Hard Rod Fluid Research Articles

FILAMENT ORDERING AND CLUSTERING BY MOLECULAR MOTORS IN MOTILITY ASSAYS

We study the cooperative behavior of cytoskeletal filaments in motility assays, in which immobilized motor proteins bind the filaments to a surface and actively pull them along this surface. Because of the repulsive interaction of filaments, the motor-driven dynamics of filaments leads to a nonequilibrium phase transition which generalizes the isotropicnematic phase transition of the corresponding equilibrium system, the hard-rod fluid. Langevin dynamics simulations and analytical theory show that the motor activity enhances the tendency for nematic ordering. At high detachment forces of motors, we observe the formation of filament clusters because of blocking effects; at low detachment forces, cluster formation can be controlled by the density of inactive motors.

Enhanced Ordering of Interacting Filaments by Molecular Motors

We theoretically study the cooperative behavior of cytoskeletal filaments in motility assays in which immobilized motor proteins bind the filaments to substrate surfaces and actively pull them along these surfaces. Because of the mutual exclusion of the filaments, the coupled dynamics of filaments, motor heads, and motor tails leads to a nonequilibrium phase transition which generalizes the isotropic-nematic phase transition of the corresponding equilibrium system, the hard-rod fluid. Langevin dynamics simulations show that the motor activity enhances the tendency for nematic ordering. We develop a quantitative theory for the location of the phase boundary as a function of motor density. At high detachment forces of motors, we also observe filament clusters arising from blocking effects.

Inelastic Takahashi hard-rod gas

We study a one-dimensional fluid of hard rods interacting with each other via binary inelastic collisions and a short-ranged square-well potential. Upon tuning the depth and the sign of the well, we investigate the interplay between dissipation and cohesive or repulsive forces. Molecular-dynamics simulations of the cooling regime indicate that the presence of this simple interparticle interaction is sufficient to significantly modify the energy dissipation rates expected by Haff's law for the free cooling. The simplicity of the model makes it amenable to an analytical approach based on the Boltzmann-Enskog transport equation which allows deriving the behavior of the granular temperature. Furthermore, in the elastic limit, the model can be solved exactly to provide a full thermodynamic description. A meaningful theoretical approximation explaining the properties of the inelastic system in interaction with a thermal bath can be directly extrapolated from the properties of the corresponding elastic system, upon a proper redefinition of the relevant observables. Simulation results both in the cooling and driven regimes can be fairly interpreted according to our theoretical approach and compare rather well to our predictions.

Entropic wetting in colloidal suspensions

We study the adsorption and wetting behaviour of colloidal hard spheres and colloidalrod-like particles at a planar hard wall using computer simulations. Our results showcomplete wetting by the hard-sphere crystal at the wall–fluid interface, and completewetting by the nematic phase of the hard-rod fluid at the wall–isotropic fluid interface. Inaddition, we investigated the effect of polymer-mediated effective interactions on thewetting behaviour of colloidal spheres. The many-body character of the effective colloidalinteractions yields an adsorption behaviour that differs enormously from those found forpairwise simple fluids; e.g., far from the triple point, we find three layering transitions inthe partial wetting regime prior to a transition to complete wetting by the colloidal liquid.

Soluble stochastic dynamics of quasi-one-dimensional single-file fluid self-diffusion

We solve a model of random-walk stochastic dynamics for hard single-file fluids in the experimentally important quasi-one-dimensional regime. This is a nontrivial extension of exact solution beyond one dimension. We point out that quasi-one-dimensional single-file self-diffusion of one-component hard fluids of diameter a under stochastic forces is equivalent at long time to a one-dimensional hard-rod fluid with the same linear density but a different diameter, a(eff). This effective diameter is controlled by the details of the relative dynamics between the transverse and longitudinal directions. There are two regimes of limiting behavior. For very fast transverse motion, the system is likely (but we cannot prove rigorously) to be equivalent to the soluble-oriented hard-rectangle or cylinder systems, with a(eff)=a. With very slow transverse motion, the self-diffusion dynamics is described by an equivalent soluble one-dimensional mixture of fluids with a(eff)=a(ave), the average longitudinal separation between nearest-neighbor particles at contact. We have explored our theoretical predictions with Monte Carlo simulations.

Effects of intramolecular dipolar coupling on the isotropic-nematic phase transition of a hard spherocylinder fluid

The thermodynamics of a simple model, containing the minimum set of features required to provide liquid crystal-like phase behavior and the dipolar coupling observable in the NMR spectrum of orientationally ordered fluids, are presented within the framework of Onsager theory. The model comprises a fluid of hard spherocylinders with a pair of embedded freely rotating magnetic dipoles. The behavior of the isotropic-nematic phase transition is explored as a function magnetic field strength and of the relative orientation between the nematic director and the external magnetic field. When the field and director are aligned the phase diagram is similar to those predicted for a hard rod fluid in flow fields, electric fields, and magnetic fields, with the field promoting orientational order in the fluid and the isotropic-nematic phase transition being replaced by a paranematic-nematic phase transition. In contrast, when the field and director are perpendicular, the field destabilizes the nematic phase and the phase transition is shifted to higher densities. The variation of the mean magnetic moment and the dipolar coupling are examined as a function of the orientational structure of the fluid. The model is used to support the hypothesis that dipolar couplings observed in the spectra of human leg muscle originate from nematic-like liquid crystal phases in relatively small metabolite molecules. The fitted theoretical predictions of the dependence of the dipolar coupling on the orientation of the field with respect to the nematic director are shown to provide a good description of the experimental data.

Colloidal hard-rod fluids near geometrically structured substrates.

Density functional theory is used to study colloidal hard-rod fluids near an individual right-angled wedge or edge as well as near a hard wall, which is periodically patterned with rectangular barriers. The Zwanzig model, in which the orientations of the rods are restricted to three orthogonal orientations but their positions can vary continuously, is analyzed by numerical minimization of the grand potential. Density and orientational order profiles, excess adsorptions, as well as surface and line tensions are determined. The calculations exhibit an enrichment [depletion] of rods lying parallel and close to the corner of the wedge (edge). For the fluid near the geometrically patterned wall, complete wetting of the wall-isotropic liquid interface by a nematic film occurs as a two-stage process in which first the nematic phase fills the space between the barriers until an almost planar isotropic-nematic liquid interface has formed separating the higher-density nematic fluid in the space between the barriers from the lower-density isotropic bulk fluid. In the second stage, a nematic film of diverging film thickness develops upon approaching bulk-isotropic-nematic coexistence.

Isotropic-nematic transition in hard-rod fluids: relation between continuous and restricted-orientation models.

We explore models of hard-rod fluids with a finite number of allowed orientations, and construct their bulk phase diagrams within Onsager's second virial theory. For a one-component fluid, we show that the discretization of the orientations leads to the existence of an artificial (almost) perfectly aligned nematic phase, which coexists with the (physical) nematic phase if the number of orientations is sufficiently large, or with the isotropic phase if the number of orientations is small. Its appearance correlates with the accuracy of sampling the nematic orientation distribution within its typical opening angle. For a binary mixture this artificial phase also exists, and a much larger number of orientations is required to shift it to such high densities that it does not interfere with the physical part of the phase diagram.

The 1-D Hard Rod Fluid Revisited Using NNPDFs

The new scheme developed in an earlier paper for the determination of the free energy of classical systems is applied to the 1-D single component fluid of hard rods. Exact results for the nearest neighbor probability density functions (NNPDFs) are obtained with origin situated at one end of the 1-D medium of interest. The formulation for NNPDFs are then used to show that the new scheme converges and actually reproduces the well-known exact results for the free energy of the 1-D hard rod system at all densities.

Free planar isotropic-nematic interfaces in binary hard-rod fluids.

Within the Onsager theory we study free planar isotropic-nematic interfaces in binary mixtures of hard rods. For sufficiently different particle shapes the bulk phase diagrams of these mixtures exhibit a triple point, where an isotropic (I) phase coexists with two nematic phases (N1 and N2) of different composition. For all explored mixtures we find that upon approach of the triple point the I-N2 interface shows complete wetting by an intervening N1 film. We compute the surface tensions of isotropic-nematic interfaces, and find a remarkable increase with fractionation, similar to the effect in polydisperse hard-rod fluids.

Continuous freezing in an infinite-range one-dimensional model.

The partition function of the classical one-dimensional hard rod fluid with a residual long range interaction can be evaluated exactly, with the aid of an auxiliary field, in the limit where the range of the potential goes to infinity. If the Fourier spectrum of the residual interaction lacks components at finite wave vector, the infinite range limit recovers the celebrated result of the Kac-Uhlenbeck-Hemmer model of condensation. Otherwise, it predicts a continuous second-order freezing transition.

Wetting and capillary nematization of binary hard-platelet and hard-rod fluids.

Density-functional theory is used to investigate the phase behavior of colloidal binary hard-platelet and hard-rod fluids near a single hard wall or confined in a slit pore. The Zwanzig model, in which the orientations of the particles of rectangular shape are restricted to three orthogonal orientations, is analyzed by numerical minimization of the grand potential functional. The density and orientational profiles as well as the surface contributions to the grand potential are determined. The calculations exhibit a wall-induced continuous surface transition from uniaxial to biaxial symmetry for the hard-rod fluid. Complete wetting of the wall-isotropic liquid interface by a biaxial nematic film for rods and a uniaxial nematic film for platelets is found. For the fluids confined by two parallel hard walls, we determine a first-order capillary nematization transition for large slit widths, which terminates in a capillary critical point upon decreasing the slit width.

Verification of the nucleation theorem for the internally constrained one-dimensional hard rod fluid

The generalized nucleation theorem as derived by Bowles et al. [J. Chem. Phys. 115, 1853 (2001)] had been verified for nonuniformities generated by a cavity and a cluster within the one-dimensional hard rod fluid. We further verify the nucleation theorem for nonuniformities created by a cavity and by a cluster containing m particles within the internally constrained hard rod fluid. The given results provide additional evidence of the validity of the generalized nucleation theorem even down to the molecular level.

Fluids of platelike particles near a hard wall.

Fluids consisting of hard platelike particles near a hard wall are investigated using density-functional theory. The density and orientational profiles, as well as the surface tension and the excess coverage, are determined and compared with those of a fluid of rodlike particles. Even for low densities, slight orientational packing effects are found for the platelet fluid due to larger intermolecular interactions between platelets as compared with those between rods. A net depletion of platelets near the wall is exhibited by the excess coverage, whereas a change of sign of the excess coverage of hard-rod fluids is found upon increasing the bulk density.

Application of the Geometric Gibbs Equation: Toward an Exact Closure Condition

The geometric Gibbs equation describes how the available space and corresponding surface area of a single-component hard particle fluid varies with the system density. When a closure condition is introduced, i.e., an additional equation describing how the surface area depends on the available space, the geometric Gibbs equation reduces to a second-order differential equation indicating how the available space varies with the system density. Solution of this new equation provides another route to the determination of the chemical potential and pressure of the hard particle fluid. The simplest proposed closure condition yields the properties of fully penetrable spheres. A modified closure condition is suggested, and its connection to thermophysical properties is derived. An extension of the exact form of the closure condition for the one-dimensional hard rod fluid yields a reasonably good approximation of the properties of the hard sphere fluid at low density, and is found to be the required form for densit...

A theorem for inhomogeneous systems: The generalization of the nucleation theorem

We show that the validity of the nucleation theorem transcends the phenomenon of nucleation and extends to all equilibrium systems containing local nonuniform density distributions stabilized by external fields, and that it remains valid down to the molecular level. This result is tested by the application of exact theory at the molecular level and is shown to be valid in all the cases for which we have been able to complete such an exact analysis. These cases include cavities and clusters in hard rod fluids, as well as the molecular excesses associated with the “atmospheres” of molecules in single and multicomponent fluids. We show that, at the molecular level, the theorem can be associated with the compressibility equation of state and, at the macroscopic level, with the Gibbs adsorption equation. It is thus a relation of great power and should be useful in many contexts.

Wetting and capillary nematization of a hard-rod fluid: a simulation study.

We present results of a simulation study of a fluid of hard spherocylinders with a length-to-diameter ratio of 15 in contact with a planar hard wall and confined by two parallel hard walls. A Monte Carlo method is developed for simulating fluids in contact with a single wall. Using this method, we find a transition from a uniaxial to a biaxial surface phase, followed, at larger bulk densities, by the formation of a thick nematic film, with the director parallel to the wall, at the wall-isotropic fluid interface. As the density far from the wall cb approaches the value at bulk isotropic-nematic coexistence cI, the thickness of the nematic film appears to increase as -ln(cI-cb). For a fluid confined by two parallel hard walls, a first-order capillary nematization transition is found. The phase equilibria are determined by Gibbs ensemble Monte Carlo simulations for several wall separations. The difference in the coexisting densities of the capillary condensed nematic and isotropic phases becomes smaller upon decreasing the wall separation, and no capillary nematization transition is found when the wall separation is smaller than about twice the length of the spherocylinders. These features imply that the capillary nematization transition ends in a capillary critical point at a critical wall separation. Our simulation results are fully consistent with the findings of our recent theoretical study of the Zwanzig model for a hard-rod fluid.

Interfaces, wetting, and capillary nematization of a hard-rod fluid: Theory for the Zwanzig model

We investigate interfacial and capillary phenomena in a simple model for a fluid of hard rods, viz. the Zwanzig model, in which the orientations of rectangular blocks are restricted to three orthogonal directions. The theory, which is based on an Onsager-like free energy functional, predicts local biaxial ordering at the “free” interface between the coexisting isotropic and nematic phases. For an isotropic bulk fluid in contact with a single planar hard wall, we find a continuous surface phase transition from uniaxial to biaxial local symmetry, followed by complete wetting of the wall–isotropic fluid interface by a nematic film with director parallel to the wall, as the reservoir density approaches its value at bulk coexistence. For a fluid confined by two parallel hard walls we determine a first-order capillary nematization transition at large wall separation, which terminates in a capillary critical point when the wall separation is about twice the length of the rods. This transition is the analog of the capillary condensation observed for simple fluids confined by attractive walls but is purely entropy driven here.

Phase behavior of two-dimensional hard rod fluids

Monte Carlo simulations are used to study two-dimensional hard rod fluids consisting of spherocylinders confined to lie in a plane. The phase behavior is mapped out as a function of the aspect ratio (L/D) of the particles, from the hard disc limit at one extreme (L/D=0) to the thin hard needle limit at the other (L/D=∞). For long rods, a 2D nematic phase is observed at high density in which the orientational correlation functions decay algebraically, indicating that the phase does not possess true long range orientational order. The simulation data indicate that the transition from this phase to the low density isotropic phase is continuous, via a Kosterlitz–Thouless disclination unbinding type mechanism, rather than first order. For short rods the nematic phase disappears so that, on expansion, the solid phase undergoes a first order transition directly to an isotropic phase. Although the latter phase is globally isotropic, we find evidence for strong local positional and orientational correlations between the particles. Where possible, the simulation results are compared and contrasted to experimental, simulation and theoretical data for other two-dimensional liquid crystalline systems.

Ensemble dependence of confined hard-rod fluids

The finite-size effects and packing constraints on the density profile of a hard-rod fluid in both open (grand canonical) and closed (canonical) walls have been investigated. For a finite system, the grand canonical density profile shows very different density behavior compared with the canonical density profile. At low packings, the convergence of series is shown to converge very quickly, even if only a few particles are confined in hard walls. However, the significant differences at high packings arise between the canonical and the grand canonical density profiles. The convergence is much slower in the region where the peak develops.