Heterogeneous dynamics in columnar liquid crystals of parallel hard rods

In the wake of previous studies on the rattling-and-jumping diffusion in smectic liquid crystal phases of colloidal rods, we analyze here for the first time the heterogeneous dynamics in columnar phases. More specifically, we perform computer simulations to investigate the relaxation dynamics of a binary mixture of perfectly aligned hard spherocylinders. We detect that the columnar arrangement of the system produces free-energy barriers that the particles should overcome to jump from one column to another, thus determining a hopping-type diffusion. This phenomenon accounts for the non-Gaussian intercolumn diffusion and shows a two-step structural relaxation that is remarkably analogous to that of out-of-equilibrium glass-forming systems and gels. Surprisingly enough, slight deviations from the behavior of simple liquids due to transient cages is also observed in the direction perpendicular to this plane, where the system is usually referred to as liquidlike.     

Glassy dynamics and kinetic vitrification of isotropic suspensions of hard rods

A nonlinear Langevin equation (NLE) theory for the translational center-of-mass dynamics of hard nonspherical objects has been applied to isotropic fluids of rigid rods. The ideal kinetic glass transition volume fraction is predicted to be a monotonically decreasing function beyond an aspect ratio of two. The functional form of the decrease is weaker than the inverse aspect ratio. Vitrification occurs at lower volume fractions for corrugated tangent bead rods compared to their smooth spherocylinder analogs. The ideal glass transition signals a crossover to activated dynamics, which is estimated to be observable before the nematic phase boundary is encountered if the aspect ratio is less than roughly 25. Calculations of the glassy elastic shear modulus and absolute yield stress reveal a roughly exponential growth with volume fraction. The dependence of entropic barriers and mean barrier hopping times on concentration for rods of variable aspect ratios can be collapsed quite well based on a difference volume fraction variable that quantifies the distance from the ideal glass boundary. Full numerical solution of the NLE theory via stochastic trajectory simulation was performed for tangent bead rods, and the results were compared to their hard sphere analogs. With increasing shape anisotropy the characteristic length scales of the nonequilibrium free energy increase and the magnitude of the localization well and entropic barrier curvatures decreases. These changes result in a significant aspect ratio dependence of dynamical properties and time correlation functions including weaker intermediate time subdiffusive transport, stronger two-step decay of the incoherent dynamic structure factor, longer mean alpha relaxation time, and stronger wavevector-dependent decoupling of relaxation times and the self-diffusion constant. The theoretical results are potentially testable via computer simulation, confocal microscopy, and dynamic light scattering.     

Dynamical correlations in Brownian hard rods

We analyze the time decay of small amplitude density perturbations in systems of highly packed Brownian hard rods, relaxing towards a uniform density distribution. The results of Brownian dynamics simulations and those of the deterministic dynamic density functional (DDF) theory, are contrasted with a new theoretical approach beyond the DDF assumptions. We characterize dynamical correlation modes which, having the lowest relaxation time, determine the late time evolution of the system. The spectrum of possible time decays has a continuous band structure, with pockets of discrete values, near the minima of the DDF results, where the validity of that theory appears to be well established.     

Inelastic hard rods in a periodic potential

A simple model of inelastic hard rods subject to a one-dimensional array of identical wells is introduced. The energy loss due to inelastic collisions is balanced by the work supplied by an external stochastic heat bath. We explore the effect of the spatial nonuniformity on the steady states of the system. The spatial variations of the density, granular temperature, and pressure induced by the gradient of the external potential are investigated and compared with the analogous variations in an elastic system. Finally, we study the clustering process by considering the relaxation of the system starting from a uniform homogeneous state.     

Brownian dynamics simulations of the self- and collective rotational diffusion coefficients of rigid long thin rods

Recently a microscopic theory for the dynamics of suspensions of long thin rigid rods was presented, confirming and expanding the well-known theory by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] and Kuzuu [J. Phys. Soc. Jpn. 52, 3486 (1983)]. Here this theory is put to the test by comparing it against computer simulations. A Brownian dynamics simulation program was developed to follow the dynamics of the rods, with a length over a diameter ratio of 60, on the Smoluchowski time scale. The model accounts for excluded volume interactions between rods, but neglects hydrodynamic interactions. The self-rotational diffusion coefficients D(r)(phi) of the rods were calculated by standard methods and by a new, more efficient method based on calculating average restoring torques. Collective decay of orientational order was calculated by means of equilibrium and nonequilibrium simulations. Our results show that, for the currently accessible volume fractions, the decay times in both cases are virtually identical. Moreover, the observed decay of diffusion coefficients with volume fraction is much quicker than predicted by the theory, which is attributed to an oversimplification of dynamic correlations in the theory.     

Microscopic collective dynamics of water

Data obtained on microscopic collective excitations in water by molecular dynamics simulation within the framework of the coarse-grained mW-model of the intermolecular interaction potential for water are reported. The calculated spectra of the dynamic structure factor and spectral densities of time correlation functions of longitudinal and transverse currents reveal the existence of propagating collective excitations of longitudinal and transverse polarization in water for a wide range of wavenumbers. The dynamics of fluctuations in the particle number density is analyzed within the framework of a microscopic theory that takes into account only the structural features of a system. The theoretically calculated data on the spectra of dynamic structure factor in a wavenumber range of 0.13–0.48 Å^–1 are in good agreement with the results of molecular dynamics simulation.     

Depletion potentials in colloidal mixtures of hard spheres and rods

The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.     

Isotropic-nematic transition of hard rods immersed in random sphere matrices

Using replica density functional theory and Monte Carlo computer simulations we investigate a system of annealed hard spherocylinders adsorbed in a matrix of quenched hard spheres. Theoretical predictions for the partition coefficient, defined as the ratio of density of rods in the matrix and that in a reservoir, agree well with simulation results. Theory predicts the isotropic-nematic transition to remain first order upon increasing sphere packing fraction, and to shift towards lower rod densities. This scenario is consistent with our simulation results that clearly show a jump in the nematic order parameter upon increasing the rod density at constant matrix packing fraction, corresponding to the isotropic-nematic transition, even for sphere matrix packing fractions < or approximately equal to 0.3.     

Crystalline ordering in lattice models of hard rods with nearest neighbour attraction

Several lattice models for hard rods with attraction between neighbouring parallel rodes are considered. It is proved that the models for sufficiently low temperature and high fugacity exhibit a phase transition to an ordered crystalline structure. Nothing is proved about the existence of a liquid crystal state.     

Event-driven Brownian dynamics for hard spheres

Brownian dynamics algorithms integrate Langevin equations numerically and allow to probe long time scales in simulations. A common requirement for such algorithms is that interactions in the system should vary little during an integration time step; therefore, computational efficiency worsens as the interactions become steeper. In the extreme case of hard-body interactions, standard numerical integrators become ill defined. Several approximate schemes have been invented to handle such cases, but little emphasis has been placed on testing the correctness of the integration scheme. Starting from the two-body Smoluchowski equation, the authors discuss a general method for the overdamped Brownian dynamics of hard spheres, recently developed by one of the authors. They test the accuracy of the algorithm and demonstrate its convergence for a number of analytically tractable test cases.     

Thermodynamics of attractive hard rods: a test of mean field density functional theory

Mean field density functional theory (MFDFT) has been employed to calculate the free energy of a pair of attractive hard rods on a ring. The results for homogeneous and optimal inhomogeneous density profiles have been compared with the exact free energy as a test of the approach. We discuss the problems in applying MFDFT to small systems and suggest modifications which allow a reasonably accurate treatment of this particular, rather extreme, case.     

Entropic forces and directed alignment of hard squares in suspensions of rods and disks

We use Monte Carlo simulations in two dimensions to study the depletion forces between two hard squares in a suspension of hard rods or disks. We determine the effects of size and concentration of rods and disks on the potential of mean force between the squares. Both rods and disks produce a short-range depletion attraction between the two squares. The depletion interaction can be strong enough to outweigh the (rotational) entropic repulsion between the squares at certain sizes and concentrations of the rods and disks. We also probe the relative orientation that two squares adopt as they approach each other and we observe rich behavior, in which the relative orientation depends on the size, concentration, and shape of the depletion agent. Simple models based on the ideas of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] can explain trends in the potentials of mean force obtained from the simulations.     

The dynamics of thin polymer films

An increasing amount of experimental data now supports the idea that the dynamics of thin polymer films is different from bulk. An experimental consensus now supports the previously controversial view that glass transition temperatures of thin polymer films on weakly interacting substrates are reduced from bulk values, but evidence for whether the surface has a higher mobility than the bulk is still contradictory.     

Isotropic-nematic interfacial tension of hard and soft rods: application of advanced grand canonical biased-sampling techniques

Coexistence between the isotropic and the nematic phase in suspensions of rods is studied using grand canonical Monte Carlo simulations with a bias on the nematic order parameter. The biasing scheme makes it possible to estimate the interfacial tension gamma(IN) in systems of hard and soft rods. For hard rods with LD=15, we obtain gammaIN approximately 1.4kBT/L2, with L the rod length, D the rod diameter, T the temperature, and kB the Boltzmann constant. This estimate is in good agreement with theoretical predictions, and the order of magnitude is consistent with experiments.     

Nematic and crystalline ordering in the lattice model of hard rods with a mean field interaction

A lattice model of long hard rods with a nearest neighbour attraction proportional to the length of overlap is considered. It is shown, that in the van der Waals approximation the model exhibits non only the isotropic and nematic phases obtained with the approximative treatment of the hard rod interaction but also a crystalline phase.     

Unexpected slow near wall dynamics of spherical colloids in a suspension of rods

In this paper, we will show the influence of an additional rodlike component, that is, fd-virus, on the diffusion of spherical polystyrene colloids close to a wall. The sphere diffusivity normal to the wall, D perpendicular, is strongly affected by the presence of the rods, while the effect on the parallel diffusivity, D||, is less pronounced except in the immediate vicinity of the wall. We show that this observation cannot be explained by describing the effect of the rods as a simple mean field depletion potential alone.     

Microscopic structure and dynamics of molten Se50Te50 alloys

In this work we investigate the microscopic structure and dynamics of the molten equimolar alloy, Se(50)Te(50) using a combination of neutron and x-ray diffraction experiments, reverse Monte Carlo analysis, and first principles molecular dynamics. The range of temperatures studied covers the semiconductor/metal transition. From our results it can be seen that the latter is associated with an increase in coordination numbers and a reduced tendency to heterocoordination. In agreement with previous inelastic neutron scattering experiments, our molecular dynamics calculation predict a certain widening of the stretching vibrational modes band in connection with the increase of coordination and the presence of longer bonds in the metallic phase.