Letter pubs.acs.org/JPCL
Dynamic Heterogeneity and Ionic Conduction in an Organic Ionic Plastic Crystal and the Role of Vacancies Fangfang Chen,*,† Simon W. de Leeuw,‡ and Maria Forsyth*,†,§ †
Institute for Frontier Materials, Deakin University, Burwood Campus, 3125 Burwood, Victoria, Australia Theoretical Chemistry, Gorleaus Laboratories, Leiden University, P.O. Box 9502, 2300 Ra Leiden, The Netherlands § ARC Centre of Excellence for Electromaterials Science, Australia ‡
S Supporting Information *
ABSTRACT: Dynamic heterogeneity was investigated for the first time in a conductive organic ionic plastic crystal by molecular dynamics simulation. A minority fraction of ions that possess above-average dynamics were identified in the plastic crystal phase. The signature of this unusual motional behavior is found in the significant increase in the nonGaussian parameter α(t). A study by incorporation of vacancies into the crystal structure shows explicit evidence of coexistence of mobile species with an otherwise rigid matrix, which particularly supports the previous explanation on heterogeneous motional narrowing in nuclear magnetic resonance. It is also found that the origin of dynamic heterogeneity here is inseparable from the inherent structural characteristics of organic ions. This work reveals the profound effect brought by heterogeneous dynamics on the conduction mechanism of this material, as well as the important role of defects on ions dynamics. SECTION: Kinetics and Dynamics
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state, which leads to their potential application as a solid-state matrix material for electrochemical devices.18−23 OIPCs typically have an ordered crystal structure at low temperatures and complex multiple plastic crystal phases as the temperature increases, which often show analogous temperature-dependent ionic conductivity.22,24 Our latest experimental25 and molecular dynamics simulation26 studies on a pure OIPC matrix material diethyl(methyl)(isobutyl)phosphonium hexafluorophosphate ([P1,2,2,4][PF6]) reveal the hierarchical changes in the local structures and dynamics during phase transitions (around 298, 353, and 393 K for plastic crystal phase transitions and 423 K for melting). The nuclear magnetic resonance (NMR) experiments highlighted interesting dynamic phenomena, which indicated a higher local mobility in some parts of the material even in the lower-temperature plastic crystal phases; this is concluded from the existence of sharp, motional narrowed peaks superimposed on the broader NMR signal,25 which is known to be due to the superposition of subspectra from both fast (sharp peak) and slow (broad peak) ions. Similar heterogeneous motional narrowing was also found in other OIPC materials24 and has also been interpreted as reflecting some fraction of mobile ions in an otherwise rigid matrix. Therefore, it is reasonable to believe that dynamic heterogeneity widely exists in the solid-state OIPCs, and this
ynamical heterogeneity is considered to be one of the key features of disordered materials that exhibit slow dynamics and is a major field of research in amorphous materials.1,2 Its significance arises in large part from the possible connection to the glass transition in supercooled liquids and may hold a key to revealing the fundamental physical mechanism of this phenomenon.2−5 Thus, intensive research has focused on the topic of dynamic heterogeneity in a wide variety of material systems spanning polymer melts,6,7 colloidal glasses and gels,8 metallic alloys, and room-temperature ionic liquids (RTILs).9−13 More recently, this fascinating topic even reaches beyond material science to life sciences (in living cells)14,15 and engineering (traffic systems).16 These intense efforts have led to significant progress not only toward the understanding of this phenomenon but also in the development of well-established, quantitative methods to characterize the process in glassy materials.1 Dynamic heterogeneity results from the coexistence of different mobile particles or molecules in a system and is now recognized as a central aspect of the structural relaxations in disordered materials. In such systems, the dynamic properties usually exhibit nonexponential relaxation of the time correlation functions. This phenomenon has been found in recent years in ionic liquids,10−13,17 a class of roomtemperature molten salts usually composed of organic ions and showing good ionic conductivity. From the chemical structural point of view, the so-called organic ionic plastic crystals (OIPCs) of interest in this work are closely related to the ionic liquids. OIPCs also exhibit fast ion conduction, but in the solid © 2013 American Chemical Society
Received: October 15, 2013 Accepted: November 18, 2013 Published: November 18, 2013 4085
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Figure 1. van Hove self-correlation functions for the P1 atom (anion) at 373, 393, 413, and 433 K. The insets compare the van Hove self-correlation functions with their Gaussian form functions. The chemical structure of one pair of a cation [P1,2,2,4]+ and anion [PF6]− is presented.
ri(t) is a time-dependent position coordinate. In an isotropic system, 4πr2Gs(r, t) describes the probability that a particle moves a distance r within a time t. The random displacement of a particle in Fickian diffusion fits into a Gaussian distribution G0(r,t) = (3/2π⟨|Δr(t)|2⟩)3/2 exp(−3r2/2⟨|Δr(t)|2⟩), where ⟨|Δr(t)|2⟩ is mean square displacement (MSD) of a particle. If the Gaussian distribution describes a typical dynamic environment, then the slowly varying, heterogeneous fluctuations of the environment will result in a non-Gaussian behavior,30 which leads to the deviation between the van Hove self-correlation function and the Gaussian form function. The van Hove self-correlation functions are calculated for the P1 atom, the geometry and mass center in [PF6]−, at different temperatures from 373 to 433 K in Figure 1. The results calculated at six time points between 1 ps to 1 ns show different temperature-dependent translational motions of anions. Obviously, anions are fixed at and below 373 K because the van Hove self-correlation functions are almost unchanged with time at 373 K. However, at the temperatures of 393, 413, and 433 K, the anion displays increased translational movements as the maximum of the peak shifts to the right with time, and the shape of the peak also broadens. It is also noticed that the translational motions of anions can be more or less constricted inside of the topological cage until at 433 K, where the largest translational distance increases quickly to over 10 Å after just 500 ps, indicating that the motions become more diffusive at 433 K. The comparisons between van Hove self-correlation functions and their Gaussian form distributions are presented in the insets of Figure 1. The deviations between two functions
unusual ion dynamics could be one reason accounting for the non-negligible ionic conductivity measured for these materials. An alternative explanation of the ionic conduction in OIPC is that an amorphous phase coexists with the crystalline phase (for example, an amorphous grain boundary phase) and ions diffuse along the grain boundaries. However, it is difficult to unequivocally prove one or the other experimentally. In this case, a simulation approach would be very valuable. Molecular dynamics (MD) has proven to be an effective tool to investigate the time-dependent dynamic behavior in a molecular system, especially as an intensive understanding toward the dynamic heterogeneity problem based on MD techniques has previously been obtained.5,12,27,28 A very recent MD study reported the heterogeneous Li+ motion in dilithium ethylene dicarbonate (Li2EDC), giving evidence of dynamic heterogeneity of the monatomic ion in the ordered state of this ionic conductor. In this work, we will conduct MD simulations to identify the unusual ionic movements in both the ordered solid phase and the melting phase of an OIPC [P1,2,2,4][PF6]. The role that a vacancy plays in this dynamic behavior will also be discussed. We believe an in-depth investigation of these unusual fast ions can yield crucial information for the fundamental understanding of ionic transport and conduction mechanisms in OIPC materials. The MD simulation details are given in the Supporting Information. The methods well-developed for analyzing the dynamic heterogeneity in supercooled liquids and ionic liquids13,28,29 are also adopted here. The translational movements of ions can be studied by the van Hove self-correlation function, defined as Gs(r,t) = ∑Ni=1 δ(r − ri(t) + ri(0))/N, where 4086
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Figure 2. MSDs and non-Gaussian parameters α(t) calculated for the P1 (a) and P2 (b) atoms at different temperatures.
migration in the solid state. Some examples are depicted in Figure 3.
are clearly seen in the tail parts, suggesting that there are different mobile ions coexisting in the system, that is, heterogeneous dynamics. A significant deviation of more than 2 Å is shown at 413 K at 500 ps (marked by a two sided arrow line), indicating some unusual highly mobile dynamics around this particular moment in the system. It is also noticeable that these deviations between two functions change with time and temperature. One quantitative method to analyze the deviation of the self van Hove function from the Gaussian function is via a nonGaussian parameter α(t) = (3/5)⟨|Δr(t)|4⟩/⟨|Δr(t)|2⟩2 − 1, where Δr(t) = ri(t) − ri(0) is the displacement of a given particle in a time interval from 0 to t and |Δr(t)|2 is the MSD.4 In Figure 2, both α(t) and the MSD are generated for the P1 and P2 atoms, in the anion and cation, respectively, for 1.2 ns. It is evident from the MSDs that the ion motions become more diffusive at 433 and 500 K, at which point the material has been in its molten phase as suggested from the previous studies.25,26 The changes of α(t) at these two temperatures resemble the typical heterogeneous behavior reported for ionic liquids, that is, α(t) exhibits a maximum at intermediate times, from tens to hundreds of picoseconds here, and the maximum of α(t) shifts to shorter times with increasing temperature.12 The plateaus in MSD curves are associated with the “in-cage” motions of ions, which are more apparent in a temperature region below 413 K. If ions are confined to a region around the lattice site, |Δr(t)|2 and |Δr(t)|4 eventually become roughly constant and so does their ratio; hence, both MSD and α(t) exhibit a much flatter plateau throughout the simulation time, as seen at 373 K in Figure 2. Once the translational movement increases slowly with time, α(t) also changes. However, at some point, the change becomes quite remarkable; for example, a prominent maximum of α(t) is reached at 413 K after a sudden increase in α(t) beyond 100 ps, which is consistent with the largest deviation displayed in Figure 1. Through tracing the trajectory file, it is found that such a significant increase in α(t) is always correlated to some individual ion’s remarkable
Figure 3. Snapshots of anions projected on the X−Y plane at four selected time points at 413 K. One anion is escaping from its lattice position at 273 ps (top left). Three other pictures show how the other two anions a and b complete the whole hopping process.
In Figure 3, snapshots of anions are saved at four selected moments when the migrations of anions are captured. For example, the image at 273 ps shows that one anion moves half of the distance between two lattice lines. Three other images, saved at 492, 500, and 517 ps, present a complete hopping process of two anions a and b toward each other’s lattice layer in the Z direction (vertical to projections). It is suggested here that these fast migration motions are closely related to the intrinsic structural characteristics of OIPCs. As we know, in a 4087
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perfectly ordered crystal system, the atoms/molecules sitting stably on the lattice sites are thought of as identical, and the migration of one of these would require significant fluctuation in the local environment. In an OIPC system, organic ions occupying lattice sites possess a certain degree of rotational or reorientational freedom; thus, the short-distance disorder in the structure of these materials is easily enhanced as the temperature increases due to structural relaxations. The local environment of ions therefore becomes no longer equal. For those ions having enough surrounding free volume to form a pathway to a neighboring layer, the migration of ions is highly stimulated. The migration of an ion requires both a transport pathway and sufficient new occupying space. As there is an absence of vacancy space in a perfect plastic crystal model, the occurrence of ion diffusion would require the temperature to be high enough to obtain adequate free volume. Our previous MD study evidenced a significant volume expansion, that is, an increase in free volume, of [P1,2,2,4][PF6] in the hightemperature plastic crystal phase,25 whereas in a real material, defects such as vacancies will naturally exist and can provide the sites that could facilitate diffusion of ions at comparatively lower temperatures, even within a more ordered structure. In fact, the NMR experiment does indeed detect a small fraction of diffusive ions in [P1,2,2,4][PF6] at a temperature as low as 333 K,25 much lower than the lowest temperature for which we could observe the migration behavior in a perfect crystal simulation. It is reasonable to conjecture that these defects in OIPCs create a nonequal local environment, which contributes to the heterogeneous dynamic behavior in the system and also leads to the diffusion of some ions in the low-temperature phases. Here, we provide the validation of this hypothesis through a vacancy model simulation. Figure 4 shows the simulation results from a vacancy model, in which one pair of ions was taken away. The pronounced increases of non-Gaussian parameter α(t) are observed again at both 353 and 393 K after hundreds of picoseconds in Figure 4a due to a small number of ions migrating at some moment. The MSDs indicate that the dynamics of the majority of ions is still localized within the cage until the temperature reaches 413 K. However, the temperatures for observing ion hopping in the vacancy model are much lower than those in the perfect crystal model. Furthermore, both the van Hove self-correlation function and MSDs in Figure 4b indicate that the system has a wellmaintained crystalline lattice structure at 353 K. However, in the perfect crystal model, ion hopping occurs only in a more disordered structure and hence needs a higher temperature. It is also noticed from the trajectory file that the hopping of one anion is accompanied by the tumbling of several surrounding cations, whereas in the rest of the simulation box, cations show less or even no tumbling. This therefore indicates the importance of the tumbling of the [P1,2,2,4]+ cation on the migration of the [PF6]− anion and shows correlated motions within this system. A snapshot to show ion hopping and the tumbling of cations in the vacancy model is available in the Supporting Information. Therefore, here, we have, for the first time, demonstrated the hopping of ions in a low-temperature plastic crystal phase with assistance of defects, which validates the hypothesis previously made but that has not been explicitly proven from experimental data in such systems. These motions are also accompanied by a significant increase in the non-Gaussian parameter. On the
Figure 4. (a) MSDs (insert) and non-Gaussian parameters α(t) calculated for the center of mass of the cation and anion and (b) the van Hove self-correlation function, MSD and α(t) for P1 and P2 atoms at 353 K.
basis of different patterns of α(t) as well as temperature, it could be possible to differentiate the material structures and physical states of an OIPC using α(t) as a signature. For example, in Figure 4a, the α(t) in the area marked “significantly increased region” is associated with a solid-state structure with a long-distance crystalline order, whereas the α(t) in the “moderately increased region” is caused by the liquid-like dynamic behavior with a more disordered structure. In conclusion, we have identified the diffusion of a very small fraction of ions in an ordered crystal lattice just as previously suggested from experiments using NMR spectroscopy. These unusual dynamics are successfully revealed by the existing analysis methods and are associated with the concept of dynamic heterogeneity. Evidently, such heterogeneous dynamics behavior contributes to the ionic conduction in the OIPC materials. Migration of ions in the crystal lattice requires α(t) changing significantly with time. Furthermore, the nonGaussian deviation caused by ion diffusion is larger in the solid state than that in the liquid state. We also prove that the vacancy plays a crucial role for ion diffusion in the lowtemperature OIPC phases. It would be interesting to extend the analysis to an OIPC material doped with an additional ionic species such as lithium in order to investigate and clarify the diffusion mechanism within a doped OIPC material. 4088
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ASSOCIATED CONTENT
S Supporting Information *
Computational methods and a figure to show ion hopping in the vacancy model. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected] (F.C.). *E-mail:
[email protected] (M.F.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge the financial support from Australian Research Council (ARC) under Grant FL110100013. This work was supported by computational resources on both the National Computational Infrastructure (NCI) through the National Computational Merit Allocation Scheme and the Victorian Partnership for Advanced Computing (VPAC).
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REFERENCES
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