Dielectric Relaxation of the Ionic Liquid 1-Ethyl-3-methylimidazolium

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Dielectric Relaxation of the Ionic Liquid 1-Ethyl-3methylimidazolium Ethylsulfate: Microwave and Far-IR Properties Nilesh Ramchandra Dhumal, Johannes Kiefer, David Andrew Turton, Klaas Wynne, and Hyung J Kim J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 25 Apr 2017 Downloaded from http://pubs.acs.org on April 25, 2017

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The Journal of Physical Chemistry

Dielectric Relaxation of the Ionic Liquid 1-Ethyl-3-methylimidazolium Ethylsulfate: Microwave and Far-IR Properties Nilesh R. Dhumal,† Johannes Kiefer,‡ David Turton,¶ Klaas Wynne,¶ and Hyung J. Kim⇤,†,§,k †Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA ‡Technische Thermodynamik, Universität Bremen, 28359 Bremen, Germany ¶School of Chemistry, University of Glasgow, Glasgow G12 8QQ, UK §School of Computational Sciences, Korea Institute for Advanced Study, Seoul 02455, Korea kPermanent address: Carnegie Mellon University E-mail: [email protected] Abstract Dielectric relaxation of the ionic liquid, 1-ethyl-3-methylimidazolium ethylsulfate (EMI+ ETS – ), is studied using molecular dynamics (MD) simulations. The collective dynamics of polarization arising from cations and anions are examined. Characteristics of the rovibrational and translational components of polarization dynamics are analyzed to understand their respective roles in the microwave and terahertz regions of dielectric relaxation. The MD results are compared with the experimental low-frequency spectrum of EMI+ ETS – , obtained via ultrafast optical Kerr effect (OKE) measurements.

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Introduction Dielectric relaxation and the related conductivity of a condensed-phase system arise from molecular motions that modulate its local electric dipole moment. 1 Far-IR (FIR) and terahertz spectroscopy offers an excellent experimental tool to probe these motions, both the individual and the collective (inter)molecular motions, subject to the influence of the local structure. Dielectric absorption data obtained by these techniques as well as via microwave spectroscopy have been very useful in theoretical modeling and understanding of the dynamics in polar solvents and ionic solutions. 2–9 Ionic liquids (ILs) consisting of bulky organic cations paired with organic or inorganic anions are characterized by an anisotropy in the charge distribution and shape. These attributes make ILs an interesting and challenging class of materials to understand their dielectric and related properties, as they have characteristics of both polar liquids and ionic melts. At the molecular level, IL ions have both a net charge and a permanent dipole moment (except for highly symmetric anions such as PF6– and BF4– ). At the dielectric or mesoscopic level, these properties result in significant ion conductivity and dielectric permittivity. According to many simulation studies, 10–15 the collective reorientational and translational motions of the ions make differing contributions to the dielectric relaxation in the GHz and THz regions. In this respect, spectroscopic measurements in both the microwave and FIR regions would be needed to fully resolve and understand the cationanion interactions and their dynamics in these Coulomb fluids. 16–18 The static dielectric constant "0 , arising from collective ion reorganization via both reorientation and translation in response to an external electric field, ranges between ⇠10 and ⇠16 for most ILs. 10,16,19–22 Despite their modest "0 value, 23 the effective polarity of ILs, which is measured as solvatochromic shifts gauging their capability of solvating dipolar solutes, is comparable to and often in excess of that of highly polar solvents, such as acetonitrile. 24 Interestingly, the "0 value of many ILs shows a weaker temperature dependence than for polar solvents. The antagonistic roles played by IL ion translations and reorientations 2


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are responsible for this behavior. The former and latter tend to increase and decrease "0 , respectively, as temperature rises. 15 In this article, we examine the dielectric relaxation of 1-ethyl-3-methylimidazolium ethylsulfate (EMI+ ETS – ), one of the first ILs that were commercially available. Its halide-free synthesis was first studied by Holbrey and coworkers 25 and aspects of reactor design were discussed by Bowing and Jess. 26 Its static dielectric constant was found to be "0 = 27.9, which is considerably higher than many other ILs. 21 In addition to its use as a green solvent, EMI+ ETS – has a potential application in chemical separation, in particular, in the separation of azeotropic mixtures. 27 Therefore, an extensive attention has been paid to its bulk and interfacial properties. 28–39 Here, we investigate the dielectric susceptibility of EMI+ ETS – in the GHz and THz region via MD and analyze the respective roles played by translational and reorientational motions of cations and anions. The spectroscopic information extracted from the MD simulations is compared with the dielectric loss spectroscopy results 40 as well as with the low-frequency spectrum obtained from ultrafast optical Kerr effect (OKE) measurements.

Theory and Methods Dielectric Relaxation and Ion Conductivity We begin with a brief reprise of the linear response theory for dielectric relaxation (for details, see refs 10 and 14). The electric susceptibility (!) is defined as

(!) =

Z

1 0

dt e

i!t

(t) ;

1 M tot (t) = V

Z

t

dt0 (t

t0 )E(t0 ) ;

1

M tot =

X

qi,↵ r i,↵ , (1)

i,↵

where M tot (t) is the average total dipole moment of the system at time t induced by a timedependent homogenous electric field E(t), V is the volume, qi,↵ and ri,↵ are, respectively, the charge and position of the site i of ion ↵, and the sum is taken over charge sites of all ions. 3



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Generalized dielectric constant "(!) and conductivity (!) are introduced as 4⇡ (!) = "0 (!) + i"00 (!)

1=i

4⇡ 0 [ (!) + i !

00

(!)] ,

(2)

where prime and double prime denote, respectively, the real and imaginary parts of "(!) and (!). "(!) and (!) are phenomenological coefficients that relate, respectively, the electric polarization and its time derivative (i.e., electric current) to the electric field. Therefore, "(!) and (!) contain precisely the same information on the system’s polarization dynamics. Since ionic systems are characterized by non-vanishing DC conductivity, i.e., (0) = 0 (0) 6= 0, we introduce "c (!)

"c (!) ⌘ "(!)

4⇡ (0) = 1 + 4⇡ i !



(!)

(0) !

i

,

(3)

which does not diverge as ! approaches 0. Experimentally, the static dielectric constant "0 is determined as 3,4



"0 = "c (0) = lim "(!) !!0

i

4⇡ (0) !

(4)

.

The fluctuation-dissipation theorem relates (!) to the time correlation of M tot as

(!) =

1 3V kB T

Z

1

dt ei!t

0

d

MM (t)

dt

;

MM (t)

= hM tot (t)·M tot (0)i ,

(5)

where kB is Boltzmann’s constant and T is the temperature. Following earlier works, 10,14 we decompose M tot into two components arising from reorientational and translational motions cm M tot = M cm rot + M tr ;

µcm,↵ =

M cm rot ⌘

X

X

µcm,↵ ;

↵

qi,↵ (r i,↵

r cm,↵ ) ;

M cm tr ⌘ q↵ =

i2↵

X

4


↵

X i2↵

q↵ r cm,↵ ;

qi,↵ ,

(6)

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where q↵ and r cm,↵ are the net charge and the position of the center of mass of ion ↵, and µcm,↵ is its dipole moment with respect to its center of mass. + cm 2 (!) ; Z 1 1 n cm 2 cm hM rot i + dt ei!t [ i! 1 (!) = 3V kB T  0 Z 1 1 i cm cm dt ei!t 2 (!) = JM (t) + 3V kB T 0 ! (!) =

cm MM (t) cm MJ (t)

(!) in eq 5 then becomes

cm 1 (!)

cm = hM cm rot (t)·M rot i ;

cm JM (t)

+

cm JJ (t)

;

cm MJ (t)]

o

; (7)

cm = hJ cm tr (t)·J tr i ;

cm JJ (t)

cm = hM cm rot (t)·J tr i ;

cm MM (t)

cm = hJ cm tr (t)·M rot i ,

where J cm tr is the ionic current due to the translational motions of ion center of mass J cm tr ⌘

X d = q↵ r˙ cm,↵ , M cm dt tr ↵

and the cross-correlation functions satisfy

cm JM (t)

=

(8)

cm MJ (t).

It should be noted that,

though ion reorientational motions about their center of mass are the main contributor to M cm rot , their internal vibrations also make a contribution (see below). As in refs 14 and 15, cm we also introduce "cm rot (!) and "tr (!)

"cm rot (!)

⌘ 1 + 4⇡

cm 1 (!)

;

"cm tr (!)

⌘ "c (!)

"cm rot (!)

= 4⇡



cm 2 (!)

i

(0) !

(9)

cm The decomposition of M tot via eq 6 and thus of "c (!) into "cm rot (!) and "tr (!) via eqs 7–9

has an important advantage in that it enables us to understand characteristics of different molecular motions in ILs and their roles in the dielectric relaxation and related phenomena. Reorientational (plus vibrational) and translational motions of ions and their cross correlations contribute to

cm 1 (!)

and

cm 2 (!)

of ILs (eq 7). Because translational and reori-

entational motions are usually decoupled, the contribution of the cross terms is very small. cm Therefore, "cm rot (!) and "tr (!) arise primarily from reorientations (and vibrations) of indi-

5



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vidual ions with respect to, and translations of, their center of mass, and thus can shed light on details of ion dynamics in ILs. We nonetheless note that the decomposition is for convenience and that physically measurable quantities such as

(!) and "(!) do not and

should not depend on the decomposition scheme employed.

Simulation Models and Methods Molecular dynamics simulations were performed in the isothermal-isobaric (NP T ) ensemble using the GROMACS simulation package. 41 Nosé-Hoover temperature coupling and Parrinello-Rahman pressure coupling were used. A fully flexible but non-polarizable allatom description based on the OPLS-AA force fields 42 was employed to describe intermolecular interactions. Specifically, the force field parameters of ref 43 were used for 1-ethyl-3methylimidazolium (EMI+ ), while the parameters for ethylsulfate (ETS – ) were taken from ref 44. The simulation cell comprises 128 pairs of EMI+ and ETS – ions in a cubic box with periodic conditions applied. The long-range electrostatic interactions were computed via the Particle-Mesh-Ewald method, resulting in essentially no truncation of these interactions. Three trajectories were simulated at 350 K and 1 atm, using the Verlet leapfrog algorithm using a time step of 1 fs. For each trajectory, simulation was carried out with 1.5 ns of annealing from 600 K and 10 ns of equilibration at 350 K, followed by a 30 ns production run. Averages were computed using three 30 ns trajectories thus generated, corresponding to a total of 90 ns simulation.

Results and Discussion Dielectric relaxation At the outset, we mention that cross correlations,

cm JM (t)

and

cm MJ (t),

between the col-

cm lective center-of-mass dipole moment M cm rot (t) and the ionic current J tr (t) are found to be + – cm insignificant and thus do not play any important role in "cm rot (!) or "tr (!) for the EMI ETS

6


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system studied here. With this in mind, we first consider "cm rot (!) in Figure 1, which arises from ion reorientational dynamics. Most noticeable is a strong band at ! ⇡ 1.2 ⇥ 10

3

ps

1

(f ⇡ 0.2 GHz), which spans a very broad frequency range from ! ⇡ 0.001 to 0.1 ps 1 . The 0 monotonically-decreasing behavior of "cm rot (!) with the increasing frequency clearly indicates

that this band is due to dissipative modes. For additional insight, we analyzed the respective contributions of the cations and anions. The results in Figure 1b show that the GHz band is dominated by the anions. This is as expected because the center-of-mass dipole moment 7.19 D for ETS – is much larger than 1.94 D for EMI+ in the force description 43,44 employed in our study. All other things being equal, the peak intensity will be proportional to square dipole moment because M cm rot scales linearly with the center-of-mass dipole moment (eqs 6 and 7). We also notice that the anion peak is shifted toward higher frequencies, compared to the cation. This suggests that the anion reorientations are slightly faster than the cation reorientations (results not shown). Recently, the microwave region of EMI+ ETS – was studied via dielectric relaxation spectroscopy. 40 Though in good qualitative agreement, we note a couple of differences. First, the MD prediction for the peak frequency of the GHz band is lower than the experimental result (! ⇡ 7 ⇥ 10

3

ps 1 ) 40 by a factor of ⇠ 6. This is not surprising in that non-polarizable

force-field models for ILs with integral ionic charges tend to underestimate their transport coefficients considerably. This state of affairs would be improved with the inclusion of electronic polarizability in the potential model; according to previous studies, 45–48 it would accelerate < 2. Another difference is the assignment of the GHz IL transport dynamics by a factor of ⇠

band; while we attribute it primarily to anions as discussed above, it is assigned mainly to cation reorientations in ref 40. Another interesting aspect of Figure 1b is that though weak in intensity, the anions yield a discernible band structure in the frequency range between ⇠ 1 and ⇠ 20 ps 1 . The result 0 that "cm rot (!) shows a transition from the anomalous to normal dispersion near ! = 10 ps

1

indicates that this absorption mode has a resonance character. This is ascribed to hindered 7



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rotations of ETS – . We note that the THz structure of "cm rot (!) arising from anion vibrations observed here was absent in EMI+ PF6– studied in ref 14 because of the highly symmetric structure of PF6– . The value of 4⇡

cm 1 (0)

0 (= "cm rot (0) 1), 12.8, measures the contribution of mainly ion reori-

entations to the static dielectric constant "0 of the IL system (Figure 1a). The contribution of the anions (12.0) is much higher than that of the cations (0.8) (Figure 1b) for precisely 00 the same reason why the "cm rot (!) peak in the GHz region above is much more intense for 0 the former than the latter. The cationic contribution to "cm rot (0) obtained here compares very 0 well with that for the EMI+ PF6– system studied in ref 14. However, the overall "cm rot (0) value

of the EMI+ ETS – system is much higher than that of EMI+ PF6– as PF6– anions of the latter 0 IL do not contribute to "cm rot (0) due to their high spherical symmetry.

We turn to

cm JJ (t)

and "cm tr (!) in Figure 2. As mentioned above, the cross-correlation

cm cm between M cm rot (t) and J tr (t) is negligible, so that "tr (!) is governed essentially by the current

autocorrelation

cm JJ (t)

(cf. eq 7), i.e., ion translational dynamics. The DC conductivity

needed in the calculation of "cm tr (!) (eq 9) was determined via (0) =

1 i lim ! (!) = !!0 3V kB T

Analogous to other imidazolium-based ILs, 11,14,15,49

Z

1

dt

0

cm JJ (t)

cm JJ (t)

(10)

.

in Figure 2a exhibits a rapid

oscillatory decay, followed by dissipative relaxation. Its oscillation period is found to be ⇠ 0.3 ps and the ionic current becomes strongly anti-correlated, viz.,

cm JJ (t)

< 0, in less

than 0.2 ps. This reveals the librational character of ion translational motions at short times. The relaxation of

cm JJ (t)

is nearly completed in less than 1 ps, indicating that its

main contribution to "c (!) occurs in the THz frequency region. As shown in Figure 2b, "cm tr (!) is characterized by a significant absorption band in the 0.1 ps

1

< ! ⇠ < 20 ps ⇠

1

Dielectric Relaxation of the Ionic Liquid 1-Ethyl-3-methylimidazolium

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