Relationship between Molecular Association and Re-entrant Phenomena in Polar Calamitic Liquid Crystals Richard J. Mandle,* ,† Stephen J. Cowling, † Ian Sage, ‡ M. Eamon Colclough, § and John W. Goodby † † Department of Chemistry, The University of York, York YO10 5DD, U.K. ‡ Nottingham Trent University, Nottingham NG1 4BU, U.K. § QinetiQ Ltd, Fort Halstead, Sevenoaks TN14 7BP, U.K. * S Supporting Information ABSTRACT: The relationship between molecular association and re-entrant phase behavior in polar calamitic liquid crystals has been explored in two families of materials: the 4′-alkoxy-4-cyanobiphenyls (6OCB and 8OCB) and the 4′-alkoxy-4-nitrobiphenyls. Although re-entrant nematic phase behavior has previously been observed in the phase diagram of 6OCB/8OCB, this is not observed in mixtures of the analogous nitro materials. As there is no stabilization of the smectic A phase in mixture studies, it was conjectured that the degree of association for the nitro systems is greater than that for the cyano analogues. This hypothesis was tested by using measured dielectric anisotropies and computed molecular properties to obtain a value of the Kirkwood factor, g, which describes the degree of association of dipoles in a liquid. These computed values of g confirm that the degree of association for nitro materials is greater than that for cyano and offer a useful method for quantifying molecular association in systems exhibiting a re-entrant polymorphism. 1. INTRODUCTION Maier−Meier theory is used to describe the relationship between the molecular properties of a material to its bulk liquid crystalline properties. 1 The Maier−Meier relationship is effectively an extension of the Onsager theory of isotropic liquids to anisotropic liquids such as liquid crystals. 2 Specifically, it relates the molecular parameters of a compound to its bulk liquid crystalline properties, specifically the molecular polarizability (α ̅ and Δα), ef fective molecular dipole moment (μ eff ), and the angle between the dipole moment vector and the molecular long axis (β) with the bulk dielectric anisotropy (Δε = ε ∥ − ε ⊥ ), reaction field vectors (F and h) and the order parameter (S), through eqs 1−3. 3,4 Typically, molecular properties are computed via semiempirical or quantum mechanical methods; 5−9 however, the accuracy of such methods must be ascertained by comparison with measured values, where available. ε ε α α μ β = + ̅ − Δ + − − ⎪ ⎪ ⎪ ⎪ ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ NFh S F kT S 1 2 3 3 [1 (1 3cos )] 0 eff 2 B 2 (1) ε ε α α μ β = + ̅ − Δ + + − ⊥ ⎪ ⎪ ⎪ ⎪ ⎧ ⎨ ⎩ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⎫ ⎬ ⎭ NFh S F kT S 1 1 3 3 1 1 2 (1 3cos ) 0 eff 2 B 2 (2) ε ε ε ε α μ β Δ = − = Δ − − ⊥ ⎪ ⎪ ⎪ ⎪ ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ NFh F kT S 2 (1 (3cos ) 0 eff 2 B 2 (3) As polar materials will tend to align antiparallel to minimize the net dipole of the bulk system, the Kirkwood factor (g) is used to reflect the degree of correlation. 10,11 The relationship between the molecular dipole moment (μ), the effective molecular dipole moment (μ eff ) and the Kirkwood factor (g) is given by μ μ = g eff 2 2 (4) The Kirkwood factor has been used successfully to account for aggregation of polar solvents 12 as well as highly polar and ionic additives in nematic solutions. 6,13 A schematic represen- tation of the relative alignment of two polar, rodlike molecules for Kirkwood factors of g = 0 and g = 2 is given in Figure 1. Re-entrant behavior in liquid crystals is now an established phenomenon, over 39 years since the first observation of a re- entrant nematic phase in 1975 by Cladis. 14,15 Re-entrant behavior is not confined to soft mater, with re-entrant superconductivity having been also observed at the super- conducting−ferromagnetic phase transition. 16 In a classical example of re-entrant behavior in liquid crystals, binary mixtures of 4-hexyloxy-4′-cyanobiphenyl (6OCB) and 4- octyloxy-4′-cyanobiphenyl (8OCB) exhibit a re-entrant nematic phase when the concentration of 6OCB is in the range of 20− 30%. 17 The incidence of re-entrancy in materials with large longitudinal dipole moments, such as the 4-alkoxy-4′-cyano- Received: December 4, 2014 Revised: January 20, 2015 Article pubs.acs.org/JPCB © XXXX American Chemical Society A DOI: 10.1021/jp512093j J. Phys. Chem. B XXXX, XXX, XXX−XXX