3.1. Carbon-Based Nano-Objects in Liquid Crystals
Effects of various carbon-based nanomaterials (fullerenes, graphene, carbon nanotubes, diamond nanoparticles, and carbon dots) on electrical properties of liquid crystals have been reported in numerous papers [
105,
116,
118,
119,
120,
121,
122,
123,
124,
125,
126,
127,
128,
129,
130,
131,
132,
133,
134,
135,
136,
137,
138,
139,
140,
141,
142,
143,
144,
145,
146,
147,
148,
149,
150,
151,
152,
153].
Table 2 provides a short summary of the reported effects. As can be seen, both decrease [
118,
119,
121,
122,
123,
124,
125,
126,
127,
143,
144,
145,
146,
147,
148,
149,
150,
151,
152] and increase [
105,
120,
128,
129,
130,
131,
132,
133,
134,
135,
136,
137,
138,
139,
140,
141,
142,
150,
151,
152,
153] in the electrical conductivity of liquid crystals doped with carbon-based nanomaterials were reported.
In the case of ferroelectric liquid crystals (FLC) doped with fullerenes
, 0.5 wt. % of
mixed with FLC reduced the concentration of ions in FLC from
to
[
118].
The effects of carbon-based nanoparticles (fullerene and carbon nanotubes) on the reduction of the screening effect in nematic liquid crystals (NLC) were reported in [
119,
143]. In the presence of ions, the reduction of the DC voltage
applied across the symmetric liquid crystal cell caused by the screening effect can be expressed as Equation (6) [
119]:
where
is the DC voltage applied across the liquid crystal cell;
is the effective voltage applied across the liquid crystal layer,
is the elementary charge;
is the concentration of ions;
is the electric constant;
and
are the thickness and the dielectric constant of liquid crystals;
and
are the thickness and the dielectric constant of the alignment layers, respectively. The Equation (6) simplifies for cells without alignment layers to the easily derivable expression Equation (7):
Results reported in [
119] suggest reducing the concentration of mobile ions in liquid crystals through ion capturing by means of carbon-based nanomaterials (fullerenes and carbon nanotubes, ~0.02 wt. %).
The authors of [
143] tried to quantify the effect of the ion capturing reported in [
119] by introducing the ion trapping coefficient
. This coefficient can be defined by writing the concentration
of the mobile ions in liquid crystals doped with carbon nanomaterials in the form of the expression Equation (8):
where
is the concentration of the mobile ions in plain (non-doped) liquid crystals. If
, then according to Equation (8),
, and all ions are trapped. For the ion trapping nano-materials the following requirement
always holds true. What is interesting, the coefficient
can also be applied to materials causing an ionic contamination of liquid crystals. In this case, the ion trapping coefficient
is negative,
and, according to Equation (8), the doping of liquid crystals with such materials leads to the increase in the concentration of ions.
Table 2.
Effect of carbon-based nanomaterials on the electrical properties of liquid crystals.
Table 2.
Effect of carbon-based nanomaterials on the electrical properties of liquid crystals.
Carbon-Based Nanomaterials | Liquid Crystals * | Results | Ref. |
---|
Fullerenes | FLC | Decrease in ion concentration | [118] |
NLC | Ion trapping | [119,141] |
NLC | Increase in the conductivity | [120] |
Graphene | FLC | Reduced AC conductivity and dielectric losses | [121,122,123] |
NLC | Decrease in ion concentration | [124,125] |
CLC | Decrease in ion concentration | [126] |
Carbon Nanotubes | NLC | Increase in the conductivity | [105,127,128,129,130,131,132,133,134,135,136,137] |
PDLC | Increase in the conductivity | [138] |
CLC | Increase in the conductivity | [139] |
FLC | Increase in the conductivity | [140,141,142] |
NLC | Ion trapping | [126,143,144,145] |
FLC | Decrease in the conductivity/dielectric losses | [146,147,148,149] |
Diamond Nanoparticles | NLC | Both decrease and increase in the conductivity | [150,151,152] |
Carbon Dots | FLC | Increase in the conductivity | [153] |
In [
143], the concentration of carbon nanomaterials in the nematic liquid crystal E7 was set to 0.05 wt. %, and the reported values of the ion trapping coefficient were 0.1 (fullerenes), 0.315 (carbon nano-fibers), 0.24 (carbon nano-coils), 0.3–0.343 (multi-wall carbon nanotubes), and 0.18 (single wall carbon nanotubes).
The authors of [
119] mentioned that the use of thicker cells (~25
) instead of thinner cells (~5
) facilitates the sample degradation through the aggregation of nanomaterials dispersed in liquid crystals. Thicker cells (~25
) and higher concentrations of the modified fullerenes (0.1–3 wt. %) in the nematic liquid crystal E25M (cyanobiphenyls/terphenyl mixture) were explored in [
120]. It was found that liquid crystals doped with modified fullerenes exhibit higher electrical conductivity than their non-doped counterparts; and the experimental data can be satisfactorily described by the simple power law Equation (9) [
120]:
Where
(planar alignment), and
(homeotropic alignment). All studied samples exhibited a high degree of aggregation with the percolation threshold at 2.0–2.5 wt. % [
120].
The electrical properties of liquid crystals doped with graphene were reported in [
121,
122,
123,
124,
125,
126]. According to [
121], graphene sheets, implemented in the design of ferroelectric liquid crystal cell as alignment layers, reduce the electrical conductivity by a factor of ~10. This reduction in the conductivity was associated with the charge annihilation process; ionic impurities combine with the surface charge of the graphene, thus annihilating each other [
121]. Graphene flakes, mixed with ferroelectric liquid crystal MX40636 (~0.04 wt. %), reduced the concentration of mobile ions by a factor of 4 [
122]. The authors of [
122] proposed that the electrostatic field of the graphene sheets (the diameter of the graphene flakes was within the range from 0.5 to 3
µm) was responsible for the ion capturing and the observed decrease in the concentration of ion. Nano-flakes made of the reduced graphene oxide and mixed with ferroelectric liquid crystals (~0.5 wt. %) led to a noticeable decrease in the imaginary part of the dielectric permittivity of FLCs [
123]. It was suggested that this decrease is caused by the ion compensation/neutralization [
123].
The effect of graphene nanoplatelets on the concentration of ions
in liquid crystal 8OCB (n-octyl cyano biphelyl) was reported in [
124]. It was found that the 0.5 wt.% dopant content led to the reduction of
from
to
, by 30% [
124]. The two-fold reduction in the concentration of mobile ions was also demonstrated in [
125] for liquid crystal 5CB doped with graphene (~0.005 wt. %). An approximately 32% reduction in the concentration of ions (from
to
) was reported in [
126] for cholesteric liquid crystals (CLC) doped with graphene nanoplatelets (0.5 wt. %). The ion trapping by graphene nanomaterial was suggested to explain experimental results reported in [
125,
126].
The electrical properties of liquid crystals doped with carbon nanotubes (CNT) were explored in numerous papers [
105,
116,
127,
128,
129,
130,
131,
132,
133,
134,
135,
136,
137,
138,
139,
140,
141,
142,
143,
144,
145,
146,
147,
148,
149]. The majority of these manuscripts [
105,
116,
117,
128,
129,
130,
131,
132,
133,
134,
135,
136,
137,
138,
139,
140,
141,
142] report the enhancement of the electrical conductivity
of liquid crystals doped with carbon nanotubes. The increase in
is associated with the percolation phenomenon and high intrinsic electrical conductivity of carbon nanotubes: a sharp transition from the ionic conductivity to the dominating charge hopping conductivity occurs at a certain concentration called the percolation concentration [
105,
116]. The measured electrical conductivity obeys the scaling Equation (10) [
105,
116]:
where
is the percolation concentration, and
is the transport exponent (or transport index). Typically, the percolation concentration is of the order of 0.001–0.1 wt. %, and the transport exponent
.
The percolation phenomena hinder/mask the ion trapping effects in liquid crystals doped with carbon nanotubes. Nevertheless, there are some papers reporting the suppression of ion-related effects in liquid crystals [
119,
127,
143,
144,
145,
146,
147,
148,
149]. The ion trapping coefficient Equation (8) of carbon nanotubes was found to be 0.18–0.34 depending on the type of the CNT [
143]. Computations reported in [
127] pointed to the possibility of the existence of the permanent dipole moment in the CNT. This dipole moment can facilitate the ion capturing in the super-fluorinated LC mixtures doped with carbon nanotubes (0.0005–0.001 wt. %) [
127,
128,
129]. The reduction of the charge concentration (from
to
) and the diffusion constant (from
to
) in the nematic liquid crystal E7 doped with carbon nanotubes (0.05 wt. %) was reported in [
144]. This observation suggests that carbon nanotubes can absorb the ionic impurity and hinder the ion transport in liquid crystals [
144]. Comparative studies of the high resistivity (CYLC-01) and low resistivity (E7) nematic liquid crystals doped with carbon nanotubes (0.05 wt. %) were performed in [
145]. Carbon nanotubes did not change the electrical properties of the high resistivity liquid crystal CYLC-01, but reduced the concentration of ions in the low resistivity liquid crystal E7 (the voltage holding ratio was improved from 48% to 61%) [
145].
Copper oxide decorated carbon nanotubes (0.5 wt. %)/ferroelectric liquid crystal (commercial name: KCFLC 7S) composites were studied in [
146]. In such systems, the reduced concentration of ions (deduced from the observed ~1.5-fold decrease in the dielectric loss factor and the simultaneous 1.75-fold increase in the measured resistance of the sample) was attributed to the ion trapping by the copper oxide decorated carbon nanotubes [
146]. Improvements in the electro-optical performance of ferroelectric liquid crystals (commercial name: LAHS7) doped with carbon nanotubes (0.01 wt. %) were also attributed to the trapping of ions through the carbon nanotubes [
147].
Electrical properties of nematic liquid crystals (E7 of different purity and MLC6609 (commercially available liquid crystal mixture exhibiting negative dielectric anisotropy)) doped with diamond nanoparticles (0–4 wt. %) were reported in [
151,
152]. It was found that diamond nanoparticles (DNPs) decrease the electrical conductivity
of low-resistivity liquid crystals such as E7. At the same time, DNPs increase
of the high resistivity liquid crystals (MLC6609 or purified E7) [
151,
152]. The concentration dependence of the electrical conductivity is very nonlinear, pointing to the manifestation of some percolation processes [
152]. The observed results were explained by considering different ratios of the ion adsorption / ion desorption at the nanoparticle’s surface: the desorption of ions from the surface of DNPs with the ion transfer along the surface of interconnected particles leads to the increase in the electrical conductivity, while the adsorption of ions at the nanoparticle’s surface accounts for the decrease in electrical conductivity [
151,
152].
3.2. Metal Nanoparticles in Liquid Crystals
Metal nanoparticles are widely used as dopants to modify/change/alter the physical properties of liquid crystals [
106,
107,
108,
110,
113,
115].
Table 3 provides a short summary of their effects on the electrical properties of liquid crystals [
154,
155,
156,
157,
158,
159,
160,
161,
162,
163,
164,
165,
166,
167,
168,
169,
170,
171,
172]. The majority of published papers report an increase in the electrical conductivity of liquid crystals doped with metal nanoparticles [
156,
157,
158,
160,
161,
162,
163,
164,
165,
166,
167,
169,
171]. In some cases, (columnar liquid crystals doped with gold nanoparticles with the concentration of the order of 1 wt. %) such an increase can be as high as six orders of magnitude [
160,
161,
162,
163,
164]. This increase in the conductivity is attributed to the formation of chains of gold nanoparticles [
162,
164]. The high electrical conductivity of nematic liquid crystal—gold nanoparticle nano-composites can be enhanced even more by mixing them with dielectric aerosil particles [
165]. The formation of chains and networks of metal nanoparticles in liquid crystal nano-composites points to the involvement of the percolation processes. Indeed, the concentration dependence of the electrical conductivity of the nematic liquid crystal PCPBB doped with gold nanoparticles was well described by the percolation scaling law Equation (10) with
[
157].
Table 3.
Effect of metal nanoparticles on the electrical properties of liquid crystals.
Table 3.
Effect of metal nanoparticles on the electrical properties of liquid crystals.
Metal Nanoparticles | Liquid Crystals * | Results | Ref. |
---|
Gold | FLC | Reduced AC conductivity and the charge transfer | [154,155] |
NLC | Two orders increase in the conductivity | [156,157,158] |
CLC | Capture and release of ions | [159] |
ColLC | Five-six orders increase in the conductivity | [160,161,162,163,164] |
Gold and Aerosil | NLC | Enhancement of the electrical conductivity | [165] |
Palladium | NLC | Increased dielectric losses | [166] |
Silver | NLC | Increased anisotropy of the conductivity | [167] |
FLC | Ion trapping | [168] |
Copper | ColLC | Enhancement of the electrical conductivity | [169] |
Nickel | NLC | Ion trapping | [170] |
FLC | Increase in the conductivity | [171] |
Titanium | NLC | Ion trapping | [172] |
The ion capturing through functionalized metal nanoparticles dispersed in liquid crystals was reported in [
154,
159,
168,
170,
172]. Ferroelectric liquid crystal LAHS 9 doped with decanethiol/dodecanethiol capped silver nanoparticles (0.1 wt. %) exhibited an increase in the resistivity as compared to the pristine FLC [
168]. According to [
168], the decanethiol/dodecanethiol organic layer around the silver nanoparticle’s surface can capture positive and negative ions, leading to the reduction of the conductivity. The ion capturing effect was also discussed in [
154]. Functionalized gold nanorods decorated with siloxane based nematogenic ligands and ionic surfactant cetyltrimethylammonium bromide (CTAB) dispersed in ferroelectric liquid crystal decreased the AC electrical conductivity of FLC from
to
(0.25 wt. %), and to
(0.5 wt. %) [
154].
The decrease in the electrical conductivity (from
to
) of the cholesteric liquid crystal BL094 doped with 0.5 wt. % gold nanoparticles, stabilized by means of the electrostatic capping made of citrate ions, was reported in [
159]. This decrease in the electrical conductivity was measured by applying 100 mV across the 8
thick cell, and the adsorption of ionic impurities at the nanoparticle’s surface was proposed to explain the observed result. Further increase in the applied voltage (up to 20–40 V) led to the increase in the electrical conductivity [
159]. These two results were obtained by using two different experimental methods (an impedance spectroscopy at low electric fields, and the cyclic voltammetry at high electric fields), and a certain degree of caution is needed to interpret them [
159]. To explain the increase in the electrical conductivity
under the action of high electric fields, it was proposed that (i) gold nanoparticles capped with citrate ions could follow the applied electric field increasing
, and (ii) a fraction of citrate ions could be stripped off thus leading to the increase in the concentration of ions [
159].
The reduction of the residual DC voltage through incorporation of Ni nanoparticles in the nematic liquid crystal (1–3 wt. %) was discussed in [
170]. According to [
170], Ni nanoparticles mixed with NLC eliminated the hysteresis of the capacitance- voltage (C-V) dependence by capturing ions. The enhancement of electro-optical properties of the nematic liquid crystal MJ001929 doped with pure (non-functionalized) titanium nanoparticles (0.1–2.0 wt. %) was reported in [
172]. The adsorption of ionic impurities at the surface of titanium nanoparticles was suggested as a possible mechanism accounting for the observed reduction of the threshold voltage and faster switching time [
172].
3.3. Dielectric and Semiconductor Nanoparticles in Liquid Crystals
Electrical properties of liquid crystals doped with metal oxide nanoparticles were reported in many papers summarized in
Table 4 [
173,
174,
175,
176,
177,
178,
179,
180,
181,
182,
183,
184,
185,
186,
187,
188,
189,
190].
Table 4.
Effect of nanoparticles made of metal oxides on the electrical properties of liquid crystals.
Table 4.
Effect of nanoparticles made of metal oxides on the electrical properties of liquid crystals.
Nanoparticles | Liquid Crystals * | Results | Ref. |
---|
, , , , , | NLC | Reduced ion current and improved voltage holding ratio, decrease in ion concentration | [173,174,175,176,177,178,179,180,181,182,183,184] |
, , , | FLC | Decrease in the conductivity | [185,186,187,188] |
| ColLC | Increase in the conductivity | [189] |
| NLC | Voltage-assisted ion reduction | [190] |
Transient currents, the concentration of ions, and electro-optical response of nematic liquid crystal MJ9915 doped with insulating nanoparticles made of
,
, and
(0.02–0.06 wt. %) were explored in [
173,
174]. The concentration of ions in liquid crystals was reduced by more than two-fold thus suppressing the undesired field-screening effect. This decrease in the concentration of ions was attributed to the ion trapping by insulating nanoparticles polarized under the action of the external electric field [
173,
174]. Similar results were obtained for the same nematic liquid crystal doped with diamond nanoparticles [
150,
175]. The effect of the anatase
nanoparticles (0.05–1 wt. %) on the voltage holding ratio, the concentration of ions, and the diffusion constant of the nematic liquid crystal E44 at different temperatures was investigated in [
178]. The concentration of ions
, the diffusion constant
, and the electrical conductivity
were reduced. For example, at room temperature and at the concentration of nanoparticles 0.5 wt%,
changed from
to
,
decreased from
to
, and
dropped from
to
resulting in the increase of the voltage holding ratio from 66% to 78% [
178]. Further increase in the concentration of nanoparticles did not lead to the decrease in
,
, and
because of the aggregation [
178]. The adsorption of mobile ions by nanoparticles along with the ability of nanoparticles to hinder the ion transport in liquid crystals were proposed as major factors accounting for the observed results [
178].
The adsorption of ions at the nanoparticle’s surface depends on the total surface area of nanoparticles dispersed in liquid crystals. This dependence was experimentally explored in [
176].
nanoparticles of different sizes (5, 10, and 30–40 nm) were dispersed in nematic liquid crystals E7 at the same concentration of 0.1 wt. %. The transient currents, the current—voltage, and the transmittance—voltage characteristic of these colloids led to the following conclusions: (i) the surface charge and induced dipole moment of
nanoparticles could physically trap ions at their surfaces through electrostatic interactions; (ii) the number of the trapped ions increases with the increase of the total surface area of nanoparticles; (iii) at the same weight concentration, smaller nanoparticles have greater surface area and capture higher number of ions [
176].
The concept of ion trapping was used to explain improvements in the electro-optical performance of nematic liquid crystals (NLC) doped with
nanoparticles (0.5–1.5 wt. %) [
179], NLC MJ001929 doped with
nanoparticles (2 wt. %) [
180], and NLC MAT-05-881 doped with
nanoparticles (up to 5 wt. %) [
181].
There are some examples of very tricky behavior of liquid crystals doped with dielectric nanoparticles. For example, the electrical conductivity of the nematic liquid crystal 5CB doped with
nanoparticles was marginally changed exhibiting both decrease (from
to
at a temperature of 23 °C and the concentration of 0.2 wt%) and increase (from
to
at a temperature of 23 °C and the concentration of 0.6 wt. %) [
182]. Complicated behavior of the same nematic liquid crystal 5CB doped with
nanoparticles (0.1–2 wt. %) was also reported in [
183,
184]. An increase in the concentration of
nanoparticles from 0 wt% to 0.2 wt% led to the unexpected increase in the concentration of ions
(from
to
at a temperature of 30 °C), the diffusion coefficient
(from
to
), and the electrical conductivity
(from
to
) of the 5CB [
183]. However, further increase in the concentration of nanoparticles from 0.2 wt. % to 1 wt. % resulted in the decrease of the above-mentioned parameters as compared to their values at the concentration of 0.2 wt. %:
dropped to
;
changed to
almost returning to its original value
;
decreased to
. For concentrations higher than 1.0 wt. %, the saturation of the measured parameters
,
, and
was observed [
183]. These experimental facts suggest that the contamination process dominates at the low concentration of nanoparticles in liquid crystals, and the purification of liquid crystals comes into effect at higher concentrations of nanoparticles. An important conclusion for practical applications is to use purified nanoparticles as dopants for liquid crystals (according to [
183,
184],
nanoparticles were not purified before their use as dopants for liquid crystals). The non-monotonous behavior of the measured electrical parameters as a function of the nanoparticles loading deserves additional experimental and theoretical studies [
183,
184].
The removal of ionic impurities through the adsorption of ions at the surface of
nanoparticles dispersed in ferroelectric liquid crystals KCFLC 7S at the concentration of 1.0 wt. % was reported in [
185]. The ion trapping effect in ferroelectric liquid crystals doped with
[
186],
[
187], and
[
188] nanoparticles was also discussed. According to [
186,
187], the applied electric field polarized the nanoparticle, and ions in liquid crystals were trapped at the surface of the polarized nano-dopant.
Semiconductor nanoparticles in liquid crystals were also studied from the perspective of the ion capturing processes [
191,
192,
193,
194].
Table 5 provides a short summary of the obtained results.
Table 5.
Effect of semiconductor nanoparticles on the electrical properties of liquid crystals.
Table 5.
Effect of semiconductor nanoparticles on the electrical properties of liquid crystals.
Nanoparticles | Liquid Crystals * | Results | Ref. |
---|
| FLC | Decrease in the concentration of ions | [191,192] |
| FLC | Decrease in the conductivity | [193] |
| NLC | Release of the trapped ions under the action of the electric field | [194] |
The ion capturing effect in ferroelectric liquid crystals Felix 16/100 doped with semiconductor
quantum dots (0.05–2 wt. %), deduced from the ~two-fold reduction in the electrical conductivity and complex dielectric permittivity, was reported in [
191,
192]. A similar trend was found in ferroelectric liquid crystal KCFLC10R doped with
nanorods (0.1–0.3 wt. %) [
193]. However, the reduction in the electrical conductivity was more than five-fold (from
to
at a temperature of 30 °C) [
192].
The ion trapping followed by the aggregation of the agglomerate “semiconductor nanoparticle/trapped ions” in nematic liquid crystals was discussed in [
194]. This process can become very important in the case of liquid crystal cells driven by high electric fields.
3.4. Ferroelectric Nanoparticles in Liquid Crystals
The ion trapping is a result of strong attractive interactions between ions and a single nanoparticle in liquid crystals. The permanent dipole of ferroelectric nanoparticles makes them superior to the conductive, dielectric, and semiconductor nanomaterials. The spontaneous polarization
of the ferroelectric nanoparticle (its absolute value equals the surface charge density
) generates a very high electric field
, which, in the vicinity of the surface, can be estimated as Equation (11) [
195]:
This equation, for the barium titanate (
[
115,
196]) immersed in a dielectric liquid (
), yields
. The estimated value of the electric field is high enough to trap ions in liquid crystals.
The ion trapping by means of various ferroelectric nanoparticles embedded in liquid crystals was explored in papers [
197,
198,
199,
200] summarized in
Table 6.
Table 6.
Effect of ferroelectric nanoparticles on the electrical properties of liquid crystals.
Table 6.
Effect of ferroelectric nanoparticles on the electrical properties of liquid crystals.
Nanoparticles | Liquid Crystals * | Results | Ref. |
---|
| FLC | Ion trapping | [197] |
| NLC | Increase in the conductivity | [198] |
| NLC | Decrease in the concentration of ions | [199,200] |
| NLC | Ion trapping and reduction of the screening effect | [200] |
Dielectric and electric properties of ferroelectric liquid crystals doped with
nanoparticles (0.01–0.1 wt. %) were studied in [
197]. Ferroelectric nanoparticles were produced by applying the method of the ball mill [
201,
202,
203], followed by the harvesting procedure [
204]. Experimental data were in favor of the ion trapping phenomenon. The estimated concentrations of ions deduced from the conductivity measurements were
(non-doped FLC),
(FLC nanocolloids, 0.01 wt. %), and
(FLC nanocolloids, 0.1 wt. %) [
197].
Effect of
ferroelectric nanoparticles on the ion transport in the nematic liquid crystal 5CB was reported in [
199]. By introducing relatively low quantities of
nanoparticles, the concentration of mobile ions in 5CB was reduced by a factor of ~1.5 (at a concentration of 0.115 wt. %), and by a factor of 2.3 (at a concentration of 0.275 wt. %). Further increase in the concentration of nanoparticles (up to 0.525 wt. %) did not lead to the corresponding decrease of the ion concentration because of the aggregation of nanoparticles. However, at this level of nanoparticle loading, the concentration of ions was still ~1.3 times smaller than that of the pure (non-doped) 5CB [
199]. The measured values of the electrical conductivity (at a temperature of 25 °C) were
(non-doped NLC),
(NLC nanocolloids, 0.115 wt. %),
(NLC nanocolloids, 0.275 wt. %), and
(NLC nanocolloids, 0.525 wt. %) [
199].
The quantification of the ion trapping in liquid crystals by means of ferroelectric nanoparticles was done in [
200] by applying the Poisson-Boltzmann (PB) equation solved in [
205].The concentration of the trapped positive (or negative) ions ,
, was estimated as Equation (12) [
200]:
where
is the concentration of ferroelectric nanoparticles;
is the area of the nanoparticle’s surface;
is the thickness of the ionic monolayer (the monolayer of the trapped ions at the nanoparticle’s surface);
is the spontaneous polarization of the nanoparticle;
;
is the dielectric permittivity of the surrounding medium;
; and
is the temperature. The parameter
is dimensionless and tells us how many positive (or negative) monovalent ions can be trapped by a single ferroelectric nanoparticle. This parameter depends on the materials’ characteristics of the nanoparticle (the spontaneous polarization), it is size
where
is the radius of the nanoparticle), the temperature, and the dielectric properties of the surrounding medium (liquid crystals). Considering the cylindrical
nanoparticle immersed in liquid dielectric (
,
,
,
), the parameter
equals
. The typical concentration of ferroelectric nanoparticles in liquid crystal colloids is
. These numbers multiplied by a
factor yield
, which is even greater than the reported ion concentration in liquid crystals 5CB or E7 (see
Table 1). As a result, even low concentrations of ferroelectric nanoparticles (equivalent to the volume fraction of the order of
) are enough to purify liquid crystals from ions [
200].
The expression Equation (12) predicts a linear dependence of the concentration of trapped ions on the concentration of ferroelectric nanoparticles. This dependence is valid only in the regime of low concentrations of nanoparticles when aggregation phenomena can be ignored. The aggregation sets a limit on the recommended concentration of nanoparticles which should not exceed the critical concentration
. The critical concentration is of the order of
(
can be estimated by finding the distance at which the thermal energy is comparable to the magnitude of the electrostatic interactions between two nanoparticles) [
200]. Nevertheless, the Equation (12) can be applied to real systems with the aggregation in the form of Equation (13) which can be obtained from Equation (12) by replacing the concentration and the spontaneous polarization of nanoparticles with their effective values (the effective concentration
, and the effective spontaneous polarization
[
200]:
It is worth mentioning that the aggregation of nanoparticles can decrease the effective concentration drastically. For example, the simplest model of the aggregation based on a reversible second order reaction predicts
[
200]. The methods of fabrication, uncontrollable contamination during the preparation/storage, and surfactants used to stabilize nanoparticles in liquid crystals can also decrease the effective spontaneous polarization. All these factors reduce the capability of nanoparticles to trap ions as can be seen from Equation (13).
By treating thermotropic liquid crystals LC13739 [
206] with ferroelectric micro-particles at the high level of loading (1 wt. % and 10 wt. %) their electrical conductivity was reduced from
to
(1 wt. %), and
(10 wt. %) [
200]. Since ferroelectric micro-particles were filtered out once the treatment was completed, the observed reduction in the electrical conductivity is equivalent to the 27-fold and 39-fold decrease in the concentration of ions in liquid crystals. This experimental fact points out to the possibility of the conversion of the low-resistivity (or contaminated) liquid crystals to the high-resistivity liquid crystals by treating them with ferroelectric materials.
Not all ferroelectric materials are good candidates for liquid crystal purification. Some materials such as
are very tricky, as they are prone to charging [
207], and a certain degree of caution is needed to interpret the experimental data [
198,
207].
3.5. Organic and Other Nanomaterials in Liquid Crystals
Papers reporting the electrical properties of liquid crystals doped with organic materials (conducting nano-fibers and polymeric nanoparticles), montmorillonite nano-clay, and
are summarized in
Table 7 [
208,
209,
210,
211,
212,
213,
214,
215,
216,
217,
218,
219].
Table 7.
Effect of organic and other nanomaterials on the electrical properties of liquid crystals.
Table 7.
Effect of organic and other nanomaterials on the electrical properties of liquid crystals.
Nanomaterials | Liquid Crystals * | Results | Ref. |
---|
Conducting nanofiber | NLC | Increase in the conductivity | [208,209] |
Polymeric nanoparticles | FLC | Decrease in dielectric losses | [210] |
Nanoclay (montmorillonite) | NLC | Ion trapping, time dependent properties, and aggregation | [211,212,213,214,215,216,217] |
| FLC | Increase in the conductivity | [218,219] |
Conducting polyaniline nano-fibers (PANI) embedded in liquid crystals (5CB and CCN-47) led to a noticeable increase in the electrical conductivity and its anisotropy [
208,
209]. The anisotropy of the conductivity was increased by ~10 times (5CB doped with PANI nanofibers at the concentration of 0.2 wt. %), and ~20 times (CCN-47 doped with PANI nanofibers at the concentration of 1.5 wt. %). Such an increase was explained due to the contribution of both ionic and electronic conductivities [
208,
209].
The decrease in the dielectric losses
and increase in the resistivity of ferroelectric liquid crystals (Felix and CS series) doped with polymeric nanoparticles made of PBA (the copolymer of polybenzene and anthracene; 0.1–10 wt. %) was reported in [
210]. The trapping of ions by PBA nanoparticles was proposed to explain the measured decrease in
[
210].
Very interesting electrical behavior was found in liquid crystal systems doped with montmorillonite platelets [
211,
212,
213,
214,
215,
216,
217]. Montmorillonite is a type of smectic clays characterized by a sandwich “tetrahedral-octahedral-tetrahedral” structure made of aluminosilicate lamellar materials. Typically, an octahedral
(or
) is sandwiched between two tetrahedral
sheets [
215]. It was reported that relatively low concentrations of PK-802 sodium montmorillonite (less than 1.0 wt. % w) dispersed in liquid crystals (E7) led to the partial suppression of the screening effect, and the reduced charge density (from
to
). These effects were attributed to the charge transfer and trapping by the nano-clay [
211,
212,
215]. A very small amount of highly purified montmorillonite CL120 (0.03–0.30 wt. %) dispersed in the nematic liquid crystal E7 decreased the electrical conductivity (from
to
at the optimal concentration of 0.07%) and the concentration of mobile ions (from
to
at the same concentration) in liquid crystals. It was also observed that the efficiency to trap ions by nano-clay was varying in time [
213]. More efficient ion trapping in liquid crystals can be achieved by combining low concentrations of nano-clay with comparable amounts of carbon nanotubes [
214]. Higher concentrations of montmorillonite in nematic liquid crystals (up to 5 wt. %) result in the percolation phenomena and an increase of electrical conductivity [
216,
217].