# Electrically Induced Structural Transformations of a Chiral Nematic under Tangential-Conical Boundary Conditions

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## Abstract

**:**

## 1. Introduction

**n**(the unit vector directed along the preferred orientation of molecule long axes) at the interface. There are four types of boundary conditions [13]:

- The boundary conditions, under which the director is in the orienting film plane and has a zero pretilt angle, are identified as the tangential ${\theta}_{T}={0}^{\circ}$;
- The boundary conditions, under which the director is perpendicular to the orienting film plane, are identified as homeotropic ${\theta}_{H}={90}^{\circ}$;
- The tilted boundary conditions are characterized by the fixed azimuthal director orientation and the tilt angle ${\theta}_{Ti}$, differing from ${0}^{\circ}$ and ${90}^{\circ}$;
- The boundary conditions, under which the tilt angle ${0}^{\circ}<{\theta}_{C}<{90}^{\circ}$ and the director orientation has azimuthal degeneration, are identified as conical.

## 2. Results

- The sample is placed on the microscope stage so that it is illuminated from the side of the substrate with tangential anchoring;
- The rubbing direction
**R**of the substrate with tangential anchoring is oriented perpendicularly to the polarizer direction P; - The analyzer A is rotated into a position corresponding to the intensity minimum of passed light for the considered sample area;
- In this case, according to the waveguide Mauguin regime, the orientation of analyzer A is parallel to the azimuthal director orientation at the substrate with conical anchoring [27].

#### 2.1. LC Cells Based on PiBMA:PMMA Films

#### 2.2. LC Cells Based on PiBMA:PtBMA Films

#### 2.3. Azimuthal Rotation of Linear Polarization of Light Passed through CLC Layer

#### 2.4. Inhomogeneous Azimuthal Transformation of the Director

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Materials

#### 4.2. Sample Preparation

#### 4.3. Measurements and Processing

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Optical scheme to determine the azimuthal director orientation at the substrate with conical anchoring by the rotating analyzer method. The azimuthal director orientation is characterized by $\varphi \left(z\right)$ angle, $\varphi \left(z\right)=0$ at $z=0$ (the border of LC layer with tangential anchoring), and $\varphi \left(z\right)={\varphi}_{dir}$ at $z=d$ (the border of LC layer with conical anchoring). The insertion on the right shows the azimuthal director orientation varying along z-axis schematically for the angles ${\varphi}_{dir}=-{198}^{\circ}$ (the angle between analyzer and polarizer is ${72}^{\circ}$) and ${\varphi}_{dir}=-{150}^{\circ}$ (the angle between analyzer and polarizer is ${120}^{\circ}$), as well as the corresponding orientations of polarizer P and analyzer A when the minimal light transmission is observed.

**Figure 2.**POM photos of CLC cell area with the orienting film based on PiBMA:PMMA:LN-396 = 80:20:20 mixture taken in (

**a**) initial state, (

**b**) 1 min and (

**c**) 10 min after voltage—on at $U=10$ V, and (

**d**,

**e**) 1 min, (

**f**) 120 min, (

**g**) 300 min after voltage—off. Here and below, the vector

**R**shows the rubbing direction on the substrate with tangential anchoring, and the double arrows indicate the orientation of polarizer and analyzer. (

**h**) Scheme of the azimuthal director orientation at the substrate covered with PiBMA:PMMA:LN-396 = 80:20:20 mixture 1 min after voltage-off. Photos are taken at the angle between analyzer and polarizer (

**a**–

**d**,

**f**,

**g**) ${76}^{\circ}$, (

**e**) ${40}^{\circ}$.

**Figure 3.**POM photos of CLC cell area with the orienting film based on PiBMA:PtBMA:LN-396 = 60:40:20 mixture. The texture (

**a**) before, (

**b**) in 3 min, (

**c**) in 27 min after voltage-on at $U=10$ V, and (

**d**) in 10 s after voltage-off. Photos are taken at the angle ${72}^{\circ}$ between analyzer and polarizer.

**Figure 4.**POM photos of CLC cells with the orienting films based on the polymer mixture and LC with the weight ratio (

**a**–

**d**) PiBMA:PMMA:LN-396 = 80:20:20 and (

**e**–

**h**) PiBMA:PtBMA:LN-396 = 60:40:20. (

**a**,

**e**) The area before, and (

**b**,

**f**) in voltage-on at $U=1.0$ V, (

**c**,

**g**) $U=1.3$ V, and (

**d**,

**h**) $U=1.4$ V.

**Figure 5.**POM photos of CLC cell with the orienting film based on PiBMA:PtBMA:LN-396 = 20:80:20 mixture. (

**a**) Initial texture, (

**b**) in voltage-on at $U=0.6$ V, (

**c**) in 3 min, (

**d**–

**f**) 7 min after voltage-on at $U=1.2$ V, and (

**g**) 40 min after voltage-off. (

**h**) Scheme of the azimuthal director orientation at the substrate covered with PiBMA:PtBMA:LN-396 = 20:80:20 mixture in 7 min after voltage-on at $U=1.2$ V. Photos are taken at the angle between analyzer and polarizer (

**a**–

**d**) and (

**g**) ${64}^{\circ}$, (

**e**) ${20}^{\circ}$, and (

**f**) ${140}^{\circ}$.

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**MDPI and ACS Style**

Kostikov, D.A.; Krakhalev, M.N.; Prishchepa, O.O.; Zyryanov, V.Y.
Electrically Induced Structural Transformations of a Chiral Nematic under Tangential-Conical Boundary Conditions. *Molecules* **2023**, *28*, 7842.
https://doi.org/10.3390/molecules28237842

**AMA Style**

Kostikov DA, Krakhalev MN, Prishchepa OO, Zyryanov VY.
Electrically Induced Structural Transformations of a Chiral Nematic under Tangential-Conical Boundary Conditions. *Molecules*. 2023; 28(23):7842.
https://doi.org/10.3390/molecules28237842

**Chicago/Turabian Style**

Kostikov, Denis A., Mikhail N. Krakhalev, Oxana O. Prishchepa, and Victor Ya. Zyryanov.
2023. "Electrically Induced Structural Transformations of a Chiral Nematic under Tangential-Conical Boundary Conditions" *Molecules* 28, no. 23: 7842.
https://doi.org/10.3390/molecules28237842