Ion ‐ Generating and Ion ‐ Capturing Nanomaterials in Liquid Crystals †

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.


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].
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.

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 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 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 . 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, ionreleasing 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]: 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), 0 n is the initial concentration of mobile ions in liquid crystals (prior to doping them with nanomaterials); and 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 , the system of Equations ( 3) and ( 4) can be used ( 2 , 1  j ; 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, 0  dt dn   ) this time constant is given by Equation ( 6): In the case of spherical nanoparticles of radius NP R , 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 steadystate.However, it should be noted that this decrease is diffusion-limited.In other words, Equation ( 6) is correct as long as  can be estimated by means of Equation ( 7):

Steady-State Regime
In the majority of the reported experimental studies, steady-state measurements are performed ( 0  dt dn ).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.   ) as shown in Table 1 (this table is created using similar table published in paper [61]).
By applying Equations ( 8) and ( 9), constant NP K can be written as expression (10): In this 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.  .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 image 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 (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:  .In other words, the ion-capturing regimes is observed (and it approaches the "no change" regime ( elevated temperatures, Figure 3a).On a 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 T .Temperature C T 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 0  E .Interestingly, liquid crystals doped with nanoparticles and characterized by negative values of this parameter (

 E
) should exhibit an opposite effect, namely, temperature-induced capturing of ions [66].This unusual effect was analyzed in paper [66].

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 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.

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 (Figures 1-3).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.
Author Contributions: Y.G. conceived the idea of the paper, performed all simulations, and wrote the paper.

(
dashed-dotted-dotted, short-dashed, and short-dotted curves); ion capturing regime, 0  dt dn (dotted, dashed, and dashed-dotted curves); and no change regime, 0  dt dn (solid curve).The ionic contamination of nanoparticles quantified by the contamination factor NP  governs the switching between these regimes.The ion releasing regime is observed if is the critical contamination factor of nanoparticles.It is defined as 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 NP  are used.

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  (

l
is the average distance between mobile ions in liquid crystals, and D is the diffusion coefficient of ions.By using typical values ( comparing it to data shown in Figure1bit can be seen that, indeed,D NP    .

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 )).The radius of nanoparticles NP R is 10 nm.Other parameters used in simulations:

...
is also posted on Nanowerk Spotlight[77].In the case of ion capturing regime, the concentration of mobile ions in liquid crystals decreases as the weight concentration of nanodopants goes up ( The ion releasing regime is characterized by the increase in the concentration of mobile ions with an increase in the weight concentration of nanoparticles ( The concentration of mobile ions in liquid crystals doped with nanoparticles does not change if Switching between these three different regimes can be achieved by changing the level of ionic contamination of nanomaterials NP  , the ionic purity of liquid crystals (an initial concentration of mobile ions 0 n ), and by varying materials used in experiments (constant

E
is the adsorption activation energy; d E is the desorption activation energy;

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 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-capturing regime.Above this temperature ( the ionreleasing regime (Figure3b).No change regime corresponds to temperature C In this equation, n is the concentration of mobile ions in liquid crystals doped with nanoparticles; t denotes time; NP n is the volume concentration of nanoparticles in liquid crystals; NP  ) is the density of liquid crystals (nanoparticles) and NP V is the volume of a single nanoparticle.

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