We propose a simple statistical mechanical theory for a strongly dipolar fluid at low densities, based on the analogy between a polymer chain and a chain formed by strongly polar particles. The general methods developed in the theory of semiflexible polymers enable one to obtain simple expressions for the energy and conformational entropy of a long dipole chain. We then consider the equilibrium between chains of different lengths and derive a general expression for the free energy as a functional of the chain length distribution. Both steric and dipolar interactions between long chains are shown to be weak and as a result the rarefied fluid of strongly dipolar spheres resembles the ideal gas of noninteracting polydisperse chains. It is shown that the chain length distributions found in simulations are compatible with the assumption of very weak interchain interactions if strong finite-size effects are taken into account. We also investigate whether sufficiently strong attractive van der Waals forces between particles can cause dissociation of the chains. Finally, we discuss the case of a dipolar fluid in an applied field and argue that the coexistence between two aligned phases of chains, as observed by computer simulation, is unlikely to occur in an infinite system.

We propose an intrinsic molecular chirality tensor based only on nuclear positions. The chirality tensor gives rise to two universal chirality indices, the first giving information about absolute chirality, and the second about the anisotropy chirality, i.e., the degree of chirality in different spatial directions. The formalism is derived using simple models obtained from the theory of optical activity. The indices are calculated analytically for a right angled tetrahedron, and numerically for a small selection of molecules.

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A model of interacting rigid rods is proposed to describe tilting phase transitions in monolayers of freely rotating long-chain molecules with hexatic in-plane order. The model takes into account steric repulsion and van der Waals attraction between neighboring rods as well as the orientational entropy of individual rods, all within a mean field approximation limited to the unit cell. Two variants of the model are proposed, with different constraints on the polar molecular headgroups. In the first, the headgroups are grafted to a hexagonal close-packed (hcp) lattice, and in the second, the headgroup lattice deforms to accommodate to the tilt. For the monolayer on a solid substrate, tilt has two opposing actions on the internal energy. The decrease in the distance between rods acts to reduce the interaction energy, while the decrease in the overlapping length of the rods acts to increase it. As the area per molecule increases, the competition between these two effects drives the first-order phase transition U(untilted molecules)→NNN (collective tilt of the molecules in the direction of the next-nearest neighbor). This transition is present for both the fixed and the deformable lattices. For the monolayer on the water surface, the molecular tilt is accompanied by an increasing contact of the polar heads with the water. In this case, the effective interaction potential appears to be temperature dependent and under some circumstances can result in the first-order phase transition being replaced by a second-order one (U→NN) with the collective tilt in the direction of the nearest neighbor. The results obtained with the help of this model are compared with computer simulations and with experiment.

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The structure of a straight interface (wall) between regions with differing values of the pitch in planar cholesteric layers with finite strength of the surface anchoring is investigated theoretically. It is found that the shape and strength of the anchoring potential influences essentially the structure of the wall and a motionless wall between thermodynamically stable regions without a singularity in the director distribution in the layer can exist for sufficiently weak anchoring only. More specifically, for the existence of such a wall the dimensionless parameter Sd = K22/Wd (where W is the depth of the anchoring potential, K22 is the elastic twist modulus and d is the layer thickness) should exceed its critical value, which is dependent on the shape of the anchoring potential. General equations describing the director distribution in the wall are presented. Detailed analysis of these equations is carried out for the case of infinitely strong anchoring at one surface and finite anchoring strength at the second layer surface. It is shown that the wall width L is directly dependent upon the shape and strength of the anchoring potential and that its estimate ranges from d to (dLp)1/2 (where Lp = K22/W is the penetration length), corresponding to different anchoring strengths and shape potentials. The dependence of the director distribution in the wall upon all three Frank elastic moduli is analytically found for some specific limiting cases of the model anchoring potentials. Motion of the wall is briefly investigated and the corresponding calculations performed under the assumption that the shape of a moving wall is the same as a motionless one. It is noted that experimental investigation of the walls in planar cholesteric layers can be used for the determination of the actual shape of surface anchoring potentials.

The transfer of optical angular momentum to birefringent particles via circularly polarized light is common. We report here on the unexpected, continuous rotation of chiral nematic liquid crystal droplets in a linearly polarized optical trap. The rotation is non-uniform, occurs over a timescale of seconds, and is observed only for very specific droplet sizes. Synchronized vertical motion of the droplet occurs during the rotation. The motion is the result of photo-induced molecular reorganization, providing a micron sized opto-mechanical transducer that twists and translates.

A theoretical investigation is made into the dynamics of pitch jumps in cholesteric liquid-crystal layers having finite strength surface-anchoring conditions. A presentation is given of general formulations which connect the dynamics of pitch jumps with the key material parameters such as the viscosity, the specific form of the anchoring potential, and the dimensionless parameter Sd=K22/Wd, where K22 is the elastic modulus, W is the depth of the anchoring potential, and d is the layer thickness. To illustrate the dependence of the pitch jump dynamics upon the shape and strength of the anchoring potential, we investigate two sets of different model surface-anchoring potentials for a jump mechanism that is connected with the slipping of the director at a surface over the barrier of the anchoring potential. Two types of 'narrow' well potentials that are natural extensions of the more familiar 'wide' potentials are considered: one type is based upon the well-known Rapini-Papoular potential and the other upon the B potential, introduced in Belyakov, Stewart, and Osipov, JETP 99, 73 (2004). Calculations for the unwinding (winding) of the helix in the process of the jump were performed to investigate the case of infinitely strong anchoring on one surface and finite anchoring on the other, which is important in applications. The results show that an experimental investigation of the dynamics of the pitch jumps will allow one to distinguish different shapes of the finite strength anchoring potential, and will, in particular, provide a means for determining whether or not the well-known Rapini-Papoular anchoring potential is the best suited potential relevant to the dynamics of pitch jumps in cholesteric layers with finite surface-anchoring strength