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Cite This: J. Phys. Chem. B XXXX, XXX, XXX−XXX

Grotthuss Transport of Iodide in EMIM/I3 Ionic Crystal Jesse G. McDaniel†,‡ and Arun Yethiraj*,† †

Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, United States S Supporting Information *

ABSTRACT: Highly ionic environments can mediate unusual chemical reactions that would otherwise be considered impossible based on chemical intuition. For example, the formation of a chemical bond between two iodide anions to form a divalent polyiodide anion is seemingly prohibited due to Coulombic repulsion. Using ab initio molecular dynamics simulations, we show that in the 1-ethyl-3methylimidazolium (EMIM)/I3 ionic crystal, the reactive formation of divalent and even trivalent polyiodide anions occurs with extremely small energetic barriers, due to the electrostatic field of the ionic lattice. A practical consequence of this anomalous reactivity is that iodide anions are efficiently transported within the crystal through a “Grotthussexchange” mechanism involving bond-breaking and forming events. We characterize two distinct transport pathways, involving 3− both I2− intermediates, with fast transport of iodide resulting from the release of an I− anion on the opposite side of the 4 and I7 intermediate species from the initial bond formation. The ordered cation arrangement in the crystal provides the necessary electrostatic screening for close approach of anions, suggesting a new counterintuitive approach to obtain high ionic conductivity. This new design principle could be used to develop better solid-state electrolytes for batteries, fuel cells, and supercapacitors.

1. INTRODUCTION The iodide/triodide redox couple is important for many electrochemical devices including dye-sensitized solar cells,1−4 hybrid-supercapacitors,5,6 and Li-iodide batteries.7 These applications utilize electrolytes either with dilute concentrations of iodide salts or consisting of pure iodide-based ionic liquids. In either case both the solvent-mediated redox potential and iodide transport/conductivity are centrally important for performance.3 The redox potential of iodide/triiodide is affected by the specific ion solvation free energies in the electrolyte, and the magnitude of this effect can be inferred from electrochemical potential measurements. However, the physics by which a specific electrolyte modulates the iodide transport and conductivity is much more difficult to determine, as evidenced by numerous experiments on different iodidebased electrolytes.3,4,8−19 Iodide transport can exhibit very intriguing dependences on the concentration and viscosity of the electrolyte. For example, the addition of neutral iodine to 1-propyl-3-methylimidazolium (PMIM)/iodide ionic liquids8,12 or similar ionic liquid mixtures9 leads to a very significant increase in the electrolyte conductivity, which is at odds with standard ion diffusion mechanisms and contrary to expected trends based on the viscosity. Additionally even though the PMIM/I/I3 ionic liquid undergoes a liquid to nematic phase transition upon cooling,15 the conductivity remains largely unchanged, even though the viscosity increases by ∼6 orders of magnitude!16 Another example of nonintuitive conductivity/viscosity trends was observed for iodide ionic liquids based on long-chain cations, 1-undecyl-3-methylimidazolium (C11MIM) and 1-dodecyl-3methylimidazolium (C12MIM).10,11 C12MIM/I/I3 forms ther© XXXX American Chemical Society

motropic liquid crystals at room temperature whereas C11MIM/I/I3 does not, and surprisingly it was found that the iodide diffusion was faster in the higher viscosity, liquid crystalline C12MIM/I/I3 electrolyte. It has been speculated that Grotthuss-type exchange mechanism between triodide and iodide may contribute to the ion transport and conductivity.3,4,13,17 In this article we provide molecular level evidence of such transport for iodide in ionic crystals. The Grotthuss mechanism relies on the formation of an intermediate followed by dissociation of I−, e.g., I−3 + I− ⇌ [I− ··· I 2 ··· I−] ⇌ I− + I−3

(1)

This bond rearrangement mechanism for iodide diffusion can potentially lead to facile ion transport, and is reminiscent of proton diffusion in water (hence the “Grotthuss” nomenclature20). A primary difference is that the mechanism in eq 1 involves the formation of a dianion I2− species from the 4 constituent iodide and triodide ions, which seemingly would be electrostatically prohibited. A central unanswered question therefore concerns how the energy barrier for I2− 4 formation is modulated by the ionic environment of electrolytes. Heavier polyiodide species (e.g., I5−, I7−) can also exist in the condensed phase,12,19,21 and the iodide/triiodide Grotthuss mechanism (eq 1) is not the only possible exchange mechanism for ion diffusion. Combined conductivity/Raman spectroscopy measurements on PMIM/I and related electrolytes as a function of I2 concentration have shown that high conductivity Received: September 18, 2017 Revised: November 29, 2017 Published: December 1, 2017 A

DOI: 10.1021/acs.jpcb.7b09292 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B regimes are correlated with the onset of I5− formation.8 Using DFT calculations, Thapa and Park22 suggested the important role of I5− species in an exchange mechanism involving neutral iodine shuttling. However, the calculated barriers for I2 exchange between two cation/anion complexes were ∼0.8− 1.0 eV depending on the separation distance, which is significantly higher than thermal energy. Additionally a true Grotthuss exchange mechanism should be symmetric in the reactants and products so as not to alter the equilibria between iodide species, which was not the case in the proposed I2 exchange mechanism.22 We will demonstrate that the following polyiodide exchange mechanism is thermally facile in ionic crystals: I24 − + I−3 ⇌ [I−3 ··· I− ··· I−3 ] ⇌ I−3 + I24 −

2. METHODS The experimental crystal structure of EMIM/I3 was taken from the recent work of Fei et al.,21 which provides a detailed discussion of the ion topology and contact distances. All of our simulations utilize this crystal structure as a starting point, and we only consider thermal fluctuations of atomic positions and do not consider distortions of the unit cell size or shape. The primitive unit cell consists of only two EMIM/I3 ion pairs and is thus too small for simulating ion diffusion and iodide defects. We thus employ a 2 × 2 × 2 supercell, consisting initially of 16 EMIM/I3 ion pairs. We then substitute an iodide ion for one of the triiodide ions, resulting in a ∼ 6% defect ratio; the system with iodide defects is more interesting than the perfect crystal, because diffusion by the mechanism of eq 1 is possible. AIMD simulations are conducted using the CP2K software package.26 The QUICKSTEP method26 is used with a mixed Gaussian/plane wave basis set consisting of optimized double-ζ (DZVP) atomic basis functions27 with Goedecker−Teter− Hutter pseudopotentials for core electrons,28 and a 300 Ry energy cutoff for plane waves, which provides sufficient energy convergence. For SCF convergence, we use the Pulay mixing scheme29 with Fermi smearing using a 400 K electronic temperature and 50 extra virtual MOs. The PBE functional is used for all calculations, and due to the system size we only sample the Brillouin zone at the Γ point. We note that similar levels of theory have been previously employed for modeling the reactivity of polyiodides,22,23,30 and the use of DFT to describe the electronic structure of triiodide has been benchmarked against multireference MRCI and CASPT2 methods previously.31 All MD simulations employ Langevin dynamics, with a 1 fs time step and 0.01 and 0.005 fs−1 friction coefficients for equilibration and production runs respectively, and are run at 400 K rather than room temperature to facilitate better sampling. Potentials of mean force (PMF) are computed using umbrella sampling in conjunction with the weighted histogram analysis method (WHAM).32 For the umbrella sampling simulations, we use harmonic potentials with a 0.01 au force constant, and each window is started from an equilibrated snapshot of an adjacent window, and equilibrated for 1 ps at the new potential. Simulations of 2−5 ps are then conducted for each window, with a spacing of 0.2−0.5 Å between windows with exact values depending on the reaction coordinate. The PMF in Figure 1 is computed by applying umbrella potentials constraining the separation distance between I3− and

(2)

From a theoretical perspective, ionic crystals are ideal systems for investigating iodide Grotthuss transport mechanisms, as well-defined experimental crystal structures provide direct information on ion proximity and organization. Additionally, relatively small crystal unit cells enable tractable application of periodic density functional theory (DFT) approaches, which would be prohibitively expensive for studying disordered liquids. Very recently, Grossi et al.23 utilized periodic DFT calculations to investigate energy barriers for iodide exchange reactions in the ionic crystal 1-butyl-3methylimidazolium iodide (BMIM/I). They considered a low defect concentration of I3− ions (adsorbed I2), to allow for the I42− exchange pathway (eq 1). The authors illustrated a rather complex reaction coordinate involving angular rotation of polyiodide species, with a rate limiting barrier of 0.48 eV for the reaction.23 It was proposed that steric constraints of the BMIM/I crystal contributed to the barrier height, and speculated that potentially lower barriers may exist in the less constrained structures of ionic liquids. In this work, we study an ionic crystal with very similar constituent ions, but with a different crystal structure topology, and propose that the ordered cation arrangement of the ionic crystal is favorable rather than unfavorable for enabling iodide Grotthuss transport. We believe that our present work and the work of Grossi et al.23 provide a very valuable comparison to illustrate the extreme sensitivity of iodide Grotthuss exchange on the geometrical and structural details of the surrounding ionic environment. In the present work, we predict two thermally accessible, Grotthuss exchange pathways for iodide transport within recently reported 1-ethyl-3-methylimidazolium (EMIM)/I3 ionic crystals.21 Employing the experimental crystal structure as a starting point, we use ab initio molecular dynamics (AIMD) simulations to investigate iodide diffusion in EMIM/I3 at a low defect concentration corresponding to a ∼ 6% I−/I3− ion ratio. The first important pathway involves triiodide/iodide exchange (eq 1) within the continuous iodide channels of the crystal structure, and is facilitated by the electrostatic stabilization of the I42− dianion species by the surrounding ionic environment. The second mechanism involves the formation of a cross-channel polyiodide I73− chain as an intermediate (eq 2). The computed free energy barriers for these processes are ∼4−5 kcal/mol at 400 K, which to our knowledge represent the lowest predicted barriers for iodide Grotthuss transport in the condensed phase; such facile ion transport in EMIM/I3 crystals is exciting for solid-state electrolyte applications.24,25

Figure 1. Comparison of potential of mean force (PMF) and potential energy scan (PES) for the minimum energy I3− + I− dissociation pathway. B

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Figure 2. Grotthuss hopping of I− within a channel in the crystal with corresponding energetics shown in Figure 4. The panels (a)−(d) show the separated I3− + I− anions, the formation of the I42− intermediate, and the release of the I− anion on the other side, completing the hopping. We note that the I− periodic image is not color-emphasized with other foreground atoms for clarity.

Figure 3. Grotthuss hopping between neighboring channels with corresponding energetics shown in Figure 5. In (b) I42− in the middle channel complexes with bottom channel I3− to form (e) I73− intermediate bridging the two channels. (f) Transition state I62− in the middle channel formed by terminal bond dissociation; (g) final state with 2 I3− in the middle channel and I42− in the bottom channel. Transition between (b) and (g) results in net transport of iodide (I42−) between middle and bottom channels.

I− ions. For the PMF in Figure 5, we use different constraint variables depending on the specific intermediate. To sample the I3− 7 formation reaction coordinate (Figure 5 (b) to (e)), we apply umbrella potentials to the I42− and I3− separation distance defined by their closest-contact atoms. During this sampling, to prevent dissociation of the I42− complex, we apply a hard wall potential at 4.5 Å to the I42− bond lengths; this only prohibits a rare dissociation event and does not alter the energetics. To sample the reaction coordinate for dissociation of I73− ⇌ I62− + I− ((e) to (f) to (g), Figure 5), we apply umbrella potentials to the distance between iodine atoms of the broken bond, and simultaneously apply a hard wall potential at 4.5 Å to the reaction coordinate of the previous step, to prevent the reverse dissociation. For calculations of the I42− gas phase PES, we employ a larger aug-cc-pwCVTZ-PP basis33,34 to reduce basis-set superposition error (BSSE), which is more problematic for the gas phase

compared to the condensed phase crystal. Bader charge analysis35 is subsequently used for atomic charge partitioning. To facilitate ease of comparison between Bader charges derived from the gas phase and crystalline phase calculations, we have normalized the charges on iodine atoms to give a whole integer charge of −2 on the entire I3−-I− complex. Such an integer charge constraint is not intrinsically reproduced by the Bader analysis, due to the numerical approach for partitioning atomic volumes and integrating the electron density. Because of our employed normalization, we are neglecting any charge transfer between anions and cations, which we believe is secondary compared to the numerical uncertainties in the partitioning method, especially in the condensed phase crystalline environment. We benchmark entropic contributions to (half of) the reaction of eq 1 for which the PES shown in Figure 4. Due to computational expense, we compute the PMF only for the C

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3.2. Free Energy Barriers for Hopping Are Low. Our observations from the AIMD simulations imply that I42− and I73− intermediates are thermally accessible starting from separated I3− and I− species. We compute the energetics along the reaction coordinate for formation/dissocation of I42− by scanning the I3− - I− distance along the channel dimension from both ends of the I42− dianion. At each scan point, we relax all other degrees of freedom in the system while constraining the relevant I3−-I− distance. The resulting potential energy surface (PES) is shown in Figure 4. Consistent with our

lower barrier dissociation between minima (a) and (b) of Figure 4. A comparison between the 0 K PES and 400 K PMF for this reaction coordinate is shown in Figure 1. The dissociated I3− + I− state is slightly stabilized by entropic contributions, resulting in equivalent free energies for minima (a) and (b), within the calculation uncertainty. In general, however, the entropic contribution is relatively small, and the 0 K PES provides a good estimate of the free energy differences between these states.

3. RESULTS AND DISCUSSION 3.1. Grotthuss Hopping in AIMD Simulations. AIMD simulations show hopping of the iodide ions via two different mechanisms. The crystal structure of EMIM/I3 consists of alternating rows of cations and anions, with the molecular axes of the I3− anions nearly aligned with the direction of the anion channel. This crystal structure topology leads to a close contact distance of ∼4.0 Å between triiodide neighbors.21 When a triiodide anion is replaced with an iodide ion, the iodide ion is then no more than ∼7.0 Å from the closest triiodide, with this displacement colinear to the anion channel. The first mechanism involves the formation of a I42− complex from the constituent iodide anion and its neighboring triiodide, with a subsequent release of the iodide from the other side. Figure 2 depicts the process observed in AIMD simulations. During a ∼ 10−15 ps simulation, we often observe association/dissociation events corresponding to the I3− + I− ⇌ I42− reaction in the EMIM/I3 crystal. A movie from the AIMD trajectory of this reactive process is included as Supporting Information. The second mechanism involves the complexation of the I42− dianion with a second triodide anion to form an I73− species, as shown in Figure 3. Interestingly, this complexation does not occur within the same iodide channel, but rather the constituent I42− and I3− species couple between neighboring, parallel anion channels, through a gap in the row of EMIM cations. This reaction mechanism is complementary to the reaction depicted in Figure 2, indicated by the fact that both reactions involve the same I42− intermediate, labeled as state (b) in both Figures 2 and 3. The trivalent I73− anion spans two adjacent anion channels of the EMIM/I3 crystal, mediating transport of the I− defect between these two channels by the transition from state (b) to (g) of Figure 3. During a ∼ 10−15 ps simulation, we sometimes observe spontaneous formation of the I73− intermediate by cross channel I42− and I3− coupling, which competes with the I42− dissociation pathway of eq 1. It is important to emphasize that iodide transport mediated by the bond breaking/forming processes (Figures 2, 3) observed in our simulations is not restricted to the particular I− defect concentration. The present system has been chosen based on practical considerations; at least one I− defect must be present for Grotthuss transport, and the 2 × 2 × 2 supercell of EMIM/I3 is the largest system currently tractable for AIMD simulations. After completion of reactions described by eqs 1 or 2, the system is restored back to its initial state, except that the iodide ion is displaced in the crystal structure. A new reaction may then be thermally initiatied, and the accumulation of such processes results in diffusion of the iodide defect for arbitrary displacement along the channel (eq 1) or across channels (eq 2). Ion transport pathways are shutoff only when one iodide defect encounters another iodide defect, and thus we expect this transport to be most important at low iodide defect concentrations.

Figure 4. Potential energy scan of I3− + I− corresponding to snapshots in Figure 2.

qualitative observations from the AIMD simulations, this PES indicates that the I42− complex (b) and dissociated I3− + I− ions (a) are separated by an energy barrier as low as ∼1−2 kcal/mol. Interestingly, the I42− complex is the global minimum for the I− defect in the EMIM/I3 crystal. This surprising result is due to the strong electrostatic stabilization of the EMIM/I3 crystalline environment, and is unique to the condensed phase, as EMIM/ I4 is not globally stable for gas phase ion pairs.22 The other half of the reaction pathway involves dissociation of I42− into I3− + I− ions, with I− splitting off from the other side of the dianion. This second half reaction has a larger barrier (c) (∼5 kcal/mol) separating I42− (b) and dissociated I3− + I− ions (d). As discussed in Section 2, entropic contributions are insignificant, and the PES of Figure 4 is nearly identical to the free energy surface for the reaction (Figure 1). These results are direct proof that the Grotthuss exchange mechanism of eq 1 is thermally accessible in the condensed phase given specific ionic environments. The PES in Figure 4 is notably asymmetric, with differences in both barrier widths (∼2 Å compared to 3 Å) and heights (∼1−2 kcal/mol compared to 5 kcal/mol). Without the I− defect, all I3− anions have identical and symmetric counterion coordination within the pristine EMIM/I3 crystal due to the alternating rows of cations on both sides of a given anion channel. This symmetry is broken, however, with introduction of the I− defect. With an I− defect, the global minimum is the I42− complex, which as seen in Figure 2 “wraps around” the EMIM cation at the top of the anion channel. The broken symmetry is then most clearly understood by considering the two different I3−+I− dissociation events, starting from the I42− complex. At the I42− minimum (b), iodine atoms are coordinated by either the ethyl or methyl group of the top EMIM cation, and are each directly coordinated by ring atoms of EMIM cations at the bottom of the channel (Figure 2). To proceed from configuration (b) to (a), the iodide ion is passed to the neighboring top EMIM cation, across its methyl group; this results in an I3− “product” that is tilted within the anion channel similar to all other triiodide anions in the crystal. To proceed from (b) to (d), however, the iodide ion on the other side of I42− is passed to the other neighboring top EMIM D

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The Journal of Physical Chemistry B cation, this time across its ethyl group. The formed I3− product in the (d) state is tilted within the anion channel in an incongruous manner relative to the other triiodide anions in the crystal, which corresponds to the asymmetry of the energy barriers in Figure 4. This is further indicated by the significant rotation of the adjacent EMIM cation toward the I− anion at the transition state (c) in Figure 2. Therefore, while the (a) and (d) minima are necessarily symmetric after full relaxation, barrier asymmetry occurs due to different tilt of the I3− product formed when I42− dissociates along the two different pathways. The reaction energy of the cross-channel Grotthuss hopping involving I73− intermediates (Figure 3) is calculated using umbrella sampling. The free energy profile is shown in Figure 5,

even seemingly similar ionic crystals (BMIM/I) may exhibit very different energy barriers and reaction pathways due to subtle differences in ion topology. To quantify the magnitude of the relative electrostatic stabilization of the I42− complex in EMIM/I3, we computed an analogous I3−−I− dissociation scan in the gas phase. The comparison between the I3−−I− PES in the gas phase and EMIM/I3 crystal is shown in Figure 6. The energies are plotted

Figure 6. Comparison of I3− + I− ⇌ I42− reaction energy in EMIM/I3 crystal relative to gasphase.

relative to the minima in each phase over the range of the scan (while the gas phase minimum occurs at infinite separation, we consider the zero in energy as the largest possible separation of these species in the crystal, as indicated in Figure 4). From this comparison, we find that the nearly isoenergetic minima of I42− (b) and I3−+I− (a) are a result of an enhanced ∼7−8 kcal/mol stabilization of I42− compared to the gas phase, due to the electrostatic environment of the EMIM/I3 crystal. The snapshot of the global minimum in Figure 4 shows that the I42− complex fits perfectly within the alternating cation structure. The central EMIM ion above I4 2− directly coordinates the middle two iodine atoms, while the two neighboring EMIM ions below the channel symmetrically coordinate the outer I atoms of I42−. The quantitative stabilization energy of I42− is thus a direct result of both the size and shape of EMIM cations, and the packing arrangement of these cations proximal to the iodide channel. The correlation between the energetics and this specific coordination geometry suggests the general conclusion that the energy barriers and propensity for iodide Grotthuss transport in the condensed phase will be highly sensitive to the microscopic chemical details of the system. We further analyze the electrostatic stabilization and screening of the EMIM/I3 ionic crystal by performing an atomic charge analysis on the four iodine atoms at different points of the I3−−I− scan. This charge analysis, conducted for both the gas phase and crystalline environment, is presented in Figure 7. As a reference, a similar charge analysis on an isolated I3− anion gives charges of ∼ −0.5 on the two outer atoms, and a charge of ∼0.0 on the central iodine atom. In Figure 7, the two outer iodide atoms of I3− are labeled I1 and I3, and the approaching I− anion is labeled I4, with the scanned distance between I3 and I4 (charge on I2 is not shown but inferred from the residual). In the case of no electrostatic interaction between the I3− and I− anions, we expect charges of −0.5 for I1 and I3 and −1.0 for I4 (Figure 7 plots absolute magnitudes, with the negative sign implied). This “non-interacting” electronic structure is observed in the crystalline environment for I3−− I− separations of 5−6 Å and deviations from the I3− symmetric charge density are only observed at shorter contact distances

Figure 5. Potential of mean force for iodide transport mechanism of eq 2. The labels correspond to the snapshots in Figure 3. We note that the reaction coordinate corresponds to distinctly different I−I bonds for the left and right portion of the figure, as discussed in the text.

where the labels (b), (e), (f), and (g) correspond to the snapshots in Figure 3. The transition between the initial and final states (b) and (g) results in exchange transfer of an iodide ion (or I42−) between two adjacent anion channels of the crystal, across the row of EMIM cations. The rate limiting barrier for this process is ∼5 kcal/mol corresponding to the transition state (f), which involves dissociation of the I73− complex at its terminal I−I bond to form transient I62− + I−. While this barrier is several times thermal energy, this process is still kinetically accessible, and importantly provides a mechanism for cross-channel iodide exchange that couples with the single channel exchange process. 3.3. Hopping Is Facilitated by the Cations in the Crystal. The ionic arrangement in the EMIM/I3 crystal structure is primarily responsible for the relatively flat nature of the I3−−I− PES. At the global minimum, the I−I bond distances in I42− are 3.28, 2.97, and 3.40 Å with the middle bond being the shortest. This wide, ∼ 0.5 Å range of I−I bond lengths has been previously observed in other polyiodide crystals,21 and indicates the “softness” of such I−I interactions. As shown in Figure 2, the I42− complex is somewhat bent, and “wraps around” the central closest EMIM cation to maximize interactions with the positively charged hydrogen atoms on the cation; this interaction motif is similar to that observed for EMIM/polyiodide gas phase ion pairs.22 Throughout the I3−− I− dissociation scan, every iodine atom is always closely coordinated by EMIM cations on opposite sites of the ion channel. The I− anion is “passed” from one EMIM cation to another down the channel, and the staggered configuration of cations on opposite sides of the channel leads to nearly continuous cation/anion coordination along the reaction coordinate. From this observation, we believe that such a staggered and continuous cation arrangement is a key structural requirement for facile Grotthuss transport of iodine. Indeed comparison to the recent work of Grossi et al.23 indicates that E

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this additional pathway provides an important cross-channel coupling mechanism, allowing iodide ions to “jump” between adjacent channels. While the exchange between I− and I3− is confined to the single dimension along the anion channel, the existence of this second mechanism enables three-dimensional transport of iodide defects within the EMIM/I3 crystal structure. More generally, this finding suggests that there may be multiple reaction pathways and intermediates for iodide exchange in electrolytes, involving several or numerous polyiodide species, with the relative importance of these different pathways determined by the condensed phase structure, ion size/shape, and iodine concentration. Although some solid-state studies exist,15,16,24,25,36 most experimental studies that have empirically motivated the iodide Grotthuss exchange mechanism have been based on liquidphase electrolytes.3,4,8−14,17−19 A central question for the generality of our results to the liquid state concerns the proximity of I3− and I− anions in solution, since the EMIM/I3 crystal structure confines iodide to be no more than 7 Å from the closest triiodide anion. However, from our analysis of the anion electronic structure (charge partitioning), we conclude that electrostatic interactions between I3− and I− anions are largely screened beyond 4−5 Å distances due to the ionic environment of EMIM/I3. This important finding suggests that the intuitive electrostatic repulsion between I3− and I− may be largely balanced by cation/anion attractions in electrolytes, facilitating the close anion approach necessary for Grotthuss exchange. Finally, our present work provides design principles for developing new high-performance solid-state electrolytes for iodide transport, which is practically important for photoelectrochemical devices.25,36−38 Previous work has demonstrated that solid-state electrolytes composed of succinonitrile plastic crystals doped with iodide salts exhibit iodide transport rates that can exceed similar liquid or gel-based electrolytes. In these systems, the iodide transport was significantly affected by the type of cation, even though the diffusion rates of the cations themselves were much slower and seemingly uncorrelated.25,36 Our results suggest that in the solid state, cations primarily influence iodide transport through their electrostatic modulation of the Grotthuss exchange reaction potential energy surface(s). Optimal choice of cations should thus involve tuning their size, shape, and functionalization to facilitate electrostatic stabilization of the higher energy intermediates/ transition states in the Grotthuss pathway. From our present ab initio predictions, we suggest that future experimental measurements of the conductivity of EMIM/I3 crystals for various I− defect concentrations would be an interesting and important endeavor.

Figure 7. Charges of iodine atoms in I42− complex as a function of I3−−I− separation distance, 3.4, 4.0 5.0, and 6.0 Å, calculated in both the EMIM/I3 crystal as well as gas phase environment. The I42− complex is nearly colinear, and atoms are indexed 1−4 sequentially, with the dissociation scan occurring between I3 and I4 atoms (charges on I2 are not shown, but are inferred from the residual).

(3.4−4 Å). On the other hand, the I3− charges are never symmetric for any of the configurations in the gas phase, but rather the charge density is always polarized from the I3 to I1 atom, away from the I− (I4) anion. This charge density analysis therefore provides a complementary picture of the electrostatic screening within the EMIM/I3 ionic environment, and suggests that interactions between I3− and I− anions are largely screened beyond 4−5 Å distances. This result importantly suggests the transferability of our conclusions to other condensed phase environments (e.g., ionic liquids), as it suggests that close proximity of I3− and I− (necessary for Grotthuss exchange) is possible due to electrostatic screening, and is not only achieved by crystal structure constraints (as in EMIM/I3 crystals).

4. CONCLUSION AIMD simulations have been utilized to study iodide exchange in a low-defect content EMIM/I3 ionic crystal, providing important theoretical description of iodide Grotthuss transport in the condensed phase. We find that the empirically proposed exchange between I− and I3− (eq 1) is indeed thermally facile when the I42− intermediate is electrostatically stabilized by a condensed-phase ionic environment. For the EMIM/I3 crystal, the I42− intermediate has an enhanced stabilization of ∼7−8 kcal/mol relative to the gas phase, which results in nearly isoenergetic minima for I42− and I3−+I− in the crystal. We find that the free energy barrier for the I3−+I− ⇌ I42− reaction is as low as ∼1−2 kcal/mol in EMIM/I3, indicating fast kinetics and justifying our observation of this bond-breaking/formation process within our short, (∼10−15 ps) unconstrained MD simulations. The full iodide Grotthuss exchange process requires asymmetric formation/dissociation of I42−, which in EMIM/I3 is kinetically controlled by a larger (but still thermally accessible) ∼ 5 kcal/mol barrier from the second half-reaction. The asymmetry of the reaction barriers is due to incongruous tilt of the I3− product for one of the dissociation pathways, and it is in principle possible that alternative ionic environments will exhibit lower maximal barriers (∼1−2 kcal/mol) with a more symmetric PES for the full Grotthuss exchange process. Beyond verifying the occurrence of the typically proposed I− + I3− exchange mechanism, we have discovered an additionally important mechanism involving the formation of I 7 3− polyiodide intermediates. The thermal formation of such trivalent anions is nonintuitive, and depends on the strong electrostatic stabilization from the surrounding ionic environment. For macroscopic iodide transport in EMIM/I3 crystals,

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b09292. Movie of AIMD trajectory showing thermally driven halfreaction of eq 1 (MPG)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: +1 (608) 262-0258. ORCID

Jesse G. McDaniel: 0000-0002-9211-1108 F

DOI: 10.1021/acs.jpcb.7b09292 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

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Arun Yethiraj: 0000-0002-8579-449X Present Address ‡

School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by Department of Energy, Basic Energy Sciences through grant DE-SC0010328. Computational resources were provided by the Center for High Throughput Computing at the University of Wisconsin. The CHTC is supported by UW-Madison, the Advanced Computing Initiative, the Wisconsin Alumni Research Foundation, the Wisconsin Institutes for Discovery, and the National Science Foundation, and is an active member of the Open Science Grid, which is supported by the National Science Foundation and the U.S. Department of Energy’s Office of Science. This research was supported in part by National Science Foundation Grant CHE-0840494.

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