Orientational order molecules

Liquid crystals may be classified as nematic, cholesteric, smectic, or columnar. Nematic liquid crystals are characterized only by orientational order. Molecules tend to be aligned with a director, as illustrated in Figure 16.1. 

R 228 R.T. Syvitski, Spectral Analysis of Orientationally Ordered Molecules , p. 89... 

Grazing incidence excitation of a fluorescent probe in a phospholipid monolayer can also be used to indicate order. The collective tilt of the molecules in a domain inferred from such measurements is indicative of long-range orientational order [222]. 

The label liquid crystal seems to be a contradiction in tenns since a crystal cannot be liquid. However, tire tenn refers to a phase fonned between a crystal and a liquid, witli a degree of order intennediate between tire molecular disorder of a liquid and tire regular stmcture of a crystal. Wlrat we mean by order here needs to be defined carefully. The most important property of liquid crystal phases is tliat tire molecules have long-range orientational order. For tliis to be possible tire molecules must be anisotropic, whetlier tliis results from a rodlike or disclike shape. 

Thennotropic liquid crystal phases are fonned by anisotropic molecules witli long-range orientational order and in many types of stmcture witli some degree of translational order. The main types of mesogen are Arose tlrat are rodlike or calamitic and Arose Arat are disclike or discotic. 

Thennotropic liquid crystal phases are fonned by rodlike or disclike molecules. However, in the following we consider orientational ordering of rodlike molecules for definiteness, although the same parameters can be used for discotics. In a liquid crystal phase, the anisotropic molecules tend to point along the same direction. This is known as the director, which is a unit vector denoted n. 

McMillan s model [71] for transitions to and from tlie SmA phase (section C2.2.3.2) has been extended to columnar liquid crystal phases fonned by discotic molecules [36, 103]. An order parameter tliat couples translational order to orientational order is again added into a modified Maier-Saupe tlieory, tliat provides tlie orientational order parameter. The coupling order parameter allows for tlie two-dimensional symmetry of tlie columnar phase. This tlieory is able to account for stable isotropic, discotic nematic and hexagonal columnar phases. 

Emsiey J W, Luckhust G R and Stockley C P 1982 A theory of orientational ordering in uniaxial liquid-crystals composed of molecules with alkyl chains Proc. R. See. A 381 117-28... 

Fig. 1. Orientational order of the molecules in a liquid crystal. 9 is the angle between the long axis of a molecule and the direction of preferred orientation...

Fig. 2. Schematic representation of the orientational distribution function f 6) for three classes of condensed media that are composed of elongated molecules A, soHd phase, where /(0) is highly peaked about an angle (here, 0 = 0°) which is restricted by the lattice B, isotropic fluid, where aU. orientations are equally probable and C, Hquid crystal, where orientational order of the soHd has not melted completely.

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... 

Eor example, bis-(T- -heptyloxyben2yHdene)-l,4-phenylenediamine [24679-01-4] exhibits seven Hquid crystal phases the nematic and six smectic phases (19). The order of appearance of the phases as the temperature is increased is usually consistent with a decrease in the long-range positional and orientational order of the molecules. Eor example, ethyl 4-(4 -ethoxyben2yHdeneamino)cinnamate [2863-94-7] (3) has three Hquid crystal phases (20). 

The plateaus ia the isotherm, where pressure does not change and area per molecule decreases, iadicates an increasing orientational order. 

The last phase transition is to the soHd state, where molecules have both positional and orientational order. If further pressure is appHed on the monolayer, it collapses, owiag to mechanical iastabiHty and a sharp decrease ia the pressure is observed. This coUapse-pressure depends on the temperature, the pH of the subphase, and the speed with which the barrier is moved. 

For a removal attempt a molecule is selected irrespective of its orientation. To enhance the efficiency of addition attempts in cases where the system possesses a high degree of orientational order, the orientation of the molecule to be added is selected in a biased way from a distribution function. For a system of linear molecules this distribution, say, g u n ), depends on the unit vector u parallel to the molecule s symmetry axis (the so-called microscopic director [70,71]) and on the macroscopic director h which is a measure of the average orientation in the entire sample [72]. The distribution g can be chosen in various ways, depending on the physical nature of the fluid (see below). However, g u n ) must be normalized to one [73,74]. In other words, an addition is attempted with a preferred orientation of the molecule determined by the macroscopic director n of the entire simulation cell. The position of the center of mass of the molecule is again chosen randomly. According to the principle of detailed balance the probability for a realization of an addition attempt is given by [73]... 

The molecular structure and dynamics of the ice/water interface are of interest, for example, in understanding phenomena like frost heaving, freezing (and the inhibition of freezing) in biological systems, and the growth mechanisms of ice crystals. In a series of simulations, Haymet and coworkers (see Refs. 193-196) studied the density variation, the orientational order and the layer-dependence of the mobilitity of water molecules. The ice/water basal interface is found to be a relatively broad interface of about... 

Finally, we assume that the fields 4>, p, and u vary slowly on the length scale of the lattice constant (the size of the molecules) and introduce continuous approximation for the thermodynamical-potential density. In the lattice model the only interactions between the amphiphiles are the steric repulsions provided by the lattice structure. The lattice structure does not allow for changes of the orientation of surfactant for distances smaller than the lattice constant. To assure similar property within the mesoscopic description, we add to the grand-thermodynamical potential a term propor-tional to (V u) - -(V x u) [15], so that the correlation length for the orientational order is equal to the size of the molecules. 

Recently an alternative approach for the description of the structure in systems with self-assembling molecules has been proposed in Ref. 68. In this approach no particular assumption about the nature of the internal interfaces or their bicontinuity is necessary. Therefore, within the same formahsm, localized, well-defined thin films and diffuse interfaces can be described both in the ordered phases and in the microemulsion. This method is based on the vector field describing the orientational ordering of surfactant, u, or rather on its curlless part s defined in Eq. (55). 

Except for Ceo, lack of sufficient quantities of pure material has prevented more detailed structural characterization of the fullerenes by X-ray diffraction analysis, and even for Ceo problems of orientational disorder of the quasi-spherical molecules in the lattice have exacerbated the situation. At room temperature Cgo crystallizes in a face-centred cubic lattice (Fm3) but below 249 K the molecules become orientationally ordered and a simple cubic lattice (Po3) results. A neutron diffraction analysis of the ordered phase at 5K led to the structure shown in Fig. 8.7a this reveals that the ordering results from the fact that... 

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