Hard particle simulations spherocylinders

It has not proved possible to develop general analytical hard core models for liquid crystals, just as for normal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. It has been found that a system of hard ellipsoids can form a nematic phase for ratios L/D > 2.5 (rods) or L/D < 0.4 (discs). However, such a system cannot form a smectic phase, as can be shown by a scaling argument in statistical mechanical theory. However, simulations show that a smectic phase can be formed by a system of hard spherocylinders. The critical volume fractions for stability of a smectic A phase depend on whether the model is that of parallel spherocylinders or, more realistically, freely rotating spherocyHnders. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

The structure formation in an ER fluid was simulated [99]. The characteristic parameter is the ratio of the Brownian force to the dipolar force. Over a wide range of this ratio there is rapid chain formation followed by aggregation of chains into thick columns with a body-centered tetragonal structure observed. Above a threshold of the intensity of an external ahgn-ing field, condensation of the particles happens [100]. This effect has also been studied for MR fluids [101]. The rheological behavior of ER fluids [102] depends on the structure formed chainlike, shear-string, or liquid. Coexistence in dipolar fluids in a field [103], for a Stockmayer fluid in an applied field [104], and the structure of soft-sphere dipolar fluids were investigated [105], and ferroelectric phases were found [106]. An island of vapor-liquid coexistence was found for dipolar hard spherocylinders [107]. It exists between a phase where the particles form chains of dipoles in a nose-to-tail... 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

The first of these was by Vieillard-Baron [5] who investigated a system of spherocylinders but failed to detect a liquid crystal phase primarily because the anisometry, L/D, of 2 was too small [37]. He also attempted to study a system of 2392 particles with the larger L/D of 5 but these simulations had to be abandoned because of their large computational cost. However, in view of the ellipsoidal shape of the Gay-Berne particles it is the behaviour of hard ellipsoids of revolution which is of primary relevance to us. 

Hard spherocylinders (cylinders with hemispherical end caps) were studied using computer simulations [118]. In addition to a nematic phase, such particles also display a smectic-A phase, in which the particles are arranged in liquid-like layers. To observe this transition, rather monodisperse particles are needed. The smectic-A phase was indeed observed in suspensions of TMV particles [17]. 

So far I have discussed the occurrence of nematic and smectic phases in dispersions of rod-like colloidal particles. Stroobants et dlM observed in their Monte Carlo simulations of systems of hard parallel spherocylinders for L/D > 3 a columnar phase intermediate between the smectic and crystalline phases. In their freeze-fracture electron microscopy study of dispersions of the rod like bacterial virus fd, Booy and Fowler may have observed the columnar phase. They report one texture (Figure 2b, in Ref. 69), where the nearly parallel fd particles are arranged randomly in the longitudinal direction but the lateral packing is regular. This is indeed characteristic of a columnar phase. 

---