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.
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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