Diffusivity of wormlike particles in isotropic melts and the influence of local nematization.

Systems of wormlike particles are studied by molecular dynamics computer simulations in the isotropic phase. The particles are modeled as a chain of nine soft repulsive, partially overlapping, spherical sites. These particles are characterized by a varying degree of internal flexibility: from very stiff and rodlike to very deformable and stringlike. Their self-diffusion coefficients have been evaluated at many thermodynamic conditions. Maintaining the temperature constant and sufficiently low, from the stiff rod case and letting the worms become more flexible, the self-diffusion coefficients first steeply increase, then reach a plateau. This behavior is rationalized in terms of local nematic domains. The presence of the latter significantly affects the equation of state of the wormlike particles as well, with the density of the stiffest rods being, respectively, the highest at lower temperatures and the lowest at higher temperatures. This fact might have significant implications for the theory of liquid-crystalline phase behavior in systems of flexible particles. If the density of all systems is fixed at the equilibrium value of the stiffest case, which is a way to single out the effects of flexibility, self-diffusion coefficients may exhibit a moderately nonmonotonic behavior: subsequently to the above-mentioned steep increase, they may reveal a shallow maximum for intermediate degrees of internal flexibility degrees, then gently decrease. This behavior is tentatively associated with the different effects that internal flexibility has on the average length and width of a wormlike particle.

Mechanism of diffusion in the smectic- A phase of wormlike rods studied by computer simulation.

Molecular dynamics computer simulations have been carried out in the smectic- A phase of stiff wormlike rods. The analysis of the long trajectories generated has allowed for a detailed insight into that diffusion mechanism which is operative in the above-mentioned liquid-crystalline phase, as recently visualized in a system of colloidal virus rods. Fast particles, i.e., those able to move abruptly out from one into an adjacent layer, have been identified. Their properties, such as the velocity autocorrelation function and the orientational distribution function, have been determined and compared to the corresponding quantities valid for a generic rod.

Chemical Detail Force Fields for Mesogenic Molecules.

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.

Two-step mechanism of rotational relaxation in lamellar phases of rods: accelerating effect of the addition of spheres.

By using computer simulation on a model colloidal rod-sphere mixture in its lamellar phase, the mechanism responsible for the rod rotational relaxation has been definitely identified and characterized. It consists of two steps: first, a rod, parallel to the director, has to escape from the layer in which it is located and go into the interlayer region mostly populated by spheres, perpendicular to the director; then, it has to insinuate again into one of the adjacent layers, with 50% of probability of resulting antiparallel to the director. While this mechanism is also operating in a pure smectic phase of rods, the presence of spheres increases notably its efficacy, thus promoting the rotational relaxation and facilitating its observation.

Atomistic computer simulation and experimental study on the dynamics of the n-cyanobiphenyls mesogenic series.

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.

Phase behavior of wormlike rods.

By employing molecular dynamics computer simulations, the phase behavior of systems of rodlike particles with varying degree of internal flexibility has been traced from the perfectly rigid rod limit till very flexible particles, and from the high density region till the isotropic phase. From the perfectly rigid rod limit and enhancing the internal flexibility, the range of the smectic- A phase is squeezed out by the concomitant action of the scarcely affected crystalline phase at higher density and the nematic phase at lower density, until it disappears. These results confirm the supposition, drawn from previous theoretical, simulational and experimental studies, that the smectic- A phase is destabilized by introducing and enhancing the degree of particle internal flexibility. However, no significant changes in the order of nematic-to-smectic- A phase transition, which appears always first order, nor in the value of the layer spacing, are observed upon varying the degree of particle internal flexibility. Moreover, no evidence of a columnar phase, which was thought of as a possible superseder of the smectic- A phase in flexible rods, has been obtained.

Subdiffusive dynamics of a liquid crystal in the isotropic phase.

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 Tc are 244+/-6 and 258+/-6 K, respectively, the latter is some 10 K below the corresponding experimental values. The different values of Tc 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.

Anomalous diffusion and cage effects in the isotropic phase of a liquid crystal.

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.

Sixfold bond orientational properties of a model liquid crystal in the dimensional crossover of B phases: a computer simulation study.

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.

Smectic order parameters from diffusion data.

Microcanonical molecular dynamics simulations have been performed in the smectic A phase of an elementary liquid-crystal model. Smectic order parameters and diffusion coefficients along directions parallel and perpendicular to the director have been calculated during the same trajectory for a number of state points. This has permitted the satisfactory testing of a procedure, adopted in the analysis of experimental self-diffusion coefficients, leading to an estimate of the temperature dependence of the smectic order parameters. This methodology has been then confidently applied to two smectogenic thermotropic liquid crystals belonging to the 4,4(')-di-n-alkyl-azoxybenzene series. The derived smectic order parameters are larger for the homologue compound with the longest alkyl chains. This is consistent with the well-established increased tendency, for members of a homologue series, to form a smectic phase as their alkyl chains become longer.

Modeling a liquid crystal dynamics by atomistic simulation with an ab initio derived force field.

Atomistic molecular dynamics (MD) simulations of 4-n-pentyl 4'-cyano-biphenyl (5CB) have been performed, adopting a specific ab initio derived force field. Two state points in the nematic phase and three in the isotropic phase, as determined in a previous work, have been considered. At each state point, at least 10 ns have been produced, allowing us to accurately calculate single-molecule properties. In the isotropic phase, the values of the translational diffusion coefficient, and even more so the activation energy for the process, agree well with experimental data. Qualitatively, also the dynamic anisotropy of the nematic phase is correctly accounted for. Rotational diffusion coefficients, which describe spinning and tumbling motions, fall well within the range of experimental values. The reorientational dynamics of our model 5CB covers diverse time regimes. The longest one is strongly temperature dependent and characterized by a relaxation time in accord with experimental dielectric relaxation data. Shear viscosity and Landau-de Gennes relaxation times, typically collective variables, reproduce the experimental results very well in the isotropic phase. In the nematic phase, despite a large statistical uncertainty due to the extremely slow relaxation of the correlation functions involved, our simulation yields the correct relative order of the three experimental Miesowicz viscosities.

Orientational dynamics in the isotropic phase of a calamitic liquid-crystal model.

We report a molecular dynamics simulation study on the isotropic phase of an idealized calamitic liquid crystal model with a length-to-width ratio of approximately 5-6. The study focuses on the characterization of single-particle and collective orientational dynamics on approaching the phase transition to the nematic phase. Recent experimental and simulation works have suggested that a power law behavior exists at relatively short times in the decay of the time derivative of the orientational correlation functions. Qualitatively, our simulation data are consistent with these findings. Both single-particle and collective time correlation function derivatives possess, in their respective log-log plots, a linear region at very short times, whose slope is essentially independent from the thermodynamic state. Nevertheless, the single-particle orientational correlation functions are better described by a function which is the sum of a fast exponential, an intermediate stretched-exponential and a slow exponential, while the collective orientational correlation functions are satisfactorily described by a sum of two exponentials, at higher density, or by just one exponential, at lower density.

Numerical study of a calamitic liquid-crystal model: phase behavior and structure.

We have studied an idealized calamitic liquid-crystal model, consisting of a linear rigid array of nine soft repulsive spheres, employing both theory and molecular dynamics simulation. The phase behavior (which includes crystalline, smectic, nematic, and isotropic phases) and structure of a collection of these rodlike particles have been determined by molecular dynamics simulation in an isothermal-isobaric ensemble. The liquid crystalline part of the phase diagram has been compared to that emerging from an Onsager-type density-functional theory. We have found a fair agreement between theory and computer simulation results, with a similar accuracy for the smectic to nematic and nematic to isotropic phase transitions.

Diffusion and viscosity of a calamitic liquid crystal model studied by computer simulation.

We report a molecular dynamics simulation study on an ensemble of rod-like particles, each composed of nine soft spheres held rigidly along a line. We have calculated translational mean square displacements and velocity autocorrelation functions in the fluid phases exhibited by the model, i.e., smectic A, nematic and isotropic. These quantities have then been used to compute diffusion coefficients. In addition, we have calculated viscosities in the nematic and isotropic phases. Despite its crude nature, the model is capable of providing a faithful reproduction of many features of the transport behavior observed in real liquid-crystalline materials. The simulation results have been compared with the predictions of the modified affine transformation theory, finding only a fair agreement.