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C: Energy Conversion and Storage; Energy and Charge Transport

Microscopic Dynamics in an Ionic Liquid Augmented with Organic Solvents Naresh C. Osti, Ray A. Matsumoto, Matthew W. Thompson, Peter T. Cummings, Madhusudan Tyagi, and Eugene Mamontov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b05119 • Publication Date (Web): 24 Jul 2019 Downloaded from pubs.acs.org on July 24, 2019

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The Journal of Physical Chemistry

Microscopic Dynamics in an Ionic Liquid Augmented with Organic Solvents

Naresh C. Osti§,*, Ray A. Matsumoto¶, Matthew W. Thompson¶, Peter T. Cummings¶, Madhusudan Tyagi£,‡, Eugene Mamontov§,* §Neutron

Scattering Division, Oak Ridge National Laboratory, PO BOX 2008 MS6455, Oak

Ridge, Tennessee 37831, United States ¶Department

of Chemical and Biomolecular Engineering, Vanderbilt University, 2201 West End

Ave, Nashville, Tennessee 37235, United States £NIST

Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States ‡Department

of Materials Science, University of Maryland, College Park, Maryland 20742, United

States

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] [email protected] Abstract: We present the complex microscopic dynamics of 1-butyl-3-methyl-imidazolium bis(trifluromethylsulfonyl)imide, [Bmim+][TFSI-], ionic liquid mixed with organic solvents to improve its properties for energy storage applications. To probe the microscopic dynamics on different length and time scales, we have employed different neutron scattering spectrometers for quasielastic neutron scattering (QENS) measurements to compare the effects of solvation in several organic solvents with nearly the same dipole moment but broadly varying bulk diffusivity.

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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

The ionic liquid-solvent mixtures show a nanoscopic phase separation into an ionic liquid-rich and a solvent-rich phase, as revealed by the model-free dynamic susceptibility data and further corroborated by the cluster histogram analysis of molecular dynamics (MD) simulation. In both phases, we observe a long-range translational mobility of the [Bmim+] cation, which scales with the bulk diffusivities of the organic solvents; this correlation becomes stronger in the solvent-rich phase. Additionally, various localized motion modes of [Bmim+] cation are observed. A combination of neutron scattering, and MD simulations reveals the parameters governing solventcontrolled diffusivity in an ionic liquid, which helps formulate new electrolytes optimized for efficient energy storage devices. INTRODUCTION Efficient, affordable, and environmentally friendly energy storage devices are of urgent need to confront the impeding energy crisis.1-3 A majority of energy storage research is focused on developing devices to achieve high power density, equivalent to that of dielectric capacitors, and of high energy density, comparable to that of batteries.4-5 To this end, electrochemical energy storage devices, also known as supercapacitors, have been in the forefront of active research. They store energy in the form of charges on the surfaces of the electrodes, which allows tuning their electrochemical performance by optimizing properties of the electrodes and electrolytes and their interactions.6-7 Electrodes are optimized by selecting the materials that facilitate charge adsorption.8 Various materials of diverse surface chemistries and topologies, particularly nanoporous materials with high specific surface areas, have been recommended as electrodes in electrical double layers capacitors (EDLCs).9-10 However, the electrolyte, which is an integral part of EDLCs, also plays a major role in controlling the performance of EDLCs.11-12 Aqueous and organic electrolytes, which are used in EDLCs, significantly limit the performance of the energy 2 ACS Paragon Plus Environment

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storage device because of their intrinsic disadvantages, such as low stability of water13-14 and high vapor pressure of conventional organic electrolytes.15 As an alternative, room temperature ionic liquids (RTILs) have emerged as promising electrolytes because they have high chemical and thermal stability, require no solvent, have low vapor pressure and can be tuned to have desired properties.16 On the basis of these properties, RTILs are considered environmentally friendly solvents in energy storage applications.15, 17 The ability of RTILs to operate at wider potential window is one of their appealing characteristics despite their generally low conductivity consistent with their low diffusivity and their high viscosity.4, 18-19 The high viscosity of RTILs is a result of strong cation-anion interactions and inherent nanophase segregation.20-22 The use of organic solvents mixed with RTILs have resulted in formulation of new electrolytes with increased conductivity and enhanced ion mobility.23-25 A recent study using quasi-elastic neutron scattering (QENS) and molecular dynamics (MD) simulations has shown an enhancement in the mobility and conductivity of the RTIL 1-butyl-3-methyl-imidazolium bis(trifluromethylsulfonyl)imide, [Bmim+][TFSI-] in the presence of organic solvents of different dipole moment.26 That study further revealed a relationship between cation diffusivity of the RTIL and the dipole moment of the aprotic solvents. A more recent study27 using MD simulations on a much larger number of solvents, however, has suggested that it is the diffusivity of the bulk solvent that governs the mobility of the RTIL cation in these mixtures. Here, using two neutron scattering spectrometers (time-of-flight and backscattering) together with MD simulations, we report the hierarchy of dynamic processes involving organic solvent-induced association of [Bmim+][TFSI-]. The combination of different neutron scattering instruments allows exploration of the mobilities of cation in both solvent-rich and the ionic liquid-rich phases. Here, we attempt to interrogate the conclusions of prior studies that separately identify solvent polarity26 (QENS and MD) and solvent



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diffusivity27 (MD) as the primary drive of ion dynamics in mixtures. To do this, we selected four solvents with similar polarity but vastly different diffusivities. We find, consistent with the predictions of the MD simulations,27 that the bulk diffusivity of the solvent dependent most strongly drives cation mobility. We have demonstrated a correlation between an ionic liquid diffusivity and the diffusivity of its solvent in the mixture, in contrast to the pure solvent’s diffusivity. This study establishes that it is not only the polarity, but also the solvent’s diffusivity in the mixture that need to be considered to formulate an ionic liquid-solvent mixture as electrolytes in supercapacitors. Our current findings advance understanding of organic solventinduced phase separation of ionic liquids, which will help optimize ionic liquid-organic solvent electrolyte systems for better charge transporting medium in electrochemical supercapacitors.

MATERIALS AND METHODS A. Samples Regular

(protonated)

1-butyl-3-methyl-imidazolium

bis(trifluromethylsulfonyl)imide,

[Bmim+][TFSI-], and deuterated form of dichloromethane (DCM) (CD2Cl2, molecular weight: 84.93 g/mol), Octanol (C8D18O, molecular weight: 130.23 g/mol), Butanol (C4D10O, molecular weight: 74.1 g/mol) and tetrahydrofuran (THF) (C4D8O, molecular weight:72.11 g/mol), were purchased from Sigma Aldrich. All the chemicals were used as received. A calculated amount of [Bmim+][TFSI-] and each deuterated solvent were mixed together separately to obtain the 25 and 50 wt% solutions of the ionic liquid for QENS measurements.


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B. Methods I.

Quasielastic Neutron Scattering

Quasielastic neutron scattering measurements of pure [Bmim+][TFSI-] and mixtures of [Bmim+][TFSI-] with deuterated organic solvents were conducted using the time-of-flight Disc Chopper Spectrometer (DCS)28 at National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR) and Backscattering Silicon Spectrometer (BASIS)29 at Oak Ridge National Laboratory (ORNL), Spallation Neutron Source (SNS). Experiments on DCS were carried out at two different instrument configurations of lowresolution modes, using incoming neutron wavelengths of 4.8 and 9 Å, which provide the corresponding energy resolutions (full width at half maximum) of ~ 120 and 20 µeV, respectively. These configurations allow to cover the dynamics range of ± 2000 µeV (4.8 Å incoming neutron wavelength) and ± 300 µeV (9.0 Å incoming neutron wavelength), with the corresponding Q ranges of 0.1-2.4 Å-1 and 0.1-1.3 Å-1. The samples were kept in a cylindrical aluminum sample holder that provided a sample thickness of 0.1 mm for the measurement. Data from a vanadium standard was also collected to determine the detectors efficiencies. Data from each sample was measured at 300 K. Temperature was controlled using a closed cycle refrigerator (CCR). Instrument resolution from each sample was measured at 20 K. Data from an empty sample holder and blocked beam were utilized during the data reduction using DAVE software.30 QENS measurements at BASIS were performed at the standard configuration of the instrument. In this configuration, the instrument provides an energy resolution of 3.5 µeV (Qaveraged full width at half maximum) and covers an energy window of ± 100 µeV with a Q range of 0.2-2.0 Å-1, with the incoming neutron bandwidth centered at 6.4 Å (described below as 6.4 Å neutrons, for brevity). We maintain the same sample thickness of 0.1 mm for this instrument as 5 ACS Paragon Plus Environment


well to control multiple scattering. QENS data at 300 K were collected from each sample. Samples were cooled down to a baseline temperature of 20 K using CCR, where sample-specific resolution functions were measured. Data were reduced using Mantid31 and analyzed (for the both instruments) with DAVE30 software packages. II.

Molecular dynamics simulations

The MD simulations reported here were a part of the large screening study of [Bmim+][TFSI-] solvated in organic solvents.27 The signac framework32-33 was used to manage each step of the simulation process, from initializing systems to performing analyses. The systems were first initialized and atom-typed with the MoSDeF software suite of tools.34-35 The first step of the MoSDeF workflow is to initialize each system with mBuild to place the ionic liquid and solvent molecules into a simulation box. The initial box size of each system was 8 nm x 8 nm x 8 nm. The 0.2 mass fraction DCM system contained 50 ionic liquid molecules and 988 DCM molecules. The adjusted box size after equilibration was 5.12 nm x 5.12 nm x 5.12 nm. The 0.5 mass fraction DCM system contained 200 ionic liquid molecules and 988 DCM molecules. The adjusted box size after equilibration for this system was 5.90 nm x 5.90 nm x 5.90 nm. To investigate possible system size effects (see SI for more details) on nanophase separations, MD simulations of larger systems were also run. Additionally, the 0.2 mass fraction DCM system was rerun for 75 ns to investigate effects due to time. Table 1 provides an overview of all the DCM systems studied. This mBuild functionality calls PACKMOL36 to ensure that the molecules are placed at random positions without overlap. Next, the atom-typing tool in MoSDeF, foyer, applies the force fields to each system. All simulations were performed in GROMACS 5.1.4,37-39 and analyses were done with various open-source tools, including MDTraj40 and packages in the SciPy software stack. The CL&P force field41-43 was used to describe the ionic liquid interactions, with partial charges scaled 6 ACS Paragon Plus Environment

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by a factor of 0.8. The solvent interactions were described by the all-atom Optimized Potential for Liquid Systems force field (OPLS-AA)44-45 by Jorgensen et al., as this is currently one of the most general force fields available and encompasses all of the solvents studied. The CL&P force field was based on OPLS-AA and as a result, both force fields use the same formatting for non-bonded interactions including 12-6 Lennard-Jones pair potentials and harmonic bonds and angles. Additionally, both force fields use Lorentz-Berthelot combining rules and 1-4 scaling factors. Table 1. Overview of DCM Simulations Solvent DCM DCM DCM DCM DCM

[BMIM+][TFSI] Mass Fraction 0.2 0.5 0.2 0.5 0.2

System size (nm3) 134.2 205.4 435.5 405.2 435.5

Number of Ionic Liquids 50 200 160 400 160

Number of Solvents 988 988 3160 1976 3160

Simulation Time (ns) 30 30 30 30 75

The first step of the workflow was to perform energy minimization simulations on the fully initialized systems using 2000 steps of the steepest descent algorithm in order to get rid of any energetic clashes. Following this step, all remaining steps were MD simulations. Similar parameters were used throughout: electrostatics were handled with the Particle Mesh Ewald (PME) method, using a real-space cutoff of 1.1 nm and a minimum grid spacing of 0.16 nm for the inverse space, non-bonded van der Waals interactions were also handled with a 1.1 nm cutoff, a timestep of 1 fs was used with all bonds constrained with the LINCS algorithm, and the v-rescale thermostat and Parrinello-Rahman barostat were used to control the temperature and pressure at a reference state of 300 K and 1 bar. The time constant for both the thermostat and barostat is 1 ps. A series of steps were taken to equilibrate each system: a 100 ps NVT simulation, a 1 ns NPT simulation at 10 bar to encourage systems towards liquid densities, another 1 ns NPT simulation at 1 bar, and



a 10 ns NVT simulation. Once the systems were properly equilibrated, the systems were sampled for 30 ns in the NPT ensemble using a 1.5 fs timestep. We employed a clustering algorithm developed by Sevick46 et al. to calculate various ion clustering quantities in each system. This algorithm was implemented in a set of Python functions and is published on Github47 Using this algorithm, a direct correlation matrix was calculated to determine which ions were directly connected. A distance criterion of 0.8 nm was used to determine which ions were directly connected, which roughly corresponds to the first valley of the cation-anion radial distribution (RDF) function. From the direct correlation matrix, we computed an indirect correlation matrix to determine which ions were indirectly connected to determine the number and sizes of clusters in each system. Results and Discussion Earlier studies21-22, 48-49 have demonstrated that ionic liquids tend to exhibit self-association resulting in a nanophase separation. The nano-aggregates are produced due to multiple ion-ion interactions within the ionic liquids associated with their relatively high viscosity. Aprotic solvents of higher dipole moments are more effective in screening the ion-ion interactions.26 In our previous study, ionic liquid-rich and solvent-rich phases have been observed in [Bmim+][TFSI-] with four solvents of different dipole moments (d): acetonitrile (d = 3.92 D), methanol (d = 2.87 D), tetrahydrofuran (d = 1.75 D), and dichloromethane (d = 1.60 D).26 We also observed that solvents with greater dipole moment produced mixtures with greater cation diffusivity. We attributed this to the solvent’s screening capacity, which scales with the solvent’s dipole moment. Here, we consider [Bmim+][TFSI-] ionic liquid in four solvents of nearly the same dipole moments (d, in units of Debye), but of different bulk diffusivities (D, in units of m2s-1), as reported from MD simulations:27 DCM (d = 1.60 D, D = 15.7 × 10-10 m2s-1), Octanol (d = 1.68 D, D = 0.4 × 10-10 8 ACS Paragon Plus Environment

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m2s-1), Butanol (d = 1.66 D, D = 2.7 × 10-10 m2s-1) and THF (d = 1.75 D, D = 8.5 × 10-10 m2s-1). This allows us to investigate how much impact solvent diffusivity, with solvent polarity behind held roughly constant, has on the transport properties of the cation. Note that the selection of solvents used in this study is guided from the results presented by Thompson et al.,27 where they have considered 22 solvents and different solvent properties (such as molecular weight, polarity, and solvent diffusivity), and have observed a robust trend between cation mobility with bulk solvent diffusivity from molecular dynamics simulations.

(a)

(b)

Figure 1: MD snap shots of [Bmim+][TFSI-] in DCM as a function of concentrations in mass fraction. (a) 0.5 [Bmim+][TFSI-] in DCM (b) 0.2 [Bmim+][TFSI-] in DCM. [Bmim+][TFSI-] is shown in red and DCM is in blue. We started by examining the clustering of the ionic liquid in the mixtures using molecular dynamics simulations. Figure 1 shows representative MD snapshots of [Bmim+][TFSI-] in DCM at two different concentrations. Separation into ionic liquid-rich and solvent-rich regions is clearly seen at both concentrations. Compared to higher concentration (Fig 1a), at lower concentration of [Bmim+][TFSI-] (Fig 1b), phase separation becomes more prominent. Cluster analyses of the MD snapshots confirm the phase separation at concentrations of 50 wt% and below. Histograms



displaying a distribution of ions in a cluster for DCM solutions at 0.2 and 0.5 [Bmim+][TFSI-]

7 6

(a)

DCM: 0.2 mass fraction

5 4 3 2 1 0

0

20

40

60

80

Number of Clusters of size Nions

mass fraction are presented in Figure 2.


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

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60

(b)

50


40 30 20 10 0

0

Cluster size, Nions

80

160

240

320

400

Cluster size, Nions

Figure 2: (a) Number of clusters as a function of cluster size,1 to Nions, for (a) 0.2 and (b) 0.5 mass fraction of [Bmim+][TFSI-] in DCM, where Nionsl is 100 for 0.2 mass fraction and 400 for 0.5 mass fraction. For instance, a “cluster” of 1 ion represents a free ion in solution and a cluster of size Nions indicates that the entire system consists of ions interconnected to all others.

The distributions of cluster sizes were determined from the indirect correlation matrices by first counting the cluster sizes for each frame of the trajectory and computing the average. This value was then multiplied by cluster size to calculate the count of each cluster size. The distributions of cluster sizes differ for these two systems. In 0.2 mass fraction solution (Fig 2a), the cluster sizes are more evenly distributed in comparison to the 0.5 mass fraction solution (Fig 2b). The ions are most likely to exist in small clusters, although some exist in larger clusters as well. In contrast, a narrow distribution of large cluster sizes exists in the 0.5 mass fraction solution, indicating that ions in this system overwhelmingly exist in large, inter-connected clusters. Based on these distributions, the ions at lower concentrations of [Bmim+][TFSI-] exist in smaller clusters, and thus are more dispersed throughout the solution. At higher concentrations of [Bmim+][TFSI-], the larger clusters of ions indicate that the effects of nanoscopic phase separation may be more pronounced. Note that the simulations performed using a larger MD box and extended simulations length appear 10 ACS Paragon Plus Environment

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to have the same degree of nanophase separation compared to the smaller system (Fig S1, and details in SI). The larger systems indicate that the difference in nanophase separation between the 0.5 and 0.2 mass fraction ionic liquid in DCM system is not an artifact of small system sizes. The cluster sizes for the larger systems replicate the cluster sizes of the smaller systems (Fig S2). The larger 0.5 mass fraction system has a slightly narrower distribution of larger cluster sizes in Q = 0.5 Å-1

Closed symbols, [Bmim+][TFSI-] (pure)

(a)

(b)

0.1

" (E,Q)

" (E,Q)

1E-4

1E-5

1E-6 1E-4

[Bmim+][TFSI-]:d-DCM 1:0 1:1 1:3

0.001

0.01

Open symbols, [Bmim+][TFSI-]+d-DCM (1:1)

1E-4

0.001

4.8 Å 6.4 Å 9.0 Å

" (E,Q) 0.001

0.01

0.1

0.1

100 % [Bmim+][TFSI-] 50% d-DCM 50% d-THF 50% d-Butanol 50% d-Octanol

0.01

-

E (meV)

Q (Å-1) 0.3 0.5 0.7 0.9 1.1

(d)

Open symbols, [Bmim ][TFSI ]+ d-DCM = (1:1)

1E-4

, , , , ,

0.1

Close symbols, [Bmim+][TFSI-] (pure) +

0.01

E (meV)

Q = 0.5 Å-1

(c) , , ,

0.1

0.01

0.01

0.001

0.1

E (meV)

Q = 0.5 Å-1

" (E,Q)

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


1

1E-4

0.001

0.01

E (meV)

0.1

Figure 3. Dynamic susceptibilities for [Bmim+][TFSI-] calculated from QENS spectra as I(Q,E)/nB(E), where nB(E) is Bose population factor. A comparison between pure [Bmim+][TFSI-], and an organic solvent, DCM, as a function of (a) concentration, (b) Q and (c) wavelength of the incident neutrons. Lines with arrows (solid line for pure [Bmim+][TFSI-] and dashed lines are for BmimTFSI with DCM) in (b) illustrate a change in the peak positions and are guides to the eyes. (d) Dynamic susceptibilities for [Bmim+][TFSI-] mixed with organic solvents of different bulk diffusivities.

comparison to the smaller system, whereas the larger 0.2 mass fraction system exhibits a slightly larger distribution of small clusters and a smaller distribution of larger clusters in comparison to



the smaller system. Furthermore, the 0.2 mass fraction DCM system that was run for 75 ns indicates that nanophase separation in these systems does not differ at longer simulation times. The existence of different phases as the concentration of [Bmim+][TFSI-] changes is further illustrated by the model-independent dynamic susceptibility plots (Fig 3) generated from the measured QENS spectra. The dynamic susceptibility is a model-free presentation of QENS signal normalized to the Bose occupation factor. The dynamic susceptibility as a function of energy transfer shows a distinct peak corresponding to a relaxation process. The number of the peaks represents the number of distinct relaxation processes detectable in the measurement of the sample, while their positions correspond to the energy/time scales of the measured relaxation processes. Note that QENS is sensitive to the hydrogen content of a sample and has been a technique of choice to explore the dynamics of fluids such as water and ionic liquids in bulk and confined states.26, 5052

Since only the cation of [Bmim+][TFSI-] has hydrogens, and all solvents used were deuterated,

QENS spectra are dominated by the cation contribution.53 However, the cations and anions of this ionic liquid have nearly identical diffusivities as reported by MD simulations27, so the behavior of the anion is likely to be similar. Similar to our previous study of [Bmim+][TFSI-] in acetonitrile,26 [Bmim+][TFSI-] in DCM also exhibits two distinct peaks (Fig 3a), which become more prominent at higher DCM concentration. Q-dependent peaks positions in both the pure BmimTFSI and its 50 wt% mixture as presented in Fig. 3b, indicate a long-range translational mobility of ions. A representative set of dynamic susceptibility plots presented in Figure 3c also shows low and high energy transfer peaks from the QENS spectra collected using neutrons of 4.8 Å (time-of-flight), 6.4 Å (backscattering) and 9.0 Å (time-of-flight) wavelengths. Furthermore, those peaks are also Q-dependent, suggesting at least some translational mobility of ions within the energy range probed at those configurations. The impact of bulk diffusivities of solvents on the mobility of 12 ACS Paragon Plus Environment

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[Bmim+][TFSI-] cation is further illustrated in the susceptibility (measured using 6.4 Å backscattering wavelength) as presented in Fig. 3d. Besides two relaxations peaks (a well resolved peak at low energy transfer and an emerging peak at high energy transfer), there is a systematic decrease in intensity and an increase in width of the low energy transfer peak in an order of the increasing bulk solvent’s diffusivities, implying a role of solvent’s viscosity in the microscopic dynamics of the cation. Since the two peaks in the dynamic susceptibility plots correspond to two different relaxation processes, we use a superposition of two Lorentzians functions to capture those dynamic phenomena. It should be noted that, even in ionic liquids without solvents, the number of microscopic dynamic processes that are measurable by neutron scattering is not just two.54 The two slowest processes are related to the center-of-mass motion of the whole ion (in particular, cation, to which neutron scattering is especially sensitive); the slowest process is related to the long-range translational ion motion, and the second slowest process is related to the localized “in a transient cage” ion motion. However, besides these universal processes, which manifest themselves in QENS spectra from any liquid, there exist a number of ion-specific processes related to various intra-particle motions of the ions side groups.54 Therefore, different processes would be measurable, depending on the accessible range of energy transfers. Furthermore, representative dynamic susceptibility plots (Fig. S3, right panel) show that the maxima of the resolution functions are always to the left of the corresponding low-energy maxima of the signals. That is, a component which is narrow, but broader than just the resolution signal would be, is a must in the fits. Then there is a visible transition in the susceptibility plots to a different slope, indicating another process that requires a separate component for the fits. There is a significant difference between the narrow and broad component signals, demonstrating the necessity of the two independent fit components per spectrum in data analysis (see also Fig. S3, 13 ACS Paragon Plus Environment


left panel). Such models have been employed successfully to investigate the dynamics of ionic liquids.52,

55-56

Therefore, the measured QENS intensity signal, I (Q,E) is analyzed using the

following equation:53

[

1

𝐼(𝑄,𝐸) = 𝑋1(𝑄)𝛿(𝐸) + (1 ― 𝑋1(𝑄))(𝑝1(𝑄)𝜋𝛤2

𝛤𝑓𝑎𝑠𝑡(𝑄)

𝑓𝑎𝑠𝑡(𝑄)

1

2

+𝐸

+ (1 ― 𝑝1(𝑄))𝜋𝛤2

𝛤𝑠𝑙𝑜𝑤(𝑄)

𝑠𝑙𝑜𝑤(𝑄)

]

)

+ 𝐸2

(1)

⊗ 𝑅(𝑄,𝐸) + 𝐵(𝑄,𝐸)

Here, 𝑋1(𝑄) and 𝛿(𝐸) are elastic incoherent scattering factor and a delta function, respectively. 𝛤𝑓𝑎𝑠𝑡(𝑄) and 𝛤𝑠𝑙𝑜𝑤(𝑄) are half width at half maxima (HWHM) of a broad (corresponding to fast dynamics) and a narrow (for slow dynamics) Lorentzian components with their respective spectral weights of 𝑝1(𝑄) and 1 ― 𝑝1(𝑄). Data were analyzed after a convolution with the instrument resolution, 𝑅(𝑄,𝐸), and with an added linear background term, 𝐵(𝑄,𝐸). The model function described by equation (1) fitted the experimental QENS spectra well, as shown by the solid lines

0.1

100% [Bmim+][TFSI-] 50% d-Octanol 50% d-Butanol 50% d-THF 50% d-DCM Fit

   Å Q   Å

0.0 0.0 -0.1

-0.1

0.0

E (meV)

0.1

0.1

100.0 10.0

QENS Intensity (Arb. U)

1.0

QENS Intensity (Arb. U)

in Figure 4 for all the configurations of the measurements. QENS Intensity (Arb. U)

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

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Å Q   Å

1.0 100% [Bmim+][TFSI-] 50% d-Octanol 50% d-Butanol 50% d-THF 50% d-DCM Fit

0.1 0.0 0.0 -0.3

-0.2

-0.1

0.0

0.1

E (meV)

0.2

0.3

100.0

   Å Q   Å

10.0 1.0

100% [Bmim+][TFSI-] 50% d-Octanol 50% d-Butanol 50% d-THF 50% d-DCM Fit

0.1 0.0 0.0 -2

-1

0

E (meV)

1

2

Figure 4. Representative QENS spectra of [Bmim+] [TFSI-] and its 50 wt % mixture with indicated deuterated organic solvents at Q = 0.5 Å-1 collected using neutron wavelengths of (a) 6.4 Å (backscattering), (b) 9.0 Å (time-of-flight) and (c) 4.8 Å (time-of-flight). Symbols represent the data and the solid lines are the model fits described in the text.

We extracted the HWHMs of both the narrow and broad components from the mode1 fits. Qdependence of HWHMs is presented in the SI (Figure S4 and S5). Variation of HWHMs with Q2 is not linear for both components at all three configurations. The narrow component HWHMs from 14 ACS Paragon Plus Environment

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the BASIS data (Fig S4) were fitted with a jump diffusion model53 (equation 2) as represented by solid lines, which gives the diffusivity of cations in ionic-liquid-rich phase. On the other hand, jump fit analysis of the broad component yields the diffusivity of the cation in solvent-rich domains. This model allows to obtain jump diffusion rate (D), jump length (L) and residence time (𝜏𝑜) as:

𝛤𝑖(𝑄) =

𝐷𝑄2 1 + 𝐷𝑄2𝜏𝑜

(2)

where D and 𝜏𝑜 are related as, L2=6D𝜏𝑜. HWHM approaches zero in the limit of Q = 0 for the narrow component (Fig S4a), indicating the long-range translational dynamics in the ionic liquidrich phase. For the broad component in Fig S4b, pure [Bmim+] [TFSI-] exhibits a plateau at low Q, indicating, in agreement with many earlier studies,54 the spatially localized character of the faster cation motion that gives rise to this component. On the contrary, the same broad component measured in the IL-solvent mixtures does approach zero in the limit of Q = 0, thus representing the long-range translational dynamics in the solvent-rich phase. The HWHMs of the QENS data from time-of-flight DCS spectrometer collected using two incident neutron wavelengths (4.8 and 9 Å) are presented in Fig. S5. There is a Q-dependence of HWHMs of the narrow and broad components measured at both wavelengths. However, only the HWHM of the narrow component obtained from 9 Å configuration (Fig S5a) shows a clear long-range translational diffusivity, approaching zero in the limit of Q = 0, and could be fitted with a jump diffusion model. The HWHM of the narrow component at 4.8 Å configuration (Fig S5c) for pure [Bmim+][TFSI-] is Qindependent, suggesting that we are probing the local dynamics of the cation, most likely, methyl group rotation. However, the HWHMs obtained from the [Bmim+][TFSI-] with solvents show some Q-dependence, albeit in rather random pattern, rendering extraction of quantitative 15 ACS Paragon Plus Environment


information impossible. We observed a similar trend of HWHMs extracted for the broad component (Fig S5b and S5d) measured at 4.8 and 9 Å wavelengths configurations. The randomness in HWHMs can be attributed to a local in-cage motion of the ionic liquid cation, which is always present in ionic liquids.54, 57-58 Diffusion coefficients of [Bmim+][TFSI-] cation obtained from the jump model fit (eqn. 2) are plotted in Figure 5 as a function of the bulk diffusivities of the solvents (calculated from MD simulations27). Cation diffusivity in the IL-rich phase follows a trend as predicted from MD simulation, generally increasing with the bulk solvents’ diffusivities.27 This trend becomes even more pronounced in the solvent-rich phase, which is quite intuitive, because, in local domains with more solvent molecules, there is stronger screening of the ion-ion interactions in the ionic liquid. Furthermore, in these particular domains, ions diffuse faster in accordance with the mobility of the involved solvent molecules. 100

DCation10-10 m2s-1

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, C8D18O; , C4D8O; Dcation(MD)

, ,

C4D10O CD2Cl2

10

1 Close symbols, [Bmim+][TFSI-] rich Open symbols, Solvent rich

0

DSol.10

-10

10

2 -1

20

m s (Mixture-MD)

Figure 5. Symbols: experimentally obtained diffusivity values for Bmim+ cation in 50 wt% [Bmim+][TFSI-]-solvent mixtures, plotted as a function of diffusivity of the organic solvent in the corresponding solution (as obtained from MD simulation). Filled symbols: IL-rich domains. Open symbols: solvent-rich domains. Stars: diffusivity values for Bmim+ cation in 50 wt% [Bmim+][TFSI-]-solvent mixtures as obtained from MD.


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Since the mobility of solvent molecules depends on the viscosity, the diffusivity of the cation increases linearly with an increase in the bulk diffusivities of the solvents. Even though our pervious study26 has revealed that the cation diffusivity of [Bmim+][TFSI-] scales with the dipole moment of solvents, this work demonstrates the strong impact of bulk diffusivity of the solvent on the cation diffusivity. Conclusion Using QENS and MD simulations, we show that mixtures of [Bmim+][TFSI-] and organic solvents undergo a nanoscopic phase separation into an ionic liquid-rich and solvent-rich domains at 20 or higher wt % of the ionic liquid. We investigate a relationship between the long-range translational diffusivity of Bmim+ cation in both phases and the bulk diffusivities of the organic solvents by employing neutron spectrometers of variable energy resolution and dynamic range. Using a selection of solvents with similar polarity but differing diffusivity, we have demonstrated that pure solvent diffusivity has a strong impact on ion dynamics in mixtures of ionic liquids and organic solvents. The relationship between the cation diffusivity and the organic solvent diffusivity is more pronounced for the cation in the solvent-rich phase. Even though the evidence of the nanoscopic mixture separation into domains with different behavior has been lacking to date, especially in the experimental studies, our results provide such evidence and demonstrate that further advancements in the current molecular-level understandings of solvent-ionic liquid mixtures are necessary for a better formulation of electrolytes in electrochemical energy storage applications.



ASSOCIATED CONTENT Supporting Information The following files are available free of charge. Simulations using larger box sizes and longer times and cluster analysis, raw spectrometer data and corresponding dynamic susceptibility plots, HWHMs of QENS data collected from DCS and BASIS. (PDF) AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] [email protected] Notes The authors declare no competing financial interests.

ACKNOWLEDGMENT This work was supported as part of the Fluid Interface Reactions, Structures and Transport (FIRST) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. Work at ORNL’s Spallation Neutron Source was sponsored by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for U.S. DOE under Contract No. DEAC05-00OR22725. Experiments on DCS at NIST Center for Neutron Research (NCNR) were supported in part by the National Science Foundation under Agreement 18 ACS Paragon Plus Environment

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Microscopic Dynamics in an Ionic Liquid ... - ACS Publications

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