Tracing the phase boundaries of hard spherocylinders

Abstract

We have mapped out the complete phase diagram of hard spherocylinders as a function of the shape anisotropy L/D. Special computational techniques were required to locate phase transitions in the limit L/D→ϱ and in the close-packing limit for L/D→0. The phase boundaries of five different phases were established: the isotropic fluid, the liquid crystalline smectic A and nematic phases, the orientationally ordered solids-in AAA and ABC stacking-and the plastic or rotator solid. The rotator phase is unstable for L/Dу0.35 and the AAA crystal becomes unstable for lengths smaller than L/DϷ7. The triple points isotropic-smectic-A-solid and isotropic-nematic-smectic-A are estimated to occur at L/D ϭ 3.1 and L/D ϭ 3.7, respectively. For the low L/D region, a modified version of the Gibbs-Duhem integration method was used to calculate the isotropic-solid coexistence curves. This method was also applied to the I-N transition for L/DϾ10. For large L/D the simulation results approach the predictions of the Onsager theory. In the limit L/D→ϱ simulations were performed by application of a scaling technique. The nematic-smectic-A transition for L/D→ϱ appears to be continuous. As the nematic-smectic-A transition is certainly of first order nature for L/Dр5, the tri-critical point is presumably located between L/Dϭ5 and L/Dϭϱ. In the small L/D region, the plastic solid to aligned solid transition is first order. Using a mapping of the dense spherocylinder system on a lattice model, the initial slope of the coexistence curve could even be computed in the close-packing limit.

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

“…22,23,27,28,33,36,39 An essential requirement for the stabilization of a LC phase is that the molecules be highly anisotropic in shape, such as long rigid rods or thin flat discs. For this reason, rodlike [41][42][43][44][45][46][47] particles are often employed as prototype models for prolate LC molecules (see reference 48 for a relatively recent review). Hard non-spherical particles are often taken as 'zeroth-order' models for lyotropic or colloidal LCs in which the appearance of anisotropic phases is controlled by the solute concentration.…”

Binary mixtures of rod-like colloids under shear: microscopically-based equilibrium theory and order-parameter dynamics

“…For smaller aspect ratios, we compare our stability limits with the coexistence densities of isotropic and nematic phases (plotted in (blue) • and ) obtained by Bolhuis et al in [11] using Gibbs-ensemble simulations. We find that two sets of data agree reasonably well.…”

“…A recent example is an experimental study of polydisperse clay rods which show an isotropic-nematic phase transition on increasing concentration [6]. From the theoretical side, such phase diagrams have been studied, e.g., by Onsager theory [7] and by more general free energy functionals [8,9,10] in the framework of classical density functional theory (DFT), as well as by computer simulations [11,12].…”

Spatial Order in Liquid Crystals: Computer Simulations of Systems of Ellipsoids

“…The phase behavior of hard spherocylinders has been studied by Frenkel and others [42,43,44,45,46,47]. The complete phase diagram for all elongations L/D as computed by Bolhuis and Frenkel [46] is shown in Figure 4.…”

“…The complete phase diagram for all elongations L/D as computed by Bolhuis and Frenkel [46] is shown in Figure 4. It differs strikingly from the corresponding phase diagram for hard ellipsoids in that sufficiently elongated spherocylinders form smectic phases.…”