Properties of the discotic-nematic to isotropic transition: influence of short range orientational order

The present investigation concerns the analysis of the influence of short range orientational correlation on the thermodynamic properties of discotic-nematic liquid crystals. Two-site cluster approximation is applied to the orientational molecular coordinates to include the short range orientational correlation. The role of short range orientational order, dispersion interaction, molecular length-to-width ratio and pressure on the thermodynamic and orientational behaviour of discotic nematogens close to the discotic-nematic to isotropic transition are analysed. It is observed that the short range orientational order has a strong influence on the thermodynamic properties and that the transition properties of both the calamitic and discotic mesogens exhibit quite similar behaviour.     

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.     

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.     

Statistical mechanical theory for discotic liquid crystals Discotic nematic-isotropic transition properties

A statistical mechanical theory is applied to study the equilibrium properties of discotic nematic liquid crystals. We report the calculation of thermodynamic properties for a model system composed of molecules interacting through angle-dependent pair potentials which can be broken up into rapidly varying short-ranged repulsions and weak long-range attractions. The repulsive interaction is represented by a repulsion between hard oblate ellipsoids of revolution and is a short-range, rapidly-varying, potential. The influence of attractive potentials, represented by dispersion and quadrupole interactions on a variety of thermodynamic properties is analysed. It is found that the thermodynamic properties for the discotic nematic-isotropic transition are highly sensitive to the form of effective one-body orientational perturbation potential. The discontinuity in the transition properties is more pronounced in the case of quadrupole interaction than for anisotropic dispersion interaction. A remarkable symmetry in the transition properties between prolate ellipsoids (ordinary nematic) and oblate ellipsoids (discotic nematic) is observed.     

Structural and dynamic properties of a new type of discotic nematic compounds

Thermodynamic, structural and dynamical properties of a new type of discotic compounds, a hydrocarbon without any heteroatoms, displaying a nematic discotic phase have been investigated by means of X-ray diffraction, electro-optical relaxation, and calorimetric studies. Of particular interest are the strength of the first order nematic—isotropic phase transition and the nature of the orientational fluctuations in the isotropic phase. The short range positional order was found to be biaxial in both the isotropic and the nematic phase. The isotropic phase displays strong pretransitional effects originating from orientational fluctuations in the neighbourhood of the transition to the nematic phase. The character of these pretransitional effects differs from that found for calamitic systems in that the number of correlated molecules g₂ is extremely large, of the order of 600 at the clearing temperature and the electro-optical relaxation time is very large, caused by the large value of g₂.     

A computer simulation of model discotic dimers

We set up a model for discotic liquid crystal dimers and study, by means of Monte Carlo simulations, their phase behaviour and self–assembling properties, in comparison with the simpler monomeric case. Each discotic dimer is described by two oblate Gay–Berne ellipsoids connected by a flexible spacer, modelled by a harmonic “spring” of three different lengths. We find that dimerization in general yields produces a significant change on the phase behaviour, with an increase of the columnar–nematic transition temperature, a widening of the nematic region and the apparent suppression of the crystalline phase in favour of the columnar phase up to very low temperatures. Longer spacers prove to ease the formation of columns and to increase the orientational order. Contribution to the Fernando Bernardi memorial issue.     

Structural changes in discotic samples during transition from crystal to discotic mesophase as revealed by electron microscopy and diffraction

Classical methods of structural analysis cannot be applied to liquid crystals because higher order reflections disappear during the transition from crystal to liquid crystal due to the reduction in long range orientational and translational correlations. However, in order to relate physical properties to the molecular architecture, it is essential to have information about molecular positions and orientations in the crystalline state as well as in the liquid crystalline state. In this work, the transition from crystalline to liquid crystalline phase is carefully monitored and the relationship between the original lattice and the new molecular positions found using electron diffraction. In addition to this, a new high resolution electron-microscopic technique is described in which the positions of molecules in the crystalline and the quenched discotic phase are directly imaged and the defects observed in the crystalline and LC phase compared and quantitatively analysed.     

Eutectic mixtures with plastic columnar discotics: molecular structure,phase morphology and kinetics of phase separation

We report the properties of eutectic mixtures of triphenylenes displaying a highly ordered columnar phase with a low molar mass non‐discotic compound. Such highly ordered triphenylenes display large charge carrier mobilities which are strongly controlled by the state of order in the discotic phase. The motivation was to establish how the state of order—molecular order, phase morphology, temperature ranges of phase stabilities and macroscopic orientational order—can be influenced by mixing. The studies reveal that the molecular order, in particular the mutual arrangement of the columns and the intracolumnar order, are unaffected by dilution of the discotic compound, whereas the phase morphology and the kinetics of phase separation change significantly with dilution. Rod‐shaped discotic domains with a hexagonal cross‐sectional area are formed via a nucleation process and the rods grow linearly as a function of time. Both the pure discotic phase as well as the discotic domains forming during phase separation can be macroscopically ordered by orientation layers.     

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.     

Dynamics of a discotic liquid crystal in the isotropic phase

Optically heterodyne-detected optical Kerr effect (OHD-OKE) experiments are conducted to study the orientational dynamics of a discotic liquid crystal 2,3,6,7,10,11-hexakis(pentyloxy)triphenylene (HPT) in the isotropic phase near the columnar-isotropic (C-I) phase transition. The OHD-OKE signal of HPT is characterized by an intermediate power law t(-0.76+/-0.02) at short times (a few picoseconds), a von Schweidler power law t(-0.26+/-0.01) at intermediate times (hundreds of picoseconds), and an exponential decay at long times (tens of nanoseconds). The exponential decay has Arrhenius temperature dependence. The functional form of the total time dependent decay is identical to the one observed previously for a large number of molecular supercooled liquids. The mode coupling theory schematic model based on the Sjogren [Phys. Rev. A 33, 1254 (1986)] model is able to reproduce the HPT data over a wide range of times from <1 ps to tens of nanoseconds. The studies indicate that the HPT C-I phase transition is a strong first order transition, and the dynamics in the isotropic phase display a complex time dependent profile that is common to other molecular liquids that lack mesoscopic structure.     

Molecular dynamics of discotic charge-transfer complexes, dielectric spectroscopy and 2H NMR studie

Using a combination of solid state ²H NMR spectroscopy on selectively deuteriated samples and dielectric spectroscopy, the molecular dynamics of discotic charge-transfer (CT) complexes were investigated. These complexes show particular thermodynamic and flow properties. Considered were mixtures of low molar mass donors and acceptors, low molar mass donors with main chain acceptor polymers and covalently linked donor-acceptor twins with different lengths of the spacer. A main result is that correlated rotational motions of discotic molecules or groups about the columnar axis are observed in all systems except for the twin with the short spacer. This type of motion seems to be a general feature of columnar phases. The non-discotic acceptor which is incorporated in the columns participates in this motion. The twin possessing a long spacer displays at high temperatures an additional process: it performs a diffusion process between the columns. A further result is that broad biphasic regions exist in CT mixtures at the transition from the discotic to the isotropic state.     

Structural ordering and molecular-optical properties of a discotic liquid crystal (Colho)

The infrared absorbance and the dispersion of the refractive indices in the region 0.49-0.63 µm of the discotic mesogen 2,3,6,7,10,11-hexaheptyloxytriphenylene were studied for the columnar and isotropic phases. The temperature dependence of the orientational order parameter S and the local field parameters of a light wave acting on the sample have been evaluated. It is shown that the mixing of molecular excitations modifies the behaviour of S as a function of temperature. Molecular-optical properties of the triphenylene derivative, such as the anisotropy of the polarizability, Δγ and the mean polarizability, &gammatilde; were investigated on the basis of the generalized Lorenz-Lorentz relation for uniaxial liquid crystals. The experimentally observed changes of these properties in the columnar phase seem to be affected by the induction mechanism of the change in the molecular polarizability with increasing S.     

Eutectic mixtures with plastic columnar discotics: molecular structure, phase morphology and kinetics of phase separation

We report the properties of eutectic mixtures of triphenylenes displaying a highly ordered columnar phase with a low molar mass non-discotic compound. Such highly ordered triphenylenes display large charge carrier mobilities which are strongly controlled by the state of order in the discotic phase. The motivation was to establish how the state of order—molecular order, phase morphology, temperature ranges of phase stabilities and macroscopic orientational order—can be influenced by mixing. The studies reveal that the molecular order, in particular the mutual arrangement of the columns and the intracolumnar order, are unaffected by dilution of the discotic compound, whereas the phase morphology and the kinetics of phase separation change significantly with dilution. Rod-shaped discotic domains with a hexagonal cross-sectional area are formed via a nucleation process and the rods grow linearly as a function of time. Both the pure discotic phase as well as the discotic domains forming during phase separation can be macroscopically ordered by orientation layers.     

Conformational and Orientational Order of Molecules in Nematic Liquid Crystals

The statistical properties of the conformational and orientational distribution of molecules with internal rotation in the isotropic and nematic phases of liquid crystal (LC) are investigated in terms of molecular statistical theory. The paper discusses the effect of mutual correlation between the molecular conformational and orientational degrees of freedom on the conformational, orientational, and mixed order parameters of molecules in LC and on the nematic–isotropic liquid transition temperature. For these order parameters, the recurrent relation method is suggested and used to derive the partial functions of the conformational and orientational distributions of molecules in LC.     

Orientational ordering, conformation, and polarizability of molecules in the reentrant phase of discoid nematics

This paper presents data on orientational ordering in a reentrant discoid nematic and on changes in the polarizability of discogenic molecules in a homologous series. The phase transition of a nematic to the discotic column phase is accompanied by a jump of the orientational ordering parameter and is characterized by close relationship between the orientational and translational ordering of molecules. The lengthening of the flexible peripheral molecular chains in the reentrant nematic phase considerably changes their conformational state, decreasing the anisotropy of their polarizability. Translated fromZhumal Strukturnoi Khimii, Vol. 38, No. 1, pp. 89–97, 1997.     

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.     

Glassiness of thermotropic liquid crystals across the isotropic-nematic transition

The orientational dynamics of thermotropic liquid crystals across the isotropic-nematic phase transition have traditionally been investigated at long times or low frequencies using frequency domain measurements. The situation has now changed significantly with the recent report of a series of interesting transient optical Kerr effect (OKE) experiments that probed orientational relaxation of a number of calamitic liquid crystals (which consist of rod-like molecules) directly in the time domain, over a wide time window ranging from subpicoseconds to tens of microseconds. The most intriguing revelation is that the decay of the OKE signal at short to intermediate times (from a few tens of picoseconds to several hundred nanoseconds) follows multiple temporal power laws. Another remarkable feature that has emerged from these OKE measurements is the similarity in the orientational relaxation behavior between the isotropic phase of calamitic liquid crystals near the isotropic-nematic transition and supercooled molecular liquids, notwithstanding their largely different macroscopic states. In this article, we present an overview of the understanding that has emerged from recent computational and theoretical studies of calamitic liquid crystals across the isotropic-nematic transition. Topics discussed include (a) single-particle as well as collective orientational dynamics at a short-to-intermediate time window, (b) heterogeneous dynamics in orientational degrees of freedom diagnosed by a non-Gaussian parameter, (c) fragility, and (d) temperature-dependent exploration of underlying energy landscapes as calamitic liquid crystals settle into increasingly ordered mesophases upon cooling from the high-temperature isotropic phase. A comparison of our results with those of supercooled molecular liquids reveals an array of analogous features in these two important classes of soft matter systems. We further find that the onset of growth of the orientational order in the parent nematic phase induces translational order, resulting in smectic-like layers in the potential energy minima of calamitic systems if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. We discuss implications of this startling observation. We also discuss recent results on the orientational dynamics of discotic liquid crystals that are found to be rather similar to those of calamitic liquid crystals.     

Glass Formation of n-Butanol: Coarse-grained Molecular Dynamics Simulations Using Gay-Berne Potential Model

Using coarse-grained molecular dynamics simulations based on Gay-Berne potential model, we have simulated the cooling process of liquid n-butanol. A new set of GB parameters are obtained by fitting the results of density functional theory calculations. The simulations are carried out in the range of 290-50 K with temperature decrements of 10 K. The cooling char-acteristics are determined on the basis of the variations of the density, the potential energy and orientational order parameter with temperature, whose slopes all show discontinuity. Both the radial distribution function curves and the second-rank orientational correlationfunction curves exhibit splitting in the second peak. Using the discontinuous change of these thermodynamic and structure properties, we obtain the glass transition at an estimate of temperature T_g=120±10 K, which is in good agreement with experimental results 110±1 K.     

MOLECULAR FIELD THEORY FOR NEMATIC LIQUID CRYSTAL POLYMER COMPRISING FLEXIBLE SPACER

Basea on the new model and concept of mtramolecular orientational order parameter, a molecular field theory was built up for main chain liquid crystalline polymer (MC-LCPs) with flexible spacers. The theory takes account of orientational correlation among all mesogens in a polymer chain and the relationship between the intramolecular orientation and spatial orientation of the mesogens. The free energy, temperature and entropy of the nematic-isotropic transition were determined with the theory and compared with experiments in current work. It was found that many unique transition properties of the MC-LCPs comprising flexible spacer are correctly predicted by the theory and the agreement of the theory with the experiments is impressive.     

Orientational melting and reorientational motion in a cubane molecular crystal: a molecular simulation study

Detailed molecular simulations are carried out to investigate the effect of temperature on orientational order in cubane molecular crystal. We report a transition from an orientationally ordered to an orientationally disordered plastic crystalline phase in the temperature range 425-450 K. This is similar to the experimentally reported transition at 395 K. The nature of this transition is first order and is associated with a 4.8% increase in unit cell volume that is comparable to the experimentally reported unit cell volume change of 5.4% (Phys. Rev. Lett. 1997, 78, 4938). An orientational order parameter, eta(T), has been defined in terms of average angle of libration of a molecular 3-fold axis and the orientational melting has been characterized by using eta(T). The orientational melting is associated with an anomaly in specific heat at constant pressure (C(P)) and compressibility (kappa). The enthalpy of transition and entropy of transition associated with this orientational melting are 20.8 J mol(-1) and 0.046 J mol(-1) K(-1), respectively. The structure of crystalline as well as plastic crystalline phases is characterized by using various radial distribution functions and orientational distribution functions. The coefficient of thermal expansion of the plastic crystalline phase is more than twice that of the crystalline phase.