Nanomaterials in Liquid Crystals as Ion-Generating and Ion-Capturing Objects

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 paper, a recently developed model of contaminated nanomaterials in liquid crystals 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.


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], lenses [5], and optical switches [6], to name a few.The performance of the aforementioned 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 ration, 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].
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 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 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 review 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 the form of a brief tutorial accessible to a broad scientific audience.

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 v PN 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 σ NP S .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, the ion-releasing process can be associated with desorption of ions from nanoparticles, and the ion-capturing process can be described as adsorption of ions onto the surface of nanoparticles.As a result, the following rate Equation (1) can be applied [69]: 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; σ NP S is the aforementioned 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); Θ NP is the fractional surface coverage of nanoparticles; k NP a is the adsorption rate constant; and k NP d is the desorption rate constant.In the majority of the reported experimental studies, weight concentration of nanoparticles ω NP is used V NP , where ρ LC (ρ 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)): In Equation ( 2), n 0 is the initial concentration of mobile ions in liquid crystals (prior to doping them with nanomaterials); and v NP is the aforementioned 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, , 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]):

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, dn /dt > 0 (dashed-dotted-dotted, short-dashed, and short-dotted curves); ion capturing regime, dn /dt < 0 (dotted, dashed, and dashed-dotted curves); and no change regime, dn /dt ≡ 0 (solid curve).The ionic contamination of nanoparticles quantified by the contamination factor v NP governs the switching between these regimes.The ion releasing regime is observed if v NP > v C NP , the ion capturing regime holds true if v NP < v C NP , and no change regime is reached if v NP = v C NP , where v C NP is the critical contamination factor of nanoparticles.It is defined as v C NP = n 0 K NP 1+n 0 K NP where K NP = k NP a /k NP d [69].Figure 1a also indicates that both ion-capturing and ion-releasing regimes depend on the concentration of nanoparticles: they are more pronounced if higher concentrations are used.ρ NP /ρ LC = 3.9.Reproduced from [69], under the Creative Commons Attribution License.
The time constant τ NP characterizing the kinetics of ion-capturing/ion-releasing process shown in Figure 1a can be defined through Equation ( 5): where n 0 = n(t = 0) and n ∞ = n(t → ∞) .In the regime of low surface coverage (Θ NP 1) this time constant is given by Equation ( 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 the time needed to achieve the steady-state.However, it should be noted that this decrease is diffusion-limited.In other words, Crystals 2018, 8, 264 5 of 14 Equation ( 6) is correct as long as τ NP τ D .The characteristic time τ D can be estimated by means of Equation ( 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 ≈ 10 20 m −3 and D = 10 −12 m 2 /s [13]), this time can be estimated as τ D ≈ 8 × 10 −3 s.By comparing it to data shown in Figure 1b it can be seen that, indeed, τ NP τ D .

Steady-State Regime
In the majority of the reported experimental studies, steady-state measurements are performed ( 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 ( dn /dω NP < 0).This regime is achieved if ν NP < ν C NP .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/dω NP > 0).It is observed if NP .The concentration of mobile ions in liquid crystals doped with nanoparticles does not change if NP .Switching between these three different regimes can be achieved by changing the level of ionic contamination of nanomaterials ν 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 NP a /k NP d ) as shown in Table 1 (this table is created using similar table published in paper [61]).

Temperature-Induced Effects
Constants describing ion-capturing (k NP a ) and ion-releasing (k NP d ) 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].
where E a is the adsorption activation energy; E d is the desorption activation energy; k 0 a and k 0 d are pre-exponential factors; k = 1.38 × 10 −23 J /K; and T is temperature [65,66].
By applying Equations ( 8) and ( 9), constant K NP can be written as Expression (10): In this equation, K NP 0 = k 0 a/k 0 d is the pre-exponential factor, and ∆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), ( 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 (this means that at a 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 to the initial concentration:  .In other words, the ion-capturing regime is observed (and it approaches the "no change" regime ( at elevated temperatures, Figure 3a).On the contrary, the ) (T n dependence of liquid crystals, doped with contaminated nanomaterials, exhibits some interesting features (Figure 3b).There are two distinct regions (Figure 3b).At temperatures  The radius of nanoparticles R NP is 10 nm.The weight concentration of nanoparticles is 0.01% (dashed curve) and 0.1% (dotted curve).This figure is also posted on Nanowerk Spotlight [78].
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 (this means that at a 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 to the initial concentration: n(T) ≤ n 0 .In other words, the ion-capturing regime is observed (and it approaches the "no change" regime ( n(T) → n 0 ) at elevated temperatures, Figure 3a).On the 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]: 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, ∆E > 0. Interestingly, liquid crystals doped with nanoparticles and characterized by negative values of this parameter (∆E < 0) should exhibit an opposite effect, namely, temperature-induced capturing of ions [66].This unusual effect was analyzed in paper [66].
Another very interesting result reported in paper [80] is the effect of a high-voltage pulse treatment on the concentration of ions in liquid crystals doped with silica nanoparticles.The model discussed in this review cannot model the kinetics of high voltage-induced effects in liquid crystals doped with nanoparticles.Indeed, in Equations ( 3) and (4), material-dependent coefficients are considered constant.However, once the treatment of liquid crystal/nanoparticle system with high voltage is completed, Equations ( 3) and (4) can still be used.It can be reasonably assumed that the applied high electric field can change some material parameters of liquid crystals doped with nanoparticles (K NP1 and K NP2 ).In addition, the applied electric field can change the contamination factor of nanoparticles v NP2 .Additional studies are needed to understand physical and chemical mechanisms involved in these processes.By applying Equations ( 3) and (4), a good agreement between reported experimental data [80] and the proposed model of contaminated nanomaterials can be achieved (Figure 5).
Another very interesting result reported in paper [80] is the effect of a high-voltage pulse treatment on the concentration of ions in liquid crystals doped with silica nanoparticles.The model discussed in this review cannot model the kinetics of high voltage-induced effects in liquid crystals doped with nanoparticles.Indeed, in Equations ( 3) and (4), material-dependent coefficients are considered constant.However, once the treatment of liquid crystal/nanoparticle system with high voltage is completed, Equations ( 3) and (4) can still be used.It can be reasonably assumed that the applied high electric field can change some material parameters of liquid crystals doped with nanoparticles ( 1 NP K and 2 NP K ).In addition, the applied electric field can change the contamination factor of nanoparticles 2 NP v .Additional studies are needed to understand physical and chemical mechanisms involved in these processes.By applying Equations ( 3) and (4), a good agreement between reported experimental data [80] and the proposed model of contaminated nanomaterials can be achieved (Figure 5).

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 paper can predict both ion capturing and ion releasing (or ion generation) regimes (Figures 1-3).Moreover, it also predicts a new effect, namely temperature-induced ion-capturing effect [66].This model is in a 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.
volume concentration n NP .They are related as n NP ≈ ω NP ρ LC ρ NP 1

Figure 1 .(Figure 1 .
Figure 1.(a) The volume concentration of mobile ions n versus time calculated using different values of the weight concentration of nanoparticles NP  and their contamination factor NP v (

Figure 2 .....
Figure 2. The volume concentration of mobile ions n in liquid crystals versus the weight concentration of nanoparticles NP  calculated at different values of their contamination factor NP v

Figure 3 .
Figure 3.The volume concentration of mobile ions n in liquid crystals doped with nanoparticles plotted as a function of temperature for two cases: (a) 100% pure nanoparticles in liquid crystals; and (b) contaminated nanoparticles in liquid crystals.Physical parameters used in simulations:

.
The radius of nanoparticles NP R is 10 nm.The weight concentration of nanoparticles is 0.01% (dashed curve) and 0.1% (dotted curve).This figure is also posted on Nanowerk Spotlight[78].
the concentration of mobile ions in liquid crystals doped with nanomaterials is less than the concentration of ions in pristine (without nanodopants) liquid crystals ( corresponds to the ion-releasing regime (Figure3b).No change regime corresponds to temperature C T .Temperature C T can be found using Equation(11) [65]:

17 Figure 4 .
Figure 4.The total ion density of mobile ions in liquid crystals doped with silica nanoparticles as a function of their weight concentration NP  : (a)

1 n
shown in Figure4a, can be explained in the following way.Pristine liquid crystals are characterized by a single type of dominant ions 1 n .Silica nanoparticles, prior to dispersing them in liquid crystals, are contaminated with ions 2 n .Once silica nanoparticles are dispersed in liquid crystals, ions are adsorbed on the surface of nanoparticles.
leads to the observed non-

Figure 5 .Figure 5 .
Figure 5.The total ion density of mobile ions in liquid crystals doped with silica nanoparticles as a function of their weight concentration NP  : (a)

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