Understanding the Properties of Ionic Liquids: Electrostatics, Structure

Subscriber access provided by UNIV OF LOUISIANA

B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution

Understanding the Properties of Ionic Liquids: Electrostatics, Structure Factors, and Their Sum Rules Jesse Gatten McDaniel, and Arun Yethiraj J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b00963 • Publication Date (Web): 01 Apr 2019 Downloaded from http://pubs.acs.org on April 2, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Understanding the Properties of Ionic Liquids: Electrostatics, Structure Factors, and Their Sum Rules Jesse G. McDaniel∗,† and Arun Yethiraj‡ †School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 ‡Department of Chemistry , University of Wisconsin , 1101 University Avenue , Madison , Wisconsin 53706 E-mail: [email protected]

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The properties of room-temperature ionic liquids (ILs) may be viewed as resulting from a balance of electrostatic interactions that are tunable at short-range, but constrained to satisfy universal, asymptotic screening conditions. Short-range interactions and ion packing provides ample opportunity for chemical tunability, while asymptotic sum rules dictate that the long-range structure and charge oscillation is similar to that in molten alkali-halide salts. In this work, we study the structure factors and long-range electrostatic interactions in six ILs: The cation in all cases is 1-butyl3-methylimidazolium (BMIM+ ), and we study six anions, namely, tetrafluoroborate − − − (BF− 4 ), hexafluorophosphate (PF6 ), nitrate (NO3 ), triflate (CF3 SO3 ), bisfluorosul-

fonylimide ((FSO2 )2 N− ), and bistriflimide ((CF3 SO2 )2 N− ). To enhance insight, we compare with similar computer simulations of a primitive molten salt model, with and without the inclusion of electronic polarization. We emphasize universal similarities among ionic liquids and molten salts in the long-range ion ordering and the influence of electronic polarization on the screening conditions, while also characterizing important differences in the short-range electrostatic interactions. We show that polarization systematically reduces charge oscillations by as much as ∼ 0.5-1 ions per radial shell, which we argue is general to all room-temperature ionic liquids as well as molten salts. We suggest that a fundamentally important distinction among BMIM-based ionic liq˚−1 peak in the uids (with different anions) is the nature of the mid-range, ∼ 1 A charge-correlation structure factor; while this correlation is straightforward to analyze in computer simulations, it may often be hidden in X-ray and/or neutron scattering structure factors.

1

Introduction

From a chemist’s perspective, room temperature ionic liquids (ILs) seem very different from molten alkali-halide salts. The constituents of the former are often organic molecular ions which are bulky, polarizable, and may be functionalized by numerous organic chemical trans2


Page 2 of 43

Page 3 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


formations. From a physicist’s perspective, however, any differences between ILs and molten salts might appear minor compared to their fundamentally similar long-range Coulombic forces that largely dictate the system properties. In this work, we attempt to show that both perspectives are necessary in order to fully understand these fascinating systems. Specifically, ˚−1 ) of the charge-correlation structure we show that peaks in the mid-range region (∼ 1 A factor acts as distinctive signatures of the IL properties, and these peaks are significantly tuned by the size, shape, charge-distribution, and rigidity of the anions. On the other hand, the universal “sum-rules” or screening conditions dictate that the liquid structure of all ILs and molten salts is similarly altered by electronic polarization, which serves to reduce ion-ion correlation even at relatively short distances (∼ 6 ˚ A). Electrostatic interactions serve as the starting point for understanding the many diverse and often surprising properties of different ionic liquids. Strong Coulombic interactions between ions lead to very large liquid cohesive energies, on the same order as cohesive energies of ionic crystals or molten salts. These large cohesive energies give rise to the high viscosities and hence slow dynamics, and relatively high melting points and glass transition temperatures. 1 In fact, it is because of these large cohesive energies that similar, but more “symmetric” organic ions instead form ionic crystals at room temperature, and room temperature ILs are liquid only because of frustrated packing due to mismatch in ion size, shape, and asymmetry. The dominant electrostatic interactions are fundamentally intertwined with the IL liquid structure itself. There is a rigorous, quantitative connection between liquid structure and electrical properties given by mutual constraints known as “sum rules.” For example, ion-pair correlation functions are not independent, but must satisfy net neutrality conditions. Furthermore, the extent of ion screening, which has an important influence on the conductivity and dielectric response, may be inferred from properties of the pair-correlation functions themselves. The goal of the present work is to provide a clearer picture of the connection between the liquid structure and the electrical properties of ionic liquids, and the distinguishing similarities and differences among ILs.

3



Page 4 of 43

It is difficult to obtain information about the electrical properties of different ionic liquids from X-ray or neutron scattering studies, due to the practical difficulty in decomposing the total structure factor into partial structure factor contributions from like-ion and counter-ion correlations. Araque et al. 2 have shown that such decomposition/grouping of partial structure factors is necessary to explicitly decouple charge and apolar contributions to the observed scattering intensity. We will show that the charge-correlation structure factor, which is a distinctly different quantity than that observed from X-ray and/or neutron scattering experiments, provides a collective order parameter that clearly distinguishes electrostatic differences among ionic liquids. Before discussing differences between the scattering structure factor and charge-correlation structure factor, we briefly summarize the interpretation of IL liquid structure using scattering techniques. Experimental X-ray and neutron scattering studies have revealed much insight into the structural properties of ionic liquids. 3–10 The very illuminating discussion of Araque et al. 2 which focuses on interpreting the structure of ionic liquids from X-ray and neutron scattering observables, provides particularly important context for the present work. These authors illustrate that X-ray (or neutron) scattering of ionic liquids should be interpreted through decomposition of the structure factor into three distinctly separate domains. Using the terminology of Araque et al., 2 these correspond to the “polarity”, “charge”, and “adjacency” domains. The “polarity” domain covers wavevectors . 0.6 ˚ A

−1

, corresponding to tens of

˚ A correlation lengthscales, and reflects heterogenous polar/non-polar domain formation in ionic liquids. Peaks in this region generally occur for ionic liquids with longer-chain cations for which the alkyl chains segregate into separate non-polar domains; 2,6,7 such long-range, heterogenous domain formation is not observed for BMIM+ -based ionic liquids, 6,7 and is not the focus of this work. The “adjacency” domain encompasses wavevectors k & 1.2 ˚ A−1 , corresponding to lengthscales that reflect “nearest-neighbor” or “adjacent” ion interactions. The “charge” alternation domain occurs at the intermediate wavevectors, generally 0.7 . k . 1.1 ˚ A−1 . The authors highlight the fact that the “charge alternation” peaks are often

4


Page 5 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


“missing” in the structure factors of ILs, not because charge-alternation isn’t present (it always is!), but because of cancellations between like-ion and counter-ion correlation in the contribution to X-ray/neutron scattering intensity. To provide explicit context for the above discussion, in Figure 1 we show both the scattering structure factor “SN N (k)” and charge-correlation structure factor “SZZ (k)” for [BMIM+ ][BF− 4 ] . SN N (k) is the observable from X-ray (or neutron) scattering experiments, while SZZ (k) may be determined utilizing computer simulations (these quantities are defined in the next section). It is immediately evident that the peaks of these structure factors correspond to distinctly different domains in the liquid; SZZ (k) exhibits a peak at ∼ 1 ˚ A−1 in the ˚−1 in the “adjacency” do“charge alternation” domain, while SN N (k) has a peak at ∼ 1.5 A main. There is little to no structure in the small wavevector (. 0.6 ˚ A

−1

) polarity domain,

which would only appear for more amphiphilic ions (e.g. longer chain alkyl-imidazolium cations). Thus for [BMIM+ ][BF− 4 ] , the primarily important “charge alternation” correlation is not apparent in the X-ray structure factor due to cancellations between scattering contributions of like-ion and counter-ion correlations. Figure 1 demonstrates that the chargecorrelation, SZZ (k), and scattering, SN N (k), structure factors are distinct quantities that each provide separate and unique information about the liquid state. 11,12 While SN N (k) has been well-characterized in ILs, 2–10 SZZ (k) has not. We will demonstrate that analysis of SZZ (k) provides essential information on both similarities and differences of the electrical properties among ionic liquids. In this work, we characterize the fundamental electrical properties of ILs through analysis of their long-range charge oscillations, charge correlation structure factors, and the corresponding asymptotic limits (sum-rules). We use molecular dynamics (MD) simulations to study six different room-temperature ionic liquids composed of 1-butyl-3-methylimidazolium − (BMIM+ ) cations and either tetrafluoroborate (BF− 4 ), hexafluorophosphate (PF6 ), nitrate − − (NO− 3 ), triflate (CF3 SO3 ), bisfluorosulfonylimide (FSI, (FSO2 )2 N ), and bistriflimide (TFSI,

(CF3 SO2 )2 N− ) anions; we also compare to simulations of a primitive molten salt (NaCl)

5



5

4

10

1000 800

8

600

2

6 400

4

200

2 0 0

0.2 0.4 0.6 0.8

1

-1

1.2 1.4 1.6 1.8

-1

6

-6

r (Å)

10 8 7

2

40 20

SNN*V /kBT (10 bar )

12

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 43

0 2

k (Å )

Figure 1: Comparison of scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors for [BMIM+ ][BF− 4] . model 11 for general insight. While scattering structure factors SN N (k) have been previously determined for some of these ILs, 2,5–7,9 to our knowledge the charge correlation structure factors for the majority of these ILs have not been previously characterized. 18,19 We show that analysis of the charge correlation structure factors, SZZ (k), provides valuable insight into the electrostatic properties of the ILs, including the lengthscales of important Coulombic interactions and electrostatic screening; much of this interpretation is not possible based on scattering structure factors alone. Furthermore, we illustrate the fundamental and general influence of electronic polarization on the structure and properties of ionic liquids and molten salts that results from the modulated asymptotic limit of the Stillinger-Lovett perfect screening condition. Based on this comprehensive analysis, we conclude that the charge oscillations within room-temperature ionic liquids and molten salts are quite similar in both their intermediate/long range behavior and modulation due to electronic polarization. However, the precise molecular structure of the organic ions of ionic liquids can lead to significant differences in Coulombic interactions at short/intermediate range (∼ 6 ˚ A), as clearly observed by the presence or absence of ∼ 1 ˚ A−1 peaks in SZZ (k), and may be the primary reason for

6


Page 7 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the wide property variation of ILs.

2

Theory/Methods

The charge correlation, SZZ (k), and scattering, SN N (k), structure factors are defined as, 12

SZZ (k) =

1 hˆ ρZ (k)ˆ ρZ (-k)i V

(1)

SN N (k) =

1 hˆ ρN (k)ˆ ρN (-k)i V

(2)

and

where V is the volume, h...i denotes an ensemble average, k is the momentum transfer variable, ρˆZ (k) =

N X

qi eik·ri

(3)

fi (k)eik·ri

(4)

i=1

ρˆN (k) =

N X i=1

fi (k) is an atomic form factor, qi is an atomic partial charge, ri is the position (of atom i ), and the summations run over all “N” atoms in the system. Note that we use the same notation (e.g. SZZ /SN N ) as employed in Hansen and McDonald’s text 12 to facilitate connection with their discussion. We also note that our definitions are slightly different (a factor of density) so that the electrostatic sum rule takes a somewhat simpler form, and we also additionally incorporate form factors into SN N to explicitly connect with X-ray scattering. The structure factors are related to Fourier transform of the pair distribution functions that characterize the liquid structure. 12 The essential difference between structure factors is the different “weighting” of each pairwise correlation; in the scattering structure factor, the weight of each pair correlation is essentially proportional to the number of electrons of each atom, while in the charge-correlation structure factor the weight is given by the partial atomic charges. This difference in “weight” is the origin of the different information conveyed 7



Page 8 of 43

by the structure factors. The scattering structure factor may be insensitive to differences between cations and anions, if the elemental composition of the different molecular ions have similar electron count. The charge correlation structure factor however, weighted by partial atomic charges, readily distinguishes cation and anion correlation. The fundamental difference between structure factors is further illustrated by their different asymptotic limits. The asymptotic limit of the charge-correlation structure factor is known as the Stillinger-Lovett (SL) sum rule or second moment screening condition and takes the general form, 11,13–19 SZZ (k) ∞ − 1 4π lim =1− 2 kB T |k|→0 k ∞

(5)

where ∞ is the infinite frequency dielectric response. The ∞ term results from the (adiabatic) electronic polarization of the system. Equation 5 is a “perfect screening” condition, resulting from the assumption that over sufficiently long lengthscale an electrolyte will perfectly screen any electric field, i.e the dielectric function at small wavevectors approaches infinity. Note that as recently discussed, 18,19 and will be further illustrated in this work, the ∞ term in Equation 5 which is due to the (adiabatic) electronic polarization of the system, implies that computer simulations with and without explicit treatment of electronic polarization will fundamentally differ in their prediction of long-range ion structure. The physical interpretation is that the polarization-mediated electronic screening (∞ ) reduces the requisite screening from ion structuring that is needed to perfectly screen electric fields within the electrolyte. We note that a complementary interpretation is that the sum rule of Equation 5 may be used as an exact approach to calculate ∞ , without resorting to approximations such as the Clausius-Mossotti relation. 17,20 The asymptotic limit of the scattering structure factor (within our definition) is given by SN N (k) kB T lim P χT 2 = |k|→0 ( V2 fi (k))

8


(6)

Page 9 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where χT is the isothermal compressibility of the liquid. The different asymptotic limits (Equations 5 and 6) of SZZ and SN N reflect the different physics elucidated by these structure factors. These limits are manifestations of linearresponse or fluctuation-dissipation theory, 12,21 but the charge and “number-density” fluctuations, reflected in SZZ and SN N respectively, connect to system responses (susceptibilities) of different driving force. Charge fluctuations (SZZ ) characterize response to external electric fields, while density fluctuations (SN N ) characterize response to mechanical stimuli (external pressure). Based on these considerations, along with the accompanying data presented in this manuscript, we suggest that SZZ serves as a much more indicative collective variable for determining IL properties than does SN N . We compute the structure factors SZZ and SN N from Equations 1 and 2 directly in reciprocal space, using an approach analogous to that employed in the well-known, particlemesh Ewald (PME) method. 22 The connection to the PME approach is obvious by noting that the SZZ (k)/k2 term in Equation 5 is proportional to the electrostatic energy of the system at wavevector k. For completeness, we outline this procedure in the Supporting Information. We conduct molecular dynamics simulations of the six ionic liquids, [BMIM+ ][BF− 4] , − − + + + − [BMIM+ ][PF− 6 ] , [BMIM ][NO3 ] , [BMIM ][CF3 SO3 ] , [BMIM ][(FSO2 )2 N ] , and

[BMIM+ ][(CF3 SO2 )2 N− ] , all at 300 K, 1 bar except for [BMIM+ ][NO− 3 ] which is studied at 320 K (to be sufficiently above the melting point). All simulations utilize the ab initio, polarizable SAPT-FF force field, which has been developed previously. 23,24 Comprehensive force field parameter files (OpenMM “xml” format) are provided as Supplementary Material, and additional parameters and ab initio benchmarks for the nitrate anion are given in the Supporting Information. Simulations are conducted with the OpenMM simulation software, 25 utilizing a dual-Langevin thermostat scheme 26 for efficient treatment of Drude oscillators, with a 1 ps−1 friction coefficient for both thermostats; pressure coupling is achieved with a Monte Carlo barostat. 25 These IL simulations employ relatively large systems of 1600 ion

9



pairs (1760 for [BMIM+ ][NO− 3 ] ) to facilitate investigation of the small wavevector limit. Simulations are run for 50 ns on Nvidia GTX-1080-Ti GPUs. In addition to these IL simulations, for comparison we simulate the primitive molten salt model, studied by Hansen and McDonald. 11 We employ the same simulation parameters as Hansen and McDonald except we utilize a system that is 125 times bigger to facilitate study of small wavvectors, namely 13500 ions pairs, with simulation cell lengths of 9.8 nm (fixed density), at 1267 K. These (symmetric) ions have an effective mass of 28.85 amu, and may be considered as a primitive model of molten NaCl. 11 In addition, we conduct analogous simulations in which we add polarizabilities of 2.1 ˚ A3 to Cl− ions, which is a reasonable value. 27 We note that simulations ˚3 ) on Na+ lead to relatively similar results as that additionally include polarization (0.5 A the simulations with polarization on Cl− only (and this latter data is not presented). We illustrate that electronic polarization fundamentally alters the ion-correlation in ILs by its contribution to the asymptotic screening condition (Equation 5). We compare simulations of the SAPT-FF force field for which polarization has been “turned-off”; this is a meaningful comparison for the following reasons: First, the polarizabilities of the SAPT-FF force field have been determined entirely on the basis of ab initio, molecular linear response calculations; 28 this should be contrasted with empirically determined polarizabilities, which may implicitly reflect additional energetic contributions. Second, polarization has a very minor effect on the IL density and cohesive energy, and thus its omission does not substantially perturb these fundamental properties (Table S1, Supporting Information). This further indicates that the influence of polarization on the ion structure is a direct result of the physics incorporated in Equation 5, rather than an energetic or density mediated effect. As a further benchmark, we compare to predictions from the (non-polarizable) force field of Canongia Lopes and Padua 29,30 for [BMIM+ ][(FSO2 )2 N− ] (Figure S1 and S2).

10


Page 10 of 43

Page 11 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3

Results

We first broadly discuss the structural analysis of ionic liquids (and molten salts), and present − + results for [BMIM+ ][BF− 4 ] for context. We then conduct similar analysis for [BMIM ][PF6 ] − + + − (Section 3.1), [BMIM+ ][NO− 3 ] (Section 3.2), [BMIM ][CF3 SO3 ] (Section 3.3), [BMIM ][(FSO2 )2 N ]

(Section 3.4), [BMIM+ ][(CF3 SO2 )2 N− ] (Section 3.5), and molten NaCl (primitive model, Section 3.6). One of the most fundamental structural properties of ionic liquids and molten salts are the anti-correlated like-ion and counter-ion oscillations within the liquid. 11 These anti-correlated charge oscillations are related to the net-neutrality condition (or “first” sum-rule), which is Z

"

∞

4πr2

# X

0

qα ρα gαβ (r) dr = −qβ

(7)

α

where, α, β denote either cations or anions, gαβ (r) is the ion-ion radial distribution function (RDF), and ρα is the ion type number density. Equation 7 must rigorously hold as the integration limit goes to infinity, but it is also insightful to evaluate the distance-dependent sum, namely Z 0

"

r

4πr02

# X

β qα ρα gαβ (r0 ) dr0 = −qsum (r)

(8)

α

Which represents the net charge within a spherical volume of radius “r” centered at a tagged ion (and not including the tagged ion charge). We will refer to Equations 7 and 8 interchangeably as the charge neutrality conditon or first sum rule. This charge neutrality condition implies that the like-ion and counter-ion correlation functions are coupled, leading to anti-correlated charge oscillations. Charge oscillations are illustrated in Figure 2 , which shows the cation/anion RDFs and the “sum-rule” of Equation 8 evaluated as a function of integration distance. The relatively large systems that we study allow for evaluation of RDFs and the sum rules out to ∼ 40 ˚ A distances, which elucidate the extent of charge oscillations in the liquid. Because the total 11



number of ions grows as r2 (Jacobian) as a function of separation distance,“small wiggles” in g(r) at long distance make significant contribution to the charge oscillations, as seen in Figure 2. In Figure 2, the net integrated ion charge at a distance from a given BF− 4 anion + is depicted by the “qan sum ” curve, and the similar quantity for BMIM cations is depicted

by “qcat sum ” (Equation 8). These curves clearly depict the charge oscillations in the liquid, which evidently extend to very long-range (>40 ˚ A). The minima/maxima of qan sum (r) and qcat sum (r) correspond to inflection points in the ion-ion RDFs (g(r)’s), and thus depict shells of cations or anions surrounding the tagged ion. At a given distance from a BF− 4 anion, the an net enclosed charge (within the sphere) qan sum (r) oscillates between values of ∼ -1 < qsum

< 3 ; for BMIM+ cations, the analogous charge oscillations qcat sum (r) are between ∼ -2.5 < qan sum < 0.5. Note according to the definitions of Equations 7 and 8, these values do not include the charge of the tagged ion itself. While the shape/magnitude/structure of these charge oscillations somewhat depends on our choice of atom pairs for computing the g(r)’s, the qualitative interpretation is independent of this choice and so is the magnitude of the long-range oscillations.

12


Page 12 of 43

Page 13 of 43

5

3

anion-anion cation-cation cation-anion an qsum

2

qsum

4

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


cat

1 0 -1 -2 -3 0

5

10

15

20

25

30

35

40

r (Å) Figure 2: Ion-ion RDFs (g(r)), and corresponding charge oscillations (Equation 8) in − an cat [BMIM+ ][BF− 4 ] ; qsum depict charge oscillations away from a BF4 anion, and qsum depict charge oscillations away from a BMIM+ cation. RDFs are computed using B atoms of anion, and ‘C1’ atoms of cations, where C1 is the bridging (N-C-N) carbon of the imidazolium ring. These charge oscillations, and correspondingly the ion-ion correlation functions, g(r)’s, are significantly modulated by electronic polarization due to the asymptotic limit of Equation 5. To explicitly illustrate this important polarization dependence, all remaining figures in this work (unless otherwise noted) compare predicted results computed with (solid lines) and without (dashed lines) polarization (see Methods section for discussion of such simulacat tions). In Figure 3, we plot the charge oscillations qan sum (r) and qsum (r) as in Figure 2, but

explicitly depicting the polarization contribution, by comparing analysis from polarizable and non-polarizable simulations. It is clear that electronic polarization significantly reduces the magnitude of charge oscillations, by as much as ∼ 0.5-1 net ions per radial shell. This is a result of Equation 5, which necessitates greater long-range ion structure for non-polarizable simulations (∞ = 1). Importantly, the perfect screening requirement (Equation 5) results in modulated ion structure at both short (∼ 6˚ A) and intermediate (∼ 10-20˚ A) distances. These significant differences in ion structure are the fundamental reason for the significant influence of electronic polarization on ionic liquid properties, most notably the ion dynamics. 18–20,31–37 13



4

an

qsum

3

cat

qsum

2

qsum

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 43

1 0 -1 -2 -3 0

10

20

30

40

r (Å) − an Figure 3: Charge oscillations in [BMIM+ ][BF− 4 ] away from tagged BF4 anion, qsum (blue), and away from tagged BMIM+ cation, qcat sum (red); as in Figure 2, but comparing predictions between polarizable (solid lines) and non-polarizable (dashed lines) models.

The charge correlation structure factor SZZ and scattering structure factor SN N for [BMIM+ ][BF− 4 ] are shown in Figure 4. In this Figure (and all similar figures in this work) P we plot SZZ /k 2 in units of kB T/4π and SN N *V2 /kB T (normalized by ( fi (k))−2 ) in units of 10−6 bar−1 so that the asymptotic limits corresponding to the SL sum rule (Equation 5) and compressibility (Equation 6) are clearly read by eye. Both the shape and asymptotic limit (compressibility) of the computed scattering structure factor are in excellent agreement with experimental X-ray scattering 38 and compressibility measurements. 39 As noted, SN N shows no signature of the characteristic charge oscillation (Figure 3) in [BMIM+ ][BF− 4] , ˚−1 region; this is not because such correlations don’t which would be evident in the ∼ 1 A exist, but rather is due to subtle cancellation of contributions from like-ion and counter-ion correlation. 2 Also, the predicted SN N and its asymptotic limit (compressibility) are relatively insensitive to the inclusion of polarization, ( χT = 44 and 42 * 10−6 bar−1 from polarizable and non-polarizable simulations respectively). Taken together, such observations could easily be misinterpreted to undermine the importance of charge oscillations and the influence of polarization on the structure and properties of [BMIM+ ][BF− 4 ] . The charge correlation 14


Page 15 of 43

structure factor SZZ , on the other hand, clearly reveals the fundamentally important charge ˚−1 wavevecoscillations and influence of polarization. SZZ shows a dominant peak at ∼ 1 A tors, corresponding to the real-space charge oscillations shown in Figure 3, with period of ∼ 6 ˚ A. In addition, the charge correlation structure factor is substantially altered by polarization in both its asymptotic limit (Equation 5) as well as the significant reduction in amplitude ˚−1 peak. The reduction in amplitude of the ∼ 1 A ˚−1 peak is the reason for the of the ∼ 1 A polarization-mediated reduction in charge oscillation in the liquid (Figure 3), and this effect stems from the SL screening condition (Equation 5). We find these conclusions are general to all other ionic liquids and molten salts studied in this work; in particular, the polarization induced shift in the asymptotic limit of SZZ modulates the magnitude of charge oscillations in the liquids, thus altering the ion structure over all lengthscales. The magnitude of these ˚−1 region of SZZ , but may often be charge oscillations is generally indicated by the ∼ 1 A hidden in SN N . 5

4

14

1200 1000

12 800

10 8

2

600

6

400

4 200

2 0 0

0.2 0.4 0.6 0.8

1

-1

1.2 1.4 1.6 1.8

-1

6

-6

r (Å)

10 8 7

2

40 20

SNN*V /kBT (10 bar )

16

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 2

k (Å )

Figure 4: Scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors of [BMIM+ ][BF− 4 ] and their asymptotic limits (Equation 5, 6). Results from simulations with electronic polarization are solid lines, and non-polarizable simulations are the corresponding dashed lines. The red and black dashed horizontal lines indicate the SL sum rule of polarizable and non-polarizable simulations respectively. Based upon the comprehensive data presented in this work along with the rigorous asymp15



totic requirement (Equation 5), we show that polarization significantly modulates charge oscillations in all room-temperature ionic liquids as well as molten salts. For all ionic liquids studied in this work, we find the asymptotic value, lim|k|→0 SZZ /k 2 ∼ 0.5 (units of kB T/4π), corresponding to an optical dielectric constant of ∞ ∼ 2 (Equation 5) predicted with the polarizable SAPT-FF force field. We generally find slightly larger values of ∞ for the ILs composed of bigger, more polarizable ions (e.g. (FSO2 )2 N− , (CF3 SO2 )2 N− ); we estimate that our employed thermal (low-temperature) treatment of Drude oscillators may affect the prediction of ∞ by ∼ 10-20% (relative to an adiabatic, SCF treatment of polarization 40 ). Because non-polarizable force fields necessarily have ∞ =1, they always predict artificially enhanced ion structure and charge oscillations as a consequence of Equation 5, which is cat shown by our analysis of qan sum (r) and qsum (r) in the six ionic liquids and primitive molten

salt. Electronic polarization reduces (in magnitude) the constraint on ion structure imposed by the perfect screening condition (Equation 5). Employing this perspective, one could consider a “zeroth” order ion structure corresponding to the non-polarizable ion model satisfying Equation 5 with value of ∞ =1. Electronic polarization, then, allows ions to re-pack and rearrange from this zeroth order structure due to enhanced screening, and thus diminished asymptotic structural constraint (∞ >1). The extent to which this ion “rearrangement” involves the cations, anions, or both, will depend on the nature of the ionic liquid or molten salt, and the size, shape, conformational flexibility, and polarization of the ions. For [BMIM+ ][BF− 4 ] which consists of relatively small anions and larger, more polarizable cations, cat the polarization-mediated reduction in charge oscillations (qan sum (r) and qsum (r), Figure 3) is

primarily due to reduced anion-anion correlation. The fact that anion-anion correlations in [BMIM+ ][BF− 4 ] (rather than cation-cation, or cation-anion) are most impacted by the screening condition (Equation 5), is not only due to the smaller size and greater charge density of the anions, but is also because the cations are more polarizable, with the latter interpretation confirmed by our molten salt simulations (Section 3.6). In Figure 5, we show the

16


Page 16 of 43

Page 17 of 43

− − + BF− 4 -BF4 correlation function in [BMIM ][BF4 ] as computed with and without polarization.

It is clear that polarization significantly reduces anion-anion correlation at all distances, including the short range (∼ 6 ˚ A) correlation of neighboring anion shells (first peak). While the reduced long-range correlation (> 20˚ A) may at first glance appear minor since 0.9 < g(r) < 1.1 at these distances, the r2 Jacobian makes such differences significant, as they lead to the substantial differences in charge oscillation shown in Figure 3. It is important to note that certain ILs may exhibit even more pronounced polarization-mediated “structural rearrangement” as is the case for the lower viscosity IL [BMIM+ ][(FSO2 )2 N− ] (Section 3.4).

3

BF4-BF4

1.1

1

2

0.9 15

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20

30

25

35

40

1

0 5

10

15

20

r (Å) Figure 5: Anion-anion RDF in [BMIM+ ][BF− 4 ] computed using B atoms of anions, from simulations with (solid line) and without (dashed line) electronic polarization.

3.1

[BMIM+ ][PF− 6]

In Figure 6a), we show calculations of the charge correlation structure factor, SZZ /k 2 , the cat scattering structure factor, SN N , and in Figure 6b) the charge oscillations qan sum (r) and qsum (r)

in [BMIM+ ][PF− 6 ] at 300K, 1 bar, computed with and without electronic polarization. We note that our computed SN N is in good agreement with corresponding experimental Xray (and neutron) scattering measurements reported by Triolo et al., 5 and the predicted 17



5

4

14

1200

4

1000

3

12 800

10 8

2

600

6

400

4 200

2 0 0

0.2 0.4 0.6 0.8

1

-1

1.2 1.4 1.6 1.8

-1

6

-6

r (Å)

10 8 7

2

40 20

SNN*V /kBT (10 bar ) qsum

16

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0 2

Page 18 of 43

an

qsum cat

qsum

2 1 0 -1 -2 -3 0

10

20

30

40

r (Å)

k (Å )

(a)

(b)

Figure 6: a) Scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors and their asymptotic limits (Equation 5, 6) and b) charge oscillations in [BMIM+ ][PF− 6 ] away from − an + cat tagged PF6 anion, qsum (blue), and away from tagged BMIM cation, qsum (red). Results from simulations with electronic polarization are solid lines, and non-polarizable simulations are the corresponding dashed lines. In a), the red and black dashed horizontal lines indicate the SL sum rule of polarizable and non-polarizable simulations respectively, and in b) the dashed lines indicate the first sum rule (Equation 7). compressibility (χT = 40 and 36 * 10−6 bar−1 from polarizable and non-polarizable simulations respectively) is also in good agreement with experiment. 39 Unlike [BMIM+ ][BF− 4] ˚−1 region of SZZ /k 2 . , [BMIM+ ][PF− 6 ] exhibits only a relatively small peak in the ∼ 1 A ˚−1 in the scattering structure factor (SN N ) of Also, there is a small shoulder at ∼ 1 A − + [BMIM+ ][PF− 6 ] , which isn’t present in the SN N of [BMIM ][BF4 ] (consistent with experi− cat + mental observations 5,38 ). The charge oscillations qan sum (r) and qsum (r) in [BMIM ][PF6 ] are

∼ 0.5 units larger in magnitude compared to the corresponding quantities in [BMIM+ ][BF− 4] , indicating more ion structure and a greater net number of counterions per radial ion shell in [BMIM+ ][PF− 6 ] . While these charge oscillations are reduced in magnitude due to electronic polarization (as is the case for all ILs), the polarization effect is slightly less significant at intermediate distances than was the case for [BMIM+ ][BF− 4 ] . Anion-anion RDFs are shown in Figure S3, indicating that correlation is reduced at intermediate and long range due to polarization, while the short-range modulation is slightly less significant than was the case

18


Page 19 of 43

for [BMIM+ ][BF− 4] .

[BMIM+ ][NO− 3] 40 20

r (Å)

10 8 7

6

5

4

16

4

1200

3

1000

-6

12 10

800

8

600

2

2

14

1400

6

400

4

200

2 0 0

-1

18


3.2

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2 0.4 0.6 0.8

1

-1

1.2 1.4 1.6 1.8

0 2

an

qsum cat

qsum

2 1 0 -1 -2 -3 0

10

20

30

40

r (Å)

k (Å )

(a)

(b)

Figure 7: a) Scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors and their asymptotic limits (Equation 5, 6) and b) charge oscillations in [BMIM+ ][NO− 3 ] away from − + cat an tagged NO3 anion, qsum (blue), and away from tagged BMIM cation, qsum (red). Depiction of curves is analogous to plots in Figure 6. Our simulations of [BMIM+ ][NO− 3 ] are conducted at 320 K, 1 bar (rather than 300 K), to stay sufficiently above the melting point of this IL. We note that structural properties of ILs are relatively insensitive to ∼ 20 degree temperature differences (of course, in the absence of a phase transition), so direct comparison with the other ILs at 300 K is valid (comparison of dynamical properties, however, would require extrapolation). In Figure 7a), we show calculations of the charge correlation structure factor, SZZ /k 2 and the scattering structure factor, SN N , of [BMIM+ ][NO− 3 ] . In Figure 7b), we show corresponding charge cat oscillations qan sum (r) and qsum (r); all properties are computed with and without electronic

polarization. The compressibility from the asymptotic limit of SN N is computed to be χT = 41 and 39 * 10−6 bar−1 from polarizable and non-polarizable simulations respectively. In general, the structure factors SZZ /k 2 and SN N appear very similar to the same quantities in ˚−1 wavevectors in SZZ /k 2 , similar [BMIM+ ][BF− 4 ] . There is a very pronounced peak at ∼ 1 A 19



to but of slightly greater magnitude to the corresponding peak in SZZ /k 2 of [BMIM+ ][BF− 4] . Like [BMIM+ ][BF− 4 ] , there is no shoulder in this charge-alternation region in the scattering structure factor, SN N , apparently due to cancelling contributions from like-ion and countercat ion correlation. The charge oscillations, qan sum (r) and qsum (r), are slightly lower in magnitude

than the oscillations in [BMIM+ ][BF− 4 ] , corresponding to slightly fewer net counterions per ion shell. The polarization effect on the short and intermediate range ion structure/Coulomb ˚−1 peak in interactions is as significant as in [BMIM+ ][BF− 4 ] , significantly reducing the ∼ 1 A SZZ /k 2 (Figure 7a), and reducing the magnitude of charge oscillations (Figure 7b). Anionanion RDFs are shown in Figure S4, and the shape, magnitude, and influence of polarization are all very similar to the corresponding anion-anion RDF of [BMIM+ ][BF− 4 ] (Figure 5). We − note that similar influence of polarization on NO− 3 -NO3 correlation was reported by Yan et

al. 31

[BMIM+ ][CF3 SO− 3] 40 20

r (Å)

10 8 7

6

5

4

1800

4

1600 1200 1000 800 600 400

-1 -6

1400

2

2

26 24 22 20 18 16 14 12 10 8 6 4 2 0 0


3.3

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 43

200 0.2 0.4 0.6 0.8

1

-1

1.2 1.4 1.6 1.8

0 2

an

qsum cat

3

qsum

2 1 0 -1 -2 -3 0

10

20

30

40

r (Å)

k (Å )

(a)

(b)

Figure 8: a) Scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors and their asymptotic limits (Equation 5, 6) and b) charge oscillations in [BMIM+ ][CF3 SO− 3 ] away − an + cat from tagged CF3 SO3 anion, qsum (blue), and away from tagged BMIM cation, qsum (red). Depiction of curves is analogous to plots in Figure 6.

20


Page 21 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


In Figure 8, we show characterization of the liquid structure of [BMIM+ ][CF3 SO− 3 ] at 300K, 1 bar. We predict compressibilities of 55 and 50 * 10−6 bar−1 from polarizable and − + non-polarizable simulations respectively. Similar to [BMIM+ ][BF− 4 ] and [BMIM ][NO3 ] ,

˚−1 region of the charge corre[BMIM+ ][CF3 SO− 3 ] exhibits a large magnitude peak in the ∼ 1 A lation structure factor, SZZ /k 2 (Figure 8a); in fact, the peak in SZZ /k 2 for [BMIM+ ][CF3 SO− 3] is the largest such peak in the six ionic liquids investigated. Unlike [BMIM+ ][BF− 4 ] and [BMIM+ ][NO− 3 ] , however, there is a small shoulder at this wavevector region in the scattering structure factor, SN N , of [BMIM+ ][CF3 SO− 3 ] , due to incomplete cancellation of like-ion cat and counter-ion correlation. The charge oscillations qan sum (r) and qsum (r) (Figure 8b) in − − + + [BMIM+ ][CF3 SO− 3 ] appear similar to those in [BMIM ][BF4 ] and [BMIM ][NO3 ] , with

electronic polarization significantly reducing these oscillations at all lengthscales. AnionAnion RDFs for [BMIM+ ][CF3 SO− 3 ] are given in Figure S5, with correlations computed for both charged (-SO3 ) and hydrophobic (-CF3 ) groups. Charged-group correlation (Figure S5a) appears very similar to the corresponding anion-anion RDFs in [BMIM+ ][BF− 4 ] and [BMIM+ ][NO− 3 ] , with similar polarization modulation. The RDF between hydrophobic groups of the triflate anions (Figure S5b) indicates some amount of hydrophobic packing, as previously analyzed by Schwenzer et al. 41

21



[BMIM+ ][(FSO2 )2 N− ] 6

5

4

16

2

14

4

1000

3

800

12 10

600

8

400

6 4

200

2 0 0

1200

0.2 0.4 0.6 0.8

1

-1

1.2 1.4 1.6 1.8

-1

r (Å)

10 8 7

-6

40 20

2

18


3.4

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 43

0 2

an

qsum cat

qsum

2 1 0 -1 -2 -3 0

10

20

30

40

r (Å)

k (Å )

(a)

(b)

Figure 9: a) Scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors and their asymptotic limits (Equation 5, 6) and b) charge oscillations in [BMIM+ ][(FSO2 )2 N− ] away + cat from tagged (FSO2 )2 N− anion, qan sum (blue), and away from tagged BMIM cation, qsum (red). Depiction of curves is analogous to plots in Figure 6. The charge correlation and scattering structure factors of [BMIM+ ][(FSO2 )2 N− ] are shown in Figure 9a), and charge oscillations of the ionic liquid are shown in Figure 9b); all properties are computed at 300K, 1 bar. We predict compressibility values of χT = 43 and 35 * 10−6 bar−1 from polarizable and non-polarizable simulations respectively. For [BMIM+ ][(FSO2 )2 N− ] , we find the exceptional behavior that the scattering structure factor, SN N , is significantly altered by electronic polarization. [BMIM+ ][(FSO2 )2 N− ] exhibits a small shoulder in the charge alternation region of SN N , and this shoulder shifts by ∼ 0.1-0.2 ˚ A−1 to smaller wavevectors (longer real-space distance) with polarization. This positional shift in the shoulder of SN N is due to restructuring of ions such that correlation of ion shells shifts to longer lengthscales, as is clearly seen in the modulated charge oscillations, qan sum (r) + − and qcat sum (r), shown in Figure 9b). It is interesting to note that [BMIM ][(FSO2 )2 N ] ex-

hibits relatively low viscosity compared to the seemingly similar [BMIM+ ][(CF3 SO2 )2 N− ] ionic liquid, 42–45 which is (at least partially) related to this significant ion repacking and rearrangement upon inclusion of polarization. This ion restructuring in [BMIM+ ][(FSO2 )2 N− ] 22


Page 23 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


is a pronounced example of the change in liquid structure due to the polarization-modulated asymptotic limit of the SL screening condition (Equation 5).

Also exceptional to the

[BMIM+ ][(FSO2 )2 N− ] ionic liquid is the entirely featureless nature of the charge-correlation ˚−1 region of structure factor, including the complete absence of any peak in the ∼ 1 A SZZ /k 2 . Note that this interpretation of significant ion restructuring (and low viscosity) of [BMIM+ ][(FSO2 )2 N− ] as a long-range, electrostatically mediated effect, is distinctly different than prior interpretations focusing on short-range interactions between ion pairs. 45 To further benchmark these predictions for [BMIM+ ][(FSO2 )2 N− ] , we compare to simulations that utilize the (non-polarizable) force field of Canongia Lopes and Padua; 29,30 we find qualitatively similar predictions for the different non-polarizable models (Figure S1 and S2). In Figure S6, we show computed anion-anion RDFs in [BMIM+ ][(FSO2 )2 N− ] . The RDF between nitrogen atoms of the FSI anions exhibits three pronounced shoulders at short to intermediate distances (< 10 ˚ A), reflecting different interaction motifs of the -SO2 groups. These three shoulders change markedly in magnitude with inclusion of polarization, with significantly enhanced magnitude of the two closest-distance shoulders, and polarization shifting the third shoulder by ∼ 1˚ A to farther distance. Like the (CF3 SO2 )2 N− (TFSI) anion (Section 3.5), the FSI anion exhibits significant conformational flexibility due to rotation about its pseudo-dihedral, F-S-S-F torsion. 24,30,45,46 In Figure S7, we show the distribution of the important FSI torsion angle for the anions in [BMIM+ ][(FSO2 )2 N− ] , which shows a slight shift in population from “transoid” to “cisoid” upon inclusion of polarization. However, this difference is minor relative to conformational differences between the gas and liquid phase, 24 and both force fields predict approximately equal populations of the cisoid and transoid conformers in the IL.

23



[BMIM+ ][(CF3 SO2 )2 N− ]

2

6

5

4

1600

16

1400

14

1200

12

1000

10

800

8

600

6 4

400

2

200

0 0

0.2 0.4 0.6 0.8

1

-1

1.2 1.4 1.6 1.8

4 -1

r (Å)

10 8 7

-6

40 20

2

18


3.5

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 43

0 2

an

qsum cat

3

qsum

2 1 0 -1 -2 -3 0

10

20

30

40

r (Å)

k (Å )

(a)

(b)

Figure 10: a) Scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors and their asymptotic limits (Equation 5, 6) and b) charge oscillations in [BMIM+ ][(CF3 SO2 )2 N− ] + away from tagged (CF3 SO2 )2 N− anion, qan sum (blue), and away from tagged BMIM cation, qcat sum (red). Depiction of curves is analogous to plots in Figure 6. The structure factors and charge oscillations of [BMIM+ ][(CF3 SO2 )2 N− ] at 300K, 1 bar are shown in Figure 10. We compute compressibilities of χT = 60 and 57 * 10−6 bar−1 for [BMIM+ ][(CF3 SO2 )2 N− ] , from polarizable and non-polarizable simulations respectively. Our predicted scattering structure factor, SN N for [BMIM+ ][(CF3 SO2 )2 N− ] is in good agreement with experimental X-ray scattering measurements of Russina et al; 9 in particular, the prominent nature of the ∼ 0.9 ˚ A−1 peak in SN N relative to the other ILs is confirmed by experiment. 9 Of the ionic liquids studied, the charge correlation structure factor of [BMIM+ ][(CF3 SO2 )2 N− ] is most similar to [BMIM+ ][PF− 6 ] , in both the relative magnitude and position of the small peak in the ∼ 1˚ A region of SZZ /k 2 . This indicates that the specific nature of electrostatic interactions in ionic liquids is not determined by simple considerations of ion size and shape alone, but rather depends on the complex synergy of cation and anion interactions and packing. The influence of electronic polarization on the ion structure is cat clearly evident in the modulation of charge oscillations qan sum (r) and qsum (r) shown in Figure

10b. The (CF3 SO2 )2 N− (TFSI) anion (like the FSI anion) exhibits significant conformational 24


Page 25 of 43

flexibility enabled by rotation about its pseudo-dihedral, C-S-S-C torsion; the influence of such conformational flexibility on the IL properties has been previously characterized. 24,46–55 As shown in Figure S8, electronic polarization significantly alters the population of “cisoid” and “transoid” anion conformations in [BMIM+ ][(CF3 SO2 )2 N− ] . Anion-anion RDFs shown in Figure S9 indicate intermediate-lengthscale, structural rearrangements due to electronic polarization.

Molten NaCl (primitive model) r (Å) 3

1.6 1.4 1.2 1 0.8 0.6 0

50 40

600

400 0.2 0.4 0.6 0.8

1

2

30

2

200

20 10 0 0

4 -1

4

-6

5

2

60

20 10


3.6

SZZ / k (kBT/4π)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


an

qsum

3

cat

qsum

2 1 0 -1 -2 -3

1

2

-1

3

0 4

-4 0

k (Å )

10

20

30

40

r (Å)

(a)

(b)

Figure 11: a) Scattering (SN N ) and charge-correlation (SZZ /k 2 ) structure factors and their asymptotic limits (Equation 5, 6) and b) charge oscillations in “NaCl” (primitive model) cat away from tagged Cl anion, qan sum (blue), and away from tagged Na cation, qsum (red). Depiction of curves is analogous to plots in Figure 6.

We have simulated a primitive model 11 of NaCl molten salt at 1267 K to allow direct comparison with the ionic liquids. Note that the primary purpose is to illustrate general similarities of ionic systems, and the reader specifically interested in molten salt properties is referred to other work. 11,56–66 Analogolous to our simulations of ionic liquids, we investigate the system with and without inclusion of electronic polarization; note in this analysis, polarization is only applied to the ‘Cl’ anion (see Methods). The scattering and charge-correlation structure

25



cat factors are shown in Figure 11a, and charge oscillations qan sum (r) and qsum (r) in the molten salt

are shown in Figure 11b. From the asymptotic limit of SN N , we compute compressibililty values of χT = 43 and 42 * 10−6 bar−1 from polarizable and non-polarizable simulations ˚−1 in SN N is absent in the original work respectively. We note that the shoulder at ∼ 1.8 A of Hansen and McDonald, 11 (probably because of their employed long-range correction to g(r)’s), but this shoulder has been reported in subsequent work. 56 Similar to the ionic liquids − − + + [BMIM+ ][BF− 4 ] , [BMIM ][NO3 ] , and [BMIM ][CF3 SO3 ] , the charge correlation structure

factor SZZ /k 2 exhibits a prominent peak at the lengthscale of neighboring shells of like-ions, which for the molten salt is ∼ 4 ˚ A. Also similar to the case for ILs, the magnitude of this peak is reduced upon inclusion of electronic polarization. The inset of Figure 11a shows the asymptotic limit corresponding to the SL screening condition; the shift in this limit due to electronic polarization is somewhat less significant than for the more polarizable ionic liquids, but still affects the magnitude of charge oscillations as shown in Figure 11b. In Figure 12, we show cation-cation and anion-anion RDFs computed for the molten salt. Interestingly, inclusion of anion polarization in the simulation primarily alters the Na-Na correlation, but not the Cl-Cl correlation. This indicates that the correlation functions of a particular ion type are primarily influenced by the polarizability of the other ion type, which is analogous to our findings for [BMIM+ ][BF− 4 ] and similar ionic liquids. We note that in their study of molten AgBr, Bitrian and Trullas 59 report a similar polarization-mediated reduction in both the SZZ peak height and the cation-cation RDF peak height. Other studies have additionally found reduced like-ion correlation in molten salts due to incorporation of electronic polarization, particularly affecting cation-cation RDFs. 60,66

26


Page 26 of 43

Page 27 of 43

Na-Na (1267 K) 2

3

1.1

Cl-Cl (1267 K)

1

2

0.9 15

20

25

30

35

40

1

1.1

1

0.9 15

g(r)

3

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20

25

30

35

40

1

0

0 5

10

15

20

5

r (Å)

10

15

20

r (Å)

(a)

(b)

Figure 12: Cation-cation and anion-anion correlation function in NaCl computed with (solid line) and without (dashed line) electronic polarization.

4

Discussion

The long-range charge oscillations in ionic liquids and molten salts, and their modulation due to electronic polarization, is a consequence of the universal sum rules that dictate charge neutrality (Equation 7) and perfect screening (Equation 5) in ionic solutions. The magnitude of these charge oscillations and the polarization effect is illustrated by our systematic analy− − + + sis of [BMIM+ ][BF− 4 ] (Section 3), [BMIM ][PF6 ] (Section 3.1), [BMIM ][NO3 ] (Section 3.2), + − + − [BMIM+ ][CF3 SO− 3 ] (Section 3.3), [BMIM ][(FSO2 )2 N ] (Section 3.4), [BMIM ][(CF3 SO2 )2 N ]

(Section 3.5), and molten NaCl (primitive model, Section 3.6). We find that the magnitude of charge oscillations in the ionic liquids are quite similar to charge oscillations in the NaCl molten salt. For all ionic systems, we find that any spherical volume of radius “r” cencat an tered around a tagged ion may exhibit a total net charge of up to |qsum (r)|,|qsum (r)| ∼ 3,

not counting the tagged ion, and these ion shell oscillations extend >40 ˚ A in ionic liquids. Note that the coordination number of counterions per ion, “Ncoord ”, may be larger than this value, with 4

Understanding the Properties of Ionic Liquids: Electrostatics, Structure

Recommend Documents