Nematic and smectic ordering in a system of two-dimensional hard zigzag particles

Abstract

The orientational and positional ordering of the two-dimensional system of hard zigzag particles has been investigated by means of Onsager theory. Analytical results are obtained for the transition densities of the isotropic-nematic and the nematic-smectic phase transitions. It is shown that the stability of the nematic and smectic phases is very sensitive to the molecular shape. In the hard needle limit, only the isotropic-nematic phase transition takes place, while increasing the tail length and the bent angle between the central core and the tails destabilizes the nematic phase. On the other hand the stability of the smectic phase is due to the increasing excluded area cost with bent angle and the tail length. The zigzag particles pack in a layered structure such that they are tilted and form semi-ideal gas in the layers to push the high cost excluded area regions into the interstitial regions. The predictions of Onsager theory are in good agreement with MC simulation data.

Phase ordering of zig-zag and bow-shaped hard needles in two dimensions

“…The tilt angle θ and the period d are also determined by minimizing the free energy functional. For details of the calculation, we refer the reader to the work of Varga et al 58 Note that we were only able to calculate a nematic-smectic transition line for zig-zag molecules. It is plotted in the phase diagram of Fig.…”

“…Based on the second-order virial expansion of the free energy introduced by Onsager, predictions for both ρ IN and ρ NS were made. 58 In the following, we summarize and extend the results of this Onsager theory.…”

“…58, because the nematic order in the smectic phase is typically very high. The evaluation of the free energy functional now involves an excluded distance d exl (z, θ), where θ is the orientation angle of the central molecular segment with respect to the smectic layer normal.…”

“…58, a density functional theory in mean-field approximation was used to determine the phase behavior of zig-zag molecules. Based on the second-order virial expansion of the free energy introduced by Onsager, predictions for both ρ IN and ρ NS were made.…”

“…57 These improved numerical results on two-dimensional liquid crystal formation are also compared to predictions from Onsager theory. 58 The paper is organized as follows. In Sec.…”