Helicoidal optical properties

Lyotropic liquid crystalline cellulose derivatives exhibit unique optical properties because of their helicoidal supramolecular structure.The chiro-optical properties of the helicoidal structure can be described by a pitch p (or its inverse, the twist p ) p = 2o/fi, where is the reflection wavelength and h is the mean refractive index of a sheet, and the corresponding handedness of the twist right-handed helicoidal structure being assigned to a positive pitch p > 0) and left-handed helicoidal structures to a negative pitch p < The nematic mesophase can be... 

Cellulose and some derivatives form liquid crystals (LC) and represent excellent materials for basic studies of this subject. A variety of different structures are formed, thermotropic and lyotropic LC phases, which exhibit some unusual behavior. Since chirality expresses itself on the configuration level of molecules as well as on the conformation level of helical structures of chain molecules, both elements will influence the twisting of the self-assembled supermolecular helicoidal structure formed in a mesophase. These supermolecular structures of chiral materials exhibit special optical properties as iridescent colors, and... 

The optical properties of chiral nematic phases are closely related to their supermolecular Structures, as stated by the considerations of de Vries. In particular, the planar textures exhibit beautiful colors correlated to the pitch P of the helicoidal structures by Eq. (1), if the selective reflection wavelength lies in the visible range, and many examples are shown in Fig. 2. 

However, this stmcture is helicoidal in which the local director processes around the helical axis Z forming a helicoidal superstmcture with helix pitch P corresponding to the turn of the director at an angle of In and a period of change in optical properties d = P/2. Hence,... 

In this chapter, we will therefore focus on this latter group of structures, in particular helicoidal stacks, where the optical properties are well understood, and whose artifieial production using biopolymers has been demonstrated. 

After a brief introduetion of helicoidal architecture and their optical properties, we will describe examples observed in nature. Then, we will discuss liquid crystals and biomimetic photonics. Finally, we will discuss the future of the field, its extension into templating, sensors, and the use of cellulose derivatives. 

It is easy to understand the difference of the optical properties of the ferroelectric and antiferroelectric helicoidal structures shown in Figures 9.5(a) and (b). For light propagating along the helicoidal axis, the two structures are apparently the same, since half the pitch is optically one period in both structures. In contrast, for obliquely incident light, the molecular orientations... 

One optical feature of helicoidal structures is the ability to rotate the plane of incident polarized light. Since most of the characteristic optical properties of chiral liquid crystals result from the helicoidal structure, it is necessary to understand the origin of the chiral interactions responsible for the twisted structures. The continuum theory of liquid crystals is based on the Frank-Oseen approach to curvature elasticity in anisotropic fluids. It is assumed that the free energy is a quadratic function of curvature elastic strain, and for positive elastic constants the equilibrium state in the absence of surface or external forces is one of zero deformation with a uniform, parallel director. If a term linear in the twist strain is permitted, then spontaneously twisted structures can result, characterized by a pitch p, or wave-vector q=27tp i, where i is the axis of the helicoidal structure. For the simplest case of a nematic, the twist elastic free energy density can be written as ... 

From the above it is clear that the optical response of helicoidal structures of liquid crystal molecules depends on the pitch, and in order to relate these optical properties to molecular structures, the dependence of pitch on molecular structure must be considered. 

As described earlier, the spectacular optical properties of chiral nematics are determined by the helicoidal pitch, the birefringence (and refractive index), the direction and polarization of the incident light, and the arrangement of the helix axis. For normally incident light the direction of the helix axis gives rise to the three classical textures depicted in Fig. 2, and typical photomicrographs taken with crossed polarizers are shown in Fig. 6 these are ... 

These optical properties of chiral nematic materials have all been observed experimentally. There have been quite extensive theoretical studies carried out by Mauguin [60], Oseen [61], and de Vries [26] to explain how these properties arise from the he-licoidal structure. Kats [62] and Nityanan-da [63] have derived exact wave equations to explain the propagation of light along the optic axis and Friedel [32] has reviewed the main textures observed with chiral nematics. We will outline the important elements of these studies in the next sections (Secs. 2.2.1.1 -2.2.1.3). In Sec. 2.2.1.4 we will consider how the helicoidal pitch, and... 

The presence of a cholesteric helicoid stracture determines the significant optical rotation of HPC in aqueous solutions p is 4 10 degml/dm-g [10]. Analysis of the optical properties indicates the formation of a left-handed cholesteric helix in aqueous solutions of HPC, solutions of cellulose carbanilate in methyl ethyl ketone, and ethylcellulose in dichloroacetic acid. In most cases. 

This structure, when it is present, appears always as the first stable tilted phase below the orthogonal SmA phase. Tilts in all layers are equal and also all phase differences a are equal. From this point of view the phase is equal to the SmC and the SmC phase. The main difference in the macroscopic properties is the magnitude of the angle a, which is neither close to zero nor close to tt (Fig. 5.4c and d). The structure is helicoidally modulated but has a very short pitch, which extends from a few tens of layers to shorter periods than four layers. Due to the short pitch, the structure optically does not differ from the orthogonal phase and does not exhibit other properties like optical rotatory power, typical for other helicoidally modulated structmes. 

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