Effects of Dispersed Carbon Nanotubes and Emerging Supramolecular Structures on Phase Transitions in Liquid Crystals: Physico-Chemical Aspects

Abstract

The current state of the study of different liquid crystalline (LC) systems doped with carbon nanotubes (CNTs) is discussed. An attempt is endeavored to outline the state-of-the-art technology that has emerged after two past decades. Systematization and analysis are presented for the integration of single- and multi-walled carbon nanotubes in thermotropic (nematic, smectic, cholesteric, ferroelectric, etc.) and lyotropic LCs. Special attention is paid to the effects of alignment and supramolecular organization resulting from orientational coupling between CNTs and the LC matrix. The effects of the specific inter-molecular and inter-particle interactions and intriguing microstructural, electromagnetic, percolation, optical, and electro-optical properties are also discussed.

Full text

Citation: Lisetski, L.; Bulavin, L.;
Lebovka, N. Effects of Dispersed
Carbon Nanotubes and Emerging
Supramolecular Structures on Phase
Transitions in Liquid Crystals:
Physico-Chemical Aspects. Liquids
2023,3, 246–277. https://doi.org/
10.3390/liquids3020017
Academic Editors: Nikolay
O. Mchedlov-Petrossyan
and Cory Pye
Received: 10 April 2023
Revised: 9 May 2023
Accepted: 24 May 2023
Published: 29 May 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Review
Effects of Dispersed Carbon Nanotubes and Emerging
Supramolecular Structures on Phase Transitions in Liquid
Crystals: Physico-Chemical Aspects
Longin Lisetski 1, Leonid Bulavin 2and Nikolai Lebovka 3, *
1Institute for Scintillation Materials, STC ISC, National Academy of Sciences of Ukraine,
61072 Kharkiv, Ukraine
2Faculty of Physics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine
3F.D. Ovcharenko Institute of Biocolloidal Chemistry, National Academy of Sciences of Ukraine,
03142 Kyiv, Ukraine
*Correspondence: lebovka@gmail.com
Abstract:
The current state of the study of different liquid crystalline (LC) systems doped with
carbon nanotubes (CNTs) is discussed. An attempt is endeavored to outline the state-of-the-art
technology that has emerged after two past decades. Systematization and analysis are presented
for the integration of single- and multi-walled carbon nanotubes in thermotropic (nematic, smectic,
cholesteric, ferroelectric, etc.) and lyotropic LCs. Special attention is paid to the effects of alignment
and supramolecular organization resulting from orientational coupling between CNTs and the LC
matrix. The effects of the specific inter-molecular and inter-particle interactions and intriguing mi-
crostructural, electromagnetic, percolation, optical, and electro-optical properties are also discussed.
Keywords: carbon nanotubes; thermotropic liquid crystals (LCs); lyotropic LCs
1. Introduction
Liquid crystal (LC) colloids constantly attract great attention from researchers. The
early historical account of the problem was presented in [
1
]. One can also mention the
recent reviews on metal oxide nanoparticles (MgO, ZnO, Fe
2
O
3
, Al
2
O
3
, Cu
2
O
3
, NiO,
SiO
2
, ZrO
2
, and TiO
2
) [
2
], semiconducting quantum dots/rods [
3
], and metal (Ag, Au,
and Pt) nanoparticles [
4
,
5
] dispersed in LCs. The effects of the LC’s material alignment
induced or enhanced by incorporated nanoparticles and the methodology of developing
new innovative devices based on this alignment process were recently discussed [
6
]. The
effects of LC phase transitions on the topological defects (defect morphogenesis) induced
by the colloidal particles dispersed in LCs were also recently reviewed [7].
Note that LCs may serve as a special type of host for anisotropically shaped nanopar-
ticles such as carbon nanotubes (CNTs), as well as graphene-derived or inorganic nano-
platelets [
8
]. These composites exhibit many intriguing properties related to the anisotropy
of individual particles and self-assembled LC systems [
9
]. LCs can assist in the aligning of
such nanoparticles, resulting in the formation of anisotropic systems with enhanced func-
tional properties. Moreover, in such systems, the inverse alignment effects of anisometric
particles on the LC’s ordering can be very important. In previous years, the composites
based on LCs doped with anisotropically shaped nanoparticles attracted great attention.
These composites can be used for creating multifunctional devices with exceptional elec-
tronic performance.
This review aims to provide an overview as well as the authors’ personal account of
the studies of LC materials doped with CNTs and their applications. A comprehensive
overview of the “state-of-the-art” technology in the field, developments, and advantages
for the recent 20–25 years is given. The critical analysis of CNTs self-assembling in LC
Liquids 2023,3, 246–277. https://doi.org/10.3390/liquids3020017 https://www.mdpi.com/journal/liquids

Liquids 2023,3247
media and the effects of CNTs on LC ordering is presented. The review starts with brief
discussions of different classes of LCs and the main properties of CNTs. A short presenta-
tion of the existing reviews in the field is presented in the table. The different properties
of thermotropic and lyotropic LCs doped with CNTs, particularly phase transitions, mi-
crostructural, electromagnetic, percolation, optical, electro-optical properties, and issues
related to the material stability, are given. Finally, the conclusions and future perspectives
of this rapidly emerging field are provided.
2. Types of Liquid Crystals
The liquid-crystalline state of matter (mesomorphic state, or mesophase) is inter-
mediate between the crystalline and liquid states, simultaneously showing some of the
anisotropic properties of solids and the fluidity of liquids [
10
]. In this state, materials
demonstrate a tendency to flow like liquids and have some properties similar to solids. LCs
may be divided into two main classes, named thermotropics and lyotropics [
2
,
6
,
11
]. Am-
photropic LCs that show both thermotropic and lyotropic phases were also identified [
12
,
13
].
For example, exhibition of amphotropic LC properties has been reported for many amino
acid, peptide, phospho- and glycolipid-based LCs, with a special attention to the LC-like
structure of cell membranes [
14
–
16
]. The properties of polymeric and elastomeric LC phases
were also discussed [
17
–
20
]. These materials combine polymer network properties with LC
anisotropy, and they are good candidates for stimuli-responsive reversible shape memory
materials [
21
]. The different polymer-modified LCs (e.g., a continuous polymer matrix with
the inclusion of LC droplets or a bicontinuous system of a polymer network dispersed in
an LC host) also represent a great interest for different practical applications [22].
For the completeness, we can also refer to important classes of unconventional LCs.
The two main categories related to supermolecular and supramolecular systems were
highlighted (for a recent review, see [
23
]). The different types of ionic LC versatile materials
(dendrimeric thermotropic, polymeric, lyotropic, zwitterionic, and mesoionic) were also
identified [24,25].
2.1. Thermotropic Liquid Crystals
Thermotropic LCs demonstrate the presence of LC phases in a certain temperature
range between the crystalline solid and isotropic liquid. Therefore, in these materials, the
mesomorphic state formation depends on temperature. These substances with anisotropi-
cally shaped molecules demonstrate the dual characteristics of solids and liquids. They
have some sort of positional or orientational order and may flow like a liquid. This duality
can lead to anisotropy in optical, viscoelastic, electrical, and magnetic properties. On the
basis of molecular shape, the LCs can be classified as calamitic (rod-like molecules), discotic
(disc-like molecules), and bent-core (banana-shaped molecules with bent cores and flexible
tails) types; other more exotic types (e.g., bowlic) have also been reported. Nowadays,
huge quantities of thermotropic LC substances (more than 70,000) with different chemical
compositions and phase transition temperatures have been discovered [26,27].
The main thermotropic LC phases are nematics, smectics, and cholesterics [
28
–
30
]. In
the simplest nematic LCs, the molecules are preferentially oriented along a single director
axis, but they have no positional order. In the smectic LCs phases with positional layered
order, the molecules have a long-range orientational order and are organized positionally
in smectic layers. In smectic A and smectic C phases, the molecules are oriented along
the layer normally and at an oblique angle to the normal angle, respectively. There also
exist many other types of smectic arrangements (B, D, E, F, etc.) with more complex self-
organization. In the cholesteric (chiral nematic) LC phase, the director shows a helical
structure and the molecules are arranged along a director axis with continuous changes of
their directions in the form of a helix [
28
]. The helical period is typically in the range from
0.1 to 100 microns, with characteristics optimal for applications observed in more narrow
ranges (10–20
µ
m in most cases). The more complex LC phases such as chiral nematic,
chiral smectic, blue phases, and twist grain boundary phases were also identified [
13
], as

Liquids 2023,3248
well as most novel twist-bend and ferroelectric nematics [
31
,
32
]. The phase transitions
between various LC phases can be first order, second order, or weakly first order.
2.2. Lyotropic Liquid Crystals
In lyotropic LCs, the phase transitions are induced by changes in the temperature
and concentration of dissolved amphiphilic molecules (including the hydrophobic and
hydrophilic blocks) in suitable solvents. In an aqueous environment, such molecules
can be self-organized in different phases depending on their molecular structure [
33
,
34
].
At temperatures above Krafft point, boundaries called CMC curves between the unimer
and aggregate solution (micellar, vesicle, or microemulsions) phases appear. Typically,
lyotropic LCs demonstrate the different types of long-range periodicity, with amphiphilic
molecules arranged in the nematic, hexagonal, lamellar, and different intermediate (e.g., cu-
bic) phases [
35
]. In a lamellar phase, bilayers with hydrophilic head groups oriented to
water are formed. In a hexagonal phase, the amphiphilic molecules are arranged as infinite
cylindrical structures on a hexagonal lattice. A cubic phase may exist between the lamellar
and hexagonal LC phases; in this phase, the arrangement is in the form of a lipid sphere
in a dense cubic lattice. These LCs can be used as efficient systems in drug delivery [
36
].
Water-based lyotropic LCs are common in biological and living systems [
37
]. The phase dia-
grams for many surfactant/water systems can be found in the review [
34
]. The anisotropic
colloidal particles (rod-like, plate-like, or their hybrids) can also form lyotropic LC phases.
These structures are called nanomesogen lyotropic LCs [38].
3. Carbon Nanotubes
The tribute to the first publication on carbon nanotubes is usually paid to Iijima,
who seems to be the first to have had them synthesized [
39
]. (However, as always, every
discovery finds its predecessors, and we mention here the work where CNTs were, in
fact, obtained, but not fully understood and advertised by the authors [
40
]). CNTs repre-
sent elongated cylindrical graphene sheets, and there exist single-walled (SWCNTs) and
multi-walled (MWCNTs) carbon nanotubes. CNTs can have extremely high aspect ratios,
ε≈100–1000
(
ε
=L/d is the length to diameter ratio). Examples of microscopy images of
MWCNTs are shown in Figure 1.
Liquids 2023, 3, FOR PEER REVIEW 3
many other types of smectic arrangements (B, D, E, F, etc.) with more complex self-organ-
ization. In the cholesteric (chiral nematic) LC phase, the director shows a helical structure
and the molecules are arranged along a director axis with continuous changes of their
directions in the form of a helix [28]. The helical period is typically in the range from 0.1
to 100 microns, with characteristics optimal for applications observed in more narrow
ranges (10–20 µm in most cases). The more complex LC phases such as chiral nematic,
chiral smectic, blue phases, and twist grain boundary phases were also identified [13], as
well as most novel twist-bend and ferroelectric nematics [31,32]. The phase transitions
between various LC phases can be first order, second order, or weakly first order.
2.2. Lyotropic Liquid Crystals
In lyotropic LCs, the phase transitions are induced by changes in the temperature
and concentration of dissolved amphiphilic molecules (including the hydrophobic and
hydrophilic blocks) in suitable solvents. In an aqueous environment, such molecules can
be self-organized in different phases depending on their molecular structure [33,34]. At
temperatures above Krafft point, boundaries called CMC curves between the unimer and
aggregate solution (micellar, vesicle, or microemulsions) phases appear. Typically, lyo-
tropic LCs demonstrate the different types of long-range periodicity, with amphiphilic
molecules arranged in the nematic, hexagonal, lamellar, and different intermediate (e.g.,
cubic) phases [35]. In a lamellar phase, bilayers with hydrophilic head groups oriented to
water are formed. In a hexagonal phase, the amphiphilic molecules are arranged as infi-
nite cylindrical structures on a hexagonal laice. A cubic phase may exist between the
lamellar and hexagonal LC phases; in this phase, the arrangement is in the form of a lipid
sphere in a dense cubic laice. These LCs can be used as efficient systems in drug delivery
[36]. Water-based lyotropic LCs are common in biological and living systems [37]. The
phase diagrams for many surfactant/water systems can be found in the review [34]. The
anisotropic colloidal particles (rod-like, plate-like, or their hybrids) can also form lyotropic
LC phases. These structures are called nanomesogen lyotropic LCs [38].
3. Carbon Nanotubes
The tribute to the first publication on carbon nanotubes is usually paid to Iijima, who
seems to be the first to have had them synthesized [39]. (However, as always, every dis-
covery finds its predecessors, and we mention here the work where CNTs were, in fact,
obtained, but not fully understood and advertised by the authors [40]). CNTs represent
elongated cylindrical graphene sheets, and there exist single-walled (SWCNTs) and multi-
walled (MWCNTs) carbon nanotubes. CNTs can have extremely high aspect ratios, ε ≈
100–1000 (ε = L/d is the length to diameter ratio). Examples of microscopy images of
MWCNTs are shown in Figure 1.
Typically, MWCNTs display very good mechanical properties and very high electri-
cal (metallic) and thermal conductivity. The combination of these aractive properties al-
lows a wide range of their applications in different sensors, field emiers, energy-storage,
energy-conversion, and gas storage devices.
Figure 1.
Scanning electron microscopy (
a
) and high-resolution electron microscopy (
b
) images of
MWCNTs. Here, the inner and outer diameters are denoted as di and d, respectively, while n is a
number of MWCNT walls. ((
a
) was reprinted with permission from Ref. [
41
]. Copyright 2009 IOP
Publishing; (b) was reprinted with permission from Ref. [42]. Copyright 2014 Elsevier).
Typically, MWCNTs display very good mechanical properties and very high electrical
(metallic) and thermal conductivity. The combination of these attractive properties allows a
wide range of their applications in different sensors, field emitters, energy-storage, energy-
conversion, and gas storage devices.
The length of CNTs can vary from hundreds of nanometers to centimeters. Their
diameter can also vary between about one and two nanometers (SWCNTs) and tens of

Liquids 2023,3249
nanometers (MWCNTs). Moreover, the shape of CNTs is not straight and they are rather
tortuous [43].
4. Liquid Crystalline Composites with CNT Dopants
Historically, the behavior of elongated particles suspended in an LC was discussed
for the first time some 50 years ago [
44
]. In such systems, the particle axis is locked and
directed parallelly to the nematic axis. A similar analysis was performed for magnetic
platelets introduced into a nematic LC [45].
About 20–25 years ago, CNTs started to be used as the dopants in different ther-
motropic and lyotropic LC systems. It seems that the dispersions of CNTs in nematic
LCs were first analyzed with the aim of improving the characteristics of LC optical
gratings [46,47]
. In pioneering works, the properties of CNTs in orientationally ordered LC
matrixes were also studied [
48
,
49
]. The existing reviews on previous works are collected
in Table 1.
Table 1.
Short description of some reviews of the behavior of LCs doped with anisotropically shaped
nanoparticles (mainly with CNTs).
Materials, References Discussed Issues
CNTs in liquid solvents [50]
The review discussed the phase behavior of CNT suspensions, formation of LC
phases, effect of surfactants, and interparticle interactions on the aggregation and
percolation threshold
CNTs in water and different LC phases [51]
LC phases of CNTs in water and the effects of insertion of CNTs into thermotropic
or lyotropic LCs were discussed.
Nanoparticles in LCs [52]The self-assembly of nanoparticles in different thermotropic, lyotropic, and
amphotropic LC phases was analyzed.
CNTs in LCs [53]
The review analyzed the alignment and efficient dispersion of CNTs in
thermotropic and lyotropic LC hosts, distortions of the LC director field. The
potentially relevant applications in displays or similar electro-optic devices were
also considered.
Nanoscale particles and CNTs in LCs [54]
A review of the impact of nanoscale particles (metal and semiconductor
nanoclusters or nanorods) and CNTs in LC nanocomposites on the improvement
of LC display (LCD) applications was given.
CNTs in thermotropic nematic LCs [55]
The different dispersion methods, stability, alignment, and distribution of the
CNTs inside the LC suspension were analyzed. The photorefractive effect,
dielectric relaxation behavior, phase transition temperatures in CNT–LC
suspensions, and improvement in LC device performance via doping CNTs were
also discussed.
Different metamaterials on the base of LCs
doped with nanoparticles [56]
The review presented discussion of linear and nonlinear optical properties of LC
materials doped with fullerene C60, CNTs, polymers, gold and silver nanospheres,
and other nanoparticulates of various shapes and forms.
CNTs in LCs [57]
The review was presented on dielectric, electro-optical, nonlinear optical, and
micro-structural properties of thermotropic nematic LCs doped with CNTs. The
impact of the spatial arrangement of CNTs on heating–cooling hysteretic behavior
of electrical conductivity and percolation effects was discussed. Mechanisms of
electro-optic memory effect and its enhancement via chiral dopant were
also analyzed.
CNTs in LCs [58]
Discussion of factors affecting the efficient dispersion of CNTs in thermotropic
LCs, preparation of the dispersions, their stability, and uniaxial CNT alignment in
the LC host was presented.
CNTs in LCs [59]Different methods of dispersion, ordering, and aligning of CNTs in thermotropic
and lyotropic LC hosts were analyzed.
Different nanoparticles in LCs [60]
Comprehensive discussion of behavior of different LC colloids of nanoparticles
was given. The data on different types of nanoparticles (aerosil, CNTs, metallic,
ferroelectric, magnetic, organic, dielectric, and semiconductor) in thermotropic
and lyotropic LCs were presented. Various applications of LC nanocolloids were
also discussed.

Liquids 2023,3250
Table 1. Cont.
Materials, References Discussed Issues
Different nanoparticles in LCs [61,62]
Considerations of ion trapping effects and related phenomena in LCs doped with
nanoparticles of various origins (carbon-based, metal, dielectric, semiconductor,
magnetic, ferroelectric, and polymeric) were presented. The percolation effects,
aggregation phenomena, ion capturing capabilities, effects of the purity of the
nanoparticle, and current challenges in the field were also reviewed.
CNTs and other nanomaterials in LCs [63]
Tutorial review on the behavior of nanorods and discs, CNTs in thermotropic and
lyotropic LCs, as well as discussion of LC phases formed by CNTs was presented.
Nanoparticle-doped LC phases [64]
Extensive discussions of properties of LC nanoparticle dispersions (LCs with
additives of nanorods, nanotubes, and nanoclays) and different electro-optic
applications were provided.
Nanoparticles dispersed in LCs [65]
Discussion of recent theories of phase separations and phase behaviors in mixtures
of nanoparticles (spherical and rod-like) and LCs was given. For nanotubes
dispersed in LCs, the effects of external magnetic and electric fields on the phase
behaviors were also considered.
LCs of CNTs and CNTs in LCs [66]
The review provided analysis of dispersion of CNTs in isotropic liquids
(particularly in water in presence of surfactants) and formation of lyotropic LC
phases (Onsager’s transition). Aligning of CNTs in thermotropic and lyotropic
LCs, LC polymers, and polymerized LCs was also discussed.
Colloidal particles organized by LCs and LC
phases from colloids [67]
The review presented comprehensive discussions of applications of LCs in
soft-matter nanotechnologies with consideration of the effects of LCs on the
organization of colloidal particles and formation of LC phases from colloids. The
particular effects related to CNT colloids were also considered.
CNTs in LCs [68]
The different aspects of the CNT–LC combination, evaluations of the CNTs’ effect
on selected properties of LCs, and the direct effect of CNT bundles on LC
reorientation were analyzed.
Nano- and microparticles in LCs [69]The ordering of nano-and microparticles in LCs, shape-induced effects, and
specific interactions on CNTs in LC matrices were analyzed.
CNTs in LCs [70]
The structure and properties of LCs doped with CNTs were critically reviewed.
Behavior of thermotropic (nematics, cholesterics, and smectics), lyotropic, and
chromonic, ionic, and hydrogen-bonded LC phases was discussed. The
discussions include behavior electrical conductivity, dielectric permittivity, phase
transitions, optical transmission, and different memory effects. Properties of
combined well-dispersed LC composites that contain CNTs and platelets of
organoclays were also discussed. The review mentioned possible practical
applications of LC + CNT-based materials in various electro-optic and
optoelectronic devices.
CNTs in LCs [71]
A comprehensive overview of CNT suspensions in LCs was given. The dispersion
and interaction of CNTs in LC matrices has been extensively discussed. The
different effects of LCs on the CNTs’ alignment and effects of CNTs on the
enhancement and fine-tuning of LC properties were presented. In particular, the
phase behavior of CNT + LC composites, optical transmittance, memory effects,
dielectric and electrical conductivity behavior, ionic effects, impacts of
electric/magnetic field, and perspectives of application of composites were
briefly discussed.
CNTs in LCs [72]
A comprehensive review on different properties of thermotropic LCs doped with
CNTs was presented. The dispersion of CNTs, electrical and magnetic switching of
LC–CNT composites, CNTs’ effects on properties of ferroelectric LCs and
perspective of practical applications of these composite LC–nanotube dispersions
were discussed.
Different nanoparticles in LCs [73]
A critical review on the behavior of dispersion of different nanoparticles
(ferroelectric, ferromagnetic, nanotubes, nanorods and nanowires,
graphene-related materials, etc.) in LCs, and the formation of LCs by
anisotropic-shaped nanoparticles was presented. The possible areas of practical
applications of such materials were discussed.

Liquids 2023,3251
Table 1. Cont.
Materials, References Discussed Issues
Different nanoparticles in LCs [74]
The properties of LCs (electro-optical, alignment, viscosity, clearing point, elastic
properties etc
. . .
) doped with various kinds of nanoparticles (ferroelectric, noble
metallic, semiconductor, and carbon) were reviewed. The possible multifunctional
applications of such materials were discussed. The self-assembly of anisotropic
nanoparticles (rods, tubes, disks, flexible chains, and wires) into lyotropic LC
phases, and applications of such materials in various functional devices, biological
sensors, and drug delivery systems were also discussed.
Low-dimensional carbon allotropes in
LCs [75]
A topical review on the behavior of LC dispersions of carbon nanomaterials, such
as fullerenes, nanotubes, and graphene variants was presented. In particular, the
behavior of nematic and ferroelectric LCs doped with CNTs, dispersibility of
CNTs, and possible practical applications of such materials were discussed.
Different nanoparticles in LCs [76]
A general review on the behavior of LCs and LC polymers doped with
nanomaterials (metals, metal oxides, layered silicates, CNTs, graphene oxides,
graphene, etc.) was presented.
CNTs in LCs [77] A general review on different properties of LCs doped with CNTs was given.
Different nanoparticles in polymer-modified
LCs [22]
The book contains discussion of polymer-modified nanoparticle-laden LCs. In
particular, the properties of polymer-stabilized CNT-reinforced LCs
were discussed.
4.1. Thermotropic Liquid Crystals
In thermotropic LCs, anisotropic interactions between the CNTs and media can dras-
tically change the alignments and physical properties of the mixtures. In these systems,
the macroscopic organization resulting from mutual interactions between CNTs and LCs
can be very pronounced [
78
]. The great interest in such systems can be explained by a
variety of intriguing effects that can be of great practical importance. In LC electro-optical
cells doped with CNTs, the response times became shorter, and the driving voltage was
lowered. This was also accompanied by the suppression of image sticking and parasitic
backflow [
79
–
82
]. Various non-trivial effects were reported for LC + CNT composites,
such as super-elongation [
83
], electromechanical memory [
84
], ultra-low percolation thresh-
olds [
41
,
85
], electrokinetic dispersion [
86
], etc. One should especially note the electro-optical
memory effects [57].
Dielectric anisotropy of SWCNT–nematic LC (E7) composites in microwave range was
studied [
87
]. It was shown that the dielectric anisotropy can be increased; this is a promising
result for creating tunable dielectric materials. In recent works, the effects of ionic impurities
on properties of LC nano-colloids were intensively discussed [
88
–
90
]. The presence of
CNTs can significantly affect the behavior of ions in LCs [
62
]. Observed non-monotonous
behavior of electrical properties at different concentrations of nanoparticles was explained
by the peculiarities of the adsorption/desorption processes. It was demonstrated that the
adding of quantum dots (QDs) may generate the ionic contamination of the LC [
91
,
92
]. The
intriguing effects in the electro-physical properties and electro-optical responses in LC cells
doped with semiconductor QDs (CdSe/ZnS) have been reported [
91
,
92
]. The concentration
of QDs significantly affected the response and relaxation time. The effects of the application
of a unipolar rectangular electric field to an LC cell were also discussed.
4.1.1. Nematic Liquid Crystals
Thermotropic LCs have been frequently applied as suitable nematic hosts for the
alignment of nanotubes, and many of the previously reported works were devoted to
studies of the CNT–nematic LC dispersions. SWCNTs and MWCNTs dispersed in nematic
LCs 5CB (nematic range 24–35
◦
C), and E7 (nematic range
−
10 to +60
◦
C) demonstrated
the presence of orientational ordering in the nematic matrix [
48
]. It was shown that CNT
alignment results from orientational coupling to the nematic matrix. Spontaneous parallel
alignment of CNTs in LCs along the director with a high level of orientational order

Liquids 2023,3252
parameter (S
≈
0.9) was explained by elastic interactions (so-called anchoring forces) of
elongated particles with the nematic LC host [93,94].
The behavior of electrical conductivity as a function of the applied voltage for the
CNT–LC composites and their possible practical applications in electrically controlled
light-steered switches and wavelength-dependent sensors were discussed [
94
]. The effect
of MWCNTs on phase transitions of nematic LCs (E7) has been investigated by means
of polarizing optical microscopy and differential scanning calorimetry [
95
]. Observed
enhancement of the isotropic–nematic phase transition temperature in a very narrow
range of CNT concentration (0.1–0.2% wt) was attributed to anisotropic alignment of LC
molecules along the CN bundles. For LCs with a biphenyl molecular core structure, the
importance of
π
-stacking interactions between CNTs and LC molecules was justified using
polarized Raman spectroscopy [
96
,
97
]. The mutual self-organizational effects in CNT
and LC subsystems results in the manifestation of versatile properties of these functional
mixtures [98].
The mixtures of MWCNTs (0.01–0.15% wt) and nematic media with different signs of
dielectric anisotropy ZhK-1282 (
∆ε
> 0) and ZhK-440 (
∆ε
< 0) have been studied by means
of optical transmission and electric conductivity measurements [
99
–
101
]. The obtained data
suggested the existence of supra-molecular organization in the studied CNT–LC mixtures.
The presence of strong anisotropic interactions between CNTs and orientationally ordered
LC matrixes was supposed.
The joint orientationally ordered arrangements for
∆ε
> 0 and
∆ε
< 0 are schematically
shown in Figure 2. The nanotubes in an LC environment are shown as “cell”-forming
elements. Here, the orientation of “large” anisotropic particles is restricted by the ori-
entational order imposed by the nematic matrix, whereas these particles also perturb
the ordering inside matrix. The different supra-molecular organizations in orientation-
ally ordered
LC + CNTs
systems with different signs of
∆ε
reflect the diversity in strong
anisotropic interactions between components in these systems. This diversity results in
different properties of such composites. In particular, for a fixed concentration of MWCNTs,
the electrical conductivity in ZhK-1282 (
∆ε
> 0) was several times high than that in ZhK-440
(
∆ε
< 0) since, in the latter case, the LC environment does not favor NT orientation along
the electric field.
Liquids 2023, 3, FOR PEER REVIEW 8
Figure 2. Schematic illustration of the supra-molecular organization in CNT–LC mixtures for ne-
matic media with different signs of dielectric anisotropy Δε. Arrows correspond to the local pre-
ferred orientation of CNTs inside the LC host (based on the model discussed in [99]).
It has been shown that the optical transmission taken at a certain wavelength well
above the eventual absorption or selective reflection bands showed a dramatic increase at
the N–I transition. The magnitude of this “transmission jump” was substantially increased
in the presence of dispersed CNTs. This increase obviously reflected the effects of the spa-
tial organization of CNTs in the orientationally ordered nematic medium. In this respect,
the studied LC–CNT composites were essentially similar to the LC systems with non-
mesogenic dopants, which are generally considered homogeneous at the microscopic
level.
The behaviors of composites of MWCNTs (0.01–0.15% wt) in nematic hosts with die-
lectric anisotropy of different signs 5CB (Δε > 0), ZhK-1282 (Δε > 0) and ZhK-440 (Δε < 0),
1:1 MBBA + EBBA mixture (weakly negative Δε) have been compared [99,102]. The com-
plex electrical conductivity versus the applied voltage dependencies (Figure 3) in these
mixtures were explained by the different impact of an LC environment on the preferred
orientation of CNTs inside the hosts. The addition of CNT dopants improved the func-
tional properties of LC composites and resulted in an increasing threshold voltage and in
the suppression of electro-hydrodynamic instability in nematics.
Figure 2.
Schematic illustration of the supra-molecular organization in CNT–LC mixtures for nematic
media with different signs of dielectric anisotropy
∆ε
. Arrows correspond to the local preferred
orientation of CNTs inside the LC host (based on the model discussed in [99]).

Liquids 2023,3253
It has been shown that the optical transmission taken at a certain wavelength well
above the eventual absorption or selective reflection bands showed a dramatic increase at
the N–I transition. The magnitude of this “transmission jump” was substantially increased
in the presence of dispersed CNTs. This increase obviously reflected the effects of the spatial
organization of CNTs in the orientationally ordered nematic medium. In this respect, the
studied LC–CNT composites were essentially similar to the LC systems with non-mesogenic
dopants, which are generally considered homogeneous at the microscopic level.
The behaviors of composites of MWCNTs (0.01–0.15% wt) in nematic hosts with
dielectric anisotropy of different signs 5CB (
∆ε
> 0), ZhK-1282 (
∆ε
> 0) and ZhK-440
(
∆ε< 0
), 1:1 MBBA + EBBA mixture (weakly negative
∆ε
) have been compared [
99
,
102
].
The complex electrical conductivity versus the applied voltage dependencies (Figure 3)
in these mixtures were explained by the different impact of an LC environment on the
preferred orientation of CNTs inside the hosts. The addition of CNT dopants improved the
functional properties of LC composites and resulted in an increasing threshold voltage and
in the suppression of electro-hydrodynamic instability in nematics.
Liquids 2023, 3, FOR PEER REVIEW 9
Figure 3. Relative changes in electrical conductivity on application of DC voltage for MWCNTs in
different LCs at fixed concentration C = 0.01% wt (a) and in MBBA/EBBA LC mixtures at different
values of C (b). (Based on the experimental data presented in [102]).
With nematic LCs of other chemical classes, the transmission jump was similar to that
of cyanobiphenyls, while it was obviously less pronounced with that of cyclohexylcyclo-
hexanes [103], probably due to the absence of aromatic rings and, respectively, weaker
interactions with CNTs. It is also clear that the transmission jump becomes more pro-
nounced with higher concentration of CNTs, monotonously increasing from ~0.01% wt to
0.1% wt.
The phase transitions and intermolecular interactions in the CNT–LC (EBBA) com-
posites were experimentally studied by means of DSC and FTIR spectroscopy, measure-
ment of electrical conductivity, optical transmiance, and analysis of microstructure
[41,85,104]. The effect of a positive temperature coefficient was observed at CNT concen-
trations above 0.05–0.1% wt. Observed heating–cooling hysteretic behavior was explained
by strong agglomeration and rearrangement of nanotubes during the thermal incubation.
The time lag of the solidification process was shown to be dependent upon a supercooling
temperature in accordance with the classical heterogeneous nucleation law [41]. In this
process, the CNTs played the role of solidification centers in LC media. Observed nonlin-
ear dependences of electrical conductivity on the applied voltage and frequency were ex-
plained by the existence of the field-enhanced charge transport through hopping junctions
in the LC gaps between CNTs.
The CNT–LC composites studied in various papers were, in most cases, non-equilib-
rium systems because of the tendency of CNTs to aggregate. For CNT concentrations in
the 0.01–0.1% wt range, the composites represent a sort of “quasi-equilibrium” system.
For these systems, quite reasonable and seemingly reproducible results can only be ob-
tained for a sufficiently short time after the preparation of samples.
The effects of CNT aggregation on the optical transmission jump at the nematic-iso-
tropic transition were discussed [41] (Figure 4). The measurements were carried out just
after ultrasonication of CNTs in the nematic host and after certain periods of time. It was
shown that, at CNT concentrations of 0.05–0.1% wt, the transmission jump noticeably de-
creased after several hours of incubation. This can be explained by aggregation processes.
In subsequent studies, these experiments were repeated with different nematic matrices,
CNTs with different aspect ratios and concentrations, different temperatures, etc. [70,105–
108]. It can be argued that the proposed method could be used as a convenient way to
Figure 3.
Relative changes in electrical conductivity on application of DC voltage for MWCNTs in
different LCs at fixed concentration C = 0.01% wt (
a
) and in MBBA/EBBA LC mixtures at different
values of C(b). (Based on the experimental data presented in [102]).
With nematic LCs of other chemical classes, the transmission jump was similar to that
of cyanobiphenyls, while it was obviously less pronounced with that of cyclohexylcyclo-
hexanes [
103
], probably due to the absence of aromatic rings and, respectively, weaker
interactions with CNTs. It is also clear that the transmission jump becomes more pro-
nounced with higher concentration of CNTs, monotonously increasing from ~0.01% wt to
0.1% wt.
The phase transitions and intermolecular interactions in the CNT–LC (EBBA) compos-
ites were experimentally studied by means of DSC and FTIR spectroscopy, measurement
of electrical conductivity, optical transmittance, and analysis of microstructure [
41
,
85
,
104
].
The effect of a positive temperature coefficient was observed at CNT concentrations above
0.05–0.1% wt. Observed heating–cooling hysteretic behavior was explained by strong ag-
glomeration and rearrangement of nanotubes during the thermal incubation. The time lag
of the solidification process was shown to be dependent upon a supercooling temperature
in accordance with the classical heterogeneous nucleation law [
41
]. In this process, the
CNTs played the role of solidification centers in LC media. Observed nonlinear depen-
dences of electrical conductivity on the applied voltage and frequency were explained by

Liquids 2023,3254
the existence of the field-enhanced charge transport through hopping junctions in the LC
gaps between CNTs.
The CNT–LC composites studied in various papers were, in most cases, non-equilibrium
systems because of the tendency of CNTs to aggregate. For CNT concentrations in the
0.01–0.1% wt range, the composites represent a sort of “quasi-equilibrium” system. For
these systems, quite reasonable and seemingly reproducible results can only be obtained
for a sufficiently short time after the preparation of samples.
The effects of CNT aggregation on the optical transmission jump at the nematic-
isotropic transition were discussed [
41
] (Figure 4). The measurements were carried out
just after ultrasonication of CNTs in the nematic host and after certain periods of time.
It was shown that, at CNT concentrations of 0.05–0.1% wt, the transmission jump no-
ticeably decreased after several hours of incubation. This can be explained by aggre-
gation processes. In subsequent studies, these experiments were repeated with differ-
ent nematic matrices, CNTs with different aspect ratios and concentrations, different
temperatures, etc. [70,105–108]
. It can be argued that the proposed method could be used
as a convenient way to monitor the CNTs’ aggregation, thus allowing optimization of
CNT–LC systems as promising nanomaterials.
Liquids 2023, 3, FOR PEER REVIEW 10
monitor the CNTs’ aggregation, thus allowing optimization of CNT–LC systems as prom-
ising nanomaterials.
Figure 4. The “optical transmiance jumps” in MWCNTs + EBBA composites. The data are pre-
sented near the transition temperature from the nematic to isotropic phase (TNI = 352 K). Open and
closed symbols denote non-incubated and incubated (at 323 K for 8 h) samples, respectively. The
microphotographs were obtained for 0.1% wt composites. (Based on the experimental data pre-
sented in [41]).
The electro-optical responses in CNTs dispersed in different nematic LCs with posi-
tive (5CB) and negative (EBBA and MLC6608) dielectric anisotropy were investigated
[109–112]. The electro-optical memory effects have been discovered and described in de-
tail. In such LC systems placed between two crossed polarizers, the optical transmiance
of the suspension layer substantially increased after the application of an electric field,
and this state was very long-lasting (persisted over months). The observed effects were
most significant after the formation of an interconnected network of CNTs in LCs. The
memory effects were explained by the incomplete relaxation of LC molecules from a pla-
nar to an initial homeotropic state after the electric field switch-off.
Relationships between electro-optical responses, optical singularities, and electrical
conductivity behavior of mixtures of MWCNTs and nematic LC (5CB) have been dis-
cussed [113–117]. The self-organization of CNTs, formation of fractal aggregates, and
spanning CNT networks was accompanied by the generation of optical singularities. The
effects were explained by optical effects related to the formation of micron-sized per-
turbed interfacial LC shells covering the CNT clusters. The inversion wall topological
structures were observed for CNT–LC composites at threshold values of the applied field
in the vicinity of Freedericksz transition [116,117]. In particular, the effects of time incu-
bation on induced optical singularities, inversion walls, and electrophysical and thermo-
dynamic characteristics of CNT–LC (5CB) composites have been investigated [118]. The
different incubation stages included the initial stage of formation of loose aggregates of
CNTs, the formation of aggregates with ramified fractal borders, and the compactization
of aggregates.
The factors affecting the efficient dispersion of CNTs in thermotropic LCs and the
stability of these systems were discussed in detail [58,105,106,119–121]. The different
methods for characterizing equilibrium CNT–LC composite materials have been dis-
cussed and compared [120]. The formation of aggregates in mixtures of CNTs (0.025–1%
Figure 4.
The “optical transmittance jumps” in MWCNTs + EBBA composites. The data are pre-
sented near the transition temperature from the nematic to isotropic phase (T
NI
= 352 K). Open and
closed symbols denote non-incubated and incubated (at 323 K for 8 h) samples, respectively. The
microphotographs were obtained for 0.1% wt composites. (Based on the experimental data presented
in [41]).
The electro-optical responses in CNTs dispersed in different nematic LCs with positive
(5CB) and negative (EBBA and MLC6608) dielectric anisotropy were
investigated [109–112]
.
The electro-optical memory effects have been discovered and described in detail. In such LC
systems placed between two crossed polarizers, the optical transmittance of the suspension
layer substantially increased after the application of an electric field, and this state was
very long-lasting (persisted over months). The observed effects were most significant
after the formation of an interconnected network of CNTs in LCs. The memory effects
were explained by the incomplete relaxation of LC molecules from a planar to an initial
homeotropic state after the electric field switch-off.
Relationships between electro-optical responses, optical singularities, and electrical
conductivity behavior of mixtures of MWCNTs and nematic LC (5CB) have been dis-

Liquids 2023,3255
cussed [
113
–
117
]. The self-organization of CNTs, formation of fractal aggregates, and
spanning CNT networks was accompanied by the generation of optical singularities. The
effects were explained by optical effects related to the formation of micron-sized perturbed
interfacial LC shells covering the CNT clusters. The inversion wall topological structures
were observed for CNT–LC composites at threshold values of the applied field in the
vicinity of Freedericksz transition [
116
,
117
]. In particular, the effects of time incubation
on induced optical singularities, inversion walls, and electrophysical and thermodynamic
characteristics of CNT–LC (5CB) composites have been investigated [
118
]. The different
incubation stages included the initial stage of formation of loose aggregates of CNTs, the
formation of aggregates with ramified fractal borders, and the compactization of aggregates.
The factors affecting the efficient dispersion of CNTs in thermotropic LCs and the sta-
bility of these systems were discussed in detail [
58
,
105
,
106
,
119
–
121
]. The different methods
for characterizing equilibrium CNT–LC composite materials have been discussed and com-
pared [
120
]. The formation of aggregates in mixtures of CNTs (0.025–1% wt) in nematic LC
(5CB) during the aging (incubation) processes was monitored [
105
,
106
,
119
,
121
]. The obser-
vations included changes in microstructure, birefringent structure of LC cladding around
CNT aggregates and induced optical singularities, and measurements of the temperature
and concentration dependences of light transmissions, DSC, and electrical conductivity
patterns. In the initial state, after intensive homogenization via ultrasonication, the CNTs
were more or less homogeneously dispersed in the nematic matrix and aligned along the
nematic director. The time incubation (several hours or days) resulted in the formation
of micron-sized aggregates consisting of inner skeletons with trapped shells of adjacent
nematic molecules [
119
] (Figure 5). Light shells near the surface of MWCNT aggregates
initiated by the applied electric field have been explained by the strong anchoring of 5CB
molecules to the surface of MWCNTs [106].
Liquids 2023, 3, FOR PEER REVIEW 11
wt) in nematic LC (5CB) during the aging (incubation) processes was monitored
[105,106,119,121]. The observations included changes in microstructure, birefringent
structure of LC cladding around CNT aggregates and induced optical singularities, and
measurements of the temperature and concentration dependences of light transmissions,
DSC, and electrical conductivity paerns. In the initial state, after intensive homogeniza-
tion via ultrasonication, the CNTs were more or less homogeneously dispersed in the ne-
matic matrix and aligned along the nematic director. The time incubation (several hours
or days) resulted in the formation of micron-sized aggregates consisting of inner skeletons
with trapped shells of adjacent nematic molecules [119] (Figure 5). Light shells near the
surface of MWCNT aggregates initiated by the applied electric field have been explained
by the strong anchoring of 5CB molecules to the surface of MWCNTs [106].
Figure 5. A simplified model of the aging of CNTs dispersed in nematic LCs. The nanotubes are
initially dispersed homogeneously via intensive ultrasonication (a), and time incubation (several
hours or days) resulted in formation of ramified aggregates with trapped nematic shells incorpo-
rated into the CNT skeleton (b). (Reprinted with permission from Ref. [119]. Copyright 2011 Else-
vier).
Analysis of the voltage dependence on the relative integral intensity of images, I/Io,
(here, Io is the integral intensity at U = 0 V) showed the presence of a strong dependence
of the thickness of birefringent interfacial shells upon the applied voltage U (Figure 6).
The value of I/Io increased noticeably for voltages above some threshold value of Uth = 3–4
V because of the Freedericksz transition. The “fresh” composites also displayed a higher
saturation level of I/Io at large U > 8–10 V as compared with incubated composites. Ob-
served aging behavior was explained by the transition from loose aggregates (L-aggre-
gates) in the “fresh” composite to the compacted aggregates (C-aggregates) in the “incu-
bated” composite.
Figure 5.
A simplified model of the aging of CNTs dispersed in nematic LCs. The nanotubes are
initially dispersed homogeneously via intensive ultrasonication (
a
), and time incubation (several
hours or days) resulted in formation of ramified aggregates with trapped nematic shells incorporated
into the CNT skeleton (b). (Reprinted with permission from Ref. [119]. Copyright 2011 Elsevier).
Analysis of the voltage dependence on the relative integral intensity of images, I/I
o
,
(here, I
o
is the integral intensity at U= 0 V) showed the presence of a strong dependence of
the thickness of birefringent interfacial shells upon the applied voltage U(
Figure 6
). The
value of I/I
o
increased noticeably for voltages above some threshold value of
Uth = 3–4 V
be-
cause of the Freedericksz transition. The “fresh” composites also displayed a higher satura-
tion level of I/I
o
at large U> 8–10 V as compared with incubated composites. Observed aging
behavior was explained by the transition from loose aggregates (L-aggregates) in the “fresh”
composite to the compacted aggregates (C-aggregates) in the “incubated” composite.

Liquids 2023,3256
Liquids 2023, 3, FOR PEER REVIEW 12
Figure 6. Relative integral intensity of images, I/Io, as function of the applied voltage U. The data are
presented “fresh” or “incubated” (during 1 week) 5CB + MWCNT (0.1% wt) composites at temper-
ature 298 K. Microphotographs of the “fresh” composites at U = 0 V and 10 V are shown in the
inserts. (Based on the experimental data presented in [106]).
The values of I/Io increased noticeably for voltages above some threshold value of Uth
= 3–4 V (Freedericksz transition inside 5CB). At large voltages (U > 8–10 V), the saturation
level of I/Io was smaller for the “incubated” composites. It can reflect compactization of
the initially formed loose aggregates into the more compact aggregates during the incu-
bation time of one week [106].
The effects of applied electric fields on the alignment of CNTs in LCs have been in-
tensively discussed in many recent theoretical and experimental studies [122–131].
In particular, the structural changes in CNT–nematic LC (6CHBT) composites in ap-
plied electric and magnetic fields have been studied using the aenuation measurement
of surface acoustic wave (SAW) propagating techniques [125]. The studied CNTs were
MWCNT and magnetically functionalized MWCNT/Fe3O4 nanoparticles. The applied
acoustic method is useful for the characterization of elastic and viscous parameters of
composites near phase transitions. Obtained data evidence the presence of orientational
coupling between MWCNTs and LC molecules. The results show that the combination of
electric and magnetic fields can be used to control the orientation of LC molecules in
doped samples.
The dynamic behavior of CNT–nematic LC composites in the electric and magnetic
fields has been analyzed both theoretically and experimentally [124,127–131]. A theoreti-
cal model based on elastic continuum theory allowed the evaluation of the relaxation
times [124]. Experimental studies of CNT–nematic (5CB) composites revealed significant
effects of CNT doping on the relaxation time. The relaxation time was shorter when the
field was switched off immediately after application and longer when the field was ap-
plied for at least one hour. Recently, the impact of dispersed CNTs on the Freedericksz
transition threshold was discussed [129].
Flexoelectric effects (appearance of electric polarization due to the strain gradient in
a dielectric material) in CNT–nematic LC composites have been evaluated using the
Helfrich theory for weak and hard anchoring conditions [123]. The calculations were per-
formed assuming the absence of aggregation of the CNTs in a nematic host. The flexoelec-
tric coefficients’ increase up to 5-fold was predicted near the phase transition temperature.
Figure 6.
Relative integral intensity of images, I/I
o
, as function of the applied voltage U. The data
are presented “fresh” or “incubated” (during 1 week) 5CB + MWCNT (0.1% wt) composites at
temperature 298 K. Microphotographs of the “fresh” composites at U= 0 V and 10 V are shown in the
inserts. (Based on the experimental data presented in [106]).
The values of I/I
o
increased noticeably for voltages above some threshold value of
Uth = 3–4 V
(Freedericksz transition inside 5CB). At large voltages (U> 8–10 V), the satura-
tion level of I/I
o
was smaller for the “incubated” composites. It can reflect compactization
of the initially formed loose aggregates into the more compact aggregates during the
incubation time of one week [106].
The effects of applied electric fields on the alignment of CNTs in LCs have been
intensively discussed in many recent theoretical and experimental studies [122–131].
In particular, the structural changes in CNT–nematic LC (6CHBT) composites in
applied electric and magnetic fields have been studied using the attenuation measurement
of surface acoustic wave (SAW) propagating techniques [
125
]. The studied CNTs were
MWCNT and magnetically functionalized MWCNT/Fe
3
O
4
nanoparticles. The applied
acoustic method is useful for the characterization of elastic and viscous parameters of
composites near phase transitions. Obtained data evidence the presence of orientational
coupling between MWCNTs and LC molecules. The results show that the combination
of electric and magnetic fields can be used to control the orientation of LC molecules in
doped samples.
The dynamic behavior of CNT–nematic LC composites in the electric and magnetic
fields has been analyzed both theoretically and experimentally [
124
,
127
–
131
]. A theoret-
ical model based on elastic continuum theory allowed the evaluation of the relaxation
times [
124
]. Experimental studies of CNT–nematic (5CB) composites revealed significant
effects of CNT doping on the relaxation time. The relaxation time was shorter when the
field was switched off immediately after application and longer when the field was applied
for at least one hour. Recently, the impact of dispersed CNTs on the Freedericksz transition
threshold was discussed [129].
Flexoelectric effects (appearance of electric polarization due to the strain gradient in a
dielectric material) in CNT–nematic LC composites have been evaluated using the Helfrich
theory for weak and hard anchoring conditions [
123
]. The calculations were performed
assuming the absence of aggregation of the CNTs in a nematic host. The flexoelectric
coefficients’ increase up to 5-fold was predicted near the phase transition temperature.

Liquids 2023,3257
For strong anchoring of nematogens over the surfaces of CNTs, the theory predicts
that the application of an electric field can change the phase behavior, and it influences the
ordering of both LC molecules and CNTs [
122
]. The effect of an electric field and LC media
on the alignment and order parameters of CNTs was examined analytically. The influence
of CNT aspect ratio (length-to-diameter ratio) on CNT and LC alignments have also been
analyzed [
126
]. The CNT and LC order parameters increased with the increasing of the
electric fields, and the electric field acted as a stimulus. It was demonstrated that the CNT
alignment can be improved and controlled by adjusting the LC anchoring strength.
Several experimental techniques (DSC, low-temperature photoluminescence, measure-
ment of electrical conductivity) were used to study low-temperature phase transformations
in CNT–LC (5CB) mixtures [
132
,
133
]. The introduction of CNTs resulted in partial elim-
ination of the low-temperature metastable states of 5CB, and several anomalies in the
temperature dependences of electrical conductivity were revealed. The effects were ex-
plained by the influence of phase transformations of 5CB in the interfacial layers on the
transport of charge carriers between CNTs [
132
]. The observed temperature transformation
of the luminescent and thermal properties of LC and CNT–LC mixtures in the temperature
interval 10–297 K were explained by the intra-crystalline transitions in 5CB medium [
133
].
The formation of interconnected percolation networks with ultra-low percolation
thresholds at some critical concentrations of CNTs (0.05–0.1% wt) was discussed in many
early works [
41
,
57
,
85
,
100
–
102
,
104
,
106
,
108
,
114
]. Note that the percolation behavior is a
complex phenomenon that can depend upon the degree of aggregation, shape of the mea-
suring cell, and distance between electrodes. The different regimes of electrical conductivity
behavior in CNT–LC composites (tunneling–hopping, percolation, and multiple-contacts)
placed between two electrodes have been revealed [
115
]. The different modes of sample
preparation in cells between two electrodes were used [
134
]. It was demonstrated that
typical capillary filling techniques may introduce some inaccuracies when the size of CNT
aggregates is comparable with the thickness of the cell. The more accurate filling technique
was based on pressing the drop of dispersion between two electrodes with a fixed distance
of 250
µ
m. The measured concentration dependencies of electrical conductivity clearly
revealed the two-step percolation transitions at concentrations 10
−4
% wt and 10
−1
% wt.
This behavior was explained using the mean-field theory, assuming a core–shell structure
of CNTs. Two types of cell geometries were used in studies of structural evolution and
dielectric properties of CNTs (10
−5
–2.5% wt) in nematic LC (5CB) mixtures. The two
sandwich-type cells with the electric field applied along (OP cells) and perpendicularly
(IP cells) to the LC layers were fabricated. The data revealed different stages of structural
evolution with the increasing of concentration of CNTs related to the dispersion of individ-
ual CNTs (at low concentrations, <3
×
10
−4
% wt), formation of branched aggregates with
non-compact structures (3
×
10
−4
–5
×
10
−3
% wt), percolation of non-compact aggregates
(5
×
10
−3
–10
−1
% wt), and formation of dense networks (>10
−1
% wt). Observed two-step
percolation thresholds at
≈
0.004% wt and
≈
0.5% wt were explained by the formation of
non-compact and dense CNT networks.
A similar two-step percolation behavior was observed for aggregating suspension of
CNTs in isotropic liquid (decane) [
135
]. A planar filtration-compression conductometric
cell was used for mechanical de-liquoring of the suspension. The first percolation threshold
was explained by the interpenetration of loose CNT aggregates, and the second one was
attributed to percolation across the compact conducting aggregates. The Monte Carlo
simulation-based core–shell structure particles also revealed the presence of two smoothed
percolation transitions though the shells and cores.
Comparative studies of optical transmission and dielectric properties of SWCNTs and
MWCNTs in nematic LC (5CB) were reported [
136
,
137
]. The studies revealed violations of
the Beer–Lambert–Bouguer (BLB) law both in cell thickness and concentration dependen-
cies. This is illustrated in Figure 7, where optical density Dversus the CNT concentration
in LC (5CB) is presented. In the isotropic phase (T= 310 K), the optical density changed
rather closely to the BLB law for both SWCNT- and MWCNT-doped systems. On the other

Liquids 2023,3258
hand, in the nematic phase (at T= 301 K), the obtained D(C) dependencies were nonlinear,
and this effect was more pronounced for SWCNTs.
Liquids 2023, 3, FOR PEER REVIEW 14
changed rather closely to the BLB law for both SWCNT- and MWCNT-doped systems. On
the other hand, in the nematic phase (at T = 301 K), the obtained D(C) dependencies were
nonlinear, and this effect was more pronounced for SWCNTs.
Figure 7. Optical density D versus the concentration of CNTs (SWCNTs and MWCNTs) in 5CB. The
data are shown for two different temperatures in the nematic (301 K) and isotropic (310 K). (Based
on the experimental data presented in [137]).
The quite different optical transmission behavior for SWCNTs and MWCNTs was
discussed, accounting for the differences in the specific surface area of CNT species, for-
mation of CNT coils, their aggregation, and perturbations of the nematic state inside the
coils [137]. This conclusion was confirmed by the data of Monte Carlo calculations for the
systems with different degrees of aggregation. The more detailed Monte Carlo studies of
optical transmission of anisotropic suspensions filled by aggregates of absorbing cylindri-
cal particles were also reported [138]. The deviations from the Beer–Lambert–Bouguer law
were analyzed for the systems with different aspect ratios (i.e., ratio of length and diame-
ter), aggregation degree, and order parameters.
Theoretical descriptions of CNT–LC composites have been also developed in many
works (for example, see [139–143]). In particular, different models proposed for the de-
scription of phase behavior, structural ordering, and alignment (para-nematic and ne-
matic) of CNTs in LC media have been reviewed. The phase behavior and orientational
properties were discussed as influenced by temperatures, volume fraction of CNTs, and
coupling strength.
4.1.2. Smectic Liquid Crystals
The behavior of CNT–smectic LC composites was discussed in many recent works.
A SWCNT thin plate was prepared using a smectic LC (40-hexyloxy-biphenyl-4-carbox-
ylic acid ethyl ester) template [144]. The induced structure in the CNT plate was aributed
to π–π stacking interactions in the hexagonal rings of the CNT wall and aromatic moieties
in the LC. The effects of MWCNTs on the phase transitions in smectic LC (8CB, octyl-
cyanobiphenyl) have been reported [145]. The observed effects were explained by the in-
teraction of CNTs with LC molecules and the elastic coupling between the CNTs and LC.
The electro-optical behavior of the MWCNTs and smectic LC (8S5, 4-n-pentylphenylthiol-
4′-n-octyloxybenzoate) mixture has been studied [146]. The CNTs with inherent surface
chirality were used. In these systems, a pronounced electroclinic effect (the tilt of the
Figure 7.
Optical density Dversus the concentration of CNTs (SWCNTs and MWCNTs) in 5CB. The
data are shown for two different temperatures in the nematic (301 K) and isotropic (310 K). (Based on
the experimental data presented in [137]).
The quite different optical transmission behavior for SWCNTs and MWCNTs was
discussed, accounting for the differences in the specific surface area of CNT species, for-
mation of CNT coils, their aggregation, and perturbations of the nematic state inside the
coils [
137
]. This conclusion was confirmed by the data of Monte Carlo calculations for the
systems with different degrees of aggregation. The more detailed Monte Carlo studies of
optical transmission of anisotropic suspensions filled by aggregates of absorbing cylindrical
particles were also reported [
138
]. The deviations from the Beer–Lambert–Bouguer law
were analyzed for the systems with different aspect ratios (i.e., ratio of length and diameter),
aggregation degree, and order parameters.
Theoretical descriptions of CNT–LC composites have been also developed in many
works (for example, see [
139
–
143
]). In particular, different models proposed for the de-
scription of phase behavior, structural ordering, and alignment (para-nematic and ne-
matic) of CNTs in LC media have been reviewed. The phase behavior and orientational
properties were discussed as influenced by temperatures, volume fraction of CNTs, and
coupling strength.
4.1.2. Smectic Liquid Crystals
The behavior of CNT–smectic LC composites was discussed in many recent works. A
SWCNT thin plate was prepared using a smectic LC (40-hexyloxy-biphenyl-4-carboxylic
acid ethyl ester) template [
144
]. The induced structure in the CNT plate was attributed to
π
–
π
stacking interactions in the hexagonal rings of the CNT wall and aromatic moieties
in the LC. The effects of MWCNTs on the phase transitions in smectic LC (8CB, octyl-
cyanobiphenyl) have been reported [
145
]. The observed effects were explained by the
interaction of CNTs with LC molecules and the elastic coupling between the CNTs and LC.
The electro-optical behavior of the MWCNTs and smectic LC (8S5, 4-n-pentylphenylthiol-
4
0
-n-octyloxybenzoate) mixture has been studied [
146
]. The CNTs with inherent surface
chirality were used. In these systems, a pronounced electroclinic effect (the tilt of the
optical axis of an LC in the plane perpendicular to an applied electric field) was observed.
The effect was explained by the interactions between the LC and the chiral surface of the

Liquids 2023,3259
CNTs. The phase transitions in MWCNTs and smectic LC (9OO4, alkoxyphenylbenzoate)
mixtures have been studied [
147
]. The impact of CNTs on phase transitions was discussed,
accounting for the LC–CNT surface coupling interactions. The properties of the smectic
C LCs (4,n-heptyloxybenzoic acid, 7OBA) on oriented SWCNTs were analyzed using
microtexture and polarized Raman spectroscopy [
148
]. The memorization strength of the
LC system was estimated, and it was explained by the trapping of LC bulk charges by
the CNTs.
The optical, thermodynamic, and microstructural properties and electrical conductivity
of MWCNTs and smectogenic LC (BBBA, 4-butoxybenzylidene-4
0
-butylaniline) composites
have been studied [
108
]. A fuzzy-type percolation behavior with multiple thresholds in
these composites was observed. The observed behavior was explained by the perturbations
of the BBBA mesogenic structure in the interfacial layers near the surface of CNT aggre-
gates. The electrical conductivity
σ
of MWCNT-BBBA dispersions versus the temperature
dependencies are shown in Figure 8[108].
Liquids 2023, 3, FOR PEER REVIEW 15
optical axis of an LC in the plane perpendicular to an applied electric field) was observed.
The effect was explained by the interactions between the LC and the chiral surface of the
CNTs. The phase transitions in MWCNTs and smectic LC (9OO4, alkoxyphenylbenzoate)
mixtures have been studied [147]. The impact of CNTs on phase transitions was discussed,
accounting for the LC–CNT surface coupling interactions. The properties of the smectic C
LCs (4,n-heptyloxybenzoic acid, 7OBA) on oriented SWCNTs were analyzed using micro-
texture and polarized Raman spectroscopy [148]. The memorization strength of the LC
system was estimated, and it was explained by the trapping of LC bulk charges by the
CNTs.
The optical, thermodynamic, and microstructural properties and electrical conduc-
tivity of MWCNTs and smectogenic LC (BBBA, 4-butoxybenzylidene-4′-butylaniline)
composites have been studied [108]. A fuzzy-type percolation behavior with multiple
thresholds in these composites was observed. The observed behavior was explained by
the perturbations of the BBBA mesogenic structure in the interfacial layers near the surface
of CNT aggregates. The electrical conductivity σ of MWCNT-BBBA dispersions versus the
temperature dependencies are shown in Figure 8 [108].
Figure 8. Electrical conductivity σ versus temperature T dependencies in MWCNT (0.05% wt)–LC
(BBBA) composites for multiple cycles of heating and cooling. (Based on the experimental data pre-
sented in [108]).
Such dependencies were obtained using multiple heating–cooling cycles. The σ(T)
plots gradually moved down in successive cycles. Near the isotropic-nematic transition
temperature, the step-like drop of σ became more clearly expressed. Thus, transition to a
more ordered phase was accompanied by the decrease in electric conductivity, which can
reflect the restricted mobility of ionic impurities and the effects of LC ordering on the
alignment of the dispersed CNTs. The effect of multiple heating–cooling cycles was ex-
plained by changes in the microstructure of the studied composites and transformations
from loose, spatially distributed aggregates to more compact and isolated aggregates.
The behavior of SWCNTs dispersed in mixtures of smectic LC (MHPOBC, 4′-Oc-
tyloxy-biphenyl-4-carboxylic acid 4-(1-methyl-heptyloxycarbonyl)-phenyl ester) and ne-
matic E7 was reported [78]. The MHPOBC has very complicated phase behavior and
demonstrates many smectic phases. The mixtures MHPOBC + E7 allowed for the improve-
ment of the CNT dispersion in higher-ordered smectic phases. The effects of carboxyl
Figure 8.
Electrical conductivity
σ
versus temperature T dependencies in MWCNT (0.05% wt)–LC
(BBBA) composites for multiple cycles of heating and cooling. (Based on the experimental data
presented in [108]).
Such dependencies were obtained using multiple heating–cooling cycles. The
σ
(T)
plots gradually moved down in successive cycles. Near the isotropic-nematic transition
temperature, the step-like drop of
σ
became more clearly expressed. Thus, transition to
a more ordered phase was accompanied by the decrease in electric conductivity, which
can reflect the restricted mobility of ionic impurities and the effects of LC ordering on
the alignment of the dispersed CNTs. The effect of multiple heating–cooling cycles was
explained by changes in the microstructure of the studied composites and transformations
from loose, spatially distributed aggregates to more compact and isolated aggregates.
The behavior of SWCNTs dispersed in mixtures of smectic LC (MHPOBC, 4
0
-Octyloxy-
biphenyl-4-carboxylic acid 4-(1-methyl-heptyloxycarbonyl)-phenyl ester) and nematic E7
was reported [
78
]. The MHPOBC has very complicated phase behavior and demonstrates
many smectic phases. The mixtures MHPOBC + E7 allowed for the improvement of
the CNT dispersion in higher-ordered smectic phases. The effects of carboxyl group
(
–COOH
) functionalized MWCNTs on physical properties (electro-optical, thermo-optical,
dielectric anisotropy, electrical conductivity anisotropy, threshold voltage, and rotational

Liquids 2023,3260
viscosity) of a highly polar smectic LC (8CB, octyl cyanobiphenyl) composite have been
studied [
149
]. Inclusion of CNTs substantially decreased phase transition temperatures,
affected the optical relaxation processes, and increased the rotational viscosity. The effects
were attributed to the strong elastic interaction between CNTs and 8CB molecules.
The dielectric, optical microscopy, elastic, and X-ray diffraction studies of SWCNTs and
smectic LCs (a mixture of the hexyloxy (6OCB)- and octyloxy-(8OCB) cyanobiphenyl) have
been performed [
150
,
151
]. The doping a small of amount of CNTs led to self-assembly of the
layered smectic phase. The introduction of CNTs significantly enriched the phase diagram
and enhanced the thermal range of the layered smectic phase. The
MWCNT–smectic
LC
(8CB, octylcyanobiphenyl) composites have been studied using high-resolution optical
birefringence measurements [
152
]. Inclusion of CNTs substantially decreased both the Ne-I
and the Ne-Sm A transition temperatures. However, the nature of the nematic and smectic
fluctuations remained essentially bulk-like for the studied composites.
SWCNT—smectic A (4-nitrophenyl-4
0
-decyloxybenzoic acid) composites have been
studied using dielectric techniques [
153
]. Observed decreases in the order parameter and
clearing temperature were explained by the inclusion of a part of the SWCNTs into the gap
between the smectic layers. The changes in electrical conductivity were attributed to the
percolation effect and the predominance of the hopping electronic conductivity over the
ionic one.
4.1.3. Cholesteric Liquid Crystals
One of the first studies of MWCNT–cholesteric LC (CLC) composites involved three
cholesteric mixtures: (1) an induced cholesteric mixture (70% wt of nematic ZhK-1282 and
30% wt of chiral dopant CB-15); (2) a mixture of steroid cholesterics (80% wt of cholesteryl
oleyl carbonate and 20% wt of cholesteryl chloride, COC/CC); and (3) a cholesterol ester
mixture exhibiting helix unwinding at temperatures close to cholesteric-smectic A phase
transition (60% wt of cholesteryl nonanoate, 20% wt of cholesteryl caprynate and 20% wt
of cholesteryl caprylate) [
103
]. With the first two types, no noticeable effects of MWCNTs
on the selective reflection spectra were observed. For the third type, changes in helical
pitch were noted, which were related to suppression of the smectic phase. The optical
transmission above the selective reflection band sharply increased at the temperature of
isotropic phase transition in a similar way as that in nematics, and the “transmission jump”
was substantially smaller with non-aromatic cholesterol esters as compared with systems
with chiral dopants. Similar behavior was also noted in [
154
], where changes in helical
pitch were attributed to the effects of CNTs on the mesophase temperature range. The
addition of chiral dopants to the nematic matrix improved the stability of CNT dispersions.
The temperature dependencies of selective reflection spectra in MWCNT-COC/CC
(4(COC)/1(CC)), and MWCNT-COC/CC + 5CB) cholesteric mixtures were also com-
pared [
155
]. In these studies, the pure cholesteric with ratio Ch = COC/CC = 4/1 and
the cholesteric–nematic mixture with ratio Ch/5CB = 7/3 were used. Figure 9presents
examples of selective reflection spectra for undoped and doped mixtures (a) and tempera-
ture dependencies of the wavelength of selective reflection maximum
λm
(b). For the pure
cholesteric mixture with ratio Ch = COC/CC = 4/1, the temperature T= 308 K was rather
close to the transition temperature into the isotropic phase (T
i≈
313 K). The data evidenced
that the incorporation of MWCNTs resulted in lowering the optical transmission and bor-
dering of the selective reflection peaks. Moreover, at lower temperature
T= 303 K
, the peak
became even more smeared and two separate peaks appeared. This can be explained by
the effects on nanotubes on helical arrangement in the host.
Analysis of temperature dependencies of the selective reflection maximums
λmax
for
both MWCNT–Ch and MWCNT–Ch/5CB cholesteric mixtures evidenced that the intro-
duction of nanotubes resulted in increasing values of
λm
, but the transition temperatures
into the isotropic phase were practically unaffected (Figure 9b).

Liquids 2023,3261
Liquids 2023, 3, FOR PEER REVIEW 17
Figure 9. Examples of selective reflection spectra undoped and doped pure cholesteric Ch(COC/CC)
mixtures (a) and temperature dependencies of the wavelength of the selective reflection maximum
λm for MWCNT–Ch (pure cholesteric), and MWCNT–Ch/5CB (cholesteric/nematic) mixtures (b).
The concentration of MWCNTs in doped mixtures was C = 0.1% wt. (Based on the experimental data
presented in [155]).
Analysis of temperature dependencies of the selective reflection maximums λmax for
both MWCNT–Ch and MWCNT–Ch/5CB cholesteric mixtures evidenced that the intro-
duction of nanotubes resulted in increasing values of λm, but the transition temperatures
into the isotropic phase were practically unaffected (Figure 9b).
The slower aggregation of MWCNTs in cholesteric matrices as compared with that
in nematic matrices was explained by the higher effective viscosity of cholesterics [155]. A
similar stabilizing effect of helical twisting, explained by the suppression of CNT aggre-
gate formation in helically twisted quasi-nematic layers, was noted in [107]. Minor effects
of CNTs on helical twisting in cholesteric mixtures were also noted in [156]. Several inter-
esting works can be noted where carbon nanotubes possessing intrinsic chirality could
induce weak but observable helical twisting in nematic matrices [157,158].
The optical and electro-optical properties, microstructure, phase transitions, and
electrical conductivity behavior of MWCNTs dispersed in the nematic 5CB (“bad” sol-
vent), cholesteryl oleyl carbonate, COC (“good” solvent), and their mixtures have been
studied [159]. Here, the terms “good” and “bad “ refer to the high and low solubility in
terms of the Hansen solubility parameters [160]. The 5CB and COC LC solvents have close
temperatures of the transitions to the isotropic state (Ti = 308–309 K for 5CB and Ti ≈ 309
K for COC) and different temperatures of solid-LC transitions (Ts ≈ 296 K for 5CB and Ts
< 273 K for COC). The pronounced agglomeration of CNTs was observed in nematic 5CB
(“bad” solvent), and the high-quality dispersion, exfoliation, and stabilization of the CNTs
were observed in COC solvent (“good” solvent). The similar agglomeration behavior was
also observed for MWCNT dispersions in 1-cyclohexyl-2-pyrrolidone (“good” solvent)
and in water (“bad” solvent) [161].
Figure 10 presents electrical conductivity heating–cooling hysteresis loops for
MWCNTs (0.1% wt) in pure 5CB and in COC/5CB = 3/1 mixture. The significant changes
in electrical conductivity in these LC solvents, effects of thermal pre-history, and hyster-
etic behaviors were observed. Such effects were explained by possible strengthening of
electric contacts between adjacent nanotubes due to intense Brownian motion in the high-
temperature isotropic phase. The 5CB-COC mixtures were found to be promising for fine
regulation of chiral and electro-physical properties of CNT–LC composites.
Figure 9.
Examples of selective reflection spectra undoped and doped pure cholesteric Ch(COC/CC)
mixtures (
a
) and temperature dependencies of the wavelength of the selective reflection maximum
λm
for MWCNT–Ch (pure cholesteric), and MWCNT–Ch/5CB (cholesteric/nematic) mixtures (
b
).
The concentration of MWCNTs in doped mixtures was C= 0.1% wt. (Based on the experimental data
presented in [155]).
The slower aggregation of MWCNTs in cholesteric matrices as compared with that in
nematic matrices was explained by the higher effective viscosity of cholesterics [
155
]. A
similar stabilizing effect of helical twisting, explained by the suppression of CNT aggregate
formation in helically twisted quasi-nematic layers, was noted in [
107
]. Minor effects of
CNTs on helical twisting in cholesteric mixtures were also noted in [
156
]. Several interesting
works can be noted where carbon nanotubes possessing intrinsic chirality could induce
weak but observable helical twisting in nematic matrices [157,158].
The optical and electro-optical properties, microstructure, phase transitions, and elec-
trical conductivity behavior of MWCNTs dispersed in the nematic 5CB (“bad” solvent),
cholesteryl oleyl carbonate, COC (“good” solvent), and their mixtures have been stud-
ied [
159
]. Here, the terms “good” and “bad “ refer to the high and low solubility in terms
of the Hansen solubility parameters [
160
]. The 5CB and COC LC solvents have close tem-
peratures of the transitions to the isotropic state (T
i
= 308–309 K for 5CB and
Ti≈309 K
for
COC) and different temperatures of solid-LC transitions (T
s≈
296 K for 5CB and
Ts< 273 K
for COC). The pronounced agglomeration of CNTs was observed in nematic 5CB (“bad”
solvent), and the high-quality dispersion, exfoliation, and stabilization of the CNTs were
observed in COC solvent (“good” solvent). The similar agglomeration behavior was also
observed for MWCNT dispersions in 1-cyclohexyl-2-pyrrolidone (“good” solvent) and in
water (“bad” solvent) [161].
Figure 10 presents electrical conductivity heating–cooling hysteresis loops for MWC-
NTs (0.1% wt) in pure 5CB and in COC/5CB = 3/1 mixture. The significant changes
in electrical conductivity in these LC solvents, effects of thermal pre-history, and hys-
teretic behaviors were observed. Such effects were explained by possible strengthening
of electric contacts between adjacent nanotubes due to intense Brownian motion in the
high-temperature isotropic phase. The 5CB-COC mixtures were found to be promising for
fine regulation of chiral and electro-physical properties of CNT–LC composites.

Liquids 2023,3262
Liquids 2023, 3, FOR PEER REVIEW 18
Figure 10. Electrical conductivity σ versus the temperature T for heating–cooling cycles for MWCNT
(0.1% wt)–CL (5CB and COC/5CB = 3/1) composites. Here, Ti ≈ 309 K is temperature of the transitions
to the isotropic state (for both the 5CB and COC) and Ts ≈ 296 K is the temperature of solid-LC
transition for 5CB. (Based on the experimental data presented in [159]).
As the use of CLC for vapor detection is one of their promising practical applications,
it was natural to increase the sensitivity and selectivity of such sensor materials by doping
cholesteric mixtures with CNTs [162–164]. A promising way to create an efficient gas sen-
sor with a wide dynamic range on the base of cholesteric mixtures doped with CNTs was
discussed [162]. Incorporation of CNT networks into the helically twisted cholesteric
structure ensured a strong response to the absorbed gas molecules, with optical and elec-
trical properties showing easily recordable changes in low and high gas concentration
range, respectively.
The presence of strong interactions between CNTs and LC director nematic E7 with
ZLI-811 chiral dopant was clearly evidenced [165]. The doping resulted in considerable
changes in the electrical conductivity and dielectric properties of composites. The effects
of CNT doping on viscoelastic and rheological properties of cholesterics have been also
discussed [166–168], which are related to the potential application of cholesterics as lubri-
cants.
CNT–cholesteric LC composites displayed interesting non-linear and even non-mo-
notonous dependences of optical density versus CNT concentration, with a minimum ob-
served at a certain point [136,169,170]. Such behavior was observed only in the presence
of chiral components—with the same nematics and without chiral dopants, these depend-
ences are close to linearity. An explanation could be based either on the formation of CNT
aggregates of stacking type, or by preferential positioning of the dispersed CNTs at topo-
logical defects of the cholesteric texture. A similar study was carried out in [171], where
carbon nanotubes were added to cholesteryl nonanoate; however, since the authors used
only two discrete concentrations of CNTs, they could not notice anything particular.
The optical density, microstructure, and electrical conductivity in SWCNT cholesteric
(the mixtures of ZhK440, 5CB with chiral M5) composites have been studied [169]. The
optical density as a function of CNT concentration was not only non-linear, but non-mo-
notonous, with pronounced extremums on the D(Cn) plots. Several tentative explanations
were proposed for such unusual behavior, including the formation of stacking-type CNT
aggregates, interaction between cholesteric structural defects (oily streaks) and CNT net-
works, localization of nanotubes on the defects, etc. Since the azoxy nematic ZhK-440 can
Figure 10.
Electrical conductivity
σ
versus the temperature Tfor heating–cooling cycles for MWCNT
(0.1% wt)–CL (5CB and COC/5CB = 3/1) composites. Here, T
i≈
309 K is temperature of the
transitions to the isotropic state (for both the 5CB and COC) and T
s≈
296 K is the temperature of
solid-LC transition for 5CB. (Based on the experimental data presented in [159]).
As the use of CLC for vapor detection is one of their promising practical applications,
it was natural to increase the sensitivity and selectivity of such sensor materials by doping
cholesteric mixtures with CNTs [
162
–
164
]. A promising way to create an efficient gas
sensor with a wide dynamic range on the base of cholesteric mixtures doped with CNTs
was discussed [
162
]. Incorporation of CNT networks into the helically twisted cholesteric
structure ensured a strong response to the absorbed gas molecules, with optical and
electrical properties showing easily recordable changes in low and high gas concentration
range, respectively.
The presence of strong interactions between CNTs and LC director nematic E7 with
ZLI-811 chiral dopant was clearly evidenced [
165
]. The doping resulted in considerable
changes in the electrical conductivity and dielectric properties of composites. The effects of
CNT doping on viscoelastic and rheological properties of cholesterics have been also dis-
cussed [
166
–
168
], which are related to the potential application of cholesterics as lubricants.
CNT–cholesteric LC composites displayed interesting non-linear and even non-monotonous
dependences of optical density versus CNT concentration, with a minimum observed at
a certain point [
136
,
169
,
170
]. Such behavior was observed only in the presence of chiral
components—with the same nematics and without chiral dopants, these dependences are
close to linearity. An explanation could be based either on the formation of CNT aggregates
of stacking type, or by preferential positioning of the dispersed CNTs at topological defects
of the cholesteric texture. A similar study was carried out in [
171
], where carbon nanotubes
were added to cholesteryl nonanoate; however, since the authors used only two discrete
concentrations of CNTs, they could not notice anything particular.
The optical density, microstructure, and electrical conductivity in SWCNT cholesteric
(the mixtures of ZhK440, 5CB with chiral M5) composites have been studied [
169
]. The
optical density as a function of CNT concentration was not only non-linear, but non-
monotonous, with pronounced extremums on the D(C
n
) plots. Several tentative explana-
tions were proposed for such unusual behavior, including the formation of stacking-type
CNT aggregates, interaction between cholesteric structural defects (oily streaks) and CNT
networks, localization of nanotubes on the defects, etc. Since the azoxy nematic ZhK-440 can
reversibly change its molecular conformation under UV irradiation, the radiation-induced
effects in such systems were also studied.

Liquids 2023,3263
The various memory effects considered promising for electro-optical applications
have been reported [
172
], with various subsequent developments [
173
,
174
]. Further efforts
showed the ways for various CLC-based materials, where doping with CNT allowed
temperature- and irradiation-induced writing and erasing effects [
175
]. Carbon nanotubes
were also reported to stabilize the “blue phase” as a promising phase state observed in
cholesterics close to the isotropic transition [
176
]. Additionally, just to be mentioned—there
are several reports of CNTs in more exotic media possessing cholesteric-like structures of
molecular arrangements, such as DNA [177] or cellulose LCs [178].
4.1.4. Ferro- and Antiferroelectric Liquid Crystals
Ferroelectric LCs have been receiving scientific attention for about fifty years, starting
from the discovery of the ferroelectric chiral smectic phases [
179
]. Ferroelectricity reflects a
spontaneous electric polarization of LC material which can be reversed by the application
of an electric field [
180
,
181
]. In these materials, the dipoles all point in the same direction.
In contrast, in anti-ferroelectric LC materials, the adjacent dipoles are oriented in oppo-
site (anti-parallel) directions. These LC materials can exhibit distinctive ferroelectric or
anti-ferroelectric, dielectric, and electro-optical properties, the presence of spontaneous
polarization, a high contrast ratio, and excellent switching characteristics. Such materials
have shown a wide area of application for improved quality of LC display, and they were
found to be useful for applications in fast-switching, low power consumption, in high
resolution and high contrast devices, spatial light modulators, holographic storage, and
other photonic devices [182].
Intensive studies of such LC materials doped with CNTs were started approximately
15 years ago. In particular, the compositions of SWCNTs with anti-ferroelectric chiral
smectic LCs have been studied [
183
]. In these experiments, CNTs were introduced in
the nematic LC and then mixed with an anti-ferroelectric chiral smectic compound. The
doping at very small concentrations of CNTs (0.002% wt) in the phase sequence significantly
affected the phase sequence of the studied LC systems.
The dielectric and electro-optical properties of different ferroelectric LC materials
doped with CNTs have been studied in many works. The fastening of the electro-optical
switching response in ferroelectric LC (LAHS7) due to the trapping of ions by CNTs
was observed [
184
–
187
]. For MWCNTs in LC mixtures (LAHS7) with SmC* and SmC*
phases, the significant changes in the performance of the LC cells were explained by the
trapping of ions through the CNTs [
184
]. The doping with MWCNTs greatly affected the
performance of cells, and significant changes in the spontaneous polarization, rise time,
and dielectric permittivity were observed [
185
]. The effects were explained by the impact of
CNTs on the screening and trapping of the ionic impurities. The fastness of the response in
MWCNT–deformed
helix ferroelectric LC composites has been attributed to the decrease in
rotational viscosity and increase in anchoring energy [
186
]. A substantial difference in tilt
angles of pure and doped samples below a certain threshold voltage of around 2 V and the
increase in conductance in doped cells were also observed. The dielectric and electro-optical
properties in mixtures of chiral SWCNT ferroelectric LC (eutectic multi-component mixture
LAHS2, LNTS1, and LNTS2) have been studied. The different properties (electro-optical
response, spontaneous polarization, rotational viscosity, dielectric permittivity, dielectric
loss factor, and electrical conductivity) of MWCNT–ferroelectric LC (LAHS 18) composites
have been studied [
187
]. Non-zero spontaneous polarization in the para-electric phase has
been attributed to the effects of surface anchoring and ionic impurities.
Dielectrical, electro-optical, and thermo-optical studies of MWCNT–LC mixtures (ZLI-
3654 and KCFLC10R) were performed [
82
,
188
]. A reduction in permittivity and electrical
conductivity with increasing MWCNT concentrations was reported. Improvements in
electro-optical responses, increased contrast ratio, and low threshold voltage in doped cells
were also observed. The increase in spontaneous polarization and decrease in response
time was explained by changes in ionic concentration in doped samples.

Liquids 2023,3264
The changes in dielectric and electro-optic responses in MWCNT–ferroelectric LC com-
posites were reported [
189
,
190
]. A switchable grating based on chiral SWCNT–ferroelectric
LC (Felix 17/100) composites was studied [
191
]. It was assumed that the decrease in ferro-
electric domain periodicity and optical activity of the SWCNTs could explain the observed
increases in diffraction efficiency.
In series of works the dielectric and electro-optical properties of SWCNT–ferroelectric
LC (Felix 17–100, 16–100) composites were studied [
192
–
194
]. The comparative studies
of spontaneous polarization, response time, rotational viscosity, dielectric permittivity,
and loss factor allowed the explanation of observed effects by the presence of strong
π
–
π
electron stacking between SWCNT and LC molecules. The dielectric and electro-optical
properties of MWCNT–ferroelectric LC composites were also discussed [
195
–
197
]. The
effects of cell thickness and anchoring energy on bistability were also discussed. Observed
changes were explained by the strong coupling between the MWCNTs and LC molecules
(the strong
π
–
π
interactions), and changes in anchoring energy, rotational viscosity, and
charge transfer mechanism. In particular, the effect of applied voltage on the mesomorphic
and electro-optical behavior has been established [
197
]. The doping with CNTs (0.03% wt)
strongly affected the optical contrast, birefringence, transmission and contrast ratio, led to
the generation of new colors, and effectively reduced the driving voltage. The fastening of
the switching time was also detected.
Effects of the alignment of SWCNTs with ferroelectric LC (3M2CPNOB) have been
studied using SEM, FTIR, and Raman spectroscopy techniques [
198
]. The SEM images
have shown the presence of good alignment of SWCNTs along the LC smectic layers. The
studies also evidenced the presence of charge transfer processes and strong
π−π
stacking
interactions between CNTs and aromatic rings of the LC molecules.
The effect of MWCNTs on the dielectric properties of a short pitch and high sponta-
neous polarization deformed helix ferroelectric LC mixture (DHFLC) in different chiral
phases (SmC*, SmA*) has been studied [
199
]. Observed changes were attributed to the
increase in elastic constant and dilution of chiral content.
The dielectric and electro-optical properties of MWCNT–ferroelectric LC (LAHS 22)
mixtures have been studied [
200
]. The native and gold-decorated nanoparticles were used
for doping. The effects of decoration on improvement in the dielectric and electro-optical
properties were discussed. The decoration also changed the phase transition temperature
(ferro to para) of LAHS 22.
The dielectric spectra MWCNT–ferroelectric LC (KCFLC10S) mixtures at different
bias voltages have been studied [
201
]. The observed distortion in the Cole–Cole plots
was explained by the overlapping of Goldstone and low-frequency relaxation modes. The
doping of mixtures by MWCNTs enhanced the effect of the bias.
The changes in dielectric properties (dielectric permittivity, strength, and conductivity)
in CNT–ferroelectric LC (KCFLC10R) systems was discussed [
202
]. Microstructure and
dielectric studies of MWCNT–ferroelectric LC ((S-(-)-4-(2-n-hexylpropionyloxy) biphenyl-
4
0
-(3-methyl-4-decyloxy) benzoate) mixtures have been studied [
203
]. In order to increase
the stability of MWCNTs in the LC medium, they were functionalized with carboxyl groups
(–COOH). The dielectric permittivity of the ferroelectric phase was enhanced with the
addition of MWCNTs. In another work, the effect of the functionalization of MWCNTs
(with –COOH, –OH, and –NH
2
groups) on dielectric, electro-optical, and photolumines-
cence properties of ferroelectric LC (LAHS-IN) composites has been studied [
204
]. A
strong dependence of the studied properties on the functional groups of MWCNTs was
observed. Fictionalization resulted in remarkable modification of the dielectric properties
and enhancement of the photoluminescence intensity.
The dielectric and electro-optic MWCNT–ferroelectric LC (Felix M4851/050) mixtures
have been studied at different MWCNT concentrations (0.005–0.04% wt) [
205
]. The be-
haviors of the tilt angle, spontaneous polarization, response time, and Goldstone mode
relaxation strength and frequency were attributed to a possible dipole moment due to the
presence of the MWCNTs and increase in rotational viscosity.

Liquids 2023,3265
The impact of different methods of MWCNT–antiferroelectric LC (MHPOBC) mixture
preparation on phase behavior has been studied [
206
]. In first method, the MWCNTs were
initially dispersed in nematic E7 and then mixed with MHPOBC, and in the second method
the dry MWCNT powder was dispersed directly in MHPOBC. The preparation method
affected the clearing transition, which was explained by differences in the dispersion and
aggregation of MWCNTs.
The microstructure, dielectric, and electro-optical properties of MWCNT–ferroelectric
(W206E) LC mixtures have been studied [
207
]. The optical micrographs revealed some
topological defects. The doping resulted in a decrease in the spontaneous polarization,
dielectric permittivity, and conductivity. These decrements were attributed to the trapping
of mobile ion MWCNTs.
The dielectric and electro-optical properties of MWCNT–high tilt anti-ferroelectric LC
(DM1) composites were studied [
208
]. The doping affected the transition temperatures (the
stability of SmA* and SmC* phases increased, whereas that of the SmCA* phase decreased).
The changes in different properties (pitch of the helicoidal structure, absorption strength
and critical frequency of the anti-phase antiferroelectric mode, and switching time) were
discussed and explained. In particular, the decrease in response time in the doped system
was attributed to the decrease in the rotational viscosity.
The theoretical description of the CNTs on the structure of ferroelectric and antiferro-
electric LC mixtures was provided on the base of a combination of Flory-Huggins theory
and Landau theory [
209
,
210
]. In particular, the changes in polarization, tilt angle and
dielectric susceptibility, and transition temperature with the increase in the concentration
of CNTs were discussed.
Structural, thermal, optical, and electrical properties in MWCNT–hydrogen bonded
ferroelectric LC (cholesteryl stearate and 4-dodecyloxybenzoic acid) mixtures have been
studied [
211
]. The effect of optical modulation in doped mixtures was observed. It was
assumed that the introduction of MWCNTs in these LC mixtures can substantially improve
the characteristics relevant to possible applications of these composites. Recently, the effects
of doping with SWCNTs and MWCNTs of fluorinated ferroelectric LC mixtures have been
studied [
212
]. The differences observed for SWCNTs and MWCNTs were explained by the
different dimensions and surface area of the nanotubes. It was concluded that the trapping
of the mobile ions by CNTs can minimize many negative effects such as high switching time,
high operating voltage, image sticking, image flickering, and non-uniformity of the images.
4.1.5. Discotic Liquid Crystals
Discotic LCs represent mesophases formed from the disc-shaped molecules. These
mesophases are commonly called columnar phases. The composites on the base of acid-
purified SWNTs dispersed in columnar LC (triphenylene-based) have been studied [
213
].
The SWCNTs were chemically functionalized by hexaalkoxytriphenylene mesogens; good
integration of SWCNTs into the columnar matrix occupying the space between the disc
columns was confirmed. In other work from the same group, the octadecylamine (ODA)-
functionalized SWCNTs were also used to prepare dispersions in columnar phases of
triphenylene- and rufigallol-based discotic monomers and polymers [
214
]. Mesophase
behavior of these composites was studied using polarizing optical microscopy, DSC, and
X-ray diffractometric methods. The doping resulted in a decrease in the isotropic transition
temperature. The well-dispersed composites of SWCNTs in imidazolium ion-appended
LC triphenylene derivatives have been prepared [
215
]. It was demonstrated that in such
composites, the shear-induced orientation of SWCNTs may be maintained for a very long
time (more than half a year). The structure and properties of different CNT–discotic LC
composites and their possible practical applications were recently reviewed [216,217].
4.2. Lyotropic Liquid Crystals
In many works, lyotropic LCs have been also used as solvents for the alignment
of CNTs [
37
]. Integration of nanoparticle guests inside lyotropic LCs may be defined

Liquids 2023,3266
by the sort of nanoparticles, details of the interactions between nanoparticles and LC
molecules, and the concentration of components and temperature. The incorporation
of CNTs in different lyotropic LC hosts has been intensively discussed for two decades.
The structure of SWCNT–lyotropic (Triton X-100/water) mixtures was studied using light
microscopy and small-angle X-ray scattering techniques [
218
]. The experimental data
provided evidence of the integration of SWNTs within the cylinders of the hexagonal
LCs and on the alignment of SWCNTs along the LC director. Similar trends in SWCNT
concentration depending on the supramolecular (d-spacing) and macroscopic (viscosity)
properties were observed. Similar findings have been reported for MWCNT–lyotropic
(ethylammonium nitrate/water) mixtures [
219
]. The MWCNTs were well-dispersed and
integrated within the cylinders of the hexagonal LCs. The studied composites demonstrated
special tribological behavior. The spontaneous alignment of SWCNTs along the director
in lyotropic (sodium dodecyl sulfate (SDS)/water) LC mixtures was verified by means of
resonant Raman spectroscopy [220–222].
Spontaneous alignment of SWCNTs in more complex lyotropic hosts, combining
cationic and anionic surfactants in a hexagonal columnar LC phase, was studied [
223
].
The applied two-step preparation procedure includes initial dispersion of nanotubes in a
low-concentration solution of anionic surfactant followed by the formation of the LC phase
with the addition of cationic surfactant. This approach allowed achieving heavily loaded
systems with controlled orientation of nanotubes. The possibility of fractionalization of the
SWCNTs according their chirality on the base of the proposed approach was mentioned.
Later on, the same group incorporated the SWCNT suspension prepared below the Krafft
temperature into a very low-surfactant concentration lyotropic host formed by charge
combination of cationic and anionic surfactants [
224
] (see [
225
] for more discussion of
this technique).
Phase behavior and shear alignment in SWNT–surfactant (cetyltrimethylammonium
bromide, CTAB) aqueous mixtures have been studied using small-angle X-ray scattering
and cryogenic transmission electron microscopy techniques [
226
]. At high CTAB concen-
trations, the SWCNTs were integrated into the ordered lyotropic LCs while preserving
the native d-spacing in the LC phase. The mechanism of carbon nanotubes’ incorporation
in lyotropic LCs has been discussed [
227
–
229
]. The percolation-like transition to aligned
and quasi-infinite micelles stabilized by chains of nanotubes and the filament formation
triggered by nanotubes were supposed.
The technique of incorporation of SWCNTs into lyotropic LCs is via phase separation
in the presence of polyelectrolytes [
230
]. The lyotropic phases of anionic surfactant sodium
dodecyl sulfate (SDS) in the presence of an anionic polyelectrolyte poly(sodium styrene-
sulfonate) (PSS) and of cationic surfactant cetyltrimethylammonium bromide (CTAB) in
the presence of a cationic polyelectrolyte poly(diallydimethylammonium chloride) (PDAD-
MAC) were studied using polarized optical microscopy and small-angle X-ray scattering
techniques. The SWCNTs were well-dispersed in the lyotropic LCs, and the obtained
SWCNTs/LLC hybrids showed considerable thermal stability. A similar approach was
applied for the incorporation of SWCNTs into lyotropic LCs, which formed n-dodecyl
octaoxyethene monoether (C
12
E
6
) via separation in the presence of a hydrophilic polymer
poly(ethylene glycol) (PEG). In these systems, by varying the ratio of PEG to C
12
E
6
, the
transition from hexagonal phase to lamellar phase was observed. Th proposed approach
allowed obtaining highly concentrated carbon nanotube LC systems.
The integration of MWCNTs into lyotropic LC phases formed in binary mixtures
of 1-tetradecyl-3-methylimidazolium chloride/ethylammonium nitrate has been studied
using polarized optical microscopy and small-angle X-ray scattering techniques [
231
]. The
incorporation of MWCNTs did not break the structure of hexagonal lyotropic LC phase
and resulted in an increase in the viscosity of this phase.
The rheological properties of SWCNT–lyotropic LC (sodium deoxycholate, NaDC)
mixtures have been studied [232,233]. The enhanced rheological properties at high NaDC

Liquids 2023,3267
concentration (30% wt) allowed the shear-induced filament formation. In these filaments
(fibrous long aggregates), the nanotubes were aligned along the shear direction.
The elastic properties of SWCNT–lyotropic LC composites have been studied [
234
].
A nematic solvent was prepared in a nonconventional mixture of sodium dodecyl sul-
fate, decanol, and water. Observed elastic behavior was interpreted accounting for the
entanglement between nanotubes dispersed in the nematic matrix.
The dispersion and alignment of SWCNTs in chromonic LCs (Di-sodium cromoglycate,
DSCG) have been investigated usings polarizing microscopy, Raman, and photolumines-
cence spectroscopy techniques [
235
]. Chromonic LCs are formed by the self-organization of
aromatic compounds with ionic or hydrophilic groups in aqueous solutions. The high level
of individual nanotube alignment in the DSCG nematic phase (with an order parameter of
approximately 0.9) was observed.
Self-assembled ordering of SWCNTs in a lyotropic LC (25% wt cetyltrimethylammo-
nium bromide (CTAB) in water) system has been studied using small-angle X-ray scattering,
optical birefringence, and electrical conductivity measurement techniques [
236
]. This ly-
otropic material shows nematic, hexagonal, and isotropic phases on heating. The MWCNTs
exhibited 2-D hexagonal ordering in nematic, hexagonal phases and 1-D ordering in the
crystalline and isotropic phases.
The electrical conductivity of SWCNTs in lyotropic LC (50% wt of Triton X-100 in
water) as a function of magnetic field and temperature has been studied [
237
]. This lyotropic
material shows hexagonal and isotropic phases on heating. The temperature dependence
of electrical conductivity exhibited a discontinuous change at the hexagonal to isotropic
transition temperature. With the increasing of the magnetic field, the transition from
spherical to hook-like SWCNT aggregates was observed.
Novel ionic LC/MWCNT composites for electrocatalytic treatment have been synthe-
sized [
238
]. MWCNTs were decorated with nano-nickel oxide (NiO). These composites are
shown to be useful for the treatment of urea-contaminated water. In several works, the
behavior of carbon nanotubes impregnated into the more complex lyotropic gels [
239
–
242
]
and the lyotropic polymers [243–247] was also discussed.
4.3. Polymer-Dispersed Liquid Crystals
Polymer-dispersed LCs can be obtained by embedding submicron-sized LC droplets
into polymer matrices. These composites have many promising optoelectronic applica-
tions [
248
]. Recently, the functionalized CNTs were integrated into the polymer-dispersed
LC in order to improve functionality of a gas (NO
2
) sensor device [
249
]. Developed com-
posites were shown to be promising candidates for use in different sensing devices. A
new technique for the preparation of polymer-dispersed LC doped with CNTs has been
reported [
250
]. The obtained films were characterized using different experimental tech-
niques. The doped LC materials demonstrated improved electro-optical characteristics.
The electro-optical properties and frequency response of polymer-dispersed LC doped
with MWCNTs have been reported [
251
]. Diffusion of MWCNTs into the LC regions was
observed during the polymerization. The ways for improving the diffraction efficiency and
threshold voltage of the prepared switchable grating devices were also discussed.
5. Conclusions
Studies of self-assembling in different types of thermotropic and lyotropic LC materials
doped with SWCNTs and MWCNTs performed in the past two decades have significantly
advanced our knowledge in the field. The discovered LC materials are based on variety of
molecular structures and exhibit many phase states with different spatial and orientational
arrangements. In LCs doped with CNTs, the mutual influences of LC-ordering on the
organization of CNTs and of the integration of CNTs on molecular arrangements in LCs are
typically observed. For each type of LC (thermotropic, lyotropic, etc.), the interaction of
anisometric CNTs with an LC host results in the manifestation of exciting and exceptional
structural, electro-magnetic, optical, thermal, and rheological properties.

Liquids 2023,3268
Nowadays, developed theoretical and experimental approaches are being widely used
in different engineering applications, and LC materials doped with CNTs have unequivo-
cally shown great potential to contribute to the creation of new electronics, electro-optics,
sensors, optical memories, and display devices. In many cases, the LC dispersions doped
with nanoparticles of different types, particularly organo-modified clay platelets, various
metal oxides, polymers, graphene, luminescent quantum dots, and composite nanoparticles
(e.g., CNTs + clay platelets composite) also display attractive properties. Current challenges
include problems related to the study of complex and synergic effects in complex composite
LC materials. These effects can depend upon the type of LC media, the nature of composite
dopants, and the presence of external fields. Therefore, further and multidisciplinary efforts
are well worth it in this field to resolve existing problems and gaps, and we are confident
that this research will produce some very exciting results over the next few years.
Author Contributions:
All the authors participated in the collection of data from the literature, anal-
ysis of the data, and drafting the manuscript. The final publication was prepared with contributions
from all authors. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was partially supported by the National Academy of Sciences of Ukraine
(projects No 6541230 (1230) and No 0122U002636), and by the Taras Shevchenko National University
of Kyiv (projects No 23BF05101).
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Abbreviations
CNTs Carbon nanotubes
SWCNTs Single-walled carbon nanotubes
MWCNTs Multi-walled carbon nanotubes
DSC Differential scanning calorimetry
FTIR Fourier-transform infrared spectroscopy
LCs Liquid crystals
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