We study the phase behavior of a mixture of colloidal hard rods with a length-to-diameter ratio of L/sigma(c)=5 and nonadsorbing ideal polymer. We map our binary mixture onto an effective one-component system by integrating out the degrees of freedom of the polymer coils. We derive a formal expression for the exact effective Hamiltonian of the colloidal rods, i.e., it includes all effective many-body interactions and it is related to the exact free volume available for the polymer. We determine numerically on a grid the free volume available for the ideal polymer coils "on the fly" for each colloidal rod configuration during our Monte Carlo simulations. This allows us to go beyond first-order perturbation theory, which employs the pure hard-rod system as reference state. We perform free energy calculations for the isotropic, nematic, smectic, and crystal phase using thermodynamic integration and common tangent constructions are used at fixed polymer fugacities to map out the phase diagram. The phase behavior is determined for size ratios q=sigma(p)/sigma(c)=0.15, 0.5, and 1, where sigma(p) is the diameter of the polymer coils. The phase diagrams based on the full effective Hamiltonian are compared with those obtained from first-order perturbation theory, from simulations using the effective pair potential approximation to the effective Hamiltonian, and with those based on an empiric effective depletion potential for the rods. We find that the many-body character of the effective interactions stabilizes the nematic and smectic phases for large q, while the effective pair potential description overestimates the attractive interactions and favors, hence, a broad isotropic-crystal coexistence.

Sedimentation and multiphase equilibria in a suspension of hard colloidal rods are explored by analyzing the (macroscopic) osmotic equilibrium conditions. We observe that gravity enables the system to explore a whole range of phases varying from the most dilute phase to the densest phase, i.e., from the isotropic (I), to the nematic (N), to the smectic (Sm), to the crystal (K) phase. We determine the phase diagrams for hard spherocylinders with a length-to-diameter ratio of 5 for a semi-infinite system and a system with fixed container height using a bulk equation of state obtained from simulations. Our results show that gravity leads to multiphase coexistence for the semi-infinite system, as we observe I, I + N , I + N +Sm, or I + N +Sm+K coexistence, while the finite system shows I, N, Sm, K, I + N , N + Sm, Sm+ K , I + N +Sm, N +Sm+K, and I + N +Sm+K phase coexistence. In addition, we compare our theoretical predictions for the phase behavior and the density profiles with Monte Carlo simulations for the semi-infinite system and we find good agreement with our theoretical predictions.

We investigate the asymptotic decay of the total correlation function h͑1,2͒ in molecular fluids. To this end, we expand the angular dependence of h͑1,2͒ and the direct correlation function c͑1,2͒ in the Ornstein-Zernike equation in a complete set of rotational invariants. We show that all the harmonic expansion coefficients h l 1 l 2 l ͑r͒ are governed by a common exponential decay length and a common wavelength of oscillations in the isotropic phase. We determine the asymptotic decay of the total correlation functions by investigating the pole structure of the reciprocal ͑q-space͒ harmonic expansion coefficients h l 1 l 2 l ͑q͒. The expansion coefficients in laboratory frame of reference h l 1 l 2 l ͑r͒ are calculated in computer simulations for an isotropic fluid of hard spherocylinders. We find that the asymptotic decay of h͑1,2͒ is exponentially damped oscillatory for hard spherocylinders with a length-to-diameter ratio L / D ഛ 10 for all statepoints in the isotropic fluid phase. We compare our results on the pole structure using different theoretical Ansätze for c͑1,2͒ for hard ellipsoids. The theoretical results show that the asymptotic decay of h͑1,2͒ is exponentially damped oscillatory for all elongations of the ellipsoids.

The determination of the nematic order parameter S and the orientational distribution function (ODF) from scattering data involve severe approximations. The validity of these are studied here using Monte-Carlo simulations of hard spherocylinders with an aspect ratio of 15 for varying densities in the isotropic and nematic phase. The "exact" ODF of the rods, the "exact" value of S, and the intensity scatter I͑q ជ͒ are determined directly in simulation. In addition, we determine the ODF and S from the simulated intensity scatter which includes spatial and orientational correlations of the particles. We investigate whether correlations present in the interparticle scatter influences the determination of the single particle orientational distribution function by comparing the results obtained from scattering with the "exact" results measured directly in our simulations. We find that the nematic order parameter determined from the intensity scatter underestimates the actual value by 2 -9%. We also find that the values of S and the ODF are insensitive to the absolute value of the scattering vector for 1.2 Ͻ ͉q ជ͉D Ͻ 2 which agrees well with the assumption proposed by Leadbetter that I͑q , ͒ along the equatorial arc is independent of ͉q ជ͉. We also observe that the best fit of the "exact" ODF is given by the Maier-Saupe distribution when nematic director fluctuations are ignored, while the Gaussian distributions provides the best fit when these fluctuations are included.

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