Rank Orientational Order Parameter Research Articles

Molecular Dynamics Simulation of 4-N-Hexyl-4’-Cyanobiphenyl Adsorbed at the Air-Water Interface

The interfacial behavior of 4-n-hexyl-4’-cyanobiphenyl (6CB) molecules at the air-water interface is investigated by full atomistic molecular dynamics simulations. To understand the morphology and the structure of adsorbed 6CB molecules in detail, the snapshots and mass density profiles of the simulation system are generated. The average tilt angles between the interface normal and various vectors defined in the rigid and alkyl parts of 6CB are in good agreement with the experimental data available. The interfacial thickness and monolayer width are obtained from the mass density profiles of water and 6CB phase, respectively. The second and fourth rank orientational order parameters of cyanobiphenyl core are found to be larger than those of an elastic alkyl chain. Bond order parameters for 6CB are also calculated. The calculated oxygen-oxygen radial distribution function and hydrogen bonding statistics for bulk water are compared with those for the interfacial region. The surface tensions of the systems are calculated. All simulation results are compared with the available literature data.

Molecular field theory for biaxial nematic liquid crystals composed of molecules withC2hpoint group symmetry

The biaxial nematic phase is generally taken, either explicitly or implicitly, to have D(2h) point group symmetry. However, it is possible for the biaxial phase to have a lower symmetry depending on that of its constituent molecules. Here we develop a molecular field theory for a nematogen composed of C(2h) molecules in terms of the nine independent second rank orientational order parameters defining the C(2h) biaxial nematic. In addition, there is a rank one order parameter constructed from two pseudovectors which is only nonzero in the C(2h) phase. The theory is simplified by removing all but the three dominant order parameters. The predicted phase behavior is found to be rich with three possible biaxial nematic phases and with the transitions involving a biaxial nematic phase exhibiting tricritical points.

Discotic Nematic-Isotropic Phase Transition Properties for a Disc-Like Mesogen

A statistical mechanical perturbation theory has been used to describe discotic nematic-isotropic phase transition for a discotic liquid crystal, hexa(p-octyl phenyl ethynyl)benzene. We have employed the decoupling approximation, which introduces anisotropy in the pair correlation function, to investigate the discotic nematic-isotropic transition properties. The variation of second rank orientational order parameter with temperature has been computed and it shows qualitatively similar behavior to that of experimental studies of Aver'yanov [1]. However, the numerical value of order parameter at the transition found in the present work is larger than that of Aver'yanov's. The various thermodynamic properties have also been calculated at the transition.

Solvent smectic order parameters from solute nematic order parameters

In liquid crystals, while the second and fourth rank orientational order parameters characterizing a nematic phase can be experimentally determined via several techniques, there is no straightforward experiment rendering the positional order parameters characterizing a smectic A phase. This work illustrates a novel method to estimate the positional order parameters of a smectogenic liquid crystal solvent from knowledge of the orientational order parameters of a number of solutes dissolved therein. The latter order parameters can be experimentally determined via liquid crystal NMR spectroscopy. These data can be then analyzed with a statistical-thermodynamic density functional theory, whose basic ingredient is a model for solute-solvent intermolecular interactions. Its parametrization and the subsequent fitting procedure eventually permit one to obtain the positional order parameters of the solvent besides the positional-orientational distribution function of the solutes. The method is applied to the smectogen 4,4(')-di-n-heptyl-azoxybenzene, in which the solutes 1,4-dichlorobenzene and naphthalene have been dissolved. With the help of this exploratory practical example, pros and cons of the method are pointed out and further developments prospected.

Liquid Crystal Properties of the n-Alkyl-cyanobiphenyl Series from Atomistic Simulations with Ab Initio Derived Force Fields

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.

Structure and Dynamics of Interfacial Water in an Lα Phase Lipid Bilayer from Molecular Dynamics Simulations

Based on molecular dynamics simulations, an analysis of structure and dynamics is performed on interfacial water at a liquid crystalline dipalmitoylphosphatidycholine/water system. Water properties relevant for understanding NMR relaxation are emphasized. The first and second rank orientational order parameters of the water O– H bonds were calculated, where the second rank order parameter is in agreement with experimental determined quadrupolar splittings. Also, two different interfacial water regions (bound water regions) are revealed with respect to different signs of the second rank order parameter. The water reorientation correlation function reveals a mixture of fast and slow decaying parts. The fast (ps) part of the correlation function is due to local anisotropic water reorientation whereas the much slower part is due to more complicated processes including lateral diffusion along the interface and chemical exchange between free and bound water molecules. The 100-ns-long molecular dynamics simulation at constant pressure (1 atm) and at a temperature of 50°C of 64 lipid molecules and 64 × 23 water molecules lack a slow water reorientation correlation component in the ns time scale. The 2H 2O powder spectrum of the dipalmitoylphosphatidycholine/water system is narrow and consequently, the NMR relaxation time T 2 is too short compared to experimental results.

Perturbation theory for discotic nematic liquid crystals of axially symmetric molecules: effect of dispersion interaction

We investigate the influence of dispersion interaction on a variety of thermodynamic properties of discotic nematic liquid crystals at the discotic nematic-isotropic transition. We report calculations for a hard oblate ellipsoidal system, superposed with an attractive interaction represented by dispersion interaction subjected to different external pressures ranging from 1 to 300 bar. We consider a model system (which simulates a discotic nematic liquid crystal) in which molecules are assumed to interact via a pair potential having both repulsive and attractive parts. The repulsion part is represented by a repulsion between hard oblate ellipsoids of revolution and is a short range, rapidly varying potential. The attractive potential, a function of centre of mass distance and relative orientation between two molecules, is represented by dispersion interaction. The properties of the reference system and first order perturbation term are evaluated using a decoupling approximation which decouples orientational from translational degrees of freedom. The inclusion of fourth and sixth rank orientational order parameters in the calculation slightly improves the result. The role of pressure on phase transition parameters has also been studied.

Nuclear magnetic shielding of noble gases in liquid crystals

A theoretical model for nuclear magnetic shielding of noble gas atoms soluted in liquid crystal solvents is developed. It is found that the solvent effect on the shielding can be represented as a linear combination of products of the liquid crystal orientational order parameters of varying rank. In a special case of pairwise additive shielding perturbations, most of the coefficients vanish and the shielding reduces to a sum of two terms, the isotropic and anisotropic parts. Both contributions are directly proportional to the density of the liquid crystal, and the anisotropic part is also directly proportional to the second rank orientational order parameter of the liquid crystal. The developed model is used to account for the behavior of the 129Xe shielding in the nematic liquid crystal 4-ethoxybenzylidene-2,6-dideutero-4′-n-butylaniline (d2-EBBA). The pairwise additivity approximation of the shielding perturbations is found to explain the observed temperature dependence of the 129Xe shielding satisfactorily. In particular, the temperature dependence of the isotropic part is mostly due to the change in the liquid crystal density, whereas the anisotropic part is mainly controlled by the temperature dependence of the Xe–liquid crystal molecule pair correlation function and the second rank orientational order parameter of the liquid crystal. This result differs from the results of the phenomenological theory of Lounila et al. [J. Chem. Phys. 97, 8977 (1992)], where only the density and the orientational order parameter were assumed to be significantly temperature dependent.

Computer simulation studies of anisotropic systems. The density and temperature dependence of the second rank orientational order parameter for the nematic phase of a Gay–Berne liquid crystal

The relative importance of anisotropic repulsive and attractive forces in stabilising a nematic liquid crystal may be assessed from the thermodynamic parameter Γ=−( ∂ln T/ ∂ln V) 〈 P 2〉 , where 〈 P 2〉 is the second rank orientational order parameter. A previous attempt to determine this quantity for the nematic phase of a Gay–Berne system has given a value about twice as large as that found experimentally. Here we report the determination of Γ from an extensive simulation study for a Gay–Berne system with parameters more appropriate for mesogenic molecules than those selected originally.

Computer simulation studies of anisotropic systems. XXVI. Liquid crystal dimers: A generic model

A generic model has been proposed with which to understand the unusual properties of liquid crystal dimers, in particular their behavior at the nematic–isotropic transition. In the model the many conformational states available to real dimers are replaced by just two, a linear and a bent conformer which are allowed to interconvert. The nematic behavior of the model has been explored with the aid of the molecular field approximation and found to be in good qualitative agreement with that of real dimers, thus providing a valuable aid to our understanding of them. To see to what extent the use of the molecular field approximation influences the predictions we have undertaken a Monte Carlo computer simulation study of the generic model. To facilitate the simulations the particles have been confined to the sites of a simple cubic lattice with the anisotropic interactions being restricted to nearest neighbors and having the form −(ε/4)P2(cos β), where β is the angle between the anisometric groups. The other advantage of this model is that for the linear conformer alone it is identical to the Lebwohl–Lasher model for nematics which has been studied in depth and so allows the influence of the presence of the interconverting bent conformer on the liquid crystal behavior to be readily discerned. We have also extended the discrete generic model, with just two interconverting conformers, to a continuous model in which the torsional angle defining the conformational state varies continuously from 180° (linear) to 0° (bent); this makes the model far more general and more analogous to real dimers. A wide range of properties have been determined from the computer simulations; these include the second rank orientational order parameter for the anisometric groups, the singlet orientational distribution function for these, the second rank short range orientational order parameter, the internal order parameters and the distribution function for the torsional angle. Armed with this wealth of information we are able to make a searching test of the molecular field theories for the two models as well as commenting on the behavior of real liquid crystal dimers.

Prediction of the transitional properties of liquid crystal dimers. A molecular field calculation based on the surface tensor parametrization

The transitional properties of the liquid crystal dimers formed by two mesogenic groups linked by a flexible chain exhibit a pronounced dependence on the number of atoms in the spacer. Here we present the results of a theoretical calculation of the nematic–isotropic transition temperature, the entropy of transition, and the second rank orientational order parameters at the transition for two homologous series of cyanobiphenyl dimers. In one the alkyl spacer is attached directly to the mesogenic groups while in the other the alkyl chain is linked via ether units to the two cyanobiphenyl groups. At the heart of the molecular field theory is its parametrization based on the surface tensor approach. In this theory the potential of mean torque for each conformer is related to its topology by the surface tensor, which ensures that molecules are aligned such that their surfaces overlap to a maximal extent. The transitional properties predicted by the theory are found to depend in a sensitive manner on the geometry of the cyanobiphenyl group and that of its link to the alkyl spacer. By using realistic geometries and allowing for the various conformational states within the rotational isomeric state model the theory is able to account for the behavior of homologous series of dimers as the spacer length is changed, and for the dependence of the transitional properties on the nature of the link between the alkyl chain and the mesogenic groups.

Computer simulation studies of anisotropic systems. XXII. An equimolar mixture of rods and discs: A biaxial nematic?

Abstract In principle, binary mixtures of rod-like and disc-like particles should exhibit a biaxial nematic phase, but in practice phase separation into two uniaxial nematic phases prevents this. Here, we report the results of a computer simulation study of an equimolar mixture of rods and discs in which phase separation is not allowed. The particles are confined to the sites of a simple cubic lattice in which each rod is surrounded by six discs and vice versa. Neighbouring particles interact such that they prefer to align with their respective symmetry axes orthogonal to each other. In contrast, the interaction between next nearest neighbours, which are either rods or discs, is such that their symmetry axes tend to be parallel. Monte Carlo simulations of this model mixture show that an orientationally ordered phase exists at low temperatures. This nematic phase has overall uniaxial symmetry and the particles have a negative second rank orientational order parameter, indicating that they tend to align at ...

Study of the molecular tilt angle and the order parameter of a ferroelectric liquid crystal mixture using IR spectroscopy

Abstract We report measurements of the molecular tilt angle of a ferroelectric liquid crystal mixture (ZLI 3654), using infra-red spectroscopy, and of the optical tilt angle using polarizing microscopy. The molecular tilt angle is found to be approximately the same for different molecular vibrations. The second rank orientational order parameter for the axis of molecular vibrations of different groups of the molecule for homogeneously aligned samples have been determined as a function of temperature. The order parameter depends slightly on the sample thickness and is about 8 per cent higher for a lower thickness (∼ 7 μm) compared to a higher thickness (∼ 12 μm). The order parameter does not change significantly at the SC∗–SA transition. The order parameter of SC∗ is found to be unaffected by the application of a constant electric field. The order parameter for the alkyl chain is found to be about three times lower than for the molecular core.

Effects of lateral diffusion on the fluorescence anisotropy in hexagonal lipid phases. I. Theory

It is shown that fluorescence anisotropy from lipidlike probes in the hexagonal HII phase gives information of (a) orientational order parameters, (b) the wobbling diffusion constant, and (c) the hopping diffusion constant of the probe, DH, equals DL/R2, the lateral diffusion constant over the square of the radius of the hexagonal tubes. Here we consider only lipidlike probes having the absorption transition movement and/or the emission transition moment along the long axis of the molecule. Three models are introduced for analysis of time-resolved data: the "WOBHOP," the "reduced WOBHOP," and the "P2P4HOP" model. The fluorescence anisotropy in response to a very short excitation pulse in each of the three models is a constant plus a number of exponentials. The WOBHOP and reduced WOBHOP models have 3 and 2 exponentials, respectively, and both contain four fitting parameters: r0 (the fundamental anisotropy), (P2) (the second rank orientational order parameter), DW (the wobbling diffusion constant), and DH (the hopping diffusion constant). The P2P4HOP model has eight exponentials and five fitting parameters: the four parameters listed above and (P4) (the fourth rank orientational order parameter). Analysis of fluorescence anisotropy data in the hexagonal HII phase using one of these models allows for obtaining the hopping diffusion constant, and, if the lateral diffusion constant is known, the radius of the hexagonal tubes. Substitution of DH = 0 in each of the three models yields an expression for the fluorescence anisotropy that is used in the literature for lamellar (L alpha or L beta) phases. The fluorescence anisotropy in coexisting L alpha/HII phases is discussed.

Perturbation theory for nematic liquid crystals of axially symmetric molecules: Numerical results at high pressures including second- and fourth rank orientational order parameters

Abstract A statistical mechanical perturbation theory is applied to study the thermo-dynamic properties of nematic liquid crystals at the nematic-isotropic (N-I) phase transition under pressure, retaining second- and fourth-rank long-range orientational order parameters. We report calculations for a hard ellipsoidal system superposed with an attractive interaction and subjected to different external pressures. The repulsive interaction is represented by a repulsion between hard ellipsoids characterized by a length-to-width ratio and the interaction arising from the dispersion interaction between two asymmetric molecules represents the attractive interaction. The inclusion of the fourth-rank order parameter in the effective one-body potential ψ(Ω) does not lead to a significant overall improvement. The influence of pressure on the stability, ordering and thermodynamic functions at the N-I transition is analysed. We find that our theoretical predictions are in accordance with experimental observations.

Can <P4> be obtained from fluorescence depolarization in nematics? Disc-like probes

Abstract The determination of the fourth rank orientational order parameter, , is an important goal in liquid crystal research. Here we have looked at the feasibility of obtaining for a disc-like probe molecule from a time dependent fluorescence depolarization experiment. Simulated data at various temperatures have been prepared and then analyzed both individually and simultaneously using the global target deconvolution procedure. We have examined, in particular, the case of molecules subject to effective potentials containing a combination of second and fourth rank terms.

Electrical Conductivity Measurements of the Orientational Order Parameter in the Micellar Nematic Phase of the Caesium Pentadecafluoroctanoate/water System

Abstract Electrical conductivity measurements are presented for the micellar mesophases of the caesium pentadecafluoroctanoate/heavy water (CsPFO/2H2O) system The electrical conductivity monitors the diffusivity of the counterions around the micelles and transforms as a second rank tensor with a reference frame coincident with the principal axes of the inertial tensor. This means that the second rank orientational order parameter can be calculated from measurements of the angular dependence of the conductivity of a macroscopically aligned sample. Values of the order parameter in both the lamellar and nematic phases have been obtained in this way. The value obtained for the order parameter exponent β = 0.31 ± 0.03 in the nematic phase of a sample with a weight fraction of CsPFO of 0.55 is substantially smaller than the corresponding value as obtained by earlier birefringence measurements

Computer simulation studies of anisotropic systems

We have studied the surface behaviour of the Lebwohl-Lasher model nematogen using the Monte Carlo technique of computer simulation. Two states of the nematogen have been investigated, one with normal periodic boundary conditions and the other with boundary conditions employed for just two dimensions thus forming two free surfaces orthogonal to the third dimension. We have determined the variation of the internal energy and the second rank orientational order parameter, associated with individual layers, with their distance from the surface, as a function of the temperature. The order in the surface is found to be less than in the bulk nematogen although this difference is far less for the isotropic phase than for the nematic. This suppression of the surface orientational order is in accord with the surface tension simulated for the nematogen. Thus the surface tension decreases rapidly with increasing temperature in the nematic mesophase but then is essentially independent of temperature in the isotropic p...

The determination of the order parameters and director alignment in the nematic phase of a liquid crystalline side-chain polymer by the resolution of dielectric loss spectra

It is shown how the broad and asymmetric dielectric loss spectra obtained for a nematogenic side-chain siloxane polymer can be fitted by the superposition of two Fuoss-Kirkwood curves. The degree of director alignment and the second rank orientational order parameters of the sample are estimated by relating the intensities of the two curves to the intensities of the loss processes as given by the generalization of the Nordio-Rigatti-Segre theory to the case of arbitrary director alignment. It appears that the nematic phase of the material studied has a high degree of planar director alignment and that the order parameters are much smaller than those observed for low molar mass nematogens.

Computer simulation studies of anisotropic systems

The Lebwohl-Lasher model of a nematogen provides a simple system with which to study the order-disorder transition and to examine the properties of the nematic phase. We have investigated the model containing 203 particles over a small temperature range characteristic of that for real nematogens using the Monte Carlo method to evaluate the internal energy, the heat capacity and the second rank orientational order parameter. Our results are in reasonable agreement with those of other simulations and are compared with the predictions of theories based on a cluster expansion of the free energy. The temperature dependence of the order parameter is used to investigate the validity of the singlet orientational distribution function predicted by the Maier-Saupe theory. The potential of mean torque is found to be linear in the order parameter as required by the theory although the orientational free energy is in error. The simulated properties are in reasonable but not complete accord with those of a real nematog...