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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 (Nu) and isotropic-tetratic nematic (Nt) spinodals and to study the order of these phase transitions. We find that the relative stability of the Nt 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 Nt phase becomes stable is predicted to increase due to three-body correlations, although the corresponding value is underestimated with respect to simulation. [ABSTRACT FROM AUTHOR]

Using density-functional theory in the restricted-orientation approximation, we analyze the liquid-crystal patterns and phase behavior of a fluid of hard rectangular particles confined in a two-dimensional square nanocavity of side length H composed of hard inner walls. Patterning in the cavity is governed by surface-induced order as well as capillary and frustration effects and depends on the relative values of the particle aspect ratio ? = L/σ with L the length and a the width of the rectangles (L≥σ), and cavity size H. Ordering may be very different from bulk (H→∞) behavior when ? is a few times the particle length L (nanocavity). Bulk and confinement properties are obtained for the cases ? = 1,3, and 6. In bulk the isotropic phase is always stable at low packing fractions r) = Lapo (with p0 the average density) and nematic, smectic, columnar, and crystal phases can be stabilized at higher rj depending on ? For increasing n the sequence of isotropic to columnar is obtained for ? = 1 and 3, whereas for ? = 6 we obtain isotropic to nematic to smectic (the crystal being unstable in all three cases for the density range explored). In the confined fluid surface-induced frustration leads to fourfold symmetry breaking in all phases (which become twofold symmetric). Since no director distortion can arise in our model by construction, frustration in the director orientation is relaxed by the creation of domain walls (where the director changes by 90°); this configuration is necessary to stabilize periodic phases. For ? = 1 the crystal becomes stable with commensurate transitions taking place as H is varied. These transitions involve structures with different number of peaks in the local density. In the case ? = 3 the commensurate transitions involve columnar phases with different number of columns. In the case ? = 6 the high-density region of the phase diagram is dominated by commensurate transitions between smectic structures; at lower densities there is a symmetry-breaking isotropic to nematic transition exhibiting nonmonotonic behavior with cavity size. Apart from the present application in a confinement setup, our model could be used to explore the bulk region near close packing in order to elucidate the possible existence of disordered phases at close packing. [ABSTRACT FROM AUTHOR]

We apply a recently proposed density functional for mixtures of parallel hard cylinders, based on Rosenfeld's fundamental measure theory, to study the effect of length-polydispersity on the relative stability between the smectic and columnar liquid crystal phases. To this purpose we derive from this functional an expression for the direct correlation function and use it to perform a bifurcation analysis. We compare the results with those obtained with a second and a third virial approximation of this function. All three approximations lead to the same conclusion: there is a terminal polydispersity beyond which the smectic phase is less stable than the columnar phase. This result is in agreement with previous Monte Carlo simulations conducted on a freely rotating length-polydisperse hard spherocylinder fluid, although the theories always overestimate the terminal polydispersity because the nematic-columnar phase transition is first order and exhibits a wide coexistence gap. Both, the fundamental-measure functional and the third virial approximation, predict a metastable nematic-nematic demixing. Conversely, according to second virial approximation this demixing might be stable at high values of the polydispersity, something that is observed neither in simulations nor in experiments. The results of the fundamental-measure functional are quantitatively superior to those obtained from the other two approximations. Thus this functional provides a promising route to map out the full phase diagram of this system. [ABSTRACT FROM AUTHOR]