Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C2 symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open. First, the real nature of the lower density nematic phase, expected to be cholesteric. Second, the influence that the latter, once allowed to form, may have on the existence and stability of the screw-like nematic phase. To address these questions, we have performed Monte Carlo and molecular dynamics numerical simulations of helical particle systems confined between two parallel repulsive walls. We have found that the removal of the periodicity constraint along one direction allows a relatively-long-pitch cholesteric phase to form, in lieu of the uniform nematic phase, with helical axis perpendicular to the walls while the existence and stability of the screw-like nematic phase are not appreciably affected by this change of boundary conditions.
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The common tenet that the thermodynamic stability of a phase is very close to that of a phase providing is sufficiently large2 and motivated the usage of an Onsager-like (density functional) theory,15,16 within the implementation originally developed by Straley,1 to explore the characteristics of the phase, in particular, its pitch handedness and value in systems of hard helical particles.5,7 These results, then reproduced also by others either using a different model17 or the same model and a different implementation of the same theory,11–13 were useful in that they confirmed that phenomena such as cholesteric handedness inversion, often explained by invoking a competition between different energetic and entropic terms that would promote opposite phase chirality, may arise also in pure systems of suitable hard chiral particles; in such cases, they are solely entropy driven. One may nonetheless note that cholesteric pitch handedness inversion, while possibly “dramatic” if viewed from the pitch side, is a more ordinary phenomenon if viewed from the corresponding wavevector side; it merely means that the wavevector versus density function has a zero at a certain density value and behaves linearly in its neighbourhood.
The results presented in this work were preliminarily shown as part of an oral communication entitled “Self-assembly of hard helical particles: cholesteric and screw-like, nematic and smectic, phases” given at the XII International Conference on Materials Chemistry, 20–23 July 2015, York, England.
