For liquid rubidium the Stokes-Einstein (SE) relation is well fulfilled near the melting point with an effective hydrodynamic diameter, which agrees well with a value from structural investigations. A wealth of thermodynamic and microscopic data exists for a wide range of temperatures for liquid rubidium and hence it represents a good test bed to challenge the SE relation with rising temperature from an experimental point of view. We performed classical molecular dynamics simulations to complement the existing experimental data using a pseudopotential, which describes perfectly the structure and dynamics of liquid rubidium. The derived SE relation from combining experimental shear viscosity data with simulated diffusion coefficients reveals a weak violation at about 1.3T_{melting}≈400 K. The microscopic relaxation dynamics on nearest neighbor distances from neutron spectroscopy demonstrate distinct changes in the amplitude with rising temperature. The derived average relaxation time for density fluctuations on this length scale shows a non-Arrhenius behavior, with a slope change around 1.5T_{melting}≈450 K. Combining the simulated macroscopic self-diffusion coefficient with that microscopic average relaxation time, a distinct violation of the SE relation in the same temperature range can be demonstrated. One can conclude that the changes in the collective dynamics, a mirror of the correlated movements of the particles, are at the origin for the violation of the SE relation. The changes in the dynamics can be understood as a transition from a more viscous liquid metal to a more fluid-like liquid above the crossover temperature range of 1.3-1.5 T_{melting}. The decay of the amplitude of density fluctuations in liquid aluminium, lead, and rubidium demonstrates a remarkable agreement and points to a universal thermal crossover in the dynamics of liquid metals.

The mechanism of diffusion of helical particles in the new screw-like nematic phase is studied by molecular dynamics numerical simulation. Several dynamical indicators are reported that evidence and microscopically characterise the special translo-rotational motion by which helical particles move in this chiral liquid-crystalline phase. Besides mean square displacements and diffusion coefficients resolved parallel and perpendicular to the nematic director, a suitable translo-rotational van Hove self-correlation function and a sequence of translational and rotational velocity, self- and distinct-, time correlation functions are calculated. The analysis of all these correlation functions elicits the operativeness of the aforementioned coupled mechanism and allows its short- and long-time quantitative characterisation.

This work discusses a few second- and third-virial (density functional) theory approaches aimed at describing the isotropic-nematic phase transition in three-dimensional freely rotating infinitesimally thin hard discs, the basic model for (colloidal) discotic liquid crystals. Both plain and resummed versions are considered, those resummed being based on a simple yet rather accurate analytic equation of state for the isotropic phase. Extensive Monte Carlo simulations, carried out to locate accurately the phase transition, are used to test the performance of these approaches and guide toward an improved ansatz.

Monte Carlo numerical simulations are used to study in detail how the characteristics of the isotropic-nematic phase transition change as infinitely thin hard platelets are bent into shallow lens-like particles. First, this phase transition in the former reference model system is re-examined and more accurately located. Then, it is shown quantitatively that this already quite weak but distinctly first-order phase transition weakens further upon curving the platelets to such an extent that, thanks to the thinness of these particles that does not favor its pre-emptying by a transition to a (partially) positionally ordered phase, an isotropic-nematic tricritical point limit can be arbitrarily closely approached.

We propose a method by which the generalized transport properties and coefficients at all wavelengths and frequencies can be obtained by inversion of an exact kinetic equation. The necessary data are the density-density, energy-energy, and density-energy time correlation functions, which can be obtained by molecular-dynamics simulation. In addition, also the coupling between viscous stress tensor and energy flux vector can be obtained without approximation. This allows one to check the validity of the Markov assumption in a straightforward way. As a first test case, the theory is applied to liquid argon in two thermodynamic states. For this system, we calculate and discuss generalized thermodynamic (enthalpy, specific heats, and thermal expansion) and transport properties (longitudinal viscosity, thermal conductivity).

In the present paper, we extend the method described in paper I [D. Bertolini and A. Tani, preceding paper, Phys. Rev. E 83, 031201 (2011)] to molecular liquids, which allows us to solve the exact kinetic equation proposed by de Schepper et al. [Phys. Rev. A 38, 271 (1988)] without approximations. In particular, generalized thermodynamic properties (enthalpy, specific heat, and thermal expansion coefficient) and transport properties (longitudinal viscosity, thermal conductivity) have been calculated for three liquids of increasing complexity, namely dimethyl sulfoxide, hydrogen fluoride, and SPC/E water. All results have been obtained by the molecular formalism as well as the atomic one, corrected for intramolecular correlations that are due to the models adopted. As done for simple liquids, the coupling between the viscous stress tensor and the energy flux vector has been calculated exactly. We also show that the Markov assumption for the dynamics related to thermal conductivity can only be adopted with caution.

Molecular dynamics computer simulations were performed on model colloidal binary mixtures of two large and many small soft repulsive spheres. Depletion forces arise between the two large spheres, as a function of their distance, because of the nonadditivity of the volume they exclude to the small spheres. The probability distribution functions of both longitudinal and transverse component of the total force exerted by the small particles were calculated and generally turned out non-Gaussian. The distributions of the collective forces were analyzed in terms of the distribution of the force that a single small sphere exerts on a large sphere and of the number of the surrounding small spheres. The reconstructed function matches well the corresponding exact distribution. Residual correlation among small particles, combined with a relatively small number of neighbors, slows the approach to the Gaussian limit. In our fully repulsive model, the direct force between a large and a small sphere is a monotonic function of their distance. On these bases, we propose and successfully test an approach that relates the probability distribution function of the depletion forces to the large-sphere-small-sphere radial distribution function. This approach can be extended to experimental data of radial distribution function, thus allowing for an estimate of depletion force fluctuations in real colloidal mixtures.

The origin of the stereochemical behavior experimentally found in a bile acid-derived biphenyl phosphite is studied by means of quantum mechanical methods. The molecular mechanisms driving the screw sense of the dihedral angle between the two phenyl rings of the biphenyl phosphite unit are investigated with density functional theory calculations. Energy, geometry, and circular dichroism spectra have been computed and compared between the two resulting diastereoisomers. We evaluated the solvent effect on the torsional energy profile by discussing the results obtained for the isolated molecule with those found with polarizable continuum model (PCM) calculations performed in different solvents. The results we obtain with the PCM model do not reproduce the solvent effect on the stereochemical equilibrium of this phosphite.

Intra- and intermolecular potential energy surfaces of the 4,4'-di-n-heptyl azoxybenzene molecule have been sampled by ab initio calculations and represented through a force field suitable for classical bulk simulations. The parametrization of the molecular internal flexibility has been performed by a fitting procedure based on single molecule Hessian, gradients and torsional energies, computed using density functional theory. The intermolecular part of the force field has been derived as a pure pair potential, by fitting the dimer potential energy surface sampled by the Fragmentation Reconstruction Method. Preliminary molecular dynamics runs have been performed on systems of 210 and 600 molecules at atmospheric pressure and different temperatures, showing the presence of ordered and isotropic phases. Several properties have been computed, all resulting in a good agreement with the corresponding experimental data.

The isotropic phase dynamics of a system of 4-n-hexyl-4'-cyano-biphenyl (6CB) molecules has been studied by molecular dynamics computer simulations. We have explored the range of 275-330 K keeping the system isotropic, although supercooled under its nematic transition temperature. The weak rototranslational coupling allowed us to separately evaluate translational (TDOF) and orientational degrees of freedom (ODOF). Evidences of subdiffusive dynamics, more apparent at the lowest temperatures, are found in translational and orientational dynamics. Mean square displacement as well as self-intermediate center of mass and rotational scattering functions show a plateau, also visible in the orientational correlation function. According to the mode coupling theory (MCT), this plateau is the signature of the beta-relaxation regime. Three-time intermediate scattering functions reveal that the plateau is related to a homogeneous dynamics, more extended in time for the orientational degrees of freedom (up to 1 ns). The time-temperature superposition principle and the factorization property predicted by the idealized version of MCT hold, again for both kinds of dynamics. The temperature dependence of diffusion coefficient and orientational relaxation time is well described by a power law. Critical temperatures T-c are 244 +/- 6 and 258 +/- 6 K, respectively, the latter is some 10 K below the corresponding experimental values. The different values of T-c we obtained indicate that ODOF freezes earlier than TDOF. This appears due to the strongly anisotropic environment that surrounds a 6CB molecule, even in the isotropic phase. The lifetime of these "cages," estimated by time dependent conditional probability functions, is strongly temperature dependent, ranging from some hundreds of picoseconds at 320 K to a few nanoseconds at 275 K. (c) 2008 American Institute of Physics.

Several dynamic properties of the 4-n-alkyl-4'-cyanobiphenyls series ( nCB) with n=5, 6, 7, 8 have been studied by atomistic molecular dynamics (MD) simulations in the NVE ensemble adopting an ab initio derived force field (J. Phys. Chem. B 2007, 111, 2130). For each homologue, at least two state points, in the nematic and in the isotropic phase, as determined from lengthy equilibration runs performed in the previous work, have been considered. More than 10 ns have been produced at each state point, allowing us to calculate single-molecule properties as the translational and rotational diffusion coefficients along the series. An oscillating behavior of the diffusion coefficients, similar to the observed odd-even effect in static properties, has been predicted by MD. A good agreement with the results of purposely carried out (1)H NMR measurements is achieved, provided the MD values are increased by a factor that accounts for density overestimation. Spinning and tumbling rotational motions, monitored by calculating the rotational diffusion coefficients for all homologues in both phases, agree well with experimental data, at least for 5CB where NMR measures are reported. Collective properties, such as the isotropic shear viscosity and the rotational viscosity coefficient, have been computed for all homologues, and the MD values agree well with the experimental data reported in the literature. Finally, the origin of the odd-even effect, found for all the computed dynamic properties, is addressed.

Structural, electronic, and optical properties calculated for an isolated infinite column of hexakis-hydroxy-triphenylene (HAT0) molecules are presented. This system is intended as a prototype model of columnar discotic liquid crystals since HAT0 is the first member of the discogenic hexakis-n-alkyloxy-triphenylenes (HATn) series; the single-column approximation can be adopted in view of the peculiar nanoseparation of the columns characteristic of these mesophases. Structural optimization of the system has been performed using Car-Parrinello molecular dynamics techniques. Kohn-Sham orbitals, density of states, and electronic energies have been calculated on the optimized structure of the infinite column and implemented in the quantum expression of the transverse dielectric function. The optical absorption spectrum calculated from the dielectric function has been discussed in comparison to a measured absorption spectrum of HAT5 in columnar discotic liquid crystal phase. Optical absorption spectra of short columns of a few HAT0 molecules arranged as in the infinite column have been calculated using the ZINDO method. These spectra are in good agreement with measured absorption spectra of HAT5 and HAT6 in organic solvents, a fact that supports the proposed columnar arrangement of the discotic molecules in these solvents. We also give an estimate of the electronic transport properties of a small column of HAT0 molecules by calculating with the nonequilibrium Green's function method, the current/voltage characteristic of a model system in which a few HAT0 molecules have been inserted between two gold electrodes under the bias of an external potential.

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.

The translational motion of 4-n-hexyl-4'-cyanobiphenyl (6CB) in its isotropic phase has been studied by atomistic molecular dynamics simulation from 280 to 330 K. The mean square displacement shows evidence of a subdiffusive dynamics, with a plateau that becomes very apparent at the lowest temperatures. A three-time self-intermediate scattering function reveals that this plateau is connected with a homogeneous dynamics that, at longer times, becomes heterogeneous and finally exponential. These features are shared by, for example, a high-density system of hard spheres, which supports the universal character of the translational dynamics of liquids in their supercooled condition. As predicted by the idealized version of the mode-coupling theory (MCT), the diffusion coefficient dependence upon temperature is well described by a power law, with a critical temperature very close to that obtained by experimental measurements on orientational relaxation. This agreement might indicate a complete freezing of both rotational and translational intradomain dynamics. The time-temperature superposition principle also holds. The shape of the cage that surrounds a 6CB molecule has been reconstructed, and this analysis suggests a preferential side-by-side arrangement of molecules, which locally tend to align their long axes even in the isotropic phase.

A wide range of NPT simulations of a bead necklace liquid crystal model in the crystal B, smectic B, smectic A, and nematic phases have been performed. Systems with up to 21 600 molecules have been studied to observe the behavior of slowly decaying spatial correlation functions. The pair correlation function and its in-plane restriction are consistent with a crystalline phase made of independent two-dimensional crystalline layers. Smectic B phase is studied by the bond orientational pair correlation functions g(6) and its extension g(6ext). The first reaches a constant value, which seems to rule out a classical hexatic phase. The latter shows a power-law decay within the layers: its typical decay exponent (eta(6ext)) is evaluated. Relationships between multiple harmonics of the C(6n) order parameter have been evaluated through the whole range of existence of B phases (crystalline and smectic): the extension to the crystalline phase holds and provides an excellent fit of the simulation data.

A method for the calculation of the two-body intermolecular potential which can be applied to large molecules is presented. Each monomer is fragmented in a number of moieties whose interaction energies are used to recover the interaction energy of the whole dimer. For these reasons this strategy has been called fragmentation reconstruction method (FRM). By a judicious choice of the fragmentation scheme it is shown that very accurate interaction energies can be obtained. The sampling of the potential energy surface of a dimer is then used to obtain intermolecular force fields at several levels of complexity, suitable to be employed in bulk phase computer simulations. Applications are presented for benzene and for some mesogenic molecules which constitute the principal interest of the authors. A number of properties ranging from phase stability, thermodynamic quantities, orientational order parameter and collective dynamics properties are computed and discussed.

Lengthy molecular dynamics (MD) simulations were performed at constant atmospheric pressure and different temperatures for the series of the 4-n-alkyl-4'-cyanobiphenyls (nCB) with n = 6, 7, and 8. The accurate atomistic force field (Bizzarri, M.; Cacelli, I.; Prampolini, G; Tani, A. J. Phys. Chem. A 2004, 108, 10336), successfully employed to reproduce thermodynamic and transport properties of the 5CB molecule, has here been extended to higher homologues. Nematic and isotropic phases were found for all members of the series, and also, a smectic phase was (tentatively) identified for 8CB at 1 atm and 300 K. Transition temperatures reproduce the experimental values within +/-10 K. Also, structural properties as second and fourth rank orientational order parameters are in good agreement with the corresponding experimental quantities. This means that the well-known odd-even effect, observed for many properties along the nCB series, is well reproduced, despite the narrow range of oscillations, e.g., in clearing temperatures. A detailed analysis of the correlation between molecular properties and odd-even effects is presented.

Recent neutron scattering results [F. Demmel et al., Phys. Rev. B 73, 104207 (2006)] on the temperature dependence of de Gennes narrowing in liquid rubidium have stimulated a molecular dynamics (MD) study in the same temperature and density range. At the $k$ value of the first peak of $S(k)$, the MD results agree very well with experimental data of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}({k}_{\mathrm{max}},\ensuremath{\omega}=0)$, $F({k}_{\mathrm{max}},t=0)$, and longitudinal viscosity ${\ensuremath{\eta}}_{L}({k}_{\mathrm{max}},\ensuremath{\omega}=0)$. Other transport properties, such as self-diffusion and shear viscosity, are also accurately reproduced. At $k=0$, on the other hand, the MD results significantly underestimate the experimental values of bulk viscosity and thermal conductivity. For the latter, this is a well known deficiency of models which do not explicitly take into account the electronic contribution to thermal exchanges. However, the large difference between MD and macroscopic experimental data for bulk viscosity casts some doubts on its indirect calculation from sound absorption data. This contradictory result, which presumably extends to all alkali metals, is discussed in the light of various theoretical models.