Multiple short time power laws in the orientational relaxation of nematic liquid crystals

Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate times and also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)--these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.     

In search of temporal power laws in the orientational relaxation near isotropic-nematic phase transition in model nematogens

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.     

Density dependence of hydrogen bonding and the translational-orientational structural order in supercritical water: a molecular dynamics study

Molecular dynamics simulation have been performed with a wide range of densities along a near critical isotherm of supercritical water (SCW) in order to study the density dependence of the structure order and hydrogen bonding (HB). It is revealed that the translational structure order is nearly invariant while the orientational tetrahedral structure order is very sensitive to the bulk density under supercritical conditions. Meanwhile, some energetically unfavorable intermediate water dimer structures are found to appear under supercritical conditions due to the reduced energy difference and the enhanced energy fluctuation. As a consequence, a general geometrical criterion or the inclusion of a energy-based criterion instead of currently widely adopted pure r(OH)-based geometric criterion is suggested to be used in the HB statistics under supercritical conditions. It is found that the average HB number per H(2)O molecule (n(HB)) reduces with the decreasing SCW bulk density although a given pair of H(2)O molecules are shown to have a stronger ability to form a hydrogen bond under lower SCW bulk densities. Accordingly, the orientational tetrahedral structure order q decreases with the reducing bulk density under supercritical conditions. However, when the fluid is dilute with ρ ≤ 0.19ρ(c) (ρ(c) = 0.322 g/cm(3)), the energy fluctuation increases sharply and the short-range order is destroyed, signifying the supercritical fluid (SCF)-gas state transition. Accordingly, the orientational tetrahedral structure order q gets reversal around ρ = 0.19ρ(c) and approaches zero under very dilute conditions. The sensitivity of the orientational order to the density implies the microscopic origin of the significant dependence of SCF's physicochemical properties on the pressure.     

Electric quadrupole model on the formation of molecular chirality dependent domain shapes of lipid monolayers at the air-water interface

Shapes and orientational deformation of a lipid monolayer domain have been analyzed taking into account the surface pressure, line tension, and electrostatic energy due to the spontaneous polarization and electric quadrupole density generated from the domain. The electrostatic energy due to the generation of spontaneous polarization and electric quadrupole density contributes to the formation of orientational deformation as the Frank elastic energy and spontaneous splay, respectively. Since the orientational configuration of the electric quadrupole density and in-plane spontaneous polarization is dependent on the molecular chirality, and the positive splay deformation of electric quadrupole density is induced by the spontaneous splay, the bending direction of in-plane spontaneous polarization depends on the chirality of constituent lipids. The electrostatic energy due to the in-plane spontaneous polarization is dependent on the orientational deformation of in-plane spontaneous polarization, and bends the domain shape towards the bending direction of the in-plane spontaneous polarization. It has been demonstrated that the chiral dependence of the domain shapes of lipid monolayers originated from the chiral dependence of orientational structure due to the electric quadrupole density.     

An extension of the McMillan theory to a bilayer smectic A phase with long range antiferroelectric order

Here an extension of the McMillan theory to describe both a monolayer smectic A phase with short range antiferroelectric order and a bilayer smectic A phase with long range antiferroelectric order in polar liquid crystals is proposed. In a molecular field approximation the single particle pseudopotential and self consistent equations which determine the usual orientational and translational order parameters and a new order parameter taking into account the antiferroelectric character of a bilayer smectic A structure are derived from a modified pair potential. The regions of existence for the isotropic, nematic, as well as both monolayer and bilayer smectic A phases together with the transitional characteristics are determined by numerical solution of the self consistent equations. In addition the temperature dependence of all the order parameters is determined. These results are compared with those from experiment.     

Attraction-driven disorder in a hard-core colloidal monolayer

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.     

Orientational dynamics and energy landscape features of thermotropic liquid crystals: An analogy with supercooled liquids

Recent optical kerr effect (OKE) studies have revealed that orientational relaxation of rodlike nematogens near the isotropic-nematic (I-N) phase boundary and also in the nematic phase exhibit temporal power law decay at intermediate times. Such behaviour has drawn an intriguing analogy with supercooled liquids. Here, we have investigated the single-particle and collective orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I-N phase boundary, the system behaves like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system.     

Pattern formation from consistent dynamical closures of uniaxial nematic liquid crystals

Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression for the free-energy like function in terms of the scalar order parameter. Considering the evolution equation of the density of the system and values of the interaction parameter for which isotropic and nematic phases coexist, our analysis predicts that patterns and traveling waves can be produced in lyotropic uniaxial nematics even in the absence of external driving.     

On the behavior of an oblate spheroidal hematite particle in a simple shear flow under a uniform magnetic field applied in the flow direction

We discuss the orientational properties of an oblate spheroidal hematite particle and also its influence on the rheological characteristics of a dilute suspension of these magnetic particles, by means of an analytical approach based on the orientational distribution function. A hematite particle with oblate spheroidal shape has an important characteristic; that is, it is magnetized in a direction normal to the particle axis. From the balance of the torques acting on a particle, we have developed the basic equation of the orientational distribution function. This basic equation has been numerically solved in order to investigate the dependence of the orientational distribution on the various factors. If both the magnetic field and the shear flow are weak, the particle does not exhibit specific directional characteristics. If the magnetic field is more dominant, the particle inclines such that the oblate surface is parallel to the magnetic field direction. If the shear flow becomes more dominant, the particle shows a sharper peak of the orientational distribution in the shear flow direction. The viscosity due to the magnetic torque increases and finally converges to a constant value as the magnetic field increases. In a sedimentation process under the gravitational field, the translational diffusion coefficient decreases with increasing magnetic field strength in the present case of the magnetic field direction.     

A systematic evaluation of the role of crystalline order in nanoporous materials on DNA separation

The role of order within a porous separation matrix on the separation efficiency of DNA was studied systematically. DNA separation was based on a ratchet mechanism. Monodisperse colloidal suspensions of nanoparticles were used to fabricate highly ordered separation media with a hexagonal close-packed structure. Doping with a second particle size yielded structures with different degrees of disorder, depending upon the volume fraction of each particle size. Radial distribution functions and orientational order parameters were calculated from electron micrographs to characterize the scale of disorder. The peak separation distance, band broadening, and separation resolution of DNA molecules was quantified for each structure. DNA separation parameters using pulsed fields and the ratchet effect showed a strong dependence on order within the porous nanoparticle array. Ordered structures gave large separation distances, smaller band broadening and better resolution than highly disordered, nearly random, porous structures. The effect dominated these three parameters when compared to the effect of pore size. However, the effect of order on separation performance was not monotonic. A small, but statistically significant improvement was seen in structures with short range order compared to those with long range order.     

Temperature- and solvation-dependent dynamics of liquid sulfur dioxide studied through the ultrafast optical Kerr effect

The ultrafast dynamics of liquid sulphur dioxide have been studied over a wide temperature range and in solution. The optically heterodyne-detected and spatially masked optical Kerr effect (OKE) has been used to record the anisotropic and isotropic third-order responses, respectively. Analysis of the anisotropic response reveals two components, an ultrafast nonexponential relaxation and a slower exponential relaxation. The slower component is well described by the Stokes-Einstein-Debye equation for diffusive orientational relaxation. The simple form of the temperature dependence and the agreement between collective (OKE) and single molecule (e.g., NMR) measurements of the orientational relaxation time suggests that orientational pair correlation is not significant in this liquid. The relative contributions of intermolecular interaction-induced and single-molecule orientational dynamics to the ultrafast part of the spectral density are discussed. Single-molecule librational-orientational dynamics appear to dominate the ultrafast OKE response of liquid SO2. The temperature-dependent OKE data are transformed to the frequency domain to yield the Raman spectral density for the low-frequency intermolecular modes. These are bimodal with the lowest-frequency component arising from diffusive orientational relaxation and a higher-frequency component connected with the ultrafast time-domain response. This component is characterized by a shift to higher frequency at lower temperature. This result is analyzed in terms of a harmonic librational oscillator model, which describes the data accurately. The observed spectral shifts with temperature are ascribed to increasing intermolecular interactions with increasing liquid density. Overall, the dynamics of liquid SO2 are found to be well described in terms of molecular orientational relaxation which is controlled over every relevant time range by intermolecular interactions.     

Thermodynamic states of nanoclusters at low pressure and low temperature: the case of 13 H(2)

A confinement model of finite-size systems that embodies an equation of state is presented. The temperature and pressure of the system are obtained from the positions and velocities of the enclosed particles after a number of molecular dynamics simulations. The pressure has static and dynamic (thermal) contributions, extending the Mie-Gru?neisen equation of state to include weakly interacting anharmonic oscillators. The model is applied to a system of 13 H(2) molecules under low-pressure and low-temperature conditions in the classical regime. The confining cage in this case is a spherical hydrogen cavity. The Born-Oppenheimer molecular dynamics in conjunction with density functional theory are used for the time evolution of the particle system. The hydrogen molecules form a noncrystalline cluster structure with icosahedral symmetry that remains so in the whole temperature range investigated. The fluctuations of the interatomic distances increase with the temperature, while the orientational order of the enclosed system of molecules fades out, suggesting a gradual order-disorder transition.     

Orientational order and rotational relaxation in the plastic crystal phase of tetrahedral molecules

A methodology recently introduced to describe orientational order in liquid carbon tetrachloride is extended to the plastic crystal phase of XY4 molecules. The notion that liquid and plastic crystal phases are germane regarding orientational order is confirmed for short intermolecular distances but is seen to fail beyond, as long range orientational correlations are found for the simulated solid phase. It is argued that, if real, such a phenomenon may not to be accessible with direct (diffraction) methods due to the high molecular symmetry. This behavior is linked to the existence of preferential orientation with respect to the fcc crystalline network defined by the centers of mass. It is found that the dominant class accounts, at most, for one-third of all configurations, with a feeble dependence on temperature. Finally, the issue of rotational relaxation is also addressed, with an excellent agreement with experimental measures. It is shown that relaxation is nonhomogeneous in the picosecond range, with a slight dispersion of decay times depending on the initial orientational class. The results reported mainly correspond to neopentane over a wide temperature range, although results for carbon tetrachloride are included, as well.     

Computer simulation investigation of the water-benzene interface in a broad range of thermodynamic States from ambient to supercritical conditions

The dependence of the properties of the water-benzene system on the thermodynamic conditions in a broad range of temperatures and pressures has been investigated by computer simulation methods. For this purpose, Monte Carlo simulations have been performed at 23 different thermodynamic states, ranging from ambient to supercritical conditions. The density profiles of the water and benzene molecules have been determined at each of the thermodynamic states investigated. Information on the dependence of the mutual solubility of the two components in each other as well as of the width of the interface on the temperature and pressure has been extracted from these profiles. The width of the interface has been found to increase with increasing temperature up to a certain point, where it diverges. The temperature of this divergence corresponds to the mixing of the two phases. The determination of the critical mixing temperature at various pressures allowed us to estimate the upper critical curve, separating the two-phase and one-phase liquid systems, of the phase diagram of the simulated water-benzene system. In analyzing the preferential orientation of the interfacial molecules relative to the interface, it has been found that the main orientational preference of the benzene molecules is to lie parallel with the plane of the interface, and the water molecules penetrated deepest into the benzene phase prefer to stay perpendicular to the interface, pointing by one of their O-H bonds almost straight toward the benzene phase, whereas the waters located at the aqueous side of the interface are preferentially aligned parallel with the interfacial plane. Although the strength of the observed orientational preferences decreases rapidly with increasing temperature, the preferred orientations themselves are found to be independent of the thermodynamic conditions. Remains of the orientational preferences of the molecules are found to be present up to temperatures as high as 650 K. The analysis of the relative orientation of the neighboring water-benzene pairs has revealed that the radius of the first hydration shell of the benzene molecules is independent of the thermodynamic conditions, even if the system consists of one single phase. It has been found that the nearest water neighbors of the benzene molecules are preferentially located above and below the benzene ring, whereas more distant water neighbors, belonging still to the first hydration shell, prefer to stay within the plane of the benzene molecule. In the two-phase systems the dipole vector of the nearest waters has been found to be preferentially perpendicular to the vector pointing from the center of the benzene molecule to the water O atom.     

Deuterium NMR Studies on the Orientational Order Generated in Strained Rubbers

The present paper deals with the induced orientational order of the probe molecules dissolved in the uniaxially strained rubbers measured by using deuterium NMR. The distinctive dependence of the quadrupolar splitting on the swelling, elongation and crosslinking density was observed. The orientational order arising from the correlation between chain segments decreases with the increase of the numbers of both links between junctions and solvent molecules around segments.     

Influence of magnetic interactions between clusters on particle orientational characteristics and viscosity of a colloidal dispersion composed of ferromagnetic spherocylinder particles: analysis by means of mean field approximation for a simple shear flow

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones that belong to the neighboring clusters, besides those that belong to its own cluster. The basic equation of the orientational distribution function, which is an integrodifferential equation, has approximately been solved by Galerkin's method and the method of successive approximation. Some of the main results obtained here are summarized as follows. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significant with increasing volumetric fraction of particles; the orientational distribution function exhibits a sharper peak in the direction nearer to the magnetic field one as the volumetric fraction increases. Such a significant inclination of the particle in the field direction induces the large increase in viscosity in the range of larger values of the volumetric fraction. The above-mentioned characteristics of the orientational distribution and viscosity come to appear more significantly when the influence of the applied magnetic field is not so strong compared with that of magnetic particle-particle interactions.     

Nucleation of NaCl nanoparticles in supercritical water: molecular dynamics simulations

Formation of NaCl nanoparticles in supercritical water is studied using molecular dynamics simulation method. We have simulated particle nucleation and growth in NaCl-H2O fluids, with salt concentration of 5.1 wt %, in the temperature and density range of 673-1073 K and 0.17-0.34 g/cm(3), respectively. The cluster size distributions, the size of critical nuclei and cluster lifetimes are reported. The size distribution of emerging clusters shows a very strong dependence on the system's density, with larger clusters forming at lower densities. Clusters consisting of approximately 14-24 ions appear critical for the thermodynamic states examined. The local structures of critical clusters are found to be amorphous. The lifetime values for clusters containing more than 20 ions are in the range of 10-50 ps. We have calculated the NaCl nucleation rates, which appear to be on the order of 10(28) cm(-3) s(-1).     

Testing assumptions about solute concentration dependence in liquid crystal NMR

The NMR spectra of four solutes, used as probes of liquid crystal orientational order, were analyzed. For each solute, samples were prepared at different solute concentrations, and the concentration dependence was used to extrapolate zero-concentration properties. The mean-field (Maier-Saupe) model when applied to solutes neglects solute-solute interactions and assumes all solutes in a mixed-solute sample see the same average environment. The first assumption is only valid as one approaches zero concentration, while experiments are typically carried out at concentrations between 0 and 10 mol %. The solute concentration dependence has in the past been "scaled out" using an internal solute reference as an orientational standard. We measured the concentration dependence of the orientational order parameter and calculate the corresponding interaction energies based on a mean-field interaction potential for a solute. We find agreement at the 3% level between experiments for different solutes while using (i) the zero-concentration values as solute-dependent orientational references and (ii) scaling to either order parameters or interaction energies; these two scalings gave equivalent but not identical results. We find, too, that errors inherent in the experiment and the calculations will limit attempts to refine the theory to push the comparisons beyond the 2% level.     

Freezing transition and interaction potential in monolayers of microparticles at fluid interfaces

The structure and the interaction potential of monolayers of charged polystyrene microparticles at fluid interfaces have been studied by optical microscopy. Microparticles of different sizes have been studied over a broad range of surface particle densities. The structural characterization is based on the analysis of images obtained by digital optical microscopy. From the experimental images, radial distribution functions, hexagonal bond order correlation functions, and temporal orientational correlation functions have been calculated for different monolayer states at both the air/water and oil/water interfaces. The interaction potential has been calculated from the structure factor using integral equations within the hypernetted chain closure relationship. For particles trapped at the oil-water interface, it was found that, upon increasing the surface coverage, a freezing transition occurs, that leads to the formation of a 2D crystalline structure. We have studied the freezing densities of particle monolayers at the oil/water interface and compared them with Monte Carlo simulation results reported by H. Lo?wen. In contrast, at the air-water interface, freezing is inhibited due to the formation of particle aggregates.     

Dielectric behaviour of a molecular liquid mixture in the one-phase precritical region

The temperature dependence of density d, electric permittivity ?_s and nonlinear high field dielectric variation Δ? are reported for various benzonitrile-alkane solutions. For the benzonitrile-isooctane mixtures which exhibit a phase separation in the considered temperature range, the phase diagram has been obtained. In the “homogeneous” one phase region, significant deviations from the normal temperature dependence of d, ?₀, Δ? have been observed and characterize a precritical region of several degrees C above the consolute temperature. These results support the hypothesis of strong precritical orientational interactions or local ordering phenomena. The precritical dielectric behaviour of the benzonitrile-isooctane system is shown to be very different from those of nitrobenzene-alkane or aniline-alkane mixtures.