Universal scaling behavior of entropy and conductivity in ionic liquids

Article abstract of DOI:10.1016/j.molliq.2020.113824

The density scaling behavior of dynamics and thermodynamics is investigated in ionic liquids. By comparing the scaling exponent of different dynamic quantities (dc-conductivity, viscosity, and diffusion) of a series of homologous ionic liquids, we discover that longer alkyl chain in the cation provides lower scaling value. Additionally, a systematic study on the entropy scaling behavior is carried out based on various samples within different structures and strength of interactions between anions and cations. Interestingly, for all tested samples, a linear relationship between Grüneisen parameter (scaling exponent) and entropy was obtained, and more importantly, the generated slope shows a close relation to the typical interactions (van der Waals and Coulomb forces, and H-bonds). Therefore, we establish a new correlation for this group of compounds.

Full text of DOI:10.1016/j.molliq.2020.113824

Journal Pre-proof
Universal scaling behavior of entropy and conductivity in ionic
liquids
S. Cheng, M. Musiał, Z. Wojnarowska, K.L. Ngai, J. Jacquemin,
M. Paluch
PII:
S0167-7322(20)31172-7
DOI:
https://doi.org/10.1016/j.molliq.2020.113824
MOLLIQ 113824
Reference:
To appear in:
Journal of Molecular Liquids
Received date:
Revised date:
Accepted date:
24 February 2020
10 July 2020
13 July 2020
Please cite this article as: S. Cheng, M. Musiał, Z. Wojnarowska, et al., Universal scaling
behavior of entropy and conductivity in ionic liquids, Journal of Molecular Liquids
(2020), https://doi.org/10.1016/j.molliq.2020.113824
This is a PDF file of an article that has undergone enhancements after acceptance, such
as the addition of a cover page and metadata, and formatting for readability, but it is
not yet the definitive version of record. This version will undergo additional copyediting,
typesetting and review before it is published in its final form, but we are providing this
version to give early visibility of the article. Please note that, during the production
process, errors may be discovered which could affect the content, and all legal disclaimers
that apply to the journal pertain.
©
2020 Published by Elsevier.

Journal Pre-proof
Universal Scaling Behavior of Entropy and Conductivity in Ionic Liquids
1
1*
1
2
3,4,5
1*
S. Cheng , M. Musiał , Z. Wojnarowska , K. L. Ngai , J. Jacquemin , M. Paluch
1
Institute of Physics, University of Silesia in Katowice, Silesian Center for Education and
Interdisciplinary Research, 75 Pułku Piechoty 1A, 41–500 Chorzów, Poland
2
CNR-IPCF, Dipartimento di Fisica, ꢀꢁꢂꢃꢄꢅꢁꢆꢇꢈꢉꢁꢈꢊꢁꢅꢋꢌꢈꢍꢋꢄꢎꢏꢈꢐꢄꢑꢀꢏꢈꢊꢏꢀꢆꢃꢒꢏꢄꢂꢏꢈꢓꢌꢈꢔ-56127, Pisa, Italy
3
QUILL Research Centre, School of Chemistry and Chemical Engineering, Qꢑꢃꢃꢀ’ꢅꢈ ꢀꢁꢂꢃꢄꢅꢁꢆyꢈꢐꢃlfꢋꢅꢆ,
David Keir Building, Belfast, Northern Ireland BT9 5AG, United Kingdom
4
Laboratoire PCM2E, Université de Tours, Parc de Grandmont 37200 Tours, France
Materials Science and Nano-Engineering, Mohammed VI Polytechnic University, Lot 660-Hay Moulay
5
Rachid, Ben Guerir, Morocco
Corresponding author: malgorzata.musial@smcebi.edu.pl; marian.paluch@us.edu.pl
ABSTRACT: The density scaling behavior of dynamics and thermodynamics is investigated in
ionic liquids. By comparing the scaling exponent of different dynamic quantities (dc-
conductivity, viscosity, and diffusion) of a series of homologous ionic liquids, we discover that
longer alkyl chain in the cation provides lower scaling value. Additionally, a systematic study on
the entropy scaling behavior is carried out based on various samples within different structures
and strength of interactions between anions and cations. Interestingly, for all tested samples, a
linear relationship between Grüneisen parameter (scaling exponent) and entropy was obtained,
and more importantly, the generated slope shows a close relation to the typical interactions (van
der Waals and Coulomb forces, and H-bonds). Therefore, we establish a new correlation for this
group of compounds.
INTRODUCTION
A century has passed since the discovery of the first ionic liquid (IL) by Walden in 1914.
The ionic liquids (ILs) research field continues to grow as more families of ILs are synthesized
and developed. ILs are composed of discrete cations and anions that can be individually
customized, allowing the design of ILs with tunable physical, chemical, and biological properties
suitable for various applications, including green chemistry, energy storage, and pharmaceutical
industry [1,2,3,4].
Because of their excellent glass-forming ability and superior thermal stability, ILs offer
new opportunities to investigate long-standing problems i.e. the dynamics and thermodynamics
of glass transition, as well as the corresponding ion transport properties, over extreme broad
temperature and pressure ranges. For this reason, many studies on the dynamic and mechanical
properties (e.g. structural and conductivity relaxation times, conductivity, and viscosity) of these
unique materials have been carried out under different thermodynamic conditions. However, so
far there is no generally accepted model and theory to either fully explain these properties or
predict the key variables over the range from simple dynamics at high temperatures to complex
dynamics at lower temperatures approaching T . An alternative solution to this problem can be
g
offered by the concept of density scaling:
1

Journal Pre-proof
ꢄ
ꢅ
ꢀ
ꢁ(ꢂꢃ )
(1)
where x represents any of the physical variables such as the structural relaxation time quantifying
the molecular dynamics, V is the specific volume, T is the temperature, and γ is the scaling
x
exponent.
This approach assumes that dynamic quantities including viscosity, conductivity, relaxation time
ꢆγ
ꢗ
or diffusion coefficient can be scaled onto a single master-curve when plotted versusꢈꢕꢖ
[
5,6,7].The magnitude of the parameter γ reflects the steepness of the repulsive part of the
x
effective short-range intermolecular potential [8] and thus it is a material constant directly related
to the structure of a given material. If the thermodynamic scaling is satisfied for a given system
one can predict the dynamic properties at any temperature and pressure conditions.
Thermodynamic scaling has been already confirmed for many van der Waals liquids and
polymers [9,10]. Very recently, our group studied the density scaling of dc-conductivity on two
ILs: 1-butyl-2,3-dimethylimidazolium bis(trifluoromethylsulfonyl)imide ([BMMIm][TFSI]) and
1
-butyl-3-methylimidazolium acetate ([BMIm][OAc]) [11]. For these ILs differing significantly
in the strength of the interactions between the ionic species, the thermodynamic scaling law has
been successfully verified over a broad density range with a state-point-independent value of γσ
(scaling exponent for dc-conductivity, σdc).
By using a revised entropy model of the glass transition dynamics originally proposed by
Avramov [12], the authors of ref. [13] suggested that the entropy, S, for a supercooled liquid
satisfies under some approximations a scaling law,
ꢄ
ꢉ
ꢇ(ꢂꢈꢃ)ꢀꢁ(ꢂꢃ ),
(2)
where the scaling exponent γ is the thermodynamic Grüneisen parameter [14,15].The entropy
G
calculated from experimental data of molecular glass-formers under different T and V has
confirmed approximately Eq.(2) [16,17,18,19]. Generally, for any model in which the relaxation
time is a function of the entropy, the scaling exponent γ in Eq.(1) should be equal to γG
x
according to the analysis presented in Refs. [13,16]. However, the value of the exponent γ is
G
significantly smaller than the parameter γ. Therefore, Grzybowska et al. [19] suggested that the
x
system entropy S is not sufficient to govern the structural relaxation time  of molecular glass-
former. It has been also reported that the entropy of IL (1-butyl-3-methylimidazolium
bis(trifluoromethylsulfonyl)imide [BMIm][TFSI]) conforms to density scaling, with the scaling
exponent identified with the Grüneisen parameter [19]. Nevertheless, the calculations of S were
made over a narrow range corresponding to temperature and pressure ranges of ΔT=30 K,
ΔP=200 MPa. The data of S collapsed to a single master curve with relatively low precision by
using a constant value of the scaling exponent [19].
In this work, we investigate the density scaling behavior of dc-conductivity and entropy
of 1-ethyl-3-methylimidazolium diethylphosphate ([EMIm][DEP]) over a broad range of T, P,
and V. We find that density scaling exponent of dc-conductivity is state-point independent. It
fluctuates around the average of 2.15±0.03 when the volume changes of 13%. We also find a
relationship between the Grüneisen parameter and the entropy for the studied IL, from which a
single master curve can be constructed. Furthermore, due to the wealth of PVT data for ILs in the
2

Journal Pre-proof
literature [20], we have selected 15 additional systems to investigate the density scaling of
entropy. In this way, the effects of strength of various intermolecular interactions between
cations and anions can be systematically analyzed and a general conclusion may be drawn from
the results.
METHODS
Materials.
Anhydrous solvents, such as N-methylimidazole (CAS number: 616-47-7; purity: 99%+), triethyl
phosphate (CAS number: 78-40-0; purity: 99.8%), dimethyl sulfoxide-d (CAS number: 2206-
6
2
7-1; purity: 99%+ with 99.96 atom %D), diethyl ether (CAS number: 60-29-7; purity: 99.7%+),
were supplied by Sigma Aldrich and used directly as received.
Synthesis of the [EMIm][DEP]. 1-Ethyl-3-methylimidazolium diethylphosphate (CAS number
8
48641-69-0; purity >98%) was synthesized at QUILL (Queen's University Ionic Liquid
Laboratories) by following the methodology reported below which is comparable to that
reported originally in the literature [21,22].
Briefly, N-methylimidazole (8.2 g, 0.1 mol) and an equimolar amount of triethyl phosphate (18.2
g, 0.1 mol) were added to a Carius tube and flushed with nitrogen. After sealing and covering in
aluminium foil the tube was then heated to 373.15 K for 24 hrs. The resulting liquid was washed
3
with diethyl ether (3×20 cm ) at room temperature followed by drying under reduced pressure
(1 Pa) at 353 K overnight to remove starting materials and solvent residues. After washing and
drying the ionic liquid resulting yield was 21.9 g, 83%. Before measurements, the sample was
again dried and degassed under low pressure (1 Pa) at temperatures not exceeding 373 K. IL was
kept under a nitrogen atmosphere and then used without any further purification. The purity of
the sample was firstly estimated by considering the water level in the sample (lower than 0.01
wt/wt% (or 100 ppm) by Karl Fischer Coulometric titration using an 899 Coulometer, Metrohm)
1
13
and by comparing H and C NMR spectra recorded at 293 K on a Bruker Avance DPX
spectrometer at respectively 300 MHz and 75 MHz with those published by either Kuhlmann et
al. [22] or Hiraga et al. [23] as shown in the Figs S1 and S2 of the supporting information (SI).
The purity of the sample was then assessed by comparing systematically density (), speed of
sound (c), viscosity () and molar isobaric heat capacity (C ) datasets collected during this work
p
at 0.1 MPa with those available in the literature reported in the Tables S1-S4 of the SI.
Density, speed of sound, and viscosity measurements. The density and the speed of sound of
the [EMIm][DEP] were simultaneously determined from 293.15 to 363.15 K (u(T) = 0.01 K) at
atmospheric pressure using a DSA 5000 M from Anton Paar. An extended calibration of this
equipment was done by following the recommendations of the manufacturer with dry air and
redistilled water. Furthermore, great care was also given during the interpretation of speed of
sound data [24], as the [EMIm][DEP] was reported as a nondispersive media for temperature
3

Journal Pre-proof
higher than 308.15 K (i.e. with a similar transducer operating at a frequency of 3 MHz) [25]. The
uncertainty of each property and stated conditions, reported in the footnote of Tables S1-S2 in
SI, were determined by the following advice reported in the literature [26].
The viscosity of the IL was measured using a Bohlin Gemini Rotonetic Drive 2 cone and plate
rheometer (± 1% repeatability) from 293.15 to 373.15 K (u(T) = 0.01 K) at atmospheric pressure.
The rheometer was calibrated using ultra-pure water and an oil viscosity standard (ASTM Oil
Standard S600, Cannon, 1053 mPa·s at 298.15 K). From this study, the relative uncertainty of
the reported viscosity measurements, u () did not exceed 3%.
r
Conductivity Measurements. The dielectric measurements at ambient pressure for
-
1
[
EMIm][DEP] series were carried out in a nitrogen atmosphere over a frequency range from 10
7
Hz to 10 Hz using Novo-Control GMBH Alpha dielectric spectrometer. At the beginning of
measurements each sample was equilibrated in active sample cell (two stainless steel electrodes
of diameter, d = 15 mm separated by quartz ring; distance between plates of the capacitor was
constant and equal to 0.08 mm) for 1 h at 373 K. Then, the material was cooled down to the
glassy state. The applied cooling rate was 5 K·min . The temperature was controlled by the
Novo-control Quattro system with a nitrogen gas cryostat. The temperature stability was within ±0.1
K. The errors from calibration, temperature (u(T) = 0.1 K), and pressure (u(p) = 2 kPa) control
yield an uncertainty of 5% of dc-conductivity determined herein.
-1
High-pressure conductivity measurements. The conductivity measurements under high-
pressure conditions were carried out with the use of capacitor Φ= 10 mm, filled with the studied
sample. The capacitor was hermetically closed and placed in the high-pressure chamber.
Compression was achieved by using the silicone oil, however without any contact between
sample and oil. The pressure was measured by the Unipress setup with the pressure resolution of
1
MPa. The temperature was stabilized by means of a Weiss fridge with an error of 0.1 K. The
errors from calibration, temperature (u(T) = 0.1 K), and pressure (u(p) = 1 MPa) control yield an
uncertainty of 7% of dc-conductivity determined herein.
Temperature Modulated Differential Scanning Calorimetry (TMDSC). Calorimetric
experiments were performed by a Mettler Toledo DSC1STAR System equipped with a liquid
nitrogen cooling accessory and an HSS8 ceramic sensor with 120 thermocouples. Enthalpy and
temperature calibrations were performed using indium and zinc standards. During these
measurements, the tested samples (about 25mg) were placed in aluminum crucibles with a 40 μL
–
1
volume and the flow of nitrogen was 60 mL·min . The measurements were performed in the
-1
temperature range from 220 to 373 K with a heating rate of 0.5 K·min and the temperature
amplitude of the pulses equal to 1 K.
4

Journal Pre-proof
RESULTS AND DISCUSSION
Density scaling of dynamic quantities
The conductivity of [EMIm][DEP] under isobar 0.1 MPa and five isotherms were studied
by means of broadband dielectric spectroscopy (see Methods for details). Representative
−
1
6
dielectric spectra collected in the frequency interval ranging from 10 to 10 Hz are
demonstrated in the conductivity formalism, σ′(f) in Fig. S3 of the SI. Three distinctly visible
regions can be observed in spectra i.e., i. a low-frequency deviation from the plateau attributed to
the polarization effect, typical for ion-conducting materials; ii. a frequency-independent region
known as the dc-conductivity, σ ; and iii. the power-law behavior observed at higher
dc
frequencies. The key quantity considered in this work is dc-conductivity.
For our purpose to present the dc-conductivity as a function of T and V, the modified
Tait-equation (Eq. 3) is applied to analyze the high-pressure density dataset reported in Ref. [23].
ꢖ
ꢍ
ꢃ(ꢂꢈꢊ)ꢀ(ꢋ ꢂ ꢎꢋ ꢂꢎꢋ ){ꢐꢑꢒꢓꢔꢕ[ꢐꢎ
]}
ꢝ
(3)
ꢌ
ꢏ
ꢍ
ꢗ ꢙꢚꢛ(ꢜꢗ ꢞ)
ꢘ
where A , A , A , C, b , and b are parameters. According to the determined parameters of Eq. 3,
0
1
2
0
1
the requested PVT data were extrapolated to the same T and P conditions as those applied during
dc-conductivity measurements. Consequently, we have transformed the σ (T,P) data determined
dc
in this work to T-V representation. The results are shown in a 3D plot (Fig. S4A in SI). These
data cover both the supercooled and normal liquid states of [EMIm][DEP]. As a result, the ion
dynamics represented by σ can be followed over 13 orders of magnitude corresponding to
dc
volume fluctuations of 13%. As seen from Fig. S3 in SI, the σ data decrease with either isobaric
dc
cooling or isothermal compression.
Different approaches to determine the dc-conductivity scaling parameter are reported in
the literature [18, 27,28]. Herein, we employed a model-independent procedure [29]. Namely,
based on the experimental -log σ (T, V) data presented in Fig. S4A in SI, we have determined a
1
0 dc
set of log T(-log V) dependences at each constant -log σ (i.e.,-log σ =3,4,5,…, 13). It can
1
0
10
10 dc
10 dc
be seen in the inset of Fig. S4A that each obtained iso-conductivity log T(-log V) dependence
1
0
10
can be well described by s simple linear fit. According to Eq.1, the yielding slope is equal to the
scaling exponent γ. In Fig. S4A in SI, two planes perpendicular to the -log σ axis are chosen
σ
10 dc
to show the method as examples. By following this methodology, the averaged γ coefficient is
σ
close to 2.15±0.03 for the tested IL. By using this value, a superposed single master curve is
ꢆγ
σ
obtained by plotting σ vs. ꢕꢖ with high precision (Fig. S4B in SI).
dc
Interestingly, it has been reported that other dynamic quantities of ILs, such as viscosity,
relaxation times, and diffusion coefficient, also satisfied this density scaling law, i.e. the scaling
exponent is a state-point-independent parameter. Herein, we collect the scaling exponents of
various ILs [11,30,31,32] having different strength of interionic interactions (Fig. 1).
5

Journal Pre-proof
3.5
3.0
2.5
2.0
1.5
dc-conductiviy
viscosity
diffusion coefficient of cation
diffusion coefficient of anion
g
]
4
]
4
]
4
]
6
]
6
]
6
]
]
]
]
Ac]
BF
BF
BF
PF
PF
PF
[
[
[
[
[
[
]
]
]
]
]
]
TFSI TFSI TFSI
[O
[TFSI]
[
[
[
[DEP
]
]
]
]
Im
Im
Im
Im
Im
Im
m]
m]
Im
Im
Im
Im
BM
HM
OM
BM
HM
OM
[
[
[
[
[
[
BM
HM
[BMI [EMI
OM
[
[
[
BMM
[
Fig. 1. The density scaling exponents of dynamic properties (dc-conductivity, viscosity, and diffusion
coefficient) of several ILs having different dominant interactions. Data are taken from: ref. [11]
([BMMIm][TFSI] and [BMIm][OAc]); ref. [30] ([BMIm][BF ], [HMIm][BF ], [OMIm][BF ], [BMIm][PF ],
4 4 4 6
[
HMIm][PF ], [OMIm][PF ], and [HMIm][TFSI]); ref. [32] ([OMIm][TFSI); ref. [30] ([BMIm][TFSI]-
6
6
visocosity and diffusion coefficient); ref. [31] ([BMIm][TFSI]-dc-conductivity).
As seen from Fig. 1, the exponents obtained from scaling of different dynamic quantities
within the single ionic liquid are not the same. However, at the same time, the ratio of γ /γ
σ
η
(
where γ is the scaling exponent of viscosity) is close to unity which results from the coupling
η
between ion transport dynamics and structural relaxation in aprotic ionic liquids. Interestingly, in
each homologous series, a clear decrease of dynamic scaling exponent with an increase of alkyl
chain length is observed. To explain this result, we return to the relationship between scaling
exponent and intermolecular potential. In general, the intermolecular potential is composed of an
attractive part and a repulsive part represented by a two-body power law [8,33,34] and the
scaling exponent is determined by the steepness of the resultant intermolecular potential at a
short distance where the repulsive part dominates. From this point of view, the effect of the
attractive part on the scaling exponent cannot be ignored, especially, in terms of ILs where
electrostatic attractions are dominated. Moreover, based on the analysis of the single-component
Lennard-Jones system, the attractive term increases the steepness of the effective repulsive part,
and thus increases the power-law exponent [35]. For imidazolium-based ILs, longer alkyl chain
attached onto the imidazolium ring is more effective in screening the electrostatic forces and then
results in weaker attractive interaction which contributes to a lower value of the power-law
exponent.
Density scaling of entropy and its relation to the structure of ILs
Based on the PVT data, we can investigate the total entropy under different
thermodynamic conditions by using the well-known thermodynamic relation,
6

Journal Pre-proof
ꢞ
ꢖ
ꢇ(ꢂꢈꢊ)ꢀꢇ ꢎ∫ ꢒ (ꢂꢈꢊ)푑ꢔꢕꢂꢑ∫ (휕ꢃ(ꢂꢈꢊ)⁄휕ꢂ) 푑ꢊ
(4)
ꢟ
ꢛ
ꢟ
ꢖ
ꢞ
ꢠ
ꢖ
ꢠ
where S is the entropy under the reference condition. The C is the molar isobaric heat capacity
r
p
at 0.1 MPa obtained from the Temperature Modulated Differential Scanning Calorimetry (TM-
DSC).
Fig. 2. A) The isothermal and isobaric values of S-S of [EMIm][DEP] plotted in a 3D plane in terms of T and
r
V. B) Density scaling plots of S-S of [EMIm][DEP]. Inset of A: the results from the horizontal crossing of the
r
S-S data of [EMIm][DEP]. Inset of B: the linear variation of the entropy scaling exponent for [EMIm][DEP]
r
calculated from the slope of the lines in the inset of A.
Moreover, it has been derived that the entropy can be well represented by:
ꢄ
ꢥ
ꢇ(ꢂꢈꢃ)ꢀꢇ ꢎꢒ ꢣꢤ ꢆ( ꢂꢃ )
(5)
ꢡ
ꢢ
where C is the molar isochoric heat capacity which could be easily calculated using the
V
thermodynamic relationship between C and C . However, the scaling exponent γ for S is
p
V
S
different from γ for conductivity [11] and γ is supposed to be γ defined as Grüneisen parameter
σ
S
G
and given by [13]
ꢢ ꢩ
ꢨ
ꢪ
ꢦꢧ ꢀ
(6)
ꢫ ꢭ
ꢬ
ꢮ
where V is the molar volume, α the isobaric thermal expansion, and κ the isothermal
m
p
T
compressibility. According to the definition of γ, one can anticipate that its value should change
G
with the thermodynamic conditions since the thermodynamic variables (V , α, and κ) are in
m
p
T
general functions of temperature and pressure. Therefore, the collapse of all data into a single
curve cannot be achieved using a constant value of γG.
Having the generated PVT data in the same wide density regime as dc-conductivity, we
calculated the values of S(T,P) using Eq. 4 with the C from TMDSC. For our purpose, we
p
converted S(T,P) to S(T,V) and determined the values of γ applying the same method as in the
G
case of dc-conductivity i.e., the model-independent procedure. Based on the S(T,V) data
presented in Fig. 2A, we chose six different values of entropy covering all the investigated
thermodynamic range. Two of them are presented in Fig. 2A as examples. Consequently, six
log T(-log V) dependencies are determined. It can be seen in the inset of Fig. 2A that each of
1
0
10
them can be well described by simple linear fit with a slope yielding the exponent γ, and it is
G
7

Journal Pre-proof
denoted herein by γ(S) to indicate that Grüneisen parameter is a function of entropy. A
G
monotonic decrease of γ(S) with increasing S-S was obtained. This simple change of γ(S) with
G
r
G
entropy draws our attention to assume that there may be a linear relationship between these two
quantities. Therefore, we plotted γ(S) as a function of S-S . As expected, we obtained a linear
G
r
function with high precision. The results are shown in the inset of Fig. 2B. But now the question
is whether the γ(S) obtained in this way can satisfy the density scaling of entropy in ILs? How it
G
works in practice is illustrated in Fig. 2B. It is evident that all isothermal and isobaric curves can
be collapsed into a perfect master curve using a γ(S) as a function of S-S .
G
r
Importantly, we have chosen more ionic liquids with various combinations of anions and
cations to confirm the behaviour pattern reported above. Specifically, a reasonably good scaling
ꢆγ (ꢙ)
ꢘ
curve S-S vs. ꢕꢖ
can be obtained for each selected IL over a broad thermodynamic range
r
with γ(S) being a linear function of S-S . The entropy scaling results of these ILs are present in
G
r
Fig. 3A and 3B. The data of PVT data and C at ambient pressure for these ILs are taken from the
p
literature [36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62].
A
a
b
B
[
BMIm][C SO ]
[BMIm][BF4]
8
4
c
d [
[
[
[
BMIm][Cl]
BMIm][TFSI]
N1114][TFSI]
BMIm][FAP]
1
1
0
0
.5
.2
.9
.6
450
300
150
0 0
e
f
[BMIm][PF6]
BMMIm][TFSI]
[BMIm][SCN]
g
h
j
i
[
BMIm][OAc]
-1
k
l
[
BMIm][BETI]
[EMIm][C SO ]
K
2
4
×
m
o
n
)
[BMPyr][TFSI]
[OMIm][TFSI]
[EMIm][TFSI]
-
1
S
l
(
G
mo
g
×
/
J
r
S
-
S
0
100
200
300
400
100
200
300
400
-
1 -1
TVgG(S)/K×cm
3g (S) -g (S)
S-S / J×mol ×K
G
×g
G
r
Fig. 3. A) The linear relation between γ (S) and S-S of chosen ILs having distinct compositions of ions. B)
G
r
The density scaling superposed curves of entropy of the chosen ILs. The corresponding PVT and C data
p
are taken from: a. ref. [39] and [46]; b. ref. [47] and [48]; c. ref. [39] and [49]; d. ref. [43] and [50]; e. ref.
[
[
[
42] and [53]; f. ref. [40] and [51]; g. ref. [41] and [52]; h. ref. [37] and [57]; i. ref. [38] and [57]; j. ref.
45] and [54]; k. ref. [55] and [55]; l. ref. [62] and [57]; m. ref. [61] and [60]; n. ref. [58] and [60]; o. ref.
56] and [60].
The chosen ILs have different ions and thus different intermolecular interactions.
Consequently, the slope k of the linear function connecting the scaling exponent with the entropy
-3
-3
varies in a broad range from -3.71×10 to -0.91×10 , and the absolute values are shown in Fig. 4.
Interestingly, the change of these values is not random but closely related to the typical
interactions: van der Waals forces, Coulomb forces, and H-bonds. Specifically, the slope
decreases with increasing carbon chain length in anion or cation. Such behavior has been found
-
-
-3
-3
for [C SO ] and [C SO ] (absolute value of k decrease from 3.35×10 to 0.91×10 ), and is also
2
4
8
4
8

Journal Pre-proof
+
+
+
observed for [EMIm] , [BMIm] and [OMIm] (Fig. 4). Thus, the slope decreases as van der
Waals interactions increase with the length of the alkyl chain and Coulomb forces decrease at the
same time. Additionally, we find that for ILs with TFSI anion, in which van der Waals and
electrostatic forces are very similar (i.e., [BMpyr][TFSI], [BMMIm][TFSI], [N4111][TFSI],
[
BMIm][TFSI]), the slope decreases with increasing of hydrogen bonds contribution. The
highest values were obtained for [BMPyr][TFSI], [BMMIm][TFSI] with negligible donor-
acceptor capabilities, and the lowest was determined for [BMIm][TFSI] which easily forms
hydrogen bonds between cation and anion. We can also assume that strong electrostatic
intermolecular interactions drive the high value of |k| e.g., for [BMIm][SCN] > [BMIm][BF ] >
4
[
BMIm][BETI] > [BMIm][FAP] where H-bond contribution is small and the van der Waals
forces are similar due to the same butyl chain in both structures, therefore it is possible to
compare only electrostatic forces (voluminous and heavy anions only weakly interact, whereas
small and light anions provide strong Coulomb interaction potential due to their higher surface
charge density). The situation is more complicated for ILs in the last group in Fig. 4, as two
interactions change significantly: H-bonds and Coulomb forces. Since both abovementioned
contributions change in the row: [BMIm]Cl > [BMIm][OAc] > [BMIm][PF ] > [BMIm][TFSI]
6
and as k decreases in the same way, one can think that electrostatic forces are decisive and
dominant even if the [BMIm][Cl] or [BMIm][OAc] form one of the strongest hydrogen bonds
between cation and anion, strong enough to disrupt the structure of cellulose [63,64].
V a
H
+
BMIm+:
SCN-
Co
BMIm :
4
- b o
4
n d
Cl-
EMIm C SO4
ul
2
TFSI-:
n d
e r W a a
omb
3
3
TFSI-:
EMIm+
c o n
+
-
O
Ac
BMpyr
|k|
|
k |
f
BF4-
t r i b u
orce
×
×
2
2
l s f o r c e
3
3
+
BMMIm
10
1 0
t i o
s in
-
1
BMIm+
PF6
1
+
n
i
-
N4111
BETI
crea
s
i n
n c
0
0
c r e a
r e a
-
se
TFSI-
BMIm C SO4
BMIm+
FAP
8
s e
OMIm+
s e
s
Fig. 4. The absolute values of the slope of the linear fitting.
CONCLUSION
Summarizing, in this paper, we analyzed the density scaling of the dc-conductivity of
EMIm][DEP]. In a broad thermodynamic range, the conductivity data, covering 13 orders of
[
ꢄ
ꢯ
magnitude, collapse onto a single master curve when plotted versus ꢂꢃ , with a constant scaling
exponent γ. At the same time, the density scaling of other dynamic properties, e.g., viscosity,

relaxation time, and diffusion, is recalled to show its general validity in the class of ILs. On the
9

Journal Pre-proof
ꢄꢥ
other hand, we found that the entropy of ILs can be scaled byꢆꢂꢃ well with γ= γ(S), being a
S
G
linear function of the entropy. From this point, the superposition of entropy data onto a single
master curve was successfully demonstrated. Since ILs with various dominant interactions are
investigated herein (using literature PVT data), the scaling behavior of entropy reported in this
work should be treated as universal. Additionally, we have made a systematic investigation of
the relationship between the strength of intermolecular interactions (Coulombic and van der
Waals interactions, and H-bonds) and the obtained slope, k. The delicate balance between all
these intermolecular interactions makes it difficult to generalize the role of each force in the
obtained slope. Nevertheless, we have extracted some important information including the
following. (i) As the contribution of electrostatic forces increases, a higher absolute value of k is
observed. (ii) A decrease of |k| is detected when van der Waals and hydrogen-bonding
interactions increase.
In addition to improve our knowledge on the thermodynamic and dynamics properties of
ILs, this work demonstrates how their physicochemical properties can be predicted for
conditions beyond those measured. This has obvious utility in the design and development of
new products and applications.
Corresponding Author
*
malgorzata.musial@smcebi.edu.pl; marian.paluch@us.edu.pl
ORCID
M. Musiał:0000-0002-1624-6617
Z. Wojnarowska:0000-0002-7790-2999
S. Cheng:0000-0002-5615-8646
K.L. Ngai:0000-0003-0599-4094
M. Paluch: 0000-0002-7280-8557
J. Jacquemin: 0000-0002-4178-8629
ACKNOWLEDGMENT
The authors are deeply grateful for the financial support by the National Science Centre within
the framework of the Opus15 project (grant nr DEC- 2018/29/B/ST3/00889). The authors would
like thank Dr Peter Goodrich from the Queen’s University Belfast and Dr Benjamin Flamme
from Tours University for their help within the ionic liquid synthesis and NMR analysis.
1
0

Journal Pre-proof
REFERENCESDeclaration of interests
☒
The authors declare that they have no known competing financial interests or personal relationships
that could have appeared to influence the work reported in this paper.
☐
The authors declare the following financial interests/personal relationships which may be considered
as potential competing interests:
1
1

Journal Pre-proof
1
2

Journal Pre-proof
Author statement
Shinian Cheng: Writing- Original draft preparation, Visualization, Methodology, Małgorzata
Musiał: Writing- Reviewing and Editing, Investigation, Data curation, Visualization, Żaneta
Wojnarowska: Writing- Reviewing and Editing, Visualization, K. L. Ngai: Writing- Reviewing
and Editing, Johan Jacquemin: Resources, Investigation, Writing- Reviewing and Editing,
Marian Paluch: Conceptualization, Supervision.
1
3

Journal Pre-proof
Highlights
•
•
•
Density scaling of the dc-conductivity and entropy in ionic liquids was investigated.
Longer alkyl chain in the cation provides lower scaling value.
Linear relationship between Grüneisen parameter (scaling exponent) and entropy was
determined.
[1] T. Welton, Ionic liquids: a brief history, Biophys Rev. 10 (2018) 691–706.
[2] M. Armand, F. Endres, D. MacFarlane, et al., Ionic-liquid materials for the electrochemical
challenges of the future, Nature Mater. 8 (2009) 621–629.
[3] Z. Wojnarowska, J. Knapik, M. Rams-Baron, A. Jedrzejowska, M. Paczkowska, A. Krause, J.
Cielecka-Piontek, M. Jaworska, P. Lodowski, M. Paluch, Amorphous protic ionic systems as
promising active pharmaceutical ingredients: the case of the sumatriptan succinate drug, Mol.
Pharm.13 (2016) 1111-1122.
[
4 ] Z. Wojnarowska, J. Zotowa, J. Knapik-Kowalczuk, L. Tajber, M. Paluch, Effect of
electrostatic interactions on the relaxation dynamics of pharmaceutical eutectics, Eur. J. Pharm.
Sci.134 (2019) 93-101.
[5] C. Alba-Simionesco, A. Cailliaux, A. Alegria, G. Tarjus, Scaling out the density dependence
of the α-relaxation in glass-forming polymers, Europhys. Lett. 68 (2004) 58-64.
[6] R. Casalini, C.M. Roland, Thermodynamical scaling of the glass transition dynamics, Phys.
Rev. E 69 (2004) 062501-1-3.
[7] C. Dreyfus, A. Le Grand, J. Gapinski, W. Steffen, A. Patkowski, Scaling the α-relaxation
time of supercooled fragile organic liquids, Eur. Phys. J. B 42 (2004) 309-319.
[
8] W.G Hoover, M. Ross, Statistical Theories of Melting, Contemp. Phys. 12 (1971) 339-356.
9] T.C. Ransom, M. Ahart, R.J. Hemley, C.M. Roland, Vitrification and density scaling of
[
polyurea at pressures up to 6 GPa, Macromolecules 50 (2017) 8274-8278.
10] T.C. Ransom, W.F. Oliver, Glass Transition Temperature and Density Scaling in Cumene at
Very High Pressure, Phys. Rev. Lett. 119 (2017) 025702.
11] Z. Wojnarowska, M. Musiał, M. Dzida, M. Paluch, Experimental Evidence for a State-
Point-Independent Density-Scaling Exponent in Ionic Liquids, Phys. Rev. Lett. 123 (2019)
25702.
[
[
1
[
12] I. Avramov, I. Viscosity of glassforming melts, J. Non-Cryst. Solids 238 (1998) 6-10.
13] R. Casalini, U. Mohanty, C.M. Roland, Thermodynamic interpretation of the scaling of the
[
dynamics of supercooled liquids, J. Chem. Phys. 125 (2006) 014505.
[
(
14] E. Grüneisen, Theorie des festen Zustandes einatomiger Elemente, Ann. Phys. (Leipzig) 39
1912) 257-306.
[15] G. Hartwig, Polymer Properties at Room and Cryogenic Temperatures: Thermal Expansion
and the Grüneisen Relation, New York Ch. 4 (Plenum Press, New York, 1994).
1
4

Journal Pre-proof
[16] C.M. Roland, R. Casalini, Entropy basis for the thermodynamic scaling of the dynamics of
o-terphenyl, J. Phys.: Condens. Matter 19 (2007) 205118.
17] R. Casalini, C.M. Roland, Effect of entropy on the dynamics of supercooled liquids: new
results from high pressure data, Philos. Mag. 87 (2007) 459-467.
18 ] C.M. Roland, J.L. Feldman, R. Casalini, Scaling of the local dynamics and the
intermolecular potential, J. Non-Cryst. Solids 352 (2006) 4895–4899.
19] K. Grzybowska, A. Grzybowski, S. Pawlus, J. Pionteck, and M. Paluch, Role of entropy in
[
[
[
the thermodynamic evolution of the time scale of molecular dynamics near the glass transition,
Phys. Rev. E. 91 (2015) 062305.
[
20] A.L. Kazakov, J.W. Magee, R.D. Chirico, E. Paulechka, V. Diky, C.D. Muzny, K.
Kroenlein, M. Frenkel, NIST Standard Reference Database 147: NIST Ionic Liquids Database -
ILThermo), Version 2.0, National Institute of Standards and Technology: Gaithersburg MD,
0899. Updated on June 11, (2019).
(
2
[21] X. C. Jiang, C. Y. Yu, J. Feng, C. X. Li and Z. H. Wang, Synthesis and application of ionic
liquid 1-butyl-3-methyl imidazolium dibutyl phosphate, J. Beijing Univ. Chem. Technol., Nat.
Sci. Ed. 33 (2006) 5-7.
[
22 ] E. Kuhlmann, S. Himmler, H. Giebelhaus, P. Wasserscheid, Imidazolium
dialkylphosphates—a class of versatile, halogen-free and hydrolytically stable ionic liquids,
Green Chem. 9 (2007) 233–242.
[
23] Y. Hiraga, A. Kato, Y. Sato, R. Smith, Densities at pressures up to 200 MPa and
atmospheric pressure viscosities of ionic liquids 1-ethyl-3-methylimidazolium methylphosphate,
-ethyl-3-methylimidazolium diethylphosphate, 1-butyl-3-methylimidazolium acetate, and 1-
butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, J. Chem. Eng. Data 60 (2015)
76–885.
1
8
[
24] M. Dzida, E. Zorębski, M. Zorębski, M. Żarska, M. Geppert-Rybczyńska, M. Chorążewski,
J. Jacquemin, I. Cibulka, Speed of sound and ultrasound absorption in ionic liquids, Chem. Rev.
17 (2017) 3883−3929.
1
[25] E. Zorębski, M. Musiał, K. Bałuszyńska, M. Zorębski, M. Dzida, Isobaric and isochoric heat
capacities as well as isentropic and isothermal compressibilities of di-and trisubstituted
imidazolium-based ionic liquids as a function of temperature, Ind. Eng. Chem. Res. 57 (2018)
5
161−5172.
26] T. J. Fortin, A. Laesecke, M. Freund, S. Outcalt, Advanced calibration, adjustment, and
operation of a density and sound speed analyzer, J. Chem. Thermodyn. 57 (2013) 276–285.
27] C.M. Roland, R. Casalini, Density scaling of the dynamics of vitrifying liquids and its
relationship to the dynamic crossover, J. Non-Cryst. Solids 251 (2005) 2581-2587.
28] R. Casalini, R.F. Gamache, C.M. Roland, Density-scaling and the Prigogine–Defay ratio in
liquids, J. Chem. Phys. 135 (2011) 224501.
29] A. Grzybowski, M. Paluch, The Scaling of Relaxation Processes: Universality of Density
Scaling Ch. 4 (Springer, Berlin, 2018).
[
[
[
[
1
5

Journal Pre-proof
[30] E.R. López, A.S. Pensado, M.J. Comuñas, A.A. Pádua, J. Fernández, K.R. Harris, Density
scaling of the transport properties of molecular and ionic liquids, J. Chem. Phys. 134 (2011)
44507.
1
[
31] Z. Wojnarowska, G. Jarosz, A. Grzybowski, J. Pionteck, J. Jacquemin, M. Paluch, On the
scaling behavior of electric conductivity in [C4mim][NTf2], Phys. Chem. Chem. Phys. 16 (2014)
0444-20450.
2
[
32] Z. Wojnarowska and M. Paluch, Dielectric Properties of Ionic Liquids: High pressure
dielectric spectroscopy for studying the charge transfer in ionic liquids and solids Ch.4 (Springer,
016).
2
[
33] N.H. March, M.P. Tosi, Introduction to the Liquid State Physics, (World Scientific,
Singapore, 2002).
[34] D. Chandler, J.D. Weeks, H.C. Andersen, Van der Waals picture of liquids, solids, and
phase transformations, Science 220 (1983) 787-794.
[
35 ] N.P. Bailey, U.R. Pedersen, N. Gnan, T.B. Schroder, J.C. Dyre, Pressure-energy
correlations in liquids. I. Results from computer simulations, J. Chem. Phys. 129 (2008) 184507.
[
36] Y. Hiraga, S. Hagiwara, Y. Sato, R.L. Smith Jr., Measurement and Correlation of High-
Pressure Densities and Atmospheric Viscosities of Ionic Liquids: 1-Butyl-1-methylpyrrolidinium
Bis(trifluoromethylsulfonyl)imide), 1-Allyl-3-methylimidazolium Bis(trifluoromethyl-
sulfonyl)imide, 1-Ethyl-3-methylimidazolium Tetracyanoborate, and 1-Hexyl-3-methyl-
imidazolium Tetracyanoborate, J. Chem. Eng. Data 63 (2018) 972-980.
[
37] M. Musiał, M. Kuczak, A. Mrozek-Wilczkiewicz, R. Musiol, E. Zorębski, M. Dzida,
Trisubstituted imidazolium-based ionic liquids as innovative heat transfer media in sustainable
energy systems, ACS Sustain. Chem. Eng. 6 (2018) 7960-7968.
[
38] J. Safarov, M. Geppert-Rybczyńska, I. Kul, E. Hassel, Thermophysical Properties of 1-
Butyl-3-methylimidazolium Acetate Over a Wide Range of Temperatures and Pressures, Fluid
Phase Equilib. 383 (2014) 144-155.
[
39] H. Machida, R. Taguchi, Y. Sato, R.L. Smith Jr., Measurement and Correlation of High
Pressure Densities of Ionic Liquids, 1-Ethyl-3-methylimidazolium l-Lactate ([emim][Lactate]),
-Hydroxyethyl-trimethylammonium l-Lactate ([(C H OH)(CH ) N][Lactate]), and 1-Butyl-3-
2
2
4
3 3
methylimidazolium Chloride ([bmim][Cl]), J. Chem. Eng. Data 56 (2011) 923-928.
[
40] H. Machida, Y. Sato, R.L. Smith, Pressure volume temperature (PVT) measurements of
+
-
+
-
+
-
ionic liquids ([bmim ][PF ], [bmim ][BF ], [bmim ][OcSO ]) and analysis with the Sanchez
6
4
4
Lacombe equation of state, Fluid Phase Equilib. 264 (2008) 147–155.
1
6

Journal Pre-proof
[41] M. Dakkach, F.M Gacino, S.K. Mylona, M.J.P. Comunas, M.J. Assael, J. Fernandez, High
pressure densities of two nanostructured liquids based on the bis(trifluoromethylsulfonyl)imide
anion from (278 to 398) K and up to 120 MPa, J. Chem. Thermodyn. 118 (2018) 67-76.
[42] C.A. Nieto de Castro, et al. Studies on the density, heat capacity, surface tension and infinite
dilution diffusion with the ionic liquids [C mim][NTf ], [C mim][dca], [C mim][EtOSO ] and
4
2
4
2
3
[
Aliquat][dca], Fluid Phase Equilib. 294 (2010) 157-179.
[43] J. Safarov, F. Lesch, K. Suleymanli, A. Aliyev, A. Shahverdiyev, E. Hassel, I. Abdulagatov,
High-temperature and high-pressure density measurements and other derived thermodynamic
properties of 1-butyl-3-methylimidazolium tris (pentafluoroethyl) trifluorophosphate,
Thermochim. Acta 658 (2017) 14-23.
[44] J. Safarov, G. Huseynova, M. Bashirov, E. Hassel, I. Abdulagatov, High temperatures and
high pressures density measurements of 1-ethyl-3-methylimidazolium methanesulfonate and
Tait-type equation of state, J. Mol. Liq. 238 (2017) 347-358.
[45] J. Klomfar, M. Souckova, J. Patek, Low-Temperature and High-Pressure p ρ T Relation for
1
-(2-Methoxyethyl)-1-methylpyrrolidinium Bis(trifluoromethylsulfonyl)imide and 1-C -3-
n
methylimidazolium Thiocyanate with n = 2 and 4, J. Chem. Eng. Data 60 (2015) 1855-1867.
46] M. J. Dávila, S. Aparicio, R. Alcalde, B. García, J. M. Leal, On the properties of 1-butyl-3-
methylimidazolium octylsulfate ionic liquid, Green Chem. 9 (2007) 221-232.
47] D. Matkowska, T. Hofman, High-pressure volumetric properties of ionic liquids: 1-butyl-3-
[
[
methylimidazolium
methylsulfate
tetrafluoroborate,
[C mim][MeSO ] and
[C mim][BF ],
1-butyl-3-methylimidazolium
4
4
1-ethyl-3-methylimidazolium ethylsulfate,
4
4
[
[
C mim][EtSO ], J. Mol. Liq. 165 (2012) 161-167.
2 4
48] Y. U. Paulechka, A. V. Blokhin, G. J. Kabo, Evaluation of thermodynamic properties for
non-crystallizable ionic liquids, Thermochim. Acta 604 (2015) 122-128.
49] H.C. Hu, A.N. Soriano, R.B. Leron, M.H. Li, Molar heat capacity of four aqueous ionic
liquid mixtures, Thermochim. Acta 519 (2011) 44-49.
50] J. Safarov, F. Lesch, K. Suleymanli, A. Aliyev, A. Shahverdiyev, E. Hassel, I. Abdulagatov,
[
[
Viscosity, density, heat capacity, speed of sound and other derived properties of 1-butyl-3-
methylimidazolium tris (pentafluoroethyl) trifluorophosphate over a wide range of temperature
and at atmospheric pressure, J. Chem. Eng. Data 62 (2017) 3620-3631.
[
51] E. Paulechka, T. Liavitskaya, A. V. Blokhin, Calorimetric study of polymorphism in 1-
butyl-3-methylimidazolium hexafluorophosphate, J. Chem. Thermodyn. 102 (2016) 211-218.
[52] Y.U. Paulechka, A.G. Kabo, A.V. Blokhin, G.J. Kabo, M.P. Shevelyova, Heat capacity of
ionic liquids: experimental determination and correlations with molar volume, J. Chem. Eng.
Data 55(2010), 2719-2724.
[
53 ] E. Zorębski, M. Geppert-Rybczyńska, M. Zorębski, ꢀcoustics as a tool for better
characterization of ionic liquids: a comparative study of 1-alkyl-3-methylimidazolium bis
(trifluoromethyl) sulfonyl] imide room-temperature ionic liquids, J. Phys. Chem. B 117 (2013)
867-3876.
[
3
1
7

Journal Pre-proof
[54] P. Navarro, M. Larriba, E. Rojo, J. Garcꢁa, F. Rodrꢁguez, Thermal properties of cyano-based
ionic liquids, J. Chem. Eng. Data 58 (2013) 2187-2193.
55] S. Cheng, M. Musiał, Z. Wojnarowska, ꢀ. Holt, C.M. Roland, E. Drockenmuller, M.
Paluch, Structurally Related Scaling Behavior in Ionic Systems, J. Phys. Chem. B 124 (2020)
240-1244.
56] M. Paluch, Z. Wojnarowska, P. Goodrich, J. Jacquemin, J. Pionteck, S. Hensel-Bielowka,
[
1
[
Can the scaling behavior of electric conductivity be used to probe the self-organizational changes
in solution with respect to the ionic liquid structure? The case of [C MIM][NTf ], Soft Matter 11
8
2
(2015) 6520-6526.
[57] E. Zorębski, M. Musiał, K. Bałuszyńska, M. Zorębski, M. Dzida, Isobaric and isochoric
heat capacities as well as isentropic and isothermal compressibilities of di- and trisubstituted
imidazolium-based ionic liquids as function of temperature, Ind. Eng. Chem. Res. 57
(2018) 5161–5172.
[58] M. Dzida, M. Chorążewski, M. Geppert-Rybczyńska, E. Zorębski, M. Zorębski, M. Żarska,
B. Czech, Speed of sound and adiabatic compressibility of 1-ethyl-3-methylimidazolium
bis(trifluoromethylsulfonyl)imide under pressures up to 100 MPa, J. Chem. Eng. Data 58 (2013)
1
571−1576.
59] J. Skowronek, M. Dzida, E. Zorębski, M. Chorążewski, S. Jężak, M. Żarska, M. Zorębski, J.
Jacquemin, P. Goodrich, high pressure speed of sound and related thermodynamic properties of
-ethyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl] imides (from 1-propyl- to 1-hexyl-),
J. Chem. Eng. Data 61 (2016) 3794−3805.
60] E. Zorębski, M. Zorębski, M. Dzida, P. Goodrich, J. Jacquemin, Isobaric and isochoric heat
[
1
[
capacities of imidazolium-based and pyrrolidinium-based ionic liquids as a function of
temperature: modeling of isobaric heat capacity, Ind. Chem. Eng. Res. 56 (2017) 2592–2606.
[61] T. Regueira, L. Lugo, J. Fernandez, Infuence of the pressure, temperature, cation and anion
on the volumetric properties of ionic liquids: New experimental values for two salts, J. Chem.
Thermodyn. 58 (2013) 440-448.
[
62] T. Regueira, L. Lugo, J. Fernandez, High pressure volumetric properties of 1-ethyl-3-
methylimidazolium ethylsulfate and 1-(2-methoxyethyl)-1-methyl-pyrrolidinium
bis(trifluoromethylsulfonyl)imide, J. Chem. Thermodyn. 48 (2012) 213–220.
[63] B. Kosan, C. Michels, F. Meister, Dissolution and forming of cellulose with ionic liquids,
Cellulose 15 (2008) 59–66.
[
64] A. Pinkert, K.N. Marsh, S. Pang, M.P Staiger, Ionic liquids and their interaction with
cellulose, Chem. Rev. 109 (2009) 6712–6728.
1
8