Electronic supplementary materials for: Optical transmission of
nematic liquid crystal 5CB doped by single-walled and multi-walled
carbon nanotubes
L.N. Lisetski1, A.P. Fedoryako1, A.N. Samoilov1, S.S. Minenko1, M.S. Soskin2, and N.I. Lebovka3
1
Institute for Scintillation Materials, NAS of Ukraine, Kharkiv, Ukraine
2
Institute of Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine
3
Institute of Biocolloidal Chemistry named after F.D. Ovcharenko, NAS of Ukraine, Kyiv, Ukraine, Email: lebovka@gmail.com
Contents
1. Optical transmission spectra
2. Static bending persistence length of nanotubes
3. Dielectric studies
3.1. Measurements of dielectric permittivity
3.2. Experimental data and their discussion
References
S1. Optical transmission spectra
Figure S1 present examples of UV-vis
absorption spectra (200-800 nm) of a 20 μm thin
film of pure 5CB and 0.02 % single-walled carbon
nanotubes (SWCNTs) dispersed in 5CB in the
isotropic (T=310 K) and nematic (T=301 K)
phases. The similar spectra were registered also
for
the
multiwalled
carbon
nanotubes
(MWCNTs). The presented data were obtained
using sandwich-type LC cells with 20 m
thickness. Before insertion of a sample into the
cell, the cell walls were treated by polyvinyl
alcohol aqueous solution and dried and rubbed in
one direction, similarly to the standard procedure
of obtaining nematic with the planar texture. The
sample was introduced between the cell walls by
capillary action at the temperature of 313 K, i.e.,
in the isotropic phase just above the phase
transition from the nematic state.
Note that UV-vis absorption spectra of pure
5CB were frequently discussed in the literature
(see, e.g., [1–3]. The cut off region of the 5CB is
located below 350 nm. It is generally known that
in conventional nematics the transmission to the
nematic phase is always substantially lower than
to the isotropic phase.
UV–vis absorption spectra of carbon
nanotubes in different solvents were also
intensively studied (see, e.g. [4]). Very broad
adsorption bands were observed in the region
below 350 nm that can associated with  plasmon
absorbance.
The absolute wavelength of the -plasmon
absorbance has been shown to vary with nanotube
diameter d (nm) as [4]
p (nm)=1239.84187/(4.80 + 0.70/d2)
(S
1)
This empirical relationship gives 255 nm for
the energy range in a single sheet of graphene and
243 nm for nanotubes with diameter of 15 nm
that were used in the present work.
Fig. S1. UV-vis absorption spectra (i.e.,
optical transmission Tr versus wavelength , 200800 nm) of a 20 μm thin film of pure 5CB and
0.02 % single-walled carbon nanotubes
(SWCNTs) dispersed in 5CB in isotropic (T=310
K) and nematic (T=301 K) phases.
In order to exclude possible impact of the
adsorption bands of 5CB matrix and nanotubes,
the optical transmission Tr was analyzed at 700
nm wave-length that was far away from the
mentioned cut off regions. The introduction of
CNTs into the 5CB matrix resulted in a noticeable
decrease of the optical transmissions. Such
behaviour was typical for LC matrixes doped by
nanotubes [5,6].
If the measured transmission of the 5CB +
CNT system is Tr, and the 5CB solvent
transmission is Tr(5CB), then the difference
Tr(5CB)- Tr can serve as a measure of the
contribution of nanotubes to the total value of
transmission
(i.e.,
absorption
+
reflectance/scattering) of the 5CB + CNT system.
In our experiments, well-defined stepwise
changes in Tr(5CB) - Tr at the nematic-isotropic
transition were clearly observed for 5CB+NT
dispersions (Fig. S2). The value of (Tr(5CB) - Tr)
can reflect the perturbation of LC medium trapped
by individual CNT coils or their aggregates.
Figure S2 presents Tr(5CB) - Tr differences
for the temperatures in the isotropic phase (T=310
K) and in the nematic phase (T=301 K). Note that
Tr(5CB) - Tr values were much smaller in the
isotropic phase than in the nematic phase. This
1
difference may be a clear indication of strong
perturbations of 5CB medium in the vicinity of
carbon nanotube aggregates.
The presence of such perturbations was
demonstrated
by
recent
electrooptical
investigations of interfacial 5CB layers bounded
by CNTs [7–10]. The 5CB molecules can be
anchored strongly to the side walls of CNTs and
retain their position upon application of the
electric field.
In the rigid random-coil limit (i.e., when
l<lp):
dc  l .
(S4)
Analyses of SEM images of CNTs with
different diameters d revealed the presence of
strong lp(d) dependence (Fig. S3) [12] that can be
approximated by the following quadratic relation:
lp  d 2 / a .
(S5)
where a = 1.54  0.02 nm and lp, d are represented
in nm.
Fig. S2. The difference in optical transmissions
Tr(5CB)-Tr of pure 5CB and 5CB+0.02 %
SWCNTs versus wavelength , 200-800 nm at
temperatures corresponding to the isotropic
(T=310 K) and nematic (T=301 K) phases.
E.g., it was shown that the mean thickness of
interfacial layers in 5CB+ 0.0025 % MWCNT
composite increases from 1 μm up to ~4.5 μm
when nematic structure of 5CB undergoes the
Freedericksz
transition
from
planar
to
homeotropic orientation under the applied
transverse electric field ~3.5 V [9]. The
investigations have also shown the presence of
quite different responses to the applied field in the
inner “lakes” and at the outer borders of MWCNT
aggregates.
S2. Static bending persistence length of
nanotubes
In many cases, the shape of carbon nanotubes
(CNTs) deviates significantly from rodlike
geometry and is rather tortuous when grown
randomly by chemical vapor deposition method
[11]. Dependence of the effective size dc upon the
length l of CNT for random coil-like CNTS can be
approximated as [12]
d c  2l p l  2l p2 (exp( l / l p )  1)
(S2)
where lp is the static bending persistence length
(i.e., the maximum straight length that is not bent
by a permanent structural deformation).
In the rigid random-coil limit (i.e., when
l>>lp):
d c  2l p l .
(S3)
Fig. S3. Static bending persistence length lp versus
diameter of CNT d experimentally determined for
analyses of SEM images (squares). Solid line
corresponds to the quadratic approximation, Eq.
(S4).
S3. Dielectric studies
3.1. Measurements of dielectric permittivity
A sandwich-type cell was used in dielectric
measurements. It consisted of a capacitor with the
metal plates. Only the perpendicular components
of
dielectric
permittivity
(real,   ,
'
and
imaginary,  ) were determined. At the
frequencies below 30 MHz, the oscilloscopic
method was used, and the measurements were
carried out using an E7-11 type Q-meter
(KALIBR,Belarus) at the frequencies above 30
MHz. The cell thickness (h=50 m) was set by a
Teflon spacer. Before the measurements, the cell
parts were washed in hexane and dried at 390 K.
The electrodes were covered by a thin polyvinyl
alcohol film rubbed in one direction for ensuring
the planar texture [13]. This procedure was similar
to that used for preparation of the optical cells.
The LC system in the isotropic state was
introduced into the pre-heated cell by the capillary
forces at the temperature 5–10 K above the
nematic–isotropic transition point. The values of
cell capacitance Cc and dielectric loss tan were
estimated from the phase difference between the
"

2
voltage and current. Then, the
  C s / Co
'

and
values of
  tan   
"

'

were
calculated, where
Cs  Cc / 1  tan 
(S6)
is the capacitance of the sample, C0 is the
capacitance of the empty cell.
3.2. Experimental data and their discussion
Many examples of applications of the
dielectric spectroscopy for study of nematics
doped by CNTs were previously presented [14–
18]. However, the results reported up to date for
an LC doped by CNTs are rather contradictory:
introduction of CNTs can cause either an increase
or a decrease of dielectric permittivity; moreover,
different behaviour of such systems at low and
high frequencies was also noted [14].
Figure S4 presents frequency dependences of
the perpendicular components of dielectric
permittivity (real,   , (a) and imaginary,   ,(b))
for pure nematic 5CB and 5CB doped by 0.01%
SWCNTs and 0.01% MWCNTs.
'
"
Note that previously reported data [14]
evidence that introduction of CNTs can also result
in a decrease of dielectric permittivity in the low
frequency range. This effect was explained by the
fact that CNTs can serve as traps for charge
carriers, thus lowering the concentration of ions in
the LC matrix. The apparent discrepancy between
our data and data of [14] can be easily explained
by difference in the degree of CNT purity. The
effect of “traps” can be only important for CNT
samples of high purity. When purity of a CNT
sample is not very high, doping of LC by CNTs
can result in increased concentration of charge
carriers, thus causing the opposite effect upon
dielectric permittivity.
The relaxation effects were also clearly
observed in   ( f ) plots at higher frequencies
above 1-10 Hz. Characteristic relaxation
frequencies were of 8 MHz, 15 kHz and 3
kHz
for
pure
5CB,
5CB+SWCNT,
5CB+MWCNT samples, respectively (Fig. S4b).
The observed characteristic frequency of pure
5CB was in full correspondence with the
previously reported data [19]. And smaller
relaxation frequencies of 5CB+SWCNT and
5CB+MWCNT samples, possibly, reflect the
effect of CNTs on restriction of director dynamics
inside nematic LC.
"
References
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Fig. S4. Frequency dependences of the
perpendicular
components
of
dielectric
permittivity: real,   , (a) and imaginary,   ,(b).
Data are presented for pure nematic 5CB, and
5CB doped by 0.01% SWCNTs and 0.01%
MWCNTs, T=301 K.
'
"
The observed dispersion at low frequencies
(f<103 Hz) can be ascribed to ions moving in the
vicinity of the surfaces of cell electrodes (for pure
nematic 5CB) or surfaces of CNTs (for 5CB
doped by CNTs). Large differences in the
obtained values of   and   for the pristine 5CB
and 5CB doped by CNTs were also observed in
the low-frequency part of the dielectric spectrum.
These differences were more pronounced for
SWCNTs than for MWCNTs, which can be easily
explained by large difference in the specific
surface areas of these CNTs. It is in full
agreement with the observed differences in optical
density D for SWCNTs and MWCNTs. It was
substantially higher for SWCNTs than for
MWCNTs due to the same reason, i.e., larger
specific surface area of SWCNTs.
'
"
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