Process based reconstruction and simulation of a three-dimensional fuel cell catalyst layer

Electrochimica Acta 55 (2010) 5357–5366

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Process based reconstruction and simulation of a three-dimensional fuel cell catalyst layer N.A. Siddique, Fuqiang Liu ∗ Electrochemical Energy Lab, Department of Material Science and Engineering, University of Texas at Arlington, Arlington, TX 76019, United States

a r t i c l e

i n f o

Article history: Received 1 March 2010 Received in revised form 14 April 2010 Accepted 16 April 2010 Available online 29 April 2010 Keywords: PEM fuel cells Catalyst layer Process based reconstruction Nanostructure

a b s t r a c t Fundamental understanding of catalyst layer nanostructure of hydrogen polymer electrolyte membrane (PEM) fuel cells is critical for improvement in performance and durability. A process based 3D mathematical model has been developed to elucidate the effect of electrode composition, porosity and ionomer weight fraction in catalyst layers on electrochemical and nano-scale transport phenomena. Numerical reconstruction of catalyst layer random structure has been performed through a controlled random algorithm, mimicking the experimental fabrication process. Nano-scale species transport properties, e.g., Knudsen diffusion of oxygen in nano-pores and proton transport in thin-film electrolyte, have been included in the model, allowing for more rigorous study of the catalyst layer. It was found that there is a threshold in both porosity and ionomer weight fractions, below which species percolation through the random structure becomes difficult due to reduced connectivity and increased isolation. The degree of mixing or size of agglomerates has been studied and it was discovered that increasing or decreasing the agglomerate number from the optimum value reduces the electrochemically active area (ECA) and deteriorates species transport, suggesting an optimum level of stirring of the catalyst ink during catalyst layer preparation is critical. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Catalyst layer is a crucial element that affects the overall performance and durability in a polymer electrolyte membrane (PEM) fuel cell. A complex mixture of catalysts (e.g., Pt/C), polymer electrolyte (e.g., Nafion) and gas pores in the thin catalyst layer (∼10 ␮m) creates a nano-scale environment (Fig. 1a) for all electrochemical reactions and transport processes, which determine the macro-properties and electrochemical characteristics [1]. Reactions and transport phenomena occurring in fuel cell catalyst layers are considered localized rather than uniform. It is believed that the localized phenomena such as oxygen reduction and catalyst decay occur in a complex environment, where species concentration, potential and overpotential, interfacial transport phenomena, and catalyst crystal orientation and defects vary in space. For example, the triple-phase boundary between catalysts/ionomer/gas pores determines the electrochemical parameters such as electrochemically active area (ECA) and exchange current density; percolation within the catalyst layer provides transport pathways for reactants, as well as water and heat. Fuel cell performance, carbon corrosion and other durability issues are all intrinsically linked

∗ Corresponding author. Tel.: +1 817 272 2704; fax: +1 817 272 2538. E-mail address: [email protected] (F. Liu). 0013-4686/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.electacta.2010.04.059

to the nano-scale, localized phenomena in catalyst layers [2–5]. However, nano-scale morphology, species transport and electrochemical reactions occurring in a catalyst layer are poorly understood. This makes it very challenging for material improvement, optimum structure design and decay mitigation of fuel cells. Extensive efforts have been made to optimize, study and model the catalyst layer in a fuel cell [6–8]. Most of the experimental efforts have been extended to achieve better fuel cell performance by varying catalyst layer composition and fabrication process [9–11] solely based on trial and error. Due to lack of effective tools in experiments, computational modeling is widely employed for basic understanding of transport and electrochemical phenomena in fuel cell catalyst layers. Macro-homogenous models have been developed for basic study of fuel cells, as well as for structure optimization. Notable work includes those of Springer and coworkers [12], and Bernardi and Verbrugge [13], whose models were used to predict water transport through the membrane. Fuller and Newman [14] and Nguyen and coworkers [15] developed multidimensional models to address heat and water management in fuel cells. In these models, the active catalyst layer is not the main point of interest, but rather simplified as an infinitely thin-film interface. There are only few detailed models specifically developed for catalyst layers. The emphasis of these studies [2,5,6,8] was mainly focused on the influence of Nafion content, porosity

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nents are excluded. Therefore, nano-scale phenomena occurring in a fuel cell catalyst layer cannot be studied in these models. Significant gaps between experimental observation and fundamental understanding, and between macroscopic models and atomic level simulation, still persist, especially when the problems to be studied are intrinsically difficult. This work aims at bridging the above gaps by developing novel, more powerful nanoscale modeling platform and tools than the existing alternatives. In this work, random nanostructures of fuel cell catalyst layers are numerically reconstructed, mimicking the experimental fabrication procedure [16]. For complete and rigorous description of a fuel cell catalyst layer, the electrochemically coupled transport equations based on nano-scale description of species and charge transport are employed. Implementation of the above equations is performed on the reconstructed nanostructure. Physically-based species transport coefficients are included in a three-dimensional transport model to elucidate the impact of composition and fabrication parameters on electrochemical and transport characteristics. This work also aims to provide a universal modeling platform for porous nanostructures and to gain insight into the mechanism of nano-scale electrochemical reaction and percolation networks of different components. 2. Model description 2.1. Nanostructure reconstruction

Fig. 1. Fuel cell catalyst layers: (a) schematic description of composition and structure and (b) SEM image of a typical fuel cell electrode.

distribution, Pt loading and thickness on performance and suggesting the corresponding optimum values for the best performance of catalyst layers. In the above-noted macroscopic approach, the exact geometric details of the catalyst layer are neglected. Instead, the catalyst layer is treated as a randomly arranged porous structure that can be described by a small number of variables such as porosity and surface area per unit volume. Furthermore, transport properties within the porous structure are based on the macroscopic theory of volume averaging, i.e., the so-called Bruggeman correlation, which was derived from a medium composed of uniformly distributed spheres. Instead, fuel cell catalyst layers are composed of inter-penetrating phases, in which localized percolating feature is important. Therefore, the macro-homogenous models using Bruggeman correlation cannot accurately predict the properties fuel cell catalyst layers. Although pore-scale models have already been reported [4,6], the way the catalyst layer was treated lacks physical basis since carbon and polymer electrolyte are treated as one phase [6]. As a result, proton transport follows the same volume-averaging manner as in the macrohomogenous models. Kim and Pitsch [4] reported a sphere based simulated annealing method to reconstruct catalyst layers. Transport properties were studied on the reconstructed layers; however, electrochemical characteristics of the reconstructed catalyst layers were not addressed as detailed structures of Pt particles are ignored. Alternatively, atomic-scale computational modeling provides the ability to predict physical properties of materials with ideal, theoretical or proposed structures under clearly defined conditions. Studies by molecular dynamics and atomic modeling are limited by the scale of the system. Complete description of transport and reaction through the thickness of a fuel cell catalyst layer is impossible in atomic-scale modeling, since the information about structure of the polymer electrolyte film at the triple-phase boundary, the voids that comprise the layer, and the connectedness between compo-

As illustrated in Fig. 1a, the catalyst layer is comprised of solid, electronically conducting carbon phase, decorated with Pt, a largely percolated network of polymer electrolyte to provide ionic transport through the thickness of the layer, and the pores (voids) that provide a pathway for gas and liquid access. The stacking and mixing of different components in an electrode is a random process as shown in Fig. 2. Most catalyst layers employ Pt particles supported on carbon (Pt/C), as catalysts. The catalysts are mixed with a solubilized form of ionomer (e.g., Nafion, trade name of a perfluorosulfonate polymer electrolyte from Du Pont), forming an ink to be printed as a thin catalyst layer about 10 ␮m thick. In this work, numerical simulation was conducted on a reconstructed catalyst layer based on fabrication process. A catalyst layer with size of 200 nm × 100 nm × 100 nm was represented by 100 × 50 × 50 unit cells with dimension of 2 nm × 2 nm × 2 nm (total cell number is 0.25 million). Each unit cell is assigned to a unique phase function, f(i,j,k), representing a unique component in the catalyst layer, e.g., carbon (f(i,j,k) =1), Pt (f(i,j,k) = 2), ionomer (f(i,j,k) = 3) and pore (f(i,j,k) = 0). The arrangement of each unit cell, i.e., location and layering sequence, is determined by a controlled, quasi-random process. As shown in Fig. 2, reconstruction started with an empty box (computational domain), followed by adding “materials” sequentially. First, the centers of the agglomerates were randomly selected in the domain; this is the process of putting down seeds as the nucleation sites for these agglomerates. Next, carbon cells were deposited onto the seeds. As shown in Fig. 3, looping was performed around any occupied cells to find out empty neighboring cells as shown in Fig. 3(a) and collect them into a set A A = {f (i, j, k) = 0 :

with pre-occupied neighbours}

(1)

A represents a base, from which a new cell to be deposit is randomly chosen (“grown”), i.e., New occupied cell ∈ A

(2)

If an empty cell is neighboring with two or more pre-occupied cells as shown in Fig. 3(b), it would be included into the set A multiple times and therefore the statistical probability to be chosen as the next occupied cell increases. This has physical meaning as materials

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Fig. 2. Illustration of experimental fabrication process of fuel cell catalyst layers and the controlled, quasi-random reconstruction process. A catalyst layer with size of 200 nm × 100 nm × 100 nm was reconstructed.

like to bond with others to reduce surface energy. The above looping and growing processes were repeated until the desired amount of deposited materials has been achieved. Following the similar way, Pt and ionomer were subsequently deposited. Comparison between the numerically reconstructed nanostructure in Fig. 2 and the SEM image of a catalyst layer sample in Fig. 1(b) suggests close similarity. The blurred “balls” (due to electron charging on nonconductive Nafion films) in the SEM image are agglomerates of Pt/C covered with Nafion films. The image indicates a random structure with agglomerate size ranging between 20 and 100 nm. The dark areas in the image are voids between the agglomerates and the size is from tens to hundreds of nm. The numerically reconstructed catalyst layer has similar agglomerate size, pore size and morphology. This suggests the validity of the reconstruction approach in this work.

diffusion and proton conduction are considered in this work. The transport property of oxygen and proton within each unit cell can be further distinguished as “transport” and “dead” phase depending on its connectivity to the network and its neighbours [16]. If a unit cell connects to the network, which forms a continuous percolation path through the domain, it is labelled as transport, or as dead otherwise. The basic idea is that if a unit cell is isolated from the percolated network, species cannot transport through it and therefore cannot contribute to the electrochemical reaction. This approach provides an effective way to pinpoint the localized transport properties in nano-scale. Fig. 4a shows the transport properties of the reconstructed nanostructure in Fig. 2.Oxygen diffuses only in the transport pore cells and ionomer cells, i.e.,

2.2. Nano-scale species transport

DO2 =

In the reconstructed nanostructure, phase boundaries and continuity of different phases can be easily tracked. Only oxygen

⎧ −1 ⎪ 1 1 ⎪ ⎪ in transport pore cells ⎪ O + O ⎪ ⎨ Db 2 Dk 2 RT

O2 Dm ⎪ ⎪ ⎪ HO2 p0 ⎪ ⎪ ⎩

0

in ionomer cells others

(3)

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molecular weight (Mi ) and radius of the pore (rp ), as described as DkO2 =

2 3

 8RT 1/2 Mi

rp

(4)

The pore radius rp in Eq. (4) varies at different location and is determined from the reconstructed 3D domain. For a given transported cell in the pore phase, looping is conducted in 3 directions, i.e., x, y and z, to find out the continuously linear length in pore space before reaching any occupied cell. The minimum length in x, y and z direction divided by 2 is used as rp in Eq. (4). Fig. 4b shows the calculated pore radius in selected sections in a reconstructed structure as shown in Fig. 4a. Special care was paid to the polymer electrolyte/pore interface, since there is an oxygen concentration jump when oxygen diffuses from air into the ionomer. The discontinuity in oxygen concentration at the interface causes instability during computational iteration. To overcome the difficulty, an equivalent gas-phase oxygen concentration determined by Henry’s law, was solved in the ionomer cells. At the ionomer/pore interface, oxygen concentration in the ionomer phase is determined by Henry’s law [17] O2 = Cm

pO2 HO2

(5)

where pO2 is the oxygen partial pressure (in atm) in gas phase, described as pO2 = C O2 RT

(6)

C O2

Fig. 3. Random growth pattern on (a) an occupied cell and on (b) a group of cells. Shaded cubes designate the pre-occupied cells and open cubes are the possible cells to be occupied. O2 , H , and p0 are bulk diffusivity, Knudsen where DbO2 , DkO2 , Dm O2 diffusivity, oxygen diffusivity in membrane, Henry constant and standard pressure. Refer to Table 1 for the parameters used in this work. The effective oxygen diffusion coefficient in the transport pore cells was determined by the local nanostructure, which accounts for both bulk diffusion (DbO2 ) and Knudsen diffusion (DkO2 ) since molecule-to-wall collision becomes significant in the nanoscale channels, as opposed to molecule-to molecule collision in bulk diffusion. Knudsen diffusion depends on temperature (T), gas

Table 1 Parameters used in the simulation of the cathode catalyst layer. Parameters

Values

Operating temperature, T (◦ C) Reference oxygen concentration, CO2 ,ref (mol/m3 ) Unit cell length,  (nm) Proton conductivity, e (S/m) Bulk oxygen diffusivity, DbO2 (m2 /s) Exchange current density, i0 (A/m2 ) Transfer coefficient, ˛c Oxygen diffusivity in ionomer, DO2 (m2 /s) Henry constant, HO2 (atm cm3 /mol)

75 14 2 4.5 3.235 × 10−5 1.0 × 10−5 1 6.2 × 10−11 4.9 × 105

where is the oxygen concentration in the gas phase. Oxygen diffusivity in the polymer electrolyte was also modified. Following the procedure described elsewhere [18,19], oxygen diffusivity in ionomer cells was substituted with the formulation shown in Eq. (3). With the above changes, a continuous oxygen concentration profile across the interface was obtained, where real oxygen concentration in ionomer phase can be back-calculated according to Eq. (6). Proton conductivity in the reconstructed 3D domain also needs to be adjusted. Proton conduction only occurs in the transport ionomer cells. It is reported that the proton conductivity of Nafion membrane decreases by ∼50% while membrane thickness reduces from 175 to 50 ␮m [20]. Conductivity of a recast 260 nm-thick Nafion membrane was found to be only ∼28% of that of a Nafion 117 membrane [21]. Therefore, the impact of thickness on effective proton conductivity has to be considered. The reported conductivity data in the literature [20] indicate a nearly linear relationship between proton conductivity (, S m−1 ) and Nafion membrane thickness (l, nm), as  = N117 − (lN117 − l) × 10−5

(7)

where N117 and lN117 are conductivity and thickness of Nafion 117. Eq. (7) indicates that the proton conductivity of an ionomer film with thickness between 2 and 6 nm is only about 20–30% of that of a Nafion 117 membrane. In the reconstructed domain, although proton conductivity should rely on thickness of the transport ionomer cells, the small slope in Eq. (7) suggests an insensitiveness of proton conductivity on thickness between 2 and 6 nm. Therefore, a constant conductivity is used as shown in Table 1. 2.3. Electrochemical reactions The simulation of electrochemical reaction based on a single-domain, control-volume approach was performed on the reconstructed 3D domain. Since the reconstructed domain automatically tracks the interfaces between different components such as Pt and ionomer; physical equations describing interfacial reaction are easily implemented. Species generation and consumption by electrochemical reactions will be incorporated into the model

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Fig. 4. Three-dimensional plots of (a) the reconstructed structures (as in Fig. 2) with identified transport properties and (b) the calculated pore radius (rp , in Eq. (4) in nm) in the transport cells at selective sections.

as source terms. The transfer current, j (A/m2 Pt ), at the interface between transport ionomer and Pt is described by Tafel equation as j = −i0O2

C O2 exp O2 C0,ref

˛ F c RT



(8)

where i0O2 , F and ˛c are the reference current density (A/m2 ) at Pt surface, Faraday constant and the symmetry factor, respectively.  equals to the negative of overpotential and is related to the thermodynamic open circuit potential (U0 ), ionic potential (e ) and electronic phase potential (s ) as  = U0 + e − s

respectively. The source terms attribute to the consumption rate of species (A/m3 s−1 or mol/m3 s−1 ) due to reaction in an electrochemically active ionomer cell (a transport ionomer cell with any transport Pt neighbor) and are described as

(9)

Se =

−

n j 

0

SO2 =

in an electrochemically active ionomer cell

(13)

others

− 0

n j  4F

in an electrochemically active ionomer cell others (14)

2.4. Governing equations Transport of oxygen and proton is driven by gradient of ionic potential, e , and oxygen concentration, CO2 , respectively. Due to high conductivity of the electronic phase, spatial variation of s can be ignored. Therefore, derivative of Eq. (9) with respect to space leads to

∇  = ∇ e

(10)

Therefore the governing equations for oxygen and proton transport are written as

∇ · (∇ ) = Se

(11)

∇ · (DO2 ∇ CO2 ) = SO2

(12)

where , CO2 , Se and SO2 are effective ionic conductivity, oxygen concentration, source term for proton, and source term for oxygen,

where n is the total number of transport neighbouring Pt cells around a active ionomer cell and  is the length of the unit cell. Since cubic unit cells with equal side length are used in this work,  in Eqs. (13) and (14) translates the reaction rate on a surface (j) into a volume-based rate.

2.5. Boundary conditions At the two boundaries perpendicular to the transport direction (i.e., the left and right boundaries), one layer of transport cells is added to the computational domain, for ease of implementation of the boundary conditions. Fixed values of oxygen concentration and overpotential, which can be obtained from a macro-homogenous half-cell model as published earlier by Liu and Wang [8], are used as boundary conditions.

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Fig. 5. Impact of porosity on morphology of reconstructed nanostructures (seed# = 100, WNF = 0.3).

At the boundaries parallel to the transport direction, symmetry conditions are applied as follows ∂ = 0, ∂x

∂CO2 ∂x

=0

(15)

Such boundary conditions are known to be true only when the computational domain size is large enough. Preliminary tests indicate that this condition is satisfied for the selected domain size. This model is capable of simulating any zone through the catalyst layer thickness (through-plane direction) or along the flow direction (in-plane direction) as long as the specific boundaries are provided, which can be obtained from a macro-homogenous model. Therefore, combing with a homogenous catalyst layer model such as the one reported in Ref. [8], this versatile model can theoretically study any portion of a catalyst layer.

determine the total volume therefore the total cell numbers of different components. Following the procedure in Section 2.1, different structures can be numerically reconstructed. A series of electrode microstructures are created, as shown in Fig. 5, with porosity ranging from 30% to 60% while seed number and ionomer weight fraction are fixed at 100% and 30%, respec-

3. Results and discussion 3.1. Impact of porosity The Pt loading for normal fuel cell electrodes is about ∼0.4 mg cm−2 , corresponding to a thickness about 10 ␮m. For Pt/C catalysts with 50% Pt weight ratio, the ionomer volume fraction, εNF , is related to electrode porosity, ε, as εNF =

2xNF /(Nafion (1 − xNF )) (1/Pt ) + (1/c ) + (2xNF /(Nafion (1 − xNF )))

(1 − ε)

(16)

where Nafion , Pt , c are the density of Nafion, Pt and carbon, respectively; and xNF is the weight fraction of Nafion in the electrode. Similarly, the carbon and Pt volume fraction in the catalyst layer can be calculated with input of porosity and ionomer weight fraction. The calculated volume fractions from Eq. (16)

Fig. 6. (a) Ratio of effective porosity to the total porosity and (b) effective ionomer volume fraction to the total ionomer volume fraction along the thickness for the reconstructed nanostructures with different porosity from 0.3 to 0.6. A ratio less than 1 means there is a fraction of the cells are dead (isolated).

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Fig. 7. Calculated effective oxygen diffusion coefficients using different methods. 2 X0 = 0.2 is used in the expression Deff = Dg · ((ε − X0 )/(1 − X0 )) as in Ref. [8].

tively. The location of the seeds are also fixed in those structures so that only the variation of porosity is studied. Fig. 5 shows that increase in porosity results in discontinuity in solid phases, as visually indicated by the blue and green regions (stand for dead carbon and ionomer cells, respectively). The impact of porosity is two-fold. First, porosity affects transport properties of the cells as material volume fraction varies correspondingly. It is indicated in Fig. 6, where the ratios of effective porosity and ionomer fraction to the total values are plotted along the thickness, that medium porosity maintains a good balance between connectivity

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in pore and ionomer phases. Large (0.6) and small (0.3) porosities result in a loss in ionomer and pore connectivity, respectively, as demonstrated by downward spikes in Fig. 6. Second, porosity impacts effective ECA. The ECA for different structures is displayed in Fig. 5. In this work, cubic Pt particles in 2 nm × 2 nm × 2 nm are assumed and the square-shape interface between transport Pt and transport ionomer cells contributes to the total ECA. The electrochemical availability of these Pt particles depends on the agglomeration between these cubic Pt particles and transport property of their neighbouring ionomer and carbon cells. The ECA first reduces slightly from 58.3 to 57.3 m2 /gPt when the porosity increases from 30% to 40%; and then significantly to 52.6 and 43.4 m2 /gPt at porosities of 50% and 60%, respectively. This indicates that there is a porosity threshold value (between 50% and 60%), below which species percolation through the solid phase becomes difficult. The impact of porosity on gas transport is studied by applying constant oxygen concentration at the two boundaries, e.g., 0 and 4 mol/m3 at the left and right boundaries, respectively. The concentration gradient thus creates an oxygen flux at the two boundaries. The flux (J, mol/m2 /s) is calculated at the two boundaries and the a ) is obtained according to Fick’s apparent diffusion coefficient (DO 2 first law a DO =J 2

l CO2

(17)

where CO2 is the concentration difference between inlet and outlet, and l is the thickness of the reconstructed domain (200 nm). During the calculation, enough iteration is conducted until the difference between the fluxes at the two boundaries is less than 1%.

Fig. 8. Impact of ionomer weight fraction on morphology of the reconstructed nanostructures (seed# = 100, ε = 0.4).

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Fig. 7 shows the apparent oxygen diffusion coefficient obtained in this work together with the values evaluated from Bruggeman correlation and from Ref. [8], where effective gas diffusivity, Deff , is described according to percolation theory [22] as Deff = Dg ·

 ε − X 2 0

1 − X0

(18)

In Eq. (18), Dg , ε, and X0 are the bulk species diffusivity, porosity and percolation critical value, respectively. Fig. 7 indicates that the apparent oxygen diffusion coefficient obtained in this work is much smaller than the other two methods, e.g., 1.8 × 10−6 m2 /s, compared to 1.14 × 10−5 m2 /s by Bruggeman correlation and 4.55 × 10−6 m2 /s by percolation theory in Ref. [8]. The above discrepancy is attributed to the different underlying physics: both Bruggeman correlation and percolation theory are based on statistical evaluation at a macrohomogenous level; while both nano-scale phase connectivity and Knudson diffusion are considered in this work, thus providing a more realistic representation of the physics. This work also suggests a moderate increase in diffusivity with porosity.

Fig. 9. Calculated effective oxygen diffusion coefficients using different methods. 2 eff X0 = 0.05 is used in the expression NF =  · ((εNF − X0 )/(1 − X0 )) as in Ref. [8].

3.2. Ionomer weight fraction Fig. 8 shows the reconstructed structures with ionomer weight fractions ranging from 15% to 35% while the number of seeds and porosity are fixed at 100% and 40%, respectively. Constant poros-

ity means that the volume fraction of Pt/C reduces with increasing ionomer weight fraction. The ionomer weight fraction affects both ECA and connectivity of ionomer cells. The ECA almost doubles from 30.3 to 58.9 m2 /gPt when ionomer fraction increases from 15% to

Fig. 10. Impact of seed number on morphology of reconstructed nanostructures (WNF = 0.3, ε = 0.4).

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Fig. 11. Impact of seed number on transport properties of oxygen and proton.

35%, corresponding to an increase in Pt utilization; while the number of dead ionomer cells reduces (as indicated by green color) simultaneously. Between 0.15 and 0.2 in weight fraction of Nafion, a significant increase (50%) in ECA is observed, indicating a percolation in ionomer phase has been achieved. Isolated carbon and Pt emerge upon further increasing ionomer fraction to 0.3 and 0.35. This suggests a good balance of mixing between ionic and electronic phases has to be maintained in order to achieve optimum connectivity of both. The impact of ionomer fraction on apparent proton transport is studied in a similar way as described in Section 3.1. Similar equation as Eq. (17) is used to calculate the apparent proton diffusivity through the reconstructed nanostructures with different ionomer weight fractions. Fig. 9 indicates that the apparent proton diffusion coefficient obtained in this work is only 30% of the value predicted by Bruggeman correlation and is in good agreement with the prediction by the percolation theory. 3.3. Impact of agglomerate number In a typical fuel cell catalyst layer, agglomerates of Pt/C and ionomer are observed. The size and number of the agglomerates could affect the effective transport and electrochemical properties of the catalyst layer. During the numerical reconstruction process in this work, carbon, Pt and ionomer grow on the seeds, as the nucleation centers of the agglomerates. If the total volume of solid materials is fixed in a reconstruction domain, the size of agglomerates would rely on the number of seeds. The impact of seed number on nanostructure and ECA is shown in Fig. 10. There is an optimum seed number to achieve better ECA and therefore catalyst utilization. The highest ECA of 63.1 m2 /gPt is obtained with 50 seeds. Decreasing or increasing seed number reduces the ECA. Small seed number corresponds to insufficient mixing between ionomer and Pt/C, and therefore a limited interface between them. At large seed number, the materials are broken into small agglomerates, and connectivity or entanglement between these small agglomerates is lost, as experimentally evidenced by reduced viscosity of ink comprised of Pt/C and Nation solution with extended stirring. The simulation result is in agreement with the results from Los Alamos National Labs [12], where measured surface area of catalyst layer decreases as processing time increases. Species transport also depends on the number of agglomerates, as demonstrated in Fig. 11 where apparent oxygen diffusivity and proton conductivity are calculated at different seed number. The general trend is that larger seed number, i.e., better dispersion of components and mixing between different phases, causes an increase in transport resistance. Comparing to the case with

Fig. 12. Three-dimensional plots of (a) reconstructed structures (seed# = 50, WNF = 0.3, ε = 0.4), (b) oxygen and (c) overpotential contours at selective sections. Fixed values of oxygen concentration and overpotential (left:  = 0.23 V, CO2 = 2 mol/m3 ; right:  = 0.2 V, CO2 = 2.05 mol/m3 ) are used at the left and right boundaries.

50 seeds, the apparent oxygen diffusion coefficient and proton conductivity for the case with 250 seeds drop 72% and 43%, respectively. This is because ionomer phase connectedness deteriorates and pore size decreases with increasing seed number. The low oxygen diffusivity at 50 seeds is due to insufficient separation between agglomerates as agglomerate size becomes bigger. 3.4. Electrochemical reactions Detailed electrochemical reaction is also studied with fixed ionic potential and oxygen concentration at the right and left boundaries. Fig. 12 shows the overpotential and oxygen concentration contours at four selective sections in a catalyst layer. Using the reconstructed nanostructure as a reference (Fig. 12a), species transport in each phase can be clearly identified. Electrochemical reaction only occurs at the interface between two neighboring transport cells. Careful studies of these contours indicate a strong dependence of localized reaction profile on nano-scale morphologies and phase interaction. Both electrochemical and transport properties of fuel cell catalyst layers depend on the triple-phase boundary between gas, ionomer and Pt/C. Effective proton conduction, oxygen transport

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and other percolation properties through the catalyst layer rely on agglomerate packing in nano-scale, which can be controlled by degree of mixing, bonding between ionomer and carbon, as well as interaction between solvents and ionomer. However, scientific guidance in nano-scale structure design is still unavailable and most of the experimental work in catalyst layer fabrication solely relies on experience. For example, Uchida et al. [23,24] achieved higher ECA and better transport properties of catalyst layers by employing toluene as a nonsolvent of Nafion and creating large agglomerates of Nafion/carbon complex. The prediction of this work helps to get mechanistic understanding of nano-scale phenomena, therefore better strategies for improvement are possible. Future work is to adopt interfacial energy of different components and get more realistic nanostructure reconstruction. 4. Conclusions Process based reconstruction and simulation on fuel cell catalyst layers have been performed in this work. The simulation starts with numerical reconstruction of the catalyst layer according to a controlled quasi-random algorithm, which is tunable to create various structures. The impact of composition, porosity, phase connectivity and agglomerate size on electrochemical and transport characteristics has been discussed. The numerical model predicts a threshold in species transport, below which percolation across the thickness of catalyst layers becomes difficult. The simulation also provides a more realistic representation of the physics of species transport in nanostructure of fuel cell catalyst layer than the statistical evaluation at a macro-homogenous level. The electrochemically active area determined by the interface between transport Pt and ionomer cells has been quantified, as a good indicator of phase connectedness and interaction. The degree of mixing or size of agglomerates has been studied and it was discovered that increasing or decreasing the agglomerate number from the optimum value reduces the electrochemical active area and deteriorates species transport.

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