Self-assembly of hard helices: a rich and unconventional polymorphism

Abstract

Hard helices can be regarded as a paradigmatic elementary model for a number of natural and synthetic soft matter systems, all featuring the helix as their basic structural unit: from natural polynucleotides and polypeptides to synthetic helical polymers; from bacterial flagella to colloidal helices. Here we present an extensive investigation of the phase diagram of hard helices using a variety of methods. Isobaric Monte Carlo numerical simulations are used to trace the phase diagram: on going from the low-density isotropic to the high-density compact phases, a rich polymorphism is observed exhibiting a special chiral screw-like nematic phase and a number of chiral and/or polar smectic phases. We present a full characterization of the latter, showing that they have unconventional features, ascribable to the helical shape of the constituent particles. Equal area construction is used to locate the isotropic-to-nematic phase transition, and results are compared with those stemming from an Onsager-like theory. Density functional theory is also used to study the nematic-to-screw-nematic phase transition: within the simplifying assumption of perfectly parallel helices, we compare different levels of approximation, that is second-and third-virial expansions and Parsons-Lee correction.arXiv:1408.1199v1 [cond-mat.soft] 6 Aug 2014 2

Effect of Size Polydispersity on the Pitch of Nanorod Cholesterics

“…We remark that this result may be different for purely steric chirality induced by some helical nanorod shape, such as a corkscrew [45][46][47]. More complicated chiral interactions-for example, those generated by a helical arrangement of charged surface groups, as in the case of viral rods [48]-can, in principle, be captured within a numerical interpretation of the van der Waals term Equation (6).…”

The Shape of Things To Come: The Formation of Modulated Nematic Mesophases at Various Length Scales

“…[1] In the N TB phase the molecules are tilted with respectt ot he helix axis, but lack positional ordering and thus the mesophasei s" nematic". [2] Similarly,o ther modulated nematic-like mesophases have been predicted to occur (splay-bendn ematic (N SB ), [3,4] ands crew nematic( N S *) [5,6] to give two examples. )T he pitch length of the N TB helix (P TB )h as been directly measured by freeze-fracture transmission electron microscopy, [1,7,8] by resonant carbon K-edge small-angle X-ray scattering [9] and by resonant selenium small-angleX -ray scattering.…”

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

“…The regime of weakly curled rods (qδ 1) is dominated by uniaxial nematic order while biaxiality enters only at very high particle concentration. The highdensity biaxial nematic phase has both chiral and polar symmetry and should be similar in nature to the screwlike nematic phase recently found in simulation [21,33] and previously observed in dense assemblies of helical…”

“…Formulating a sound statistical mechanical theory of these systems is extremely challenging in view of the complexity of the underlying chiral interactions, the anisotropic shape of the building blocks and the inhomogeneous and anisotropic symmetry of the * wensink@lps.u-psud.fr structure [13,14]. As far as cholesteric order goes, most theoretical predictions for the pitch modulation based on microscopic theory to date have focussed either on long-ranged chiral forces of a dispersive nature treated within (van der Waals) perturbation theory [15][16][17][18][19] or on hard helices of arbitrary amplitude and pitch where elaborate numerical schemes are required to compute the intricate excluded-volume terms in the free energy [20,21]. Other mechanical models for steric chirality that have been proposed are based on density functional theory of twisted hard boards [22], Maier-Saupe theory of rigid and semiflexible corkscrews [23] and Onsager-Parsons theory for chiral two-site segment particles with planar orientations [24].…”