Abstract:
A grand canonical Monte Carlo method for the simulation of a simple colloid-polymer mixture called the AO model will be described. The phase separation known to occur in this model is driven by entropy. The phase diagram of the unmixing transition, the surface tension and thecritical point will be determined. To appear in: "Computer Simulation Studies in Condensed Matter Physics XVIII, Eds. D.P. Landau, S.P. Lewis, and H.B. Schuettler (Springer Verlag, Heidelberg, Berlin, 2004).

Abstract:
The isotropic-to-nematic transition in a two-dimensional fluid of hard needles is studied using grand canonical Monte Carlo simulations, multiple histogram reweighting, and finite size scaling. The transition is shown to be of the Kosterlitz-Thouless type, via a direct measurement of the critical exponents eta and beta, of the susceptibility and order parameter, respectively. At the transition, eta=1/4 and beta=1/8 are observed, in excellent agreement with Kosterlitz-Thouless theory. Also the shift in the chemical potential of the nematic susceptibility maximum with system size is in good agreement with theoretical expectations. Some evidence of singular behavior in the density fluctuations is observed, but no divergence, consistent with a negative specific heat critical exponent. At the transition, a scaling analysis assuming a conventional critical point also gives reasonable results. However, the apparent critical exponent beta_eff obtained in this case is not consistent with theoretical predictions.

Abstract:
The critical behavior of the Widom-Rowlinson mixture [J. Chem. Phys. 52, 1670 (1970)] is studied in d=3 dimensions by means of grand canonical Monte Carlo simulations. The finite size scaling approach of Kim, Fisher, and Luijten [Phys. Rev. Lett. 91, 065701 (2003)] is used to extract the order parameter and the coexistence diameter. It is demonstrated that the critical behavior of the diameter is dominated by a singular term proportional to t^(1-alpha), with t the relative distance from the critical point, and alpha the critical exponent of the specific heat. No sign of a term proportional to t^(2beta) could be detected, with beta the critical exponent of the order parameter, indicating that pressure-mixing in this model is small. The critical density is measured to be rho*sigma^3 = 0.7486 +/- 0.0002, with sigma the particle diameter. The critical exponents alpha and beta, as well as the correlation length exponent nu, are also measured and shown to comply with d=3 Ising criticality.

Abstract:
Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently ``sharp and narrow''. This implies phase coexistence between isotropic and quasi-nematic domains, separated by interfaces. The corresponding line tension is determined, and shown to be very small, giving rise to strong interface fluctuations. When the interactions are no longer ``sharp and narrow'', the transition becomes continuous, with non-universal critical behavior obeying hyperscaling, and approximately resembling the two-dimensional Potts model.

Abstract:
The isotropic-to-nematic transition in liquid crystals is studied in d=3 spatial dimensions. A simulation method is proposed to measure the angle dependent interfacial tension g(theta), with theta the anchoring angle of the nematic phase at the interface. In addition, an alternative liquid crystal model is introduced, defined on a lattice. The advantage of the lattice model is that accurate simulations of anchoring effects become possible. For the lattice model, g(theta) depends sensitively on the nearest-neighbor pair interaction, and both stable and metastable anchoring angles can be detected. We also measure g(theta) for an off-lattice fluid of soft rods. For soft rods, only one stable anchoring angle is found, corresponding to homogeneous alignment of the nematic director in the plane of the interface. This finding is in agreement with most theoretical predictions obtained for hard rods.

Abstract:
Computer simulations are presented of the isotropic-to-nematic transition in a liquid crystal confined between two parallel plates a distance H apart. The plates are neutral and do not impose any anchoring on the particles. Depending on the shape of the pair potential acting between the particles, we find that the transition either changes from first-order to continuous at a critical film thickness H=Hx, or that the transition remains first-order irrespective of H. This demonstrates that the isotropic-to-nematic transition in confined geometry is not characterized by any universality class, but rather that its fate is determined by microscopic details. The resulting capillary phase diagrams can thus assume two topologies: one where the isotropic and nematic branches of the binodal meet at H=Hx, and one where they remain separated. For values of H where the transition is strongly first-order the shift DT of the transition temperature is in excellent agreement with the Kelvin equation. Not only is the relation DT~1/H recovered but also the prefactor of the shift is in quantitative agreement with the independently measured bulk latent heat and interfacial tension.

Abstract:
We present Monte Carlo simulation results of the two-dimensional Zwanzig fluid, which consists of hard line segments which may orient either horizontally or vertically. At a certain critical fugacity, we observe a phase transition with a two-dimensional Ising critical point. Above the transition point, the system is in an ordered state, with the majority of particles being either horizontally or vertically aligned. In contrast to previous work, we identify the transition as being of the liquid-gas type, as opposed to isotropic-to-nematic. This interpretation naturally accounts for the observed Ising critical behavior. Furthermore, when the Zwanzig fluid is extended to more allowed particle orientations, we argue that in some cases the symmetry of a q-state Potts model with q>2 arises. This observation is used to interpret a number of previous results.

Abstract:
We present simulation data of first-order isotropic-to-nematic transitions in lattice models of liquid crystals and locate the thermodynamic limit inverse transition temperature $\epsilon_\infty$ via finite-size scaling. We observe that the inverse temperature of the specific heat maximum can be consistently extrapolated to $\epsilon_\infty$ assuming the usual $\alpha / L^d$ dependence, with $L$ the system size, $d$ the lattice dimension and proportionality constant $\alpha$. We also investigate the quantity $\epsilon_{L,k}$, the finite-size inverse temperature where $k$ is the ratio of weights of the isotropic to nematic phase. For an optimal value $k = k_{\rm opt}$, $\epsilon_{L,k}$ versus $L$ converges to $\epsilon_\infty$ much faster than $\alpha/L^d$, providing an economic alternative to locate the transition. Moreover, we find that $\alpha \sim \ln k_{\rm opt} / {\cal L}_\infty$, with ${\cal L}_\infty$ the latent heat density. This suggests that liquid crystals at first-order IN transitions scale approximately as $q$-state Potts models with $q \sim k_{\rm opt}$.

Abstract:
We consider the main transition in single-component membranes using computer simulations of the Pink model [D. Pink {\it et al.}, Biochemistry {\bf 19}, 349 (1980)]. We first show that the accepted parameters of the Pink model yield a main transition temperature that is systematically below experimental values. This resolves an issue that was first pointed out by Corvera and co-workers [Phys. Rev. E {\bf 47}, 696 (1993)]. In order to yield the correct transition temperature, the strength of the van der Waals coupling in the Pink model must be increased; by using finite-size scaling, a set of optimal values is proposed. We also provide finite-size scaling evidence that the Pink model belongs to the universality class of the two-dimensional Ising model. This finding holds irrespective of the number of conformational states. Finally, we address the main transition in the presence of quenched disorder, which may arise in situations where the membrane is deposited on a rough support. In this case, we observe a stable multi-domain structure of gel and fluid domains, and the absence of a sharp transition in the thermodynamic limit.

Abstract:
We demonstrate that the law of the rectilinear coexistence diameter in two-dimensional (2D) mixtures of non-spherical colloids and non-adsorbing polymers is violated. Upon approach of the critical point, the diameter shows logarithmic singular behavior governed by a term t ln(t), with t the relative distance from the critical point. No sign of a term t^2b could be detected, with b the critical exponent of the order parameter, indicating a very weak or absent Yang-Yang anomaly. Our analysis thus reveals that non-spherical particle shape alone is not sufficient for the formation of a pronounced Yang-Yang anomaly in the critical behavior of fluids.