The Nematic Phase

The first mesophase type is represented by the nematic phase or its chiral variant, the so-called cholesteric phase, which is fluid in all three dimensions of space. The second type is defined by layered phases, which are two-dimensionally fluid. They 

In Table 3.1 analogies between some thermotropic and lyotropic mesophases are pointed out. Only mesophases commonly accepted in literature are included in this synopsis. It is classified into the three major mesophase types discussed previously. From this comparison it is obvious, that there is a considerable amount of thermotropic mesophases, mainly smectics, for which no lyotropic analog is known. 

A more detailed description of the structure and properties of the mesophases in Table 3.1 is provided in the following subchapters. In principal, the properties and textures of analog phases are also similar due to the equivalent strucmre of the mesophases and thus are discussed simultaneously. However, the texmres of lyotropic liquid crystals often appear less colorful. This is due to the lack of aromatic units in most of the typically used surfactant molecules, as the aromatic cores of thermotropic liquid crystal largely contribute to their birefringence. Exemplary texture images of the discussed thermotropic mesophase are shown in Refs. [11, 12], while texture images of lyotropic mesophases are found in Refs. [13, 14, 15]. 

Of all liquid crystalline phases, the nematic phase is the phase with the highest symmetry, i.e. Dooh, and the least order. As shown in Fig. 3.3a, b, the mesogens solely possess orientational order. Positional order of the mass centers does not occur in this phase. Nematic phases are usually built up by either rod-like or disc-like mesogens. For thermotropic liquid crystals these mesogens are therefore calamitic or discotic molecules, respectively. In both cases the phase is simply denoted with the abbreviation N. For lyotropics, the notation typically distinguishes between nematic phases Nc, which are formed by rod-like micelles, and nematic phases Np, which are composed of disc-like micelles. 

Nematic phases typically show a schlieren texture between crossed polarizers if the director is oriented perpendicular to the viewing direction. One feature of the schlieren texture is the occurrence of topological point defects. At these point defects either two or four dark brushes meet. The corresponding defects are denoted as 1/2 or 1, respectively. Further characteristic textures of the nematic phase are the thread-like texture, which exhibits n disclinations parallel to the substrate, and the marble texture, in which areas of differing uniform director orientations occur. 

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NMR is not the best method to identify thennotropic phases, because the spectmm is not directly related to the symmetry of the mesophase, and transitions between different smectic phases or between a smectic phase and the nematic phase do not usually lead to significant changes in the NMR spectmm [ ]. However, the nematic-isotropic transition is usually obvious from the discontinuous decrease in orientational order. NMR can, however,... 

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model [201. It is applied in the case of a second-order phase transition by combining a Landau expansion for the free energy in tenns of an order parameter for smectic layering with the elastic energy of the nematic phase [20]. It is first convenient to introduce an order parameter for the smectic stmcture, which allows both for the layer periodicity (at the first hannonic level, cf equation (C2.2A)) and the fluctuations of layer position ur [20] ... 

Using this order parameter, the free energy in the nematic phase close to a transition to the smectic phase can be shown to be given by [20, 88, 89, 91]... 

C and I account for gradients of the smectic order parameter the fifth tenn also allows for director fluctuations, n. The tenn is the elastic free-energy density of the nematic phase, given by equation (02.2.9). In the smectic... 

Hamley I W, Garnett S, Luckhurst G R, Roskilly S J, Pedersen J S, Richardson R M and Seddon J M 1996 Orientational ordering in the nematic phase of a thermotropic liquid crystal A small angle neutron scattering study J. Chem. Phys. 104 10 046-54... 

The cholesteric phase maybe considered a modification of the nematic phase since its molecular stmcture is similar. The cholesteric phase is characterized by a continuous change in the direction of the long axes of the molecules in adjacent layers within the sample. This leads to a twist about an axis perpendicular to the long axes of the molecules. If the pitch of the heHcal stmcture is the same as a wavelength of visible light, selective reflection of monochromatic light can be observed in the form of iridescent colors. 

AH distortions of the nematic phase may be decomposed into three basic curvatures of the director, as depicted in Figure 6. Liquid crystals are unusual fluids in that such elastic curvatures may be sustained. Molecules of a tme Hquid would immediately reorient to flow out of an imposed mechanical shear. The force constants characterizing these distortions are very weak, making the material exceedingly sensitive and easy to perturb. 

Chira.lNema.tlc, If the molecules of a Hquid crystal are opticaHy active (chiral), then the nematic phase is not formed. Instead of the director being locaHy constant as is the case for nematics, the director rotates in heHcal fashion throughout the sample. This chiral nematic phase is shown in Figure 7, where it can be seen that within any plane perpendicular to the heHcal axis the order is nematic-like. In other words, as in a nematic there is only orientational order in chiral nematic Hquid crystals, and no positional order. Keep in mind, however, that there are no planes of any sort in a chiral nematic Hquid crystal, since the director rotates continuously about the heHcal axis. The pitch of the helix formed by the director, ie, the distance it takes for the... 

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

Chiral Smectic. In much the same way as a chiral compound forms the chiral nematic phase instead of the nematic phase, a compound with a chiral center forms a chiral smectic C phase rather than a smectic C phase. In a chiral smectic CHquid crystal, the angle the director is tilted away from the normal to the layers is constant, but the direction of the tilt rotates around the layer normal in going from one layer to the next. This is shown in Figure 10. The distance over which the director rotates completely around the layer normal is called the pitch, and can be as small as 250 nm and as large as desired. If the molecule contains a permanent dipole moment transverse to the long molecular axis, then the chiral smectic phase is ferroelectric. Therefore a device utilizing this phase can be intrinsically bistable, paving the way for important appHcations. 

Disk-shaped molecules based on a metal atom possess discotic Hquid crystal phases. An example is octasubstituted metaHophthalocyanine. FiaaHy, metallomesogens which combine both rod-like and disk-like features iato a single molecule adopt the biaxial nematic phase. In addition to there being a preferred direction for orientation of the longest molecular axis as is tme for the nematic phase, perpendicular to this direction is another preferred direction for orientation of the shortest molecular axis (12). NonmetaHomesogens which combine both rod- and disk-like features iato a single molecule also adopt a biaxial nematic phase, but at least ia one case the amount of biaxiaHty is very small (15). 

The positional order of the molecules within the smectic layers disappears when the smectic B phase is heated to the smectic A phase. Likewise, the one-dimensional positional order of the smectic M phase is lost in the transition to the nematic phase. AH of the transitions given in this example are reversible upon heating and cooling they are therefore enantiotropic. When a given Hquid crystal phase can only be obtained by changing the temperature in one direction (ie, the mesophase occurs below the soHd to isotropic Hquid transition due to supercooling), then it is monotropic. An example of this is the smectic A phase of cholesteryl nonanoate [1182-66-7] (4), which occurs only if the chiral nematic phase is cooled (21). The transitions are aH reversible as long as crystals of the soHd phase do not form. 

An exception to the mle that lowering the temperature causes transitions to phases with iacreased order sometimes occurs for polar compounds which form the smectic phase. Decreasiag the temperature causes a transition from nematic to smectic but a further lowering of the temperature produces a transition back to the nematic phase (called the reentrant nematic phase) (22). The reason for this is the unfavorable packing of the molecules ia the smectic phase due to overlap of the molecules ia the center of the layers. As the temperature is lowered, the steric iateractions overpower the attractive forces, causiag the molecules to pack much more favorably ia the nematic phase. The reentrant nematic phase can also be produced from the smectic phase by iacreasiag the pressure (23). 

In the ordered smectic or nematic phase, the rigid rods are arranged in parallel arrays that allow for close packing. The nematic phase is the most common type found with synthetic polymer molecules. The molecules long axes are parallel, but there is no layering. Aromatic polymer chains that have stiff ester or amide linkages are ideal. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

For rigid-chain crystallizable polymers, spontaneous transition into the nematic phase is accompanied by crystallization intermolecular interactions should lead to the formation of a three-dimensional ordered crystalline phase. 

It seems of importance to elucidate what the stresses are that should be applied to the melt in order to (1) ensure formation of a nematic phase in the melt, and (2) attain values of > fiCI so that the crystallization caused by melt extension should proceed by the chain-extension mechanism. It is also desirable to answer the question whether the formation of the nematic phase is an indispensable intermediate stage preceding formation of ECC51). 

First of all the term stress-induced crystallization includes crystallization occuring at any extensions or deformations both large and small (in the latter case, ECC are not formed and an ordinary oriented sample is obtained). In contrast, orientational crystallization is a crystallization that occurs at melt extensions corresponding to fi > when chains are considerably extended prior to crystallization and the formation of an intermediate oriented phase is followed by crystallization from the preoriented state. Hence, orientational crystallization proceeds in two steps the first step is the transition of the isotropic melt into the nematic phase (first-order transition of the order-disorder type) and the second involves crystallization with the formation of ECC from the nematic phase (second- or higher-order transition not related to the change in the symmetry elements of the system). 

FIGURE 5.49 A representation of the nematic phase of a liquid crystal. The long molecules lie parallel to one another but are staggered along their long axes. 

The three classes of liquid crystals differ in the arrangement of their molecules. In the nematic phase, the molecules lie together, all in the same direction but staggered, like cars on a busy multilane highway (Fig. 5.49). In the smectic phase, the molecules line up like soldiers on parade and form layers (Fig. 5.50). Cell membranes are composed mainly of smectic liquid crystals. In the cholesteric phase, the molecules form ordered layers, but neighboring layers have molecules at different angles and so the liquid crystal has a helical arrangement of molecules (Fig. 5.51). 

Small chemical changes to the tolane family of mesogenic molecules are also known to bring about major changes in phase behaviour [22]. Two examples are shown in Fig. 5 where subtle changes in the tail can eliminate the nematic phase. 

The factors Kn are elastic constants for the nematic phase and Icb is the Boltzmann constant. Therefore a combination of molecular electronic structure, orientational order and continuum elasticity are all involved in determining the flexoelectric polarisation. Polarisation can also be produced in the presence of an average gradient in the density of quadrupoles. This is... 

The low frequency Raman spectrum of 5CB in the nematic phase and several solid polymorphs is shown in Fig. 13. 

It is clear that the nematic phase exhibits a featureless Rayleigh wing and that several distinct solid phases can be formed depending on cooling rate [79]. This includes an apparently glassy phase. The vertical tick marks indicate the calculated frequencies of vibrational modes as obtained from density functional methods. 

The question arises as to how useful atomistic models may be in predicting the phase behaviour of real liquid crystal molecules. There is some evidence that atomistic models may be quite promising in this respect. For instance, in constant pressure simulations of CCH5 [25, 26] stable nematic and isotropic phases are seen at the right temperatures, even though the simulations of up to 700 ps are too short to observe spontaneous formation of the nematic phase from the isotropic liquid. However, at the present time one must conclude that atomistic models can only be expected to provide qualitative data about individual systems rather than quantitative predictions of phase transition temperatures. Such predictions must await simulations on larger systems, where the system size dependency has been eliminated, and where constant... 

Fig. 12. The distance dependence of P2+(r ), the second rank orientational order parameter for the intermolecular vector in the nematic phase formed hy GB(0.345, 0.2, 1, 2)at T of 2.6...

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