Ultrasonic Relaxation Spectra for Pyrrolidinium Bis ... - ACS Publications

Subscriber access provided by AUBURN UNIV AUBURN

Article

Ultrasonic Relaxation Spectra for Pyrrolidinium Bis(trifluoromethylsulfonyl)imides: A Comparison with Imidazolium Bis(trifluoromethylsulfonyl)imides Edward Zorebski, Micha# Zor#bski, Ma#gorzata Musia#, and Marzena Dzida J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b07433 • Publication Date (Web): 26 Sep 2017 Downloaded from http://pubs.acs.org on September 29, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29

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

The Journal of Physical Chemistry

Ultrasonic Relaxation Spectra for Pyrrolidinium Bis(trifluoromethylsulfonyl)imides: A Comparison with Imidazolium Bis(trifluoromethylsulfonyl)imides

Edward Zorębski, Michał Zorębski, Małgorzata Musiał, Marzena Dzida Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland

Corresponding author, e-mail: [email protected]

ABSTRACT: Ultrasound absorption spectra within the frequency range of 10-300 MHz were determined

for

1-propyl-

and

1-butyl-1-methylpyrrolidinium

bis(trifluoromethylsulfonyl)imides at ambient pressure and at temperatures in the ranges (293.15-313.15) K and (293.15-323.15) K, respectively. For both compounds, a single Debye model (relaxation times between 0.451 ns and 0.778 ns) thoroughly describes the observed ultrasound absorption spectra in the investigated ranges. The spectra resemble those observed for imidazolium-based ionic liquids with the same anion. The ultrasound relaxation is dependent on the alkyl chain length of pyrrolidinium ring. In comparison to adequate imidazolium-based bis(trifluoromethylsulfonyl)imides, the relaxation in pyrrolidinium-based bis(trifluoromethylsulfonyl)imides is stronger; the pyrrolidinium cation causes clearly greater absorption than the imidazolium cation. Also estimated ultrasound velocity dispersion is stronger in the case of pyrrolidinium imides in comparison to imidazolium imides. In turn, comparison of the ultrasonic data and literature data for the dielectric spectra exemplified for 1-butyl- side chain in the cation indicates strong coupling in the case of imidazolium ring and weak in the case of pyrrolidinium ring. The effect of absorption on the speed of sound is also discussed. 1

ACS Paragon Plus Environment


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

Page 2 of 29

1. INTRODUCTION The response of ionic liquids to external perturbations is a topic of great current interest and ultrasound absorption spectroscopy can be here a valuable tool. This ultrasonic technique can be a significant and integral source of information for elucidating different chemical and physical processes that occur in the liquids as well as their molecular structure at an almost perfect thermal equilibrium.1 Ultrasonic absorption studies are very useful and very important also in connection with pressure-temperature studies of thermodynamic properties by means of an indirect acoustic route because these studies must be performed outside of relaxation regions2-4; unfortunately, because of lack of such data, this crucial fact can sometimes be overlooked. In spite of the usefulness of ultrasound absorption, studies are scarce. It is especially visible in the case of ionic liquids (ILs) because only a handful of reports about the dynamics and dissipative processes connected with the absorption of the ultrasonic wave exist. A concise review of the reported results can be found elsewhere.5 It appears that in practice, only data for imidazolium-based ILs are available to date.5 For given imidazolium cations, the clear influence of anionic structures on ultrasound absorption is beyond the scope of discussion.5-7 Also, the influence of alkyl chain length in the imidazolium cation is clearly observable and indisputable.5,8,9 However, because the influence of the cation type has not been studied, it is very interesting to analyze the behaviour of ILs with other cation types; therefore, we chose a pyrrolidinium cation (Figure 1) for our present investigations. The pyrrolidinium cation contains a five member non-aromatic pyrrolidinium ring in contrast to the five member aromatic imidazolium ring of the imidazolium cation. In this work, investigations of the ultrasound absorption as function of frequency and temperature

for

two

(1-propyl-,

and

1-butyl-)

1-alkyl-1-methylpyrrolidinium

bis(trifluoromethylsulfonyl)imides, i.e., [CnC1pyr][NTf2] (n = 3 and 4) are presented. Based 2


Page 3 of 29

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


on measurements of ultrasound absorption, the relaxation spectra, the ratios of the experimental absorption to the classical absorption, the ratios of volume to shear viscosity, the relaxation strengths as well as the dispersion of the ultrasound velocity are calculated. Results are analyzed in terms of differences in the length of the side alkyl chain of the pyrrolidinium cation. The results are then compared with the ultrasound absorption results of imidazoliumbased ILs [CnC1im][NTf2] reported previously.8 The liquids under test are hydrophobic ILs containing a large hydrolysis-stable fluorinated anion. These ILs are aprotic liquids at the same time. For the second from the studied liquids, i.e., [C4C1pyr][NTf2], the relaxation times associated with transport properties have been determined experimentally: (i) by the dielectric spectroscopy

to clarify the ionic

conduction mechanism10 and (ii) by the shear impedance spectroscopy to clarify the shear viscosity behavior.11 The coupling between these dynamics processes has also been analyzed.11 Comparing these literature results with ultrasound absorption spectra obtained in this work, a complex analysis of ultrasound, shear and dielectric relaxation phenomena is executed as well.

2. EXPERIMENTAL SECTION 2.1. Chemicals. The ILs used in this study were acquired from Iolitec (Germany). The ILs were stored under an inert gas atmosphere (argon) and Karl Fisher’s method was used to determine the water content. The samples refer to the same batch of liquids described in previous studies.12 Table 1 gives a summary of the acronyms, CAS numbers, molar mass M, and purity of the test ILs. Figure 1 shows cation and anion structures.

3



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

Page 4 of 29

Figure 1. Structures of (a) cation (1-alkyl-1-methylpyrrolidinium) and (c) anion (bis (trifluoromethylsulfonyl)imide) for ILs studied in this work. For comparison structure of (b) cation of 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imides studied previously is shown. 8 Table 1 Sample Table Ionic liquid

CAS number

M /g⋅mol-1

mass

water content

fraction

halides

ppm

a

purity [C3C1pyr][NTf2]

223437-05-6

408.38

>0.99

100a/66b

< 100a

[C4C1pyr][NTf2]

223437-11-4

422.41

>0.99

100a/370b

< 100a

a

Declared by supplier. b Coulometric Karl Fisher titration, TitroLine 7500.

2.2. Experimental Systems. The ultrasound absorption was measured by means of a home-made measuring set and the standard pulse method. This method with a variable path length allows absolute measurements of the absorption coefficient α. The measurements within the frequency range of 10 to 300 MHz were carried out at selected frequencies using two sets of broadband ultrasonic heads (lithium niobate transducers) at temperatures (determined according to ITS-90) in the range of 293.15 to 323.15 K under atmospheric pressure. The sample temperature was stabilized within ±0.05 K. To avoid contact of the sample with air, the measuring cell was filled with argon. The uncertainty of the α⋅f--2 values reported in this work was estimated to be of ±2.5%. Further details of measuring set (design, construction) and the measurement procedures can be found in the previous paper.13 4


Page 5 of 29

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


3. ULTRASOUND ABSORPTION 3.1. Classical Absorption. Generally, the ultrasound absorption can be expressed as a sum of so-called classical absorption and relaxational absorption. A classical part of the absorption in the form of αcl⋅f

-2

(a classical absorption coefficient per squared frequency) can be

generally expressed as a sum of the three contributions:

α cl ⋅ f −2 = α St ⋅ f −2 + α K ⋅ f −2 + α r ⋅ f −2 ,

(1)

dependent in succession on shear viscosity, thermal conduction, and radiation. As the third term in eq.1 is very small and can be omitted, the first term (Stokes term) can be calculated from the following formula:

α St ⋅ f −2 = 8 ⋅ π 2 ⋅ ηs o ⋅ (3 ⋅ ρ ⋅ co3 ) -1 ,

(2)

whereas the second term in eq.1 can be calculated from the formula:

α K ⋅ f −2 = 8 ⋅ π 2 ⋅ (3 ⋅ ρ ⋅ co3 ) −1 ⋅ (0.75 ⋅ (γ − 1) ⋅ λ ⋅ c p−1 )

(3)

where ηso is the steady-state shear viscosity (the shear viscosity for 2⋅π⋅f → 0, i.e., Newtonian), co is the speed of sound, ρ is the density, γ is the ratio of heat capacities, λ is the thermal conductivity coefficient, and cp is the specific isobaric heat capacity. The resulting values for αSt⋅f -2 and αK⋅f -2 are summarized in Table 2. Examination of Table 2 shows that energy dissipation caused by λ can be here neglected because the so-called Kirchhoff term (eq.3) is very small in comparison to the value of the viscous term (eq.2). Thus, according to classical absorption theory, absorption is entirely controlled in practice by viscosity. In other words, the classical absorption (eq.1) is equal in practice to the Stokes term (eq.2). The data for calculations were taken from the literature; the values of densities, speeds of sound, isobaric heat capacities, and thermal conductivities were taken from reference 12, whereas the values of steady-state shear viscosities were taken from references 14 and 15. Table 2 5



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

Page 6 of 29

The Stokes (eq.2) and Kirchhoff (eq.3) Terms of the Classical Absorption (eq.1) Along with the Ratio of Experimental to Classical Absorption α /αcl and Temperature Coefficient of Experimental Absorption (in the Low Frequency Non-Relaxation Region) T/K

1015⋅αSt⋅f -2/

1015⋅αK⋅f -2/

m-1⋅s2

m-1⋅s2

102⋅α -1⋅dα/dT /

α /αcl

K-1

[C3C1pyr][NTf2] 293.15

583.9

0.0803

2.13

-3.73

298.15

445.3

0.0813

2.31

-3.76

303.15

357.9

0.0823

2.39

-3.62

313.15

257.9

0.0845

2.42

-2.50

[C4C1pyr][NTf2] 293.15

886.1

0.0809

1.83

-3.74

298.15

718.6

0.0820

1.87

-3.87

303.15

592.6

0.0831

1.82

-4.00

313.15

421.0

0.0852

1.85

-3.28

323.15

314.1

0.0879

1.86

-1.35

3.2. Ultrasound Absorption Spectra. The quotients α⋅f

-2

(the experimental ultrasound

absorption coefficients α per squared frequency f ) as function of log f are shown in Figures 2 and 3; the raw data are reported in Table S1 of the Supporting Information (SI). In the investigated frequency range, a clear dependence of the α⋅f--2 values on frequency is observed (d(α⋅f−2)/df < 0) for both samples at each temperature. The variable dependence of the quotient α⋅f--2 on T at constant frequency is clearly observed as well, however, always d(α⋅f— 2

)/dT < 0. At the same time the activation energy Eα of the dissipative processes related to

ultrasound absorption decreases with increasing frequencies for both ILs studied; the Eα values calculated by the use of an Arrhenius-type formula are shown in Table S2 of the SI. In both cases, Eα changes with the frequency stronger than in the case of adequate imidazolium homologs that were reported in reference 8.

6


Page 7 of 29

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


The Eα values in the case of [C3C1pyr][NTf2] are smaller than those in the case of [C4C1pyr][NTf2]. Also the Eηso values (activation energies of the steady state shear viscosity) show the same relation (27.9 and 29 kJ⋅mol-1, respectively).15,16 In addition, in the case of [C4C1pyr][NTf2], comparison of Eα obtained by us at lowest frequency (29.5 kJ⋅mol-1 at 10 MHz) with the literature Eηso value (29 kJ⋅mol-1)16 shows also very good agreement. What is more, our results for [C4C1pyr][NTf2] are roughly consistent with energy activation reported by Palumbo et al.17 (34.7 kJ⋅mol-1) obtained from the temperature dependence of relaxation times; these relaxation times were estimated using the so-called dynamic mechanical analysis (DMA) at very low frequencies (1 and 10 Hz; see also Section 3.4). Thus, summing up, there is a clear correlation between Eα and Eηso, and at lowest frequencies Eα is roughly (within experimental uncertainty) accordant with Eηso. This result confirms dominating role of the viscosity in processes of ultrasound absorption for such type ILs (with negative temperature absorption coefficients). To describe the experimental ultrasound absorption spectra the following function was used:

α ⋅ f −2 = c ⋅ co −1 ⋅ A ⋅ (1 + ( f / f rel ) 2 ) -1 + B ,

(4)

where A is the relaxation amplitude and B is so-called background high-frequency limiting absorption value. Precisely, B is the sum of the two contributions from: (i) the classical part of the absorption and (ii) the potential processes with relaxation frequencies considerably higher than frel, which is the relaxation frequency of a discrete single Debye relaxation process. In turn, co is the speed of sound, i.e., independent of frequency ultrasound velocity at low frequency limit (in this study experimental data at 2 MHz and at 0.101 MPa) while c denotes dependent on frequency ultrasound velocities. Assuming in the first step that c⋅co-1 is equal to 1, the values of A, B, and frel can be estimated by the least-squares method; these

7



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

Page 8 of 29

values are shown in Table 3. Thus, in this analysis of the absorption spectra any dispersion in ultrasound velocity has been neglected. Table 3 Coefficients of Equation 4 Along with the Standard Mean Deviation from Regression Line δ a and Relaxation Strength εrb for [CnC1pyr][NTf2] Studied at p = 0.101 MPa and Various Temperatures T. T/ K

1015⋅B /

1015⋅A /

frel /

m-1⋅s2

m-1⋅s2

MHz

a

1015⋅δ / 102⋅εr b m-1⋅s2

[C3C1pyr][NTf2] 293.15

544.7

697.7

227

0.0

6.45

298.15

537.9

491.7

235

0.0

4.66

303.15

525.8

330.6

271

0.0

3.58

313.15

514.7

109.0

353

0.0

1.51

[C4C1pyr][NTf2]

a

293.15

542.7

1083

205

0.0

9.04

298.15

519.2

822.1

239

0.0

7.92

303.15

490.0

589.7

284

4.9

6.69

313.15

469.0

308.4

341

3.7

4.13

323.15

464.5

120.4

325

3.8

1.51

n

δ = (∑ ( y i ,exp − y i ,calc ) 2 /(n − m))1 / 2 where m denotes the number of statistically i =1

significant fitted coefficients, n denotes the number of experimental points, and y denotes α⋅f -2. b The relaxation strength εr is calculated as A⋅co⋅frel /π, where the co values are taken from ref.12.

8


Page 9 of 29

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


Figure 2. Ultrasonic absorption spectra in the form of the α⋅f -2 quotient as a function of log f for [C3C1pyr][NTf2] at temperatures T. The solid lines represent fitted relaxation functions according to eq.4. The dashed lines in the same sequence indicate the classical absorption according to eq.2.

Figure 3. Ultrasonic absorption spectra in the form of the α⋅f -2 quotient as a function of log f for [C4C1pyr][NTf2] at temperatures T. The solid lines represent fitted relaxation functions according to eq.4. The dashed lines in the same sequence indicate the classical absorption according to eq.2. For better clarity, the line showing the classical absorption (314.1⋅10-15 s2⋅m-1) at 323.15 K is not shown. Inspection of the ultrasound absorption spectra shows that in both cases the calculated values of A and εr decreased with the temperature increase, whereas the values of frel increased with increase of temperature. However, unfortunately, none of the obtained spectra reaches a high frequency non-relaxation region. The results are however similar and consistent with that observed in the case of [CnC1im][NTf2].8 Generally, the length of the alkyl chain in the pyrrolidinium cation produces clear differences in ultrasound absorption spectra of the ILs 9



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

Page 10 of 29

studied. In other words, the results can be connected with changes of the nonpolar part of the cation. However, when differences in the A and εr values are evident, i.e., as the alkyl chain length increases, the A and εr values increase clearly too, the values of frel show very weak differences only. In other words, the shifting of the relaxation region

towards lower

frequencies with the increasing alkyl chain length in the cation is imperceptible. The observed distinct increase of the magnitude of the α⋅f—2 quotient with the increasing length of the alkyl chain in the pyrrolidinium cation (α⋅f−2 for [C3C1pyr][NTf2] is smaller than

α⋅f−2 for [C4C1pyr][NTf2]) is in accordance with similar increase in the case of the imidazolium cation as reported previously.8 In this report, α⋅f--2 in the low non-relaxation region increases near linearly with the increasing number of methylene groups in the imidazolium cation and the magnitude of this effect was clearly anion dependent. Anion dependent were also relaxation regions.8 The [NTf2]− anion is a fluorinated, non-globular, and relatively large anion with the possibility of internal rotations (as stated theoretically18 and shown experimentally19) around the two S-N bonds (Figure 1). These rotations are the reason for large internal anion flexibility, and its flexible nature is reflected in the occurrence of cis and trans structures. For ILs, the ultrasonic absorption spectra can be generally discussed assuming that aggregation processes are determined by Coulomb forces, dispersion forces and hydrogen bonding’s. But H-bonds do not occur in the case of [CnC1pyr][NTf2] studied. However, the existence of the hydrogen-bonding in the case of aprotic imidazolium-based ILs is accepted at present and well documented, for example, by the far-infrared (FIR) and terahertz (THZ) spectroscopy.20-22 Generally, ILs are treated today as structured solvents in which the polar domains are not homogeneously distributed but rather form a continuous 3D polar networks.23 The polar domains coexist with nonpolar domains, and in the case of short alkyl groups in the cations, small and globular nonpolar domains form within the polar network. However, in the 10


Page 11 of 29

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


case of longer alkyl chains in the cations, the nonpolar domains interconnect in a bicontinuous sponge-like nanostructure. The progression seems be marked by the presence of a butyl alkyl side chain.24 While the imidazolium ring is aromatic and has two nitrogen atoms, the pyrrolidinium ring is non-aromatic, has only one nitrogen atom (Figure 1), and does not create hydrogen bonds due to the fact that the positive charge is distributed over the whole structures (lack of acid proton). Despite this, pyrrolidinium-based ILs aggregate forming heterogeneous domains in a way that it is analogous to that of imidazolium-based ILs, especially for longer alkyl chain homologs. Thus, assuming that the test ILs can be considered as a mixture of polar and nonpolar domains, various equilibria can be reduced to one process. This process can be described in a satisfactory way using Eq.4, i.e., using a single Debye-type term. However, results obtained using neutron spin echo spectroscopy (NSE) suggest that the relaxation mechanism in ILs is most probably much more complex and this mechanism cannot be assigned solely to the domain dynamics or microscopic dynamics.25,26 The relaxation strengths analysis (Table 3) shows that the εr values are greatest in the case of [C4C1pyr][NTf2]. Because, however, the relaxation strength depends on the change both enthalpy ∆H and volume ∆V (changes are obviously related to a process that is disturbed by the acoustic wave), the above changes (at least one) must be large. This is in accordance with higher compressibility (reflects ∆V changes with respect to pressure) and isobaric heat capacity (reflect ∆H changes with respect to temperature) in the case of [C4C1pyr][NTf2] in comparison to [C3C1pyr][NTf2].12 In accordance with Eq.4, the spectra are satisfactorily described by means of a single Debye type exponential function of time. This is consistent with results for lower homologues (n = 2-6) of the [CnC1im][NTf2] series.8 However, this is in contrary to higher homologues such as [C8C1im][NTf2] as well as paramagnetic and dicationic ILs [CnC1im]2[Co(NCS)4] (n = 2,4) where the single Debye model has evidently failed.8 It 11



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

Page 12 of 29

should be remembered, however, that even if the absorption data are fitted very good to a single relaxation curve, it does not necessarily mean that it is factually a single relaxation process. Unfortunately, sometimes it is impossible to separate the contributions to the absorption spectrum from different processes. For example, this occurs when they have similar relaxation times. As a result, the absorption data will look like a single relaxation curve. The shape of the spectra and values of background absorption B for both investigated ILs indicate also clearly that the frequency range covers only part of the relaxation area; probably other relaxation processes could be present at higher frequency range (B values are in most cases significantly higher than values obtained using Eq.2). On the other hand, it appears that in some cases, the values of α⋅f--2 are above some frequencies (Figure 2 and 3) smaller than those obtained by the Stokes relation (Eq.2; the classical absorption). For example, in the case of [C4C1pyr][NTf2], the experimental absorption is lower than the classical ones (α⋅f

-2

< αcl⋅f -2) above 300, 400, and 630 MHz at 293.15, 298.15, and 303.15 K, respectively.

In turn, in the case of [C3C1pyr][NTf2], it is observed only at 293.15 K above 900 MHz. This indicates the occurrence of a shear viscosity relaxation in this range. Thus, the dependence of

α⋅f -2 on frequency can also be attributed to a shear viscosity relaxation (ηs must decrease with an increase in frequency). Such behavior is not surprising because it has been previously reported several times in the case of ILs

8,9

; also, in the case of molecular liquids, such

behavior has been demonstrated.13,27 In practice, however, a longitudinal ultrasound wave is not a suitable tool to investigate the behavior of the shear viscosity because of difficulty in separating the contributions of volume and shear viscosities to the ultrasound absorption measurement results. Therefore, determination of the shear viscosity behavior requires a separate investigations. Such investigations using the shear ultrasound wave are not straightforward and are connected with measurements of so-called shear impedance.28,29 In 12


Page 13 of 29

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


the case of ILs, such shear impedance studies have shown indeed the presence of shear relaxation in the megahertz range.11,26,29 It appears that our conclusions related to shear viscosity dependence on frequency, which are based on ultrasound absorption results, agree very well with the reported shear viscosity spectra.11 A more detailed discussion is given in Section 3.4. The values of the α /αcl ratio in the low frequency non-relaxation region (shown in Table 2) together with the negative temperature coefficients of the ultrasound absorption

α-1⋅dα/dT

in this non-relaxation region are typical for structural relaxation. The

α /αcl ratio can be easily used for estimation of the ηv/ηs0 ratio from the simple relationship: η v / ηs0 = 4 / 3 ⋅ (α / α cl − 1) ,

(5)

where ηv denotes the volume viscosity. The volume viscosity of a liquid is a measure of its resistance to a pure compression or expansion. To date, absorption measurements are the only way to determine the volume viscosity; note that the ηv values cannot be directly measured. Inspection of Table S3 of SI shows that the obtained ηv/ηs0 values are around 1 for [C4C1pyr][NTf2]. Thus, the magnitudes of the ηv values are very close to the ηs0 values just as for [CnC1im][NTf2]8 and many associated molecular liquids.13 Generally, if ηv/ηs0 ≈ 1 and approximately temperature independent (as for [C4C1pyr][NTf2]), a similar activation enthalpy for both viscosities can be assumed. It is well established for molecular liquids, and a similar scenario may be present in the case of [C4C1pyr][NTf2]. In the case of [C3C1pyr][NTf2], the ηv/ηs0 values are clearly higher than 1 and they increase up to 1.9 with increasing temperature. Thus, it can be here assumed that activation enthalpy for ηv is lower than that for ηs0.

3.3. Ultrasound Velocity Dispersion. It is known that the dissipation of energy during propagation of the ultrasound wave is always practically present because the classical absorption is present in all real liquids. However, as long as α

Ultrasonic Relaxation Spectra for Pyrrolidinium Bis ... - ACS Publications

Recommend Documents