Theoretical and experimental comparative study of nonlinear properties of imidazolium cation based ionic liquids

Article abstract of DOI:10.1016/j.molliq.2021.115391

This work describes the experimental and theoretical investigation of the nonlinear optical properties of the imidazolium cation based ionic liquids and the corresponding thermo-optical parameters. The experimental results of nonlinear optical properties, such as nonlinear refractive index and thermo-optical properties are determined by Z-scan and EZ-scan techniques with a femtosecond laser source. Theoretical simulations of linear and nonlinear optical properties performed by density functional theory (DFT) are discussed in terms of polarizabilities and hyperpolarizabilities. A correlation between the theoretical and experimental results is presented, where the variation of the experimental signals of each ionic liquid can be compared with their calculated nonlinear optical properties.

Full text of DOI:10.1016/j.molliq.2021.115391

Journal of Molecular Liquids 328 (2021) 115391
Contents lists available at ScienceDirect
Journal of Molecular Liquids
journal homepage: www.elsevier.com/locate/molliq
Theoretical and experimental comparative study of nonlinear properties
of imidazolium cation based ionic liquids
a,
b
b
c
Vinícius Castro Ferreira ⁎, Letícia Zanchet , Wesley Formentin Monteiro , Letícia Guerreiro da Trindade ,
b
a,
Michèle Oberson de Souza , Ricardo Rego Bordalo Correia ⁎
OPTMA - Optics, Photonics and Materials Group, Institute of Physics, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
LRC - Laboratorio de Reatividade e Catalise, Institute of Chemistry, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
Department of Chemistry, Universidade Estadual Paulista, Bauru, São Paulo, Brazil
a
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 10 August 2020
Received in revised form 21 December 2020
Accepted 12 January 2021
Available online 23 January 2021
This work describes the experimental and theoretical investigation of the nonlinear optical properties of the
imidazolium cation based ionic liquids and the corresponding thermo-optical parameters. The experimental re-
sults of nonlinear optical properties, such as nonlinear refractive index and thermo-optical properties are deter-
mined by Z-scan and EZ-scan techniques with a femtosecond laser source. Theoretical simulations of linear and
nonlinear optical properties performed by density functional theory (DFT) are discussed in terms of polarizabil-
ities and hyperpolarizabilities. A correlation between the theoretical and experimental results is presented,
where the variation of the experimental signals of each ionic liquid can be compared with their calculated non-
linear optical properties.
Keywords:
Ionic liquid
Nonlinear refractive index
Z-scan
© 2021 Elsevier B.V. All rights reserved.
EZ-scan
Thermo-optical properties
1. Introduction
[16]. ILs can be part of new technologies that enable to solve current
problems faced by society, emerging as effective alternatives.
Ionic liquids (ILs), also named organic molten salts, are composed
Among the numerous ionic liquids properties that can be studied,
optical characterizations are undoubtedly valuable because of the struc-
tural and electronic information provided. In the linear optical domain,
the optical properties of materials are independent of the light intensity.
In contrast, the light field can modify several optical properties in the
nonlinear optical regime. The understandings of nonlinear optical
(NLO) phenomena are essential to the development of new materials
and technology applications, ranging from conversion of wavelength
frequencies and optical switches [17] up to ultra-fast laser sources
[18] and health sciences [19].
The optical properties of ILs have been widely studied since early
2000. A substance with NLO activity must be polarizable and/or have
an asymmetric charge distribution and contain a π-conjugated electron
moiety, so ILs were recognized as good candidates to be studied in NLO
[20]. The ILs present a strong dependence on the properties and nature
of the cation and anion. Thus the anionic and cationic moieties' choice
may generate materials with optimized properties [21]. Several non-
linear characteristics were studied in these materials, such as fast
molecular dynamic processes [22–24]. The study of NLO properties in
ILs is crucial since this response is fundamental in applications in
supercapacitors, optoelectronics on a large scale, and laser ablation pro-
cess [25,26]. Few studies report data about ILs nonlinear index of refrac-
tion, property covered in this work. The variation in refractive index
of ions, a large organic cation, and an anion having a delocalized
charge. The cation's asymmetry and flexibility lead to weak ion inter-
actions which result in compounds with a low tendency to crystallize
[
1,2]. Since their rediscovery, the ILs have been applied in several
branches of chemistry due to a unique combination of physicochemi-
cal properties, highlighting a wide electrochemical window, negligible
vapor pressure, high electrical conductivity, high ionic mobility, high
thermal stability, low flammability and low toxicity [2]. This set of
properties, coupled with the possibility of designing ILs by choosing
the ions, enables the use of ILs in pharmaceutical and environmental
applications [3,4].
The impact of ILs has become important due to their tunable physi-
cochemical properties and electronic characteristics [5]. In recent years,
ionic liquids have had their main characteristics explored, generating
promising science and technologies for academic and industrial applica-
tions in areas such as catalysis [6–8], materials science [9,10], physical
chemistry [11], electrochemistry [12], polymer science [13,14], biology
[
15], among others, which gives them a multidisciplinary character
⁎
Corresponding author.
E-mail addresses: castroferreiravinicius@gmail.com (V.C. Ferreira), rego@if.ufrgs.br
R.R.B. Correia).
(
https://doi.org/10.1016/j.molliq.2021.115391
167-7322/© 2021 Elsevier B.V. All rights reserved.
0

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
generated by thermal effects was evaluated by self-induced thermal ef-
fects for different aromatic and alicyclic ILs [27,28]. Most of these values
agree with standard interferometric measurements of ILs, as observed
for eleven 1-alkyl-3-methylimidazolium-based ionic liquids, registering
negative values of the thermo-optical coefficient, dn/dT, in the order of
The synthesized ILs were characterized by Fourier-transform infra-
red spectroscopy (FTIR) using Attenuated Total Reflectance Fourier
Transform Infrared Spectroscopy (ATR-FTIR) with a Bruker Alpha-P in
the spectral range 4000–500 cm , and ultraviolet-visible spectropho-
tometry performed in a Cary 5000 UV–Vis-NIR equipment from Agilent
using a 2.0 mm quartz cuvette.
−1
−
4
−3
−1
10
0
–10
K
. Nonlinear indexes of refraction in the order of
−
16
2
−1
1
cm W were measured in femtosecond laser systems for colloi-
4
dal solution of silver nanoparticles dispersed in BMI.BF IL [29] and mix-
2
.3. Theoretical calculations
tures of azobenzene containing IL crystalline polymer [20], the latter
displaying subpicosecond responses. However, to our knowledge, the
literature does not describe thermal and electronic effects related to
the nonlinear index of refraction of pure ILs exposed to a femtosecond
laser source and discusses experimental data associating them to theo-
retical studies.
In order to study these effects, this paper aimed to evaluate the non-
linear optical behavior of four specific ILs, combining theoretical and ex-
perimental approach to prospect the prediction of its optical properties.
The four ILs characterized and discussed here are the methylimidazole
Density functional theory (DFT) study was performed to understand
the molecular behavior and structural conformation of the ionic liquids.
DFT calculations were achieved using the Becke‘s three-parameter ex-
change functional in combination with the Lee, Yang and Parr correla-
tion functional (B3LYP) [33,34] with a 6–311++G(d,p) basis set as
implemented in the GAUSSIAN 16 package. Structures were fully opti-
mized, under no symmetry constraints, and vibrational frequency calcu-
lations were performed. Final structures have no imaginary frequencies
associated with them. The frontier orbital energies were calculated in a
single point run in the same theory level. Molecular electrostatic poten-
tial maps (MEPs) of total electronic densities using the partial charges
were analyzed with Gabedit software [35]. For each ILs, a DFT study
was performed for determining the polarizability (α), the first-order
hyperpolarizability (β), and the second-order hyperpolarizability (γ),
varying the frequencies relations.
hydrogen sulfate (MImH.HSO
BImH.HSO ), 1-butyl-3-methylimidazolium hydrogen sulfate (BMI.
HSO ), and 1-butyl-3-methylimidazolium trifluoromethane sulfonate
BMI.CF SO ). The length and nature of the cation's alkyl chain, as well
4
), butylimidazole hydrogen sulfate
(
4
4
(
3
3
as the nature of the anion, were modified to verify their influence on
the optical properties. Fast and slow response, related to the electronic
and thermal effects, respectively, were characterized by Z-scan and
EZ-scan techniques for these ILs. Theoretical simulation of the Fourier-
transform infrared spectroscopy (FTIR) analysis of the ILs was also per-
formed and corroborated with the experimental results.
2.4. Nonlinear optical and thermo-optical properties measurements
The optical and thermo-optical properties of the ILs were evaluated
by Z-scan and EZ-scan techniques for the determination of the thermo-
optical coefficient, nonlinear absorption and nonlinear refractive index
(also called intensity-dependent refractive index). Z-scan is a widely
used technique that characterizes the nonlinear refractive index, non-
linear absorption/saturation, and thermo-optical properties by the var-
iation of wavefront curvature [36]. The eclipse configuration, EZ-scan,
can measure the same properties of the Z-scan technique but with bet-
ter sensitivity and signal-noise ratio [37]. The difference between them
is the spatial filter used to select the portion of the beam to be detected:
Z-scan uses an aperture while EZ-scan uses a disc. In both cases, a laser
source with a high repetition rate produces cumulative effects, which
must be distinguished between fast (electronic) and slow (thermal) ef-
fects [38,39]. A third experimental setup variant without a spatial filter
was also used. In this case, any change transmittance variation will be
due to the nonlinear absorption/saturation in the sample [36]. These
configurations were used to characterize the nonlinear optical proper-
ties of the ILs. The experimental setup was the same, only the change
of the spatial filter (disc or aperture) or no filter according to their
intended measurement. The light source was a chopped laser beam of
a mode-locked Ti: Sapphire laser oscillator (76 MHz, 150 fs, 780 nm) fo-
cused at a beam waist radius of 35 μm, where the sample is scanned in
2
. Experimental
2.1. Materials
The ionic liquids were synthesized using 1-methyl imidazole
99%, (Sigma-Aldrich), 1-chlorobutane 99% (Sigma-Aldrich), ethyl ac-
etate (Sigma-Aldrich) 99.8%, sulfuric acid 98% (Merck), trifluoro-
methanesulfonic acid 99% (Sigma-Aldrich), and 1- butylimidazole
98% (Sigma-Aldrich).
2.2. Synthesis and characterization of the ionic liquids
4
The 1-butyl-3-methylimidazolium hydrogen sulfate (BMI.HSO )
and 1-butyl-3-methylimidazolium trifluoromethane sulfonate (BMI.
CF SO ) ionic liquids were synthesized by ion exchange reaction from
the 1-butyl-3-methylimidazolium chloride (BMI.Cl) IL according to the
procedures reported in the literature [30–32]. H SO was added to a so-
lution of BMI.Cl dissolved in deionized water. The resulting solution was
maintained under reflux for 4 h at 100 °C and then dried under vacuum
at 90 °C. The final compound is a colorless viscous liquid.
3
3
2
4
BMI.CF
3
SO
3
was synthesized, adding dropwise the trifluorome-
SO H) to an aqueous solution of BMI.Cl placed
thanesulfonic acid (CF
3
3
0
the z-direction over a range of few Rayleigh lengths (z ). The detection
in an ice bath. After the complete addition of the acid, the solution
was kept under stirring for 24 h. Dichloromethane was then used
was performed by a fast Si photodiode detector positioned in front of
the spatial filter. A second chopper generates a beam modulation at
9 Hz (duty cycle of 2.4% and beam time exposure of 2.66 ms), providing
the relaxing time needed for the thermal management procedure [40].
At each sample position, the time evolution of the transmitted signal
was recorded with a digital oscilloscope, which allows time-resolved
analyses. The normalized transmittance to the fast response is acquired
at the beginning of the time exposure window, t = 0.
(
5 times 50 mL) to extract the IL from the aqueous phase. The organic
phase was then washed with deionized water (10 times 100 mL) to re-
move any chloride salt and acid. Then the IL was dried under vacuum at
1
20 °C until the complete removal of the residual water and dichloro-
methane, resulting in yellowish IL.
The two protic ILs, the methylimidazole hydrogen sulfate (MImH.
HSO
4
) and butylimidazole hydrogen sulfate (BImH.HSO
4
), were pro-
The EZ-scan configuration was used to characterize the fast response
properties, as in the case of a nonlinear refractive index. A measurement
without spatial filter, open aperture Z-scan, was performed to measure
the nonlinear absorption/saturation of the liquids. The Z-scan configu-
ration was used to evaluate the thermal response, since this method al-
lows the fitting of the Z-scan curve by an analytical model based on the
thermo-optical properties [39].
duced by reacting a 0.2 mol of sulfuric acid with 1-methylimidazole
and 1-butylimidazole respectively at room temperature placed under
stirring in an ice bath for 24 h. The resulting solution was heated
below 90 °C for removing the solvent leading to the production of a
white viscous liquid (MImH.HSO
uid (BImH.HSO , 93% yield) respectively.
4
, 98% yield) and a brown viscous liq-
4
2

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
3. Results and discussion
3.1. Ionic liquids characterizations
Fig. 1a shows the experimental Fourier-transform infrared spectros-
copy (FTIR) of BMI.CF SO , BMI.HSO , MImH.HSO and BImH.HSO , and
3 3 4 4 4
the corresponding theoretical spectra performed for this study (Fig. 2b).
The results show that experimental and theoretical data converge. The
BMI.CF
3 3
SO IL spectrum (Fig. 1a) shows the following vibration bands:
−
1
C–H aromatic at 3173 and 3107 cm ; aliphatic C–H at 2968 and
−
1
−1
−1
2
882 cm ; C–N at 1573 cm ; C=C at 1468 cm ; C–F at
−1
−1
−1
1
249 cm ; O=S=O at 1031 cm and S–O at 1157 cm . The band
−
1
at 853 cm
is due to the C–H in-plane bending vibration of the
−1
imidazolium ring, and the band at 750 cm can be assigned to the C–
H out-of-plane bending vibration of the imidazolium ring [41,42].
The spectrum of BMI.HSO
4
presents vibrations of imidazolium ring
−
1
at 3149 and 3105 cm
bands at 1467 and 1571 cm
corresponding to the C–H bonds, and the
−
1
correspond to the C=C and C=N
bonds. The band at 837 cm is due to C–H in-plane bending vibration
−1
−1
of the imidazolium ring, and the band at 753 cm can be assigned to
the C–H out-of-plane bending vibration of the imidazolium ring. The al-
iphatic C–H asymmetric and symmetric stretching vibrations of the
alkyl chain are represented by the bands at 2962 and 2875 cm
while the peaks at 1024 and 1229 cm are assigned to the S–O and S
Fig. 2. Absorption spectra of the ILs studied. The arrow pointing at λ = 780 nm indicates
the absorption coefficient values of the experimental laser wavelength used in the
experimental optical study.
−
1
,
−1
−1
−
OH stretching vibrations of HSO
the stretching vibration of C–N [43,44].
About the MImH.HSO and BImH.HSO
075 cm are attributed to the stretching vibrations of the imidazole
4
. The band at 1161 cm indicates
used in the study of optical and thermo-optical properties of the ILs
since low UV absorption interference occurs in this region. The deter-
mined absorption coefficient values (a) related to the laser wavelength
4
4
ILs, the bands at 3150 and
−1
3
used experimentally (λ = 780 nm) for MImH.HSO
4
was 0.1 ±
was 0.05 ± 0.01 cm , for BMI.HSO was
0.02 ± 0.01 cm and for BMI.CF SO
was 0.04 ± 0.01 cm−1
−
1
−1
ring C–H bonds. The aliphatic asymmetric and symmetric (C–H)
stretching vibrations of the lateral chain of the imidazole ring appears
0.04 cm , for BImH.HSO
4
4
−1
3
3
.
−
1
−1
at 2960 cm for MImH.HSO
HSO . The bands at 1578 and 1454 cm in both ionic liquids corre-
spond to C=C and C=N stretching vibrations of the imidazole ring, re-
4
and at 2965 and 2930 cm for BImH.
−
1
4
3.2. Theoretical calculations
−1
spectively. The bands at 1222 and 1023 cm are assigned to the S–O
and S—OH stretching vibrations of HSO [43]. The bands at 1162, 840,
Fig. 3 presents the DFT results corresponding to the molecular elec-
trostatic potential (MEP) maps obtained for the four ionic liquids
MImH.HSO , BImH.HSO BMI.HSO and, BMI.CF SO ). According to
the color scale, the red color present on all the anions' surface indicates
nucleophilic domains, while the blue color on the surface of the cation
represents their electrophilic character [47].
4
−
1
and 752 cm can be attributed to the stretching vibration of C–N, the
C–H in-plane bending vibration and the C–H out-of-plane bending vi-
bration of the imidazole ring [45,46]. The simulated spectra (Fig. 1b)
of the four ILs structures reported in Fig. 1a, besides being like the exper-
imental spectra do not present imaginary frequencies, i.e., no negative
wavenumber. These results confirm that the molecular model obtained
theoretically is satisfactory.
(
4
4
4
3
3
4 4
In the case of the protic ILs (MImH.HSO and BImH.HSO ), this study
enables to identify the acidic hydrogen of the cation that is interacting
highly, probably through an H-bonds with the oxygen atoms of the
anion. Both of these ILs present favored anion-cation charge transfer
due to this interaction. The observed distance in the interaction
Fig. 2 presents the absorbance spectra to the ILs studied. This analy-
sis allows us to choose λ = 780 nm for the laser wavelength value to be
Fig. 1. FTIR spectrum of ILs: a) experimental and b) simulated with DFT/B3LYP/6–311++G(d,p).
3

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
Fig. 3. Molecular electrostatic potential maps for ionic liquids. Red color: negative potential; blue color: positive potential.
between the cation's hydrogen atom and the anion's oxygen atom in-
volved in this charge transfer was 1.45, 1.46, 1.95, and 2.09 Å (for the
the presence of the methyl group in the imidazolium ring that generates
an increase in the HOMO and a decrease in the LUMO values. This re-
duced gap energy allows the transfer of electrons from the anion to
the cation.
Fig. 4 also shows that the HOMO orbitals have the lowest electron dis-
tribution in the atoms that have the shortest distances of interaction. This
ILs MImH.HSO
About the BMI.CF
more centralized place, comparing the structure of MImH.HSO
BImH.HSO . This localization of the anion regarding to the imidazolium
ring is probably due to the presence of a methyl group on it.
4
, BImH.HSO
4
, BMI.HSO
4
, and BMI.CF
anion is located at a
and
3 3
SO , respectively).
3
SO and BMI.HSO
3
4
ILs, the HSO
4
4
4
correlation is the most significant in the case of MImH.HSO
4
and BImH.
Fig. 4 shows the results of the frontier molecular orbital (FMO) anal-
ysis of the studied ILs. The Highest Occupied Molecular Orbital (HOMO)
is nucleophilic and it is considered as an electron donor, while the Low-
est Unoccupied Molecular Orbital (LUMO) is usually electrophilic and it
is then an acceptor of electron given by a nucleophilic species [48]. The
larger orbital volumes represented in Fig. 4 evidence that for all the ILs,
the HOMOs are localized in the anion, while the LUMOs are localized in
the imidazole ring where the positive charge density is located. The en-
ergy difference between the HOMO and LUMO energy (energy gap) is
associated with the charge transfer interaction within the frontier or-
bitals. Comparing the gap energy obtained for all the ILs, the lowest
HSO that are protic ionic liquids. This result can be associated with an im-
portant degree of intramolecular charge transfer from the anion to the
cation [49]. The interaction energies of ion-pairs are defined as follows:
4
ꢂ
ꢀ
ꢁꢃ
þ
−
E
−1 ¼ 2625:5 E − E þ E
ð1Þ
ðkJ mol
Þ
is
+
-
where E is the energy of the ionic system, and E and E - are the en-
is
ergy of the cation and anion, respectively. The interaction energies
values obtained for MImH.HSO , BImH.HSO , BMI.HSO and BMI.
4
4
4
−
1
−1
CF
3 3
SO were -412.20 kJ.mol , -401.70 kJ.mol , -360.20 and
-339.21 kJ.mol . The comparison of the values obtained for the two
−1
4
one is observed for the BMI.HSO IL. This result can be attributed to
Fig. 4. Atomic orbital HOMO - LUMO composition of the frontier molecular orbital of ILs.
4

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
protic ILs (BImH.HSO
4
4
and MImH.HSO ) shows that the increase in the
Table 2
DFT results for the polarizability α, and the first-order hyperpolarizability, β, and for the
second-order hyperpolarizability, γ, for different frequencies relations.
alkyl chain of the imidazole ring leads to an increase in the interaction
energy, indicating a favorable charge transfer between the ions [49].
The interaction energy obtained values for BMI.HSO
SO , in comparison with the results obtained for BImH.HSO
MImH.HSO , indicates that the presence of a methyl group in the
imidazolium ring increases the values of interaction energy between
the cation and the anion. This result can be corroborated with the results
obtained through the MEPs study (Fig. 3), which showed that the anion
4
and BMI.
Properties
MImH.HSO
4
BImH.HSO
4
BMI.HSO
4
3 3
BMI.CF SO
CF
3
3
4
and
−24
α(−ω; ω) (10
esu)
14.31
19.98
24.40
10.84
19.95
17.76
21.48
16.17
20.30
21.63
31.43
40.05
19.44
25.76
23.28
35.10
44.11
20.22
26.30
β(−ω; ω, 0) (10− esu)
31
31
4
−
β(−2ω; ω, ω) (10
esu)
γ(−ω; ω, 0, 0) (10− esu)
36
γ(−2ω; ω, ω, 0) (10− esu) 13.94
36
4
HSO was located nearest to the imidazolium ring center in comparison
with the protic ILs. A correlation between the interaction energies and
the HOMO-LUMO energy gap can then be made.
The dipole moment (μ) in a molecule infers the molecular charge
distribution, and its determination enables the study of intermolecular
interactions [49]. The polarizability (α) and the first hyperpolarizability
DFT software has no library to evaluate this. These three presented
terms are all related to the third-order susceptibility. The theoretical re-
sults presented are the response of parallel polarization in relation to
the applied field.
(β) of a compound, that are associated with the intramolecular charge
The values of polarizability, the first-order hyperpolarizability and
transfer, result from the electron cloud movement, for example,
from an electron donor group to an acceptor group through the
π-conjugated framework. Results obtained with DFT are directly related
to the linear and nonlinear optical properties. The polarizability is pro-
portional to the static or the frequency-dependence polarizability,
while Δα represents the anisotropy of polarizability, i.e., the variation
between the polarizability value obtained on the axis of the polarizabil-
ity and a perpendicular axis to the polarizability axis. The first-order
hyperpolarizability, (β), is proportional to the second-order susceptibil-
ity effects, as second a harmonic generation, optical rectification,
electro-optical Pockels effect and three-wave mixing. The second-
order hyperpolarizability (γ) is proportional to the effects of the third-
order susceptibility, as four-wave mixing and the responses measured
by the Z-scan and EZ-scan techniques.
the second-order hyperpolarizability are higher for BMI.CF
followed by BMI.HSO , indicating that a large chain in the cation, follow-
ing by the presence of the methyl group in the imidazolium ring pre-
sented a stronger influence in these properties. The IL MImH.HSO
3 3
SO ,
4
4
,
which has the smallest chain in the cation, showed the lowest values
of the first-order hyperpolarizability and the second-order hyperpolari-
−31
zability. The unique difference observed is for β(−ω; ω, 0) (10
esu)
obtained for BImH.HSO IL, that is the lowest value comparing all ILs.
4
The imidazolium ring of this IL presented an acid hydrogen that favored
charge transfer (see results of Figs. 3 and 4) associated to the cation
chain can be related to these values, however, more detailed studies
need to be carried out to better explain this phenomenon.
To compare the obtained results, we evaluated by DFT analyses,
under the same conditions, properties of urea and carbon disulfide
since they are standard comparative molecules in NLO studies
We evaluated the linear and nonlinear optical properties of the ILs to
several optical responses using the wavelength λ = 780 nm. Table 1
presents the theoretical values of μ, α and β, as well the anisotropy of
polarizability Δα calculated for the studded ILs. The comparison of the
[
40,49,51]. The results obtained for urea to terms of first-order
−34
hyperpolarizability was β(−ω; ω, 0) = 0.91 × 10
ω, ω) = 1.02 × 10
esu and β(−2ω;
−34
4
esu. These values are typically 10 times smaller
μ values obtained for the protic ILs (MImH.HSO
ported in Table 1 shows that the increase in the alkyl chain of the IL
BImH.HSO ) causes an increase in the dipole moment. The presence
4 4
and BImH.HSO ) re-
than the obtained values to ILs presented in this work. The second-
order hyperpolarizability of carbon disulfide was γ(−ω; ω, 0, 0) =
−36
−36
(
4
4
.17 × 10
esu and γ(−2ω; ω, ω, 0) = 5.61 × 10
esu. Both values
of the methyl group in the imidazole ring rather than a proton decreases
the dipole moment.
vary from 2 to 5 times smaller than the obtained to studied ILs.
The highest first hyperpolarizability values (α) are observed for the
BMI.HSO and BMI.CF SO . As this property is dependent on the dipole
4 3 3
3.3. Local and nonlocal nonlinear optical characterization
moment, this result can be associated with the presence of the methyl
group in the imidazole ring that promotes a change in the symmetry
of the molecule, increasing then the α values [50].
The fast responses of molecules measured by the refractive index
change techniques are usually generated by effects related to the
highorders of the susceptibility. These effects are spatially restricted to
the presence of the light fields, corresponding to a local response. Exam-
ples of these effects are nonlinear refractive index and nonlinear absorp-
tion. Otherwise, thermal effects, which are slower and promote heat
diffusion, are not spatially restricted to the beam region and are, there-
fore, a nonlocal effect.
The measurements for rapid response analysis were performed in
the EZ-scan configuration. The nonlinear refractive index was evaluated
using a model based on literature [37]:
Table
2 presents the polarizability, α, and the first-order
hyperpolarizability, β, for different frequencies relations: α(−ω; ω) is
the frequency-dependent polarizability, β(−ω; ω, 0) and β(−2ω; ω,
ω) are related to the electro-optic Pockels effect and the second har-
monic generation respectively, both effects from the second-order sus-
ceptibility. Related to the terms of the second-order hyperpolarizability
(Table 2), γ(-ω; ω, 0, 0) presents electro-optic Kerr effect, γ(−2ω; ω, ω,
0) presents a DC-induced second harmonic generation or electric field-
induced second harmonic. Another response of the second-order
hyperpolarizability, γ(−ω; ω, ω, -ω), is related to the intensity-
dependent refractive index or degenerate four-wave mixing, but the
ΔTp−v
n2 ¼
,
ð2Þ
−
0,44
0:68 ð1−SÞ
Leff k I0
where ΔTp-v is the peak-valley amplitude of the normalized transmit-
tance variation in the EZ-scan technique, S is the factor of disc blockage
Table 1
of the total beam power, k is the wave vector, I
eff = (1 − exp (−aL))/a is the sample effective length.
A previously presented procedure of systematic errors reduction
0
is the peak intensity and
Theoretical values of dipole moment, μ, polarizability, α, the anisotropy of polarizability,
Δα, and first hyperpolarizability, β, for the ionic liquids.
L
μ (Debye) α (x 10 − esu) Δα (x 10 −24 esu) β(x 10 −31 esu)
24
Sample
was employed by our group in these measurements [52]. The scans cor-
responding to the fast responses obtained with the ILs are presented in
the left graphs of Fig. 5. In these results, the light leak through the disc
MImH.HSO
4
12.47
12.96
12.55
13.78
14.08
19.64
21.29
22.92
6.66
7.96
6.95
7.00
18.37
16.42
28.51
31.87
BImH.HSO
BMI.HSO
BMI.CF SO
4
4
was S = 3.3%; the beam waist radius was w
0
= 32 μm; the Rayleigh
3
3
length was z = 4.0 mm, and liquid sample cell thickness was L =
R
5

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
Fig. 5. Variation of transmittance registered for the four ILs exposed to a laser beam (λ = 780 nm). The left side graphs were registered in the time equals zero (condition for minimizing
the thermal effects [39]), while the right-side graphs were recorded after 2.3 ms of beam exposure to identify predominantly the thermal effects. The respectively IL is presented in the
−2
figure and as well as the intensity and power used in the measurements. Open aperture Z-scan are inset, all them performed with beam peak intensity equals to 1.7 GW/cm
.
2
.0 mm. The right side of Fig. 5 presents the results of measurement in
Eq. (2) and are summarized in Table 3. The system was calibrated
using a carbon disulfide sample as the reference. To this sample, the
nonlinear refractive index of carbon disulfide was determined as
the EZ-scan setup 2.3 ms after the chopper aperture corresponding to
exposure time to the beam. Under these conditions, the thermal effects
influenced by the average power predominate, which is why this is
shown instead of the peak intensity. In order to optimize the fast re-
sponse signal at the beginning of the temporal exposure window, the
used power of the laser beam was reduced accordingly for each sample.
An open aperture Z-scan was also performed to analyze nonlinear ab-
sorption/saturation, but no sample evidenced that type of response.
These results are present inset of Fig. 5. All open aperture measurements
−15
2
−1
n
2
= 2.6 ± 0.3 × 10
cm W , which is consistent with the literature
[38,40].
The real part of the third-order susceptibility, χ(3), is directly related
to the degenerate nonlinear refractive index. This term can be evaluated
by the equation [53],
2
n
0
2
χ
ð3Þð−ω; ω, ω, −ωÞ ¼
n2ðωÞ
ð3Þ
were performed with beam peak intensity of 1.7 GW/cm . The nonlin-
ear refractive indices of those ILs were determined according to
283
6

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
Table 3
Experimental nonlinear optical properties values of the ILs obtained: values of the nonlinear refractive index (n
2
), third-order susceptibility, χ(3), the molecular number density (N), and
the second-order susceptibility, γ(−ω; ω; ω; -ω).
(
3)
(3)
Sample
n
2
χ
χ
N
γ(−ω; ω, ω, -ω),
−
16
cm2 W−1
−22
2
2
−14
(10 cm−3
21
−36
(10
)
(10
m /V )
(10
esu)
)
(10
esu)
MImH.HSO
4
2.7 ± 0.7
4.2 ± 0.6
4.5 ± 0.5
2.7 ± 0.4
2.0 ± 0.6
3.1 ± 0.5
3.3 ± 0.4
2.3 ± 0.4
1.4 ± 0.5
2.2 ± 0.3
2.4 ± 0.4
1.6 ± 0.3
4.7 ± 0.1
3.8 ± 0.1
3.6 ± 0.1
3.1 ± 0.1
0.9 ± 0.2
1.6 ± 0.3
1.9 ± 0.2
1.3 ± 0.2
BImH.HSO
BMI.HSO
4
4
3 3
BMI.CF SO
Table 4
Experimental optical properties values of the ILs obtained: values of the absorption (α),characteristic thermal lens time (tc0), thermal lens strength to the laser power of 300 mW (θ), ther-
mal conductivity (κ), thermo-optical coefficient (dn/dT) and the thermal diffusivity (D). The laser beam wavelength was λ = 780 nm.
Sample
a
(
t
c0
θ
κ
dn/dT
(10
D
(10
cm−1)
(ms)
(W m
−1
K−1
)
−6
K−1
)
−3
cm2 s−1
)
MImH.HSO
4
0.13 ± 0.04
0.05 ± 0.01
0.02 ± 0.01
0.04 ± 0.01
2.3 ± 0.2
2.6 ± 0.4
3.0 ± 0.3
4.5 ± 0.5
0.31 ± 0.03
1.04 ± 0.02
0.58 ± 0.05
0.36 ± 0.03
0.17 ± 0.02
0.15 ± 0.02
0.14 ± 0.02
0.13 ± 0.02
5.2 ± 0.8
4.6 ± 0.6
5.4 ± 0.7
1.5 ± 0.6
1.1 ± 0.1
0.9 ± 0.2
0.8 ± 0.2
0.6 ± 0.2
BImH.HSO
BMI.HSO
BMI.CF SO
4
4
3
3
Fig. 6. Temporal evolution for the four ILs exposed to a laser beam (λ = 780 nm) with the power equals of 300 mW. The fits were performed using the Eq. (5). The respectively IL is
presented in the figure.
7

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
−3
where A = 0.1130 g cm W m−1 K−1, and B = 22.65 g cm
K
−
3
2
W
where n
0
is the linear refractive index at the same frequency. Consider-
m−
1
−1
mol are constants defined in the temperature of 293.15 K,
−1
ing that the main contribution would correspond to the electronic portion
of the second-order hyperpolarizability, γ(−ω; ω, ω, -ω), can be estimated
from the correspondent susceptibility and thus from the nonlinear refrac-
tive index by the relation considering the local field factor [54]:
ρ is the density, and M is the molar mass of the liquid. The thermal
conductivity values and uncertainties calculated from the respective
densities of each IL studied here are displayed in Table 4.
These properties were estimated to perform a Z-scan analysis with the
ILs. The absorption coefficient (a), the thermal characteristic time (t ), the
c
ð3Þ
χ
γ ¼
ð4Þ
ꢂ ꢀ
ꢁꢃ
4
1
3
2
n þ 2
N
thermal lens strength for a laser power of 300 mW (θ), the thermal con-
ductivity (κ) calculated from Eq. (7) and the thermo-optical coefficient
(dn/dT), are given in Table 4 for the four ILs. The thermo-optical values ob-
tained on these samples are consistent with the typical values reported
for ionic liquids [64,65]. The characteristic thermal lens time also agrees
with previous results of similar samples referenced in the literature
[66,67]. Fig. 6 presents the time evolution for each ILs, in the maximum
and minimum (peak and valley) of the Z-scan curve, all of them acquired
with the laser power of 300 mW. The adjustments were performed with
the Eq. (5). Except for the absorption coefficient, all results presented in
Table 4 were obtained by this fit in the temporal evolution of the Z-scan
measurements or from derivations of these values.
0
where N is the molecular number density, presented in Table 3. In
this analysis, the linear refractive index used for estimation for all liq-
uids ranges from n = 1.42 to 1.45 [55,56], and this deviation is smaller
0
than the error associated of the measured nonlinear refractive index.
Table 3 shows these estimated hyperpolarizabilities values for each
IL. In comparison, these are an order of magnitude smaller than theo-
retical results obtained with the DFT theory. This discrepancy may be
associated with a refractive different response, e.g., with the one corre-
sponding to the signal modified by the ILs local structure and the inter-
action with their vicinities. Another behavior that can result in this
difference is the induced birefringence. Based on the value evaluated
for the polarization anisotropy, Δα, one should also consider the optical
Kerr effect, which arises from the molecular alignment produced by the
optical torque on the induced dipoles [57]. This effect could be evi-
denced by a technique that discriminated against these effects, as the
polarization-resolved Z-scan technique [58], or performing analyses
via OKE spectroscopy [59]. Although the demonstrated discrepancy be-
tween theoretical and experimental values of the second-order
hyperpolarizability, the results obtained by the EZ-scan technique for
the first three ILs shown in Table 3 presented the same growth rate ver-
ified by DFT to the terms γ (-ω; ω,; 0, 0) and γ(−2ω; ω, ω, 0), which can
assist in predicting the nonlinear properties prior to sample synthesis.
Even if a short femtosecond pulse with nanojoules of energy is suffi-
cient not to heat the sample during a single propagation, high repetition
rates of these pulses produce cumulative effects that alter the wavefront
curvature of the propagating beam. The time evolution of transmittance
variation in a high-repetition system was modeled by Falconieri [60]. In
the case of linear absorption, i.e. in our situation, the variation of trans-
mittance can be written as [61,62]:
All these data were determined for the first time for the MImH.HSO
4
,
BImH.HSO , BMI.HSO , and BMI.CF SO ILs As previously pointed, the
4
4
3
3
.
literature of thermo-optical properties and nonlinear refractive index
involving ILs with a femtosecond laser source is not extensive. Beyond
that, no further studies for ILs were found that relate the electronic ef-
fects on experimental results with theoretical simulations.
4. Conclusion
4 4
The nonlinear optical properties of four ILs, MImH.HSO , BImH.HSO ,
BMI.HSO and BMI.CF SO were determined theoretically and experi-
4
3
3
mentally. All four ILs exhibited nonlinear refractive indices under our
experimental conditions, and their thermo-optical coefficients were
also evaluated. The DFT analysis was able to estimate the polarizability
as well as first- and second-order hyperpolarizabilities.
Based on this comparison we observe that in accordance to the in-
crease of the alkyl chain of the imidazole ring on the sulfate ILs, the
growth of nonlinear values in the DFT analyses of the second-order
hyperpolarizabilities, γ, is coherent with the measured growing nonlin-
ear susceptibilities. This result shows that the DFT method can help in a
qualitative prediction of ILs before they are synthesized and character-
8
0
19
2
<
=
T ¼ 1 þ θ tan −
2ez
ð5Þ
1@
A
ꢄ
ꢅꢄ
ꢅ
3 3
ized. However, this correlation was not observed for BMI.CF SO , for
:
2
2
2
2
;
9
þ ez
1 þ ez tc0=2t þ 3 þ ez
which the difference between DTF and the nonlinear susceptibility
was the largest when compared to the result set, which could be due
to a contrasting charge transfer. Moreover, an exact agreement was
not expected because DFT analysis simulates only a single molecule
and does not consider the entire vicinity or the orientational molecular
dynamics responsible for the optical Kerr effect. The technique of
polarization-resolved Z-scan measurements will now be introduced to
discriminate between electronic and orientational nonlinear effects in
these systems. Exceptionally, various thermo-optical coefficients to
the ILs were determined in the same procedure, which extends the
characterization of these materials. The thermodynamic properties of
thermal characteristic time, thermal lens strength, thermal conductivity
an diffusivity were here evaluated and presented.
where tc0 is the characteristic thermal lens time associated with the
beam waist radius and ez = z/z
is the normalized scanning parameter.
/ 4 tc0. The thermal
0
The thermal diffusivity is related to the tc0 by D = w
0
lens strength, θ, represents the intensity of the lens induced by the sam-
ple heating, which curves the beam wavefront and generates the varia-
tion of transmittance in this regime. Eq. (5) considers the quadratic
terms of thermal lens strength since it is not negligible in our situation.
The thermo-optical coefficient, the variation of refractive index (n) with
the temperature, can be determined by:
dn
dT
λκ
P a Leff
¼
−
θ
ð6Þ
Authorship statement
where P is the laser power in the sample and κ is the thermal conductiv-
ity, which can be evaluated for ILs applying the model based on equa-
tion proposed by Fröba et al. [63]:
All persons who meet authorship criteria are listed as authors, and
all authors certify that they have participated sufficiently in the work
to take public responsibility for the content, including participation in
the concept, design, analysis, writing, or revision of the manuscript. Fur-
thermore, each author certifies that this material or similar material has
AM þ B
k ¼
ð7Þ
Mρ
8

V.C. Ferreira, L. Zanchet, W.F. Monteiro et al.
Journal of Molecular Liquids 328 (2021) 115391
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Declaration of Competing Interest
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Acknowledgements
Vinícius Castro Ferreira and Letícia Zanchet thank the finance in part
by the Conselho Nacional de Desenvolvimento Científico e Tecnológico
(
CNPq) and Letícia Guerreiro da Trindade thanks the finance in part
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to thank the Theoretical Chemistry Group (TCG/UFRGS) for providing
computational resources and the Universidade Federal do Rio Grande
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