On the molecular origins of liquid crystal phases

[Nature India Special Issue: Lighting the way in physics]

Thermotropic liquid crystals (LC) are exhibited by many organic molecules and they all have shape anisotropy¹. Nematic LCs (NLC) having a pure orientational order of rod-like molecules and were first identified more than 130 years ago. Max Born proposed the first molecular theory for the order in 1916², when he suggested that the medium is a ferroelectric liquid with the order resulting from dipolar interactions. Later, it was established that the nematic-isotropic transition point depends on anisotropic dispersion interactions¹ and the order is apolar in nature.

The operating voltage of liquid crystal displays can be brought down by increasing the dielectric anisotropy of NLC, usually by attaching the highly polar -C≡N or -NO₂ end groups to the molecules. The electrostatic interaction energy of neighbouring polar molecules is lowered by a mutually antiparallel orientation, with the nematic retaining the apolar order³. X-ray studies showed that the strong dispersion interaction leads to a short-range order with a partial bilayer structure with spacing around 1.4 times the molecular length as the chains of neighbours are also thrown apart in opposite directions¹. Later, several compounds were found to exhibit the sequence Iso-N-SmAd-Nre-SmA1 as the temperature is lowered; the reentrant nematic Nre and reentrant SmA1 with a layer spacing equal to the molecular length occurring at temperatures lower than that of the partial bilayer smectic SmAd phase¹.

Jacques Prost developed a phenomenological Landau theory⁴ showing that frustration between the order parameters corresponding to the two layer-spacings leads to the above sequence of phases. The molecular origin of the two spacings is traced by noting that in the SmAd phase the chains are thrown apart and do not have a significant interaction. The dispersion interaction between the chains is favourable if the two neighbouring molecules are parallel. The repulsive dipolar interaction is mitigated by the effect of the dipole induced in the aromatic core of a given molecule by the dipole of the neighbour, which reduces the net dipole moment. As both dispersion energy and dipole-induced dipole energy favouring the parallel orientation are proportional to r^-6, where r is the intermolecular separation and the repulsive dipole-dipole interaction to r^-3, when the molecules come closer at lower temperatures, the observed sequence is the result⁵. In some favourable cases, a nematic-nematic transition was also predicted⁶, with a relative jump in the two types of short-range order, which has been seen in some experiments⁷. There have been a number of theoretical and computer simulation studies looking for the ferronematic (Nf) phase in small, highly polar molecules8⁸, but only polar discs were found to favour the Nf phase.

In 2017, two very different types of compounds with highly polar rod-like molecules were synthesised^9,10, which were shown to form the Nf phase^10,11 with a polarisation of ~6-8 μC/cm², which is about an order of magnitude larger than that shown by some types of smectic liquid crystals in the plane of the layers^11,12. Remarkably, at the isotropic to nematic transition temperature, the nematic phase is of the usual type, with an antiparallel short-range order and an apolar long-range order. As it is cooled to a specific temperature, there is a transition to the Nf phase with a long-range polar order.

The intrinsic interest in the physical properties of a liquid with polar order – and its possible applications – have triggered intensive research activity on the topic. Over 200 new compounds exhibiting the Nf phase have been synthesised. Again, a fundamental question concerns the molecular origin of the Nf phase and an idealised generic model has been proposed. Each molecule is assumed to be a cylindrical rod with four surface charge density waves³. Detailed calculations have been used to show that near neighbour rods favour antiparallel orientation for a moderate inter-rod separation r, which switches over to parallel orientation below some r, only if the waves of charge density at the end half have lower amplitudes than those of the interior waves13¹³. This is borne out by the structures of the molecules synthesised so far¹⁴. For example, in many compounds exhibiting the Nf phase, the polar group at one end is -NO2, the nitrogen atom effectively reducing the negative charges of the oxygen atoms projecting out towards the sides of the molecules. If this group is replaced by the equally polar -C≡N group, this structure is lost and the compound exhibits only the nematic (N) phase with antiparallel short-range order, which does not go over to the Nf phase⁹.

The basic physical mechanism for the stability of the Nf phase is the following: when the neighbouring molecules are very close, they can sense the detailed charge distributions from their neighbour. The lowered charge densities of the end half waves reduces the interaction energy of antiparallel rods with full overlap and increases the attractive energy of parallel molecules having the favoured structure with a shift by half a wavelength along the length. The proposed mechanism and experimental observations show that the orientational order of the N phase does not arise from dipolar interactions as proposed by Max Born2², but by the usual anisotropic dispersion interactions. The Nf phase is seen only in some compounds with special charge structures when the density is high enough^13,14. Interestingly, the ferroelectric SmAf phase in which the polarisation is along the normal layer has been discovered only recently¹⁵. Work carried out at the Raman Research Institute has clarified the molecular origins of all the unusual LC phases shown by polar molecules.