is introduced, which is assumed to correspond to the filament maximum size.
<figure><img src="image_11.png" /><figcaption>Fig.5 - (a) 3D visualization of the Maximum Inscribed Sphere size distribution in a sample of 250 x 250 x 250 nm³. (b)-(c) detected filament distribution in image (a) for an upper thresholding size of 18 nm (b) and 25 nm (c) corresponding to relative ionomer volume fraction of 7%, (b) and 25 % (c) respectively. (d-f) Identification of ionomer filament (in green) in a sample of 250x750x750 nm³: (d) upper thresholding size of 18 nm, (e) upper thresholding size of 25 nm, (f) upper thresholding size of 30 nm.</figcaption></figure>

A filament minimum size is also introduced. This minimum size is first limited by the resolution of 5 nm. In addition, to avoid considering isolated voxels, the ionomer filament minimum size is slightly increased by considering that ionomer filament voxels must belong to voxel groups of at least three solid connected voxels (two voxels are considered as connected if they share a common face). This minimum size is consistent with TEM images (Fig. 2a is an example) showing some filaments with an apparent diameter on the order of 10 nm. Figure 5 illustrates the ionomer filament voxels (in green) identified for various upper thresholding sizes in the MSI distribution, i.e. the solid voxels associated with inscribed spheres in the solid phase smaller than the considered size limit.

The ionomer filament distributions obtained for the upper thresholding size of 18 nm and 25 nm are shown over a smaller sample in Figs.5b and 5c. Ionomer shapes resembling those
observed by TEM (Fig.2a) can be observed in both cases.

<table><caption>**Table 1.** Filament relative ionomer fraction (fraction of total ionomer volume detected as ionomer filaments) and filament ionomer relative solid fraction (fraction of total volume of solid phase) obtained for various values of the upper thresholding size (see text).</caption><tr><td>Upper thresholding size</td><td>18 nm</td><td>25 nm</td><td>30 nm</td></tr><tr><td>Filament relative Ionomer Fraction</td><td>7%</td><td>25%</td><td>48%</td></tr><tr><td>Relative Solid Fraction</td><td>2.3%</td><td>8.1%</td><td>16%</td></tr></table>

Table 1 gives the filament volume fractions corresponding to various values of the upper thresholding size. As shown in Fig. 3a and indicated in Table 1, the majority of the solid phase voxels is in inscribed spheres larger than 25nm. This observation is consistent with the average carbon particle size of 30 nm considered in many previous studies [2, 21, 51, 59, 61]. It is reported in [17] that only 60 to 76% of the ionomer is under the form of coating ionomer, depending on the ionomer-to-carbon ratio. Therefore, the filament ionomer cannot exceed 25 to 40% of the ionomer volume fraction. For Ketjen Black, it is assumed that not all the ionomer is in the coating or the filaments. This complementary fraction, referred to as the inter-carbon grain ionomer, is discussed further in Sections 5.3 and 7. Therefore, the ionomer fraction in the filaments should be even less than the 25-40% fraction mentioned above. In addition, the presence of some smaller carbon particles (20-25nm) is not impossible [51]. For all these reasons, an upper thresholding size of 18 nm is considered as a reasonable choice in what follows. Although slightly lower, this size is also consistent with the ionomer thickness upper size of (20-24 nm) reported in [21]. As indicated in Table 1, this leads to an ionomer filament volume fraction of 7% for the image under consideration.

## 5.2 Coating ionomer. Computation of the solid phase surface local curvature

In this section, the approach for reconstructing the coating ionomer film in the image is presented. As discussed for instance in [1, 5, 56], the CCL is obtained via a rather complex drying process starting from a liquid dispersion containing ionomer, Pt/C particles and a multi-component solvent. As discussed in the Introduction, it is considered that this drying process leads to the preferential accumulation of the ionomer in the cavities at the surface of the solid phase as it is also observed in the TEM images (Fig.2b), see also [21, 50]. In other words, it is assumed that the concave zones at the solid surface are preferential sites for the
ionomer deposit. As a result, the coating model presented in this work is based on the computation of the local curvature along the surface of the segmented solid phase. In this approach all the voxels corresponding to ionomer filaments identified in the previous step are excluded from the segmented solid phase.

The computation of the solid phase surface local curvature begins with the definition of a phase indicator $\phi$ taking the value 1 in the solid phase and 0 in the void phase. In other words, after excluding the filament ionomer voxels, the solid voxels are labelled by 1, and the pore voxels (as well as the ionomer filament voxels in this step) are labelled by 0. This labelling is illustrated in Fig.6a. The next step consists in creating an interface indicator $\alpha$ from the phase indicator $\phi$. All solid voxels neighbor to a 0 voxel are considered as interface voxels $I$ (shown in orange in the figure). The label attributed to these voxels is an average value of neighboring voxels (again two voxels are considered as neighbors if they share a common face). For the voxels $\bar{I}$ which are not interface voxels, the label remains the same as for the phase indicator $\phi$.

$$ \left\{ \begin{array}{l} \alpha_{\bar{I}} = \phi \\ \alpha_I = \frac{1}{N} \sum_{\text{neighbor}} \phi \end{array} \right. \qquad (8) $$

where $N = 6$ is the number of neighbor voxels to a given voxel in the image. The method to compute the local curvature for each interface voxel is a method classically used in the framework of the Volume Of Fluid Method [62] in computational fluid dynamics.

The curvature is computed from the unit normal vector to the interface as,

$$ C = \nabla \cdot \mathbf{n} \qquad (9) $$

where $\mathbf{n}$ is the interface unit normal pointing out from the solid phase into the void phase. The latter is computed from the interface indicator $\alpha$ as,

$$ \mathbf{n} = \frac{\nabla \alpha}{\|\nabla \alpha\| + \Delta} \qquad (10) $$

where $\Delta$ is a constant to avoid the division by 0 [63]. Note that a curvature is computed for each voxel with the procedure. However, the zone of interest where the curvature varies is obviously the interfacial region between the solid and the void.
<figure><img src="image_12.png" /><figcaption>a)</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>b)</figcaption></figure>

**Fig.6.** - (a) Illustration of curvature computation procedure on the voxel structure after exclusion of ionomer filaments (length in voxel size unit). (b) 3D rendering of curvature distribution (expressed in m⁻¹) at the surface of the solid phase in a sub-region of the CCL of 250 x 250 x 250 nm³. The curvature in a concave zone is negative due to the chosen unit normal vector orientation.

The procedure is implemented in OpenFOAM [63]. Due to the size of the image, a sequential approach is used, similar to that presented in our previous work on the computation of the effective diffusion tensor of a microporous layer [42]. For the present study, a cubic block
with a side length of 1500 nm is considered as a representative elementary volume (Fig. 3c).
A smaller cubic sample with a side length of 250 nm is extracted from this block for
visualizations and illustrations. Figure 6b shows the computed local curvature after
application of a smoothing procedure used to limit resolution effects. This smoothing
procedure is illustrated in Fig.6a. As sketched in Fig.6a, the smoothed curvature is the
curvature averaged over a sphere with a radius of 3 voxels. As can be seen from Fig.6b, the
curvature distribution is heterogeneous and cavities with high concave curvature are present.
This is in contrast with the model presented in [39], which assumes an iso-curvature after
ionomer coating.

5.3 Coating ionomer film. Coverage modeling

The next step is to identify interface voxels as ionomer interface voxels. If one considers that
the ionomer deposit occurs preferentially in the zones of higher concave curvature, one can
then identify solid phase voxels at the solid phase surface corresponding to coating ionomer
by setting a threshold value in the curvature distribution. It can be noted that these
considerations imply that the coating by the ionomer does not smooth out the cavities at the
surface of the Pt-carbon phase. Thus, our approach relies on the assumption that the ionomer
coated Pt-carbon phase surface has about the same shape as the underlying Pt-carbon phase
surface. This is consistent with the expected small thickness of the ionomer coating (on the
order of a few nm, as mentioned in the introduction). Note that the curvature is negative in
the concave zones due to the chosen normal orientation (and thus the more concave the
surface, the more negative is the local curvature).

Thus, all the interface voxels with a lower curvature than the threshold are identified as belonging to the ionomer coating whereas all the interface voxels with a greater curvature are identified as Pt-carbon phase voxels. The fraction of the interface voxels identified as coating ionomer voxels defines the coverage. Note that this step does not require to introduce explicitly an ionomer film thickness. This step is only based on the consideration of the interface voxels.

The coating ionomer distribution at the surface of the segmented solid phase obtained with this approach varying the curvature threshold value is illustrated in Fig.7. According to this approach, convex zones are coated by the ionomer only for the higher values of the curvature threshold, which correspond to high values of the coverage. This agrees with the ionomer distribution shown in [21], where convex zones are free of ionomer as well as with the reconstructed distributions shown in [4] or [38].
<figure><img src="image_14.png" /><figcaption>Fig.7 - (a) Examples of ionomer coverage determined from thresholding the local solid surface curvature distribution (see text) in a sub-region of the CCL of 250 x 250 x 250 nm³. The coverage increases with an increasing curvature threshold.</figcaption></figure>

The obtained value of the coverage over a selected CCL sub-image of 1500 x 1500 x 1500 nm³ is plotted as a function of curvature threshold in Fig.8. Two cases are distinguished in Fig. 8: the case where the ionomer filaments are considered in the determination of the coverage and the case where the ionomer filaments are not considered. When the ionomer filaments are considered only the interface voxels not in contact with filament voxels are considered in the identification of coating ionomer from the local curvature. It is recalled that the considered volume fraction of the filament ionomer relative to the total volume of ionomer is 7% based on the discussion presented in section 5.1. Therefore, the ionomer coverage corresponding to ionomer filaments is not surprisingly quite low in Fig.6. It approximately represents 5% of the solid surface voxels. As a result, the impact of the filaments on the coverage is only visible at low levels of coverage. For higher levels of coverage, the zones covered by the ionomer filaments are superimposed with those with coating ionomer and both cases become indistinguishable in Fig. 8.
<figure><img src="image_15.png" /><figcaption>Fig.8 - Ionomer coverage as a function of curvature threshold (see text).</figcaption></figure>

## 5.4 Coating ionomer film. Ionomer film thickness distribution

An ionomer average thickness of about 5 nm for Ketjen Black support is reported in the literature [38]. However, the TEM image in Fig. 2b, see also [21], indicates that the coating ionomer film thickness is not uniform with more coating ionomer in zones of greater concave curvature at the Pt-carbon phase surface. The next step is therefore to consider the variability of the coating ionomer film thickness. This is important not only in the prospect of computing the proton conductivity but also the CCL wettability properties [6]. The local thickness is correlated to the local curvature, i.e. the lower the curvature, the greater is the thickness (it is recalled that the curvature is negative in the concave region for the chosen unit normal vector orientation at the surface, thus the most negative values of the curvature correspond to the most concave regions). Due to resolution constraints, a discrete distribution of the coating ionomer thickness is considered. The thickness can take the following values: 2.5 nm, 5 nm, 7.5 nm and 10 nm with an average value of 5 nm. This range is consistent with the ionomer film thicknesses reported in [21] from cryo-electron-tomography analysis. The consideration of the ultra-thin thickness of 2.5 nm is made possible by using a numerical artificial resolution consisting in subdividing the segmented FIB-SEM image in voxels of 2.5 x 2.5 x 2.5 nm³. It can be noted that this thickness is consistent with results reported in [25], where an ionomer film thickness as small as approximately 2.7 nm is identified from small-angle neutron scattering (SANS) experiments.
<figure><img src="image_16.png" /><figcaption>Fig.9 - (a) Coating ionomer film thickness histogram based on the curvature obtained considering a 1500 x 1500 x 1500 nm³ image. (b) 3D rendering of coating ionomer film thickness distribution obtained for the coverage of 82% determined from the considered correlation (Fig.9a) between the local surface curvature and the film thickness in a sub-region of the CCL of 250 x 250 x 250 nm³. Each color corresponds to a value of the ionomer film thickness.</figcaption></figure>
The ionomer film thickness histogram in Fig.9a shows the considered correlation between thickness and curvature whereas Fig.9b shows 3D renderings of the obtained ionomer film thickness distribution in a sub-region of the CCL of 250 x 250 x 250 nm³. A different colour is assigned to each discrete thickness in Fig.9b. The various 3D images in Fig.9b correspond to different side views of the same sample. As can be seen, the thickest ionomer film (10 nm in thickness) is present in the more concave zones while the thinnest ionomer film (2.5 nm in thickness) is present only on convex surfaces. The obtained distribution is qualitatively in agreement with the segmented distribution obtained from cryo-electron tomography analysis in [21]. The results shown in Fig.9b are for a coverage of 82%. The reconstruction algorithm can be of course used for other values of the coverage.

Fig.10 shows the obtained ionomer network with (right column) and without (left column) the complementary solid phase, i.e. the solid phase voxels not identified as filament or coating ionomer. It can be seen in Fig. 10 that the coating ionomer distribution is not homogeneous over the CCL but varies from one region to the other. Nevertheless, as illustrated in Fig.10, the ionomer is well connected. This feature is further investigated by identifying the coating ionomer percolating cluster using the cluster labeling algorithm available in Porespy [57], where the percolating cluster is the cluster connecting two opposite sides of the considered domain. The coating ionomer percolating cluster is illustrated in Fig.11 for four values of the coverage. The ratio of the percolating coating ionomer volume to the total volume of the coating ionomer, referred to as the percolating volume fraction, is also indicated in Fig.11 for the four coverage values. As can be seen from Fig.11, the percolating coating ionomer forms a poorly connected structure only for a quite low coverage (0.23 in the example shown in Fig.11). For such a low value of the coverage, the coating ionomer is mostly distributed in the non-percolating clusters (the percolating volume fraction is only of 9%). However, for the expected values of the coverage in a CCL, i.e. greater than at least 0.6, it can be seen from Fig.11 that the situation is completely the opposite. Almost all the coating ionomer is in the percolating cluster. This is in line with the experimental observations reported in [21]. In other words, the coating film ionomer forms a very well-connected percolating pathway for the H+ transport within the CCL for the usual values of the coverage expected in a CCL.
<figure><img src="image_17.png" /><figcaption>Fig.10 - Computed coating ionomer distribution in a CCL slice of 75 nm in width and 1500 nm in lateral extension for a coverage of 0.82. In the left column, only the coating (in blue) and filament (in green) ionomer is shown. The phase with the platinum loaded carbon particules is not shown. The distribution is shown in three directions, with one direction (dX, dY, or dZ) reduced in width compared to the two other ones for visualization purposes. The through-plane direction is the y-direction. The right column shows the same distributions together with the phase containing the platinum-carbon</figcaption></figure>
particles (in grey).

<figure><img src="image_18.png" /><figcaption>Fig.11 - Illustration of the coating ionomer percolating (in blue) and non-percolating (in red) coating ionomer clusters in a CCL sample of 1500 x 1500 x 1500 nm³ for four different values of the coverage. The right column shows only the percolating cluster.</figcaption></figure>

In terms of computational resources, the ionomer filament and coating reconstruction for the representative 1500 x 1500 x 1500 nm³ CCL image illustrated in Fig.11 takes approximately 30 mins on a HP Z420 workstation with Intel Xeon E5-1620 3.60 Ghz and 16 GB of RAM.

### 5.5 Inter-carbon grain ionomer

The filament and coating ionomer only represent a fraction of the ionomer originally present in the ink. This is illustrated in Fig.12 showing the variation of the volume fraction of the ionomer (considering or not the filaments) identified so far, i.e., filament and coating ionomer, as a function of the coverage, i.e., the local curvature threshold, for two average values of the ionomer film thickness, namely 5 nm and 7.5 nm, consistent with the values considered in previous studies [16, 20, 24, 44], considering here for simplicity that the ionomer film thickness is uniform.

As illustrated in Fig.12, the coverage would be about 100% for the film thickness of 7.5 nm and greater than 100% for the film thickness of 5 nm if one assumes that all the ionomer is in the filaments and the coating (data for the ionomer fraction of 100% in Fig.12). This is not
consistent with the experimental observations indicating that the coverage is only partial [17, 21, 23, 64]. Another way of illustrating this point is to compute the apparent I/C ratio. The latter is defined as the mass of ionomer identified as filament and coating ionomer in our approach, divided by the mass of carbon in the considered domain. The evolution of the apparent I/C ratio as a function of the coverage is depicted in Fig.12 (right vertical axis). This ratio is less than the expected I/C ratio of 0.8 for the considered CCL (except for the particular case of the average film thickness of 7.5 nm and the coverage of 100%).

<figure><img src="image_19.png" /><figcaption>**Fig.12** - Computed ionomer volume fraction (with and without consideration of the ionomer filaments) as a function of ionomer coverage for two values of coating ionomer film thickness (assumed spatially uniform) with comparison with some studies from the literature.</figcaption></figure>

**Table 2.** Filament ionomer, coating ionomer and inter-carbon grain ionomer volume fractions relative to the total volume of ionomer in the CCL for various values of the coverage for the I/C ratio of 0.8, an average ionomer coating film thickness of 5 nm and the filament upper filtering size of 18 nm.

<table><tr><td>Coverage (with ionomer filaments)</td><td>0.28</td><td>0.47</td><td>0.67</td><td>0.84</td><td>1.0</td></tr><tr><td>Filament ionomer relative volume fraction</td><td>7%</td><td>7%</td><td>7%</td><td>7%</td><td>7%</td></tr><tr><td>Coating ionomer relative volume fraction</td><td>16%</td><td>28%</td><td>43%</td><td>54%</td><td>66%</td></tr><tr><td>Inter-carbon grain ionomer relative volume fraction</td><td>77%</td><td>65%</td><td>50%</td><td>39%</td><td>27%</td></tr></table>
Table 2. gives the distribution of ionomer between the three forms discussed in this paper, namely the filament ionomer, the coating ionomer and the inter-carbon grain ionomer for the I/C ratio of 0.8, an average ionomer coating film thickness of 5 nm and the filament filtering size of 18 nm for various values of the coverage. As can be seen from Table 2, the inter-carbon grain ionomer represents a quite significant fraction of the ionomer for the range of coverage ([0.5 -0.9]) expected from the literature, i.e. [17], [20, 21]. The inter-carbon grain ionomer and the fact that the coating ionomer represents only a fraction of the ionomer in the CCL are further discussed in Section 7 in relation with the literature and the results shown in Fig.7. The result of our ionomer reconstruction procedure is illustrated in Fig.13 with a schematic of the inter-carbon grain ionomer.

<figure><img src="image_20.png" /><figcaption>Fig.13 – Reconstructed filament and coating ionomer with schematic of the inter-carbon grain ionomer.</figcaption></figure>

## 6. Platinum nanoparticles

The volume of platinum in the CCL is quite small compared to the volume of ionomer or carbon as illustrated in Fig.4b. However, platinum nanoparticles play a key role in the oxygen reduction reaction in the CCL. In addition, the platinum nanoparticles have an impact on the local contact angle [6], and thus on the liquid water distribution in the CCL. Therefore, it is interesting to insert platinum nanoparticles in the reconstructed CCL images, notably in the prospect of performing numerical simulations of transport phenomena coupled
to electro-chemistry in the CCL [48].

To this end, platinum nanoparticles are added in the segmented image as an additional step of the CCL microstructure reconstruction, i.e. after segmentation of the solid phase in filament ionomer, coating ionomer film and complementary solid phase. It is known that the major fraction of platinum nanoparticles is inside the carbon particle porosity, about 75% according to [4]. Since the reconstruction of the porosity inside the carbon particles is beyond the scope of the presented reconstruction method, only the 25 % remaining platinum nanoparticles present on the carbon phase external surface are considered. From TEM image analysis, it is known that the platinum particle size distribution can be approximated by a Gaussian law, with an average diameter around 4 nm and a variance of 3nm [48]. This leads to consider a truncated Gaussian distribution of Pt spherical particle sizes in the range [2 nm – 10 nm]. According to the results reported in [65], the external Pt particles are on average larger than the internal Pt particles (3.5 nm vs 2.5 nm in term of mean diameter in [65]). The used distribution is therefore considered to be representative of the external Pt particles. From this information, the platinum nanoparticles are distributed randomly on the external surface of the complementary solid phase, i.e. the solid phase remaining after exclusion of the filament and coating ionomer voxels, assuming that particle centres are level with the complementary solid phase surface. This means that about 50% of the volume of each platinum particle is embedded in the complementary solid phase at the complementary solid phase surface.

<figure><img src="image_21.png" /><figcaption>Fig. 14 - Reconstructed CCL sample of 250 x 250 x 250 nm³ with platinum nanoparticles after sub-division of the sample in 0.5 x 0.5 x 0.5 nm³ voxels. (a) Without the filament and coating ionomer, (b) with the filament and coating ionomer. The complementary solid phase is in grey, the platinum is in red, the filament ionomer is in green and the coating ionomer is in blue.</figcaption></figure>
Illustration of the obtained distribution on the complementary solid phase surface is shown in Fig.14a whereas Fig.14b shows the distribution together with the reconstructed filament and coating ionomer. Note that due to the size of the Pt nanoparticles compared to the FIB-SEM image voxel size of 5 nm, the considered image sample is sub-divided in much smaller voxels of size 0.5 nm to distribute the Pt nanoparticles over the complementary solid phase surface.

As can be seen from the comparison between Fig.14a and Fig.14b, some platinum nanoparticles are entirely coated by ionomer (in concave regions of the carbon phase surface) whereas other nanoparticles are not in contact at all with ionomer (convex regions). Intermediate cases, i.e. platinum nanoparticles in partial contact with ionomer are also visible in Fig. 14b. Thus, the thickness of the ionomer fully or partially coating the platinum nanoparticles varies, which is consistent with literature, e.g. [6].

## 7. Discussion

Three forms of ionomer are distinguished in our approach, namely the filament ionomer, the coating ionomer and the inter-carbon grain ionomer with the filament ionomer representing a small fraction compared to the coating ionomer or the inter-carbon grain ionomer according to Table 2. This is consistent with results reported in [17] or [21] showing that the coating ionomer cannot be expected to represent the full amount of ionomer, in the CCL. In the present work, the coverage corresponds to the fraction of the secondary pore internal surfaces covered with ionomer and corresponds only to the filament and coating ionomer. The coating of the carbon particles by the inter-carbon grain ionomer is not considered to define the coverage. This is in line with the literature, e.g. [33], [38], [66], [67], where the coverage is defined considering the ionomer localized at the interface with the secondary pores. However, in some experimental studies, e.g. [17], [21], where small assemblies of carbon particles are considered, the coverage could include the ionomer referred to as the inter-carbon grain ionomer in the present study. The coverage can thus be defined as the fraction of the carbon particle surface coated by ionomer, e.g. [21], or the fraction of the carbon particle agglomerate surface coated by ionomer, e.g. [33]. In the present work, the second option is therefore considered. As reported in [17, 21], the ionomer coverage depends on the ink composition. Different models of coverage, depending on the I/C ratio, are presented in the literature, e.g. [38]. For an I/C ratio of 0.8, numerical simulations of ionomer coating on reconstructed carbon particle aggregates leads to a coverage of approximately 0.82 for Ketjen Black [37] and 0.95 for Vulcan XC72 [38]. However, these values overestimate the coverage
determined in experimental studies [17, 21, 23, 68]. From [68], the fraction of the coating ionomer is 50%. Then, if only 50% of the ionomer initially present in the ink is assumed to form the coating, the simulation results presented in [39] agrees reasonably well with the experimental data. As can be seen from Table 2, this value of 50% is consistent with our results. As reported in [39], the simulation results (with the 50% correction) can be expressed according to the logarithmic fitted law $\theta = 0.18 \ln(I/C) + 0.74$ relating the coverage, denoted by $\theta$ and the I/C ratio. A coverage of 0.78 for an I/C ratio of 0.7 is reported in [20], which agrees with the logarithmic fitted law from [39]. As illustrated in Fig.12, this result agrees well with our data (consistently with the average film thickness of 5 nm reported in [39] for Ketjen Black). Also, it can be seen that the agreement is less good with the simulations reported in [38] for the case of Vulcan XC72. This is attributed to the approach used in [38], which assumes a constant coating ionomer fraction of 50% of the total ionomer, which is not accurate since the coating ionomer volume fraction depends on the ionomer-carbon ratio and the ionomer coverage, as demonstrated in [17]. In [17], two ink compositions of I/C ratio of 0.5 and 0.2 respectively are considered. It is reported that 60% (76% respectively) of the ionomer present in the ink is available for the covering for the ink with I/C ratio of 0.5 (0.2 respectively).

Based on the results reported in Table 2 and in the literature, the fraction of the ionomer not in the coating and the filaments, i.e. the ionomer referred to as the inter-carbon grain ionomer in the present article, is therefore significant. This inter-carbon grain ionomer is further discussed now.

The structure of the CCL is classically described as resulting from the aggregation of carbon particle aggregates during the drying step [5]. In the ink, the ionomer is considered to coat the aggregates [68]. In [68], this fraction of the ionomer in the ink is referred to as the adsorbed ionomer whereas the complementary ionomer fraction in the solvent is referred as the free ionomer [19]. According to [19] or [68], the adsorbed ionomer in the ink evolves into the ionomer coating on the platinum loaded carbon particles whereas the free ionomers randomly deposit to form ionomer bridges (called deposited ionomers in [19] or [68]) during the drying step. The presence of ionomer filaments is consistent with this description. They could correspond to deposited ionomer according to the terminology used in [19], [68].

These considerations provide hints as regards the inter-carbon grain ionomer. Consider Fig.2c. The vertical length of the ionomer region between the two dashed yellow lines is about 60 nm. This region is identified as solid phase in the FIB-SEM image segmentation procedure. Since the maximum ionomer film thickness considered in our reconstruction
procedure is 10 nm (Fig. 9a) only a fraction of the ionomer visible in Fig.2c will be identified
as ionomer. The central region of vertical extension of at least 40 nm is considered as
complementary solid phase in our reconstruction procedure. Of course, Fig.2c is a two-
dimensional image. This means that we have implicitly considered that the thickness of the
ionomer region in the direction perpendicular to the image was at least greater than 20 nm.
Nevertheless, it can be reasonably assumed that the situation depicted in Fig.2c exists also in
three-dimensions. A three-dimensional version of the considered situation would thus be an
example of inter-carbon grain ionomer.

One may argue that some ionomer is in the nanoporosity of the HSA carbon particles.
However, this option is generally discarded and it is considered that the ionomer cannot
intrude into the very small pores of the HSA carbon particles [4, 53]. As mentioned in the
introduction, a fraction of the ionomer present in the ink could correspond to ionomer
deposited on the surfaces onto which the CCL is in contact during the fabrication process [2].
Nevertheless, it is reasonable to consider that most of the ionomer not in the coating and the
filaments correspond to carbon-grain ionomer in the CCL as illustrated in Fig.2c, i.e. in
between the carbon particles. This is in line with the schematics reported in [18] where the
ionomer distribution is split into a network corresponding to the coating ionomer and an
ionomer network in between the coated carbon, which would therefore correspond to the
inter-carbon grain ionomer. It is argued in [18] that the latter network does not form a
percolating network in the case of Nafion. This would be an important feature since an
objective of the ionomer reconstruction is to characterize the proton and the oxygen transfers
from numerical simulations, e.g. [34, 37] and references therein.

The question arises indeed as to whether the inter-carbon grain ionomer fraction plays a
significant role or not in the proton or oxygen transfer. Thus, in the case of Nafion, based on
the consideration reported in [18], reconstructing only the ionomer coating could be
sufficient to characterize the transport. On the other hand, the proton conductivity is
generally underestimated in simulations based on reconstructed CCL or CCL sub-region
[34]. Since, as discussed in the introduction, very often, only the coating ionomer is
considered in the reconstruction procedure, this might be due to the impact of the transport
within the ionomer localized elsewhere than in the coating, i.e. in particular in the inter-
carbon grain ionomer in our approach. This is confirmed by the simulations reported in the
companion paper [69].

It can be argued that our approach is based on rather qualitative considerations. For instance,
we argue that the ionomer coating localization and thickness depend on the local curvature of
the void – solid phase interface in the FIB-SEM segmented image from qualitative consideration of the drying process leading to the catalyst layer formation but not from a detailed analysis or simulation of the drying process in question. Although our approach is in line with various results from the literature (i.e. ionomer coating partial coverage, non-uniform thickness of the ionomer coating, preferential ionomer accumulation in concave regions), the relevance of our approach needs validation.

As reported in the companion paper [69], the computation of the effective proton conductivity from our reconstructed ionomer distribution leads to somewhat better results than in previous works based on the generation of synthetic images of the CCL microstructure. This is considered as a significant indication of the validity and interest of our approach. Also, the computations presented in [69] confirm the significant impact of liquid water in the primary pores on the effective proton conductivity.

However, as pointed out in [33] for instance, many factors (Pt loading, type of carbon support, type of ionomer, ink solvent and processing parameters, etc) can affect the final ionomer distribution. For example, the molecular dynamics simulations presented in [70] indicate that the Pt particles influence the thickness and structure of the ionomer film. The impact of the Pt particles on the structure of the ionomer film is for instance considered in the companion paper [71] on the contact angle distribution. Part of the impact of the Pt loading on the ionomer distribution is perhaps included in the segmented FIB-SEM image used to reconstruct the ionomer. However, this remains to be clarified and further work is clearly need to develop a CCL reconstruction method able to consider the impact of the above-mentioned factors.

Also, as shown in the companion paper [71], the three-dimensional images of the CCL with the reconstructed ionomer coating and filaments can be used to characterize the wettability properties of CCL in the secondary pores.

## 8. Conclusion

In this work, a real cathode catalyst layer structure was imaged using FIB-SEM. Data analysis using the macro-porosity determined from the segmented FIB-SEM image led to the conclusion that the ionomer is included in the segmented solid phase. However, the ionomer cannot be directly identified in the three-dimensional segmented image of the CCL microstructure obtained by FIB-SEM. To overcome this limitation, a computational method was presented for studying the ionomer distribution in the CCL and reconstructing the ionomer distribution in the three-dimensional image. The method is based on the
consideration of three forms of ionomer structure: the ionomer distributed under the form of ionomer filaments partially occupying the secondary pore space, the ionomer thin films partially coating the wall of the secondary pores and the inter-carbon grain ionomer localized inside the FIB-SEM segmented solid phase. The ionomer filaments were identified by using an upper bound filter in the size distribution in the solid phase identified from the Maximum Sphere Inscription (MSI) algorithm whereas the reconstruction of the coating ionomer film was performed from the computation of the segmented solid phase surface curvature and the consideration that the concave regions of the surface are preferential sites at the surface for ionomer accumulation.

The method allows reconstructing the ionomer coating and the ionomer filaments over the full size of the CCL FIB-SEM image, i.e. over representative images of the CCL microstructure. It was also shown how platinum particles, which are not directly visible in the segmented FIB-SEM images, can be added computationally in the reconstructed image. Thus, a comprehensive representation of the full catalyst structure is obtained, which includes ionomer, carbon, and platinum particles. The reconstructed coating ionomer is found to form a well-connected percolating network over the CCL thickness whereas the ionomer filaments are likely to have an impact on the gas transport as they can occlude, at least partially, pores, as well as on the proton conductivity [69].

The inter-carbon grain ionomer is considered as ionomer coating the Pt-carbon grains inside the FIB-SEM image segmented solid phase. It could also correspond to the ionomer bridges mentioned in the literature [19]. Contrary to the filament and coating ionomer, the inter-carbon grain ionomer is not reconstructed in the image. An option to perform such a reconstruction could be to combine our approach with the approach presented in [32] in which carbon grains are explicitly distributed in the FIB-SEM image segmented solid phase. This is left for a future work.

As reported in the companion papers [69, 71], the results resented in the present article pave the way towards the computations of the CCL wettability properties [71] and effective transport properties [69], such as the oxygen effective diffusion tensor or the CCL proton conductivity, from numerical simulations of the considered transport phenomena on three-dimensional digital images obtained via high resolution imagery techniques.

The proposed ionomer coating reconstruction method can be applied to three-dimensional images obtained by imaging techniques as in the present article but also to virtual microstructures generated numerically.
CRediT authorship contribution statement

**Mohamed Ahmed-Maloum:** Investigation, Methodology, Software, Writing – Original draft. **Thomas David:** Visualization. **Laure Guetaz:** Visualization, Writing - Review & Editing. **Arnaud Morin:** Writing - Review & Editing. **Joel Pauchet:** Writing - Review & Editing. **Michel Quintard:** Conceptualization, Methodology, Supervision, Writing - Review & Editing. **Marc Prat:** Conceptualization, Methodology, Supervision, Writing - Review & Editing.

**Declaration of Competing Interest**

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

**Acknowledgements:** This project has received funding from the Fuel Cells and Hydrogen 2 Joint Undertaking (now Clean Hydrogen Partnership) under Grant Agreement No 875025. This Joint Undertaking receives support from the European Union's Horizon 2020 Research and Innovation program, Hydrogen Europe and Hydrogen Europe Research

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