Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.

We report the nematic and smectic ordering in a new aqueous suspension of monolayer α-Zirconium phosphate platelets possessing a high polydispersity in diameter but uniform thickness. We observe an isotropic-nematic transition as the platelet volume fraction increases, followed by the formation of a smectic, an elusive phase that has been rarely seen in discotic liquid crystals. The smectic phase is characterized by X-ray diffraction, high-resolution transmission electron microscopy, and optical microscopy. The phase equilibria in this highly polydisperse suspension is rationalized in terms of a theoretical approach based on density-functional theory.

We show that simple liquids, with appropriate choices of the isotropic pair interaction, may exhibit surface layering above the melting temperature. Results for the liquid surface have been obtained by Monte Carlo simulations in slab geometry. Surface layering appears at temperatures below approximately one-third of the critical temperature for very different choices of pair interaction. The high melting temperature of the Lennard-Jones crystal preempts the observation of the oscillatory density at the free liquid interface, while model pair interaction potentials, built to reproduce some properties of mercury and the alkali metals, have low melting temperature, uncovering the region of surface layering.

FtsZ is a bacterial protein that forms filaments that play an essential role in midcell constriction during the process of cell division. The shape of individual filaments of different lengths imaged with atomic force microscopy was modeled considering the protein monomers as beads in a chain and a few parameters to represent their effective interactions. The flexural rigidity and persistence length of the filaments were estimated. This latter value was comparable to the filament length, implying that these biological polymers are halfway between the perfectly stiff linear aggregate whose shapes are fully controlled by the angle between the monomers and highly flexible polymers whose shapes follow a random walk model. The lateral interactions between adjacent filaments, also estimated in the modeling, were found to play an essential role in determining the final shape and kinetics of the coiled structures found in longer polymers. The estimated parameters were used to model the behavior of the polymers also on a cylindrical surface. This analysis points to the formation of helical structures that suggest a mechanism for force generation and amplification through the development of FtsZ spirals at the midcell division point.

We investigate the effect of three-body correlations on the phase behavior of hard rectangle two-dimensional fluids. The third virial coefficient B3 is incorporated via an equation of state that recovers scaled particle theory for parallel hard rectangles. This coefficient, a functional of the orientational distribution function, is calculated by Monte Carlo integration, using an accurate parametrized distribution function, for various particle aspect ratios in the range of 1-25. A bifurcation analysis of the free energy calculated from the obtained equation of state is applied to find the isotropic (I)-uniaxial nematic (N(u)) and isotropic-tetratic nematic (N(t)) spinodals and to study the order of these phase transitions. We find that the relative stability of the N(t) phase with respect to the isotropic phase is enhanced by the introduction of B3. Finally, we have calculated the complete phase diagram using a variational procedure and compared the results with those obtained from scaled particle theory and with Monte Carlo simulations carried out for hard rectangles with various aspect ratios. The predictions of our proposed equation of state as regards the transition densities between the isotropic and orientationally ordered phases for small aspect ratios are in fair agreement with simulations. Also, the critical aspect ratio below which the N(t) phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation.