Speeds of sound in ionic liquids under elevated pressures. New experimental data and CP-PC-SAFT modelling

Article abstract of DOI:10.1016/j.molliq.2020.112669

This study reports synthesis of a new ionic liquid ethyl-1-octyloxymethylimidazolium bis(trifluoromethylsulfonyl)imide ([C₂imC₁OC₈][NTf₂]) and its speed of sound data at 295.15 K ≤ T ≤ 373.15 K and 1 bar ≤ P ≤ 1471.5 bar. In addition, the atmospheric pressure densities of this IL were measured at 292.05 K ≤ T ≤ 423.65 K and determined at 295.15 K ≤ T ≤ 373.15 K and 1 bar ≤ P ≤ 1500 bar. Basing on a representative variety of ILs, it is demonstrated that the CP-PC-SAFT EOS adjusted to their high-pressure density data by a standardized numerical procedure and attached by a simple expression for estimating the ideal gas heat capacities is capable to predict sound velocities in a particularly accurate manner, with AAD around 1% and at times even smaller that the experimental uncertainties.

Full text of DOI:10.1016/j.molliq.2020.112669

Journal Pre-proof
Speeds of sound in ionic liquids under elevated pressures. New
experimental data and CP-PC-SAFT modelling
Jeremiasz Pilarz, Joanna Feder-Kubis, Vyacheslav V. Melent'ev,
Olga S. Ryshkova, Vadim I. Korotkovskii, Anton K. Radchenko,
Eugene B. Postnikov, Mirosław Chorążewski, Ilya Polishuk
PII:
S0167-7322(19)36768-6
DOI:
https://doi.org/10.1016/j.molliq.2020.112669
MOLLIQ 112669
Reference:
To appear in:
Journal of Molecular Liquids
Received date:
Revised date:
Accepted date:
9 December 2019
30 January 2020
9 February 2020
Please cite this article as: J. Pilarz, J. Feder-Kubis, V.V. Melent'ev, et al., Speeds of
sound in ionic liquids under elevated pressures. New experimental data and CP-PC-
SAFT modelling, Journal of Molecular Liquids(2020), https://doi.org/10.1016/
j.molliq.2020.112669
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2020 Published by Elsevier.

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Speeds of sound in ionic liquids under elevated pressures. New experimental
data and CP-PC-SAFT modelling.
a
b
c
c
Jeremiasz Pilarz , Joanna Feder-Kubis *, Vyacheslav V. Melent'ev , Olga S. Ryshkova , Vadim
c
c
d
a
I. Korotkovskii , Anton K. Radchenko , Eugene B. Postnikov *, Mirosław Chorążewski *, Ilya
e
Polishuk *
a
Institute of Chemistry, The University of Silesia in Katowice, Szkolna 9, 40-006 Katowice, Poland.
b
Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27,
50-370 Wrocław, Poland.
c
Laboratory of Molecular Acoustics, Kursk State University, Radishcheva st., 33 305000 Kursk, Russia.
Department of Theoretical Physics, Kursk State University, Radishcheva st., 33 305000 Kursk, Russia.
Department of Chemical Engineering, Ariel University, 40700, Ariel, Israel.
d
e
Abstract
This study reports synthesis of
a
new ionic liquid ethyl-1-octyloxymethylimidazolium
bis(trifluoromethylsulfonyl)imide ([C imC OC ][NTf ]) and its speed of sound data at 295.15 K ≤ T ≤
2
1
8
2
373.15 K and 1 bar ≤ P ≤ 1471.5 bar. In addition, the atmospheric pressure densities of this IL were
measured at 292.05 K ≤ T ≤ 423.65 K and determined at 295.15 K ≤ T ≤ 373.15 K and 1 bar ≤ P ≤ 1500
bar. Basing on a representative variety of ILs, it is demonstrated that the CP-PC-SAFT EOS adjusted to
their high-pressure density data by a standardized numerical procedure and attached by a simple
expression for estimating the ideal gas heat capacities is capable to predict sound velocities in a
particularly accurate manner, with AAD around 1% and at times even smaller that the experimental
uncertainties.
___________________________________________________________________
Keywords: Ionic liquids; synthesis; speed of sound; predictive modelling; CP-PC-SAFT.
1

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*
Corresponding authors. E-mail addresses: joanna.feder-kubis@pwr.edu.pl, postnicov@gmail.com,
miroslaw.chorazewski@us.edu.pl, polishuk@ariel.ac.il.
Introduction
The increasing practical significance of ionic liquids (ILs) makes their thermodynamic properties
particularly important for process design. Besides that, reliable estimation of these properties poses a
significant challenge for chemical engineering thermodynamics. In this respect, speed of sound presents a
specific interest for development and examining thermodynamic approaches because this property can be
accurately measured in the particularly wide range of conditions. Moreover, the accuracy in estimating
speeds of sound evidences on reliability in predicting other auxiliary thermodynamic properties which can
hardly be determined experimentally, such as the isentropic compressibility, etc.
The current experimental database on speeds of sound in ILs has been assessed by Wu et al. [1] and
Dzida et al. [2]. These reviews reveal that most of these data are restricted to atmospheric pressure. Thus
far only 10 studies [3-12] have reported the experimental data on speeds of sound in 21 ILs under
elevated pressures. These data are scored by Table 1. As seen, most of them are restricted to the relatively
narrow low-temperature ranges, while the maximal temperature is 343.15 K [8].
This study reports speeds of sound in a new IL, namely ethyl-1-octyloxymethylimidazolium
bis(trifluoromethylsulfonyl)imide ([C imC OC ][NTf ]). This quaternary imidazolium salt has a common
2
1
8
2
anion with many commercial ILs, while its major structural difference is expressed by presence of an
oxygen atom in the alkyl chain adjacent to the azomethine nitrogen atom of imidazolium. At the same
time, the stages of its synthesis and purification are relatively simple. Moreover, the pertinent metathesis
reaction does not require any energy input. In addition, the current study is the first one to expand the
investigated conditions to higher temperatures, covering 295.15 K ≤ T ≤ 373.15 K in the pressure range 1
bar ≤ P ≤ 1471.5 bar. In this condition interval, the densities have been determined basing on the speeds
of sound along with the at atmospheric pressure densities measured at 292.05 K ≤ T ≤ 423.65 K.
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Predicting speed of sound data is a challenging test for Equation of State (EoS) approaches. Recently,
Hosseini et al. [13] reviewed the approaches predicting thermophysical properties of pure ILs. Although
thus far major efforts have been invested into modelling the atmospheric pressure data (see for example
[
1,14-17]), only 7 studies [18-24] dealt with estimating speeds of sound under elevated pressures. The
absolute average deviations (AAD%) from experimental data yielded by these models are summarized by
Table 2. Typically, their substance-specific parameters have been adjusted to the volumetric data of ILs,
while the sound velocities have been predicted. The molecularly grounded approaches belonging to the
Statistical Association Fluid Theory (SAFT) family of models fit the high-pressure volumetric properties
of liquids better than the simpler Cubic equations because they estimate the packing fractions in a more
appropriate manner [25]. Thus, unsurprisingly, they exhibit more accurate results for the speeds of sound
that the models such as CPA [18]. At the same time, in the case of ILs some SAFT approaches should be
implemented to ILs with the precaution due to the possible appearance of undesired numerical pitfalls
[
26]. Besides that, Table 2 reveals that different SAFT approaches exhibit dissimilar accuracies in
estimating speeds of sound under elevated pressures. In particular, it can be seen that the ePC-SAFT
21,23,24] is characterized by an inferior precision. At the same time, the heterosegmented SAFT-BACK
[
model [20] has the much lower AAD%, apparently thanks to its 7 substance-specific adjustable
parameters. Although the CP-PC-SAFT EoS is implemented to ILs with only 3 adjustable parameters
(
which were moreover generalized for the [C mim][NTf ] ILs), it has also achieved a relatively good
x 2
accuracy [22].
In this study CP-PC-SAFT [27] is implemented for predicting the speed of sound data measured in a
new [C imC OC ][NTf ] IL. As known, such calculations require the ideal gas isobaric heat capacity
2
1
8
2
o
P
C
values. Unfortunately, this property could hardly be determined for the considered substance in a


o
P
reliable manner. Therefore, a simple empirical
C
expression developed on a basis of the density
functional theory (DFT) data of [C mim][NTf ] ILs [28] is proposed. A validity of this approach is
x
2
3

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confirmed by considering the available high-pressure speed of sound experimental data for those ILs
whose pertinent volumetric properties have are available as well.
Synthesis of a new [C imC OC ][NTf ] IL
2
1
8
2
For the synthesis the following materials were purchased from Merck: octanol (≥98%),
paraformaldehyde (powder, 95%), hydrochloric acid (35-38%), sulfuric acid (≥96%). The lithium
bis(trifluoromethylsulfonyl)imide (99%) was provided by IoLiTec. The drying agents sodium sulphate
(
anhydrous, pure) and phosphorus pentoxide (powder, anhydrous, ≥98%) were purchased from P.O.Ch
(
Gliwice, Poland). The solvents were provided by P.O.Ch and Merck. All the reagents were purified and
dried according to basic procedures and stored over molecular sieves.
The synthesis was performed in 3 stages as depicted by Fig. 1. At the first stage the chloromethyl
octyl ether (1) was synthesized and the new 3-ethyl-1-octyloxymethylimidazolium chloride [C -IM-
2
C OC ][Cl] IL (2) – at the second one. The new 3-ethyl-1-octyloxymethylimidazolium
1
8
bis(trifluoromethylsulfonyl)imide IL (3) was synthesized at the third stage. The synthesized ILs were kept
in Schlenk flasks in a desiccator between each experiment to minimize contact with air moisture.
Synthesis of chloromethyl octyl ether (1).
As described previously [29], chloromethyl octyl ether (1) was prepared by passing HCl through a
mixture of formaldehyde and 1-octanol and it was purified by the vacuum distillation method. At the
conditions of vacuum distillation (bp 98–99 °C at 1 mmHg) the yield was 99.0%.
Synthesis of 3-ethyl-1-octyloxymethylimidazolium chloride [C -IM-C OC ][Cl] (2) by the Menschutkin
2
1
8
quaternization.
This synthesis was conducted under anhydrous conditions. 25 mL of dry hexane and freshly distilled 1-
ethylimidazole (4.800 g, 0.05 mol) were introduced into a three-necked, round-bottomed flask equipped
with reflux condenser, mechanical stirrer and thermometer. The latter substance was previously prepared
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according to the procedure described by Pernak et al. [30]. The distilled just before the reaction
chloromethyl octyl ether (1) (9.460 g, 0.053 mol) was dropwise added to this vigorously stirred mixture.
An appearance of [C -IM-C OC ][Cl] was confirmed by ascending the layer chromatography (TLC) on
2
1
8
the silica gel G (Merck 1.05570.0001) and subsequently visualised by UV light. Despite an almost
immediate precipitation of the product from the reaction mixture, the stirring was continued for the next 2
hours at the room temperature. Afterwards [C -IM-C OC ][Cl] was separated, washed with dry hexane
2
1
8
(
3×30 mL) and dried overnight under the reduced pressure of 0.2 mmHg at 40 °C to get an analytically
pure transparent liquid salt. The yield was 98.5% (0.049 mol, 13.519 g).
Synthesis of 3-ethyl-1-octyloxymethylimidazolium
C imC OC ][NTf ](3) by the metathesis process.
bis(trifluoromethylsulfonyl)imide
[
2
1
8
2
The obtained 3-ethyl-1-octyloxymethylimidazolium chloride (2) (10.980 g, 0.040 mol) was dissolved in
distilled water and the saturated aqueous solution of lithium bis(trifluoromethylsulfonyl)imide (12.341g,
0
2
.043 mol) was added. The metathesis was conducted at the room temperature under vigorous stirring for
4 hours. Afterwards the crude product was separated and washed with distilled water three times. Then it
was dissolved in acetone and stirred for approximately 30 min to precipitate any residues of the chloride
precursor. Afterwards the solution was filtrated off. This procedure was repeated until the sediment of
LiCl has stopped appearing, which was detected by using AgNO . The yield was 98.0% (0.039 mol,
3
20.364 g).
Spectral, elemental and thermal analyses.
The structure and purity of each of the synthesized compounds were confirmed by the spectral
analysis. The deuterated chloroform (CDCl ) purchased from Merck was used for an NMR analysis. The
3
1
13
H NMR and C NMR spectra were recorded for all the synthesized quaternary imidazolium salts on the
Bruker DRX instrument with tetramethylsilane as a standard (at 400 and 100 MHz, respectively). The
results of this analysis are provided in the Supplementary material. The elemental analysis was carried out
for all the substances using the VARIO EL-III apparatus. The results for [C -IM-C OC ][Cl]: calc. (%)
2
1
8
for C H N OCl (274.83): C 61.18, H 9.90, N 10.19, found: C 61.24, H 9.99, N 10.08. The results for
1
4
27
2
5

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[
C imC OC ][NTf ]: calc. (%) for C H N O S F (519.52): C 36.99, H 5.24, N 8.09, found: C 36.82, H
2
1
8
2
16 27
3
5 2 6
5.34, N 8.14.
The STARe System (Mettler Toledo) and the Huber TC100 immersion cooler were used for a
Differential Scanning Calorimetry (DSC). Samples weighing between 6 and 15 mg were placed in the
aluminium pans and stored under argon with flow rate of 10 mL/min. At the first heating cycle the
heating ramp was set from 25 °C to 50 °C with the heating rate of 5 °C/min. The samples were kept at 50
°C for 15 minutes. Afterwards they were cooled from 50 °C to -80 °C with the cooling rate of 10 °C/min.
The samples were kept at -80 °C for 5 minutes. During these procedures it has been found that a new IL
has a glass transition temperature (T ) with a value of –76.6 °C.
g
At the second heating cycle the heating ramp was set from -80 °C to 50 °C with the heating rate of 5
°C/min. The thermogravimetric analysis (TGA) was performed using the TGA Q50 Texas Instrument
apparatus. The samples weighing between 5 and 10 mg were heated first from 25 °C to 75 °C with the
heating rate of 10 °C/min under nitrogen atmosphere, while maintaining the flow rate of 40 mL/min. The
samples were kept at 75 °C for 45 minutes to remove the residues of water and other volatile impurities.
Afterwards, the samples were heated from 75 °C to 500 °C with the heating rate of 5 °C/min. The
decomposition profile of the investigated IL was established as an onset temperature for decomposition of
the first 5% of the sample (T5%onset) and, furtherly, – on the regular onset temperature for decomposition
(
Tonset) for each of the two sequential decomposition steps. The thermogravimetric analysis has indicated
that the decomposition process occurs in two steps at 229.9 °C and 358.9 °C.
Speeds of sound measurements and determination of densities under elevated pressures
Speeds of sound (c) in the [C imC OC ][NTf ] IL were measured at the temperatures 295.15, 313.15,
2
1
8
2
333.45, 353.45, 373.15 K and the pressures from 1 till 1471.5 bar by a pulse phase echo ultrasonic device
−
1
having the standard uncertainty u(c) = 1 m·s . This device is comprised of the electronic pulse generator
and the receiver, measuring the time delays between generated and two reflected pulses. It is installed on
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the base of the universal digital signal processing board, DSP-310-K (for additional details see Verveyko
et al. [31]). Construction and operation principles of this acoustic piezometer cell have been described in
great details by Bolotnikov et al. [32]. Additional information concerning this apparatus can also be found
in the previous publications [33,34]. Briefly, the sound propagation velocity in the investigated liquids is
determined by the simple relation:
c = 2L/( −  )
(1)
2
1
where L is the acoustic path and  and  are the total delay times of the second and the first pulses,
2
1
respectively.
The speeds of sound were measured at the dispersionless frequency of 3.3 MHz. A single
piezoceramic emitter having 20 mm in diameter was fixed at L/2=24.9863 ± 0.0005 mm from the
reflecting cell's wall. The length of an empty measuring base was measured by the IZV-2 device (Russia),
while the deformations caused by high temperature and pressure were pertinently corrected [32]. The
apparatus was calibrated by n-decane. The stainless-steel container of an acoustic piezometer containing
the measuring cell was placed into the oil thermostat, whose standard absolute temperature uncertainty is
u(T) = 0.1 K. The external pressure was produced by a MP-2500 dead-weight pressure gauge with the
relative uncertainty of ur(P) = 0.0002. The results of speed of sound measurements are listed by Table 3.
−
1
−1
Their standard uncertainties are u(c) = 0.5m∙s and u(c) = 1.0m∙s at the atmospheric and the high
pressures, respectively.
The atmospheric pressure densities were measured at 292.05 K ≤ T ≤ 423.65 K by an Anton Parr DMA
−
3
5
000 M densitometer with standard uncertainty u(ρ) = 0.01 kg∙m . Its calibration was performed using
pure water. The temperatures were measured by a platinum resistance thermometer with resistance of 100
Ω and the standard uncertainty u(T) = 0.01 K. The results of these measurements are displayed by Table
4. Basing on the measured speed of sound and atmospheric pressure densities data, the densities under
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elevated pressures were determined by a numerical procedure described by Lowe et al. [35]. These results
are listed by Table 5.
Modelling
CP-PC-SAFT [27] is a development of the original PC-SAFT [36] aiming at eliminating certain
undesired numerical problems [26,37,38] along with replacing the fitting of substance-dependent
molecular parameters by their standardized critical point-based numerical solution. Unfortunately, the
imaginary character of the IL critical constants substantially hinders the implementation of such
procedure. Therefore, previously [22] it was proposed to implement CP-PC-SAFT EoS for predicting
thermodynamic properties of [C mim][NTf ] ILs by solving the values of m,  and /k at the three nearly
x
2
b
standard experimental density points with their further generalization. For further simplification, the
association and polar contributions have been omitted. The capability of this approach to predict speeds
of sound in ILs is examined in the current study.
Unfortunately, the PVT equations of state themselves are not enough for predicting speeds of sound.
o
P
Such predictions also require the ideal gas heat capacity (
C
) data from some external source, while in
the cases of ILs their experimental determination does not seem possible. In most of the studies
o
P
[
18,21,22,24] the
C
data of ILs have been obtained by interpolating the results of the DFT calculations
of Paulechka et al. [28,39]. At the same time, the reliability of these calculations was criticized by
Verevkin et al. [40,41]. Besides that, Verevkin et al. [41] and Blokhin et al. [42] have reported the lower
o
P
C
values of [C mim][NTf
x
2
] ILs obtained by the DFT method than the results of Paulechka et al. [28].
o
P
In some studies [20,23] the
C
data have also been estimated by the Joback – Reid group contribution
method [43], which does not consider ILs. Moreover, this method does not cover phosphorus and boron,
therefore its implementation to the ILs containing such atoms is impossible.
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o
P
As seen, currently the
C
data of ILs determined by different approaches can be characterized by
the particularly high uncertainty. Thus, in the current study we propose implementation of the following
expression derived by fitting the data of Paulechka et al. [28] to all ILs:
o
P
8
2
1.74
w
C (J molK)  0.003265330.0000326126 T 1.56461*10 T M


(
2)
Obviously, this expression cannot pretend to provide accurate results for the ILs other that
C mim][NTf ] because it considers just the molecular weights of ILs and neglects their chemical
[
x
2
background. However, unlike the Joback – Reid group contribution method [43] it can be applied to all of
o
P
them. Figure 2 compares the predictions of CP-PC-SAFT [22] with the
C
values generated by Eq. (2)
and the yielded by a Joback – Reid group contribution method [43] for [C mim][NTf ] and
3
2
o
[
C
C mim][NTf ] at 318.15 K. In this particular case the Joback – Reid method overestimates the data
P
5
2
in comparison with both Eq. (2) and the DFT calculations [28] by ~14% and ~12%, respectively.
Nevertheless, the predictions of speeds of sound remain nearly identical and they do not exhibit mutual
deviations higher than the data from different sources [4,5].
As can be seen that CP-PC-SAFT underestimates a pressure dependence of the data. Consequently, its
accuracy deteriorates with the increase of pressure. At the same time, Fig. 2 reveals that in the case of
[
C mim][NTf ] the speeds of sound exhibit a somewhat stronger pressure dependence, which is correctly
5 2
predicted by the model. As discussed previously [44], the better pronounced pressure dependency of
densities and sound velocities indicates inter alia a closer proximity to the critical point. Indeed,
according to CP-PC-SAFT the critical temperature of [C mim][NTf ] is slightly lower than of
5
2
[
C mim][NTf ]. Remarkable, as estimated elsewhere [45-48], the imaginary critical temperatures of ILs
3 2
decrease with growth of the alkyl chains because they weaken the cation-anion interactions. As seen, CP-
PC-SAFT is capable of confirming this assessment.
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As already indicated [22], the generalized M -based expressions derived for the CP-PC-SAFT
w
molecular parameters m,  and /k of the [C mim][NTf ] family are not applicable to other ILs. Thus, for
b
x
2
the particular substances considered in the current study these parameter triplets were obtained by a
previously described [22] standardized numerical procedure. This procedure implies solving the model at
three experimental density data: two low-temperature points at the lowest and the highest available
pressures along with one point of the highest available isotherm. The obtained values of molecular
parameters, the available T-P ranges, the experimental data sources and the resulting AAD% are listed by
Table 6. A graphical representation of these results can be found in the Supplementary material (Fig. S1).
As seen, in all the cases the accuracy of modelling is pretty high.
o
P
[
C mim][PF ] provides another opportunity to examine an impact of the
C
values on predicting
4
6
speeds of sound. The pertinent results of the molecular and spectral calculations were reported by
Paulechka et al. [39] and Eq. (2) significantly deviates from these data by ~31%. As seen (Fig. 3), even in
such case the accuracy of predicting the speeds of sound is not majorly affected and the model with both
o
P
C
sets yield satisfactorily accurate results. Indeed, the experimental data at 283.16 K are predicted
o
P
more precisely with the
C
generated by Eq. (2), while an accuracy at the higher temperatures is
advantageous with the values of Paulechka et al. [39]. Consequently, the lower AAD% yielded by the
latter source could rather be attributed to the distribution of experimental points. At the same time, Fig. 3
–
demonstrates that in the case of [PF ] anion CP-PC-SAFT predicts the pressure dependence of the speed
6
–
of sound data more accurately comparing with the [NTf ] one.
2
The latter observation can be confirmed considering the results of the model for the speeds of sound in
currently synthesized [C imC OC ][NTf ] IL. Figure 4 reveals that although the over-all accuracy of
2
1
8
2
these predictions is satisfactorily good (AAD = 1.47%), the pressure dependence of the data is
underestimated in a way similar to the [C mim][NTf ] ILs. Remarkable, yet both Eq. (2) and the Joback –
x
2
Reid group contribution method [43] yield the almost identical results.
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For evaluating the general robustness and reliability of CP-PC-SAFT in predicting the high-pressure
speed of sound data in ILs, this model was implemented to the additional substances listed in Table 1 (see
Fig. 5). Unfortunately, some of them were excluded due to absence of the relevant density data.
Nevertheless, the considered compounds for which such data are available still represent a convincing
diversity of ILs. Their molecular weights vary from 206.26 g/mol ([C mim][C SO ]) till 519.52 g/mol
2
1
3
3
(
[C imC OC ][NTf ]), the densities at 313.15 K and 1 bar diverging from 1051.5 kg/m
2 1 8 2
3
(
[C mim][N(CN) ]) and till 1407.1 kg/m ([C mmim][NTf ]), and the speeds of sound at these conditions
4 2 4 2
–
from 1179 m/s ([C imC OC ][NTf ]) till 1728.59 m/s ([C mim][C SO ]).
2 1 8 2 2 1 3
As seen (Fig. 5), despite this variety, CP-PC-SAFT always yields more accurate predictions with Eq. (2)
than with the Joback – Reid group contribution method [43]. In some cases application of the latter
method results in the noteworthy deterioration of accuracy. With Eq. (2), the minimal AAD of 0.37% for
[
C mim][N(CN) ] (Fig. 5C) and maximal AAD = 1.27% - for [C mpyrr][NTf ] (Fig. 5A). The somewhat
4 2 4 2
higher AAD% values previously reported [22] for the [C mim][NTf ] ILs should be explained by
x
2
implementation of the generalized expressions for the model parameters. It can also be observed that the
model exhibits a slightly better performance in the cases of ILs having lower densities and higher speeds
–
–
–
–
–
of sound ([N(CN) ] , [BF ] , [C SO ] , [C SO ] , and [C SO ] anions). At the same time, in the cases of
2
4
1
3
1
4
2
4
–
–
ILs having higher densities ([NTf ] and [TFO] anions), the results are affected by underestimating the
2
pressure dependency of data. Remarkable, in the latter case the predictions of CP-PC-SAFT are in better
agreement with the pρT-determined data of Safarov et al. [52] than with the directly measured ones [8]
(
Fig. 5E). Unlike that, as follows from Fig. 5F, in the case of [C mim][C SO ] the model exhibits a better
2 1 3
agreement with the genuine experimental data [11]. Moreover, it can be seen that at the higher
temperatures the predictions of CP-PC-SAFT are apparently more realistic than the determined data [11,
52].
Conclusions
1
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The current study has reported synthesis of a new IL ethyl-1-octyloxymethylimidazolium
bis(trifluoromethylsulfonyl)imide ([C imC OC ][NTf ]) and its speed of sound data in a particularly wide
2
1
8
2
range of conditions covering 295.15 K ≤ T ≤ 373.15 K and 1 bar ≤ P ≤ 1471.5 bar. In addition, the
atmospheric pressure densities of this IL were measured at 292.05 K ≤ T ≤ 423.65 K. Basing on all these
experimental data the densities of [C imC OC ][NTf ] were determined at 295.15 K ≤ T ≤ 373.15 K and 1
2
1
8
2
bar ≤ P ≤ 1500 bar.
Besides that, the currently available sources reporting the experimental data on speeds of sound under
elevated pressures in ILs were accumulated. The CP-PC-SAFT EoS was implemented for predicting
speeds of sound in [C imC OC ][NTf ] along with 9 additional ILs for which the high-pressure density
2
1
8
2
data are available. These ILs represent a considerable diversity of these substances with molecular
weights ranging from 206.26 to 519.52 g/mol and densities with speeds of sounds varying by more than
30%. It has been demonstrated that the unavailable for ILs ideal gas isobaric heat capacity data can be
estimated by an effortless empirical expression developed on a basis of the [C mim][NTf ] ILs DFT data.
x
2
Unlike the Joback – Reid group contribution method, this expression can be applied to all ILs and it
improves the accuracy of predicting the speed of sound data by CP-PC-SAFT. For the ILs having
relatively low densities and high speeds of sound these predictions have exhibited deviations even smaller
that the experimental uncertainties. Although in the cases ILs having higher densities and smaller speeds
of sounds the predictions were affected by underestimating the pressure dependences of the data, the
AAD were still about 1%.
Acknowledgments
M.Ch. and J.P. are grateful for the financial support based on decision no. 2016/23/B/ST8/02968 from the
National Science Centre (Poland).
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2

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J. F-K. is grateful for the financial support given from the Polish Ministry of Science and Higher
Education by subvention activity for the Faculty of Chemistry of Wrocław University of Science and
Technology.
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3

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+
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0

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Table 1. The current experimental database on speeds of sound in ILs under elevated pressures.
IL abbreviation
CAS number
174899-82-2
216299-72-8
216299-72-8
174899-83-3
174899-83-3
280779-53-5
280779-53-5
382150-50-7
174899-90-2
350493-08-2
623580-02-9
223437-05-6
223437-11-4
223437-11-4
321746-49-0
187863-42-9
448245-52-1
174645-81-9
174899-66-2
401788-98-5
342573-75-5
516474-04-7
145022-45-3
174501-65-6
174501-64-5
T range (K)
P range (bar)
152–1013.2
152–1013.2
5-2000
Reference
[
[
[
[
[
[
[
[
C mim][NTf ]
288.05–318.24
292.89–318.30
298.15–338.15
292.99–323.28
283.15–323.15
298.16–318.34
288.15–338.15
303.05–323.37
298.06–323.31
298.07–323.30
283.15–343.15
292.85–318.36
283.15–343.15
302.82–308.1
283.15–343.15
283.15–343.15
283.15–343.15
283.15–343.15
283.15–343.15
283.15–343.15
292.86–318.34
292.82–318.35
293.15–323.15
283.15–323.15
283.16–323.25
3
4
2
2
C mim][NTf ]
3
2
C mim][NTf ]
5
3
2
C mim][NTf ]
152–1013.2
1–1512
4
4
2
C mim][NTf ]
6
4
2
C mim][NTf ]
152–1013.2
5-1500
4
5
2
C mim][NTf ]
5
5
2
C mim][NTf ]
152–1013.2
1–759.9
1–759.9
1–950
4
6
2
[
[
C mmim][NTf ]
7
2
2
C mmim][NTf ]
7
4
2
[
C mpip][NTf ]
8
4
2
[
C mpyrr][NTf ]
1–1013.2
1–950
9
3
2
[
[
C mpyrr][NTf ]
8
4
2
C mpyrr][NTf ]
1–1013.2
1–950
9
4
2
[
S ][NTf ]
8
2
22
2
[
C pyr][NTf ]
1–950
8
4
2
[
C mim][N(CN) ]
1–950
8
4
2
[
C mim][SbF ]
1–950
8
4
6
[
C mim][TfO]
4
1–950
8
[
C mim][C SO ]
1–950
8
4
1
4
[
C mim][C SO ]
1–1013.2
1–1013.2
1–607.9
1–1514.16
1–1509.25
10
10
11
12
12
2
2
4
[
C C im][C SO ]
2 2 2 4
[
C mim][C SO ]
2 1 3
[
C mim][BF ]
4
4
[
C mim][PF ]
4
6
2
1

Journal Pre-proof
Table 2. AAD% from the experimental data on speeds of sound in ILs under elevated pressures achieved
by the previously considered EoS approaches.
[
C mim][NTf ] [C mim][NTf ] [C mim][NTf ] [C mim][BF ] [C mim][PF ]
3 2 4 2 5 2 4 4 4 6
CPA [18]
-
-
21.0
3.57
1.49
2.10
7.10
7.6
-
-
PC-SAFT [18]
4.36
0.69
1.78
7.69
8.2
3.74
1.74
1.92
7.38
7.5
-
-
1.06
2.03
1.45
3.61
6.3
(
G)SAFT+Cubic [18]
hetero-SAFT-BACK [20]
ePC-SAFT [21]
2.12
-
ePC-SAFT [23]
6.0
ePC-SAFT with partial
dissociation approach [24]
3.99
3.73
4.15
1.91
ePC-SAFT
dissociation approach [24]
with
full
6.93
2.37
6.04
1.32
6.42
1.76
2.64
-
CP-PC-SAFT [22]
-
2
2

Journal Pre-proof
Table 3. Experimental speed of sound data (m/s) in [C imC OC ][NTf ].
2
1
8
2
P(bar) / T(K)
295.15
1216
1255
1288
1321
1353
1382
1411
1438
1465
1491
313.15
1179
1221
1255
1289
1321
1351
1379
1407
1433
1457
1482
1507
1531
1552
1573
1594
333.45
1133
1176
1213
1247
1280
1311
1340
1368
1398
1421
1448
1471
1495
1517
1538
1560
353.45
1088
1134
1172
1207
1242
1274
1305
1333
1360
1387
1413
1439
1463
373.15
1046
1092
1133
1170
1205
1238
1269
1300
1328
1356
1383
1408
1432
1
98.1
1
2
3
4
5
6
7
8
96.2
94.3
92.4
90.5
88.6
86.7
84.8
82.9
981
1
1
1
1
1
079.1
177.2
275.3
373.4
471.5
2
3

Journal Pre-proof
Table 4. Experimental atmospheric pressure densities of [C imC OC ][NTf ].
2
1
8
2
T(K)
292.05 302.05 312.00 323.50 343.40 363.10 383.35 403.55 423.65
3

(kg/m ) 1326.96 1318.50 1309.56 1300.00 1281.69 1264.52 1247.51 1230.47 1213.39
3
Table 5. Determined densities (kg/m ) of [C imC OC ][NTf ] under elevated pressures.
2
1
8
2
P(bar) / T(K)
295.15
1324
1332
1339
1346
1352
1358
1364
1370
1375
1381
1386
1391
1395
1400
1404
1409
313.15
1309
1317
1324
1331
1338
1344
1351
1356
1362
1368
1373
1378
1383
1388
1392
1397
333.45
1291
1299
1307
1315
1322
1329
1335
1342
1348
1353
1359
1364
1369
1374
1379
1384
353.45
1273
1282
1291
1299
1307
1314
1321
1327
1334
1340
1345
1351
1356
1362
1367
1371
373.15
1256
1266
1275
1284
1292
1300
1307
1314
1320
1326
1332
1338
1344
1349
1354
1359
1
1
2
3
4
5
6
7
8
9
00
00
00
00
00
00
00
00
00
1
1
1
1
1
1
000
100
200
300
400
500
Table 6. The molecular weights, CP-PC-SAFT molecular parameters and the accuracy of density
modelling for the considered ILs.
IL abbreviation
Mw
m
[Å]
T range of the
P range of the
Number
A

[
K]
k
density data (K) density data (bar) of points
[
C imC OC ][NTf ] 519.52 12.814 3.5637 262.99
295.15-373.15
278.15-398.15
278.15-398.15
1-1500
1-1200
1-1200
80
63
63
0
2
1
8
2
[
C mmim][NTf ]
433.39 11.738 3.3653 257.57
422.41 11.528 3.3807 263.26
0
0
4
2
[
C mpyrr][NTf ]
4 2
2
4

Journal Pre-proof
[
C mim][N(CN) ]
205.26 7.1466 3.4361 307.48
288.29 8.1477 3.4288 280.80
250.32 8.6403 3.2978 297.49
236.29 7.8688 3.3136 308.11
206.26 6.9844 3.2931 319.71
226.02 5.9300 3.6426 338.02
284.18 6.8113 3.5923 325.28
293.15-393.15
283.14-413.21
283.15-353.15
283.12-413.18
273.14-413.15
313.1-472.2
1-600
1.01-1399.96
1-350
170
153
261
144
90
0
0
0
0
0
0
0
4
2
[
C mim][TfO]
4
[
C mim][C SO ]
4 1 4
[
[
C mim][C SO ]
9.1-1402.09
1.01-603
1-2000
2
2
4
C mim][C SO ]
2
1
3
[
C mim][BF ]
189
189
4
4
[
C mim][PF ]
312.8-472.3
1-2000
4
6
Figure captions
Figure 1. The synthesis scheme of new a new [C imC OC ][NTf ]) IL with the octyloxymethyl
2
1
8
2
substituent.
Figure 2. Speeds of sound in [C mim][NTf ] and [C mim][NTf ] ILs at 318.15 K. Points – experimental
3
2
5
2
o
P
o
data [4,5]. Solid lines predictions of CP-PC-SAFT with
C
yielded by Eq. 2, dashed lines – with
C
P
obtained by the Joback – Reid group contribution method [43].
Figure 3. Speeds of sound in [C mim][PF ]. Points – experimental data [12]. Solid lines – predictions of
4
6
o
P
o
CP-PC-SAFT with
C
generated by Eq. (2), dashed lines – with the
C
values obtained by
P
interpolating the data of Paulechka et al. [39].
Figure 4. Speeds of sound in [C imC OC ][NTf ]. Points – experimental data (Table 3). Solid lines –
2
1
8
2
o
o
predictions of CP-PC-SAFT with
C C
generated by Eq. (2), dashed lines – with obtained by the
P P
Joback – Reid group contribution method [43].
Figure 5. Speeds of sound in 8 ILs. Points – experimental data [7-12]. Solid lines – predictions of CP-PC-
o
o
SAFT with
C C
generated by Eq. (2), dashed lines – with obtained by the Joback – Reid group
P P
contribution method [43]. The AAD% data refers to the results obtained with Eq. (2).
2
5

Journal Pre-proof
Figures
2
6

Journal Pre-proof
Figure 1
1
750
[
C mim][NTf ] 318.29 K [4]
3
2
[
[
[
C mim][NTf ] 318.15 K [5]
3 2
c (m/s)
C mim][NTf ] 318.33 K [4]
5
2
C mim][NTf ] 318.15 K [5]
5
2
1
1
1
550
350
150
0
700
1400
2100
P (bar)
Figure 2
2
7

Journal Pre-proof
1
800
o
P
AAD with C obtained by spectral calculations[39] = 0.357%
o
AAD with C generated by Eq. (2) = 1.36%
P
c (m/s)
1650
1500
1350
2
3
3
83.16 K
03.16 K
23.25 K
[
C mim][PF ]
4 6
0
530
1060
1590
P (bar)
Figure 3
2
8

Journal Pre-proof
1
650
[
C imC OC ][NTf ]
2 1 8 2
c (m/s)
AAD = 1.47%
1
1
1
440
230
020
2
3
3
3
3
95.15 K
13.15 K
33.45 K
53.45 K
73.15 K
0
530
1060
1590
P (bar)
2
9