Influence of the alkyl side chain length on the thermophysical properties of chiral ionic liquids with a (1R,2S,5R)-(–)-menthol substituent and data analysis by means of mathematical gnostics

Article abstract of DOI:10.1016/j.molliq.2017.07.012

A comprehensive physico-chemical characterization of the chiral ionic liquids of a 3-alkyl-1-[(1R,2S,5R)-(–)-menthoxymethyl]imidazolium bis(trifluoromethylsulfonyl)imides homologous series with a linear alkyl substituent ranging from the methyl up to the

Full text of DOI:10.1016/j.molliq.2017.07.012

Influence of the alkyl side chain length on the thermophysical properties
of chiral ionic liquids with a (1R,2S,5R)-(–)-menthol substituent and data
analysis by means of mathematical gnostics
Ade´la Andresova´, Magdalena Bendova´, Jaroslav Schwarz, Zdeneˇk Wag-
ner, Joanna Feder-Kubis
PII:
DOI:
Reference:
S0167-7322(17)31130-3
doi:10.1016/j.molliq.2017.07.012
MOLLIQ 7589
To appear in:
Journal of Molecular Liquids
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Revised date:
Accepted date:
17 March 2017
24 May 2017
4 July 2017
Please cite this article as: Ad´ela Andresova´, Magdalena Bendova´, Jaroslav Schwarz,
Zdenˇek Wagner, Joanna Feder-Kubis, Influence of the alkyl side chain length on the ther-
mophysical properties of chiral ionic liquids with a (1R,2S,5R)-(–)-menthol substituent
and data analysis by means of mathematical gnostics, Journal of Molecular Liquids (2017),
doi:10.1016/j.molliq.2017.07.012
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ACCEPTED MANUSCRIPT
Influence of the alkyl side chain length on the
thermophysical properties of chiral ionic liquids with a
(1R,2S,5R)-(–)-menthol substituent and data analysis
by means of mathematical gnostics
Ad´ela Andresov´aa, Magdalena Bendov´aa,∗, Jaroslav Schwarzb, Zdenˇek
Wagnera, Joanna Feder-Kubisc,∗∗
aE. Hala Laboratory of Separation Processes, Institute of Chemical Process Fundamentals
CAS, v. v. i., Rozvojova 135/1, 165 02 Prague 6 – Lysolaje, Czech Republic.
bLaboratory of Aerosol Chemistry and Physics, Institute of Chemical Process Fundamentals
CAS, v. v. i., Rozvojova 135/1, 165 02 Prague 6 – Lysolaje, Czech Republic.
cWrocl aw University of Science and Technology, Faculty of Chemistry, Wybrz˙eze
Wyspian´skiego 27, 50-370 Wrocl aw, Poland.
Abstract
A comprehensive physico-chemical characterization of the chiral ionic liquids
of a 3-alkyl-1-[(1R,2S,5R)-(–)-menthoxymethyl]imidazolium bis(trifluoromethyl-
sulfonyl)imides homologous series with a linear alkyl substituent ranging from
the methyl up to the dodecyl group was carried out experimentally to investi-
gate the way in which the measured thermophysical properties were influenced
by the alkyl chain length on the cation. Refractive index, density, speed of
sound, and isobaric heat capacity were measured as a function of temperature
at atmospheric pressure and analyzed by methods based on mathematical gnos-
tics. A robust linear regression along a gnostic influence function was used to
optimize parameters of the relationships used in this work and to estimate the
changing nanosegregation in the studied ionic liquid series by finding the Criti-
cal Alkyl Length Size (CALS) from heat capacity data. In addition, we propose
the use of the marginal analysis to assess the quality of the measured data as
an alternative to the estimate of the measurement uncertainty.
∗
Principal corresponding author
∗∗
Corresponding author
Email addresses: bendova@icpf.cas.cz (Magdalena Bendova´),
joanna.feder-kubis@pwr.edu.pl (Joanna Feder-Kubis)
Preprint submitted to Journal of Molecular Liquids
July 5, 2017

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Keywords: chiral ionic liquids, natural terpene substituent, thermophysical
properties, differential scanning calorimetry, structure-property relationships,
mathematical gnostics
1. Introduction
In spite of the ever-increasing number of papers on ionic liquids (ILs), this
class of compounds still hasn’t used up its potential in terms of their possible
applications. Not least importantly, establishing reliable relationships between
their properties and structure will facilitate the utilization of ionic liquids and
the design of new structures task-specific structures. Indeed, the number of
possible combinations of different cations and anions is very large a rough esti-
mate giving as many as 1018 ILs to be synthesizable. With a good knowledge of
their structure-property relationships, their thermophysical characteristics such
5
10 as the volumetric, transport, and thermal properties could thus be fitted to the
advantage of a particular application [1].
To contribute to a better understanding of the structure-property relation-
ships of ionic liquids, a homologous series of ionic liquids with a chiral (1R,2S,5R)-
(–)-menthol substituent and a bis(trifluoromethylsulfonyl)imide anion is dis-
15 cussed. A series of 3-alkyl-1-[(1R,2S,5R)-(–)-menthoxymethyl]imidazolium
bis(trifluoromethylsulfonyl)imides was therefore studied in this work. Previ-
ously, the syntheses and basic physico-chemical characterization of the consid-
ered salts were described by our group [2, 3]. The presence of an optically active
alcohol substituent in the cationic part causes these compounds to belong to the
20 group of the chiral ionic liquids (CILs). We have noticed that the discussed op-
tically active bis(trifluoromethylsulfonyl)imides series of salts might be applied
in various fields of chemistry, among others in organic catalysis [4] or in stabi-
lization and activation of laccase [5]. Furthermore, they have been proved to
be effective antielectrostatic agents [2]. In a context of studies by other groups,
25 Vasiloiu et al. [6] have for instance studied chiral ionic liquids that can be used
as chiral selectors, chiral recognition being very difficult to predict.
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Even though numerous papers address the influence of the linear alkyl side-
chain length on the cation on the thermophysical and thermodynamic properties
of ionic liquids, e.g. [7–15] to cite but a few, the relationships between those
30 properties and the IL structure is far from established. Indeed, the interaction
between the alkyl side chain and its cation and between the entire cation and the
anion of the ionic liquid is very sensitive to even very small changes in structure.
The influence of the alkyl chain length may often seem straightforward, how-
ever, nanostructure rearrangement was found to differ as a function of the alkyl
35 chain length in homologous series based on the 1-alkyl-3-methylimidazolium
cation. In a possibly first studies on the subject, Canongia-Lopes and P´adua [16]
have explored nanostructure in 1-alkyl-3-methylimidazolium hexafluorophos-
phate ionic liquids by means of molecular simulation, showing nanosegregated
polar and non-polar domains occurred, changing from disperse microphases
40 for shorter chain lengths (C2) to continuous ones in ionic liquids with long
alkyl substituents (C12). Later, Rocha et al. [17] used very precise mea-
surements of vaporization enthalpies in a series of 1-alkyl-3-methylimidazolium
bis(trifluoromethylsulfonyl)imides to determine a shift in the slope of the de-
pendence of the vaporization enthalpy on the number of carbons in the alkyl
45 chain on the cation, pointing towards that starting with hexyl-substituted ionic
liquids nanostructuring changed its nature due to different coiling of the alkyl
substituent. They state that this phenomenon was due to percolation effects and
a pronounced decrease of the relative cation–anion interaction energy towards
an almost constant value for alkyl substituents longer than hexyl, a finding they
50 were able to confirm in several subsequent papers [8, 10, 18]. In the same ho-
mologous series, Garaga et al. [19] have used the NMR and vibrational spectra
to show the displacement of the bis(trifluoromethylsulfonyl)imide anion for the
methyl- to hexyl-substituted ionic liquids with a concomitant increase of the
trans conformers and no further significant displacement for ionic liquids with
55 alkyl chains longer than C6.
In this work a comprehensive physico-chemical experimental characterization
of the chiral ionic liquids of the 3-alkyl-1-[(1R,2S,5R)-(–)-menthoxymethyl]imida-
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zolium bis(trifluoromethylsulfonyl)imide series with alkyl ranging from the methyl
up to the dodecyl substituent is carried out for two main reasons. In spite of
60 the promising application potential of the entire series, such a study hasn’t
been carried out yet. The measured data not only prove useful in the design
and optimization of a possible process in which the present ionic liquids will be
used, but also contribute to the growing knowledgebase of the physico-chemical
properties of pure ionic liquids and set them in context of previous studies by
65 this group and other authors. The properties selected for study in this work,
density, speed of sound, and heat capacity are linked through relationships fol-
lowing from the First and the Second Law of Thermodynamics and allow for a
deriving of further material properties. Furthermore, density and heat capacity
are related by the cohesive energy density, providing an insight into the influ-
70 ence of the microstructure of the studied compounds on their bulk properties.
As a consequence, specific heat capacity per unit volume calculated from the ex-
perimental molar heat capacity and liquid density may enable us to investigate
possible structure rearrangement in the studied compounds, as their structure
changes with the changing alkyl chain length on the cation [18].
75
More importantly though, methods based on mathematical gnostics [20] were
used in this work to process the measured data and to assess their quality.
Mathematical gnostics not only enabled us to evaluate the repeatability of the
measurements for the properties studied in this work, but mainly proved to be
a valuable tool in assessing the structure-property relationships for the experi-
80 mentally measured heat capacity in the studied series via the implementation
of a robust linear regression along a gnostic influence function.
2. Theoretical section
2.1. Data quality assessment using the marginal analysis
The quality of experimental data is usually assessed from the measurement
85 uncertainty the value of which follows from unknown systematic, random, and
other, unidentified, errors of measurement. According to the NIST guidelines,
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[21] the combined uncertainty or preferably the expanded uncertainty of the
measurement should be calculated from the data using any valid statistical
method. However, this requires an a priori knowledge or at least an approxi-
90 mation of the error distribution function and a data sample large enough to be
statistically significant. Mathematical gnostics (MG) [20, 22] on the other hand,
provides us with a non-statistical approach towards the uncertainty treatment
without the need for an a priori assumption of the distribution of errors. The
underlying theory was derived considering the uncertainty of every single mea-
95 surement, the properties of a data sample are then evaluated by aggregation
of properties of each measurement. Small data samples can thus be analyzed
and a sound estimate of the experimental uncertainty obtained. The theory
offers several tools each of which is suitable for a different application. For the
purpose of this work we make use of the marginal analysis which is based on
100 the properties of the estimating local distribution function (ELDF), namely on
its natural robustness with respect to outliers. The mode of the ELDFs density
(Z0), i.e. the location of the density’s maximum, is the most probable value of
the data sample and is considered as an estimate of the true value of the mea-
sured quantity. The uncertainty is assessed by an estimation of the tolerance
105 interval (Z0U, Z0L), and the interval of typical data (ZU, ZL) [20].
The intervals reflect the sensitivity of the ELDF’s mode location to a single
added data value. No matter how outlying the added value is the position of the
mode cannot be shifted outside the tolerance interval (Z0U, Z0L). Depending
on the kind of analyzed data the tolerance interval represents either repeata-
110 bility or reproducibility. The sensitivity of the mode location to the additional
datum belonging to the interval of typical data (ZU, ZL) behaves typically, the
dependence is increasing. If the additional datum falls outside this interval, the
dependence becomes decreasing owing to the natural robustness of the ELDF.
The interval of typical data thus delimits the range where a measured value can
115 be expected. Values outside the interval of typical data are suspicious.
The symmetricity or asymmetricity of the estimating local distribution func-
tion, which can also be seen from the symmetricity or asymmetricity of the tol-
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erance interval and the interval of typical data, provides us with an additional
information on the character of experimental errors. The symmetric shape shows
120 that probability of positive and negative deviations is equal similarly as e.g. in
the case of the Gaussian distribution. Asymmetric distribution is frequently
found if the measured value is close to a physical limit of the quantity, typical
example being data on trace analysis.
If the tolerance interval is symmetric or only slightly asymmetric, the un-
125 certainty of the measurement for each datapoint can be expressed in a simpler
form as:
Z = Z0 (Z0U − Z0L)/2
(1)
The overall measurement repeatability can then be estimated as the median
of the uncertainties of the individual modes.
As already mentioned, this approach to uncertainty assessment does not re-
130 quire knowledge of distribution of experimental errors and is robust and reliable
even if outliers are present in the data sample. The method suggested by the
NIST guidlines [21] is based upon estimation of a variance of an a priori known
distribution. If the data sample is small, we cannot verify the statistical dis-
tribution of errors and the relative error of estimated variance is high, often as
135 much as 40%. Data with improperly assiged uncertainty based on statistical
analysis do exist in the literature. One such case was mentioned in [23] and
later in [22] where an analysis of reliability of estimation of a tolerance interval
and an interval of typical data from real experimental data is presented.
2.2. Robust optimization along a gnostic influence function
140
We have already shown in our previous work the importance of a reliable
optimization algorithm in nonlinear regression tasks and how these can be car-
ried out by means of robust regression along a gnostic influence function [24].
The regression along an influence function is not per se a concept derived in
mathematical gnostics, it is indeed a statistical notion derived under an as-
145 sumption that a limited number of measured values are subject to gross errors
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with known non-Gaussian distribution [25]. However, such an assumption on
the distribution of the gross errors can rarely be verified. Gnostic methods are
based on more general assumptions of taking into account the uncertainty of the
individual data points where the distribution function is also estimated during
150 data analysis. Therefore, even though in this work the experimental data can
be described by simple equations the parameters of which can be estimated by
linear regression, the robust linear regression along the gnostic influence func-
tion based on mathematical gnostics was applied [20, 26]. For instance, if an
outlier is identified, the regression algorithm assigns them with a lower weight.
155 The optimized parameters can thus be considered as more reliable than the ones
obtained from the statistical regression methods. On the other hand, when no
outliers are present, the optimization becomes identical with the ordinary least-
squares method. In addition, the marginal analysis described in Section 2.1.1
enabled us to choose the appropriate empirical equation where there are no rec-
160 ommended or thermodynamically justified relationships, e.g. in the description
of the heat capacity data or to describe the dependencies of the measured prop-
erties on the number of carbon atoms in the alkyl substituent on the cation.
Indeed, the marginal analysis of the regression residua provides us with the in-
formation of the residua dataset homogeneity or non-homogeneity. In the latter
165 case the relationship may be considered as unsuitable for the given regression.
3. Experimental section
3.1. Chemicals used
(1R,2S,5R)-(–)-Menthol (99%), 1-methylimidazole (99%), 1-butylimidazole
(98%), bromoethane (≥99%), 1-bromopropane (99%), 1-bromopentane (98%),
170 1-bromohexane (98%), 1-bromoheptane (99%), 1-bromooctane (99%), 1-bromo-
nonane (98%), 1-bromodecane (98%), 1-bromoundecane (98%), 1-bromodode-
cane (97%), paraformaldehyde (powder, 95%), imidazole (≥99%), sodium (cubes,
contains mineral oil, 99.9% trace metals basis) were purchased from Sigma-
Aldrich, whereas lithium bis(trifluoromethylsulfonyl)imide (99%) was provided
7

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175 by IoLiTec. For the NMR analysis, the deuterated chloroform (CDCl3) pur-
chased from Merck was used. All the solvents were purchased from the com-
mercial suppliers: Sigma-Aldrich and Fluka and were dried before use.
The structure and purity of all of the synthesised substances were confirmed
by spectral and elemental analysis, respectively. The 1H NMR and 13C NMR
180 spectra were recorded on a Bruker DRX with tetramethylsilane as standard
(at 600 and 151 MHz, respectively). Elemental analyses were carried out using
VARIO EL-III.
The syntheses of 3-alkyl-1-[(1R,2S,5R)-(–)-menthoxymethyl]imidazolium
bis(trifluoromethylsulfonyl)imides, abbreviation: [Cn-Im-CH2OMen][Tf2N],
185 where n = 1 to 12, presented in this study were described in our previous
publication [2]. For the sake of brevity the bis(trifluoromethylsulfonyl)imide
anion will be referred to in this text as bistriflate. Elemental analysis was per-
formed for all obtained salts and has been presented in the results section. All
reagents were dried and purified before use by usual procedures, all substrates
190 were freshly distilled before use [2]. Chloromethyl (1R,2S,5R)-(–)-menthyl ether
was prepared by passing HCl through a mixture of (1R,2S,5R)-(–)-menthol and
paraformaldehyde. 1-alkylimidazole were synthesized following the method by
Pernak et al. [2]. Briefly, for quaternization chloromethyl (1R,2S,5R)-(–)-menthyl
ether was slowly added to a solution of proper 1-alkyl-imidazole in dry hexane
195 and vigorously stirred (from 60 min to 120 min) at room temperature. Then,
the phases were separated and the product was washed with dry hexane. The
o
volatile materials were removed under reduced pressure at 60 C overnight. Ob-
tained chlorides (200 mmol) were dissolved in water and saturated aqueous so-
lution of lithium bis(trifluoromethylsulfonyl)imide (220 mmol) was added. The
200 metathesis reaction was stirred at room temperature for 24 h. Then, the crude
product was separated and washed with distilled water three times. Respec-
tively, each of the obtained ionic liquids was dissolved in acetone and stirred for
30 min to precipitate any residues of the halide salt, which was filtrated off (0.2
o
m filter). The filtrate was placed in the fridge (approx. –5 C) for one night in
205 order to complete precipitation of the halide salt. In the case of precipitation
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of inorganic salt, another filtration was carried out and the resulting filtrate
was evaporated. This work-up was repeated until no more LiCl precipitate was
observed (detected using AgNO3) [27]. Elemental analysis was performed for
all obtained salts and has been presented in the results section.
210
1-butanol anhydrous (purity 99.8%, Sigma-Aldrich) was used as received
without any additional purification as a calorimetric standard. Throughout the
experiments the amount of water in 1-butanol was checked by means of the Karl-
Fischer titration and kept lower than 0.075 wt.%. Hydranal Titrant Compos-
ite 2 (titer 1.6–2.4 mg/ml) and Hydranal Methanol Dry (≥0.01 % water) used in
215 the Karl-Fischer titrations were purchased from Sigma-Aldrich and used as re-
ceived. 1-hexyl-3-methylimidazolium bis(trifluoro-methylsulfonyl)imide (abbr.
[hmim][Tf2N]) with a declared purity of 98% was purchased from IoLiTec to be
used to validate the density, speed of sound, refractive index, and isobaric molar
heat capacity measurements using the experimental protocol described herein.
220 [hmim][Tf2N] was decolorized before the experiments using the procedure de-
scribed in the Electronic Supporting Information.
To further check the purity of the studied chiral ionic liquids and [hmim][Tf2N],
ion chromatography analysis both for cations (Li+, Na+, NH4+, K+, Ca2+, and
2−
−
−
−
−
−
Mg2+) and anions (F , Cl , Br , SO4 , NO3 , H2PO4 ) was carried out in
225 parallel using a Dionex 5000 system. An IonPac AS11-HC 2 x 250 mm column
was used for anions using hydroxide eluent, IonPac CS18 2 x 250 mm for cations
using methane sulfonic acid solution as an eluent. Both anion and cation setup
were equipped with electrochemical suppressors. External calibration was done
using NIST traceable calibration solutions. The relative uncertainty of the ion
230 concentration determination was of 20% and the detection limit 0.001 ppm.
Of the most important impurities that influence the properties of ionic liquids,
chloride contents were found to be lower than 9.3 ppm for all the studied ionic
liquids, whereas lithium contents were always lower than 0.1 ppm or below the
detection limit of the device (see Table 2). IoLiTec states the level of the chloride
235 anion in [hmim][Tf2N] to be lower than 100 ppm; it is evident from the present
data that the real content of the impurities is much lower. The amounts of other
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ionic impurities were found to be similarly low in the studied ionic liquids and
are listed in Table SI-1. The overall purity of the ionic liquids studied in this
work is then summarized in Table 1.
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240
To minimize contact with air moisture, the studied ionic liquids were kept in
Schlenk flasks in a dessicator between the individual experiments. The samples
were then dried before every experiment, for at least 16 hours under vacuum
(8-10 mbar) at approximately 60 oC. The water content in the samples was
determined by means of the volumetric Karl-Fischer titration using a Schott
245 Instruments GmbH TitroLine KF Titrator and did not exceed 0.00073 mass
fraction units. The water contents in the samples along with the refractive
indices of the studied ionic liquids are summarized in Table 2.
Table 2: Molar mass M r, water and ion impurities contents, and refractive index, n2D5, at
298.15 K of the studied chiral ionic liquids.
−1
Chiral ionic liquid
M r / g·mol
H2O / wt% Cl / ppm Li+ / ppm nD25
−
[Cn-Im-CH2OMen][Tf2N]
[C1-Im-CH2OMen][Tf2N]
[C2-Im-CH2OMen][Tf2N]
[C3-Im-CH2OMen][Tf2N]
[C4-Im-CH2OMen][Tf2N]
[C5-Im-CH2OMen][Tf2N]
[C6-Im-CH2OMen][Tf2N]
[C7-Im-CH2OMen][Tf2N]
[C8-Im-CH2OMen][Tf2N]
[C9-Im-CH2OMen][Tf2N]
531.53
545.56
559.59
573.61
587.64
601.67
615.69
629.72
643.75
0.036
0.018
0.023
0.021
0.039
0.017
0.019
0.010
0.073
0.000
0.020
0.024
5.356
2.061
2.658
1.109
3.260
7.798
4.787
4.230
2.354
5.598
1.968
9.306
0.004
0.014
n.a.
1.4483
1.4476
1.4484
1.4487
1.4492
1.4503
1.4499
1.4502
1.4507
1.4508
1.4511
1.4518
n.a.
n.a.
n.a.
n.a.
n.a.
n.a.
[C10-Im-CH2OMen][Tf2N] 657.77
[C11-Im-CH2OMen][Tf2N] 671.80
[C12-Im-CH2OMen][Tf2N] 685.83
0.020
0.045
0.075
U(wH )=0.00001 weight fraction units, Ur(wions) = 20%, U(n2D5)=0.00005 refractive index
O
2
units, U(T)=0.1 K, U(p)=0.02 MPa)
250 3.2. Experimental methods
All the experimental measurements were validated by measuring the ther-
mophysical properties studied in this work for 1-hexyl-3-methylimidazolium
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bis(trifluoromethylsulfonyl)imide, analyzing the measured values by the marginal
analysis described in Section 2.2.1 and comparing them with literature values
255 (see Section 3.3).
3.2.1. Refractive index
The refractive index at 298.15 K at 0.1 MPa, n2D5 for the studied ionic liq-
uids was measured by means of an AR Abbe refractometer 2 (A. Kru¨ss Optronic
GmbH) with an uncertainty of 0.0003 nD units stated by the manufacturer. Be-
260 fore each measurement the refractive index of pure distilled water was measured
and compared with its literature value (n2D5=1.3325). [28]
3.2.2. Density and speed of sound
The density and the speed of sound as a function of temperature at 0.1
MPa were measured by means of an Anton Paar DSA5000 Density and Sound
265 Velocity Analyzer within the temperature range from (288.15 to 343.15) K. The
speed of sound analyzer working frequence is of 3MHz. The apparatus was
calibrated using degassed redistilled water (ρ=(0.997043 0.00001) g·cm–3 at
T= 298.15 K) [29] and a high-density standard tetrachloroethylene supplied by
H&D Fitzgerald Ltd. (ρ=(1.61420 0.00001) g·cm–3 at T=298.15 K).
270
The uncertainty of the device stated by the manufacturer is of 0.00001 g·cm–3
for the density and of 0.1 m·s–1 for the speed of sound. The apparatus is kept
at the experimental temperature within 0.001 K by means of a built-in solid
state thermostat.
3.2.3. Isobaric heat capacity
275
The isobaric heat capacity as a function of temperature at 0.1 MPa was
measured by means of the differential scanning calorimetry. A Setaram µDSC 3
Evo microcalorimeter based on the Tian-Calvet principle using batch cells was
used. The continuous method with the heating rate of 0.3 K·min–1 was used in
this work, the initial and final temperatures of the scans being held constant for
280 40 min in the same way as in [30]. The calibration data of 1-butanol that was
used as the calibration standard were taken from the monograph by Z´abransky´
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et al. [31]. The heat capacity was then calculated by means of the Calisto
software.
The standard and samples of pure ionic liquids, respectively, were prepared
285 into the measuring cell by weighing using a SCALTEC SBC 21 balance with an
accuracy of 1·10–5 g.
3.3. Validation of the density, speed of sound and heat capacity measurements
Due to the small amount of samples of the chiral ionic liquids available in
this work, repeated measurements of the studied properties could not be carried
290 out. To make sure that the present data were measured with adequate accuracy,
density, speed of sound, refractive index, and isobaric molar heat capacity were
measured using the experimental protocols described in Sections 3.2.1 to 3.2.3
for 1-hexyl-3-methylimidazolium bistriflate. The ionic liquid [hmim][Tf2N] was
selected as a benchmark ionic liquid for the IUPAC Project #2002-005-1-100
295 (Thermodynamics of ionic liquids, ionic liquid mixtures, and the development of
standardized systems), [32] the literature data on its thermophysical properties
following from this project [33–42] may thus be considered as reliable. In addi-
tion, it is an imidazolium-based ionic liquid with a bistriflate anion, its chemical
character is therefore similar to the ionic liquids studied in this work, being
300 both prone to water uptake from air moisture as well as showing low solubility
in water due to the hydrophilic character of the bistriflate anion.
Each measurement has been repeated at least five times and the data were
analyzed by means of the marginal analysis described in Section 2.1. The mea-
sured refractive index, density, and speed of sound data are listed along with
305 the estimated repeatability for the individual temperatures Tables SI-2 to SI-5
of the Electronic Supporting Information (ESI). The data are also compared
with selected literature data in Tables SI-2 to SI-5 and Figure SI-4 of the ESI.
Table 3 then lists the repeatability of the measurements found by the marginal
analysis as the median value of the individual datapoints uncertainty, the de-
310 vice precision stated by the manufacturers of the devices used in this work,
and the reproducibility of the measurements found by the marginal analysis of
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our data together with literature values that followed from the IUPAC Project
#2002-005-1-100 density [32–37], speed of sound [33], and isobaric molar heat
capacity [38–42]. Data for the refractive index were not measured in the above-
315 mentioned project, the data by Tariq et al. were therefore used [43]. As the
literature data were not all measured at the same temperatures as the present
data, the comparison was made at a single temperature, i.e. at 298.15 K. The
comparison of the individual values in Table 3 shows that the repeatability of
the measurements found in this work is in good agreement with the uncertainty
320 stated by the manufacturers of the devices used in this work. The overall un-
certainty of the measurements can be estimated as where R is the measurement
reproducibility, obtained in this work from the marginal analysis of our data
together with the literature values, and N is the uncertainty following from the
influence of the impurities in the studied ionic liquids. As the impurity levels
325 found by the elemental analysis, ion chromatography, and Karl-Fischer titration
for the studied chiral ionic liquids and [hmim][Tf2N] are insignificantly low and
sometimes even below the detection limit (especially for chloride and lithium
ions, that are known to significantly influence the thermophysical properties of
ionic liquids), the uncertainty following from the presence of impurities could be
330 neglected and the overall measurement uncertainty was estimated as equivalent
to the repeatability found by the marginal analysis.
To compare the density, speed of sound, and isobaric molar heat capacity
measured for [hmim][Tf2N] in this work with the data published within the IU-
PAC Project #2002-005-1-100 and some more recent papers not related [44–46],
335 a robust regression along a gnostic influence function described in Section 2.2
using equations used to describe the studied properties as a function of tempera-
ture was carried out for our data and literature values following from the IUPAC
project. First all data, i.e. our data along with the literature values, were re-
gressed. This regression was compared with that of literature data only and our
340 data only, respectively, in Tables SI-6 to SI-8. Then, using the regression param-
eters obtained from both our and literature data, the studied properties were
calculated to obtain deviations of the calculated data from the experimental
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ones. These deviations are shown in Figures SI-1 to SI-3. From the regression
parameters and the calculated deviations it appears that our data are in overall
345 good agreement with literature values. Indeed, the deviations calculated for the
density data presented in this work are for all the three properties comparable
with those obtained from the literature values. For instance, the isobaric molar
heat capacity has been reported on in several works for [hmim][Tf2N] in which
different calorimetric methods over a wide range of temperatures were used.
350 Furthermore, the robust regression along the gnostic influence function deter-
mines the weights of the individual datapoints a posteriori. From the regression
of literature data along with those measured in this work it was evident that
our data were assigned weights close to unity. This indicates that our data were
not detected as outliers of the entire analyzed dataset. The comparison of our
355 data with the literature is shown in Figure SI-3 and Figure SI-4. It appears
that our data are in good agreement with those by Blokhin et al. [39] and
Shimizu et al. [40], both obtained using adiabatic calorimetry with a state un-
certainty of 2.5 J·K-1·mol-1 and 0.8 J·K-1·mol-1, respectively. Other data found
in the literature [41, 42, 47, 48] show a larger scatter and deviation from the
360 present data, however, our data mostly fit into their uncertainty intervals of 11
J·K-1·mol-1 for Archer [41], 35 J·K-1·mol-1 for Diedrichs and Gmehling [42], and
22 J·K-1·mol-1 for Huges et al. [48]. It appears that the data measured in this
work are of comparable if not better uncertainty than those obtained by these
other authors.
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Table 3: Data quality evaluation for the repeated measurements and the comparison with
literature values of the refractive index at 298.15 K, and density and speed of sound as a
function of temperature for [hmim][Tf2N]
Measured property
Refractive index
Density
Device precisiona Repeatabilityb
Reproducibilityc
0.00005 nD units
0.0003 nD units
0.0001 nD units
−3
−3
−3
1·10−5g·cm
1·10−5g·cm
0.00015 g·cm
−1
−1
−1
Speed of sound
0.1 m·s
0.04 m·s
<0.1 m·s
−1
−1
Molar heat capacity n/a
0.17 J·K−1·mol
1.1 J·K−1·mol
365
astated by the manufacturer
bfound from the marginal analysis
cfound from the marginal analysis from our and literature data [32–43]
Validating the use of 1-butanol as a reference liquid in heat capacity measure-
370 ments was carried out in a previous work [30]. By measuring the heat capacity
of water using the 1-butanol standard it was shown that heat capacity could
be measured with good accuracy, the deviation from the recommended data
not exceeding 0.25%. Thus 1-butanol can be considered as a suitable reference
material despite its relatively high hygroscopicity. This was further confirmed
375 by validating the measurements against the literature values of heat capacity
of [hmim][Tf2N]. To make sure that the standard did not absorb an excessive
amount of water during the calibration run, a Karl-Fischer titration was per-
formed before and after each calibration, the amount of water not exceeding
0.0007 mass fraction units in any of the experiments.
380 4. Results and Discussion
4.1. Synthesis
The homologous series of chiral ionic liquids with a (1R,2S,5R)-(–)-menthol
substituent and bistriflate anion were prepared. The synthesized salts were
obtained in very good yields, higher than 96% in each case. All details are
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385 given in Table 4. All ionic liquids discussed in here are hydrophobic, colourless
liquid and are stable in water solution.
Schema 1 shows the general structure of the synthesized 3-alkyl-1-[(1R,2S,5R)-
(–)-menthoxymethyl] imidazolium bis(trifluoromethylsulfonyl)imides. The ionic
1
liquids were characterized by H NMR and 13C NMR (see Electronic Support-
390 ing Information File 2). Elemental analysis was performed for all discussed salts
and the details are given in Table 4.
Schema 1. Structure of the synthesized 3-alkyl-1-[(1R,2S,5R)-(–)-menthoxymethyl]imidazolium
bis(trifluoromethylsulfonyl)imides (R=CH3 to C12H25
)
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395 4.2. Measurement of thermophysical properties
4.2.1. Refractive index
Figure 1: Refractive index, n2D5, at 298.15 K of the studied chiral ionic liquids [Cn-Im-
CH2OMen][Tf2N] as a function of carbon atoms, n(C), in the alkyl chain on the cation.
Black circles are experimental data.
Refractive indices measured at 298.15 K for the studied ionic liquids are summa-
rized in Table 2 and plotted as a function of the number of carbons of the alkyl sub-
stituent in Figure 1. The data display a slight deviation from a regular increase. Since
400 the refractive index is very sensitive to small changes in concentration, this deviation
could be caused by minor impurities in the individual IL samples and/or slightly dif-
fering water contents. The deviation of the refractive index of the methyl-substituted
ionic liquid [C1-Im-CH2OMen][Tf2N] might also be attributed to the different packing
of this first member of the homologous series as for instance in the homologous series
405 of alkanes [49].
4.2.2. Density and speed of sound
The experimental data on density and speed of sound as a function of temperature
are listed in Tables SI-9 and SI-10 of the ESI, respectively. Density of the studied
ionic liquids decreases with increasing temperature. The experimental density data
410 were described with the linear equation
ρ = A + BT
(2)
Figure 2: Experimental density, ρ, at 298.15 K of the studied chiral ionic liquids [Cn-Im-
CH2OMen][Tf2N] as a function of the number of carbons of the alkyl side chain length n(C).
Black circles are experimental data, full line corresponds to the fit by Eq. 5.
Some authors seem to point to a controversy around the choice of a linear or
quadratic dependence of the logarithm of density on temperature [50, 51]. However, the
reasons for choosing one or another are purely empirical (assuming that the coefficient
of the isobaric expansivity barely changes with temperature) or based on the goodness
415 of fit. In the case of the data presented in this work, the linear and quadratic fit
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for the logarithm of density as a function of temperature were both found to provide
non-random patterns for the calculated residuals. However, the selected fit influences
the value of the coefficient of isobaric expansivity defined as

1
∂ρ
∂T
αp = −
(3)
ρ
A differentiable function can be approximated by an expansion to a Taylor series.
420 Considering the partial derivative of the density with respect to temperature at con-
stant pressure as the first term of a Taylor series and that the coefficient of isobaric
expansivity is almost independent of temperature, it increases only very slightly with
temperature in the condensed phase, it becomes evident that a linear function should
be sufficient to describe the temperature dependence of density.
425
The parameters of Eq. 2 that are summarized in Table 5 were optimized using a
robust linear regression algorithm along a gnostic influence function as described in
section 2.1.2. For this and all the following regression functions used in this work,
the Standard Estimation of Error, SEE, was calculated from the sum of squares of
weighted regression residua as
n
!
"
#
$%
2
SEE =
wi yiexp − yicalc
(4)
i=1
430
where n is the number of datapoints, wi is the robustifying weight of the point i
exp
obtained on the regression of data along a gnostic influence function and yi
and
calc
yi
are experimental and calculated values, respectively.
Density at 303.15 K of the studied chiral ionic liquids that have already been
reported in previous work were compared with those found in this work. Differences
435 between the values reported herein and in Ref. [2] range between (0.1 and 30) kg·m–3
and may explained by two main aspects. In Ref. [2] a simple gravimetric method
using a Mettler Toledo DA 110 M scale was used to measure the density of the studied
ionic liquids the uncertainty of which is significantly higher than that of the vibrating
tube densitometry used in this work. Further contributing to the different values of
440 the measured density was the different purification protocol used in previous work; as
compared with the procedure described in Section 3.1 the ionic liquids in Ref. [2] were
only washed with distilled water. The density reported on was thus not only measured
with lower uncertainty and as a function of temperature, but also using ionic liquids
with higher purity.
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Table 5: Parameters A and B of the linear relationship Eq. 2 used to describe density, ρ, of
the chiral ionic liquids [Cn-Im-CH2OMen][Tf2N] as a function of temperature.
−3
−1
−3
Chiral ionic liquid
A/ g·cm
B 104/ g·cm−3·K
SEE 107/ g·cm
[Cn-Im-CH2OMen][Tf2N]
[C1-Im-CH2OMen][Tf2N]
[C2-Im-CH2OMen][Tf2N]
[C3-Im-CH2OMen][Tf2N]
[C4-Im-CH2OMen][Tf2N]
[C5-Im-CH2OMen][Tf2N]
[C6-Im-CH2OMen][Tf2N]
[C7-Im-CH2OMen][Tf2N]
[C8-Im-CH2OMen][Tf2N]
[C9-Im-CH2OMen][Tf2N]
1.5998
1.5746
1.5510
1.5296
1.5111
1.4871
1.4731
1.4622
1.4480
–8.9592
–8.8238
–8.7013
–8.5662
–8.4850
–8.3716
–8.2991
–8.2233
–8.1521
–8.1174
–8.0493
–7.9754
1.5
1.8
1.1
0.9
0.7
0.6
0.7
0.5
0.5
0.5
0.5
0.3
[C10-Im-CH2OMen][Tf2N] 1.4363
[C11-Im-CH2OMen][Tf2N] 1.4227
[C12-Im-CH2OMen][Tf2N] 1.4108
445
Data listed in Table 6 and shown in Figure 2 then illustrate the influence of the
alkyl chain length on the cation on the density and molar volume of the studied ionic
liquids at 298.15 K. Not surprisingly, the molar volume shows an increasing function
of the alkyl chain length, the density decreasing correspondingly. Indeed, due to steric
hindrance, the longer alkyl side chain was found to contribute to a poorer packing, a
450 trend described not only for imidazolium-based ionic liquids by e.g. Rocha et al. [7, 8],
but also in one of our previous work addressing a series of alkyl-triethylammonium-
based ionic liquids [9].
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Table 6: Experimental density, ρ, and molar volume, V m , for the studied chiral ionic liquids
[Cn-Im-CH2OMen][Tf2N] at 298.15 K.
−3
−1
Chiral ionic liquid
ρ/ g·cm
Vm / cm3·mol
[Cn-Im-CH2OMen][Tf2N]
[C1-Im-CH2OMen][Tf2N]
[C2-Im-CH2OMen][Tf2N]
[C3-Im-CH2OMen][Tf2N]
[C4-Im-CH2OMen][Tf2N]
[C5-Im-CH2OMen][Tf2N]
[C6-Im-CH2OMen][Tf2N]
[C7-Im-CH2OMen][Tf2N]
[C8-Im-CH2OMen][Tf2N]
[C9-Im-CH2OMen][Tf2N]
1.33263
1.31157
1.29152
1.27421
1.25813
1.23746
1.22565
1.21701
1.20491
398.86
415.96
433.28
450.17
467.07
486.20
502.34
517.43
534.27
550.76
568.00
584.65
[C10-Im-CH2OMen][Tf2N] 1.19429
[C11-Im-CH2OMen][Tf2N] 1.18275
[C12-Im-CH2OMen][Tf2N] 1.17306
−3
U(ρ)=0.00015 g·cm
, U(T)=0.01 K, U(p)=0.02MPa
The dependence of the density on the alkyl chain length was correlated with a
455 cubic function that was found to optimally describe the data:
ρ = A + Bn(C) + Cn2(C) + Dn3(C)
(5)
Using the gnostic marginal analysis, residua of both a quadratic and cubic equa-
tion fit were analyzed showing that in the former, the regression residua were non-
homogeneous whereas for the latter they were found homogeneous. The parameters
of the cubic equation fit are given in Table 7.
Table 7: Coefficients A, B , C, and D of the cubic relationship Eq. 5 used to describe density,
ρ, at 298.15 K of the chiral ionic liquids [Cn-Im-CH2OMen][Tf2N] as a function of the number
of carbons in the alkyl side chain on the cation.
−3
−3
−3
−3
−3
A/ g·cm
B/ g·cm
C/ g·cm
D/ g·cm
SEE 105/g·cm
1.356
-0.02448
0.00112
-0.00003
4.9
460
Similarly to density, speed of sound of the studied ionic liquids is a decreasing
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function of temperature. In this work the dependence was found to be non-linear.
Marczak [52] and Bilanyuk and Wong [53] proposed a simple fifth-order polynomial
to model the temperature-dependence of the speed of sound in pure water. In this
work, using a robust linear regression algorithm along a gnostic influence function (see
465 section 2.4.) to the fourth-order polynomial was found to fit the data more precisely,
with a lower SEE than a fit with a fifth-order polynomial. Table 8 lists the optimized
parameters of Eq. 6 for the studied [Cn-Im-CH2OMen][Tf2N] chiral ionic liquids
u = A + BT + CT2 + DT3 + ET4
(6)
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Figure 3 represents the speed of sound as a function of the alkyl chain length on
the cation at 298.15 K. Similarly to the refractive index data, it appears that there is
470 no straightforward trend in this dependence, the first six members of the homologous
series not corresponding to the increasing trend of the remaining ionic liquids with
alkyl chain substituents longer than C3. Methyl- through pentyl-substituted ionic
liquids show an alternation in the values of the speed of sound with odd-numbered
members of the homologous series showing higher values than the even-numbered ones.
475 This trend was not observed in the measured density. It may, however, be said that a
similar alternation is given for alkanes for their melting points in almost every organic
chemistry textbook. Boese et al. [49] have shown this alternation in melting points and
density of alkanes who used X-ray crystallography to explain this phenomenon by the
different crystallization patterns. Considering ionic liquids as molten salts that unlike
480 molecular liquids do not have a completely random structure in the liquids phase, the
difference in the odd-even alkyl chain packing could be a plausible explanation of the
trend found in this work for the speed of sound of the studied ionic liquids
Figure 3: Speed of sound, u, at 298.15 K for the studied chiral ionic liquids [Cn-Im-
CH2OMen][Tf2N] as a function of number of carbon atoms in alkyl chain n (C). Black circles
are experimental data.
The coefficient of isobaric expansivity αP calculated as a function of temperature
using its definition (Eq. 3) and the linear fit of the density dependence on temperature
485 (Eq. 2) is summarized in Table SI-10 and in Figure SI-5. It appears from the calculated
values that it increases only insignificantly with temperature, in the range of 6.7 10-4 to
6.9 10- 4 K-1 for the studied temperature range. Figure 4 then shows that the coefficient
of isobaric expansivity shows a rather irregular increase with the increasing alkyl chain
length on the cation. Interestingly, such an irregular trend was also found by Rocha
490 et al. [8] for αP as well as for the standard molar Gibbs energy, and enthalpy and
entropy of vaporization in series of asymmetric 1-alkyl-3-methylimidazolium bistriflate
and symmetric 1,3-dialkylimidazolium bistriflate ionic liquids.
Figure 4: The coefficient of the isobaric expansivity αP for the chiral ionic liquids [Cn-Im-
CH2OMen][Tf2N] at 298.15 K as a function of the number of carbons in the alkyl substituent,
n(C).
28

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Using the speed of sound data, the isentropic compressibility was also calculated
and is given in Table SI-12 and Figure SI-6 of the ESI
#
$
κS = 1/ ρu2
(7)
495 4.2.3. Isobaric molar heat capacity
The experimental isobaric molar heat capacity Cp,m as a function of temperature
is summarized for all the studied ionic liquids in Table SI-13 and represented in Figure
SI-7 of the ESI. The heat capacity is an increasing function of temperature, usually best
fitted with a function of a polynomial character [54]. In this work the robust linear
500 regression along the gnostic influence function was used to find that the following
function gives the best fit
Cp,m = A + BT + CT2 + DT3
(8)
Table 9 then lists the coefficients of Eq. 8 for the studied [Cn-Im-CH2OMen][Tf2N]
chiral ionic liquids.
29