Universality and scaling in the disordering of a smectic liquid crystal

Isotropic to nematic transition of aerosil-disordered liquid crystals

We present a high-resolution study of the isotropic to nematic phase transition of a low birefringence liquid-crystal compound incorporating an aerosil gel. Calorimetry, light scattering, and microscopy data coherently combine to allow for an accurate determination of the temperature dependence of the onset of the nematic state. The nematic order develops on cooling through two distinct processes while the nematic correlation length mildly decreases. We understand the doubling of the phase transition as due to a crossover from a random-dilution regime, where the silica gel couples to the scalar part of the nematic order parameter, to a low-T random-field regime, where the coupling induces distortions in the director field.

First-order isotropic-smectic-A transition in liquid-crystal-aerosil gels

The short-range order which remains when the isotropic to smectic- A transition is perturbed by a gel of silica nanoparticles (aerosils) has been studied using high-resolution synchrotron x-ray diffraction. The gels have been created in situ in decylcyanobiphenyl, which has a strongly first-order isotropic to smectic- A transition. The effects are determined by detailed analysis of the temperature and gel density dependence of the smectic structure factor. In previous studies of the continuous nematic to smectic- A transition in a variety of thermotropic liquid crystals the aerosil gel appeared to pin, at random, the phase of the smectic density modulation. For the isotropic to smectic- A transition the same gel perturbation yields different results. The smectic correlation length decreases more slowly with increasing random-field variance in good quantitative agreement with the effect of a random pinning field at a transition from a uniform phase directly to a phase with one-dimensional translational order. We thus compare the influence of random fields on a freezing transition with and without an intervening orientationally ordered phase.

Random anisotropy nematic model: connection with experimental systems

We study theoretically the phase behavior of the continuum Random Anisotropy Nematic model. A domain-type pattern is assumed to appear in a distorted nematic liquid crystal (LC) phase. We map the model parameters to physical quantities characterizing LCs confined to Controlled-Pore Glasses and LC-aerosil dispersions. The domain size dependence on the disorder strength is obtained in accordance with the Imry-Ma prediction. The model estimates for temperature shifts of the paranematic-nematic phase transition and for the critical point, where this transition ceases to exist, are compared to the available experimental results.

Controlling disorder in liquid crystal aerosil dispersions

The effect of disorder in the behavior of liquid crystal (LC) is assessed and controlled by dispersing known amounts of silica aerosil in the liquid crystal material. Using deuteron nuclear magnetic resonance, the director configuration and the orientational order was determined for hydrophilic aerosil dispersions in octylcyanobiphenyl. The confined liquid crystal exhibits a well-defined alignment as the silica spheres stabilize the molecular configuration. At low silica densities, a silica network is eventually established, forming a soft gel. When the sample orientation in the magnetic field is changed, a few silica strands links are broken and a fraction of the LC molecules is realigned. The field anneals the random disorder introduced by the aerosil up to a certain density beyond which, in the so-called stiff-gel regime, disordering effects completely dominate. At a fixed temperature in the isotropic phase, there is surface-induced order that is linearly proportional to the silica density.

Broadband dielectric spectroscopy study of molecular dynamics in the glass-forming liquid crystal isopentylcyanobiphenyl dispersed with aerosils

The glass-forming liquid crystal isopentylcyanobiphenyl (CB15) filled with different concentrations of hydrophilic and hydrophobic aerosils has been investigated by broadband dielectric spectroscopy in the frequency range from 10(-2) Hz to 10(7) Hz over a temperature range of 173 K-300 K. CB15 that consists of chiral molecules has a monotropic system of phases nematic (N*) and smectic-A upon supercooling and forms a glass further on. In the isotropic phase a single Davidson-Cole process exists in the substance, which is due to the rotation of the molecules around their short axes. In the supercooled N* phase a Cole-Cole process that is an order of magnitude faster is additionally present and is due to the rotation in a cone around the local director. The relaxation times of the process due to rotation around short axes obey the empirical Vogel-Fulcher-Tamman behavior typical for glass-forming systems. Filling of the liquid crystal (LC) with different concentrations of hydrophilic aerosils leads to the emergence of a slow relaxation process that grows with the increasing concentration of the aerosils. The aerosil particles, which form a three-dimensional network dividing the LC phase into domains, have little effect on the relaxation times of the bulk processes. As a consequence the glass transition temperature is merely affected. On the other hand, in LCs dispersed with hydrophobic aerosils the slow process is quite weak. The slow process is attributed to the relaxation of the molecules that are homeotropically attached at the surfaces of the aerosil particles. The LC-aerosil surface interaction leads to a considerable slowing down of the molecular rotation around their short axis. The process has an Arrhenius-like temperature dependence of the relaxation times with an activated type of dynamics, which can be explained by considering a nonincreasing rearranging region of cooperativity in surface layers.

Evolution of the isotropic-to-nematic phase transition in octyloxycyanobiphenyl+aerosil dispersions

High-resolution ac calorimetry has been carried out on dispersions of aerosils in the liquid crystal octyloxycyanobiphenyl (8OCB) as a function of aerosil concentration and temperature spanning the crystal to isotropic phases. The liquid crystal 8OCB is elastically stiffer than the previously well studied octylcyanobiphenyl (8CB)+aerosil system and so general quenched random-disorder effects and liquid crystal specific effects can be distinguished. A double heat capacity feature is observed at the isotropic to nematic phase transition with an aerosil independent overlap of the heat capacity wings far from the transition and having a nonmonotonic variation of the transition temperature. A crossover between low and high aerosil density behavior is observed for 8OCB+aerosil. These features are generally consistent with those on the 8CB+aerosil system. Differences between these two systems in the magnitude of the transition temperature shifts, heat capacity suppression, and crossover aerosil density between the two regimes of behavior indicate a liquid crystal specific effect. The low aerosil density regime is apparently more orientationally disordered than the high aerosil density regime, which is more translationally disordered. An interpretation of these results based on a temperature dependent disorder strength is discussed. Finally, a detailed thermal hysteresis study has found that crystallization of a well homogenized sample perturbs and increases the disorder for low aerosil density samples but does not influence high-density samples.

High-resolution x-ray study of the nematic-smectic-A and smectic-A-smectic-C transitions in liquid-crystal-aerosil gels

The effects of dispersed aerosil nanoparticles on two of the phase transitions of the thermotropic liquid-crystal material 4-n-pentylphenylthiol-4(')-n-octyloxybenzoate (8;S5) have been studied using high-resolution x-ray diffraction techniques. The aerosils hydrogen bond together to form a gel which imposes a weak quenched disorder on the liquid crystal. The smectic-A fluctuations are well characterized by a two-component line shape representing thermal and random-field contributions. An elaboration on this line shape is required to describe the fluctuations in the smectic-C phase; specifically the effect of the tilt on the wave-vector dependence of the thermal fluctuations must be explicitly taken into account. Both the magnitude and the temperature dependence of the smectic-C tilt order parameter are observed to be unaffected by the disorder. This may be a consequence of the large bare smectic correlation length in the direction of modulation for this transition. These results show that the understanding developed for the nematic to smectic-A transition for octylcyanobiphenyl and octyloxycyanobiphenyl liquid crystals with quenched disorder can be extended to quite different materials and transitions.

Calorimetric study of octylcyanobiphenyl liquid crystal confined to a controlled-pore glass

We present a calorimetric study of the phase behavior of octylcyanobiphenyl (8CB) liquid crystal confined to a controlled-pore glass (CPG). We used CPG matrices with characteristic void diameters ranging from 400 to 20 nm. In bulk we obtain weakly first-order isotropic to nematic (I-N) phase transition and nearly continuous character of the nematic to smectic-A (N-SmA) phase transition. In all CPG matrices the I-N transition remains weakly first order, while the N-SmA one becomes progressively suppressed with decreasing CPG pore radius. With decreased pore diameters both phase transition temperatures monotonously decrease following similar trends, but increasing the stability range of the N phase. The heat-capacity response at the weakly first order I-N and continuous N-SmA phase transitions gradually approaches the tricritical-like and three-dimensional XY behavior, respectively. The main observed features were explained using a bicomponent single pore type phenomenological model.

Universal elasticity and fluctuations of nematic gels

We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to d(lc)<3.

Effect of a quenched random field on a continuous symmetry breaking transition: nematic to smectic-A transition in octyloxycyanobiphenyl-aerosil dispersions

High-resolution x-ray diffraction and ac-calorimetric experiments have been carried out on the liquid-crystal octyloxycyanobiphenyl in which aerosil particles are dispersed. The measurements were made over a temperature range around the bulk nematic to smectic-A transition temperature. At this transition the liquid crystal breaks translational symmetry in a single direction. The silica particles, which hydrogen bond together to form a very low density gel, provide the quenched disorder. The random gel leads to observable broadening of the x-ray reflection from the smectic layers. The structure factor is well described by modeling the effect of the aerosils as a quenched random field. Dispersed aerosils are thought to pin both the direction of the translational ordering and the position of the layers. The latter appears to have the greatest effect on the x-ray line shape. We show that the aerosil surface area, as verified by small-angle scattering, equates to the variance of the random field. Calorimetric results reveal substantial change in the specific heat peak associated with the nematic to smectic-A transition. As the concentration of aerosil increases, the specific heat peak remains sharp yet decreases in magnitude and shifts in temperature in a nonmonotonic fashion. In this regime, the critical exponent alpha becomes progressively smaller. For the samples with the largest concentrations of aerosil particles the C(p)(N-A) peak becomes highly smeared and shifts smoothly to lower temperatures.

Smectic ordering in liquid-crystal-aerosil dispersions. II. Scaling analysis

Liquid crystals offer many unique opportunities to study various phase transitions with continuous symmetry in the presence of quenched random disorder (QRD). The QRD arises from the presence of porous solids in the form of a random gel network. Experimental and theoretical work supports the view that for fixed (static) inclusions, quasi-long-range smectic order is destroyed for arbitrarily small volume fractions of the solid. However, the presence of porous solids indicates that finite-size effects could play some role in limiting long-range order. In an earlier work, the nematic-smectic-A transition region of octylcyanobiphenyl (8CB) and silica aerosils was investigated calorimetrically. A detailed x-ray study of this system is presented in the preceding paper, which indicates that pseudocritical scaling behavior is observed. In the present paper, the role of finite-size scaling and two-scale universality aspects of the 8CB+aerosil system are presented and the dependence of the QRD strength on the aerosil density is discussed.

Smectic ordering in liquid-crystal-aerosil dispersions. I. X-ray scattering

Comprehensive x-ray scattering studies have characterized the smectic ordering of octylcyanobiphenyl (8CB) confined in the hydrogen-bonded silica gels formed by aerosil dispersions. For all densities of aerosil and all measurement temperatures, the correlations remain short range, demonstrating that the disorder imposed by the gels destroys the nematic (N) to smectic-A (SmA) transition. The smectic correlation function contains two distinct contributions. The first has a form identical to that describing the critical thermal fluctuations in pure 8CB near the N-SmA transition, and this term displays a temperature dependence at high temperatures similar to that of the pure liquid crystal. The second term, which is negligible at high temperatures but dominates at low temperatures, has a shape given by the thermal term squared and describes the static fluctuations due to random fields induced by confinement in the gel. The correlation lengths appearing in the thermal and disorder terms are the same and show a strong variation with gel density at low temperatures. The temperature dependence of the amplitude of the static fluctuations further suggests that nematic susceptibility becomes suppressed with increasing quenched disorder. The results overall are well described by a mapping of the liquid-crystal-aerosil system onto a three-dimensional XY model in a random field with disorder strength varying linearly with the aerosil density.

Symmetries and elasticity of nematic gels

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

Nematics with quenched disorder: how long will it take to heal?

Nematics with quenched disorder have been repeatedly predicted to form glass phases. Here we present turbidity experiments and computer simulations aimed at studying glass key features such as dynamics and history dependence in randomly perturbed nematics. Electric field-cooling alignment has been employed to prepare samples in suitably oriented starting states. Remarkable remnant order and slow dynamics are found both by experiment and simulations, indicating that random disorder can, by itself, induce a nematic glass state even without perturber restructuring.

Hydrogen-bonded silica gels dispersed in a smectic liquid crystal: a random field XY system

The effect on the nematic to smectic-A transition in octylcyanobiphenyl (8CB) due to dispersions of hydrogen-bonded silica (aerosil) particles is characterized with high-resolution x-ray scattering. The particles form weak gels in 8CB creating a quenched disorder that replaces the transition with the growth of short-range smectic correlations. The correlations include thermal critical fluctuations that dominate at high temperatures and a second contribution that quantitatively matches the static fluctuations of a random field system and becomes important at low temperatures.

Elastic coupling of silica gel dynamics in a liquid-crystal-aerosil dispersion

The dynamics of a thixotropic silica aerosil gel dispersed in an octylcyanobiphenyl liquid crystal were directly probed by x-ray intensity fluctuation spectroscopy. For all samples, the time-autocorrelation function of the gel was well described by a modified-exponential function over the q range studied. Compared to a pure gel sample, a dilute (0.06 g cm(-3)) gel embedded within the liquid crystal displayed more complex and temperature dependent dynamics. Near the second-order smectic-A-to-nematic phase transition of the liquid crystal the gel relaxation became significantly more complex and slower (tau approximately 2150 s) compared to relaxations observed well within either phase. This clearly demonstrates coupling between the dynamics of the gel and the host liquid crystal, consistent with critical slowing down of smectic and director fluctuations. A random dampening field, elastically coupled to the liquid crystal, would explain the earlier observed crossover of this transition towards 3d-XY behavior.