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

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## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Model

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

^{2}/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, ${\tau}_{NP}\gg {\tau}_{D}$.

#### 2.3. Steady-State Regime

#### 2.4. Temperature-Induced Effects

## 3. Case Studies: A Brief Survey

## 4. Case Study: Non-Monotonous Dependence $n({\omega}_{NP})$

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

LCD | Liquid crystal display |

## References

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**Figure 1.**(

**a**) The volume concentration of mobile ions $n$ versus time calculated using different values of the weight concentration of nanoparticles ${\omega}_{NP}$ and their contamination factor ${v}_{NP}$ (${v}_{NP}={10}^{-4}$ (dotted, dashed, and dotted–dashed curves); ${v}_{NP}=3\times {10}^{-4}$ (solid curve); ${v}_{NP}=5\times {10}^{-4}$ (dashed–dotted–dotted, short-dashed, and short-dotted curves). The radius of nanoparticles ${R}_{NP}$ is 5 nm. (

**b**) The time constant ${\tau}_{NP}$ as a function of the weight concentration of nanoparticles ${\omega}_{NP}$ calculated at different values of the nanoparticle radius ${R}_{NP}$ (${R}_{NP}=5\text{}\mathrm{nm}$ (dashed–dotted curve); ${R}_{NP}=10\text{}\mathrm{nm}$ (dashed curve); ${R}_{NP}=25\text{}\mathrm{nm}$ (dotted curve); ${R}_{NP}=50\text{}\mathrm{nm}$ (solid curve)). Other parameters used in simulations: ${K}_{NP}={10}^{-23}\text{}{\mathrm{m}}^{3}$, ${k}_{d}^{NP}={10}^{-3}\text{}{s}^{-1}$, ${\sigma}_{S}^{NP}=0.8\times {10}^{18}\text{}{\mathrm{m}}^{-2}$, ${n}_{0}=3\times {10}^{19}\text{}{\mathrm{m}}^{-3}$, ${\rho}_{NP}/{\rho}_{LC}=3.9$. Reproduced from [69], under the Creative Commons Attribution License.

**Figure 2.**The volume concentration of mobile ions $n$ in liquid crystals versus the weight concentration of nanoparticles ${\omega}_{NP}$ calculated at different values of their contamination factor ${v}_{NP}$ (${v}_{NP}={10}^{-4}$ (solid curve); ${v}_{NP}=3\times {10}^{-4}$ (dotted curve); and ${v}_{NP}=5\times {10}^{-4}$ (dashed curve)). The radius of nanoparticles ${R}_{NP}$ is 10 nm. Other parameters used in simulations: ${K}_{NP}={10}^{-23}\text{}{\mathrm{m}}^{3}$, ${\sigma}_{S}^{NP}=0.8\times {10}^{18}\text{}{\mathrm{m}}^{-2}$, ${n}_{0}=3\times {10}^{19}\text{}{\mathrm{m}}^{-3}$, ${\rho}_{NP}/{\rho}_{LC}=3.9$. This figure is also posted on Nanowerk Spotlight [77].

**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: ${v}_{NP}=0$ (

**a**) and ${v}_{NP}=4\times {10}^{-4}$ (

**b**); ${K}_{NP}(T=293K)={10}^{-23}\text{}{\mathrm{m}}^{3}$; $\Delta E=+0.3$ eV; ${\sigma}_{S}^{NP}=0.8\times {10}^{18}\text{}{\mathrm{m}}^{-2}$; ${n}_{0}=3\times {10}^{19}\text{}{\mathrm{m}}^{-3}$; ${\rho}_{NP}/{\rho}_{LC}=3.9$. 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 4.**The total ion density of mobile ions in liquid crystals doped with silica nanoparticles as a function of their weight concentration ${\omega}_{NP}$: (

**a**) $n({\omega}_{NP})={n}_{1}({\omega}_{NP})+{n}_{2}({\omega}_{NP})$; (

**b**) ${n}_{1}({\omega}_{NP})$ (solid curve) and ${n}_{2}({\omega}_{NP})$ (dashed curve). Reported experimental data points [80] are represented by circles. A blue curve shows theoretical fit according to Equations (3) and (4). Fitting parameters: ${n}_{01}=6.4\times {10}^{20}\text{}{\mathrm{m}}^{-3}$; ${K}_{NP1}=6.25\times {10}^{-25}\text{}{\mathrm{m}}^{3}$; ${\sigma}_{S1}^{NP}=2.5\times {10}^{18}\text{}{\mathrm{m}}^{-2}$; ${v}_{NP1}=0$; ${n}_{02}=0\text{}{\mathrm{m}}^{-3}$; ${K}_{NP2}={10}^{-27}\text{}{\mathrm{m}}^{3}$; ${\sigma}_{S2}^{NP}=2.5\times {10}^{18}\text{}{\mathrm{m}}^{-2}$; ${v}_{NP2}=5.75\times {10}^{-5}$; ${R}_{NP}=3.5\text{}\mathrm{nm}$; ${\rho}_{NP}/{\rho}_{LC}=2.4$.

**Figure 5.**The total ion density of mobile ions in liquid crystals doped with silica nanoparticles as a function of their weight concentration ${\omega}_{NP}$: (

**a**) $n({\omega}_{NP})={n}_{1}({\omega}_{NP})+{n}_{2}({\omega}_{NP})$; (

**b**) ${n}_{1}({\omega}_{NP})$ (solid curve) and ${n}_{2}({\omega}_{NP})$ (dashed curve). Reported experimental data points [80] are represented by circles. A blue curve shows theoretical fit according to Equations (3) and (4). Fitting parameters: ${n}_{01}=5.59\times {10}^{20}\text{}{\mathrm{m}}^{-3}$; ${K}_{NP1}=1.1\times {10}^{-23}\text{}{\mathrm{m}}^{3}$; ${\sigma}_{S1}^{NP}=2.5\times {10}^{18}\text{}{\mathrm{m}}^{-2}$; ${v}_{NP1}=0$; ${n}_{02}=0\text{}{\mathrm{m}}^{-3}$; ${K}_{NP2}=3\times {10}^{-26}\text{}{\mathrm{m}}^{3}$; ${\sigma}_{S2}^{NP}=2.5\times {10}^{18}\text{}{\mathrm{m}}^{-2}$; ${v}_{NP2}=2\times {10}^{-6}$; ${R}_{NP}=3.5\text{}\mathrm{nm}$; ${\rho}_{NP}/{\rho}_{LC}=2.4$.

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

Physical Parameters | Ion-Capturing Regime | No Change Regime | Ion-Releasing Regime |
---|---|---|---|

Contamination level of nanomaterials, ${\nu}_{NP}$ | ${\nu}_{NP}<\frac{{K}_{NP}{n}_{0}}{1+{K}_{NP}{n}_{0}}$ | ${\nu}_{NP}=\frac{{K}_{NP}^{}{n}_{0}}{1+{K}_{NP}{n}_{0}}$ | ${\nu}_{NP}>\frac{{K}_{NP}{n}_{0}}{1+{K}_{NP}{n}_{0}}$ |

Initial concentration of ions in liquid crystals, ${n}_{0}$ | ${n}_{0}>\frac{1}{{K}_{NP}\left(\frac{1}{{\nu}_{NP}}-1\right)}$ | ${n}_{0}=\frac{1}{{K}_{NP}\left(\frac{1}{{\nu}_{NP}}-1\right)}$ | ${n}_{0}<\frac{1}{{K}_{NP}\left(\frac{1}{{\nu}_{NP}}-1\right)}$ |

Constant, ${K}_{NP}$ | ${K}_{NP}>\frac{1}{{n}_{0}\left(\frac{1}{{\nu}_{NP}}-1\right)}$ | ${K}_{NP}=\frac{1}{{n}_{0}\left(\frac{1}{{\nu}_{NP}}-1\right)}$ | ${K}_{NP}<\frac{1}{{n}_{0}\left(\frac{1}{{\nu}_{NP}}-1\right)}$ |

Materials | Reported Effects | Physical Parameters |
---|---|---|

Anatase ($Ti{O}_{2}$) nanoparticles in nematic liquid crystals (E44) | Ion-capturing effect [49] | ${K}_{NP}={10}^{-23}$ m^{3}; ${\nu}_{NP}=1.5\times {10}^{-4}$; ${\sigma}_{S}^{NP}=0.8\times {10}^{18}$ m^{−2}; ${R}_{NP}=5$ 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] | ${K}_{NP}=0.7\times {10}^{-23}$ m^{3}; ${\nu}_{NP}=9.5\times {10}^{-6}$; ${\sigma}_{S}^{NP}={10}^{18}$ m^{−2}; ${R}_{CNT}=2.5$ nm; ${L}_{CNT}=500$ 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] | ${K}_{NP}={10}^{-22}$ m^{3}; ${\nu}_{NP}={10}^{-2}$; ${\sigma}_{S}^{NP}=1.25\times {10}^{17}$ m^{−2}; ${R}_{NP}=5$ 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] | ${K}_{NP}=0.8\times {10}^{-25}$ m^{3}; ${\nu}_{NP}=0.25$; ${\sigma}_{S}^{NP}=1.25\times {10}^{17}$ m^{−2}; ${R}_{NP}=5$ 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] | ${K}_{NP}=0.8\times {10}^{-23}$ m^{3}; ${\nu}_{NP}=8.5\times {10}^{-6}$; ${\sigma}_{S}^{NP}=0.33\times {10}^{18}$ m^{−2}; ${R}_{GNF}=5$ nm; ${L}_{GNF}=10$ nm; $\raisebox{1ex}{${\rho}_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho}_{LC}$}\right.=1.8$ [62] |

Ferroelectric nanoparticles ($LiNb{O}_{3}$) in liquid crystals | Ion-capturing effect [55] | ${K}_{NP}=7\times {10}^{-23}$ m^{3}; ${\nu}_{NP}=0.1075$; ${\sigma}_{S}^{NP}=5\times {10}^{18}$ m^{−2}; ${R}_{NP}=12.5$ nm; $\raisebox{1ex}{${\rho}_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho}_{LC}$}\right.=4.65$ [62] |

Ferroelectric particles ($BaTi{O}_{3}$) in nematic liquid crystals | Ion-capturing effect [57] | ${K}_{NP}=4\times {10}^{-20}$ m^{3}; ${\nu}_{NP}=0.3$; ${\sigma}_{S}^{NP}={10}^{19}$ m^{−2}; ${R}_{NP}=1000$ nm; $\raisebox{1ex}{${\rho}_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho}_{LC}$}\right.=6.02$ [62] |

Ferroelectric nanoparticles ($BaTi{O}_{3}$) in nematic liquid crystals (E44) | Temperature-induced release of ions [58] | ${\nu}_{NP}=0$; ${K}_{0}^{NP}=1.93\times {10}^{-30}$ m^{3}; $\Delta E=0.4$ eV; ${\sigma}_{S}^{NP}=5\times {10}^{18}$ m^{−2}; ${R}_{NP}=20$ 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] | ${\nu}_{NP}=4.35\times {10}^{-4}$; ${K}_{NP}=1.6\times {10}^{-23}$ m^{3}; ${\sigma}_{S}^{NP}=0.8\times {10}^{18}$ m^{−2}; ${R}_{NP}=25$ 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] | ${\nu}_{NP}=0$; ${K}_{NP}=3.65\times {10}^{-24}$ m^{3}; ${\sigma}_{S}^{NP}=2\times {10}^{18}$ m^{−2}; ${R}_{NP}=25$ 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] | ${\nu}_{NP}=3.379\times {10}^{-3}$; ${K}_{NP}={10}^{-26}$ m^{3}; ${\sigma}_{S}^{NP}={10}^{18}$ m^{−2}; ${R}_{NP}=3$ 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] | ${\nu}_{NP}=0.3075$; ${K}_{NP}={10}^{-23}$ m^{3}; ${\sigma}_{S}^{NP}=7\times {10}^{18}$ m^{−2}; ${R}_{NP}=58.5$ nm; $\raisebox{1ex}{${\rho}_{NP}$}\!\left/ \!\raisebox{-1ex}{${\rho}_{LC}$}\right.=4.907$ [71] |

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**MDPI and ACS Style**

Garbovskiy, Y.
Nanomaterials in Liquid Crystals as Ion-Generating and Ion-Capturing Objects. *Crystals* **2018**, *8*, 264.
https://doi.org/10.3390/cryst8070264

**AMA Style**

Garbovskiy Y.
Nanomaterials in Liquid Crystals as Ion-Generating and Ion-Capturing Objects. *Crystals*. 2018; 8(7):264.
https://doi.org/10.3390/cryst8070264

**Chicago/Turabian Style**

Garbovskiy, Yuriy.
2018. "Nanomaterials in Liquid Crystals as Ion-Generating and Ion-Capturing Objects" *Crystals* 8, no. 7: 264.
https://doi.org/10.3390/cryst8070264