Generalized van der Waals theory for the twist elastic modulus and helical pitch of cholesterics

Abstract

We present a generalized van der Waals theory for a lyotropic cholesteric system of chiral spherocylinders based on the classical Onsager theory for hard anisometric bodies. The rods consist of a hard spherocylindrical backbone surrounded with a square-well potential to account for attractive (or soft repulsive) interactions. Long-ranged chiral interactions are described by means of a simple pseudoscalar potential which is appropriate for weak chiral forces of a predominant electrostatic origin. Based on the formalism proposed by Straley [Phys. Rev. A 14, 1835 (1976)], we derive explicit algebraic expressions for the twist elastic modulus and the cholesteric pitch for rods as a function of density and temperature. The pitch varies nonmonotonically with density, with a sharp decrease at low packing fractions and a marked increase at higher packing fractions. A similar trend is found for the temperature dependence. The unwinding of the helical pitch at high densities (or low temperatures) originates from a strong enhancement of the local nematic order and the corresponding increase in the twist elastic resistance associated with near-parallel local rod configurations. This contrasts with the commonly held view that the increase in pitch with decreasing temperature as often observed in cholesterics is due to layer formation resulting from presmectic fluctuations. The increase in pitch with increasing temperature is consistent with an entropic unwinding as the chiral interaction becomes less significant than the thermal energy. The variation of the pitch with density, temperature, and contour length is in qualitative agreement with recent experimental results on colloidal fd rods.

Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

“…The repulsive interactions between the various conformations of the polypeptide rods are taken into account with a simple hardspherocylindrical core of variable aspect ratio. The effective attractive interactions between helical rods can be described with an enveloping isotropic SW potential, 92,93 where the depth of the well 0 is tuned to take into account the effect of the solvent medium (and its dielectric properties). In this sense our model is similar to the DLVO potential commonly employed to describe the interactions between colloidal particles in solution.…”

“…A number of studies have been carried out after the early attempts by Kimura 71 to describe the properties of a system which combines Onsager's hard-rod model with anisotropic dispersion forces. [72][73][74][75][76][77][78][79][80][81][82][83] Some progress has also been made in introducing dipolar [84][85][86][87][88][89] or chiral [90][91][92][93] interactions between LC molecules. Of particular relevance to our current work is the closed-form algebraic equation of state developed within a van der Waals-Onsager treatment for systems of attractive hard-core particles, 94 in which the attractive potential is expanded in spherical harmonics 95 representing different multipolar contributions to the anisotropic attractions.…”

Density functional theory for chiral nematic liquid crystals

“…A fundamental open question regards the relationship between macroscopic and microscopic chirality, i.e., between the handedness of the phase and that of the constituent particles [14][15][16][17]. Moreover, it is still to be unambiguously proved that hard chiral interactions alone can give rise to an entropy-stabilized…”

Chiral assembly of weakly curled hard rods: Effect of steric chirality and polarity

“…Several conclusions can be drawn from this result. As expected, the cholesteric pitch length 2π/k * decreases with concentration but the quadratic scaling differs from the linear one predicted for longranged chiral interaction based on a pseudoscalar potential [16,19,41]. This suggests that purely steric helicity leads to a much harsher microscopic twist compared to those generated by long-ranged dispersion forces.…”