Optical constants of ethylene glycol over an extremely
wide spectral range
Elisa Sania,1,, Aldo Dell’Orob
a
b
INO-CNR, Istituto Nazionale di Ottica, largo E. Fermi, 6, 50125 Firenze (Italy)
INAF Osservatorio Astrofisico di Arcetri, largo E. Fermi, 5, 50125 Firenze (Italy)
Abstract
Besides providing insights into the fundamental properties of materials, the
knowledge of optical constants is required for a large variety of applications.
In this work, for the first time to the best of our knowledge, an extremely
wide spectral range from 181 to ∼54000 cm−1 has been explored for ethylene
glycol in the liquid phase, and optical constants in the whole range have been
given. The approach we propose can also be applied to different fluids.
Keywords: Optical constants, Optical properties, Solar energy, Liquid
phase, Ethylene glycol
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
1. Introduction
The knowledge of the complex refractive index of materials is required
in many fields and both for fundamental and applied research. The present
work reports on the determination of optical constants (i.e. the real n and
the imaginary part k of the complex refractive index) of ethylene glycol in the
liquid phase. Ethylene glycol is a fluid widely used in many industrial processes such as heating or cooling, chemical processes and thermal solar energy
systems [1]. It is the main non-aqueous base fluid used for the preparation of
so-called nanofluids [1]-[12], as well as in mixed aqueous-non aqueous systems
[13]-[15] for different thermal applications. Recently, it has been proposed as
1
Corresponding author, email: [email protected]
Preprint submitted to Optical Materials
February 19, 2015
2 EXPERIMENTAL SETUP
base fluid for novel direct solar absorbers [16] [17]. However, for a realistic
assessment of the system performances when a direct interaction with light is
required, both fundamental optical constants, including n, have to be characterized. The transmission spectrum and the k optical constant of liquid
ethylene glycol have been reported in the literature for the spectral range
0.2-1.5 µm [18]. Some discrete infrared absorption peaks for glycol molecules
isolated in Ar or Xe matrices have been listed in [19] and for the liquid phase
in [20]. Infrared transmittance spectra in limited spectral ranges have been
reported in [21] (300-1500 cm−1 ) and in [22] (∼450-3794 cm−1 ) but without
giving any optical constant. n has been measured by several Authors at the
single wavelength of the sodium D line (0.5893 µm) [23]-[30] or at few discrete wavelengths in the range 0.22-0.58 µm ([31]). In this work, the optical
constant k is obtained in an extremely wide wavelength range, from 0.185 µm
to about 55 µm (∼ 54000-181 cm−1 ) from transmittance measurements. The
experimental k spectrum is then used to calculate n in the whole investigated
range by means of a Kramers-Kronig transform.
2. Experimental setup
The optical transmittance spectra of ethylene glycol (Aldrich ≥99%) have
been measured over the considered spectral range by means of three different
experimental setups: a ”Lambda 900” Perkin-Elmer dispersive spectrophotometer for the range ∼54054-∼3333 cm−1 (0.185-3 µm), a Fourier transform ”Excalibur” Bio-Rad spectrometer with KBr optics for the wavenumber
range 5500-400 cm−1 (∼ 1.8-∼25 µm) and finally a Fourier transform ”Scimitar” Bio-Rad spectrometer with polyethylene windows and mylar beam splitter for the range 420-181 cm−1 (∼24-∼55 µm). Except when differently specified, the transmittance has been measured at different sample thicknesses
using a demountable variable-path cell composed by two optical windows and
by a series of calibrated spacers. When the sample transmittance was too
low to have a detectable signal at the output, we assembled the cell without
spacer as described in the following. We choose the cell window materials
on the basis of their spectral transparency: CaF2 for the 0.185-3 µm range,
KBr for ∼1.8-25 µm (available spacers from 50 to 350 µm) and polyethylene
for ∼24-55 µm (available spacers from 15 to 350 µm). Moreover, for the visible range, where the ethylene glycol transmittance was very high, we used
also quartz cuvettes with 5 and 10 mm path length to reduce the relative
uncertainty on k, as discussed in the following.
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
3 TRANSMITTANCE
3. Transmittance
The spectral transmittance of the liquid τ (ν), with ν wavenumber, can
be expressed as a simple function of the spectral absorption coefficient α(ν)
as
τ (ν) = exp(−α(ν) · x)
(1)
where x is the liquid thickness. However, the transmittance T we measure
is the total transmittance of the layered system window-liquid-window, immersed in air. At each interface (air-window, window-liquid) the light is
partially reflected and partially transmitted. Let’s we consider, for simplicity, that the window has no absorption in the considered spectral range.
Under the hypotheses of absence of scattering and negligible coherent effects
[32], the total transmittance T can be expressed as a function of τ and of
reflectances R1 and R2 at the interfaces as follows [33]:
[
]
2R1 R2
2
2
2 2
4
T = (1 − R1 ) (1 − R2 ) τ 1 +
+ (R1 + R2 ) τ + S(τ )
(2)
1 − R1 R2
in this expression, S(τ 4 ) is the sum of contributions with powers of τ higher
than four. The terms with powers of τ are generated by multiple passes
through the liquid due to multiple reflections. If they are negligible compared
to other terms, the total transmittance T is proportional to the transmittance
τ of the liquid sample. The reflectances R1 (at the air-window interface) and
R2 (at the window-liquid interface) are given by [34]:
(nw − 1)2
(nw + 1)2
(3)
(nw − n)2 + k 2
(nw + n)2 + k 2
(4)
R1 =
R2 =
with nw real part of the refractive index of the window and n, k optical
constants of the liquid. The optical constant k(ν) is connected to α by [32]:
k=
α(ν)
4πν
(5)
Eqs. 3 and 4 assume, for the medium surrounding the cell, optical constants
nm = 1 and km = 0.
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
3 TRANSMITTANCE
If we acquire two transmittance spectra T1 and T2 at two different thicknesses x1 and x2 of the liquid, α can be directly obtained from the expression:
α(ν) = −
1
T2 (ν)
1
T2 (ν)
=−
ln
ln
x2 − x1 T1 (ν)
∆x T1 (ν)
(6)
without requirement of a prior knowledge of optical properties of the window
and with no need of a fitting procedure for n, k, as it would be required using
a single transmittance measurement and Eqs. 2-5.
The possibility to obtain α from two independent trasmittance measurements relies on the experimental error on a single trasmittance and how much
the considered trasmittance values differ each other. The smaller is α, the
more T1 and T2 must be different, i.e. the larger the difference of thicknesses
|x2 − x1 | = |∆x| should be. A simple analysis of the error propagation shows
that, in the hypothesis here fulfilled that the error on the thicknesses is negligible respect to |∆x|, the obtained
√ value of α is at least twice as large as its
error, if α itself is larger than 2 2ϵ/|∆x|, where ϵ is the relative uncertainty
of transmittance. This condition is fulfilled simply when
√
|T1 − T2 |
> 2 2ϵ
T2
(7)
In the determination of α we checked this condition and, in the spectral
regions where it was not satisfied, we took as upper limit for α its standard
error.
In the range 0.185-3.00 µm we acquired the transmittance spectra at several cell thicknesses from 50 to 350 µm, and we kept as α to be used in further
calculations the value obtained by averaging the result of Eq. 6 for several
(x1 , x2 ) couples. Moreover, as in the spectral range from about 0.3 µm to
1.1 µm wavelength the trasmittance was very high and near to 100% also
with the largest available spacer, to reduce as much as possible the spectral
interval of uncertainty of α discussed above, additional transmittance measurements were carried out, with a different cell model allowing much longer
path lengths of 5 and 10 mm. The spectral resolution is 5 × 10−3 µm in the
range 0.185-0.860 µm and varies from 7 × 10−3 to 2 × 10−2 µm at longer
wavelengths. The relative uncertainty ϵ of transmittance values is 0.5%.
For the Mid-Infrared range (5500-400 cm−1 wavenumbers, ∼1.8-∼25 µm
wavelength), the transmittance fell to zero in a large part of the spectrum
even with the thinnest spacer available for KBr windows (50 µm). Thus, we
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
3 TRANSMITTANCE
used the demountable cell without spacer. This allowed to measure the transmittance for a very thin layer of liquid. Similarly to the method described
in [33], we took several measurements at different tightening levels of the
cell nuts (i.e. at different sample thicknesses). The spectral resolution is 4
cm−1 . The relative uncertainty on transmittance is between 0.05% and 0.3%
depending on the spectral region. For the determination of α, Eq. 6 requires
only the knowledge of the thickness difference ∆x among two measurements,
which was inferred as follows: for each considered couple of Mid-IR measurements, ∆x was chosen to match, in the regions of spectral superposition of
the Mid-IR and UV-Vis-NIR instruments, the value of α determined by the
UV-Vis-NIR measurements.
In the Far Infrared (FIR) (420-181 cm−1 , ∼24-∼55 µm) we used a slightly
different cell model, able to mount polyethylene windows and equipped with
thinner spacers than the previous one. Transmittance measurements were
taken at different thicknesses, analogously to the UV-Vis-NIR case, and α
was analogously calculated. The minimum available thickness was 15 µm.
In the infrared, the spectra we acquired (Figure 1) are in good agreement
with published transmittance data ([22], available from ∼450 to 3794 cm−1
and [21] from 400 to 1500 cm−1 ). In the region 300-400 cm−1 our results show
a better agreement with [20], which lists a weak transmittance minimum at
360 cm−1 , rather than [21], observing instead two weak minima at 430 and
330 cm−1 .
Once α(ν) was obtained as described for the whole investigated range, we
calculated the optical constant k(ν) from Eq. 5. The experimental values of k
versus the wavenumbers, for the whole investigated range, are plotted in red
color in Figure 2. The obtained k values in the range ∼6670-∼45000 cm−1
(1.40-0.22 µm) well agree with the data in [18], while some discrepancies can
be found around 50000 cm−1 . Table 1 lists at the third column the values of
k at some discrete wavelengths.
Table 1: Optical constants at some discrete wavenumbers. Bold fonts mark relative maxima and minima in
the n and k spectra. Maxima are identified by ∩ and
minima by ∪.
Wavenumber
cm−1
n
k
Wavelength
µm
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
3 TRANSMITTANCE
182.0±0.5
342.0±0.5
418±2
501±2
519±2
545±2
599±2
741±2
832±2
854±2
865±2
872±2
883±2
897±2
952±2
1025±2
1043±2
1054±2
1065±2
1076±2
1086±2
1097±2
1137±2
1192±2
1203±2
1232±2
1254±2
1283±2
1308±2
1330±2
1352±2
1370±2
1381±2
1406±2
1446±2
1457±2
1475±2
1.47± 0.01 ∪
1.48± 0.01
1.48±0.01 ∩
1.46±0.01
1.45±0.01
1.44±0.01
1.42±0.01 ∪
1.45±0.01
1.48±0.01 ∩
1.45±0.01
1.45±0.01
1.41±0.01
1.38±0.01
1.44±0.01
1.54±0.01
1.44±0.02
1.38±0.02 ∪
1.40±0.01
1.44±0.02 ∩
1.36±0.02
1.28±0.02 ∪
1.378±0.004
1.407±0.004 ∩
1.404±0.004
1.404±0.004
1.407±0.004
1.411±0.004
1.417±0.004 ∩
1.413±0.005
1.412±0.005
1.411±0.005
1.410±0.005
1.405±0.005
1.398±0.005
1.395±0.005
1.385±0.004 ∪
0.09± 0.02
0.053±0.007
0.042±0.005 ∪
0.07±0.01
0.09±0.01 ∩
0.07±0.01
0.073±0.006 ∩
0.041±0.006
0.018±0.003 ∪
0.048±0.007
0.08±0.01 ∩
0.07±0.01 ∪
0.11±0.02 ∩
0.038±0.006
0.011±0.002 ∪
0.08±0.01
0.18±0.03 ∩
0.13±0.02
0.09±0.01 ∪
0.12±0.02
0.18±0.03 ∩
0.09±0.01
0.010±0.002 ∪
0.022±0.003
0.026±0.004 ∩
0.018±0.003 ∪
0.021±0.003 ∩
0.017±0.003 ∪
0.023±0.004
0.028±0.004 ∩
0.026±0.004 ∪
0.031±0.005 ∩
0.030±0.005 ∪
0.034±0.005 ∩
0.028±0.004 ∪
0.031±0.005 ∩
0.019±0.003
∼55
∼29
∼24
∼20
∼19
∼18
∼17
∼13
∼12
∼11.7
∼11.6
∼11.5
∼11.3
∼11.1
∼10.5
∼9.7
∼9.6
∼9.5
∼9.4
∼9.3
∼9.2
∼9.1
∼8.8
∼8.4
∼8.3
∼8.1
∼7.9
∼7.8
∼7.6
∼7.5
∼7.4
∼7.3
∼7.2
∼7.1
∼6.9
∼6.8
∼6.7
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
4 REFRACTIVE INDEX
1595±2
1653±2
2271±2
2859±2
2878±2
2903±2
2943±2
2968±2
3008±2
3212±2
3364±2
3477±2
3854±2
4007±2
4371±2
5000±2
5378±4
5705±5
6035±5
6361±4
6689±4
7016±4
14000±50
21000±50
26000±170
30000±230
34000±290
38000±360
42000±440
46000±530
50000±630
54000±730
1.407±0.002
1.409±0.003
1.425±0.002
1.448±0.004 ∩
1.441±0.005
1.438±0.004
1.429±0.005
1.418±0.004 ∩
1.431±0.002
1.457±0.007 ∩
1.41±0.01
1.366±0.007 ∪
1.404±0.002
1.408±0.002
1.412±0.002
1.416±0.002
1.417±0.002
1.418±0.002
1.419±0.002
1.420±0.002
1.420±0.002
1.420±0.002
1.428±0.002
1.438±0.002
1.447±0.002
1.457±0.002
1.468±0.002
1.482±0.002
1.498±0.002
1.517±0.002
1.540±0.002
1.567±0.002
(3.5±0.6)·10−3 ∪
0.005±0.002 ∩
(1.5±0.3)·10−3
0.021±0.003
0.028±0.004 ∩
0.021±0.003 ∪
0.032±0.005 ∩
0.018±0.003
0.008±0.001 ∪
0.041±0.006
0.08±0.01 ∩
0.040±0.006
(5.7±0.2)·10−4 ∪
(12.4±0.4)·10−4 ∩
(8.3±0.3)·10−4 ∩
(1.57±0.08)·10−4
(6.3±0.5)·10−5 ∪
(1.12±0.06)·10−4
(9.0±0.5)·10−5
(1.50±0.06)·10−4 ∩
(1.26±0.04)·10−4 ∩
(7.0±0.3)·10−5
<6.4·10−8
<4.3·10−8
<3.5·10−8
<1.4·10−7
<6.4·10−7
(9±4)·10−7
(1.5±0.4)·10−6
(3.4±0.4)·10−6
(9.4±0.3)·10−5
(4.9±0.1) · 10−4 ∩
∼6.3
∼6.0
∼4.4
∼3.5
∼3.47
∼3.44
∼3.4
∼3.37
∼3.32
∼3.11
∼2.97
∼2.87
∼2.59
∼2.49
∼2.29
∼2.00
∼1.86
∼1.75
∼1.66
∼1.57
∼1.49
∼1.42
∼0.71
∼0.48
∼0.38
∼0.33
∼0.29
∼0.26
∼0.24
∼0.22
∼0.20
∼0.19
4. Refractive index
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
4 REFRACTIVE INDEX
100
80
60
60
40
40
20
20
% Transmittance
% Transmittance
80
0
0
0.2
0.4
0.6
0.8
1.0
Wavenumber (10
3
1.2
1.4
-1
cm )
Figure 1: Acquired transmittance spectra in the range 181-1500 cm−1 . The spectra respectively shown as red circles and black line have been acquired at two different sample
thicknesses. For a better visual comparison with literature data, they are reported in the
picture with shifted ordinates and intentionally left with a small vertical gap.
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
4 REFRACTIVE INDEX
0.25
1.60
1.55
0.20
1.50
n
0.15
1.45
n
k
1.40
1.35
0.10
1.30
k
0.05
1.25
1.20
0.00
0.5
1.0
1.5
Wavenumber (10
3
2.0
-1
cm )
0.25
1.60
1.55
0.20
1.50
n
0.15
1.45
n
k
1.40
1.35
0.10
1.30
k
0.05
1.25
1.20
0.00
2.0
2.5
3.0
3.5
4.0
Wavenumber (10
3
4.5
5.0
-1
cm )
0.6
1.60
n
1.55
0.5
1.50
0.4
k x 10
-3
1.45
1.40
n
0.3
1.35
0.2
k
1.30
0.1
1.25
1.20
0.0
5
10
15
20
25
30
35
Wavenumber (10
3
40
45
50
-1
cm )
Figure 2: The optical constants n and k in the whole investigated range. The only
spectral data available in the literature for optical constants [18] [31] are also plotted for
comparison, showing a fair agreement (blue circles in the lower picture). The infrared k
bands are due to molecular vibration modes [20], [21].
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
4 REFRACTIVE INDEX
On the basis of the experimental value of k(ν) we calculated the corresponding values of the refractive index n(ν). Being n(ν) and k(ν) respectively the real and complex part of the complex refractive index m(ν) =
n(ν) + ik(ν), they are related each other through the Kramers-Kronig relationship:
∫ ∞ ′
2
ν k(ν ′ ) ′
n(ν) = n(∞) + P
dν
(8)
π
ν ′2 − ν 2
0
where P identifies the Cauchy’s principal part of the integral and n(∞) is
the value of the refractive index at high wavenumbers. In the usual practice,
the constant value n(∞) is not known. Generally it is indirectly obtained
imposing, for a given wavenumber, that n is equal to a value already known.
The integral in Eq. 8 has been numerically computed using the Maclaurin’s
formula [36]. The uncertainty on n(ν) has been calculated propagating the
experimental uncertainty on k(ν).
The major technical limitation of the method based on the KramersKronig relationship is that the integral in Eq. 8 should be calculated from
zero to infinity, or in other words the value of n at a given wavenumber could
be computed only if k is know for all wavenumbers. Different approaches
have been discussed in the literature to overcome this issue [37]-[39]. Although this requirement is not experimentally possible, nevertheless it does
not means that n(ν) cannot be computed with a satisfactory accuracy if k
is know in an enough wide interval of wavenumbers around ν. Problems can
occur at the edges of the spectral interval for which a measure of k has been
possible. In our case, the value of n(ν) for ν slightly larger than 181 cm−1 or
a little less than 54000 cm−1 , computed by means of Eq. 8, could be affected
by truncation errors depending on the values of k respectively below 181
cm−1 and above 54000 cm−1 . For the present work, as it has been motivated
by solar energy applications of ethylene glycol, the spectral range of main
interest for us is that of sunlight (0.3-2.5 µm wavelength, ∼ 34000-∼ 4000
cm−1 ). Towards long wavelengths (low wavenumbers), the range of our measurements is consistently larger than the spectral interval of interest, thus we
could reasonably expect that truncations errors on this side will have a small
or negligible effect on n(ν) in this region[37]. In fact, at a given wavenumber
ν, the error ∆n due to the truncation of the integral in Eq. 8 for ν ′ < νc can
be estimated evaluating the integral from 0 to νc . For νc ≪ ν, it is simple to
show that
2 ννc
(9)
∆n ∼ k 2
π ν
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
4 REFRACTIVE INDEX
where k and ν are respectively the mean values of k and ν over the interval
[0, νc ]. Being νc = 181 cm−1 , a conservative case is that ν ∼ 90 cm−1 and
k ∼ 10−1 , it turns out that ∆n ∼ 0.03 for ν = 200 cm−1 , ∼ 0.004 at 500
cm−1 and ∼ 0.001 at 1000 cm−1 . For ν = 200 cm−1 the condition νc ≪ ν
used in Eq. 8 to approximate the denominator to ν 2 is not fulfilled, so in this
case the evaluation of ∆n is probably underestimated. Therefore we expect
that, for ν larger than 300/400 cm−1 , ∆n is comparable or smaller than the
uncertainty of n due to the measurement errors. At short wavelengths (high
wavenumbers) we have a clear effect of truncation because the computed values of n in the range 20000-45000 cm−1 result to be independent on ν while
from literature we know that in the same range n increases with wavenumber [31]. This clearly suggests the presence of a big spectral feature above
54000 cm−1 . The behavior of n is compatible with the increasing phase of
the refractive index before a region of anomalous dispersion, corresponding
to a peak of k. We explored the space of lorentzian peak solutions by fitting
the literature value of n in the range 20000-45000 cm−1 . The best solution
consists of a peak (A) around ∼ 100000 cm−1 , and all compatible solutions
reproduce the values of n within an error of 2 × 10−3 , while providing negligible values of k in the same range. The increasing of the experimental k curve
from ∼ 40000 cm−1 cannot be explained by the peak A, but it is reproduced
by a much weaker peak (B) at ∼ 55000 cm−1 , that in turn gives a negligible
contribution to the values of n in the range 20000-45000 cm−1 . Thus, peaks
A and B together are able to reproduce in a satisfactory way both n and k
in the range 20000-54000 cm−1 . Such extrapolation of the k spectrum has
been used as input of Kramers-Kronig transform correcting the truncation
error at high wavenumbers, reproducing the correct behavior of n and allowing the correct determination of the zero point n(∞). More precisely, it was
obtained imposing n = 1.432 at ν = 17241.4 cm−1 , as reported in [31], and
considering the uncertainty on its value produced by the uncertainty on the
k extension (i.e. ∆n = 2 · 10−3 ).
Figure 2 shows the values of n as a function of the wavenumber (black
line). The n values at some discrete wavelengths are listed in Table 1 (second
column).
For operating purposes, e.g. the use of n in optical design and ray tracing software packages, it can be useful to give the obtained n in terms of a
phenomenological expression. Thus we fitted n as a function of the wavelength λ with a four-parameter Sellemeier equation [40], using a least-squares
Paper published on: Optical Materials Volume 37, November 2014,
Pages 36-41; DOI: 10.1016/j.optmat.2014.04.035
REFERENCES
algorithm:
1.01887 · λ2
0.01778 · λ2
+
(10)
λ2 − 9.02
λ2 − 0.01028
This equation is valid for λ expressed in µm and lying in the range 0.185-2.8
µm.
It should be noticed that Sellmeier-type expressions are intrinsically limited to spectral regions with no absorption. In fact, in the vicinity of absorption peaks (corresponding to the zeros of denominators), Sellmeier equations
give the unphysical result of diverging n values. If we relax the physical meaning of the equation used for fitting n(λ) and we accept to obtain a purely
phenomenological expression useful for analytically writing n in limited spectral ranges, it is possible to find, for instance, the following expression, valid
for λ ∈ (3.4, 6.8) µm and reproducing n within its uncertainty:
n2 = 1 +
n2 = 1 +
0.6 · λ2
12.55 · λ2
60.1 · λ2
+
−
λ2 − 4.05 λ2 + 153.3 λ2 + 1008.2
(11)
5. Conclusions
In conclusion, we have obtained the optical constant k(ν) of ethylene
glycol from transmittance measurements over a range as wide as from 181
to ∼54000 cm−1 . The Kramers-Kronig theory, in combination with an adhoc technique of extrapolation to avoid truncation errors at the edges of the
experimental spectrum, has been used to calculate the real part n(ν) of the
refractive index. Limitations and tricks of this approach are discussed. The
Sellmeier equation for n in the wavelength range 0.185-2.8 µm is given, as
well as a purely phenomenological polynomial expression for fitting n in the
range 3.4-6.8 µm.
Acknowledgements
Authors are grateful to S. Barison and C. Pagura (CNR-IENI, Italy) for
kindly supplying ethylene glycol.
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