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Rotational dynamics of benzene and water in an ionic liquid explored via molecular dynamics simulations and NMR *T* _{1} measurements

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10.1063/1.3685100

### Abstract

The rotational dynamics of benzene and water in the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride are studied using molecular dynamics (MD) simulation and NMR*T* _{1} measurements. MD trajectories based on an effective potential are used to calculate the ^{2}H NMRrelaxation time,*T* _{1} via Fourier transform of the relevant rotational time correlation function,*C* _{2R}(*t*). To compensate for the lack of polarization in the standard fixed-charge modeling of the IL, an effective ionic charge, which is smaller than the elementary charge is employed. The simulation results are in closest agreement with NMR experiments with respect to the temperature and Larmor frequency dependencies of *T* _{1} when an effective charge of ±0.5*e* is used for the anion and the cation, respectively. The computed *C* _{2R}(*t*) of both solutes shows a bi-modal nature, comprised of an initial non-diffusive ps relaxation plus a long-time ns tail extending to the diffusive regime. Due to the latter component, the solute dynamics is not under the motional narrowing condition with respect to the prevalent Larmor frequency. It is shown that the diffusive tail of the *C* _{2R}(*t*) is most important to understand frequency and temperature dependencies of *T* _{1} in ILs. On the other hand, the effect of the initial ps relaxation is an increase of *T* _{1} by a constant factor. This is equivalent to an “effective” reduction of the quadrupolar coupling constant (QCC). Thus, in the NMR*T* _{1} analysis, the rotational time correlation function can be modeled analytically in the form of *a*exp (−*t/τ*) (Lipari-Szabo model), where the constant *a*, the Lipari-Szabo factor, contains the integrated contribution of the short-time relaxation and *τ* represents the relaxation time of the exponential (diffusive) tail. The Debye model is a special case of the Lipari-Szabo model with *a* = 1, and turns out to be inappropriate to represent benzene and water dynamics in ILs since *a* is as small as 0.1. The use of the Debye model would result in an underestimation of the QCC by a factor of 2–3 as a compensation for the neglect of the Lipari-Szabo factor.

© 2012 American Institute of Physics

Received 08 August 2011
Accepted 27 January 2012
Published online 16 February 2012

Acknowledgments: Y.Y. and M.L.K. thank H. H. Sheikh Saud for generous support provided by the RAK CAM Sheikh Saqr Fellowship program. This research was supported in part by the National Science Foundation (NSF) through major research instrumentation grant number CNS-09-58854. N.M. is supported by the Grants-in-Aid for Scientific Research (Nos. 21300111 and 23651202) from the Japan Society for the Promotion of Science, by the Grant-in-Aid for Scientific Research on Innovative Areas (No. 20118002) from the Ministry of Education, Culture, Sports, Science, and Technology, and by the Nanoscience Program and the Computational Materials Science Initiative of the Next-Generation Supercomputing Project. The authors thank Dr. Shun Sakuraba (Kyoto University) for insightful comments.

Article outline:

I. INTRODUCTION

II. METHODS

III. RESULTS AND DISCUSSIONS

A. Rotational time correlation function and the relaxation time constant

B. Spectral density function

C. *T* _{1} and its temperature and frequency dependence

D. *T* _{1} comparison with experiments

E. Relaxation model for NMR study

F. QCC determination in NMR study

IV. CONCLUSIONS

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2012-02-16

2014-04-24

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