Mechanisms Underlying Ion Transport in Polymerized Ionic Liquids

Jul 7, 2017 - We report the results of atomistic molecular dynamics simulations informed by quantum-mechanically parametrized force fields, which iden...
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Mechanisms Underlying Ion Transport in Polymerized Ionic Liquids Santosh Mogurampelly, Jordan R. Keith, and Venkat Ganesan* Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States S Supporting Information *

observations are also partially consistent with the results reported by Salas-de la Cruz et al.,17 but are in contradiction with those of Choi et al.18 who observed the conductivities to be related to the glass transition temperature and the segmental dynamics of the polyILs. Such observations motivate the questions considered in this work, viz., “What are the mechanisms and time scales underlying ion-transport in polyILs?”, “What is the origin of differences, if any, in ion transport phenomena between polyILs and pure ILs, and their relationship to the structural relaxation dynamics?”, “Are the ion transport properties of polyILs indeed decoupled from the segmental relaxations and glass transition temperatures?” In this work, we embarked on a computer simulation study to identify the mechanistic features underlying ion transport in polyILs. Explicitly, we used atomistic molecular dynamics (MD) simulations that employed quantum-mechanically parametrized force fields to characterize ion motion in both poly(1-butyl-3vinylimidazolium-hexafluorophosphate) electrolytes and 1butyl-3-methylimidazolium hexafluorophosphate ILs. The following general interaction potential was used in our classical MD simulations: U(r) = Ubonded(r) + Unonbonded(r), where Ubonded(r) refers to bonded interactions and includes contributions arising from all intramolecular bonds, angles, dihedrals, and impropers:

ABSTRACT: We report the results of atomistic molecular dynamics simulations informed by quantum-mechanically parametrized force fields, which identify the mechanisms underlying ion motion and diffusivities in poly(1-butyl-3-vinylimidazolium-hexafluorophosphate) polymerized ionic liquid (polyIL) electrolytes. Our results demonstrate that anion transport in polyILs occurs through a mechanism involving intra- and intermolecular ion hopping through formation and breaking of ionassociations involving four polymerized cationic monomers bonded to two different polymer chains. The resulting ion mobilities are directly correlated to the average lifetimes of the ion-associations. Such a trend is demonstrated to contrast with the behavior in pure ILs, wherein structural relaxations and the associated times are dominant mechanism. Our results establish the basis for experimental findings that reported ion transport in polyILs to be decoupled from polymer segmental relaxations.

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olymerized ionic liquids (polyILs) represent a class of battery electrolytes consisting of either the cation or anion of traditional ionic liquids (IL) as polymeric repeating units.1,2 PolyILs have widely advanced as materials that can combine the unique physicochemical and ion transport characteristics of ILs with the desirable mechanical properties of solid polymer electrolytes. Moreover, as a consequence of possessing a single category of mobile ions, polyILs also minimize the effects of concentration polarization and exhibit transference numbers close to unity.3 Unfortunately, covalently linking the ions to the polymer backbone renders the conductivity of polyILs 2−3 orders of magnitude lower relative to pure IL electrolytes.1 As a result, active research is underway to increase the ion transport properties of polyILs without negatively impacting their mechanical strength.4−9 Optimization of the property characteristics of polyILs has been hampered by a lack of fundamental understanding of the mechanisms underlying ion transport in polyILs. Although ion transport is understood to be governed by the ion-association structural relaxation times in pure ILs,10 and by the polymer backbone segmental dynamics in polymer electrolytes such as poly(ethylene oxide),11−13 little clarity exists on mechanisms prevailing in polymerized versions of ILs. For instance,recent experiments14,15 reported a decoupling between ionic conductivity and structural dynamics in polyILs,16 and demonstrated the dc conductivity of the polyIL can exceed that of its pure IL counterpart by almost 4 orders of magnitude at their respective calorimetric glass transition temperatures. Such © 2017 American Chemical Society

U bonded(r ) = k r(r − r0)2 + kθ(θ − θ0)2 +

1 2

4

∑ K n[1 + (−1)n+ 1cos(nϕ)] + K[1 − cos(2ϕ)] n=1

The nonbonded interactions, Unb(r) included the Lennard-Jones and Coulomb interaction potentials: 4ϵ[(σ/r)12 − (σ/r)6] + q1q2/r. The geometric combining rules were used to calculate interaction parameters for cross-terms in the nonbonded potential. ϵ ij = ϵ iiϵjj and σij = σiiσjj . The force field (FF) parameters for Unonbonded(r) were extracted from the OPLS-all atom (OPLS-AA) force field set developed by Jorgensen19 with improved intramolecular parameters from the work of Acevedo.20 In addition, refined FF parameters compatible with empirical charge scaling of ions were adapted from Bhargava and Balasubramanian.21 For intramolecular force fields, we employed ab initio quantummechanical calculations to develop the appropriate parameters. Details of intramolecular force field development are provided in the Supporting Information (SI). Briefly, equilibrium values of bonds and angles were extracted from the optimized geometries for poly(1-butyl-3-vinylimidazolium)2 dimer using density functional theory (DFT) calculations at B3LYP/6-311g** Received: May 30, 2017 Published: July 7, 2017 9511

DOI: 10.1021/jacs.7b05579 J. Am. Chem. Soc. 2017, 139, 9511−9514

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Journal of the American Chemical Society level.22,23 The force constants for the harmonic bonds and angles were evaluated from the calculation of Hessian normal-mode frequencies at the same level of theory. In addition, a few important dihedral types for the covalent linking of the cationic BMIM+ monomers with vinyl linker were parametrized from the potential energy surface scans using DFT calculations. The BMIM+ cations were covalently attached with vinyl backbone to construct a polyIL chain containing 32 monomers (equivalent to 4.87 kDa). The simulation box contained a total of 8 polyIL chains and 256 neutralizing PF6− ions. Classical MD simulations were performed at constant number of particles, temperature and pressure (NPT) ensemble with periodic boundary conditions in all three directions. The MD trajectories of length 20−50 ns for pure IL s and 350 ns for polyILs were generated at different temperatures ranging between 300 and 600 K. Additional simulation details along with a complete list of bonded and nonbonded FF parameters for polyILs are provided in the SI. As a first step toward clarifying the mechanisms underlying ion transport in polyILs, we sought to probe the influence of the structural relaxation dynamics on the anion diffusivities, DPF6−, and the differences, if any, in relation to the behavior in the corresponding pure IL systems. We determined DPF6− from the long-time slope of mean squared displacements, and in Figure 1a, display DPF6− as a

A number of previous studies have established the ion mobilities in pure ILs to be directly correlated to the time scales underlying structural relaxation times.10 To verify if similar considerations apply for the system considered in our study, we probed the intermittent correlation function C(t)=⟨h(t)h(0)⟩/ ⟨h⟩, where h(t) is assigned a value unity if an ion-association that is present at initial t = 0 remains intact at a given time t. The ions are assumed to be associated if their centers of mass distance is found to be within a cutoff distance of 6.5 Å, corresponding to the first coordination shell of the cation−anion radial distribution functions.24 (refer to SI Section S1.8 for further discussion on the influence of cutoff distance). By definition, C(t) captures relaxation behavior of all possible types of ionassociations including isolated ion-pairs, multiplets, and clusters.26,27 By fitting the resulting relaxations to a stretched exponential, a structural relaxation time τC was extracted. The decay of C(t) was found to be much slower for polyILs, and the relaxation times τC were only obtained for the highest four temperatures probed. In SI Section S1.9, we present results for an alternative structural relaxation time scale τq extracted from the intermediate scattering function, S(q,t). Results discussed in the context of Figure 1c,d are shown to hold equally well based on τq. In Figure 1c, we display a comparison of the structural relaxation times of polyIL and pure IL systems. Consistent with expectations, we observe that the time scales underlying the polyIL and pure IL systems correlate directly with T/Tg. Such results indicate at the level of structural relaxations, polyILs and pure ILs exhibit similar features in their dependence on the temperature relative to Tg. More interesting is the result displayed in Figure 1d, in which the ion mobilities for the polyIL and pure IL systems are displayed as a function of the inverse 10 structural relaxation times τ−1 C . Consistent with earlier reports, we observe DPF6− in pure ILs exhibits an excellent correlation with τ−1 C , indicating the structural relaxations serve as the primary mechanism underlying ion transport in such systems. In contrast, we observe the DPF6− in polyIL systems follows τ−λ C with λ < 1, and more interestingly, exhibits ionic mobilities higher than those of pure IL.16 Such behavior is consistent with experimental reports14 and point to a more careful consideration of ion transport mechanisms in polyILs. To understand the mechanism of anion diffusion in the polyILs, we characterized both the association statistics and the hopping events exhibited by anions. Explicitly, we quantified the probability, P(n), an anion is associated with n polymerized cationic monomers, and P(N), an anion is associated with N number of polymer molecules. From the results in Figure 2a,b at different temperatures, it is observed that P(n) and P(N) exhibit a maximum at n = 4 and N = 2, respectively. Such results are indicative of a state in which the most probable anion association involves four monomers of two different polymer chains (snapshot presented in the SI). We observe the identity of the most probable stable association state (i.e., n = 4 and N = 2) is not influenced by temperature. However, with increase in temperature, the probability of anion association with fewer polymer chains (and consequently, fewer polyBMIM+ cations) is seen to increase at the expense of association states with N > 2 and n > 4. The limiting case N, n = 0, corresponds to anions free from ion-association, and is also seen to increase with temperature, a trend that is consistent with increased thermal fluctuations (seen more clearly in the normalized representation displayed in Figure 2c,d).

Figure 1. (a) DPF6− in polyIL and pure IL as a function of temperature T, (b) DPF−6 and (c) τC as function of T scaled by respective glass transition temperatures (Tg). The simulation extracted Tg values are 453 and 201 K, respectively for polyIL and pure IL (in good agreement with experimental values of 43624 and 196 K,25 respectively). The simulation results for Tg discerned from temperature dependence of densities are presented in SI Section S1.6. (d) Correlations between anion diffusivities and structural relaxation times of ion-associations, where λ represents the exponent in the fit: DPF6− = a0/τλC.

function of the temperature T. Consistent with experimental observations,1 at a specified temperature T we observe that the polymerization of the IL cation leads to an almost 3 orders of magnitude lowering of DPF6−. More interestingly, however, at a specified T/Tg (where Tg denotes the glass transition temperature) we observe that the polyILs possess ion mobilities which are approximately 2 orders of magnitude larger relative to pure ILs (Figure 1b). Such results are qualitatively consistent with the experimental observations reported by Sangoro et al.,14 and suggests fundamentally different mechanisms may underlie ion transport in polyIL and pure ILs. 9512

DOI: 10.1021/jacs.7b05579 J. Am. Chem. Soc. 2017, 139, 9511−9514

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Journal of the American Chemical Society

Figure 4. (a) Percentage of occurring different hopping events in polyIL electrolytes, (b) decomposition of type1 events along polymer backbone mediated by N number of polymer chains. Lines are guide to the eye.

Figure 2. (a) P(n): Probability that a given PF6− is associated with n polyBMIM+, (b) P(N): Probability that a given PF6− ion is associated with N chains. (c) P̃ (n) and (d) P̃ (N) are the P(n) and P(N) normalized by their values at 300 K depicting the temperature effects at different n and N, respectively. Lines are guide to the eye.

consistent with the increased influence of thermal motion at higher temperatures. The results in Figures 2 and 4 suggest intramolecular anion hopping as the dominant mode of ion transport in polyIL membranes. If this were the case, we expect the ion mobilities to be slaved to the average lifetimes of anion−cation associations in such systems. To quantify the time scales underlying such features, we probed the continuous time correlation function:26 S(t) = ⟨H(t)h(0)⟩/⟨h⟩, where h(t) is assigned a value unity if an ion-association which is present at initial t = 0 remains intact at a given time t and H(t) is assigned a value unity if an ionassociation that is present at initial t = 0 remains intact continuously up to time t. S(t) measures the probability that an initially present ion-association remains intact up to time t, and the time scale underlying its relaxations, τS, provides a useful quantification of the average lifetime of the ion-associations (in SI Section S1.10, we present an extended discussion of the influence of simulation sampling time scales on the identification and quantification of hopping events and associated time scales).26 Figure 5 displays the anion diffusivities of polyIL systems as a function of τ−1 S . Consistent with our findings in relation to the

To gain deeper insights on the manner by which anions move in polyILs, we also characterized the different hopping events exhibited by anions. For this purpose, we decomposed the transport events into three main categories as represented in Figure 3a: type1, intramolecular anion hopping events along

Figure 3. Definition of ion hopping types adopted in this paper for investigating different types of ion hopping events in polyIL electrolytes. Note an ion transport event is defined as a transition of anion association from an existing state at time t to a different state at time t′ as indicated by arrow marks, i.e., An(t) ≠ An(t′), where A is a column matrix whose elements are sorted indices of polyBMIM+ monomers associated with a given anion. The transition events are categorized into three types to represent intrachain (type1), interchain (type2), and chain-to-free space (and vice versa) hopping events.

polymer backbone occurring by means of the formation and breaking of ion-associations; (b) type2, intermolecular ion hopping events between different polymer chains; (c) type3, anion hopping from polymer chains to free medium and vice versa. At all temperatures investigated, we observe the type1 events are the dominant mechanism by constituting more than 95% of anion transport (Figure 4a). More interestingly, from the results of Figure 4b, the majority of type1 events occur when anions are bound to two polymer chains, consistent with the results in Figure 2. In considering the influence of temperature, the probability of the events involving two polymer chains (N = 2) is seen to be insensitive to temperature, whereas the probability of ion hopping events along one (three) chain(s) is seen to increase (decrease) with increasing temperature. The latter trends are

Figure 5. Diffusion coefficient of PF6− ions versus inverse ionassociation lifetimes in polyIL electrolytes. The line is a power law fit to the simulation data.

anion transport mechanism, DPF6− displays an excellent correlation to τ−1 S . Together, the results of Figures 2, 4, and 5 conclusively demonstrate that ion motion in polyILs involve a mechanism of anion hopping in a framework of transient ionassociations with four polymerized cationic monomers in two different polymer backbones. Moreover, the mobilities arising 9513

DOI: 10.1021/jacs.7b05579 J. Am. Chem. Soc. 2017, 139, 9511−9514

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ACKNOWLEDGMENTS The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing computing resources that have contributed to the research results reported within this paper. We acknowledge funding in part by grants from the Robert A. Welch Foundation (Grant F1599), the National Science Foundation (DMR1306844), the U.S. Army Research Office under grant W911NF-13-1-0396, and the Donors of the American Chemical Society Petroleum Research Fund (56715-ND9).

from such ion motion is seen to be correlated to the average ionassociation lifetimes which quantify the dynamics of breaking and formation of ion-associations. Our results demonstrate the mechanisms underlying ion motion in polyILs are distinct from those in pure ILs. The results displayed in Figure 1c (and earlier studies10) demonstrate the mobilities in pure ILs are correlated to the structural relaxation dynamics, and the time scale accompanying such relaxations, τC, is significantly slowed upon approach to the calorimetric glass transition. In contrast, the mobilities of anions in polyILs are correlated to the average ion-association lifetimes τS. Such time scales, although influenced by Tg, are affected to a lesser extent relative to τC (Figure 6). Physically, such a result can be

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understood as a consequence of the fact anion hopping and the association−dissociation events can proceed even in a dynamically frozen matrix of cation monomers. As a consequence, the ion diffusivities in polyILs exhibit significantly larger magnitudes at the same T/Tg when compared to pure ILs. In conclusion, we reported molecular level insights on the mechanisms underlying ion transport in imidazolium-based polyIL electrolytes using atomistic molecular dynamics simulations aided by quantum-mechanically developed force fields. An important outcome of this work is the identification of the mechanism underlying ion transport in polyILs and the importance of the average lifetime of ion-association as the underlying time scale. Our results demonstrate a significant contrast with the transport and time scales underlying pure ILs, and help rationalize and provide quantitative support to the mechanisms hypothesized in the literature.14,15,28

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b05579.

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Figure 6. Comparison of the T/Tg dependence of τS of polyIL against the τC of polyILs and pure ILs.

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Corresponding Author

*[email protected] ORCID

Venkat Ganesan: 0000-0003-3899-5843 Notes

The authors declare no competing financial interest. 9514

DOI: 10.1021/jacs.7b05579 J. Am. Chem. Soc. 2017, 139, 9511−9514