ARTICLE pubs.acs.org/JPCA
Hydrodynamic Interpretation on the Rotational Diffusion of Peroxylamine Disulfonate Solute Dissolved in Room Temperature Ionic Liquids As Studied by Electron Paramagnetic Resonance Spectroscopy Yusuke Miyake, Nobuyuki Akai, Akio Kawai,* and Kazuhiko Shibuya* Department of Chemistry, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 H57 Ohokayama, Meguro-ku, Tokyo 152-8551, Japan
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ABSTRACT: Rotational motion of a nitroxide radical, peroxylamine disulfonate (PADS), dissolved in room temperature ionic liquids (RTILs) was studied by analyzing electron paramagnetic resonance spectra of PADS in various RTILs. We determined physical properties of PADS such as the hyperfine coupling constant (A), the temperature dependence of anisotropic rotational correlation times (τ and τ^), and rotational anisotropy (N). We observed that the A values remain unchanged for various RTILs, which indicates negligible interaction between the NO PADS group and the cation of RTIL. Large N values suggest strong interaction of the negative sulfonyl parts of PADS with the cations of RTILs. Most of the τ , τ^, and (τ τ^)1/2 values are within the range calculated on the basis of a hydrodynamic theory with stick and slip boundary conditions. It was deduced that this theory could not adequately explain the measured results in some RTILs with smaller BF4 and PF6 anions.
1. INTRODUCTION Room temperature ionic liquids (RTILs) are salts in the liquid state with various unique physicochemical properties17 and have been extensively studied since 1990s.811 To better understand RTILs from a theoretical and practical perspective, it is necessary to know their properties, such as solutesolvent interactions and diffusion motion. Many experimental studies have been performed related to the rotational motion of solutes in RTILs.1231 Most of the experiments for investigating the solvation and rotational dynamics of dye molecules in RTILs are based on fluorescence decay. For example, Jin et al.22 measured the rotational correlation times for coumarin 153 in various RTILs using a time-correlated single-photon counting method and concluded that the rotational correlation times follow the StokesEinsteinDebye (SED) hydrodynamic equation in RTILs as well as in conventional solvents. Previous studies1231 suggest that the rotational diffusion dynamics of solutes in RTILs are similar to those in conventional molecular solvents. In the SED hydrodynamic equation, the solvent is assumed to be either a continuum media or the solvent molecule is assumed to have a much smaller size than the solute. However, the RTIL salt is composed of anions and cations, and the ion pair is usually larger than conventional organic solvent molecules. This feature of RTILs may suggest that the SED equation is valid only for systems with larger solute and smaller solvent molecules. From this perspective, the rotational dynamics of small solutes in RTIL is interesting. r 2011 American Chemical Society
However, it is difficult to study the rotational motion of small solutes by observing their fluorescence in a condensed phase. Yasaka et al.15 measured the rotational correlation times of D2O and C6D6 in BmimPF6 and BmimCl, respectively, by NMR spectroscopy and concluded that the rotational activation energy is lower than that calculated by the SED hydrodynamic equation. In this study, we focused on the rotational motion of solutes and the solutesolvent interactions in RTILs. We selected a small radical molecule of the peroxylamine disulfonate (PADS) nitroxide solute (Chart 1) that has a molecular volume of approximately 110 Å3, smaller than the well-studied dye molecules.14,18,22 The 14N isotropic hyperfine coupling constant (A) of PADS in RTILs and the rotational anisotropy (N) were determined by analyzing the EPR spectra32 and are discussed to understand the solvated structure of PADS. The measured rotational correlation times of PADS are discussed with respect to a hydrodynamic theory under stick and slip boundary conditions for the solutesolvent interactions.
2. EXPERIMENTAL METHODS Materials. Potassium peroxylamine disulfonate (K2PADS) and N-methylimidazole were purchased from Tokyo Kasei. Ionic liquid Received: December 22, 2010 Revised: April 26, 2011 Published: May 16, 2011 6347
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Chart 1. Structure of PADS and Molecular Axes Employed
Chart 2. Structures of Cations and Anions in RTILs and Their Abbreviates
Figure 1. EPR spectra of PADS in BmimPF6 measured at (a) 295 K and (b) 320 K. The parameters used for eqs 2 and 3 are given in (a).
Table 1. A Summary of g and A Values of PADS in Various Solvents
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samples, with the exception of EmimC2H5OSO3 (BASF) and BmimCH3OSO3 (Fluka), were supplied by Kanto Chemical. The structures of PADS and these RTILs are listed in Charts 1 and 2, respectively. To estimate the shape of PADS, density functional calculations were performed using a Gaussian 03 program34 at the B3LYP/6-31G(d, p) level of theory. All RTILs were treated in a globe box, and the sample solutions were kept under vacuum for 3 days at approximately 320 K to remove impurities such as dissolved gases and water. N-Methylimidazole was dehydrated with a 3A 1/16 (Kanto Chemical) molecular sieve for 3 days and subsequently deoxygenated by bubbling with Ar for approximately 10 min. The PADS concentration was less than 2 mM in a silica tube of 2.6 mm diameter. The sample solution was filtered to remove undissolved solutes. Apparatus. EPR spectra were recorded by an X-band EPR spectrometer (Bruker, ELEXIS 580E) with a rectangular cavity resonator in TE102 mode. The microwave power was 0.6 mW and the modulation width was 0.1 G. The magnetic field was calibrated using a tesla meter (Bruker, ER036TM). Sample temperatures in the range 240330 K were modified using a controller (Bruker, ER4131VT). Solvent viscosity was measured by a rotational viscometer (Brookfield, DV-IIþPro) with cone-and-plate geometry in the range 293330 K using a temperature controller (Eyela, UA-100). The temperature dependence of viscosity was fitted by empirical equations used to estimate viscosity values at low temperatures ( 0. According to literature,46,47 C^slip is determined by the r /r^ ratio and is calculated to be approximately 0.09 for PADS. Hence, we adopted this value. The τ^ values of (a) BmimTf2N, (b) Nmethylimizaole, and (c) BmimBF4 solutions were calculated for slip boundary conditions, and the resultant curves were plotted using the dotted lines, as shown in Figure 5. The measured τ^ values are smaller than the calculated τ^stick values (solid lines) but are larger than the calculated τ^slip values (dotted lines). On the basis of this observation, it can be inferred that the microscopic viscosity around the solute rotor is much smaller than the macroscopic viscosity of the solvent. However, as τ^ > τ^slip, the microscopic viscosity is not negligible. We therefore conclude that our measured τ^ values can be reasonably explained using the theory proposed by Youngren and Acrivos.46,47 Regarding rotation around the parallel y axis, the experimental τ values are much smaller than the theoretical τ tick values. The theoretical C lip value is equal to zero and, thus, we must stop the
;0 r^, are calculated as follows45
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experiment
which is derived from eqs 813. The resultant N value is then calculated as 1.4 for PADS. This theoretical value is closer to the experimental value of the organic solvent N-methylimidazole (2.4) than to that of RTILs (approximately 35) (Table 2). A larger N value implies that the rotational rate of PADS around the perpendicular axis is less than that around the parallel y axis. PADS contains two negatively charged sulfonyl groups. The Coulombic interaction between the sulfonyl groups and the RTIL cations may hinder the rotation of PADS around the perpendicular axis. This may be the reason for the anisotropy of PADS (N = 35) in RTILs being much larger than the theoretical value (N = 1.4) (Table 2). As a result, the Coulombic interactions between the solutes and solvents will be less effective in the organic solvent (N-methylimidazole) than in RTILs. Second, we discuss the absolute value of the rotational correlation times τ^ and τ . For this purpose, we examine the temperature dependence of τ^ and τ by comparing the experimental and theoretical values. Theoretical τ^ and τ values may be calculated according to eqs 913. Figure 5 shows the plot of τ^ and τ against temperature (solid lines). The comparison of the theoretical values with the experimental τ^ and τ values for all solvents shows that the theoretical values are larger than the experimental values for the entire temperature range. This implies that the microscopic viscosity of the solute is lower than the macroscopic viscosity of the solvent. To explain the difference between the macroscopic viscosity of the solvent and the microscopic viscosity around the solute rotor, the boundary conditions between the solute and solvent based on rotational motion are described below. According to Youngren and Acrivos,46 eq 9 can be modified as
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Figure 5. Plots of rotational correlation times of τ^ and τ vs T measured in three solvents: (a) BmimTf2N, (b) N-methylimidazole, and (c) BmimBF4. The experimental data are presented by filled squares (9). The simulations based on hydrodynamic diffusion theory are shown by solid and dotted lines, which are calculated under stick and slip boundary conditions, respectively.
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quantitative discussion on the measured τ value based on the hydrodynamic theory. We will examine instead another hydrodynamic theory in the subsequent section. Theoretical Evaluation of Nonspherical Slip Model for Isotropic Rotation of PADS. According to Perrin,48 the rotational correlation times of nonspherical solutes can be described by introducing an f-parameter into the SED equation of spherical solutes. This parameter is a dimensionless hydrodynamic
frictional coefficient and depends on the shape of a solute. Hu and Zwanzig49 modified the equation by considering the boundary conditions and the shape of a solute, which is represented by the coefficient Ci. Using these modifications, the following equation is obtained. τiR ¼ 6352
Vp η fCi ; ði ¼ stick or slipÞ kB T
ð16Þ
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Table 3. Activation Energy for the Rotational Motion of PADS
a
f ¼
31.0 ( 2.0 30.8 ( 1.3
BmimTf2N
29.9 ( 2.9
28.7 ( 1.9
Py13Tf2N
32.4 ( 1.5
32.3 ( 1.6 40.2 ( 1.1
EmimC2H5OSO3
34.0 ( 1.0
N3111Tf2N
35.2 ( 1.7
33.3 ( 1.4
Py14Tf2N
37.7 ( 3.1
37.7 ( 1.8
DemeTf2N
38.0 ( 2.0
35.5 ( 1.6
BmimCH3OSO3 PP13Tf2N
40.7 ( 0.6 43.5 ( 1.8
42.4 ( 0.9 32.7 ( 2.3
BmimPF6
46.1 ( 2.1
42.8 ( 3.2
DemeBF4
50.1 ( 1.4
44.1 ( 0.8
N-methylimidazole
12.3 ( 1.1
14.2 ( 1.1
Rotational motion around an axis on the xz plane perpendicular to the y axis (Chart 1). b Rotational motion around the y axis.
2 ðR 2 þ 1ÞðR 2 1Þ3=2 pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi 3R ð2R 2 1Þ lnðR þ R 2 1Þ R R 2 1
ð17Þ
where R denotes r^/r .48,50 The f value of PADS is 1.18. Because the theory mentioned above48,49 provides the mean value of τR, we employed τRobs, which is obtained by averaging the experimental values of τ and τ^ according to the following equation,32 pffiffiffiffiffiffiffiffi τobs τ τ^ ð18Þ R ¼ )
23.7 ( 1.1 25.0 ( 1.0
Ea ( )/kJ 3 mol1
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EmimBF4 BmimBF4
Ea (^)/kJ 3 mol
parallel rotationb
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solvents
1
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perpendicular rotationa
Here, Vp denotes the volume of the solute and Cstick = 1 and Cslip = 0.075 for the shape of PADS.49 For a solute having a prolate top shape, the f parameter is expressed as
To compare the measured τRobs values with the calculated τRstick and τRslip values, we plotted the observed and calculated τR values of PADS against η/T for (a) BmimTf2N, (b) N-methylimidzole, (c) DemeTf2N, and (d) N3111Tf2N, as shown in Figure 6. Similar plots for PADS dissolved in solvents of (a) BmimBF4 and (b) BmimPF6 are shown in Figure 7. Figure 6 shows that the τRobs
Figure 6. Logarithmic plots of measured τR values (9) of PADS vs η T1 in (a) BmimTf2N, (b) N-methylimidazole, (c) DemeTf2N, and (d) N3111Tf2N. Theoretical τR values calculated under the stick and slip conditions are shown by solid and dotted lines, respectively (see text for the details). 6353
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Table 4. Comparison of Experimental and Theoretical τR as a Function of Temperature or Viscosity t parametera
τRobs/τRslip b
BmimBF4
0.70 ( 0.02
0.350.65c
BmimPF6 DemeBF4
0.82 ( 0.05 0.84 ( 0.02
0.410.67c 1.571.97c 1.12
solvent
PP13Tf2N
0.90 ( 0.03
BmimCH3OSO3
0.91 ( 0.01
1.53
Py13Tf2N
0.94 ( 0.03
1.16
Py14Tf2N
0.96 ( 0.05
1.63
BmimTf2N
0.96 ( 0.04
1.45
N3111Tf2N
0.97 ( 0.02
2.17
DemeTf2N EmimC2H5OSO3
0.99 ( 0.03 1.06 ( 0.03
1.98 1.35
EmimBF4
1.09 ( 0.05
1.19
N-methylimidazole
0.96 ( 0.07
2.53
Parameters were determined by fitting the data to eq 19. b The τRobs values are derived by eq 18 and experimental data on τ and τ^. The τRslip values are estimated by eq 16 under the slip condition (Cslip = 0.075). c The values depend on the temperature. )
a
used in this study. We assume the experimental data points follow the equation t η obs ð19Þ τR T
Figure 7. Logarithmic plots of measured τR values (9) of PADS vs ηT1 in (a) BmimBF4 and (b) BmimPF6. Theoretical τRstick and τRslip values are shown by solid and dotted lines, respectively.
values are located between two theoretical lines that correspond to the τRstick and τRslip estimations. This indicates that τRobs for BmimTf2N, N-methylimidzole, DemeTf2N, and N3111Tf2N can be explained by a modified hydrodynamic theory, where microscopic viscosity is lowered.49 On the other hand, Figure 7 shows that the τRobs values measured in BmimBF4 and BmimPF6 solvents are smaller than the τRslip values. The experimental results shown in Figure 7 cannot be interpreted by Hu and Zwanzig’s theory49 of the slip boundary condition and may be understood introducing a subslip boundary condition. Table 4 lists the calculated τRobs/τRslip ratios. Most of the ratios are larger than unity, and the rotation of PADS in these solvents can be characterized using Hu and Zwanzig’s theory.49 On the other hand, the τRobs/τRslip ratios derived for the BmimBF4 and BmimPF6 solutions are smaller than unity. These experimental results cannot be explained using Hu and Zwanzig’s theory49 because the boundary condition appears to fall into a subslip region. Therefore, some modifications are required for eq 16, which was derived using Hu and Zwanzig’s theory.49 Fractional η/T dependence of rotational correlation time for BmimPF6. In this section, we discuss another experimental finding observed in Figure 7. It is observed that the slopes log(τRobs)/log(η/T) are not unity, although they are close to unity in Figure 6 as well as in similar plots for the other RTILs
where the fractional parameter t is introduced to correct η/T dependence.51 The t values determined are listed in Table 4. If the rotational motion is in accordance with the hydrodynamic theory in eq 16, the t values become unity. It is noteworthy that the t values are unity in RTILs that possess relatively large Tf2N or C2H5OSO3 anions. On the other hand, the t values are less than unity for BmimBF4, BmimPF6, and DemeBF4 solvents. This suggests that the dependence of τRobs on η/T follows a different pattern from that of the dependence on the hydrodynamic estimation in the above three solvents that have relatively small PF6 or BF4 anions. Previously, the relation t < 1 was reported for rotation of solutes such as proxyl radicals, D2O, and C6D6 in BmimPF6 and BmimBF4.7,13 Subslip Rotation Region and t < 1 Relation of PADS in BmimPF6 and BmimBF4. We now discuss interesting experimental findings related to the subslip rotation and the t < 1 relation in BmimPF6 and BmimBF4. We consider three features (1) the inhomogeneous structure in RTILs as proposed by MD simulation by Lopes et al.,52 (2) the frequency dependence of shear viscosity,53,54 and (3) impurity effects.55 Fruchey et al.14 recently reported similar subslip rotation of dye molecules in alkyl-substituted imidazolium-based RTILs. The subslip boundary condition usually originates from the inhomogeneous nature of the solvent, which cannot be characterized by one macroscopic viscosity value. They proposed that fast rotation in RTILs may be due to selective solvation of dye molecules in a hypothetical nonpolar and low-viscous region of RTIL. This interpretation may not be applicable to PADS because PADS has two negatively charged sulfonyl groups and may dissolve in the polar region of RTIL. Recently, Yao et al.53 reported the frequency dependence of the shear viscosity η for PF6-based RTILs having 1-alkyl-3-methylimidazolium cations in their sound absorption and velocity measurements. Yamaguchi and Koda54 measured the frequency-dependent η values 6354
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of BmimPF6 and BmimTf2N at 298 K for a frequency range 00.2 GHz. Note that the η values of BmimTf2N are almost constant in this frequency range, whereas the values of BmimPF6 are clearly dependent on frequency. For example, shear viscosity at 0.2 GHz is approximately one-third of the zero-frequency value. For [Bmim][PF6], the Debye relaxation time was estimated to be 1.1 ns at 298 K. This value is close to the present τRobs value of 0.6 ns for PADS in BmimPF6. These experimental observations suggest that the subslip rotation in BmimPF6 identified in our study may result from a reduction of shear viscosity for PADS rotational diffusion at high frequency. Unfortunately, temperature dependence of η was not reported; therefore, t < 1 for BmimPF6 cannot currently be explained by their results. Although frequency-dependent shear viscosity appears to explain the results of both subslip condition and the t < 1 relation for BmimPF6 and BmimBF4, we could not eliminate the possibility of an HF impurity effect. The BF4 anion may decompose and release small quantities of HF impurity,55 although we attempted to suppress this process by using careful experimental procedures. Further research aimed at understanding the rotational dynamics in BF4 and PF6 based RTILs is still in progress.
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4. CONCLUSION This study focuses on the rotational motion and solvation of PADS dissolved in various RTILs. By analyzing the EPR spectra, we determined the hyperfine coupling constant (A), the temperaturedependent anisotropic rotational correlation times (τ and τ^), and rotational anisotropy (N), which is defined as τ^/τ . The A values are constant for most RTILs (Table 1). This indicates that there is negligible interaction between the NO group and the cations of RTILs. Second, the N values determined in RTILs and the Nmethylimidazole solvent were compared with the N value of 1.4 calculated by the hydrodynamic theory (Table 2). The N value of 2.4 for the N-methylimidazole solvent is slightly larger than 1.4 but still close to the value that was calculated using the hydrodynamic theory. On the other hand, the N values determined in RTIL solvents are in the range 35, clearly larger than 1.4. The interaction between the PADS sulfonyl groups and the cations of RTILs appears to prolong τ^, which results in larger N values. Third, the experimental values of τ and τ^ are compared with those calculated by the hydrodynamic theory. Most of the experimental values are smaller than the calculated τRstick values but larger than the calculated τRslip values (Figure 6). The hydrodynamic theory with the slip boundary condition appears to provide a better agreement with the experimental τRobs values. However, in some RTILs, experimental τR values are smaller than the calculated τRslip values. Finally, η/T dependence of the rotational correlation times is evaluated by applying eq 19 and using the t parameter. The t values are usually close to unity, but values below unity were derived from the experiments carried out using BmimBF4, BmimPF6, and DemeBF4 solvents (Table 4). ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (K. Shibuya); akawai@ chem.titech.ac.jp (A. Kawai).
’ ACKNOWLEDGMENT The authors express their thanks to Professor Tomoya Kitazume (Tokyo Institute of Technology), Dr. Shinichi Koguchi
(Tokai University), Professor Yoshifumi Kimura (Kyoto University), and Professor Anunay Samanta (University of Hyderabad) for their invaluable guidance. This work was supported in part by Grants-in-Aid for scientific research on Priority Areas (No. 22018005) and for Young Scientists (B) (No. 22750010) from the Ministry of Education, Culture, Sports, Science and Technology, Japan. The authors express their thanks to financial supports for scientific research and international collaboration of the year 2010 from the Heiwa-Nakajima Foundation and for scientific research (No. 22328) from Kurita Water and Environment Foundation. This study was performed using a pulsed ESR system at one of the on-campus cooperative research facilities at the Tokyo Institute of Technology.
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dx.doi.org/10.1021/jp112151d |J. Phys. Chem. A 2011, 115, 6347–6356
