The Liquid Crystal & Advanced Materials Group

About Liquid Crystals

The Liquid-crystalline State - Molecular Shape and Structure and Liquid Crystals - Thermotropic Liquid Crystals - Lyotropic Liquid Crystals - Plastic Crystals - Structures of Thermotropic Liquid Crystals - Structures of Smectic Liquid Crystals

Structures of Thermotropic Liquid Crystals

Consider the melting of a hypothetical calamitic, rod-like, thermotropic liquid-crystalline material where all of the liquid crystal mesophases are represented and they are enantiotropic with respect to the melt point. As noted previously, three general types of liquid crystal state will be found; an anisotropic plastic mesophase range, a smectic liquid crystal region and an orientationally ordered nematic state. The first two of these sates can be further sub-divided into a number of subgroups depending on the packing structures of the consituent molecules. The nematic phase is not subdivided. With respect to the smectic and soft crystal states, the mesophases have a defined thermodynamic order, ie, as the hypothetical liquid-crystalline compound is heated the mesophases will occur in a certain defined sequence as shown below,

Crystal, H, K, E, G, J, S_F, B_(cryst), S_B(hex), S_I, S_C, S_A, N, Isotropic Liquid
‡Decreasing Order ‡

where the soft crystal phases are denoted by capital letters, except for the nematic phase which is denoted as N, and the smectic liquid crystal phases are given the captial letter S and the various subgroups are given capital subletters. The nomenclature system is based on a miscibility grouping method; for example when a phase of a test material is found to miscible with a phase of a standard material across the whole concentration range of a composition/temperature phase diagram, then the phase of the test compound is said to belong to the same miscibility group as that of the standard. Historically, phases of diverse structures were identified and characterised at different points in time, and consequently the labelling system is not systematic or in an alphabetical order. Therefore, the information conveyed by the code letter is of little value in the description of the phase. Thus, it should be noted that the classification is not based on the structural parameters of a mesophase, but rather on the fact that the phase mixes with that of a standard material. Immiscibility therefore is not a valid criteria in the determination of group type.

More recently X-ray diffraction techniques have been used to investigate the structure of the smectic state. This has led to the combination of miscibility classifications with structural observations. Thus, certain structural features, such as the extent of the positional ordering, tilt ordering, packing structures, and bond orientational ordering are also associated with each smectic miscibility class.

The Nematic Phase

The nematic phase is essentially a one-dimensionally ordered elastic fluid in which the molecules are orientationally ordered, but where there is no long range positional ordering of the molecules. Thus, this least ordered of liquid crystal phases has an opaque liquid-like appearance, the opacity being due to the birefringent nature of the anisotropic ordering and anisotropic optical propties of the molecules. (The birefringent nature of liquid crystals is used in thermal polarized light micrscopy for the identification of phase type). In the calamitic nematic phase the rod-like molecules tend to align parallel to each other with their long axes all pointing roughly in the same direction. The average direction along which the molecules point is called the director of the phase, and is usually given the symbol n. The rod-like molecules in the nematic phase are free to rotate about their short axes and to some degree about their long axes, however, the relaxation times for rotations about the long axes are much longer (~10^-6 s^-1) than those about their short axes (~10^-11 s^-1). The structure of the nematic phase is depicted in figure 1.

In the bulk nematic phase, there are as many molecules pointing in one direction relative to the director as there are pointing in the opposite direction (a rotation of 180°), ie, the molecules have a disordered head-to-tail arrangement in the phase. Thus the phase has rotational symmetry relative to the director. The degree to which the molecules are aligned along the director is termed the order parameter of the phase. The order parameter is defined by the equation

S = 1/2<3cos²θ - 1>

where θ is the angle made between the long axis of each individual rod-like molecule and the director. The brackets in the equation imply that this is an average taken over a very large number of molecules.

An order parameter of zero implies that the phase has no order at all (it is liquid-like) whereas a value of one indicates that the phase is perfectly ordered, ie, all the long axes of the molecules are parallel to one another and to the director. For a typical nematic phase the order parameter has a value in the region of between 0.4 and 0.7 indicating that the molecules are considerably disordered. The order parameter has the same symmetry properties as the nematic phase, in that the order parameter is unchanged by rotating any molecule through an angle of 180°.

The Chiral Nematic, N* (Cholesteric) Phase

In the cholesteric phase some or all of the molecules have asymmetric chemical structures. Typically, compounds that exhibit cholesteric phases possess a chiral carbon atom, however, other chiral atoms or a reduced space symmetry (ie, axial symmetry) can also induce the formation of this phase. The structure of the cholesteric phase is one where the local molecular ordering is identical to that of the nematic phase. In the direction normal to the director the molecules pack to form a helical macrostructure, ie, in the calamitic variation, the director is rotated in a direction perpendicular to the long axes of the molecules, hence the phase is sometimes called the chiral nematic phase, N*. As in the nematic phase the molecules have no long range positional order, and no layering exists. The pitch of the helix can vary from about 0.1 x 10^-6 m to almost infinity. When the pitch of the phase is comparable to the wave length of light, the mesophase will selectively reflect light of a relatively narrow wavelength band and appear iridescent. The pitch of the phase is temperature dependent, and therefore the selective refection properties are also temperature dependent thereby making this phase useful in the area of surface thermography. The optic axis of the phase is along the helical axis so the phase has a negative birefringence and is optically uniaxial. Disc-like molecules can also exhibit cholesteric phases when they possess chiral molecular structures.