M olecular P hysics, 1996, V ol. 89, N o. 4, 1087±1103 The in¯uence of association and isomerization on re-entrant nematic and smectic A polymorphism By A. FERRARINI ‹, G. R. LUCKHURSTŒ, P. L. NORDIO ‹ and E. SPOLAORE ‹ ‹ Department of Physical Chemistry, University of Padova, 2 via Loredan, 35131 Padova, Italy Œ Department of Chemistry, University of Southampton, High®eld, Southampton SO17 1BJ, UK ( Recei Šed 11 March 1996; accepted 11 April 1996) The eŒect of chemical equilibria on the phase behaviour of mesogenic molecules which exhibit nematic and smectic A phases is investigated by using a molecular ®eld approach, which is an extension of the McMillan theory. The particular reactions of isomerization and dimerization are treated in detail, for two species in equilibrium, taken as uniaxial particles experiencing diŒerent potentials of mean force and mean torque. The change of the equilibrium between the two species in the various phases is described in terms of an equilibrium constant for the isotropic phase. Lowering of the temperature below the ®rst smectic phase can give rise to re-entrant nematics when (i) the isomerization equilibrium is shifted in favour of the most elongated molecules, or (ii) dimer dissociation increases the concentration of the species with lower translational order. In both cases, nematic and smectic A re-entrant phases are predicted under physically reasonable conditions. 1. Introduction Liquid crystals exhibit a rich polymorphism, including examples of re-entrant behaviour, that is transitions to phases of apparent increasing disorder with decreasing temperature. There have been numerous experimental studies of the smectic A to nematic transition in pure systems and in mixtures: in addition to the usual S±N±I or S±I sequences, phase series such as N re ±S±N±I or S re ±N re ±S±N±I and others even more complex have been detected, with the various smectic A phases diŒering in the layer organization of the constituent molecules [1±3]. The most common structures are represented by the monolayer smectics A " in which the layer spacing d is approximately equal to the molecular length l , the bilayer smectics A # with d E 2 l , and the partially bilayer A d which has l ! d ! 2 l, with d E 1 ±4 l in most cases [2]. In addition, there are undulated layer smectic A phases, denoted as A 4 or antiphase, while other less common intercalated smectic A phases have been discovered [4]. The large amount of experimental data on the phase properties of mesogenic molecules makes it possible to begin to correlate the mesomorphic behaviour to the molecular structure. A number of theoretical models have been formulated to interpret the experimental observations, and they invariably start by considering those molecular interactions whose competition is expected to determine the phase sequence and the structure of the diŒerent smectic phases. From the beginning, the association between molecules, resulting from interactions between the strong electric dipoles located at the head of many smectogenic species, has been singled out as an important feature for re- 0026± 8976 }96 $12± 00 ’ 1996 Taylor & Francis Ltd