Solution of a molecular statistical model for chiral nematic liquid crystals

Modulated structures in a Lebwohl–Lasher model with chiral interactions

“…These sketchy calculations, however, are sufficient to illustrate the origins and the main qualitative features of modulation associated with helical nematics (cholesteric states) in liquid-crystalline systems. We hope this investigation will be a guide for future (and more extensive)work, including connections with earlier calculations for statistical molecular models [21][22][23] and predictions of the phenomenological elastic theories [18].…”

“…In this preliminary analysis, calculations have been restricted to the simplest versions of these nematic clock models, which are already sufficient to point out the statistical origin of spatially modulated phases, to draw representative global phase diagrams, and give an indication of the change of the pitch with temperature and model parameters. We remark that it is easy to see that there is a correspondence between the essential terms in the Hamiltonians associated with the p-state nematic clock model and of a planar version of Goossen's proposal, as it has been used by Krutzen and Vertogen [22] and by Lin-Liu and collaborators [23]. This paper is organized as follows.…”

“…From the molecular point of view, according to an early work by Goossens [20], the consideration of an induced dipole-quadrupole contribution to the dispersion interactions can give rise to a cholesteric phase. This picture has been extended by some investigators [21] [22], with the formulation of a statistical model, of mean-field type, which might be able to describe the temperature effects in a cholesteric phase. In the calculations of van der Meer and collaborators [21], there is a modulated structure, which is not affected by temperature.…”

“…In the calculations of van der Meer and collaborators [21], there is a modulated structure, which is not affected by temperature. Although there is no attempt to draw a global phase diagram, the numerical mean-field calculations of Krutzen and Vertogen [22] point out the possibility of a temperature-dependent pitch if one includes a nematic-twist term in the original pair potential. Along Goossens's ideas, Lin-Liu and collaborators [23] considered a planar model for the cholesteric phase, which does lead to the description of a temperature sensitive pitch.…”