Abstract
Keywords
The ability of controlling and manipulating the rearrangement of molecules through external stimuli to obtain tunable and reversible structural characteristics is a major driving force towards the development of multifunctional devices. The cholesteric liquid crystal (CLC) or chiral nematic liquid crystal (LC) with self-organized helical superstructure and typical stimulus-response characteristics has undoubtedly served as a model system for better understanding orientation-related supramolecular dynamic helical structures and exploring their potential in technological applications[
As early as 50 years ago, Meyer and de Gennes[
In this Letter, we demonstrated the theoretical framework of the electrically induced CLC heliconical superstructure and employed numerical simulations to quantitatively evaluate the importance of the bend and twist elastic effects on the formation and tunability of the superstructure, as well as the evolution of pitch length and oblique angle. To further confirm the optical properties of the heliconical superstructure, we utilized the Berreman’s matrix method to numerically analyze the corresponding selective reflection characteristics, including the circular polarization selectivity, reflective intensity, and the reflection band shifting under the dual stimuli of applied electric fields and system chirality.
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The electric-field-induced LC director arrangement can be described by using the Oseen–Frank free energy function. The elastic energy density for the CLC helical superstructure is written as where , , and are the splay, twist, and bend elastic constant, respectively; is a unit vector denoting the LC director; , representing the system chirality determined by the chemical composition; is the initial pitch length when there is no electric field; , is the dielectric anisotropy, representing the difference between the dielectric constant of the LC director along the long axis and the short axis; is the permittivity of vacuum; is the external electric field. Generally, the electric-field correlation of the CLC structure is the perturbation of the helix at low fields, followed by complete unwinding at a certain threshold field. As shown in Fig.
Figure 1.Schematic illustration of LC director configurations in cholesteric (a) helicoidal, (b) heliconical, and (c) unwound states under increased applied electric fields.
In the absence of an external electric field, the chirality from intermolecular interaction will guide the LC molecules to self-organize into a helicoidal superstructure, where the LC director twists at a right angle around the helical axis , as shown in Fig.
The azimuth angle , is determined by the position of the LC on the axis, and the negative sign indicates left-handedness. When an electric field parallel to is applied, the distortion in the CLC system involves both bending and twisting, which depends on the relative magnitudes of the twist elastic constant and bend elastic constant . If , there is no distortion until the electric field reaches a threshold value , where the helix is completely unwound into a homeotropic alignment, as shown in Fig.
For , it can reach a regime under the action of the external electric field, where there is a delicate equilibrium between bending and twisting elastic effects and a competitive coupling between the dielectric torque and the twist torque of the CLC system, resulting in the heliconical state, in which the helix remains unchanged without any distortion or re-orientation, and the director rotates around the helix with an oblique angle (), as shown in Fig.
The electric-field-induced CLC heliconical superstructure exists between the helicoidal superstructure and the unwound state with the corresponding applied electric field being located between the lower induction threshold and the upper unwinding threshold , which can be calculated by the following equations:where is the ratio of the bend and the twist elastic constants, denoting the elastic effect coupling. Equation (
The CLC heliconical state demonstrated here is distant from the electric-induced layer undulation of the ordinary CLC, which usually exhibits fingerprint texture[
Then, we employed numerical calculations to quantitatively describe the phase diagram of the CLC heliconical superstructure and the importance of the value for the and changes under the application of an electric field. As shown in Fig.
Figure 2.Electrical tuning performance of the (a) oblique angle
The initial chirality (or initial pitch length ) of the system is also of great significance during the formation and tuning of the oblique angle and pitch length in the heliconical superstructure. In addition, the advanced light-responsive CLC systems manipulating their helical characteristics are based on the mechanism that light irradiation changes the initial system chirality[
Figure 3.Electrical tuning performance of the (a) transformation threshold, (b) oblique angle, and (c) pitch length in the heliconical superstructure on the effects of chirality changes.
The stronger the chirality of the system, the corresponding two threshold values both show a linear increasing trend, where the slopes are related to the elastic effect coupling. In the case of weak chirality, the dielectric torque dominates the orientation of LCs, and the system is more likely to unwind under the applied electric field. Therefore, the heliconical state can only exist within a limited electric-field range. In contrast, attributed to the comparable competition between elastic toque and dielectric torque under high chirality, the system establishes better stability and is difficult to be untwisted, so the electric-field range where the heliconical superstructure can exist is extended. Then, we assume that an electric field acts on the CLC heliconical superstructure by gradually reducing the chirality to illustrate the evolution of oblique angle and pitch length [Figs.
Such delicate field-dependent pitch and oblique angle tunability endows the heliconical superstructure with a wide range of the periodicity and effective refractive index modulation in the spiral direction, thereby enabling selective control over the reflection band or the photonic band gap. To further evaluate the optical properties of the heliconical superstructure, we utilize Berreman’s 4 × 4 matrix method to numerically analyze the selective reflection properties, including the circular polarization selectivity of the structural reflection band, the reflective intensity, and the reflection band shifting under different electric fields. For hierarchical optical media, its precise transmission and reflection spectral properties can be directly calculated by Berreman’s matrix method[
Consider a CLC system with the following parameters: chirality , with left-handed helix; necessary elastic effect coupling ; birefringence index , , ignoring the refractive index dispersion; and dielectric anisotropy is sandwiched in a 35 μm LC cell with a homogeneous alignment. In the situation of ideal circularly polarized light normal incidence, the corresponding structure reflection spectra from the heliconical state under some certain electric fields are shown in Fig.
Figure 4.Simulated selective reflection spectra from the left-handed heliconical superstructure with various electric fields in the cases of R-CP and L-CP normal incidence.
We also simulated the effect of initial chirality change on the corresponding reflection band while maintaining the external electric field. Taking as an example, the heliconical superstructure exhibits a reflection band at 1240 nm. Gradually reducing the initial chirality of the system from 2.42 to results in a significant reduction in the reflection intensity, but with only a small spectral blue shift. A further reduction in chirality will lead to unwinding of the system, thereby completely losing the reflection. The modulation of chirality breaks the original equilibrium between the dielectric torque and the twist torque, giving rise to the prominent changes on both the arrangement transformation of the helix and the reflection performance. According to the calculation results of Figs.
Figure 5.Calculated reflection spectra from the heliconical superstructure with the changes of electric field and initial chirality.
In conclusion, we have systematically described the phase transition in a cholesteric system in the presence of a longitudinal external field parallel to the helical axis. The unique heliconical superstructure appears between the right-angle helicoidal state and unwinding state under the external field in the CLC system equipped with the necessary elastic effect of . Both the oblique angle and the pitch length in the heliconical superstructure decrease as the electric field decreases, thus generating a wide range of tunable selective structure reflection bands. Moreover, our calculations show that the phase behavior and helical properties can be drastically manipulated by changing the chirality. This work is useful to further understand the characteristics of the CLC heliconical superstructures and the twisting and bending distortion in the chiral system, thereby providing some new insights for further exploring scientific research and developing related multifunctional devices.
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