Phase transitions in liquid crystals

Recent studies have established that many compounds composed of disc-shaped molecules exhibit stable thermotropic liquid crystalline phases. They are now referred to as discotic liquid crystals. Structurally, most of them fall into two distinct categories, the columnar and the nematic. The columnar phase, in its simplest form, has long-range translational periodicity in two dimensions and liquid-like disorder in the third, whereas the nematic phase is an orientationally ordered arrangement of discs without any long-range translational order. This review article describes the detailed structures of the various discotic phases and some of their important physical properties.

https://iopscience.iop.org/article/10.1088/0034-4885/53/1/002/pdf

Discotic liquid crystals

Thermotropic columnar mesophases from N–H⋯O, and N⋯H–O hydrogen bond supramolecular mesogenes

We present a joint molecular dynamics (MD)/kinetic Monte Carlo (KMC) study aimed at the atomistic description of charge transport in stacks of liquid-crystalline tetraalkoxy-substituted, metal-free phthalocyanines. The molecular dynamics simulations reproduce the major structural features of the mesophases, in particular, a phase transition around 340 K between the rectangular and hexagonal phases. Charge transport simulations based on a Monte Carlo algorithm show an increase by 2 orders of magnitude in the hole mobility when accounting for the rotational and translational dynamics. The results point to the formation of dynamical structural defects along the columns.

Theoretical Characterization of the Structural and Hole Transport Dynamics in Liquid-Crystalline Phthalocyanine Stacks

The synthesis of a homologous series of octaalkoxy-substituted silicondihydroxo-phthalocyanines is described. The mesomorphic properties of these new materials were studied by DSC, optical microscopy and X-ray investigations. Compounds with n ≤ 4 (n is the number of carbon atoms in a single alkoxy side chain) show a discotic mesophase transition. A transition to the isotropic state is only observed when n ≤ 8. X-ray diffraction patterns of the mesophases confirm that all compounds form a hexagonal columnar mesophase of the type Dhd.

Control of the Discotic to Isotropic Transition in Alkoxy-Substituted Silicondihydroxo-Phthalocyanines by Axial Substituents

In this paper we propose to estimate the role of chain conformations in bringing about reentrant polymorphism in a nonpolar sample of mesogens. To this end we also show that the reentrant phenomenon is built in the McMillan model, if one explicitly incorporates the e8'ect of tail-chain conformations in the molecular potential instead of treating the chains as an extension of the rigid part. The model is next utilized to predict the single reentrance I-N-Sm-N„with lowering of ternperature in a nonpolar system. I. INTRQDUCTIOlV Since the discovery of reentrant polymorphism in a binary mixture of two polar compounds, ' a large number of investigations have been carried out in this field. Liquid-crystalline systems exhibiting such reentrant polymorphism I X Sm X„-, a-nd -the double (or triple) reentrant phase sequence consist of organic molecules usually with three or four aromatic rings with ester linkages and having polar cyano or nitro-end groups. Apart from pure compounds, ' such reentrant polymorphism with a lowering of temperature is also exhibited by binary mixtures of polar-polar, ' ' polar-nonpolar, ' or even by nonpolar-nonpolar compounds. "' The last one however only shows the single reentrant phase sequence. Further, as a given homologous series is ascended the reentrant phase sequence is shown by the higher homologs (e.g. , usually by the octyloxy, nonyloxy, etc. members) which are neither very short nor very long. These findings indicate that the dipolar force plays a crucial role in the reentrant polymorphism. There are theoretical models' ' that emphasize this role of dipolar force to bring about the phase sequence. A number of theories assume some sort of bimolecular organization (dimers)' ' or even trimers or n-mers with antiparallel association that compensates (not always fully) the dipole moments. This system of dimers or n-mers together with existing monomers can bring about the desired phase sequence. Such theories can also explain the variation of layer thickness' ' as an interdigitation or reorientation' (in the case of constant layer thickness) of the component systems in a mean-field approach. These theories essentially show that the high-temperature smectic phase is an induced phase and the reentrant nematic phase is brought about by a competition between two incommensurate lengths. This two-length theory is also one of the main ingredients of the Landau theory of the phase transition developed by Prost and Barois. ' A further review of theories and experiments for reentrant nematic phases can be found in Refs. 24 and 25. However, the occurrence of single reentrance I-X-SmX„(Refs. 11 and 12) in a binary mixture of nonpolar compounds cannot possibly be due to such dipolar forces. In fact, for such systems, observation' on layering thickness shows no hint for the kind of dimerization as is found in reentrant systems with polar compounds. The above result, together with the observation that in all the systems discussed the reentrant phase usually occurs for certain members (usually eighth or ninth) of the homologous series, indicate that the tail chains should have some active role in bringing about the reentrance. Dowell proposed a lattice model for condensed phases that predicted reentrance in a single-component nonpolar system. In that model, it is seen that a segregated packing of cores beside cores and chains beside chains occurs with a lowering of temperature leading to a usual smectic phase. With further lowering of temperature, the chains become less flexible, and packing differences between the rigid cores and tail chains decrease. Thus, the need for segregated packing of rigid cores with cores (and tail chains with tail chains) is overcome by entropy of unsegregated packing, leading to the disappearance of the smectic-A phase and the appearance of the reentrant nematic phase. In other words, the Dowell model holds the change in chain configuration responsible for reentrance. We present in this section some results we have obtained on the role of chains in bringing about reentrance in a single-component nonpolar sample. As in the case of polar systems, ' ' our present study is also based on a molecular mean-field approach and the starting point, so to say, is again the McMillan model. Here, however, we show that the reentrant phenomenon is built in the McMillan model, if one explicitly incorporates the efFeet of tail-chain conformations in the molecular potential instead of treating the chains as an extension of the rigid part. The model is used next to predict the single reentrant phase sequence I-iV-Sm-X„with lowering of temperature in an idealized nonpolar system. Our results also indicate that chain conformations alone can give rise to reentrance for certain intermediate members of a homologous series only under some very restrictive conditions.

Role of end chains in the reentrant behavior of a nonpolar system.

A mean field model for a rectangular columnar to hexagonal columnar phase transition, assuming thatthe molecules are biaxial in both the phases, is presented. The theory is developed for a face centeredrectangular lattice taking the molecular cores to be tilted in a particular direction with respect to thecolumn axis by the same angle at each lattice site. Phase diagrams for a homologous series for twovalues of biaxiality parameter are presented. With increasing temperature a phase sequence rectangular-hexagonal-nematic-isotropic is found for shorter members while for higher members of a homologousseries the nematic phase is absent in the calculated phase sequence.

A Molecular Mean Field Model for a Rectangular to Hexagonal Phase Transitionin Discotic Liquid Crystals

The variational method of Lee et. al., for calculating the phase diagrams of systems consisting of rod-like molecules, has been extended to the discotic systems. Compared to the existing models of the discotic phase, the present results are in much better agreement with experimental observations. According to this theory the N-I transition temperature (T N-1) varies inversely as the square of the molecular diameter whereas in the work of Lee et. al., on rod-like molecules, T N-1 varies inversely as the molecular length.

Phase diagram for discotic liquid crystals

In the earlier intercalation model of the present authors, it was shown how gradual dimerization of polar molecules with lowering of temperature necessitates intercalation of neighboring layers for space filling and how the resulting decrease in layer thickness of SAd phase brings about a nematic reentrant phase. In the present work, an alternative mechanism for space filling is proposed which can account for SAd-Nre transition with an accompanying increase of layer thickness. It is also shown that the present mechanism of space filling coupled with intercalation can lead to the SAd-Nre transition at constant layer thickness. These are in conformity with experimental observations where the said transition often occurs with virtually no change in layer thickness and in some cases with an increase in layer thickness.

A Mean Field Model for Reentrant Polymorphism

A molecular meanfield model for a rectangular columnar to hexagonal columnar phase transition, as observed in case of the HAT series, is presented here assuming the molecules basically to be biaxial objects The theory is developed for a rectangular lattice having herring-bone packing of the tilted molecules Various types of phase diagrams for a homologous series are reproduced for different values of molecular biaxiality Some of them are very similar to the experimentally observed cases but others, particularly involving biaxial nematic phase, are not yet observed It is shown that a gradual lowering of biaxiality with the addition of flexible chain segments can lead to the full phase sequence observed in the HAT series

C. D. Mukherjee

Papers

Role of end chains in the reentrant behavior of a nonpolar system.

A Molecular Mean Field Model for a Rectangular to Hexagonal Phase Transitionin Discotic Liquid Crystals

Phase diagram for discotic liquid crystals

A Mean Field Model for Reentrant Polymorphism

A Molecular Meanfield Model for the Biaxial Rectangular Discotic Phase with Herring-Bone Packing of Tilted Molecules