Solute Rotation in Ionic Liquids: Size, Shape, and Electrostatic Effects

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Solute Rotation in Ionic Liquids: Size, Shape, and Electrostatic Effects Christopher A Rumble, Caleb Uitvlugt, Brian Conway, and Mark Maroncelli J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b01704 • Publication Date (Web): 21 Apr 2017 Downloaded from http://pubs.acs.org on April 29, 2017

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The Journal of Physical Chemistry

Solute Rotation in Ionic Liquids: Size, Shape, and Electrostatic Effects

Christopher A. Rumble, Caleb Uitvlugt, Brian Conway, and Mark Maroncelli* Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, United States Abstract: Herein are reported temperature-dependent measurements and molecular dynamics simulations designed to investigate the effects of molecular size, shape, and electrostatics on rotational dynamics in ionic liquids. Experiments were performed in the representative ionic liquid 1-butyl-3-methylimadazolium tetrafluoroborate ([Im41][BF4]) and simulations in the generic ionic liquid model ILM2 as well as a more detailed representation of [Im41][BF4].

2

H

longitudinal spin relaxation times were measured for deuterated versions of 1,4dimethylbenzene, 1-cyano-4-methylbenzene, and 1,4-dimethylpyridinium between 296–337 K. Fluorescence

anisotropy

measurements

were

made

on

the

larger

solutes

9,10-

dimethylanthracene, 9-cyano-10-methylanthracence and 9,10-dimethylacridnium between 240292 K. Both experiment and simulation showed the nonpolar solutes rotate ~2-fold faster than their dipolar and charged counterparts.

The rotational correlation functions measured in

fluorescence experiments are significantly nonexponential and can be fit to stretched exponential functions having stretching exponents 0.4 ≤ β ≤ 0.8, with β decreasing with decreasing temperature.

Rotational correlation times in both the NMR and fluorescence experiments

conform approximately to the hydrodynamic expectation τ rot ∝ (η / T ) p with p ≅ 1, and observed times are reasonably close to slip hydrodynamic predictions.

Simulations, even with the

idealized ILM2 solvent model, are in semi-quantitative agreement with experiment when compared on the basis of equal values of ηT-1. When rotational diffusion coefficients (Di) rather than correlation times were considered, much larger departures from hydrodynamic predictions are found in many cases (p~0.5 and Di >> slip predictions). Rotational van Hove functions and trajectory analyses reveal the importance of large-angle jumps about some axes, even in the larger solutes. -----------------------------------------------*corresponding author, [email protected]

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Introduction Ionic liquids (ILs), salts that are molten below 100ºC, have been a focus of intense study over the past decade. Such liquids can be synthesized with a variety of cation-anion pairs, allowing for the tuning of solvent properties to the task at hand. As such, ionic liquids have found uses in fields such as energy,1 synthesis,2 and green chemistry.3,4 The elucidation of the structure,5-7 solvation,8-11 and reaction dynamics12-15 of these unusual solvents have also been targets of intense interest. Molecular friction and transport properties play an important role in these phenomena, and have been investigated using a broad array of experimental and simulation approaches. Herein we describe an extension of our recent study of rotational dynamics of benzene in ionic liquids,16 now employing a broader more representative set of solutes. The present work focuses on how solute size, shape, and charge distribution affect the rotational friction felt by solute molecules in a common ionic liquid using NMR T1 relaxation, fluorescence anisotropy, and molecular dynamics (MD) simulation techniques. Below we describe some of the research in this area most relevant to the present work; a more extensive survey of studies of rotation in ionic liquids is provided in Ref. 16. Measurements of the rotational dynamics of small solutes in ionic liquids have primarily come from spin relaxation measurements.17-25 For example, Yasaka and coworkers20,21,23-25 used both 2H and 17O spin relaxation measurements to determine rotation times of CO, D2O, and C6D6 in a number of common ionic liquids. Their findings, in conjunction with MD simulations,21 showed that rotations of these small molecules are poorly represented by hydrodynamic models, and that rotational correlation times, τrot, scale with viscosity (η) and temperature (T) according to τ rot ∝ (η T ) p with 0.49 < p 85° jumps in the smaller solutes (Table 5). Nevertheless, even in the anisotropy probes, the presence of jump-like motion, particularly about the x axis, is clear from visual inspection of trajectory data. Three features of the angular jumps observed here should be noted. First, contrary to the the connotations associated with the term ‘jump’, these large-amplitude motions do not reflect inertial dynamics. This point is illustrated in the inset to Figure 17 for one of the largest, most distinctive jumps in the DMBz trajectories. During the ~5 ps required for ∆φz to decrease by 180° the angular velocity about this axis changes sign approximately 30 times. Thus, the process is the diffusive crossing of an orientational barrier created by the relatively immobile surroundings of the ionic liquid, rather than any ballistic type of motion. Second , although some jump angles (90° and 180°) are slightly favored in some cases, a continuous distribution of jump angles exists, as illustrated in Figure SI-8. Finally, it should be appreciated that rotational jump are integral to the rotation process and not merely a curiosity if little impact. One indication of this fact is that the rotational diffusion coefficients of all six solutes are well correlated to their jump frequencies (Figure SI-9). Moreover, assuming rotation occurs only through uncorrelated jumps of ∆φ = ±85°, using the relation Di = (∆φ ) 2ν i / 2 with the jump frequencies (νi) listed in Table 5, one calculates values of Di that are comparable to the simulated values in all cases

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where jumps occur at frequencies >1 ns-1. Thus, for all NMR probes and also for DMAn, jump motions account for a sizeable fraction of the rotational rotational displacements taking place in the ionic liquid.

Concluding Remarks In this study we sought to disentangle the effects of solute size and electrostatics on rotational friction in ionic liquids, through experimental and computational comparisons of two sets of nearly isosteric molecules in the prototypical ionic liquid [Im41][BF4].

This work

generalizes and extends our previous study of benzene in the same ionic liquid to less symmetric solutes that span the size range over which prior studies have suggested a changeover between different types of rotational motion.

2

H-NMR measurements of the smaller solutes provided

rotational correlation times, whereas fluorescence anisotropy measurements of the larger set provided complete rotational correlations for specific in-plane vectors. The variations in charge distribution within each set of solutes cause relatively modest ( 85° ∆φi > 170° y z x y z DMBz 1.0 23 0.25 -1.7 CMBz 0.3 23 --2.2 DMPy+ 0.4 23 0.01 -1.6 ∆φi > 40° ∆φi > 85° DMAn 30 12 8.6 1.2 -~.01 CMAn 2.6 2.0 0.4 0.22 -~.01 DMAc+ 12 8.1 6.7 0.20 -~.01 Frequencies of large angular displacements, ∆φi, during 5 ps intervals. Absence of a numerical value indicates no jumps were observed throughout the 200 ns simulation (νi < 0.005 ns-1). Solute

x 15 1.0 3.5

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Scheme 1. Probe and solvent structures, axis definitions, and naming conventions. Note the different definitions of the y/z axes for the NMR and anisotropy solutes. The arrows in red represent the axes probed in experiments.


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DMBz

DMAn +.07

+.11

z = 4.3 Å

+.11

CMBz

CMAn -.48

-.43 +.12

+.14

+.12

+.13 +.12

DMPy+ +.18

x = 2.0 Å

y = 3.2 Å

+.14

+.20

x = 2.0 Å

+.14

DMAc+ +.14 +.16

y = 4.2 Å

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+.18 +.19

+.14 +.14

z = 5.7 Å

Figure 1. Spatial and electrostatic properties of the probes studied. The multi-colored images show electrostatic potentials mapped onto isodensity surfaces (4×10-4 au). ESP-fit charges derived from these electrostatic potentials on some peripheral atoms are also shown. The magenta figures at the right show two views of the DMBz and DMAn surfaces together with cross sections of the ellipsoids used for hydrodynamic calculations. Figures were generated using GaussView 5.0.



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( 2) Figure 2: Hydrodynamic predictions for Crot ( t ) corresponding to ILM2 simulations at 350 K

(25.9 mPa·s, ηT −1 = 0.074 mPa s K-1). Also shown for comparison is a single exponential function (τ = 40 ps). The data in both panels are the same, but plotted as semilog-x on the top and semilog-y on the bottom.


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( 2) Figure 3. Crot ( t ) of the NMR and anisotropy probes from ILM2 simulations at 350 K compared

to hydrodynamic predictions ( ηT −1 = 0.074 mPa s K-1).



1

DM Bz

DM An

(2) rot

C (t)

0.8

300 K

400 K

0.6 0.4 0.2 0 1

CM Bz

CM An

DM Py+

DM Ac +

(2) rot

C (t)

0.8 0.6 0.4 0.2 0 1 0.8 (2) rot

C (t)

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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0.6 0.4 0.2 0 10

1

0

1

2

10 10 10 10 t / ps

3

10

1

0

1

2

3

4

10 10 10 10 10 t / ps

( 2) Figure 4. Simulated Crot ( t ) in ILM2 (lines; 300 – 400 K) and UA [Im41][BF4] (×’s) at 350 K. Arrows on the inset models indicate the experimentally measured vectors being simulated. Closest agreement between the value of ηT-1 in the UA model at 350 K (0.042 mPa s K-1) and ILM2 occurs at 375 K (cyan curve) where ηT-1 = 0.035 mPa s K-1.


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DMBz T1 / ms

10

10

10

10

10

10

10

1

10

0

2

CMBz

Sim 500 Sim 300 Sim ENL Exp 500 Exp 300

10 10

1

10

0

2

10

DMPy+ 10

1

10

0

300 325 350 375 400 T/K

1

10 η T / mPa s K 1

1

10

0

10

2

1

0

2

1

0

2

1

T1 / ms

T1 / ms

10

10

T1 / ms

T1 / ms

10

2

T1 / ms

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

Figure 5. Experimental (points) and simulated (curves) T1 relaxation times vs. temperature (left) and viscosity/temperature (right) . Arrows on the inset molecules indicate the vector accessed by experiment. Error bars on the experimental data representing the 95% confidence interval of 3 repeated measurements typically lie within the symbols.



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Figure 6. Rotation times (τrot) of DMBz, CMBz, and DMPy+ from T1 experiments (points) and simulation (curves) and. Black lines represent stick (solid) and slip (dashed) hydrodynamic predictions. Error bars representing estimates of the 95% confidence interval of 3-4 repeated T1 measurements lie in most cases within the symbols.


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Figure 7. Emission anisotropy vs. excitation wavelength (red points) superimposed on the absorption spectrum (blue curve) of DMAn in 1,2- propanediol at 200 K. Emission is monitored at 450 nm. Error bars indicate the standard deviation of 3 consecutive measurements.



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Figure 8. Representative anisotropy data (points) for DMAn in [Im41][BF4] at two temperatures illustrating fits of r(t) using bi-exponential (blue) and stretched exponential (red) models. The top panels show weighted residuals of the fits. Note that the anisotropy data and residuals have been thinned by a factor of 2 before 0.1 ns and a factor of 30 for all longer times for clarity. Time constants in the tables are in units of ns.


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( 2) Figure 9. Rotational correlation functions Crot ( t ) from fluorescence anisotropy experiments

(lines) and simulations (circles) at ηT −1 = 0.2 mPa s K-1. The time axis for each data set is normalized to its correlation time for ease of comparison. The black ×’s on the experimental −1 curves indicate the points at which τ rot t = 25 ps, the FWHM of the instrumental response function. DMAn and CMAn data are vertically offset by 0.25 and 0.5, respectively, for clarity. The dashed blue curve represents the DMAn data scaled to the literature vale of rss = 0.345 instead of the value of 0.31 measured here.



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Figure 10. Top panel: initial anisotropies in [Im41][BF4]. Points are the average of stretched and bi-exponential fits to the time-resolved (TR) data and error bars are 2× the difference between the these two fits. Dashed colored lines represent the values of the steady state (SS) anisotropies in frozen solution (200 K). Bottom panel: stretching parameters from experiment (points) and simulation (lines). Error bars are 2× the standard deviation from stretched exponential fits of three consecutive measurements.


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Figure 11. Rotational correlation times from anisotropy experiments (points) and simulation (lines). Dashed horizontal lines represent 10× the probe’s fluorescent lifetime. Correlation functions from the 300 K ILM2 simulations of the anisotropy probes were not fully converged, and rotation times from these simulations are omitted.



300 K 325 K 350 K 375 K 400 K

2

1

0

10 10 10 10

1

2

a)

3 DMBz CMBz DMPy+ DMAn CMAn + DMAc

2

10 2

Scaled 10×

10

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/ rad

2

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10

Scaled 10×

0

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2

/ rad

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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10 10

1

2

b)

3

10 10

1

0

10

1

10 10 t / ps

2

10

3

Figure 12. Mean-squared angular displacements, ∆φ y2 ( t ) , about the y molecular axes of the probes simulated in ILM2. a) ∆φ y2 ( t ) for DMBz (solid lines) and DMAn (dashed lines) at different temperatures. b) ∆φ y2 ( t ) at 350 K for the NMR (solid lines) and anisotropy (dashed lines) probes. NMR probe displacements in both panels are scaled by 10× for clarity. Arrows on the inset images indicate the y axis directions observed. 50 ACS Paragon Plus Environment

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NMR

2

10 1

10

0

10

x

2

D / rad ns

Anis.

X

1

10 10

1

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DMBz CMBz

DMAn CMAn

DMPy+

DMAc+

Y

1

0

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y

2

D / rad ns

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10

10 10

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Z

1

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10

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10

z

2

D / rad ns

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


10 10

1

2

10

0

1

Tη

1

10

/ K mPa

2

1

s

1

0

10 10

Tη

1

10

1

/ K mPa

2

1

s

1

10

Figure 13: Rotational diffusion coefficients about inertial axes of all solutes as functions of Tη-1. Dashed lines represent slip hydrodynamic predictions.



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Figure 14: Relative rotational diffusion coefficients Di/Dsph in ILM2 at 350 K and corresponding slip predictions as functions of relative rotational volume Vrot,i/VvdW. Diffusion coefficients are normalized to stick predictions for a sphere of the same volume and rotational volumes are normalized by the van der Waals volumes. Colored points are simulated values and the colored dashed lines are visual aids connecting values of each solute. The gray points labeled “Bz” are values for a benzene solute.16 The small “×”s are slip hydrodynamic predictions based on the ellipsoid representations of all six probes and benzene, and the black curves are the slip predictions for rotation about axes perpendicular to the symmetry axes of prolate (solid) and oblate (dashed) spheroids.74 The figures at the top illustrate the axial ratios τ corresponding to different values of Vrot ,i / VvdW = (τ −1 − 1) .


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0.015

θ of axes

∆ φ about axes

DMBz, 68 ps CMBz, 74 ps + DMPy , 74 ps

10

x

10

1

2

x

Gx(θ, t)

0.01

G (∆φ, t)

10

3

0.005 10 0 0.015

10


10 0.01

4

1

2

y

Gy(θ, t)

y

G (∆φ, t)

10

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0.005 10 0 0.015

10


4

1

z 10

2

z

Gz(θ, t)

0.01

G (∆φ , t)

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


50 ps

0.005

10

5 ps 10

0 0

3

50

100 θ/°

150

0

90

180 ∆φ / °

270

4

360

Figure 15. Left panels: Gi (θ , t ) for rotation of the x-, y- and z axes of the NMR probes from ILM2 simulations at 350 K. All times are chosen so that Gi (θ , t ) = 60º . The black × symbols in these panels show the predictions of Brownian diffusion on a sphere. Right panels: Gi ( ∆φ, t ) for rotation about the x-, y- and z-axes of the NMR probes at t = 5 ps (dashed) and t = 50 ps (solid). The black × symbols are the average predictions at 5 ps calculated from Equation 16. 53 ACS Paragon Plus Environment


DMBz

00 psps

150 ps 150 ps

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DMAn

300 ps 300 ps

00 psps

150 ps 150 ps

300 ps 300 ps

Figure 16. Representative 300 ps trajectories for rotation of the y-axis of DMBz and DMAn at 350 K. The inset molecular images show the molecule’s orientation at t = 0.


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3x

z y

x

y z x

Figure 17. Representative trajectories, ∆φi(t), for rotation about the x-, y-, and z- axes of DMBz (top) and DMAn (bottom) at 350 K. The ordinate scale is the same for both plots, but shifted for clarity. The inset plot shows the angular velocity about the DMBz z axis, ωz, during the large jump observed between 105 and 135 ps.



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TOC Figure


Solute Rotation in Ionic Liquids: Size, Shape, and Electrostatic Effects

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