Relaxation in a Prototype Ionic Liquid: Influence of Water on the

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Relaxation in a Prototype Ionic Liquid: Influence of Water on the Dynamics David L. Price, Oleg Borodin, Miguel A. González, Maiko Kofu, Kaoru Shibata, Takeshi Yamada, Osamu Yamamuro, and Marie-Louise Saboungi J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02871 • Publication Date (Web): 20 Jan 2017 Downloaded from http://pubs.acs.org on January 23, 2017

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The Journal of Physical Chemistry Letters

Relaxation in a prototype ionic liquid: influence of water on the dynamics David L. Price,a Oleg Borodin,b,§ Miguel A. González,c Maiko Kofu,d Kaoru Shibata,e Takeshi Yamadaf, Osamu Yamamurod and Marie-Louise Saboungig,h

a

CNRS, UPR 3079 and Université d'Orléans, Conditions Extrêmes et Matériaux: Haute Température et Irradiation, 1d avenue de la recherche scientifique, 45071 Orléans Cedex 2, France b Electrochemistry Branch, Sensor and Electron Devices Directorate, U.S. Army Research Laboratory, Adelphi, MD 20783, USA c Institut Laue Langevin, 71 avenue des Martyrs, 38042 Grenoble Cedex 9, France d Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan e Materials and Life Science Division, J-PARC Center, JAEA, Tokai, Ibaraki 319-1195, Japan f Neutron R&D Division, CROSS-Tokai, Tokai, Ibaraki 319-1106, Japan g IMPMC-Université Pierre et Marie Curie and CNRS, 4 Place Jussieu, F-75252 Paris, France h Institute of Functional Nano & Soft Materials (FUNSOM), Soochow University, Suzhou, Jiangsu 215123, China § [email protected]; *[email protected]

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Abstract The influence of water on the relaxation of a prototype ionic liquid (IL) C8mimBF4 is examined in the IL-rich regime combining quasi-elastic neutron scattering (QENS) and molecular dynamics (MD) simulations. The QENS and MD simulations results for relaxation of IL and the equimolar mixture with water probed by the dynamics of the C8mim hydrogen atoms in the time range of 2 ps - 1 ns are in excellent agreement. The QENS data show that translational relaxation increases by a factor of 7 on addition of water, while rotational relaxation involving multiple processes fitted by a KWW function with low β values is speeded up by a factor of 3 on the timescale of QENS measurements. The MD simulations show that the cation diffusion coefficient, inverse viscosity and ionic conductivity increase on addition of water, consistent with the very small change in ionicity. The difficulties in obtaining rotational and translational diffusion coefficients from fits to QENS experiments of pure ILs and IL-water mixtures are discussed. Room-temperature ionic liquids (ILs) have been intensively investigated due to favorable properties that make them ideal green materials for applications such as sensors, batteries and solar cells as well reaction media for IL-assisted production of electrode materials and catalysts for fuel cells, photo-induced water splitting and dye-sensitized solar cells.1,2 The effect of water on ILs is paramount for many of these applications. Water is often used as co-solvent to reduce the viscosity of the liquid, and ILs are hygroscopic and prone to absorb water in practical situations. Even small amounts of water can have significant effects on e.g. viscosity and conductivity as well as the structure in bulk and electrified interfaces, which may significantly alter reaction rates in actual applications.3,4 It is important to understand these effects since the design of task-specific ILs may depend on the dynamics and arrangements of molecules in different environments. Among the large body of published work on ILs and their solutions, their atomic dynamics has received relatively less attention. Fayer5 has reviewed time-resolved fluorescence anisotropy and optical-heterodyne-detected optical Kerr effect measurements while IR, Raman spectroscopy and NMR results have been reported. 6,7,8,9 Quasielastic neutron scattering (QENS) is a powerful probe of dynamics providing temporal and spatial information simultaneously covering time scales of ps to ns and length scales of 0.1 to 1 nm, both appropriate for a wide range of translational and rotational motions in complex liquids.10 It has been applied to a number of imidazolium-based ILs.11,12,13,14 While the effect of water on the structure of C8mimBF4 has recently been studied,15 there are no published investigations of the effects of water on the dynamics of ILs using QENS. Our present work fills this gap and reports an experimental (QENS) and molecular dynamics (MD) simulation study of the dynamics of an IL with the C8mim+ cation and the BF4- anion, along with its mixtures at low concentrations of water. In these measurements D2O is used to avoid the large incoherent scattering contribution from H2O, which would obscure the cation dynamics. Here we report our results for the pure IL and the equimolar mixture, below the miscibility gap in C8mimBF4-H2O, which extends from 69.8 to 99.88 mol% water.16,17 The intermediate scattering function I(Q,t) for the cation hydrogen atoms measured by QENS is fitted by the product of a Debye-Waller factor, a slow exponential relaxation and a fast stretched exponential (KWW) relaxation: 2 ACS Paragon Plus Environment

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(

)

{

}

β I (Q, t ) = exp −Q 2 u 2 / 3 exp ( −t / τ 1 (Q ) ) F (Q ) + (1− F (Q )) exp − ( t / τ KWW (Q ))    , (1)

where Q is the scattering vector, t the elapsed time, the mean square displacement for vibrational modes, τ1 and τKWW relaxation times for the slow and fast relaxations, F(Q) the form factor for fast localized relaxations and β the KWW stretching parameter. Assuming that the relaxation processes can be decoupled, and that coherent scattering can be neglected, the first factor is associated with vibrational modes, the second with translational relaxation and the third with rotational relaxation. While translational relaxation in ILs is often found to have a stretchedexponential behavior at long times as observed by neutron spin-echo measurements13, we find that a simple exponential function is a reasonable approximation over the times covered by QENS. The rotational relaxation undergone by the cation is expected to have many different components with a wide variety of relaxation times, which are represented by a KWW stretched exponential function. Typical I(Q,t)s with fits of Eq. (1), normalized so that I(Q,0) = 1, are shown in Figure 1.

Figure 1. Intermediate scattering function for C8mimBF4 at 0.4 Å-1 (left) and C8mimBF4.D2O (right), together with the fits of Eq. (1).

The slow relaxation time shows the 1/Q2 dependence at low Q characteristic of translational diffusion:

τ 1 (Q) = 1 / DQ 2

(2)

where D is an apparent translational diffusion coefficient. Figure 2 shows the data of τ1(Q) with fits of Eq. (2) giving D = (0.055±0.005) x 10-10 m2.s-1 for the pure salt and (0.38±0.02) x 10-10 m2.s-1 for the equimolar mixture, indicating a substantial speeding up in the translational relaxation with the addition of water.

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Figure 2. Translational relaxation times vs. scattering vector Q obtained from fits of Eq. (1) for pure C8mimBF4 and C8mimBF4.D2O. The solid curves represent fits of Eq. (2).

The third factor in Eq. (1) shows behavior characteristic of localized relaxation. Fitting F(Q) with a function representing diffusion within a sphere,18

 3 j (Qa )  F (Q ) = c + (1− c )  1   Qa 

2

(3)

where j1 is the spherical Bessel function of the first kind and c the fraction of atoms not participating in the relaxation process, gives estimates of the average radius a of the loci of the various local hydrogen motions. The fits to Eq. (3) are given in Figure S1 in the Supplementary Information (SI). The fitted values of a are essentially the same – 3.25 ± 0.04 Å and 3.34 ± 0.03 Å – for the pure salt and the mixture, respectively. They are longer than the jump distances of the ethyl end groups in the simpler liquid C2mimBr, which lie on a circle of radius 1.2 Å.19 The values of c are also similar in the two liquids – 0.164 ± 0.002 and 0.178 ± 0.002, respectively. The values of τKWW shown in Figure S2 of the SI show a significant dependence on Q that is fitted by

 3 j (QaR )  τ KWW (Q) = τ R  1   QaR 

2

(4)

where τ R is a representative time of the rotational relaxation. The strong Q dependence reflects the various rotational modes that contribute at different values of Q, but with jump distances that are represented on average by Eq. (3). While the values of τ R are similar for both liquids, τ R = 13.3 ± 0.3 and 10.4 ± 0.2 ps, the values of β, remarkably independent of Q, increase 4 ACS Paragon Plus Environment

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significantly with the water, from β = 0.355 ± 0.002 to 0.468 ± 0.002; the mean times for the KWW distribution = Γ(1/β)/β.τR decreases by a factor of 2.7 from 64 ± 3 to 24 ± 1 ps. The local motions sampled by the KWW distribution are thus significantly speeded up by the addition of water. Comparing now the experimental results with those of the MD simulations, the I(Q,t)s obtained from the fits of Eq. (1) to the QENS data are plotted against those derived from MD in Figure 3. The MD results are corrected for the finite size of the box by dividing time by the ratio (1+∆DFSC/Dcation), where the finite-size correction (FSC) ∆DFSC is given by Eq. (S5) of SI; the ratio is equal to 1.28 and 1.18 for the pure IL and the mixture. At each Q value the QENS I(Q,t)s are multiplied by a scale factor – equivalent to the Debye-Waller factor in Eq. (1) – to match the MD. The agreement is seen to be extremely good. The discrepancies at longer times at Q = 0.4 Å-1 are due to the stretched exponential behavior discussed earlier and could be probably resolved by neutron spin-echo measurements, as mentioned above.

Figure 3. Comparison of I(Q,t) from QENS (curves) and MD (symbols) at three Q values for the Im+ hydrogens in (a) pure C8mimBF4 and (b) C8mimBF4.D2O.

The situation becomes more complex when we compare the results for the different relaxation processes from the simulations as shown in Table 1. Addition of water increases the diffusion: Dcation increases by a factor of 6.1 from the simulations and 6.9 from the experiments. However, the magnitude of the apparent Dcation from QENS is significantly larger by a factor of 2.3 for pure IL and 2.7 for the equimolar mixture than the magnitude of self-diffusion coefficient from the MD. Such discrepancy is significant given that the simulations predict conductivity and viscosity for pure C8mimBF4 within 35% of experiments, as shown in Table 1. In order to understand this discrepancy, the sub-diffusive behavior of ion relaxation is examined as shown in Figures S3-S4 of the SI. The log-log plot for the C8mim+ mean-square displacement (MSD) vs. time (Figure S3) indicates that the sub-diffusive behavior of C8mim in the pure salt extends to ~60 ns for the cation center-of-mass MSD, so the QENS values of D overestimate Dcation. Fitting the MSD of the C8mim+ center of mass from 0.1 to 1 ns yields an apparent Dcation = 0.052 x 10-10 m2.s-1 (Figure S4), quite close to the QENS value of 0.055 x 10-10 m2.s-1 and significantly higher than that obtained from fitting the diffusive regime from 70 to 110 ns. Similarly, fitting the center of mass MSD for C8mimBF4.H2O from 0.1 to 1 ns yields an apparent Dcation = 0.23 x 10-10 m2/s that 5 ACS Paragon Plus Environment


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is higher than the value Dcation = 0.14 x 10-10 m2/s obtained from fitting MSD in the diffusive regime. The apparent viscosity is also time-dependent on the 5-10 ns timescale as shown in Figure S5 of the SI. The connection between rotational relaxation of ionic liquids and the frequency dependence of the viscosity has been previously discussed.20 When examined over the timescale from 0.1 to 1 ns, the rotational MSD for hydrogen atoms of the C8mim+ cation speeds up by a factor of 3.5 in the simulations as shown in Figure S7a of the SI, in good agreement with the value of 3 predicted from fits to QENS measurements. When a long-time limit of the rotational MSD is examined in the simulation, the speedup appears to be larger (by 6.2 times) as shown in Figure S7b, further indicating that the speedup for rotational relaxation is time-dependent. In addition to the sub-diffusive behavior, the Gaussian approximation inherent in the model used for QENS data analysis could introduce errors up to 20%, depending on the timescale, as shown in Figure S6 of the SI. Further analysis of the simulations further indicates that adding water to C8mimBF4 does not significantly change the degree of ion correlated motion αd that is often called ionicity (see Figure S8 of the SI and Table 1), which quickly increases within a fraction of ns and saturates. A much larger fraction of solvent is needed in order to significantly increase the already high ionicity, indicating that the cation and anion motion is weakly correlated over long times in both systems. Interestingly, an increase of ionicity of pyr15TFSI was observed with addition of the high dielectric constant propylene carbonate solvent for a higher fraction of solvent, above 0.9. 21 Addition of one water molecule per ion pair in C8mimBF4 decreases the ionic liquid viscosity from > 280 to 67 mPa.s and increases the ionic conductivity from 0.58 to 4.15 mS.cm-1. This is due to the increased ion motion since αd does not change significantly. In conclusion, the QENS and MD results for relaxation, probed by the dynamics of the hydrogen atoms in the time range of 2 ps - 1 ns, are in excellent agreement. Analysis of QENS results indicates that the cation translational motion increases by approximately a factor of seven with water addition. Rotational relaxation involves multiple processes and can be fitted by a KWW function with low β values. The average rotational relaxation time decreases by a factor three on the addition of water on the timescale of QENS experiments but is dependent on the timescale probed. The MD simulation shows that the cation diffusion coefficient, inverse viscosity and ionic conductivity increase significantly on the addition of water, consistent with the very small change in the ionicity. The apparently higher diffusion coefficients obtained from QENS can be reconciled by viewing the QENS translational relaxation in the time range up to 1 ns as subdiffusive, with true diffusion only reached around 100 ns. Overall, this work demonstrates the importance of combining molecular simulations employing realistic potentials with experimental determinations of dynamics in a highly correlated system. Experimental Section and Computational Methods The QENS measurements were carried out at the near-backscattering spectrometer DNA22 at the J-PARC pulsed spallation neutron source. The final energy was 2084 µeV with the Si(111) analyser array. Two configurations were used, with and without the pulse-shaping chopper, giving FWHM resolutions of 3.6 and 14 µeV and dynamic ranges of (-40, 100) and (-500, 1500) µeV, respectively. The samples were contained in annular Al containers with a wall thickness 0.25 mm, inner diameter of the outer cylinder 14.0 mm and outer diameter of the inner cylinder 13.6 mm for a reference sample of pure water and 13.4 mm for the other samples. The pure salt 6 ACS Paragon Plus Environment

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was measured at 10 K in the two configurations to obtain the resolutions and join the data from the two configurations. The scattering data were reduced with the Utsusemi software 23 and analyzed with the DAVE software.24 The raw data were deconvoluted by the resolution function and converted to the scattering function S(Q,E) by interpolation onto the Q grid 0.2(0.2)1.8 Å-1 and then Fourier transformed into the intermediate scattering function I(Q,t). Since the scattering is dominated by the incoherent scattering from hydrogen, I(Q,t) is approximately equal to the self intermediate scattering function averaged over the non-deuterated hydrogen atoms in the sample. For the MD simulations we extend the many-body polarizable APPLE&P force field that accurately predicted properties of pure ILs25,26,27, 28, IL-solvent26 and IL-Li salt21,27,28 mixtures to C8mimBF4-H2O mixtures followed by validation of its ability to adequately predict structural and transport properties in the IL-rich regime. Simulation cells had linear dimensions of 43.45 Å and 44.35 Å for IL and IL+water, respectively. A revised SWM4-DP water model modified to work under the APPLE&P was used.29 Simulations were carried out for 192 ion pairs of C8mimBF4 and the C8mimBF4.H2O (1:1mol) solution at 300 K, corresponding to the experimental conditions. Acknowledgments We thank Professor L. Paulo Rebelo for helpful discussions of phase diagrams. We are grateful to Professor M. Arai and J-PARC staff for their help and scientific discussions. DLP acknowledges a visiting appointment at J-PARC, Tokai, Japan, and MLS acknowledges a fellowship from the Japan Society for the Promotion of Science. The DAVE data analysis software suite was developed at NIST in work supported by the National Science Foundation under Agreement No. DMR-0944772. Justin Hooper (University of Utah) assisted with TOC graphic. Supporting Information Available. The supporting information contains values of the form factor and relaxation time for the local relaxation, formulae for derivation of physical quantities from the MD simulations, mean-squared displacements and self-intermediate incoherent scattering functions and MD simulation methodology.Table 1. MD results for diffusion constants D, viscosity η, ionic conductivity κ and ionicity αd, together with experimental values where available.

Dcation (1010 m2.s-1) Apparent Dcation(1010m2s-1)

C8mimBF4.H2O

C8mimBF4

MD 0.14 (0.23)c

MD 0.023(a) (0.052)c

Experiment (0.38±0.02)(b)

Experiment (0.055±0.005)(b)

Danion (1010 m2.s-1) Dwater (1010 m2.s-1) η (mPa.s) κ (mS.cm-1)

0.25 0.027(a) 3.16 67 >280(a 336.3(d) (a) (a) 4.15 0.58 0.875(e) 0.75 0.78 αd (a) With the finite simulation size correction due to hydrodynamic interactions across periodic boundary discussed in the text. (b)

Apparent diffusion coefficients representing local diffusion fitted to QENS data in present work

(c)

Apparent diffusion coefficients obtained by fitting the cation center of mass MSD from 0.1 ns to 1.0 ns in MD simulations as shown in Figure S4. (d)

Ref.30

(e)

Ref. 31



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Relaxation in a Prototype Ionic Liquid: Influence of Water on the

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