# Investigating the Electro-Optic Response of Steroid Doped Liquid Crystal Devices
## 1 Introduction  
The cholesteric liquid crystal (CLC) phase is a chiral, self-assembled helicoidal superstructure that exhibits a circularly polarized reflection of light on the nano- to micrometer length scale. The characteristic helical structure is formed through the intrinsic molecular chirality of the liquid crystals (LC), also called mesogens, or through the mixing of achiral mesogens with nonracemic chiral molecules [1, 2]. Pioneering work on cholesterol benzoate led to the initial discovery of \"flowing crystals\" in 1888 by botanist [PERSON] and physicist [PERSON] [3, 4]. In this system, the CLC phase spontaneously formed through the molecular chirality of the mesogenic cholesterol benzoate itself. Later work on achiral nematic liquid crystals (NLCs) indicated that a transformation to the CLC phase occurred upon the addition of a non-racemic chiral molecule [5]. Here, the molecular interactions between the chiral molecule and the nematic mesogens induce a chirality transfer process to form a CLC phase that has the same handedness as the added chiral dopant [6]. The ability to form the CLC phase, sometimes referred to as the chiral nematic phase, by combining chiral molecules and NLCs has enabled a plethora of combinations to be explored with customizable properties. NLCs possess long-range orientational order and exhibit dielectric anisotropy. The anisotropy of the NLCs enables the modulation of their orientation via external stimuli such as temperature, electric fields, or mechanical pressure. The stimuli responsive property is also observed in CLC systems. These materials have been used industrially in LCDs [7] and reflective displays/optics [8, 9], temperature responsive photonic devices [10], rewritable color recording [11], tunable band pass filters [12, 13],and smart windows [14; 15]. CLCs can also be polymer stabilized to improve the thermal stability and response time of electrically responsive devices (i.e., reflection tuning or switching), making them promising materials for displays [16]. The choice of chiral dopant is significant for determining the handedness of the helicoidal superstructure and reflection wavelength of a CLC. The selective reflection of a CLC system is determined by the ability of a chiral dopant to induce a twist in the nematic phase, referred to as the helical twisting power (HTP), according to the equation:  
\[\beta=(\mathrm{pCr})^{-1}\]  
where \(\beta\) is the HTP of the chiral dopant, \(\mathrm{p}\) is the pitch of the CLC, \(\mathrm{C}\) is the dopant concentration, and \(\mathrm{r}\) is the enantiomeric excess of the chiral dopant [17]. Increasing the chiral dopant concentration typically blue shifts the reflection peak as the CLC pitch length decreases. Subsequently, dopants with higher HTP values enable a selective reflection notch to be generated at lower concentrations. The HTP is dependent on the NLC matrix and will have slight variations across mesogenic systems. Other important properties are the chiral dopant's phase stability and miscibility as phase separation can be a limiting issue. Therefore, the selection of a chiral dopant is crucial for the creation and utilization of CLC systems. The stability and miscibility of the dopants are controllable through the structural modification of a chosen chiral molecule. The HTP of a chiral dopant can be increased by affixing aromatic moieties that are quasi-planar to increase interactions with the rigid nematic mesogens [16]. An increase in the aromaticity and rigidity of a chiral dopant often lead to a reduction in the miscibility of the dopant and must be balanced through the addition of alkyl chains. Many chiral dopants are fully synthetic, needing numerous synthetic modifications to meet the design rules [17]. Naturally occurring molecules have garnered attention as potential dopants due to their inherent chirality, high enantiomeric purity, and functional groups that enable chemical modification.