StructureâProperty of LithiumâSulfur Nanoparticles via Molecular

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Structure-Property of Lithium-Sulfur Nanoparticles via Molecular Dynamics Simulation Ying Li, Nichols A. Romero, and Kah Chun Lau ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b09128 • Publication Date (Web): 09 Oct 2018 Downloaded from http://pubs.acs.org on October 11, 2018

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ACS Applied Materials & Interfaces

Structure-Property of Lithium-Sulfur Nanoparticles via Molecular Dynamics Simulation Ying Li,a,b,* Nichols A. Romero,a,b Kah Chun Lauc,* a

Computational Science Division, Argonne National Laboratory, IL 60439, USA Leadership Computing Facility, Argonne National Laboratory, IL 60439, USA c Department of Physics & Astronomy, California State University Northridge, CA 91330, USA * [email protected]; [email protected] b

Keywords: Molecular dynamics, Nanoparticles, Lithium sulfur materials, ReaxFF force field, Structural property Abstract: Lithium-sulfur (Li-S) batteries offer higher energy densities than most reported lithium-ion batteries. However, our understanding of Li-S battery is still largely unknown at the level of the nanoscale. The structural properties of Li-S materials were investigated via molecular dynamics (MD) simulations using the ReaxFF force field. everal Li-S nanoparticles with different Li:S composition ratios (2:1 and 2:8) and various structures are studied. Our MD simulations show that, among the four structures we constructed for Li2S8 nanoparticles, the core-shell structure is the most thermodynamically stable one during the charging (delithiation) process. In contrast to bulk crystal Li2S, we find the presence of mixed lithium sulfide and polysulfide species are common features for these Li-S (Li2S, Li2S8) nanoparticles. The complex distribution of these sulfide and polysulfide speciation are dictated by both stoichiometry and local atomic structures in the nanoparticle. These findings will provide insight into further development of functionalized lithium-sulfur cathodes. 1. Introduction As the demand for electrical energy continues to increase due to economic and population growth, the development of robust electrical energy storage technologies (such as batteries) is urgent to store sustainable energy resources (e.g., solar, wind) in a safe and environmentally friendly manner.1-3 To catch up to the efficiency of energy production with conventional fossil fuels technologies, a substantial enhancement of the energy density for rechargeable batteries is required.4 This requirement has attracted much attention to a new rechargeable battery design based on lithium-sulfur (Li-S) 5-6. The energy density of Li-S is several times higher than conventional Li-ion batteries.3,7 However, to date, the advances in Li-S battery technologies are hindered by low rechargeability, rapid capacity fading, polysulfide dissolution,8 insufficient control and lack of basic understandings of the electrode/electrolyte interface.5,9 Thus, fundamental and systematic studies of the structure and properties of Li-S batteries and related materials are critical for the development of a practical rechargeable Li-S battery. One of the serious challenges in Li-S batteries is the design of a robust cathode.10 Lithium sulfide (Li2S) is currently under intense study because it is the main insulating discharging product of Li-S batteries and an interesting candidate cathode material.11-13 When Li2S solid is employed as the cathode material, the mechanical vulnerability of the cathode due to volume expansion of sulfur particles caused by the lithiation in the discharging process can be reduced significantly in contrast to a pure sulfur cathode.3,14-16 The advantages of using Li2S as the cathode material are obvious, but there are still lots of fundamental problems waiting to be solved. One of the most common issue is that there are many higher order polysulfide (Li2Sn, n > 2) species found together with the Li2S species.17 In contrast to Li2S, the chemical properties of the polysulfide (Li2Sn, n > 2) are erratic due to the complicated molecular structures and unpredictable (electro)chemical reactions.18-20 Thus resulting in wide distributions of neutral or anionic Li2Sx, or radical LiSx species in electrolyte solutions.21-22 In attempt to improve the electronic conductivity and suppress polysulfide dissolution at cathode, methods of confining sulfur within the cathodes will continue to be an active research area.23-24 To fabricate composite cathodes for lithium–sulfur batteries (depicted in figure 1), ACS Paragon Plus Environment

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fundamental studies of the structural properties, speciation of lithium sulfide, polysulfide species, and the nanoscale of Li-S system are needed. To investigate the basic structural property of these lithium sulfide and polysulfide species at the nanoscale, it is important to study these systems (i.e., lithium sulfide and polysulfide species) in their nanoparticle morphology by focusing solely on nanoparticles (Fig. 1) using atomistic simulation. This in turn will provide us detailed molecular species characterization and spatial distributions of lithium sulfide and polysulfide species that generally present in Li-S battery. Thus, the study here is an important baseline study for future investigations of functionalized lithium-sulfur cathodes. 2. Method and Model We perform MD simulations using LAMMPS25 with ReaxFF potential,26 where the interaction of LiLi, Li-S and S-S atoms are based on the interatomic force field parameters proposed by van Duin et. al.27 The reactive force-field (ReaxFF) interatomic potential is a powerful computational tool for exploring material properties. Approaching from the classical side, ReaxFF casts the empirical interatomic potential within a bond-order formalism, thus implicitly describing chemical bonding without expensive quantum mechanics calculations. This allows ReaxFF to accurately model both covalent and electrostatic interactions for a diverse range of materials. The ReaxFF force field is an empirical interatomic potential that is based on classical principles require reasonable computational resources, which enables simulations to better describe dynamic processes over long timeframes and on large scales. Energy contributions to the ReaxFF potential are summarized by the following: 𝐸"#"$%& = 𝐸()*+ + 𝐸)-%. + 𝐸/*01% + 𝐸$)." + 𝐸-+2 + 𝐸3)41)&( + 𝐸56%78987 Ebond is a continuous function of interatomic distance and describes the energy associated with forming bonds between atoms. Eangle and Etors are the energies associated with three-body valence angle strain and four-body torsional angle strain. Eover is an energy penalty preventing the over coordination of atoms, which is based on atomic valence rules (e.g., a stiff energy penalty is applied if a carbon atom forms more than four bonds). ECoulomb and EvdW are electrostatic and dispersive contributions calculated between all atoms, regardless of connectivity and bond-order. ESpecific represents system specific terms that are not generally included, unless required to capture properties particular to the system of interest, such as lone-pair, conjugation, hydrogen bonding, and C2 corrections. Full functional forms can be found in the Supplementary Information of the 2008-C/H/O publication.28 Different from previous work on the effect of lithiation on Li-S material bulk mechanical properties (e.g., ultimate strength, yield strength, and Young’s modulus) reported by van Duin et. al. 27, the focus of current work is the large-scale Li-S nanoparticles structural property that presents as the discharging and charging products in Li-S battery. Studies on the structures are conducted on the crystalline and amorphous Li2S nanoparticles, as well as various stoichiometric Li2S8 nanoparticles. The ring and fragment analysis are performed by analyzing various LixSy species and other intermediates. In the ring analysis, a group of end-to-end bonded atoms is counted as a ring. In the fragment analysis, a group of non-end-to-end bonded atoms is counted as a fragment. 2.1. Crystalline and Amorphous Li2S Nanoparticles First, the system studied are crystalline and amorphous Li2S nanoparticles with diameter D = 10.0 nm consisting of 32,832 atoms. To construct the crystalline Li2S nanoparticle, the initial configuration of the nanoparticle is obtained by cutting bulk crystal Li2S. To guarantee the stoichiometry of the LixSy nanoparticle (i.e., x:y=2:1), the crystalline Li2S nanoparticle is maintained by removing the outer-most redundant atoms, which are defined as any Li atom has a coordination number less than 3 or any S atom has a coordination number less than 5, after cutting the bulk crystal Li2S structure into a sphere. The amorphous (Li2S)10944 nanoparticle is constructed by placing the crystalline (Li2S)10944 nanoparticle in a ACS Paragon Plus Environment

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vacuum environment with periodic boundary conditions in all three dimensions in the MD simulation, which initially relaxed using a conjugate gradient method, then subjected to NPT simulations for 1 ns at T = 1400 K such that all three dimensions of the external stress tensors equal zero. Then the subsequent thermal equilibration process is followed by NVT simulations for an additional 4 ns at T = 1400 K. To obtain a stable structure of amorphous (Li2S)10944 nanoparticle, the system is then quenched to T = 300 K for additional 2 ns to ensure the proper amorphization at T = 300 K with NVT conditions. Throughout the simulation, the velocity-Verlet time stepping method is adopted and the integration time step is Dt = 1 fs. In the thermal equilibration process (i.e., NPT and NVT), the fluctuation (to the mean value) in total energy and temperature is smaller than 0.005 eV/atom and 0.50 K, respectively. Throughout the system preparation, the temperature and pressure are controlled by a Nosé-Hoover thermostat and barostat 29-30 with damping constants of 100 fs and 1000 fs, respectively. 2.2. Stoichiometric Li2S8 Nanoparticles The fundamental structure and properties of Li2S8 in the condensed phase and its agglomeration, aggregation, and precipitation at confined nanoscale in Li-S battery remain elusive31-33. In this work, we assume a model nanoparticle with a Li2S8 stoichiometry obtained by maintaining the number of sulfur atoms the same as the Li2S nanoparticle discharging product, i.e., (Li2S)10944 amorphous nanoparticle that subsequently leads to stoichiometric Li2S8 (i.e., (Li2S8)1368) nanoparticle due to the delithiation process during charging process. To construct a model system for Li2S8 aggregates in the nanoparticle morphology, a hybrid Monte Carlo/molecular dynamics (MC/MD) approach is used. Based on this approach, four different strategies are adopted to construct the Li2S8 nanoparticles: (1) extracting lithium atoms randomly from the outmost layer of the (Li2S)10944 amorphous nanoparticle to form (Li2S8)1368 nanoparticle, which has the distinct core-shell structure, where the outside shell is sulfur-rich, and the inner core is still Li2Salike; (2) extracting lithium atoms from the (Li2S)10944 amorphous nanoparticle according to a spindle distribution such that the lithium concentration is higher in the core region than the outer shell region to form an indistinguishable core-shell boundary throughout the structure of nanoparticle (where the spindle distribution is constructed by randomly extracting lithium atoms within the unit volume in the spherical coordinate of the (Li2S)10944 amorphous nanoparticle using Monte Carlo method); (3) maintaining sulfur atoms uniformly throughout the (Li2S)10944 amorphous nanoparticle to form a nearly homogeneous (Li2S8)1368 nanoparticle, (4) randomly packing the Li2S8 molecules obtained from density functional theory 34-36 to form an assembled (Li2S8)1368 nanoparticle. From all these four approaches, the stoichiometry of these LixSy nanoparticles is constrained to be x:y=2:8. We refer to these four (Li2S8)1368 nanoparticles with the following names: core-shell, spindle distribution, homogenous and assembled Li2S8 structures. The initial configurations of these nanoparticles are placed in vacuum environments with periodic boundary conditions in all three dimensions, subsequently relaxed using the conjugate gradient method and then subjected to NPT simulations for 1.32 ns at T = 300 K, such that all three dimensions of the external stress tensor are set to zero. The thermal equilibration is then followed by NVT simulations for an additional 2 ns at T = 300 K. For these simulation, the velocity-Verlet time stepping method is adopted and the integration time step is Dt = 1 fs. During the thermal equilibration process (i.e., NPT and NVT), the fluctuation (to the mean value) in total energy and temperature is smaller than 0.005 eV/atom and 0.50 K, respectively. The temperature and pressure are controlled by a Nosé-Hoover thermostat and barostat29-30 with damping constants of 100 fs and 1000 fs, respectively. 3. Results and Discussion The focus of this study is on the structural property of Li-S nanoparticle apart from the idealized stoichiometric lithium sulfide (Li2S) crystal with accurate atomistic descriptions. Reactive force field (ReaxFF) is applied in our large-scale molecular dynamics (MD) simulations to probe the structural properties of Li-S nanoparticles during the battery charging process. The path of improving the performance ACS Paragon Plus Environment


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of Li-S batteries begins with an in-depth structural property understanding of the Li-S system, which can be investigated either by advanced experimental characterization techniques or the state-of-the-art simulation methods. In an operating Li-S battery, systematic studies on the evolution of all possible LixSy speciation during discharging and charging process are not trivial. For Li2S solid embedded in conducting carbon electrodes (e.g., Fig. 1), the charging process happens when Li2S is delithiated, which leads to the presence of lithium-poor or sulfur-rich lithium polysulfide species (e.g., Li2Sn, n > 2). For these lithium polysulfide Li2Sn molecules and their intermediaries, the energetics and thermodynamic stability can be determined by quantum chemistry calculations at the molecular level.37 However, the condensed phase of those species remain elusive, especially the detailed structural property for nano-aggregates of these lithium polysulfide LixSy species. To study the structural property of LixSy nano-aggregates at the nanoscale, we focus our studies on these Li-S model systems: crystalline and amorphous Li2S nanoparticles, and various stoichiometric Li2S8 nanoparticles as described in Section 2.1 and 2.2. Figure 2 depicts the crystalline and amorphous configurations of the Li2S nanoparticles, along with the computed radial distribution function g(r) for different atomic pairs. From Fig. 2(c) and 2(d), the similarity between the crystalline and amorphous configuration of the Li2S nanoparticle can only be found within the first coordination shell for Li-Li, Li-S, and S-S bonds. The long-range crystallinity disappears beyond ~ 6.0 Å for the amorphous Li2S nanoparticle. Figure 3 shows the thermally equilibrated configurations of the various stoichiometric Li2S8 model nanoparticles (core-shell, spindle distribution, homogeneous and assembled), along with the computed radial density distribution of each element (i.e., Li and S) and radial pair distribution functions g(r) of the nanoparticles in the Li2S8 model systems. 3.1. Nanoparticle Energetic Analysis To understand how the structures of these nanoparticles correlated with thermodynamic stability, we compare the potential energy of amorphous and crystalline Li2S nanoparticles and the various Li2S8 nanoparticles along with the bulk 𝛼-sulfur. Heat of formation of the lithiated sulfur configuration as a function of lithium content with respect to 𝛼-sulfur and bcc-Li bulk were calculated using the relation ∆𝐸 = 𝐸 20 atoms) species are relatively small. 4. Conclusion We carried out MD simulations of the thermodynamic stability, structural analysis of mixed lithium sulfide and polysulfide speciation and its complex distribution in Li-S (stoichiometric Li2S and Li2S8) nanoparticles. These complex nanostructures are related to discharging and charging products in Li-S batteries. Our simulations show that the local atomic structure in a Li-S nanoparticle may prescribe its stability despite the similarity in stoichiometric compositions. In contrast to end discharge products, i.e., Li2S nanoparticles, our thermodynamic stability analysis suggests that the core-shell Li2S8 nanoparticles are most likely present during the charging process due to delithiation of Li2S nanoparticles. Based on our structural (ring and fragment) analysis, a broad distribution of sulfur, lithium sulfide and lithium polysulfide (i.e., Sn, LixS, and LixSy(y>1)) species are found in both stoichiometric Li2S and Li2S8 nanoparticles. A wide distribution in the population of sulfur Sn rings, and lithium polysulfide LixSy rings for the Li2S8 nanoparticles suggests that there is a complex energy landscape of competing intermediates within a narrow voltage window. Overall, in contrast to bulk crystal Li2S, the presence of mixed lithium sulfide and lithium polysulfide species and its complex distribution are found to be common features for these Li-S (Li2S and Li2S8) nanoparticles. To validate this prediction, characterization by operando x-ray absorption spectroscopy might be needed. The complex distribution of these sulfide and polysulfide speciation (i.e., sulfur (Sn), lithium sulfides (LixS) and lithium polysulfides (LixSy(y>1)) rings and fragments) are dictated by both stoichiometry and local atomic structures in the nanoparticle. The complicated Li-S speciation distribution and local atomic structures within these nanoparticles cannot be accessed via standard XRD spectra analysis. We believe the current systematic study will provide useful structuralproperty insights to the further development of functionalized cathode in Li-S battery. Acknowledgment This research used resources of the Argonne Leadership Computing Facility, which is a U.S. Department of Energy Office of Science User Facility operated under Contract DE-AC02-06CH11357. Y. Li acknowledges support from the Margaret Butler Postdoctoral Fellowship at Argonne National

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Laboratory. K. C. Lau acknowledges the support of California State University Northridge Faculty start-up fund.



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Figure 1. A schematic description of lithium sulfide/polysulfide nanoparticles that present in Li-S batteries cathode with carbon interfaces inspired by Nazar et. al. Reprinted in part with permission from reference 23 and reference 24. 


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Figure 2. Schematic visualizations of (a) crystalline and (b) amorphous configuration of a (Li2S)10944 nanoparticle with 10 nm in diameter. Sulfur and lithium atoms are colored yellow and pink, respectively. Radial pair distribution function g(r) for (c) crystalline and (d) amorphous configurations. gLi-Li(r), gLi-S(r) and gS-S(r) is pink, orange and yellow, respectively.



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Figure 3. Cross-section of (Li2S8)1368 nanoparticles in (a) core-shell (b) spindle distribution (c) homogeneous and (d) assembled structures. Sulfur and lithium atoms are colored yellow and pink, respectively. Radial distribution of density d(r) for (e) core-shell (f) spindle distribution (g) homogeneous and (h) assembled structures of (Li2S8)1368 nanoparticles. d Li(r), dS(r) and dtot(r) is pink, blue and cyan, respectively. Radial pair distribution function g(r) for (i) core-shell (j) spindle distribution (k) homogeneous and (l) assembled structures of (Li2S8)1638 nanoparticles. g Li-Li(r), gLi-S(r) and gS-S(r) is pink, orange and yellow, respectively.


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Figure 4. Energy profile of various model Li-S nanoparticles in the unit of electronic voltage per atom as a function of simulation time.



Figure 5. The simulated XRD spectra of various Li2S and Li2 S8 nanoparticles (plotted in lines) in comparison with the known bulk crystal Li2S (plotted in dots).


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Figure 6. The fraction of atoms in the ring (red bars) and in the fragment (blue bars) for various Li-S nanoparticles.



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Figure 7. The number of various lithium polysulfide rings (red bars) and positions of rings (blue bars) for the (a) crystalline Li2S and (b) amorphous Li2S nanoparticles. The position of rings is defined as the averaged distance of the center of the ring to the center of the nanoparticle (with standard deviation represented as the error bar). Various lithium polysulfide rings in (c) crystalline and (d) amorphous Li2S nanoparticle on real space, with ring sizes color coded as the color bar shown. The circles outline the shape of the nanoparticles.


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Figure 8. The number of lithium polysulfide and sulfur rings (red bars) and position of rings (blue bars) for the (a) core-shell (b) spindle distribution (c) homogeneous and (d) assembled Li2S8 nanoparticles. Various lithium polysulfide and sulfur rings for the (e) core-shell (f) spindle distribution (g) homogeneous and (h) assembled Li2S8 nanoparticles in real space, with stoichiometry ratio of rings color coded as shown in the color bar. The circles outline the shape of the crosscut nanoparticles.



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Figure 9. The number of sulfides (blue bars) and polysulfide fragments (green bars) for the (a) crystal and (b) amorphous Li2S nanoparticles. Various sulfide and polysulfide fragments for a (c) crystal and (d) amorphous Li2S nanoparticles in real space, with the fragment sizes color coded as shown in the color bar. The circles outline the shape of the crosscut nanoparticles.


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Figure 10. The number of various sulfur fragments (red bars), sulfide fragments (blue bars) and lithium polysulfide fragments (green bars) in (a) core-shell (b) spindle distribution (c) homogeneous and (d) assembled Li2S8 nanoparticles. Various fragments distribution in the crosscut (e) core-shell (f) spindle distribution (g) homogeneous and (h) assembled Li2S8 nanoparticle in real space, with the fragment size color coded as the color bar shown. The circles outline the shape of the cross-cut nanoparticles.


StructureâProperty of LithiumâSulfur Nanoparticles via Molecular

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