Insights into the Transport of Alkali Metal Ions Doped into a Plastic

Mar 19, 2015 - The application of organic ionic plastic crystals (OIPCs) as a new class of solid electrolyte for energy storage devices such as lithiu...
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Insights into the Transport of Alkali Metal Ions Doped into a Plastic Crystal Electrolyte Fangfang Chen, Jennifer M. Pringle, and Maria Forsyth* Institute for Frontier Materials, Deakin University, 221 Burwood Highway, Burwood 3125, Victoria, Australia S Supporting Information *

ABSTRACT: The application of organic ionic plastic crystals (OIPCs) as a new class of solid electrolyte for energy storage devices such as lithium batteries and, more recently, sodium batteries is attracting increasing attention. Key to this is achieving sufficient target ion transport through the material. This requires fundamental understanding of the structure and dynamics of OIPCs that have been doped with the necessary lithium or sodium salts. Here we report, for the first time, the atomic level structure and transport of both lithium and sodium ions in the plastic crystalline phases of an OIPC diethyl(methyl)(isobutyl)phosphonium hexafluorophosphate. These molecular dynamics simulations reveal two types of coordination geometries of the alkali metal ion first solvation shells, which cooperate closely with the metal ion hopping motion. The significantly different ion migration rates between two metal ion doped systems could also be related to the differences in solvation structures.

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INTRODUCTION The development of high performance Li batteries has enabled the uptake of portable electronic devices at unprecedented levels in recent years. However, there is a continuous demand for improvements in safety, cycle life, power, and energy density, which are also the key factors to the widespread use of these devices in transport applications. As an alternative technology there are compelling advantages to using sodium in place of lithium, such as increased material supply and lowercost, and the performance of sodium batteries has now made significant progress.1−4 Fundamental to the performance of both devices is the electrolyte, as this dictates the transport rate of the target ions (Li or Na) between the electrodes, facilitates the electrochemical reactions at the electrode interface, and also largely dictates the safety of the device. The use of solid electrolytes, most commonly ceramics or solid polymers, can help to overcome the safety concerns associated with dendrite formation and the volatile organic solvent electrolytes used in commercial Li batteries. However, the challenge for new solid battery electrolytes is achieving the high ionic conductivity, good electrochemical and thermal stability, and appropriate mechanical properties required. Organic ionic plastic crystals (OIPCs) are an alternative class of solid-state fast ion conductor recently shown to support good all solid state Li battery performance.5−9 Composed entirely of ions, these plastic materials are structurally analogous to the better-known room temperature ionic liquids (RTILs), but the use of shorter alkyl chains in typical cations such as pyrrolidinium or tetraalkylphosphonium increases the melting point to above room temperature. Crucially, the combination of these cations with anions of high symmetry can create short-range disorder in the material as a result of © 2015 American Chemical Society

rotational or translational degrees of freedom. This short-range disorder, within a long-range ordered lattice, is able to create defects such as vacancies and slip planes that impart mechanical plasticity and enable good ionic conductivity.9−11 The plasticity of these solid electrolyte materials is beneficial for battery applications as it allows good contact to be maintained with the electrodes upon cycling or changes in operating temperature. More importantly, fast ion conduction of target ions can be achieved upon doping a small amount of a Li salt into the OIPC matrix, and thus application of these materials in Li batteries is being realized.8,12 In contrast, investigations into Na-doped OIPCs for emerging Na battery technologies is still in its infancy.13 Furthermore, while a number of different possible conduction mechanisms for Li-doped OIPCs have been suggested experimentally,10,14−16 there remains a lack of fundamental understanding of the structure and dynamics in doped OIPCs at an atomic level. Previous work has amply demonstrated the efficiency of computational modeling in the exploration of new materials; this has been widely used for RTILs, contributing significantly to the understanding of these materials for battery applications.1,17−21 However, related studies on OIPCs are relatively rare, partly due to the difficulties in determining accurate single crystal structures that are desirable as a first starting configuration for the simulation box and also for determining the potential functions to be used during the simulation. A small number of previous MD studies have investigated the structures and dynamics (rotation and diffusion) of ions in pure OIPC systems,22−25 plus we have Received: February 10, 2015 Revised: March 12, 2015 Published: March 19, 2015 2666

DOI: 10.1021/acs.chemmater.5b00538 Chem. Mater. 2015, 27, 2666−2672

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Chemistry of Materials recently reported the first study of a Li-doped OIPC system.26 These investigations have helped to elucidate the complicated thermodynamics and phase behavior of these materials from a structural point of view. However, thus far no molecular modeling studies on Na-doped OIPCs have been reported. Driven by the promising experimental studies of Liconducting OIPCs and the high expectations of Na-conducting OIPCs, in this work we report a molecular dynamics study of an OIPC, diethyl(methyl)(isobutyl)phosphonium hexafluorophosphate ([P1,2,2,4]-[PF6]), doped with either Li+ or Na+ ions. In our previous work, studies of the undoped [P1,2,2,4][PF6], using a combination of experimental techniques and second moment-based solid static NMR line width simulations, allowed a phase-dependent transport model to be proposed.27 Subsequently, MD simulations of this pure material allowed the hierarchal local rotational and translational ion motions to be elucidated,23 and intrinsic heterogeneous ion motions were identified so that the ionic conductivity of this material was better understood.25 Here we particularly focus on the dynamics of those alkali metals in the plastic crystal phase of this material in order to provide new insights into the mechanism of transport for these important target ions. Such understanding is the foundation for developing new electrolytes with optimum ion transport characteristics for Li or Na batteries.

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closer to the crystalline structure if using diffuse functions, and the significant difference in binding energy of around 30 to 40 kcal/mol was also found without diffuse functions. However, the difference caused by two DFT functions M052X and B3LYP is small if both adopt a basis set with diffuse functions. The frequencies were also calculated to check imaginary frequency for optimized ion-pairs. Only one triangular Li solvation structure with bidentate Li−F coordinating geometry was shown as a transition state at the M052X/6-31+G* level, but it is still a minimum structure if using the other two methods.

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RESULTS AND DISCUSSION Structures of the Doped Systems. The Na and Li doping of [P1,2,2,4][PF6] was investigated, at doping concentrations of 0.93 and 8.3 mol %. The structural data were collected at selected temperatures across four solid phases of the material; the pure OIPC undergoes solid−solid phase transitions at 298, 343, and 393 K before melting at 423 K.27 The structures of the matrix ions were first examined by calculating the radial distribution function (RDF) between phosphorus atoms in the anion (P1) and cation (P2). This function describes how density varies as a function of distance from the reference particle. For an ordered crystalline structure, the RDF profile presents multiple distinct sharp peaks resulting from regularly arranged neighboring atoms, which are usually seen at low temperature phases, as shown in Figure 1. However, when the temperature increases, these sharp RDF peaks gradually broaden and merge because of the increased structural disorder, as also observed in the pure material.23 The matrices with either Li or Na ion doping, at the same doping concentration, clearly undergo similar temperature-dependent structural changes. At the lower concentration of 0.93 mol % there is also little difference between the structures of the two doped materials. However, as the doping concentration is increased to 8.3%, the RDF peaks, especially the second and third peaks between 7.5 and 10 Å, are a little sharper for the Na-doped system than for the Li-doped system, illustrating a slightly more disordered matrix structure of the Li-doped system. In addition to the overall structure of the matrix ions, the structure immediately surrounding the alkali metal ions was also investigated−in particular, the interactions with the PF6− anion. Both Li+ or Na+ ions incorporated within an electrolyte system will have a coordination sphere of counterion species, such as is observed in RTILs, with the precise speciation being dependent on the nature of both cation and anion.1,4,18 In a recent MD study of a Li-doped N,N,N,N-tetramethylammonium dicyanamide ([TMA][DCA]) system,26 the formation of a coordination complex between a Li+ dopant and several neighboring [DCA]− anions was reported. This was suggested to be key to the increased conductivity of the Li-doped system, due to the creation of more free volume in the plastic crystal matrix, which enhances the self-diffusion of unbound ions. Here, our simulations show ion-association between a Li+ or Na+ dopant and neighboring anions at all investigated solid phase temperatures of this material; this coordination environment defines the “solvation structure” of the dopant ions. Importantly, the simulations suggest that hopping of these metal ions is inseparable from the dissociation and reassociation of these solvation structures. The clearest evidence of these solvation structures is in the RDF profiles of Li−P1 and Na−P1 in Figure 2. The first and only prominent peak here, at around 3 Å for Li and 3.45 Å for Na, is attributed to the Li or Na first solvation structures; the distance between the metal ion and PF6− is much less than the distance between the matrix P1,2,2,4+ cations and PF6−. Clearly,

COMPUTATIONAL SECTION

The doped OIPC system was constructed in a 3 × 3 × 3 supercell based on the X-ray crystalline structure determined experimentally at 123 K.27 The initial structure consists of 215 [P1,2,2,4][PF6] ion pairs (8385 atoms) and one cation and anion vacancy. The Li+/Na+ ions were arbitrarily placed into the plastic crystal matrix by replacing the equivalent number of [P1,2,2,4]+ cations, at two different doping concentrations of 0.93 mol % and 8.3 mol %, respectively. The molecular dynamics simulations were performed following the same procedures as reported in our previous work,23,25 using the same CHARMM force field,25 which is described in the Supporting Information. The system was first equilibrated for sufficient time (over one nanosecond) in an isothermal−isobaric (NPT) ensemble using a Nośe-Hoover thermostat/barostat method until all of the thermal dynamics parameters (energy, volume, etc.) reached equilibrium. The average off-diagonal shear stress was checked to ensure less than tens of atmospheres (atm). Since a large shear stress of 108 atm was found for the 8.3% doped system, the anisotropic NPT (NST) calculations were also conducted, which allowed the changes of both size and shape of the simulation box and thus reduced the shear stress. The orthorhombic shape of the simulation box does not change significantly below 313 K in the NST calculations. At higher temperatures, of between 333 and 373 K, the angles of simulation box are within 90 ± 3°. The production calculation in a NPT/NST ensemble was run for 400 ps. The dynamics properties were generated for several nanoseconds using a NVE ensemble. The van der Waals forces cutoff was 12 Å. The Coulombic interactions were evaluated via the Ewald sum method.28 The real space cutoff of Ewald was 12 Å. All MD calculations were carried out using the DL_POLY program (version 2.20).29 The binding energies of solvation structures were calculated by density functional theory (DFT) using the Gaussian 09 package.30 The geometry optimizations were carried out using two DFT functionals: the most famous exchange-correlation functional B3LYP31,32 which has been widely used for structure predictions and a recently developed Minnesota functional M05-2X33 which shows a satisfactory accuracy for calculating binding energy of RTILs.34 A number of basis sets were adopted including 6-31G*, 6-31+G*, and 6-311+G**. It showed that using a diffuse function affects both energy and structure. The calculated distance between the metal ion and PF6− was much 2667

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Figure 1. Radial distribution functions of P1−P2 in [P1,2,2,4][PF6] OIPC at doping concentrations of 0.93 mol % [(a) and (b)] and 8.3 mol % [(c) and (d)], at selected temperatures from different solid phases of the pure material as marked in (a). P1 and P2 are the heaviest atom in the anion and cation, respectively, which were used to study the relative arrangements of the anions and cations.

Figure 2. Temperature dependent radial distribution functions and coordination numbers for Li−P1 and Na−P1 ion pairs in [P1,2,2,4][PF6] at doping concentrations of 0.93 mol % [(a) and (c)] and 8.3 mol % [(b) and (d)]. RDF and Coordination Number share the same Y scale.

both the shape and the position of this peak change little with temperature, suggesting that such a closely coordinated solvation structure is very stable in all phases. The next RDF peaks, between 7 and 13 Å, are relatively broad and more visible at the lower doping concentration and temperatures. These represent the distribution of PF6− anions that are farther away from the cation than those inside the first solvation structure. These peaks change with temperature, merging into one above 353 K, and this new peak also shifts slightly closer to the first peak when the temperature is further increased; this is due to some structural rearrangement and an increase in longrange disorder at higher temperatures. The effect of concentration of the dopant ion on the structure is also reflected from Figure 2, where the merged second peak appears at a lower temperature (313 K) with a higher doping concentration (8.3%). The coordination number (CN) between the metal ion and the anion in the first coordination shell has also been calculated

using the first peak in the RDF, as presented in Figure 2. This shows that Li+ has a CN that varies between 3 and 3.5, whereas it can be as large as 4 for Na+, especially at higher temperatures. This could be due to the larger ion size of Na+, as a result of which the Na+ would be expected to interact with more PF6− anions. The Na+−P1 distance is also longer than the Li+−P1 distance, as reflected in the position of the first RDF peak. These results are consistent with the study of solvation structures of Li+ and Na+ in [TFSI]− based ILs, in which Na+ interacts with five TFSI (i.e., [N(SO2CF3)2]−) oxygen atoms, but Li+ only interacts with four.1,19,35 Two types of metal ion solvation structures were revealed in these MD simulations: one having a triangular shape and the other a tetrahedral shape. As illustrated in Figure 3, a triangular solvation shell consists of three PF6− anions in the same plane, and this structure is the most common in the Li-doped system at low concentration and temperature. The tetrahedral 2668

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tetrahedral solvation structure revealed. However, at the t2 time-point, during its move from one side to the other, the Na+ coordinates with three, not four, PF6− anions. In contrast, the three snapshots for the Li+ outline a hopping process that is dominated by a triangular solvation structure. From t1 to t2, only a rolling movement occurs for the three PF6− ions in the same triangular solvation shell; the hopping of Li+ happens between the t2 to t3 time-points, also accompanied by a restructure of its solvation shell. Two movie files showing these ion movements throughout the 2 ns simulation time are provided in the Supporting Information. The hopping of metal ions can be quantitatively assessed using the van Hove selfcorrelation function, Gs(r,t), defined as

Figure 3. Illustration of triangular (Li[PF6]32−) and tetrahedral (Na[PF6]43−) solvation structures. The green and purple atoms stand for the metal ions.

N

Gs(r , t ) =

solvation shell is made up of four PF6− anions, with the alkali metal ion in the center, and this structure is dominant in the Na-doped system. Transport of Ion Species. Transport of the Li+ or Na+ ions is key to achieving high performance of the Li or Na based energy storage devices. The hopping dynamics of the Li+ or Na+ ions in the plastic crystal were clearly observed in our MD simulations. Interestingly, we show here that this movement is associated with the various anion motions in the first solvation shell. Selected snapshots, taken from the trajectory file at three points in time, are presented in Figure 4 in order to demonstrate the typical hopping process of Li+ and Na+ within the lattice. The density volumetric map of one metal ion (orange for Na+ and green for Li+) was generated over two nanoseconds simulation time. This shows the space that the metal ion occupies during this period, which was found to distribute over several possible sites. The metal ion at three moments in time appears at three different sites and coordinates with different PF6− anions, demonstrating that the rearrangement of the solvation structure is involved in the diffusion process. For example, at either the t1 or t3 time-point, the Na+ is located at one end of the volumetric map, with a

∑ ⟨δ(r − ri(t ) + ri(0))⟩/N i=1

which describes the probability that the metal ion moves a distance of r within a time of t, where ri(t) is a time dependent position coordinate, and N is the total number of metal ions. This function was calculated for both Li+ and Na+ in the 8.3 mol % doped OIPC, as shown in Figure 5. These profiles were produced at seven time-points (10, 50, 200, 500, 100, 2000, and 3000 ps) for Na+ and six time-points (10, 50, 200, 500, 1000, and 1500 ps) for Li+ within 3 ns simulation time, thereby demonstrating changes in the ion dynamics with time. If all metal ions remained static throughout the simulation time, all profiles generated at the different time points would overlap with each other. In contrast, ion diffusion would result in a broadening and shifting of the profile with time. Thus, clearly neither the Li+ nor Na+ ions are static, and the largest ion displacement achieved, shown by the width of the profile, increases with both time and temperature. The emergence of additional peaks over time is also indicative of the hopping of the metal ions. The first peak in the plots represents the chance of finding the majority of ions that move around their initial equilibrium positions. The second peak appears as the

Figure 4. Snapshots of the Na (a-c) and Li (d-f) doped system at three points in time (t1, t2, and t3) demonstrating a hopping process of the metal ion that involves its first solvation shell. The orange and green contours are isosurfaces of the density distribution of Li+ and Na+ generated throughout 2 ns, using an isovalue (ρr = ρ(x,y,z)/ρbulk) of 0.01. Square/triangular frames are used to highlight the tetrahedral/triangular solvation structures. The highlighted PF6− anions in the Li-doped system are labeled to illustrate the movements of three PF6− anions inside the solvation shell. Some of the matrix anions are shown as background to demonstrate the solid plastic crystal phase. 2669

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Figure 5. Van Hove self-correlation functions generated at different time points of 10, 50, 200, 500, 1000, 2000, and 3000 ps for Na+ (solid lines) and 10, 50, 200, 500, 1000, and 1500 ps for Li+ (dotted lines), at four selected temperatures in the 8.3 mol % doped systems.

solvation structures are higher, at between −38 and −42 kcal/ mol for optimized conformers. This suggests that the tetrahedral structure is less tightly bound than the triangular one, and thus the Na+ would more easily escape from the tetrahedral solvation structure. This is consistent with the hopping behavior of the Na+ in the simulation. Finally, it is also important to consider the ionic conductivity resulting from the matrix cations and anions. Comparison of the mean square displacement functions (Figure 6), calculated for both the phosphorus atoms in the anion (P1 anion) and cation (P2 cation) and the metal ions, shows that the displacement of the cation or anion is larger than that of the metal ions, over the same period of time and at the same temperature. Thus, the contribution to the ionic conductivity from the matrix ions is larger than the contribution from the metal ions in this doped OIPC system. This difference in mobility of the dopant or solute ion relative to the solvent or matrix ions has also been observed in related RTIL analogues,36 where the mobility of the dopant ion is still sufficient to support good device performance. The mean square displacement functions also show that, on average, both cation, anion, and metal ion in the Li+ doped system move faster than in the Na+ doped system at the same temperature, which is consistent with the Van Hove self-correlation functions discussed above. It takes approximately half of the time for ions to move a similar distance in the Li+ doped system compared to the Na+ doped system, at the same temperature and doping concentration.

simulation time evolves, due to a proportion of the ions hopping to new equilibrium sites and residing at this new center. Therefore, the evolution of additional peaks in all of the profiles shows that the hopping of Li+ and Na+ ions occurs at all temperatures studied. For example, at 293 K new shoulderpeaks appear between 3 and 4 Å for both Li+ and Na+. This peak is particular clear for Li+ at t =1.5 ns. At 313 K a proportion of the metal ions can move to new equilibrium sites 6 to 7 Å away from their initial positions. The farthest distance that the ions move increases to over 10 Å when the temperature is above 333 K, with the formation of multiple peaks evident. Furthermore, the profile for Li+ (dotted lines) is generally broader than that of Na+ (solid lines) when compared at the same point in time, particularly above 313 K, indicating that the Li+ moves faster than the Na+ in this OIPC system. One characteristic that could help explain the difference in dynamics between Li+ and Na+ in this material is the difference in the dominant structure of their first solvation shells. Our simulations suggest that a large proportion of Li ions would adopt a triangular solvation structure, whereas the tetrahedral solvation structure is prevalent for Na+. Clearly the tetrahedral solvation structure is less mobile than the triangular one, as shown by the progression of the density volumetric maps in Figure 4. Na+ diffuses together with anions in a triangular solvation shell [Figure 4(b)], whereas it becomes less mobile upon the formation of a tetrahedral shell [Figure 4(a) and 4(c)]. This can be understood from the binding energy, Eb, of two types of Na solvation structures, which was calculated by subtracting the energy of each optimized single ion molecule, E(Na) and E(PF6), from the total energy of the whole solvation structure E(Na[PF6]n) in the gas phase, such that

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CONCLUSIONS In summary, we have shown that hopping mechanism of both Li and Na ions in doped solid OIPC electrolytes is directly related to the solvation structures of the dopant ions. The hopping movement of the metal ion involves a sequence of breaking and reforming of the solvation structures; for Na+ ion transport this predominantly involves interchange between a tetrahedral and triangular solvation shell coordination geometry, whereas for Li+ only cooperative motion between the metal ion and a triangular solvation shell is observed. The higher mobility of the Li+ compared to the Na+ ions in the OIPC has

ΔE b(Na[PF6]n ) = E(Na[PF6]n ) − E(Na) − n × E(PF6)

The energy of the triangular or tetrahedral type solvation structures was estimated based on a number of optimized Na[PF6]n complexes differentiated by Na−F contacting orientations, i.e. monodentate, bidentate, or tridentate geometry. The binding energy of triangular solvation structure is in a range of −120 to −130 kcal/mol, at the M052X/6-31+G* level of theory. However, the binding energies of tetrahedral type 2670

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and also through Multimodal Australian Sciences Imaging and Visualisation Environment (MASSIVE).

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Figure 6. Mean square displacement of P1, P2 and the metal ions in an 8.3 mol % doped Li+ (a) and Na+ (b) system, calculated at four temperatures. MSDs were calculated for 1.8 ns for the Li doped system and 4 ns for the Na doped system, reflected in the different x-axis values. The dotted vertical line marked in (b) is inserted to assist comparison of the MSD of the ions in the Na doped system after 1.8 ns with the MSD of the ions in the Li doped system at the end of the simulation time (a).

thus been related to the different shapes and energies of their solvation structures. This transport model for the different alkali metals in the OIPC is significant for the fundamental understanding and application of these materials as solid electrolytes in Li or Na batteries. Furthermore, this type of analysis can be used to screen OIPC systems with different structures and chemistry as well as optimize the concentration of Na or Li for optimum transport.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

REFERENCES

S Supporting Information *

Force field information and two movie files showing hopping of the metal ion in two types of solvation structures. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge the Australian Research Council (ARC) for financial support under FL110100013. This work was supported by computational resources on ’Raijin’ through the National Computational Merit Allocation Scheme 2671

DOI: 10.1021/acs.chemmater.5b00538 Chem. Mater. 2015, 27, 2666−2672

Article

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DOI: 10.1021/acs.chemmater.5b00538 Chem. Mater. 2015, 27, 2666−2672