Ion-Generating and Ion-Capturing Nanomaterials in Liquid Crystals ^†

Abstract

The majority of tunable liquid crystal devices are driven by electric fields. The performance of such devices can be altered by the presence of small amounts of ions in liquid crystals. Therefore, the understanding of possible sources of ions in liquid crystal materials is very critical to a broad range of existing and future applications employing liquid crystals. Recently, nanomaterials in liquid crystals have emerged as a hot research topic, promising for its implementation in the design of wearable and tunable liquid crystal devices. An analysis of published results revealed that nanodopants in liquid crystals can act as either ion-capturing agents or ion-generating objects. In this presentation, a recently developed model of contaminated nanomaterials is analyzed. Nanoparticle-enabled ion capturing and ion generation regimes in liquid crystals are discussed within the framework of the proposed model. This model is in very good agreement with existing experimental results. Practical implications and future research directions are also discussed.

1. Introduction

A great variety of existing liquid crystal devices relies on reorientation effects when applied electric fields change the orientation of mesogenic molecules [1]. These devices include liquid crystal displays (LCD) [2], tunable optical elements such as filters [3], retarders [3], waveplates [4], and lenses [5], and optical switches [6], to name a few. The performance of the afore-mentioned devices can be altered by mobile ions, typically present in liquid crystals, through the screening effect [2,7,8]. In the case of liquid crystal displays, this screening effect can result in an image sticking, image flickering, reduced voltage holding ratio, and overall slow response of the display [2,8]. That is why it is of a paramount importance to understand possible sources of ion generation in liquid crystals [7,8,9].

Sources of ions in liquid crystals can be of different origins [7,8,9,10]. Ionic species can be deliberately added to liquid crystals [10,11,12]. Such ionic dopants (for example, tetrabutyl-ammonium tetraphenyl-boride) in liquid crystals were extensively studied back in 1970s [11,12]. Small traces of ions (metal ions and inorganic anions) in liquid crystals can originate during chemical synthesis [13,14]. Alignment layers and glue used to seal liquid crystal cells are also important sources of ions in liquid crystals [15,16,17,18]. External factors such as electric fields [19,20,21,22] and ionizing radiation [23,24] can enrich liquid crystals with ions. Electrochemical reactions taking place in the near-electrode areas can also generate ions in liquid crystals [25,26,27].

Recently, nanomaterials in liquid crystals became a hot research topic with a rapidly increasing number of publications (more details can be found in numerous review papers [28,29,30,31,32,33,34,35,36,37,38], and collective monographs [39,40]). Accumulated research data reviewed in paper [41] indicate that nanomaterials in liquid crystals can alter the behavior of ions in liquid crystals. It was reported by different research groups that carbon-based nano-objects [41,42,43,44], metal [41,45,46,47,48], dielectric [41,49,50,51,52], semiconductor [41,53,54], ferroelectric [41,55,56,57,58,59,60], and other nanomaterials ([41] and references therein) can change the concentration of ions in liquid crystals. In many reported cases, nano-objects in liquid crystals can behave as ion-capturing objects thus decreasing the concentration of mobile ions in liquid crystals [41]. Interestingly, in many other cases, nanodopants in liquid crystals act as a source of ions increasing the concentration of mobile ions [41].

In an attempt to explain different, even seemingly contradictory reported results, a concept of contaminated nanomaterials was introduced [61]. In short, nanoparticles were considered contaminated with ions in liquid crystals prior to dispersing them in liquid crystals [61]. This simple approach applied to a variety of existing experimental results shows a very good agreement between the modelled and experimental data [61,62]. By dispersing contaminated nanodopants in liquid crystals, three different regimes, namely, the ion capturing regime (nanoparticles decrease the concentration of mobile ions in liquid crystals), the ion releasing or ion generation regime (nanomaterials increase the concentration of mobile ions in liquid crystals), and no change regime can be achieved [61]. The model of contaminated nanomaterials was extended to account for several types of dominant ions in liquid crystals [63,64], for possible temperature-induced effects [65,66], for weakly-ionized ionic species [67] and for the presence of substrates [68]. In addition, the kinetics of ion-capturing/ion releasing processes in liquid crystals doped with nanomaterials [69] and ion trapping coefficients of nanodopants [70] were also discussed.

All of these results indicate that, generally, we have to consider nanomaterials as a very important source of ions or ion traps in liquid crystals [71]. The goal of this conference paper is to summarize the most important features of the model of contaminated nanomaterials in liquid crystals [61,62,63,64,65,66,67,68,69,70,71,72] in a form of a brief tutorial accessible to a broad scientific audience.

2. Results and Discussion

2.1. Model

Consider nanoparticles in a liquid crystal host. In the most general case, these nanoparticles can be contaminated with ions prior to dispersing them in liquid crystals. To account for this ionic contamination of nanoparticles, a contamination factor ${\nu }_{NP}$ is introduced [61]. It equals a ratio of the number of surface sites of nanoparticle occupied by ionic contaminants to the total number of all surface sites of nanoparticle [61]. Typically, the number of surface sites can be characterized by their surface density ${\sigma }_S^{NP}$. Once contaminated nanoparticles are dispersed in liquid crystals, some fraction of ions can be released from their surface whereas some fraction of ions present in liquid crystals can be captured by nanoparticles. To simplify the discussion, consider the case of fully ionized ionic species characterized by their volume concentration $n=n^{+}=n^{-}$. In this case, the competition between ion-capturing and ion-releasing processes will result in the change of the concentration of mobile ions in liquid crystals doped with nanoparticles. In many practical cases, ion-releasing process can be associated with desorption of ions from nanoparticles and ion-capturing process can be described as adsorption of ions onto surface of nanoparticles. As a result, the following rate Equation (1) can be applied [69]:

$$\frac{dn}{dt}=-k_a^{NP}{n}_{NP}{A}_{NP}{\sigma }_S^{NP}n\left(1-{\Theta }_{NP}\right)+k_d^{NP}{n}_{NP}{A}_{NP}{\sigma }_S^{NP}{\Theta }_{NP}$$

(1)

In this equation, $n$ is the concentration of mobile ions in liquid crystals doped with nanoparticles; $t$ denotes time; $n_{NP}$ is the volume concentration of nanoparticles in liquid crystals; ${\sigma }_S^{NP}$ is the afore-mentioned surface density of all adsorption sites of a single nanoparticle; $A_{NP}$ is its surface area (for simplicity, spherical nanoparticles of a radius $R_{NP}$ are assumed); ${\Theta }_{NP}$ is the fractional surface coverage of nanoparticles; $k_a^{NP}$ is the adsorption rate constant; and $k_d^{NP}$ is the desorption rate constant. In the majority of reported experimental studies, weight concentration of nanoparticles ${\omega }_{NP}$ is used instead of their volume concentration $n_{NP}$. They are related as $n_{NP}\approx {\omega }_{NP}\frac{{\rho }_{LC}}{{\rho }_{NP}}\frac{1}{V_{NP}}$ where ${\rho }_{LC}$(${\rho }_{NP}$) is the density of liquid crystals (nanoparticles) and $V_{NP}$ is the volume of a single nanoparticle.

The first term of Equation (1) accounts for the ion-capturing process, whereas the second term originates from the ion-releasing phenomenon. This equation should be solved considering the conservation law of the total number of ions (Equation (2)):

$$n_0+n_{NP}{A}_{NP}{\sigma }_S^{NP}{\nu }_{NP}=n+n_{NP}{A}_{NP}{\sigma }_S^{NP}{\Theta }_{NP}$$

(2)

In Equation (2), $n_0$ is the initial concentration of mobile ions in liquid crystals (prior to doping them with nanomaterials); and ${\nu }_{NP}$ is the afore-mentioned contamination factor of nanoparticles. It accounts for possible contamination of nanodopants with ions [61].

It should be stressed that Equation (1) is an approximation which can be applied to liquid crystals doped with nanoparticles with certain restrictions discussed in recent papers [64,67,72]. In a general case, a more rigorous approach based on Boltzmann-Poisson equation should be considered [73,74,75,76].

Equations (1) and (2) can also be generalized to account for several types of dominant ions in liquid crystals [63,64]. In the simplest case of two dominant types of fully ionized ionic species characterized by their volume concentrations $n_1=n_1^{+}=n_1^{-}$ and $n_2=n_2^{+}=n_2^{-}$, the system of Equations (3) and (4) can be used ($j=1,2$; the meaning of physical quantities entering these equations are similar to that of Equations (1) and (2) [61,63,64]):

$$\frac{d{n}_j}{dt}=-k_{aj}^{NP}{n}_j{n}_{NP}{A}_{NP}{\sigma }_{Sj}^{NP}\left(1-{\Theta }_{NP1}^{}-{\Theta }_{NP2}^{}\right)+k_{dj}^{NP}{n}_{NP}{A}_{NP}{\sigma }_{Sj}^{NP}{\Theta }_{NPj}^{\pm }$$

(3)

$$n_{0j}+n_{NP}{\sigma }_{Sj}^{NP}{A}_{NP}{\nu }_{NPj}=n_j+n_{NP}{\sigma }_{Sj}^{NP}{A}_{NP}{\Theta }_{NPj}^{}$$

(4)

2.2. Kinetics of Ion-Capturing and Ion-Releasing Processes

The kinetics of ion-capturing and ion-releasing processes in liquid crystals doped with nanoparticles was analyzed in a recent paper [69]. This analysis was based on Equations (1) and (2) and the results are shown in Figure 1 [69].

According to Figure 1a, depending on the level of ionic contamination of nanoparticles, three different regimes can be achieved: the ion releasing regime, $\raisebox{1ex}{$dn$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.>0$ (dashed-dotted-dotted, short-dashed, and short-dotted curves); ion capturing regime, $\raisebox{1ex}{$dn$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.<0$ (dotted, dashed, and dashed-dotted curves); and no change regime, $\raisebox{1ex}{$dn$}\!\left/ \!\raisebox{-1ex}{$dt$}\right.\equiv 0$ (solid curve). The ionic contamination of nanoparticles quantified by the contamination factor ${\nu }_{NP}$ governs the switching between these regimes. The ion releasing regime is observed if ${\nu }_{NP}>{\nu }_{NP}^C$, the ion capturing regime holds true if ${\nu }_{NP}<{\nu }_{NP}^C$, and no change regime is reached if ${\nu }_{NP}={\nu }_{NP}^C$, where ${\nu }_{NP}^C$ is the critical contamination factor of nanoparticles. It is defined as ${\nu }_{NP}^C=\frac{n_0{K}_{NP}}{1+n_0{K}_{NP}}$ where $K_{NP}=\raisebox{1ex}{$k_a^{NP}$}\!\left/ \!\raisebox{-1ex}{$k_d^{NP}$}\right.$ [69]. Figure 1a also indicate that both ion capturing and ion releasing regimes depend on the concentration of nanoparticles: they are more pronounced if higher concentrations ${\omega }_{NP}$ are used.

The time constant ${\tau }_{NP}$ characterizing the kinetics of ion-capturing/ion-releasing process shown in Figure 1a can be defined through Equation (5):

$$n({\tau }_{NP})-n_0=\left(1-1/e\right)\left(n_{\infty }-n_0\right)$$

(5)

where $n_0=n(t=0)$ and $n_{\infty }=n(t\to \infty )$. In the regime of low surface coverage (${\Theta }_{NP}<<1$) this time constant is given by Equation (6):

$${\tau }_{NP}=1/k_d^{NP}\left(K_{NP}{n}_{NP}{A}_{NP}{\sigma }_S^{NP}+1\right)$$

(6)

In the case of spherical nanoparticles of radius $R_{NP}$, the dependence of the time constant on the weight concentration of nanodopants is shown in Figure 1b. As can be seen, by using smaller nanoparticles and their higher concentrations one can decrease time needed to achieve the steady-state. However, it should be noted that this decrease is diffusion-limited. In other words, Equation (6) is correct as long as ${\tau }_{NP}>>{\tau }_D$. The characteristic time ${\tau }_D$ can be estimated by means of Equation (7):

$${\tau }_D=\frac{l_D^2}{6D}\approx \frac{1}{6D\sqrt[3]{n^2}}$$

(7)

where $l_D$ is the average distance between mobile ions in liquid crystals, and $D$ is the diffusion coefficient of ions. By using typical values ($n\approx {10}^{20}$ m⁻³ and $D={10}^{-12}$ m²/s [13]) this time can be estimated as ${\tau }_D\approx 8\times {10}^{-3}$ s. By comparing it to data shown in Figure 1b it can be seen that, indeed, ${\tau }_{NP}>>{\tau }_D$.

2.3. Steady-State Regime

In the majority of the reported experimental studies, steady-state measurements are performed ($\frac{dn}{dt}=0$). In regard to the concentration of mobile ions in liquid crystals doped with nanomaterials, an analysis of possible regimes achieved in such systems was done in paper [61]. Three regimes, namely, the ion capturing regime (solid curve), ion releasing regime (dashed curve), and no change regime (dotted curve) are shown in Figure 2 where the concentration of mobile ions in liquid crystals is plotted as a function of the weight concentration of nanoparticles.

In the case of ion capturing regime, the concentration of mobile ions in liquid crystals decreases as the weight concentration of nanodopants goes up ($\raisebox{1ex}{$dn$}\!\left/ \!\raisebox{-1ex}{$d{\omega }_{NP}$}\right.<0$). This regime is achieved if ${\nu }_{NP}<{\nu }_{NP}^C$. The ion releasing regime is characterized by the increase in the concentration of mobile ions with an increase in the weight concentration of nanoparticles ($dn/d{\omega }_{NP}>0$). It is observed if ${\nu }_{NP}>{\nu }_{NP}^C$. The concentration of mobile ions in liquid crystals doped with nanoparticles does not change if ${\nu }_{NP}={\nu }_{NP}^C$. Switching between these three different regimes can be achieved by changing the level of ionic contamination of nanomaterials ${\nu }_{NP}$, the ionic purity of liquid crystals (an initial concentration of mobile ions $n_0$), and by varying materials used in experiments (constant $K_{NP}=k_a^{NP}/k_d^{NP}$) as shown in

Table 1. Ion-capturing, ion-releasing, and no change regimes in liquid crystals doped with contaminated nanoparticles [61].

	Ion-Capturing Regime	No Change Regime	Ion-Releasing Regime
$\mathrm{Contamination} \mathrm{level} \mathrm{of} \mathrm{nanomaterials}, {\nu }_{NP}$	${\nu }_{NP}<\frac{K_{NP}{n}_0}{1+K_{NP}{n}_0}$	${\nu }_{NP}=\frac{K_{NP}^{}{n}_0}{1+K_{NP}{n}_0}$	${\nu }_{NP}>\frac{K_{NP}{n}_0}{1+K_{NP}{n}_0}$
$\mathrm{Initial} \mathrm{concentration} \mathrm{of} \mathrm{ions} \mathrm{in} \mathrm{liquid} \mathrm{crystals}, n_0$	$n_0>\frac{1}{K_{NP}\left(\frac{1}{{\nu }_{NP}}-1\right)}$	$n_0=\frac{1}{K_{NP}\left(\frac{1}{{\nu }_{NP}}-1\right)}$	$n_0<\frac{1}{K_{NP}\left(\frac{1}{{\nu }_{NP}}-1\right)}$
$\mathrm{Constant}, K_{NP}$	$K_{NP}>\frac{1}{n_0\left(\frac{1}{{\nu }_{NP}}-1\right)}$	$K_{NP}=\frac{1}{n_0\left(\frac{1}{{\nu }_{NP}}-1\right)}$	$K_{NP}<\frac{1}{n_0\left(\frac{1}{{\nu }_{NP}}-1\right)}$

(this table is created using similar table published in paper [61]).

2.4. Temperature-Induced Effects

Constants describing ion-capturing ($k_a^{NP}$) and ion-releasing ($k_d^{NP}$) processes in liquid crystals doped with nanomaterials are temperature-dependent [65,66]. By approximating this temperature dependence through Equations (8) and (9), temperature-induced ionic effects in liquid crystals doped with nanoparticles can be analyzed [65,66]:

$$k_a^{NP}=k_a^0{e}^{-\raisebox{1ex}{$E_a$}\!\left/ \!\raisebox{-1ex}{$kT$}\right.}$$

(8)

$$k_d^{NP}=k_d^0{e}^{-\raisebox{1ex}{$E_d$}\!\left/ \!\raisebox{-1ex}{$kT$}\right.}$$

(9)

where $E_a$ is the adsorption activation energy; $E_d$ is the desorption activation energy; $k_a^0$ and $k_d^0$ are pre-exponential factors; $k=1.38\times {10}^{-23}\raisebox{1ex}{$J$}\!\left/ \!\raisebox{-1ex}{$K$}\right.$, and $T$ is temperature [65,66].

By applying Equations (8) and (9), constant $K_{NP}$ can be written as expression (10):

$$K_{NP}=\frac{k_a^{NP}}{k_d^{NP}}=K_0^{NP}{e}^{\raisebox{1ex}{$\Delta E$}\!\left/ \!\raisebox{-1ex}{$kT$}\right.}$$

(10)

In this equation, $K_0^{NP}=\raisebox{1ex}{$k_a^0$}\!\left/ \!\raisebox{-1ex}{$k_d^0$}\right.$ is the pre-exponential factor, and $\Delta E=E_d-E_a$ [65,66].

Temperature dependence $K_{NP}(T)$ (Equation (10)) can result in temperature-induced release of ions experimentally observed in liquid crystals doped with nanoparticles [65]. Typical dependence calculated using Equations (1), (2) and (10) is shown in Figure 3.

Figure 3a illustrates the so-called temperature-induced release of ions in liquid crystals doped with nanoparticles. The concentration of mobile ions in liquid crystals doped with nanomaterials increases as its temperature goes up. In the case of 100% pure nanodopants, this increase saturates at higher temperatures approaching an initial concentration of ions in liquid crystals (it means at high enough temperature nanoparticles lose their ion-capturing properties, see Figure 3a). It should be stressed that if 100% pure nanoparticles are mixed with liquid crystals, the concentration of mobile ions in such systems is always less or equal the initial concentration: $n(T)\le n_0$. In other words, the ion-capturing regimes is observed (and it approaches the “no change” regime ($n(T)\to n_0$) at elevated temperatures, Figure 3a). On a contrary, the $n(T)$ dependence of liquid crystals doped with contaminated nanomaterials, exhibits some interesting features (Figure 3b). There are two distinct regions (Figure 3b). At temperatures $T<T_C$ the concentration of mobile ions in liquid crystals doped with nanomaterials is less than the concentration of ions in pristine (without nanodopants) liquid crystals ($n(T)<n_0$) which corresponds to the ion-capturing regime. Above this temperature ($T>T_C$), an opposite inequality holds true $n(T)>n_0$ which corresponds to the ion-releasing regime (Figure 3b). No change regime corresponds to temperature $T_C$. Temperature $T_C$ can be found using Equation (11) [65]:

$$n_0=\frac{{\nu }_{NP}}{K_{NP}(T_C)\left(1-{\nu }_{NP}\right)}$$

(11)

Thus, a temperature-induced switching between ion-capturing and ion-releasing regimes can be achieved in liquid crystals doped with contaminated nanomaterials [65].

Temperature-induced release of ions is observed in systems characterized by positive values of their parameter $\Delta E>0$. Interestingly, liquid crystals doped with nanoparticles and characterized by negative values of this parameter ($\Delta E<0$) should exhibit an opposite effect, namely, temperature-induced capturing of ions [66]. This unusual effect was analyzed in paper [66].

3. Case Studies: A Brief Survey

The proposed model of contaminated nanoparticles in liquid crystals [61] was successfully applied to existing experimental data [62,71].

Table 2. Case studies: reported experimental data and physical parameters of the model.

Materials	Reported Effects	Physical Parameters
$\mathrm{Anatase} (Ti{O}_2$) nanoparticles in nematic liquid crystals (E44)	Ion capturing effect [49]	$K_{NP}={10}^{-23}$${\mathrm{m}}^3; {\nu }_{NP}=1.5\times {10}^{-4}$$; {\sigma }_S^{NP}=0.8\times {10}^{18}$$\mathrm{m}{-}^2; R_{NP}=5$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=3.9$ [62]
Carbon nanotubes (CNT) in nematic liquid crystals (E7)	Ion capturing effect [42]	$K_{NP}=0.7\times {10}^{-23}$${\mathrm{m}}^3; {\nu }_{NP}=9.5\times {10}^{-6}$$; {\sigma }_S^{NP}={10}^{18}$$\mathrm{m}{-}^2; R_{CNT}=2.5$$\mathrm{nm}; L_{CNT}=500$$\mathrm{nm} \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=1.6$ [62]
Diamond nanoparticles in nematic liquid crystals (E7)	Ion capturing effect [43]	$K_{NP}={10}^{-22}$${\mathrm{m}}^3; {\nu }_{NP}={10}^{-2}$$; {\sigma }_S^{NP}=1.25\times {10}^{17}$$\mathrm{m}{-}^2; R_{NP}=5$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=3.3$ [62]
Diamond nanoparticles in nematic liquid crystals (E7)	Ion releasing effect [43]	$K_{NP}=0.8\times {10}^{-25}$${\mathrm{m}}^3; {\nu }_{NP}=0.25$$; {\sigma }_S^{NP}=1.25\times {10}^{17}$$\mathrm{m}{-}^2; R_{NP}=5$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=3.3$ [62]
Graphene nano-flakes (GNF) in nematic liquid crystals (8OCB)	Ion capturing effect [79]	$K_{NP}=0.8\times {10}^{-23}$${\mathrm{m}}^3; {\nu }_{NP}=8.5\times {10}^{-6}$$; {\sigma }_S^{NP}=0.33\times {10}^{18}$$\mathrm{m}{-}^2; R_{GNF}=5$$\mathrm{nm}; L_{GNF}=10$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=1.8$ [62]
$\mathrm{Ferroelectric} \mathrm{nanoparticles} (LiNb{O}_3$) in liquid crystals	Ion capturing effect [55]	$K_{NP}=7\times {10}^{-23}$${\mathrm{m}}^3; {\nu }_{NP}=0.1075$$; {\sigma }_S^{NP}=5\times {10}^{18}$$\mathrm{m}{-}^2; R_{NP}=12.5$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=4.65$ [62]
$\mathrm{Ferroelectric} \mathrm{nanoparticles} (BaTi{O}_3$) in nematic liquid crystals	Ion capturing effect [57]	$K_{NP}=4\times {10}^{-20}$${\mathrm{m}}^3; {\nu }_{NP}=0.3$$; {\sigma }_S^{NP}={10}^{19}$$\mathrm{m}{-}^2; R_{NP}=1000$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=6.02$ [62]
$\mathrm{Ferroelectric} \mathrm{nanoparticles} (BaTi{O}_3$) in nematic liquid crystals (E44)	Temperature-induced release of ions [58]	${\nu }_{NP}=0$$; K_0^{NP}=1.93\times {10}^{-30}$${\mathrm{m}}^3; \Delta E=0.4$$\mathrm{eV}; {\sigma }_S^{NP}=5\times {10}^{18}$$\mathrm{m}{-}^2; R_{NP}=20$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=6.02$ [65]
$Ti{O}_2$ nanoparticles in nematic liquid crystals (ZhK1282)	Ion releasing effect [51]	${\nu }_{NP}=4.35\times {10}^{-4}$$; K_{NP}=1.6\times {10}^{-23}$${\mathrm{m}}^3; {\sigma }_S^{NP}=0.8\times {10}^{18}$$\mathrm{m}{-}^2; R_{NP}=25$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=3.9$ [71]
$Ti{O}_2$ nanoparticles in nematic liquid crystals (ZhK1282)	Ion capturing effect [51]	${\nu }_{NP}=0$$; K_{NP}=3.65\times {10}^{-24}$${\mathrm{m}}^3; {\sigma }_S^{NP}=2\times {10}^{18}$$\mathrm{m}{-}^2; R_{NP}=25$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=3.9$ [71]
$CdSe/ZnS$ core/shell nanoparticles in nematic liquid crystals (ZhK1289)	Ion releasing effect [53]	${\nu }_{NP}=3.379\times {10}^{-3}$$; K_{NP}={10}^{-26}$${\mathrm{m}}^3; {\sigma }_S^{NP}={10}^{18}$$\mathrm{m}{-}^2; R_{NP}=3$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=5.091$ [71]
$C{u}_{7}P{S}_6$ nanoparticles in nematic liquid crystals (6CB)	Ion releasing effect [52]	${\nu }_{NP}=0.3075$$; K_{NP}={10}^{-23}$${\mathrm{m}}^3; {\sigma }_S^{NP}=7\times {10}^{18}$$\mathrm{m}{-}^2; R_{NP}=58.5$$\mathrm{nm}; \raisebox{1ex}{${\rho }_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho }_{LC}$}\right.=4.907$ [71]

provides a summary of the observed experimental effects and physical parameters used in calculations to achieve a very good agreement between the model and experiments.

4. Conclusions

Existing experimental results (Table 2) unambiguously show that nanomaterials in liquid crystals can affect the concentration of ions in different ways. The dispersion of nanomaterials in liquid crystals can result in the ion capturing effect, ion releasing effect, or the combination of them. Therefore, nanomaterials in liquid crystals should be considered as new sources of ions or as ion trapping objects. The model of contaminated nanomaterials in liquid crystals reviewed in this conference paper can predict both ion capturing and ion releasing (or ion generation) regimes (Figure 1, Figure 2 and Figure 3). Moreover, it also predicts a new effect, namely temperature-induced ion capturing effect [66]. This model is in very good agreement with reported experimental data (Table 2).

So far, the origin of ionic contamination of nanomaterials is poorly understood. In many practical cases, this contamination can originate from particular chemical procedures utilized during chemical synthesis of nano-objects. Ionic contaminants can also originate from the contact of nanomaterials with environment and due to external factors such as ionizing radiation, high electric fields, excessive heating and chemical degradation. The aforementioned possible causes of ionic contamination of nanomaterials are caused by external factors and, therefore, are extrinsic in nature. This type of ionic contamination is typically characterized by relatively low values of the contamination factor. It can be reduced or even eliminated by improving physical/chemical procedures used to produce, storage, and handle nanomaterials. There is also an intrinsic source of ionic contamination of nanoparticles. For example, self-dissociating nanomaterials can generate ions because of their chemical/physical composition. In this case, the contamination factor of nanoparticles is relatively high and cannot be reduced by improving the purification procedure. Interestingly, both types of ionic contamination (intrinsic and extrinsic) can be successfully analyzed by the model reviewed in this paper. Further studies are needed to understand mechanisms of ionic contamination of nanomaterials and their impact on the properties of liquid crystals.