Parallel Large-Scale Molecular Dynamics Simulation Opens New

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Parallel Large-Scale Molecular Dynamics Simulation Opens New Perspective to Clarify the Effect of a Porous Structure on the Sintering Process of Ni/YSZ Multiparticles Jingxiang Xu,† Yuji Higuchi,† Nobuki Ozawa,† Kazuhisa Sato,‡ Toshiyuki Hashida,‡ and Momoji Kubo*,† †

Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan Fracture and Reliability Research Institute, Graduate School of Engineering, Tohoku University, 6-6-11 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan

‡

S Supporting Information *

ABSTRACT: Ni sintering in the Ni/YSZ porous anode of a solid oxide fuel cell changes the porous structure, leading to degradation. Preventing sintering and degradation during operation is a great challenge. Usually, a sintering molecular dynamics (MD) simulation model consisting of two particles on a substrate is used; however, the model cannot reflect the porous structure effect on sintering. In our previous study, a multi-nanoparticle sintering modeling method with tens of thousands of atoms revealed the effect of the particle framework and porosity on sintering. However, the method cannot reveal the effect of the particle size on sintering and the effect of sintering on the change in the porous structure. In the present study, we report a strategy to reveal them in the porous structure by using our multi-nanoparticle modeling method and a parallel large-scale multimillion-atom MD simulator. We used this method to investigate the effect of YSZ particle size and tortuosity on sintering and degradation in the Ni/YSZ anodes. Our parallel large-scale MD simulation showed that the sintering degree decreased as the YSZ particle size decreased. The gas fuel diffusion path, which reflects the overpotential, was blocked by pore coalescence during sintering. The degradation of gas diffusion performance increased as the YSZ particle size increased. Furthermore, the gas diffusion performance was quantified by a tortuosity parameter and an optimal YSZ particle size, which is equal to that of Ni, was found for good diffusion after sintering. These findings cannot be obtained by previous MD sintering studies with tens of thousands of atoms. The present parallel large-scale multimillion-atom MD simulation makes it possible to clarify the effects of the particle size and tortuosity on sintering and degradation. KEYWORDS: multimillion-atom molecular dynamics simulation, porous structure, sintering, degradation, solid oxide fuel cell

1. INTRODUCTION Solid oxide fuel cells (SOFCs), which produce electricity by electrochemical conversion, are a promising power generation method due to their high thermal efficiency, low cost, and low emissions.1,2 The nickel and yttria-stabilized zirconia (Ni/YSZ) porous anode material is most widely used for SOFCs because of its low cost and high conductivity.2 However, Ni has high mobility at high temperatures and the coalescence and densification of Ni particles occur in the Ni/YSZ anode during sintering.3 Sintering of the Ni particles decreases the Ni surface area, which reduces hydrogen adsorption sites for hydrogen oxidation,4 degrading the SOFC performance. Moreover, in the Ni/YSZ anode, the pore framework of the porous structure creates a path for gas fuel diffusion. The change in the Ni/YSZ porous structure induced by sintering increases the concentration overpotential, which also results in the degradation of SOFC performance.5,6 Experiments have shown that sintering is strongly related to the porous structure.7−12 A detailed understanding of the sintering and degradation behaviors in the © 2017 American Chemical Society

porous anode during operation is important to improve the SOFC performance. However, the sintering and degradation mechanisms and the changes in the porous structure during operation are poorly understood. In particular, the question of how sintering affects the degradation induced by the porous structural change during operation is still open. Experimental techniques can identify the coalescence and densification of Ni particles due to sintering; nevertheless, the understanding of the atomic-scale sintering mechanism by an atomistic approach is required because atomic forces play important roles in sintering. Molecular dynamics (MD) simulations provide a good platform for investigating the atomistic behaviors in SOFCs.13−15 Several researchers have used MD simulations to investigate the sintering process of two Pd,16 two Cu,17 two Received: May 31, 2017 Accepted: August 29, 2017 Published: August 29, 2017 31816

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Figure 1. Schematic diagrams: (a) two-nanoparticle sintering model, (b) small Ni/YSZ multi-nanoparticle sintering model, and (c) porous structure of the Ni/YSZ anode.

Ag,18 and two Au19 nanoparticles on a support substrate. These studies focused on two-nanoparticle systems (Figure 1a) and explained the surface area loss and the effect of the substrate. However, the Ni/YSZ anode has a porous structure and is constituted of many Ni and YSZ nanoparticles. Although the two-nanoparticle models are useful for investigating the fundamental sintering mechanisms, they cannot simulate the effects of the porous structure on sintering. In our previous work, a multi-nanoparticle modeling method (Figure 1b) is developed to examine the effect of the YSZ framework on sintering.20 We showed that this method reproduces the sintering process in the SOFC anode well.20−22 Moreover, the multi-nanoparticle modeling method was used to examine the effect of porosity on sintering in the SOFC anode.22 However, we investigated the sintering process in small multi-nanoparticle models consisting of less than 30 000 atoms (Figure 1b). The effects of the particle size, tortuosity, and composition on sintering and the effect of sintering on the porous structure, such as the gas diffusion path of the porous structure during operation (Figure 1c), should be investigated to reveal the sintering and degradation mechanisms in the porous anode. However, small multi-nanoparticle models are unsuitable for this type of simulation and a simulation of a large-scale model consisting of several million atoms is required to reflect the effects of the particle size, tortuosity, and composition on sintering and to reproduce the change in the gas diffusion path of the Ni/YSZ porous structure during sintering. Monte Carlo23,24 and phase-field25−27 simulations have been used to simulate the change in the porous structure during sintering. In these methods, empirical macroscopic parameters, such as surface and interfacial energies, and assumptions about the mobility and sintering mechanisms in relation to the sintering process are required. These parameters and assumptions are difficult to obtain experimentally; however, MD simulations do not require them.28 In MD simulations, the forces between the particles and their potential energies are calculated by using the interatomic potentials. Thus, the surface and interfacial energies are not required for MD simulations because they can be calculated on the basis of the interaction of atoms. Moreover, the assumptions about the mobility and sintering mechanisms are also not required in MD simulations because the trajectories of atoms during the sintering process are obtained from the interactions of atoms in the system. Thus, a large-scale MD simulation of a multi-nanoparticle model is essential for unraveling the sintering and degradation mechanisms in the

porous structure. However, this type of MD simulation has not been performed. In this study, we report a strategy to reveal the sintering and degradation mechanisms in the porous structure to improve the design of a durable, high-performance porous anode by using our multi-nanoparticle modeling method and a parallel largescale MD simulator. Our sintering simulation reveals the effects of the porosity, particle size, tortuosity, and composition on sintering, and the effect of sintering on the change in the porous structure, including the Ni surface area and gas diffusion path. Moreover, experimental results have shown that the durability and performance of SOFC are related to the particle size in the Ni/YSZ anode.9−11 However, the sintering and degradation mechanisms for the change in the gas diffusion properties during sintering are still unclear. Thus, we used our parallel large-scale multi-nanoparticle simulation method to investigate the YSZ particle size effect on sintering and degradation in Ni/YSZ anodes. The different sintering behaviors in the Ni/YSZ models with different YSZ particle sizes and the change in the tortuosity by sintering in Ni/YSZ porous structures were discussed. The sintering and degradation mechanisms for the change in the gas diffusion properties during sintering in Ni/YSZ models with different YSZ particle sizes were discussed. To the best of our knowledge, this is the first study that uses the parallel large-scale multimillion-atom MD simulation method to reveal these effects and changes, which could not be obtained by previous MD sintering studies with tens of thousands of atoms (Figure 1a,b). Our large-scale multimillion-atom MD study may help guide the design of a durable, high-performance porous structure.

2. COMPUTATIONAL DETAILS To investigate the sintering and degradation mechanisms in the Ni/YSZ anode, large-scale sintering simulations of Ni/YSZ multi-nanoparticle models consisting of 3 million atoms were performed with our parallel large-scale MD package, LASKYO. This simulator was developed on the basis of a divide and conquer framework29 for parallel calculation and showed good linear scaling up to 768 cores (Xeon CPU E5-2620, Intel; 2.00 GHz), with a parallel efficiency of over 0.98. All large-scale MD sintering simulations were performed with the canonical (N, V, T) ensemble at a common operating temperature of 1273 K for 500 ps after the stabilization simulation. In this study, we employed the Born−Mayer−Huggins potential to reproduce YSZ.30 To describe the interactions of Ni with Ni and YSZ, we 31817

DOI: 10.1021/acsami.7b07737 ACS Appl. Mater. Interfaces 2017, 9, 31816−31824

Research Article

ACS Applied Materials & Interfaces used the Morse potential.31 These potential parameters can be found in our previous study and have been validated by comparing the MD simulation results with density functional theory calculation data.20 To determine the effect of YSZ particle size on sintering and degradation mechanisms in Ni/YSZ porous anodes, our multinanoparticle modeling method20 was employed. In this method, Ni and YSZ nanoparticles were packed into the simulation cell at random.20 This modeling method reflects the effect of the YSZ framework and porosity on sintering. The large-scale multi-nanoparticle model was used to model the effects of the particle size and tortuosity on sintering and the change in the porous structure, such as the Ni surface area and gas diffusion path. In an SOFC, the length of a cell in one direction is larger than that in the other two directions. Moreover, numerous experimental studies of Ni/YSZ porous anodes by focused ion beam-scanning electron microscopy have used samples in which the lengths in the x, y, and z directions are different and the length in one direction is larger than that in the other two directions.32−34 In this study, we used a Ni/YSZ model that is longer in the x direction than in the y and z directions to model an SOFC cell. Ni/YSZ largescale multi-nanoparticle sintering models consisting of 3 million atoms were built, which was made possible by our parallel largescale MD simulator. We examined the effects of YSZ particle size on the sintering and tortuosity. In a previous theoretical study of tortuosity, it was found that the tortuosity is affected by the size of the simulation model.35 Thus, we also checked the effect of the size of the simulation model on the tortuosity before the sintering simulation and the details are described in the Supporting Information. The results showed that our Ni/ YSZ large-scale multi-nanoparticle model is large enough to describe the tortuosity. In all Ni/YSZ multi-nanoparticle models, the Ni particle diameter was 40 Å. To elucidate the size effect of the YSZ nanoparticles on sintering, the sintering simulations were performed on Ni/YSZ models with YSZ particle diameters of 20, 30, 40, 50, and 60 Å. To compare the sintering behaviors of Ni nanoparticles in the Ni/YSZ models with different YSZ nanoparticle sizes, the porosity of all models was 45% because the typical experimental porosity value is 45%.36 The volume ratio of Ni to YSZ nanoparticles was 1:1. In the multi-nanoparticle sintering simulations, we employed the periodic boundary condition. All of the Ni/YSZ large-scale models were stabilized at 300 K for 50 ps. To confirm the repeatability of the simulations, we performed large-scale sintering simulations using Ni/YSZ multi-nanoparticle models with three different initial arrangements of Ni and YSZ nanoparticles for each YSZ particle size.

Figure 2. Snapshots of Ni sintering simulations of the Ni/YSZ multinanoparticle models with YSZ particle diameters of (a) and (b) 60 Å and (c) and (d) 20 Å at 1273 K; for (a) and (c), t = 0 ps, and for (b) and (d), t = 500 ps. The cell sizes of the Ni/YSZ multi-nanoparticle models with YSZ particle diameters of 60 and 20 Å are 0.10 × 0.02 × 0.02 μm3 and 0.08 × 0.02 × 0.02 μm3, respectively, along the x, y, and z directions.

particles grows, and then the Ni nanoparticles form a large compact aggregate at 500 ps due to sintering (circles in Figure 2b). Figure 2c,d shows the structure of the 20 Å YSZ nanoparticle model before and after sintering. The Ni nanoparticles shown by the circle in Figure 2d make contact with each other. Although the Ni nanoparticles make contact with each other, large Ni aggregates do not form at 500 ps in the 20 Å YSZ nanoparticle model (Figure 2d). In contrast, the 60 Å YSZ nanoparticle model after sintering shows the formation of large Ni aggregates (Figure 2b). These results suggest that the sintering processes are different in the Ni/YSZ anodes with YSZ particle diameters of 20 and 60 Å. Previous experimental studies showed that larger Ni particles were formed due to sintering in Ni/YSZ anodes with larger YSZ particles.7,12 Thus, our large-scale simulation results agree well with the experimental results. We quantified the sintering processes in the Ni/YSZ models by evaluating the Ni surface area loss.37 The increase in the Ni surface area loss indicates an increase in the sintering degree.36 We calculated the relative surface loss, defined as (S0 − St)/S0, where S0 and St are the Ni surface areas at 0 and t ps, respectively. The Ni surface area was calculated with our code, and the calculation method is described in our previous paper.22 Figure 3 shows time evolution of the averaged relative Ni surface losses in the Ni/YSZ multi-nanoparticle models with YSZ particle diameters of 60 and 20 Å. The averaged relative surface losses with error bars are calculated from three sintering simulations with different initial arrangements of Ni and YSZ nanoparticles, with YSZ particle sizes of 60 and 20 Å. For the 60 Å particles, the relative surface loss increases rapidly from 0 to 0.19 until 50 ps, indicating that sintering occurs. The averaged relative surface loss is 0.23 at 500 ps. For the 20 Å particles, the averaged relative surface loss increases (around 0.03) during the initial stage (∼50 ps), indicating that sintering also occurs. The averaged relative surface loss is 0.23 at 500 ps for the 60 Å particles, whereas it is 0.06 for the 20 Å particles, indicating a smaller degree of sintering. These results suggest that using smaller YSZ particles inhibits sintering.

3. RESULTS AND DISCUSSION We used our parallel large-scale multi-nanoparticle simulation method to clarifying the Ni sintering processes in Ni/YSZ anodes with different YSZ particle sizes. To determine the size effect of YSZ particle on sintering, we first performed 3-millionatom simulations of sintering in Ni/YSZ multi-nanoparticle models with YSZ particle diameters of 60 and 20 Å and a Ni particle diameter of 40 Å. Figure 2 shows snapshots of Ni sintering with YSZ particle diameters of 60 and 20 Å. The stabilized structure of the 60 Å YSZ nanoparticle model before sintering (Figure 2a) shows that the Ni nanoparticles are surrounded uniformly by the YSZ nanoparticles. After sintering, Ni nanoparticles approach and make contact with each other (Figure 2b). The contact area between the two Ni nano31818

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particles. The Ni nanoparticles do not move readily from the interspace between 20 Å YSZ nanoparticles (circle in Figure 4d) because the interspace is small relative to the Ni nanoparticle size. Thus, the growth of the Ni nanoparticle contact area is suppressed, and the Ni sintering is inhibited in the 20 Å YSZ nanoparticle model (circle in Figure 4d). This may explain why large Ni nanoparticles form in the 60 Å YSZ model and not in the 20 Å YSZ model. Furthermore, we performed large-scale multi-nanoparticle sintering simulations by using three Ni/YSZ models with three different arrangements of Ni and YSZ nanoparticles to confirm the repeatability of the large-scale multi-nanoparticle sintering simulations. The simulation results in the 20 and 60 Å YSZ nanoparticle models show that the growth of the Ni nanoparticle contact area was suppressed during sintering in all of the 20 Å YSZ nanoparticle models owing to the small interspace between YSZ nanoparticles. The simulation results show that decreasing the YSZ particle size decreases the interspace between YSZ nanoparticles, which prevents the growth of the Ni nanoparticle contact area, suppressing sintering. Therefore, our large-scale multi-nanoparticle simulation reveals the sintering mechanism in the Ni/YSZ anodes with different YSZ particle sizes. In previous experimental and simulation studies of metallic nanoparticles, it was reported that the nanoparticle melting point decreases with decreasing nanoparticle size.38−41 In our simulation, the calculated melting temperature is 1780 K for Ni nanoparticles with a diameter of 40 Å, which is lower than the melting point of bulk Ni (2320 K). All of the sintering simulations were performed at the typical experimental temperature of 1273 K, which is much lower than the melting point. The aim of this study is to reveal the effects of YSZ particle size on the Ni sintering process below the melting point of Ni nanoparticles. Thus, we conclude that the decreased melting temperature induced by 40 Å nanoparticles has no influence on our sintering simulation results and conclusions. In the Ni/YSZ anode, the Ni/YSZ porous structure is changed by sintering during operation, and the pore framework in the Ni/YSZ model affects the gas diffusion path and contributes to the concentration overpotential.5,6 To reveal the degradation induced by sintering, we calculated the pore size distribution (PSD) to examine the time evolution of the pore framework for YSZ particle diameters of 60 and 20 Å. The PSD of the Ni/YSZ models was calculated on the basis of a smart method for computing PSD at the atomic scale developed by Gubbins et al.42 Figure 5a shows the PSD of the Ni/YSZ models with a YSZ particle diameter of 60 Å at 0 and 500 ps. The mean pore diameter of the Ni/YSZ model is 29.4 Å at 0 ps and increases to 38.8 Å at 500 ps after sintering. This indicates the coalescence of the pores during sintering. Figure 5b shows the PSD of the Ni/YSZ models with a YSZ particle diameter of 20 Å at 0 and 500 ps. The mean pore diameters are 16.8 and 19.2 Å at 0 and 500 ps, respectively. This indicates that the increase in the pore size in the 60 Å YSZ nanoparticle model after sintering is larger than that in the 20 Å YSZ nanoparticle model because of the larger sintering degree in the 60 Å YSZ nanoparticle model. We discussed the time evolution of the diffusion path of hydrogen fuel in the Ni/YSZ models with YSZ particle diameters of 60 and 20 Å on the basis of the change in the pore size by sintering. Figure 6 shows cross-sectional snapshots of the pore framework at 0 and 500 ps. The solid lines in Figure 6a,c indicate diffusion paths. Figure 6a,b shows cross-sectional snapshots of the pore framework in the 60 Å YSZ nanoparticle model at 0 and 500 ps, respectively. After the

Figure 3. Time variation of the relative surface loss in Ni/YSZ multinanoparticle models, with YSZ particle diameters of 60 and 20 Å at 1273 K. The averaged data with error bars for three simulation runs of the Ni/YSZ multi-nanoparticle models are shown.

To reveal the difference in the sintering process in the two Ni/YSZ models, cross-sectional snapshots of the sintering simulation were examined. Figure 4 shows cross-sectional

Figure 4. Cross-sectional snapshots of Ni sintering simulations on the Ni/YSZ multi-nanoparticle models with YSZ particle diameters of (a) and (b) 60 Å, and (c) and (d) 20 Å at 1273 K. (a) and (c) t = 0 ps, and (b) and (d) t = 500 ps.

snapshots of the sintering process in the 20 and 60 Å YSZ nanoparticle models. For the 60 Å particles at 0 ps, the YSZ nanoparticles are located around the Ni nanoparticles (Figure 4a). Then, the Ni nanoparticles approach each other from the interspace between the YSZ nanoparticles (circle in Figure 4b), which indicates full growth of the two Ni nanoparticles’ contact area. For the 20 Å nanoparticles, there are many small YSZ nanoparticles around the Ni nanoparticles (Figure 4c). The number of YSZ nanoparticles around the Ni nanoparticles is greater in the 20 Å YSZ nanoparticle model than in the 60 Å YSZ nanoparticle model (Figure 4a,c), decreasing the interspace between the YSZ nanoparticles around the Ni nano31819

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We quantified the degradation of the gas diffusion performance during sintering in the Ni/YSZ models with YSZ particle diameters of 60 and 20 Å. In a porous material, tortuosity is commonly used to evaluate the diffusion through the free space quantitatively.33 Thus, to quantify the degradation of gas diffusion performance caused by sintering, we calculated the tortuosity in the Ni/YSZ models on the basis of our previous method.43 Tortuosity is defined as Lp/Ln, where Lp and Ln are the diffusion path lengths in the pore space of the Ni/YSZ porous structure and the free space without the Ni and YSZ phases, respectively. Smaller tortuosity indicates better gas diffusion properties. The simulation cell is divided into rectangular meshes, and the 0th to Nth meshes along the xaxis are defined. Gas fuel is injected from the 0th mesh and diffuses to the Nth mesh along six directions in the threedimensional model with equal probability on the basis of a random walk. Figure 7a,b shows the time evolution of the

Figure 5. Changes in the PSD in Ni/YSZ multi-nanoparticle models with YSZ particle diameters of (a) 60 and (b) 20 Å at 0 and 500 ps.

Figure 6. Cross-sectional snapshots of the pore framework before and after sintering in Ni/YSZ multi-nanoparticle models with YSZ particle diameters of (a) and (b) 60 Å, and (c) and (d) 20 Å at 1273 K. For (a) and (c), t = 0 ps and for (b) and (d) t = 500 ps. Figure 7. Time variation of the tortuosity in Ni/YSZ multinanoparticle models with YSZ particle diameters of (a) 60 and (b) 20 Å at 1273 K. The averaged data with error bars for three simulation runs of the Ni/YSZ multi-nanoparticle models are shown. In each model, the tortuosities of five different diffusion paths were calculated with a random walk process using 10 different random numbers for each path.

pores coalesce due to sintering, the diffusion path is blocked (circles in Figure 6b). This result indicates that the gas diffusion is not smooth, and thus the concentration overpotential increases after sintering when the YSZ particle diameter is 60 Å. Figure 6c,d shows cross-sectional snapshots of the pore framework in the 20 Å YSZ nanoparticle model at 0 and 500 ps, respectively. After sintering, pore coalescence is not observed at 500 ps (Figure 6d), showing little change in the gas diffusion path. However, the diffusion path is blocked in the Ni/YSZ models with 60 Å YSZ nanoparticles. Thus, the increase in the pore size due to sintering produces a discontinuous diffusion path. Our large-scale multi-nanoparticle sintering simulation clarified the change in the gas diffusion path during sintering and revealed the degradation mechanism in the Ni/YSZ anodes with different YSZ nanoparticle sizes.

averaged tortuosity during the sintering simulation in the Ni/ YSZ models with YSZ particle diameters of 60 and 20 Å. The averaged tortuosity with error bars are calculated from the three sintering simulations with different initial nanoparticle arrangements at YSZ particle sizes of 60 and 20 Å. The averaged tortuosity before sintering in the 60 Å YSZ nanoparticle model (1.55) is smaller than that with 20 Å YSZ nanoparticles (1.96). This indicates that the Ni/YSZ porous structure with large YSZ particles has good gas diffusion properties before sintering. The 31820

DOI: 10.1021/acsami.7b07737 ACS Appl. Mater. Interfaces 2017, 9, 31816−31824

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nanoparticles and 50 Å nanoparticles are similar to those for the 20 (Figure 2b) and 60 Å (Figure 2d) nanoparticles, respectively. To quantify the relationship between the degree of sintering and YSZ nanoparticle size, we calculated the relative average surface loss of Ni nanoparticles using (S0 − Sa)/S0, where S0 is the surface area of Ni nanoparticles at 0 ps and Sa is the average surface area of Ni nanoparticles from 200 to 500 ps.22 We used this average because there is little change in the relative average surface loss after 200 ps in Figure 3. Figure 8

tortuosity increases drastically at the initial stage of the sintering simulation (∼50 ps) in both Ni/YSZ models because of the change in the Ni/YSZ porous structure caused by sintering. The increase in tortuosity indicates the decrease in gas diffusion. Thus, sintering degrades the gas diffusion performance. Moreover, the averaged tortuosity increases by 1.11 from 1.55 to 2.66 for the 60 Å YSZ nanoparticles during sintering, whereas for the 20 Å YSZ nanoparticles, the averaged tortuosity increases by 0.55 from 1.96 to 2.51. Thus, the gas diffusion performance is more degraded in the 60 Å YSZ nanoparticle model. A previous phase-field study showed that the tortuosity increases due to the sintering.27 In our simulation results, the sintering of Ni nanoparticles increases the tortuosity (Figures 7 and 9), which agrees well with the previous phase-field results.27 Here, the phase-field and Monte Carlo methods require assumptions about sintering mechanisms before the simulation, whereas the MD simulation does not. Thus, our large-scale MD simulation is more suitable for investigating the sintering mechanism. Furthermore, in previous studies,23−27 the phase-field and Monte Carlo methods required empirical macroscopic parameters, such as surface and interfacial energies, and thus the surface and interfacial energies in the Ni/YSZ anode were constant with time evolution. However, the surface and interfacial energies depend on the surface and boundary structure of the Ni/YSZ porous structure and change with time evolution. In our large-scale MD simulation, these surface and interfacial energies change with time evolution, unlike the phase-field and Monte Carlo methods. Thus, the MD simulation method reproduces the sintering process in the Ni/YSZ anode more closely. Primdahl et al. showed that the increase in concentration overpotential in the Ni/YSZ anode with large YSZ particles during operation was larger than that in the anode with small YSZ particles.44 The degradation of gas diffusion performance in our sintering simulation results agrees well with the experimental results. Our large-scale multinanoparticle simulation reveals that the degradation of gas diffusion performance is strongly dependent on the degree of sintering, which could not be obtained from previous MD sintering studies with tens of thousands of atoms.16−22 In addition, previous phase-field and Monte Carlo simulations23−27 focused on predicting the porous structure evolution, and the effect of YSZ particle size on the sintering has not been revealed theoretically. To the best of our knowledge, this is the first study that uses the simulation method to reveal the effect of the particle size on sintering and the effect of sintering on the change in the porous structure on the atomic scale. Our method clarifies the change in the gas diffusion path during sintering. Although the tortuosity before sintering is small in the 60 Å YSZ nanoparticle model compared with the 20 Å YSZ nanoparticle model, the tortuosity after sintering is large in the 60 Å YSZ nanoparticle model (Figure 7). Thus, the gas diffusion properties are strongly affected by sintering. The YSZ nanoparticle size plays important roles in the sintering and degradation of the gas diffusion performance in the Ni/YSZ porous anode. To design a highly durable Ni/YSZ anode, it is essential to evaluate the sintering process and its effect on the gas diffusion properties after sintering in Ni/YSZ models with many different YSZ nanoparticle sizes. We also performed 3million-atom simulations of sintering in Ni/YSZ models with YSZ particle diameters of 30, 40, and 50 Å. In all Ni/YSZ models, Ni nanoparticles approach and make contact with each other. The sintering processes for the 30 and 40 Å

Figure 8. Effect of YSZ particle size on the relative average surface loss in the Ni/YSZ multi-nanoparticle models. The averaged data with error bars for three simulation runs of the Ni/YSZ multi-nanoparticle models at each YSZ particle diameter are shown.

shows the size effect of YSZ nanoparticles on the averaged relative average Ni surface losses in the Ni/YSZ models, with YSZ particle diameters of 20, 30, 40, 50, and 60 Å after sintering. The averaged relative average surface losses with error bars are calculated from the three sintering simulations with different initial arrangements of Ni and YSZ nanoparticles at each YSZ particle size. The relative average surface loss increases gradually with increasing the YSZ nanoparticle size from 20 to 40 Å and then increases rapidly from 40 to 60 Å. Our simulation shows that the interspace between the YSZ nanoparticles decreases as the YSZ nanoparticle size decreases. The small interspace suppresses the growth of the Ni nanoparticle contact area, which inhibits sintering in the Ni/ YSZ model with small YSZ nanoparticles. The rapid increase in the relative average surface loss due to sintering in the models with YSZ particle diameters larger than 40 Å suggests that the Ni nanoparticles move easily through the large interspace between YSZ nanoparticles, allowing the contact area between Ni nanoparticles to grow. To confirm the repeatability of the simulations, we performed large-scale sintering simulations by using Ni/YSZ multi-nanoparticle models with three different initial nanoparticle configurations and YSZ particle diameters of 30, 40, and 50 Å. The degree of sintering decreases with decreasing the YSZ nanoparticle size in all of the models. The effect of the YSZ nanoparticle size on the degradation of gas diffusion performance was examined by calculating the tortuosity before and after sintering in Ni/YSZ models with YSZ particle diameters of 20, 30, 40, 50, and 60 Å. The tortuosity after sintering was obtained by calculating the average tortuosity from 200 to 500 ps because of the small change in the tortuosity after 200 ps (Figure 7). Figure 9 shows the dependence of the average tortuosity on the YSZ nanoparticle size, with error bars for three Ni/YSZ multinanoparticle models with different initial nanoparticle arrangements. In each model, the tortuosities of five different diffusion 31821

DOI: 10.1021/acsami.7b07737 ACS Appl. Mater. Interfaces 2017, 9, 31816−31824

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studies,16−22 which could not consider the effects of the particle’s size and tortuosity on sintering and the effect of sintering on the gas diffusion properties. Our present large-scale MD simulation reflected the effect of the porous structure on sintering and clarified the change in the diffusion properties during sintering in the porous structure. This study revealed the effect of the porous structure on sintering and degradation and may help create theoretical designs for durable high-performance porous anodes. In the present method, Ni and YSZ nanoparticles were packed into the simulation cell at random. It is difficult to decouple the effect of YSZ particles from the effect of the initial tortuosity on sintering because the tortuosity before the sintering is affected by the particle size, pore size, and porosity.6 Furthermore, to improve the performance of SOFC, the tortuosity effect on the sintering, which is decoupled from the effect of the YSZ particle size, should be investigated. Future work is necessary to develop a method to achieve these goals.

Figure 9. Changes in the tortuosity in the Ni/YSZ multi-nanoparticle models, with YSZ particle diameters of 20, 30, 40, 50, and 60 Å. The average values of tortuosity with error bars for three Ni/YSZ multinanoparticle models with different initial nanoparticle arrangements are shown. In each model, the tortuosities of five different diffusion paths were calculated with a random walk process using 10 different random numbers for each path.

4. CONCLUSIONS We revealed the sintering and degradation mechanisms in a porous structure by using our multi-nanoparticle modeling method and a large-scale MD simulator. Our method clarified the effects of the particle size and tortuosity on sintering and the effect of sintering on the change in the porous structure, which results in degradation. Our large-scale multi-nanoparticle MD sintering simulation was used to investigate the effect of the YSZ particle size and tortuosity on sintering and degradation in Ni/YSZ anodes. We performed large-scale simulations on Ni/YSZ multi-nanoparticle models, with YSZ particle diameters of 20 and 60 Å. The Ni nanoparticles approached and made contact with each other in both Ni/YSZ models. The Ni nanoparticle contact area increased, and sintering occurred. The increase in the contact area between Ni nanoparticles in the 60 Å YSZ nanoparticle model was larger than that in the 20 Å YSZ nanoparticle model because the interspace between the YSZ nanoparticles was small relative to the Ni nanoparticle size in the 20 Å YSZ nanoparticle model. The small interspace between YSZ nanoparticles formed by the small YSZ nanoparticles inhibited the increase in the contact area between Ni nanoparticles and thus suppressed sintering in the 20 Å YSZ nanoparticle model. In addition, we simulated sintering in Ni/YSZ models with YSZ particle diameters of 30, 40, and 50 Å to reveal the dependence of the particle size on sintering. The degree of sintering in Ni/YSZ models increased as the YSZ nanoparticle size increased. Next, we investigated the degradation induced by sintering. The gas fuel diffusion path was blocked by the pores coalescing during sintering. The degradation of gas diffusion increased with the increase in the degree of sintering. We used tortuosity to quantify the gas diffusion properties in Ni/YSZ models with different YSZ nanoparticle sizes. The tortuosity increased in all Ni/YSZ models after sintering, and the difference in the tortuosity before and after sintering corresponded to the degree of sintering. The minimum tortuosity after sintering was observed in the model with 40 Å YSZ nanoparticles which were of the same size as the Ni nanoparticles. Our large-scale multinanoparticle MD sintering simulations enabled the analysis of the gas diffusion properties in the porous anode. These findings obtained with our large-scale multi-nanoparticle sintering simulation method could not be obtained by previous MD sintering studies with tens of thousands of atoms.16−22 This multimillion-atom study revealed the effect of the particle size

paths were calculated with a random walk process, using 10 different random numbers for each path. Before sintering, the tortuosity decreases as the YSZ particle diameter increases from 20 to 60 Å. Thus, the Ni/YSZ model with large YSZ nanoparticles shows good gas diffusion properties owing to the larger pores before sintering. Shimada et al. showed experimentally that Ni/YSZ porous structures with large pores have good gas diffusion properties before sintering.6 Our results agree well with this experimental result. After sintering, the tortuosity increases in all Ni/YSZ models. The difference in the tortuosity before and after sintering increases slightly as the diameter of YSZ particles increases from 20 to 40 Å and increases sharply from 40 to 60 Å. These results indicate that the increase in tortuosity caused by sintering corresponds to the degree of sintering. Interestingly, after sintering, the tortuosity decreases as the YSZ particle diameter increases from 20 to 40 Å and then increases as the YSZ particle diameter increases from 40 to 60 Å. The size-dependent trends of the tortuosity before and after sintering are different because the tortuosity after sintering is determined by the intrinsic properties of the porous structure and the degree of degradation. Furthermore, Figure 9 shows minimum tortuosity after sintering in the 40 Å YSZ nanoparticle model, which is equal to the Ni nanoparticle size, suggesting good gas diffusion properties after sintering. The tortuosity before the sintering decreases slightly with increasing YSZ particle size (Figure 9). However, the degree of sintering increases as the YSZ particle size increases from 20 to 40 Å and increases sharply above 40 Å (Figure 8). When the YSZ particle size is smaller than 40 Å, the degree of sintering and the increase in the degree of sintering with increasing YSZ particle size are small, which leads to a little difference in the slope of the change in tortuosity after sintering. When the YSZ particle size is larger than 40 Å, the degree of sintering and the increase in the degree of sintering with the increasing YSZ particle size are large (Figure 8). Thus, the tortuosity after sintering increases with the increasing YSZ particle size, which leads to an inflection point at 40 Å, at which the minimum tortuosity after sintering occurs. Therefore, our large-scale multi-nanoparticle MD sintering simulation provides a method for optimizing the particle size. The results presented in this study could not be obtained by previous MD sintering 31822

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and tortuosity on sintering and degradation. Our large-scale multi-nanoparticle sintering MD simulation provides a new way to understand the sintering and degradation mechanisms in a porous structure and offers useful theoretical guidance for designing durable porous anodes.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.7b07737. Additional text and figure showing the effect of the simulation model size (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +81-22-215-2050. Fax: +81-22-215-2051. ORCID

Jingxiang Xu: 0000-0002-1484-9692 Yuji Higuchi: 0000-0001-8759-3168 Nobuki Ozawa: 0000-0002-8759-0327 Momoji Kubo: 0000-0002-3310-1858 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the JSPS Grant-in-Aid for Young Scientists (Start-up) (Grant No. 16H06629) and MEXT as “Exploratory Challenge on Post-K computer” (Challenge of Basic Science-Exploring Extremes through Multi-Physics and Multi-Scale Simulations). This research used computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research project (Project ID: hp160271 and hp170245). We also acknowledge SR16000 supercomputing resources from the Center for Computational Materials Science of the Institute for Materials Research, Tohoku University (Proposal No. 15S0202, 16S0406, and 17S0408).

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