Multiscale simulation approach to investigate the binder distribution in catalyst layers of high-temperature polymer electrolyte membrane fuel cells

A multiscale approach involving both density functional theory (DFT) and molecular dynamics (MD) simulations was used to deduce an appropriate binder for Pt/C in the catalyst layers of high-temperature polymer electrolyte membrane fuel cells. The DFT calculations showed that the sulfonic acid (SO3−) group has higher adsorption energy than the other functional groups of the binders, as indicated by its normalized adsorption area on Pt (− 0.1078 eV/Å2) and carbon (− 0.0608 eV/Å2) surfaces. Consequently, MD simulations were performed with Nafion binders as well as polytetrafluoroethylene (PTFE) binders at binder contents ranging from 14.2 to 25.0 wt% on a Pt/C model with H3PO4 at room temperature (298.15 K) and operating temperature (433.15 K). The pair correlation function analysis showed that the intensity of phosphorus atoms in phosphoric acid around Pt (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{\mathrm{P}}{g}_{\mathrm{Pt}-\mathrm{P}}\left(r\right)$$\end{document}ρPgPt-Pr) increased with increasing temperature because of the greater mobility and miscibility of H3PO4 at 433.15 K than at 298.15 K. The coordination numbers (CNs) of Pt–P(H3PO4) gradually decreased with increasing ratio of the Nafion binders until the Nafion binder ratio reached 50%, indicating that the adsorption of H3PO4 onto the Pt surface decreased because of the high adsorption energy of SO3− groups with Pt. However, the CNs of Pt–P(H3PO4) gradually increased when the Nafion binder ratio was greater than 50% because excess Nafion binder agglomerated with itself via its SO3− groups. Surface coverage analysis showed that the carbon surface coverage by H3PO4 decreased as the overall binder content was increased to 20.0 wt% at both 298.15 and 433.15 K. The Pt surface coverage by H3PO4 at 433.15 K reached its lowest value when the PTFE and Nafion binders were present in equal ratios and at an overall binder content of 25.0 wt%. At the Pt (lower part) surface covered by H3PO4 at 433.15 K, an overall binder content of at least 20.0 wt% and equal proportions of PTFE and Nafion binder are needed to minimize H3PO4 contact with the Pt.

) in poly(2,5-benzimidazole) (ab-PBI) were investigated with various doping levels of H 3 PO 4 to elucidate the proton transfer mechanism 45 . Notably, MD simulation methods have been used to investigate the detailed distribution of polymer binders and H 3 PO 4 in catalyst layers 46,47 . The results of such MD simulations have indicated that a suitable amount of PTFE binder is required to prevent H 3 PO 4 from reaching the Pt-C surface and thereby improve the durability of the catalyst layers 47 . The adsorption of H 3 PO 4 onto the Pt surface was found to be substantially increased by an increase in temperature from room temperature (298.15 K) to the operating temperature of HT-PEMFCs (433.15 K). A follow-up study on the selection of polymer binders is needed to minimize carbon corrosion and Pt poisoning at the PEMFC operating temperature.
In the present MD simulation study, we used density functional theory (DFT) calculations to find appropriate binder candidate groups for use in the catalyst layers in HT-PEMFCs. In particular, we analyzed the adsorption energy between the binder candidate groups and the Pt/C surface, which strongly influences durability. Moreover, we discovered that the interactions can affect the distribution morphologies of polymer binders on the Pt/C surface with H 3 PO 4 and that Nafion binders can protect the carbon surface and Pt particles by preventing excess adsorption of H 3 PO 4 . For this purpose, we used both PTFE and Nafion binders on a Pt/C surface to demonstrate the advantages of each binder in the presence of H 3 PO 4 at room temperature (298.15 K) and at the HT-PEMFC operating temperature (433.15 K).

Simulation methods and model preparation
To select the appropriate binder candidates for the Pt/C in catalyst layers, we performed DFT calculations to determine the adsorption energy between the binder candidate polymers and the components of the catalyst layers, such as the carbon surface and the Pt particles. In addition, we performed full-atomistic MD simulations to describe the binder deposit manufacturing process 35  www.nature.com/scientificreports/ DFT simulation for selection of binder candidates. To calculate the adsorption energy of the Pt and carbon surface with binder candidates such as PTFE, PVDF, Nafion, PBI, and ab-PBI, we calculated the DFT adsorption energy using the Vienna ab initio Simulation Package (VASP) 48,49 . The generalized gradient approximation Perdew-Burke-Ernzerhof (GGA-PBE) exchange-correlation functional 50 was used with projectoraugmented-wave (PAW) pseudopotentials 51 for all geometry optimizations. An energy cut-off of 400 eV was applied with convergence criteria for force (2.0 × 10 −2 eV/Å) and energy (1.0 × 10 −5 eV). Moreover, the dipole interaction 52 along the z-axis direction and the DFT-D3 correction of the Grimme scheme 53 were applied to calculate the adsorption energy between the Pt and carbon surfaces and the binder candidates. The periodic boundary conditions (PBCs) were applied to all directions, and the slab of the Pt and carbon surface was constructed using three atomic layers of a Pt (111) slab and graphite layers with cell sizes of 9.612 × 11.099 × 30.000 Å 3 and 8.522 × 9.840 × 30.000 Å 3 , respectively. The k-points of the Pt (111) slab and the carbon surface were set to a 5 × 5 × 1 and 6 × 5 × 1 Monkhorst-Pack k-point meshes 54 which correspond to the actual spacing of ~ 0.02 Å −1 to the x-and y-axis of PBCs, respectively. The adsorption energies ( E adsorption ) between the Pt, carbon surface, and binder candidates were calculated using Eq. (1): where E total represents the total energy of the Pt or carbon surface with the adsorbed binder, E slab represents the total slab energy of the three layers of Pt (111) slab and the graphite layers, and E binder represents the energy of the binder candidates in the PBCs. The adsorption energy of each component of the binder candidates was calculated to predict detailed adsorption mechanisms during binder distribution on the Pt/C surface.
Force fields and MD simulations. The modified DREIDING force field 55 was applied to describe the PTFE, Nafion, H 3 PO 4 , and the carbon surface. The H 2 O and the H3O + ions were modeled using an F3C force field 56 to construct the binder solvent, and a Pt particle was modeled using an embedded atom method (EAM) force field 57 to describe the catalyst system in a HT-PEMFC. The DREIDING and F3C force fields have been successfully used to describe fuel cell systems 47,[58][59][60][61][62][63][64] . For the nonbonded interaction between a Pt particle and the Nafion or PTFE binder, we used the nonbonded interaction parameters reported by Brunello et al. 65 ; for the nonbonded interaction parameters between a Pt particle and H 3 PO 4 , we used those reported by Kwon et al. 47 The total potential energies ( E total ) of the HT-PEMFC systems were calculated using Eq. (2): where E vdW , E Q , E bond , E angle , E torsion , E inversion , and E EAM represent the van der Waals, electrostatic, bondstretching, angle-bending, torsion, inversion, and EAM energies, respectively. The large-scale atomic/molecular massively parallel simulator (LAMMPS) code 66 from S. Plimpton at Sandia National Laboratory was used to carry out the entire MD simulation for HT-PEMFC systems. The electrostatic interactions were calculated using the particle-particle particle-mesh method 67

Model preparation.
To construct the catalyst layers in the HT-PEMFCs, the carbon surface and Pt particles were constructed at full-atomistic scale. The carbon surface was constructed using six graphite layers with 10,752 carbon atoms. In addition, a Pt particle with a diameter of 2.6 nm was constructed using 586 Pt atoms with a truncated octahedral shape with eight (111) planes and six (100) planes because the Pt particles of the commercial TEC10E50E Pt/C (Tanaka Kikinzoku Kogyo, TKK) have a diameter of 2.5 ± 0.4 nm 71 . The weight ratio between the Pt particles and the carbon surface was matched to the commercial Pt/C concentration (45.9 wt% Pt in the TKK catalyst) 35 . The Pt particle was placed on the carbon surface with a PBC of 68.18 × 68.88 × 500.00 Å 3 , and the length of the z-direction was set to 500.00 Å with a sufficient vacuum region to prevent interactions beyond the PBC. The chains of the PTFE and Nafion binders were prepared to have 100 and 10 degrees of polymerization (DP), respectively, so that their molecular weight per chain was approximately the same. The PTFE and PTFE-Nafion binder chains were determined to have contents ranging from 14.2 to 25.0 wt%. To prepare the PTFE and PTFE-Nafion binder solvent, 6687 water molecules with 10 additional H 3 O + ions per Nafion chain were used for a solvent. In the binder deposit manufacturing process of the PTFE binder with solvent, an isopropyl alcohol (IPA)-water mixture is typically used to prepare catalyst layers with a PTFE binder 29,33,35,36,72 . Nafion binders have also been deposited using a similar manufacturing process with an IPA-water mixture to prepare catalyst layers 29 . Because the IPA molecules in the IPA-water mixture evaporate more easily than water molecules because of the IPA-water vapor-liquid equilibrium 73 , water molecules eventually remain with the PTFE binders after evaporation of the IPA molecules at a 70:30 (w/w) IPA/water composition 46 . Therefore, we assumed that the water molecules can mainly affect the final dispersion morphology of the PTFE and Nafion binders on the Pt/C surface. Thus, the water molecules were used to construct the PTFE and Nafion solvent to reduce the computational cost. The initial models of PTFE and Nafion solvent with different binder contents were generated by the Monte Carlo method using the Amorphous Cell module in the Materials Studio software 69 .
To obtain equilibrium structures, the PTFE and Nafion solvent models were distributed on a Pt/C surface and canonical ensemble (NVT) MD simulations were performed for 10 ns at 298.15 K. Evaporation simulations in which the temperature was gradually increased from 298.15 to 333.15 K over 30 ps were then performed by NVT simulation, along with an NVT simulation at 333.15 K over 7 ns for evaporation of the water molecules to deposit

Results and discussion
Adsorption properties of binder candidates. The binder-Pt, binder-carbon surface, H 3 PO 4 -Pt, and H 3 PO 4 -carbon surface binding energies strongly affect the distribution of H 3 PO 4 on the Pt/C surface 47 . In particular, to prevent excessive contact of H 3 PO 4 on the Pt surface and carbon corrosion in the catalyst layers, the binder-Pt and binder-carbon surface adsorption energies should be greater than the H 3 PO 4 -Pt and H 3 PO 4 -carbon surface adsorption energies to prevent excess leaching of the carbon surface and Pt particles. We therefore performed DFT calculations to determine and compare the adsorption energies of various binders. Figure 1 shows the molecular structures of the binders, which are commonly used as binders in the catalyst layers of HT-PEMFCs. We prepared the main component in binders for DFT calculations to compare their binding energies on Pt and the carbon surface. In particular, the Nafion (CF 3 -O-CF 3 , CF 3 -SO 3 − , C 4 F 10 ), PTFE (C 4 F 10 ), PVDF (C 4 H 5 F 5 ), PBI (benzene, 2,5-benzimidazole), ab-PBI (2,5-benzimidazole) components were calculated on Pt and graphite layers. The results of the binding energies are shown in Table 2. We also normalized the binding energies according to the adsorption areas to enable a quantitative comparison. Figure 2 shows the binding-energy diagram for selecting appropriate binder candidates by comparing the adsorption energy between Pt and the carbon surface on the basis of the adsorption energy of H 3 PO 4 ( Table 2). The binding energy of H 3 PO 4 on the Pt and carbon surfaces is − 0.0281 eV/Å 2 and − 0.0151 eV/Å 2 , respectively. The appropriate binder candidates need to have stronger binding energy than H 3 PO 4 on the Pt and carbon surfaces to prevent permeation of H 3 PO 4 into the binders. For example, the binding energies between the PTFE binder and the Pt surface (− 0.0118 eV/ Å 2 ) and between the PTFE binder and the carbon surface (− 0.0085 eV/Å 2 ) are lower than those between H 3 PO 4 and the Pt surface and between H 3 PO 4 and the carbon surface. These results mean that the PTFE binder does not readily prevent excessive leaching of the Pt and carbon surfaces in the presence of H 3 PO 4 at the HT-PEMFC operating temperature. Therefore, the H 3 PO 4 can contact the Pt surface by permeating into the PTFE binder at the HT-PEMFC operating temperature. However, the binding energies between the sulfonic acid groups (SO 3 − ) and the Pt surface (− 0.1078 eV/Å 2 ) and between the SO 3 − groups and the carbon surface (− 0.0608 eV/Å 2 ) are much greater than the corresponding H 3 PO 4 binding energies. Thus, the SO 3 − groups in Nafion may prevent excess leaching of the Pt and carbon surfaces, thereby improving the mechanical performance and cell durability at the HT-PEMFC operating temperature. We therefore performed MD simulations to investigate the possibil-  Visualization of evaporated Pt/C structures with binders. Figure 3 shows snapshots of the structures after the evaporation MD simulations. The x-and y-axes indicate the number of PTFE and Nafion chains, respectively, on the Pt/C surface. At the first stage, we conducted the MD simulations with only Nafion binder deposited onto the Pt/C surface to protect both the Pt and the carbon surface by minimizing the adsorption of H 3 PO 4 . However, the Nafion binder tended to predominantly locate on the Pt surface because of the strong adsorption energy between the Pt and the SO 3 − groups of the Nafion chains. Doo et al. 62 have reported experimental data showing that Nafion strongly adsorbs onto the Pt surface. Thus, Nafion binders can possibly prevent the excess adsorption of H 3 PO 4 onto the Pt surface. However, preventing the excess adsorption of H 3 PO 4 onto the carbon surface is difficult because of the strong Nafion-Pt interaction. Notably, the authors of another study 47 revealed that a sufficient amount of PTFE binder can prevent the adsorption of H 3 PO 4 onto a carbon surface. It means that not only binding energies between PTFE binders and carbon surface, but also distribution procedure is important to form hydrophobicity surface while PTFE binders were preferentially distributed on carbon surface than H 3 PO 4 . Therefore, not only Nafion but also PTFE binders can be used on Pt/C surfaces to protect both the Pt surface and the carbon surface in the catalyst layers.
As shown in Fig. 3, the influence of the PTFE and Nafion binders was easily identified at low binder contents. For example, simulations for an overall binder content of 14.2 wt% on the Pt/C surface show that more polymer binder with 2 PTFE/2 Nafion chains was attached near the Pt surface than polymer binder with 3 PTFE/1 Nafion chains. By contrast, simulations for an overall binder content of 14.2 wt% also show that more binder with 3 PTFE/1 Nafion chains was attached onto the carbon surface than binder with 2 PTFE/2 Nafion chains. These distribution features show that the PTFE-containing binders positively affect the carbon surface coverage and that the Nafion-containing binders positively affect the Pt surface coverage. With increasing binder content, the Pt and carbon surfaces were gradually covered by PTFE and Nafion binders and each Nafion and PTFE binder was mainly located near the Pt surface and carbon surface, respectively.
We propose a scheme for the distributions of PTFE and Nafion binders on the Pt/C surface. As shown in Fig. 4a, 100% PTFE binder on the Pt/C surface well covers the carbon surface; however, H 3 PO 4 still contacted www.nature.com/scientificreports/  www.nature.com/scientificreports/ between carbon and Pt particle surface by pushing out the PTFE binder which located near carbon surface and Pt particles. Thus, although the PTFE binder well protects the carbon surface against carbon corrosion by H 3 PO 4 , excess PTFE binder is needed to protect the Pt against poisoning by excess adsorption of H 3 PO 4 onto the Pt surface. On the contrary, as shown in Fig. 4b, 100% Nafion binder well protects the Pt surface, whereas the Nafion binder poorly protects the carbon because of agglomeration of the SO 3 − groups and strong interaction with the Pt. Therefore, the appropriate PTFE/Nafion binder ratio (Fig. 4c) to protect both the Pt and the carbon surface needs to be determined. Moreover, the total contents of the polymer binders should be reduced to prevent a reduction of the electrical conductivity in the catalyst layers because of the electrical insulating character of the PTFE binder and also to determine the optimum binder content 35 . Therefore, the distribution characteristics of H 3 PO 4 as a function of the contents and ratio of PTFE/Nafion binders on the Pt/C surface were evaluated to deduce appropriate structures for improving the durability of HT-PEMFC catalyst layers.

Distribution of H 3 PO 4 on Pt/C structures with binders.
For catalyst layers consisting of Pt/C and a polymer binder with H 3 PO 4 , the distribution of H 3 PO 4 strongly influences their durability. In particular, excess contact between H 3 PO 4 and Pt can cause undesirable effects such as Pt poisoning and carbon corrosion 20,23,25,26 . Therefore, understanding the distributions of H 3 PO 4 molecules on the Pt/C surface with PTFE and Nafion-PTFE binders is important for establishing a balance between performance and durability. Figure 5 shows cross-sectional snapshots of equilibrated Pt/C structures with H 3 PO 4 and with PTFE and Nafion binders at contents of 14.2 to 25.0 wt% at 298.15 K. The binders initially covered near the Pt and carbon surface. The binders which are located between Pt and carbon surface can protect the Pt particle and carbon surface by preventing excess adsorption of H 3 PO 4 onto the Pt and carbon surfaces. Notably, the distributions of the Nafion and PTFE binders were easily distinguished at low binder contents of 14.2 and 17.3 wt%, where the SO 3 − groups in the Nafion were mainly located near the Pt surface, whereas the PTFE was mainly located near  www.nature.com/scientificreports/ the carbon surface. For example, at a binder content of 17.3 wt%, the 2 PTFE/3 Nafion binder showed greater contact with the Pt surface than the 4 PTFE/1 Nafion binder. As the binder content was increased, both the PTFE and the Nafion gradually encapsulated the Pt particle and the carbon surface (Fig. 5).
As the temperature was increased from 298.15 K to 433.15 K (HT-PEMFC operating temperature) in Fig. 6, the H 3 PO 4 molecules permeated into the binders and contacted the Pt surface. In particular, a high proportion of the PTFE binder was permeated by H 3 PO 4 molecules at 433.15 K because H 3 PO 4 molecules at this temperatures exhibit greater mobility and miscibility than those at 298.15 K 47 and because the binders located near the Pt and carbon surface was difficult to maintain at this higher temperature. However, the SO 3 − groups in the Nafion binders were still located near the Pt surface even after the increase in temperature because the SO 3 − groups have a higher adsorption energy than H 3 PO 4 on the Pt surface.  .0 wt%, respectively. All intensities of ρ P g Pt−P (r) increased with increasing temperature from 298.15 to 433.15 K, indicating that the H 3 PO 4 molecules were more strongly correlated with the Pt surface at the higher temperature of 433.15 K because the H 3 PO 4 molecules exhibit greater mobility and greater miscibility with the PTFE binder 47 . To quantitatively analyze the distribution of H 3 PO 4 molecules on the Pt particles as functions of the temperature and the binder ratio, the first coordination numbers (CNs) of Pt-P(H 3 PO 4 ) are shown in Fig. 7d. The CNs were calculated by integrating the first peaks of the intensities of ρ P g Pt−P (r) in Fig. 7a-c. The intensities of ρ P g Pt−P (r) decreased as the Nafion ratio was increased to 50% (PTFE 50%). This result means that the adsorption of H 3 PO 4 onto the Pt surface decreased with increasing Nafion binder content because of the high adsorption energy between SO 3 − groups and Pt. However, the intensities of ρ P g Pt−P (r) increased as the Nafion ratio was increased beyond 50% (< PTFE 50%) because the excess Nafion binder agglomerated with itself via its SO 3 − groups. Compared with the CNs of Pt-P(H 3 PO 4 ) at 433.15 K, those at 298.15 K slowly decreased with decreasing PTFE binder ratio (increasing Nafion binder ratio) until the ratio reached 50%. This result means that the Nafion binder more strongly affected the distribution of H 3 PO 4 on the Pt surface at 433.15 K than at 298.15 K. Therefore, the distribution of H 3 PO 4 molecules in the catalyst layers was apparently more sensitive to the Nafion content than to the PTFE content.
Surface coverage analysis. Not only the distribution of H 3 PO 4 on the Pt surface but also its distribution on the carbon surface strongly affects cell durability in HT-PEMFCs because of Pt poisoning and carbon corrosion. Therefore, we also conducted surface analyses to investigate the detailed distribution of H 3 PO 4 on the Pt and carbon surfaces as functions of the contents and ratio of PTFE and Nafion binders at 298.15 and 433.15 K. The equation for surface coverage is where S contact represents the number of Pt or C atoms in contact with H 3 PO 4 molecules and S surface represents the number of Pt or C atoms at the surface of the Pt particle or carbon layer. The contact atoms were counted under the first peak distance of each PCF. Figure 8a   www.nature.com/scientificreports/ H 3 PO 4 . At 298.15 K, the lower part of the Pt surface was covered with fewer H 3 PO 4 molecules than the upper part of the Pt surface because the binders were mainly distributed between the carbon surface and the Pt 46,47 . At 433.15 K, the binders with a higher ratio of PTFE did not prevent the Pt surface from contacting H 3 PO 4 compared with the binders with other ratios because of the lower adsorption energy of PTFE on the Pt surface compared with that of H 3 PO 4 on the Pt surface. As the Nafion content in the binders increased at the same overall binder content, the Pt (lower part) surface coverage by H 3 PO 4 decreased because of less adsorption of H 3 PO 4 onto the lower part of the Pt surface. Therefore, an overall binder content of at least 20.0 wt% with equal PTFE and Nafion contents should be used to protect the lower part of the Pt surface against H 3 PO 4 at 433.15 K and thereby improve the durability of the catalyst layers in HT-PEMFCs by protecting the carbon and Pt surfaces.

Conclusions
DFT calculations were performed to determine appropriate binder candidates for protecting Pt/C catalyst layers and thereby improving cell durability. The SO 3 − groups in Nafion appear to make Nafion an appropriate binder candidate because the SO 3 − -Pt and SO 3 − -carbon surface binding energies are greater than the H 3 PO 4 -Pt and H 3 PO 4 -carbon surface binging energies. Consequently, we performed full-atomistic MD simulations for binders with various contents (14.2 to 25.0 wt%) of Nafion and PTFE combined in different ratios. The Nafion binders were mainly located near the Pt surface because of higher binding energy of SO 3 − groups with the Pt surface. The intensities of ρ P g Pt−P (r) increased with increasing temperature from 298.15 to 433.15 K. At 298.15 K, the coordination numbers of Pt-P(H 3 PO 4 ) decreased more slowly than at 433.15 K with decreasing PTFE binder ratio (increasing Nafion binder ratio) until the ratio reached 50%. The carbon surface coverage by H 3 PO 4 almost converged at binder contents greater than 20 wt% at both 298.15 and 433.15 K. The Pt surface coverage by H 3 PO 4 was lowest in the case of binders with the same ratio of PTFE and Nafion and at a total binder content 25.0 wt%. For the Pt (lower part) surface coverage by H 3 PO 4 at 433.15 K, binders with the same contents of PTFE and Nafion and an overall binder content of at least 20.0 wt% were needed to minimize the H 3 PO 4 contact. We expect that our multiscale approach will aid in the selection of other binder candidates for improving the cell durability and the performance of the catalyst layers in HT-PEMFCs.