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.     

Comparative study of temperature dependent orientational relaxation in a model thermotropic liquid crystal and in a model supercooled liquid

Recent optical Kerr effect experiments have revealed a power law decay of the measured signal with a temperature independent exponent at short-to-intermediate times for a number of liquid crystals in the isotropic phase near the isotropic-nematic transition and supercooled molecular liquids above the mode coupling theory critical temperature. In this work, the authors investigate the temperature dependence of short-to-intermediate time orientational relaxation in a model thermotropic liquid crystal across the isotropic-nematic transition and in a binary mixture across the supercooled liquid regime in molecular dynamics simulations. The measure of the experimentally observable optical Kerr effect signal is found to follow a power law decay at short-to-intermediate times for both systems in agreement with recent experiments. In addition, the temperature dependence of the power law exponent is found to be rather weak. As the model liquid crystalline system settles into the nematic phase upon cooling, the decay of the single-particle second-rank orientational time correlation function exhibits a pattern that is similar to what has been observed for supercooled liquids.     

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.     

Molecular dynamics investigation of a density-driven glass transition in a liquid crystal system

Molecular dynamics simulations are carried out to address the density-driven glass transition in a system of rodlike particles that interact with the Gay-Berne potential. Since crystallization occurs in this system on the time scale of the simulations, direct simulation of the glass transition is not possible. Instead, glasses with isotropic orientational order are heated to a temperature T, and the relaxation times by which nematic orientational order develops are determined. These relaxation times appear to diverge at a critical density rho(c); i.e., the system can equilibrate at rhorho(c) (at the temperature T). The relaxation times follow a power-law scaling as the critical density is approached, suggesting that this density-driven glass transition concurs with mode coupling theory.     

Computer simulations of molecular motion in liquid crystals by the method of Brownian dynamics

Computer simulations of the molecular motion of polymer chains in the presence of a strong nematic field were carried out by the method of Brownian dynamics. Two models were studied: the first model (linear liquid crystal) is a freely jointed chain with rigid bonds, the second model (comb-like liquid crystal) is a chain with fixed bond angles and rigid side groups. The influence of ordering on chain conformations, orientational and translational mobility and spectra of relaxation times was investigated.     

Quenched disorder in a liquid-crystal biosensor: adsorbed nanoparticles at confining walls

We analyze the response of a nematic liquid-crystal film, confined between parallel walls, to the presence of nanoscopic particles adsorbed at the walls. This is done for a variety of patterns of adsorption (random and periodic) and operational conditions of the system that can be controlled in experimental liquid-crystal-based devices. We compute simulated optical textures and the total optical output of the sensor between crossed polars, as well as the correlation function for the liquid-crystal tensor order parameter; we use these observables to discuss the gradual destruction of the original uniform orientation. For large concentrations of particles adsorbed in random patterns, the liquid crystal at the center of the sensor adopts a multidomain state, characterized by a small correlation length of the tensor order parameter, and also by a loss of optical anisotropy under observation through crossed polars. In contrast, for particles adsorbed in periodic patterns, the nematic at the center of the cell can remain in a monodomain orientation state, provided the patterns in opposite walls are synchronized.     

Chiral symmetry-breaking dynamics in the phase transformation of nematic droplets

Dynamic simulations of the isotropic–nematic phase transformation of liquid crystal droplets with homeotropic surface anchoring are found to predict chiral symmetry-breaking dynamics. These observations occur when using material parameters for pentyl-cyanobiphenyl (5CB) but not with the single elastic constant approximation for this material, which is frequently used in simulations. The twisting dynamic process occurs during the relaxation of the domain from an unstable radial texture to a stable uniform texture and involves simultaneous defect loop motion and twisting of the bulk nematic texture.     

Glass formation in the Gay-Berne nematic liquid crystal

We present the results of molecular dynamics simulations of the Gay-Berne model of liquid crystals, supercooled from the nematic phase at constant pressure. We find a glass transition to a metastable phase with nematic order and frozen translational and orientational degrees of freedom. For fast quench rates the local structure is nematic-like, while for slower quench rates smectic order is present as well.     

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.     

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.     

Three homeotropically aligned nematic liquid crystals: comparison of ultrafast to slow time-scale dynamics

The dynamics of two nematic liquid crystals, 4-(trans-4(')-n-octylcyclohexyl)isothiocyanatobenzene and 4-(4-pentyl-cyclohexyl)-benzonitrile, are investigated as a function of temperature both in the homeotropically aligned nematic phase and in the isotropic phase using optical heterodyne-detected optical Kerr effect experiments, which measures the time derivative of the polarizability-polarizability-correlation function (orientational relaxation). Data are presented over a time range of 500 fs-70 micros for the nematic phase and 500 fs to a few hundred nanoseconds for the isotropic phase. The nematic dynamics are compared with a previously studied liquid crystal in the nematic phase. All three liquid crystals have very similar dynamics in the nematic phase that are very different from the isotropic phase. On the slowest time scale (20 ns-70 micros), a temperature-independent power law, the final power law, t(-f) with f approximately 0.5, is observed. On short time scales (approximately 3 ps to approximately 1 ns), a temperature-dependent intermediate power law is observed with an exponent that displays a linear dependence on the nematic order parameter. Between the intermediate power law and the final power law, there is a crossover region that has an inflection point. For times that are short compared to the intermediate power law (approximately <2 ps), the data decay much faster, and can be described as a third power law, although this functional form is not definitive. The isotopic phase data have the same features as found in previous studies of nematogens in the isotropic phase, i.e., the temperature-independent intermediate power law and von Schweidler power law at short to intermediate times, and a highly temperature-dependent long time exponential decay that is well described by the Landau-de Gennes theory. The results show that liquid-crystal dynamics in the nematic phase exhibit universal behavior.     

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.     

Theory for an order-driven disruption of the liquid state in water

Water is known to exhibit a number of peculiar physical properties because of the strong orientational dependence of the intermolecular hydrogen bonding interactions that dominate its liquid state. Recent full-atom simulations of water in a nanolayer between graphite plates submersed in an aqueous medium have raised the possibility of a new addition to this list of peculiarities: they show that application of a strong, uniform electric field normal to and between the plates can cause a pronounced decrease in particle density, rather than the increase expected from electrostriction theory for polarizable fluids [Vaitheeswaran et al., J. Phys. Chem. B 70, 6629 (2005)]. However, in seeming contradiction to this result, another study that simulated a range of similar systems has reported a less surprising electrostrictive increase in particle density upon application of the field [Bratko et al., J. Am. Chem. Soc. 129, 2504 (2007)]. In this work, we attempt to reconcile these conflicting simulation phenomena using a statistical mechanical lattice liquid model of water in an applied field. By solving the model using mean-field theory, we show that a field-induced transition to a markedly lower-density phase such as that observed in recent simulations is possible within a certain parameter regime, but that outside of this regime, the more conventional electrostrictive result should be obtained. Upon modifying the model to treat the case of bulk water under constant pressure in an applied field, we predict a density drop with rising field, and subsequently observe the predicted behavior in our own molecular dynamics simulations of liquid water. Our findings lead us to propose that the model considered here may be useful in a variety of contexts for describing the trade-off between orientational ordering of water molecules and their participation in the liquid phase.     

Molecular orientational and dipolar correlation in the liquid crystal mixture E7: a molecular dynamics simulation study at a fully atomistic level

Molecular dynamics simulations are reported for the four component nematic liquid crystal mixture E7, which is used commercially. We are able to show the growth of a nematic phase directly from an isotropic liquid over a 100 ns period for an all-atom model, and study orientational and dipole order within the nematic phase. The simulations show that the cyanoterphenyl component of the mixture, 5CT, is more ordered than the three cyanobiphenyl components. The simulations show also that both parallel and anti-parallel dipole correlation take place in E7 but that the strong anti-parallel dipole correlation is localised to particular arrangements of molecules. It is possible to identify two key preferred configurations for molecular pairs in the fluid, which explain the form of the dipole correlation function, g(1)(r).     

Molecular dynamics simulation of the nematic liquid crystal phase in the presence of an intense magnetic field

The influence of an intense external field on the dynamics of the nematic liquid crystal phase is investigated using a molecular dynamics simulation for the Gay-Berne nematogen under isobaric-isothermal conditions. The molecular dynamics as a function of the second-rank orientational order parameter P<2> for a system consisting of a nematic liquid crystal in the presence of an intense magnetic field is compared with that of a similar system without the field. The translational motion of molecules is determined as a function of the translational diffusion coefficient tensor and the anisotropy and compared with the values predicted theoretically. The rotational dynamics of molecules is analyzed using the first- and the second-rank orientational time correlation functions. The translational diffusion coefficient parallel with respect to the director is constrained by the intense field, although the perpendicular one is decreased as the P<2> is increased, just as it is in the system without the field. However, no essential effect of the strong magnetic field is observed in the rotational molecular dynamics. Further, the rotational diffusion coefficient parallel with respect to the director obtained from the first-rank orientational time correlation function in the simulation is qualitatively in agreement with that in the real nematic liquid crystalline molecules. The P<2> dependence of the rotational diffusion coefficient for the system with the intense magnetic field shows a tendency similar to that for the system without the field.     

Phase and orientational ordering of low molecular weight rod molecules in a quenched liquid crystalline polymer matrix with mobile side chains

We study the phase diagram and orientational ordering of guest liquid crystalline (LC) rods immersed in a quenched host made of a liquid crystalline polymer (LCP) matrix with mobile side chains. The LCP matrix lies below the glass transition of the polymer backbone. The side chains are mobile and can align to the guest rod molecules in a plane normal to the local LCP chain contour. A field theoretic formulation for this system is proposed and the effects of the LCP matrix on LC ordering are determined numerically. We obtain simple analytical equations for the nematic/isotropic phase diagram boundaries. Our calculation show a nematic-nematic (N/N) first order transition from a guest stabilized to a guest-host stabilized region and the possibility of a reentrant transition from a guest stabilized nematic region to a host only stabilized regime separated by an isotropic phase. A detailed study of thermodynamic variables and interactions on orientational ordering and phases is carried out and the relevance of our predictions to experiments and computer simulations is presented.     

Phase separations in liquid crystal-colloid mixtures

We present a mean-field theory to describe phase separations in mixtures of a nematic liquid crystal and a colloidal particle. The theory takes into account an orientational ordering of liquid crystals and a crystalline ordering of colloidal particles. We calculate phase diagrams on the temperature-concentration plane, depending on interactions between a liquid crystal and a colloidal surface and a coupling between nematic and crystalline ordering. We find various phase separation processes, such as a nematic-crystal phase separation and nematic-isotropic-crystal triple point. Inside binodal curves, we find new unstable and metastable regions which are important in phase ordering dynamics. We also find a stable nematic-crystalline (NC) phase, where colloidal particles dispersed in a nematic phase can form a crystalline structure. The coexistence between two NC phases with different concentrations can be appear though the coupling between nematic and crystalline ordering.     

Relaxation processes of the liquid crystal ME6N in the isotropic phase studied by Raman scattering experiments

We have investigated the Raman profiles of the nu(C[Triple Bond]N) and nu(C=O) vibrational modes of the nematic liquid crystal ME6N (4-cyanophenyl-4(')-hexylbenzoate) in the isotropic phase at different temperatures and used them as probes of the dynamics and structural organization of this liquid. The vibrational time correlation functions of the nu(C[Triple Bond]N) mode, rather adequately interpreted within the assumption of exponential modulation function (the Kubo-Rothschild theory), indicate that the system experiences an intermediate dynamical regime that gets only slightly faster with increasing temperature. However, this theory fails in predicting the non-exponential behavior that the time correlation functions manifest in the long time range (t>3 ps). For this reason we have additionally approached the interpretation of vibrational correlation functions in terms of the theory formulated by Rothschild and co-workers for locally structured liquids. The application of this theory reveals that the molecular dynamics in this liquid crystal in the isotropic phase is that deriving from a distribution of differently sized clusters, which narrows as the temperature increases. Even at the highest temperature reached in this study (87 degrees C above the nematic-isotropic transition), the liquid has not yet achieved the structure of the simple liquid and the dynamics has not reached the limit of the single channel process. The vibrational and orientational relaxations occur in very different time scales. The temperature independence of the orientational dynamics in the whole range from 55 degrees C to 135 degrees C has been referred to the nonhydrodynamic behavior of the system, arising when local pseudonematic structures persist for times longer than the orientational relaxation. The occurrence of the process of resonant vibrational energy transfer between the C=O groups of adjacent molecules has been revealed in the isotropic phase by a slightly positive Raman noncoincidence effect in the band associated with the nu(C=O) mode. A qualitative interpretation is tentatively given in terms of partial cancellation of contributions deriving from structures having opposite orientations of their C=O groups.     

Orientations of nematic liquid crystals on surfaces presenting controlled densities of peptides: amplification of protein-peptide binding events

We report a study of the orientations of nematic liquid crystals (LCs) in contact with peptide-modified, oligoethylene glycol-containing, self-assembled monolayers (SAMs). The SAMs were formed on gold films that were prepared by physical vapor deposition at an oblique angle of incidence. Two peptides were investigated: the optimized substrate for the Src protein kinase (IYGEFKKKC) and the synthetic equivalent of that peptide after kinase modification (IpYGEFKKKC). Polarization modulation-infrared reflectance absorbance spectroscopy (PM-IRRAS) was used to characterize the relative areal densities and orientations of these peptides at the interface. We conclude that the presence/absence of a phosphate group can influence the maximum packing density of immobilized peptide. We evaluated the orientations of the nematic liquid crystal 5CB in contact with these peptide-modified surfaces by using polarized microscopy. The time required for the nematic phase of 5CB to exhibit long-range orientational ordering (uniform alignment) was found to increase with increasing areal densities of immobilized peptide. We also found that the specific binding event between anti-phosphotyrosine IgG and the surface-immobilized phosphopeptide leads to an increase in the time required for the liquid crystal to achieve uniform anchoring (exceeding the experimentally accessible time scales). These results, when combined, suggest that the areal density and size of biomolecules at an interface can influence the time required for liquid crystals in contact with nanostructured surfaces to exhibit long-range orientational order. Finally, we illustrate the potential utility of this system by demonstrating that liquid crystals can be used to amplify and report protein binding events occurring on a spatially resolved peptide array.     

Molecular simulation of liquid water confined inside graphite channels: thermodynamics and structural properties

We carried out molecular dynamics simulations to describe the properties of water inside a narrow graphite channel. Two stable phases were found: a low-density one made of water clusters adsorbed on the graphite sheets and a liquid one that fills the entire channel, forming several layers around a bulk-like region. We analyzed the interfacial structure, orientational order, water residence times in several regions, and hydrogen bonding of this last water phase, calculating also a quantity of electrochemical interest, the probability of electron tunneling through interfacial water. The results are in good qualitative agreement with the available experimental data.