Nematic interaction

It is occasionally desirable to retain a small proportion of molecular orientation, in order to quantitate the dipolar interactions present, whilst minimizing their contribution to the linewidth. Partial orientation may be achieved by using a nematic solvent. In large, magnetically anisotropic molecules it may occur naturally at the highest magnetic fields. 

For structures with a high curvature (e.g., small micelles) or situations where orientational interactions become important (e.g., the gel phase of a membrane) lattice-based models might be inappropriate. Off-lattice models for amphiphiles, which are quite similar to their counterparts in polymeric systems, have been used to study the self-assembly into micelles [ ], or to explore the phase behaviour of Langmuir monolayers [ ] and bilayers. In those systems, various phases with a nematic ordering of the hydrophobic tails occur. 

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

This can be inserted in equation (02.2.3) to give tlie orientational distribution function, and tlius into equation (02.2.6) to deteniiine the orientational order parameters. These are deteniiined self-consistently by variation of tlie interaction strength iin equation (c2.2.7). As pointed out by de Gemies and Frost [20] it is possible to obtain tlie Maier-Saupe potential from a simple variational, maximum entropy metliod based on tlie lowest-order anisotropic distribution function consistent witli a nematic phase. 

Monte Carlo computer simulations of spheres sectioned into a disc [104, 105] show tliat steric interactions alone can produce a nematic phase of discotic molecules. Columnar phases are also observed [104, 105]. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

This condition means that for f < 0.63 the disordered arrangement of molecules is thermodynamically unstable and the system is spontaneously reorganized into an ordered liquid crystalline phase of a nematic type (Flory called this state crystalline ). This result has been obtained only as a consequence of limited chain flexibility without taking into account intermolecular interactions. 

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. 

Berardi et al. [66] have also investigated the influence of central dipoles in discotic molecules. This system was studied using canonical Monte Carlo simulations at constant density over a range of temperatures for a system of 1000 molecules. Just as in discotic systems with no dipolar interaction, isotropic, nematic and columnar phases are observed, although at the low density studied the columnar phase has cavities within the structure. This effect was discovered in an earlier constant density investigation of the phase behaviour of discotic Gay-Berne molecules and is due to the signiflcant difference between the natural densities of the columnar and nematic phases... 

The structures of phases such as the chiral nematic, the blue phases and the twist grain boundary phases are known to result from the presence of chiral interactions between the constituent molecules [3]. It should be possible, therefore, to explore the properties of such phases with computer simulations by introducing chirality into the pair potential and this can be achieved in two quite different ways. In one a point chiral interaction is added to the Gay-Berne potential in essentially the same manner as electrostatic interactions have been included (see Sect. 7). In the other, quite different approach a chiral molecule is created by linking together two or more Gay-Berne particles as in the formation of biaxial molecules (see Sect. 10). Here we shall consider the phases formed by chiral Gay-Berne systems produced using both strategies. 

The dimer model proposed by Wilson [83] was found not to exhibit a nematic phase but smectic A and B phases and so, although semi-realistic features are included, the model is not able to reproduce the behaviour of real dimers such as the a,co-bis(4 -cyanobiphenyl-4-yloxy) [87], which exhibit nematic phases, although liquid crystal dimers exhibiting smectic phases are also known [88]. In these simulations, the GB-GB interaction appears to be too strong and so the system forms a smectic phase in which the GB and LJ units... 

---