Layer Compression Modulus Research Articles

Elastic response of colloidal smectic liquid crystals: Insights from microscopic theory.

Elongated colloidal rods at sufficient packing conditions are known to form stable lamellar or smectic phases. Using a simplified volume-exclusion model, we propose a generic equationof state for hard-rod smectics that is robust against simulation results and is independent of the rod aspect ratio. We then extend our theory by exploring the elastic properties of a hard-rod smectic, including the layer compressibility (B) and bending modulus (K_{1}). By introducing weak backbone flexibility we are able to compare our predictions with experimental results on smectics of filamentous virus rods (fd) and find quantitative agreement between the smectic layer spacing, the out-of-plane fluctuation strength, as well as the smectic penetration length λ=sqrt[K_{1}/B]. We demonstrate that the layer bending modulus is dominated by director splay and depends sensitively on lamellar out-of-plane fluctuations that we account for on the single-rod level. We find that the ratio between the smectic penetration length and the lamellar spacing is about two orders of magnitude smaller than typical values reported for thermotropic smectics. We attribute this to the fact that colloidal smectics are considerably softer in terms of layer compression than their thermotropic counterparts while the cost of layer bending is of comparable magnitude.

Hydrodynamics of a superfluid smectic

We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose–Einstein condensates with strong dipolar interactions as well as of the stripe phase in Bose gases with spin–orbit coupling. We show that the presence of a finite normal fluid density in the ground state of these systems gives rise to a well-defined second-sound type mode even at zero temperature. It replaces the diffusive permeation mode of a normal smectic phase and is directly connected with the classic description of supersolids by Andreev and Lifshitz in terms of a propagating defect mode. An analytic expression is derived for the two sound velocities that appear in the longitudinal excitation spectrum. It only depends on the low-energy parameters associated with the two independent broken symmetries, which are the effective layer compression modulus and the superfluid fraction.

Effect of interlamellar interactions on shear induced multilamellar vesicle formation.

Shear-induced multilamellar vesicle (MLV) formation has been studied by coupling the small-angle neutron scattering (SANS) technique with neutron spin echo (NSE) spectroscopy. A 10% mass fraction of the nonionic surfactant pentaethylene glycol dodecyl ether (C12E5) in water was selected as a model system for studying weak inter-lamellar interactions. These interactions are controlled either by adding an anionic surfactant, sodium dodecyl sulfate, or an antagonistic salt, rubidium tetraphenylborate. Increasing the charge density in the bilayer induces an enhanced ordering of the lamellar structure. The charge density dependence of the membrane bending modulus was determined by NSE and showed an increasing trend with charge. This behavior is well explained by a classical theoretical model. By considering the Caillé parameters calculated from the SANS data, the layer compressibility modulus B¯ is estimated and the nature of the dominant inter-lamellar interaction is determined. Shear flow induces MLV formation around a shear rate of 10 s-1, when a small amount of charge is included in the membrane. The flow-induced layer undulations are in-phase between neighboring layers when the inter-lamellar interaction is sufficiently strong. Under these conditions, MLV formation can occur without significantly changing the inter-lamellar spacing. On the other hand, in the case of weak inter-lamellar interactions, the flow-induced undulations are not in-phase, and greater steric repulsion leads to an increase in the inter-lamellar spacing with shear rate. In this case, MLV formation occurs as the amplitude of the undulations gets larger and the steric interaction leads to in-phase undulations between neighboring membranes.

Finite Element Analysis of Deformation Characteristic for Weak Interlayer Foundation

In accordance with settlement observation data of weak interlayer foundation in The North China Plain, finite element model was made to analyze vertical settlement and horizontal deformation by MIDAS/GTS software. Then, Influence factors of subgrade settlement were studied through changing the fill height, crust layer thickness and compression modulus. The results show that crust layer has the board supporting and closing the substratum functions during the period of loading and a relatively short period after loading. The maximum horizontal deformation occurs in weak interlayer rather than the ground surface. The horizontal deformation increases generally with the increase of the fill height. When the crust layer thickness increase, its settlement grows larger and the settlement of soft soil layer has the decrease trend. The settlement of crust layer and weak layer is decreased with the compression modulus increase of crust layer. It explains that the shell effects of crust layer increase with the compression modulus increase of crust layer.

Mechanics of Homeotropically Ordered Smectic‐A Elastomers with Global Oblate Chain Conformation

Smectic-A elastomers combine one-dimensional translational order of rod-like segments with the rubber elasticity of a polymer network. In recent years, detailed investigations were carried out on elastomers showing a global prolate chain conformation. In this communication, the first experiments on fluorinated SA elastomers exhibiting a global oblate chain conformation are presented, where the polymer chains are on average compressed along the layer normal of the lamellar phase structure. The mechanical anisotropy is studied by means of thermoelastic experiments and stress-strain measurements. For the first time, the layer compression modulus B of smectic elastomers is directly measured. B is significantly larger as compared to conventional low molar mass liquid crystals and decreases significantly with increasing local disorder introduced by the isotropic crosslinker.

Elasticity of smectic liquid crystals with focal conic domains

We study the elastic properties of thermotropic smectic liquid crystals withfocal conic domains (FCDs). After the application of the controlled preshearat different temperatures, we independently measure the shear modulusG′ and theFCD size L. We find out that these quantities are related by the scaling relationG′≈γeff/L, whereγeff is the effective surface tension of the FCDs. The experimentally obtained value ofγeff shows the same scaling as the effective surface tension of the layered systems , where K and B are the bending modulus and the layer compression modulus, respectively. The similarity ofthis scaling relation to that of the surfactant onion phase suggests an universal rheologicalbehavior of the layered systems with defects.

Mechanically induced tilt in smectic-A elastomers

Recently it has been predicted that shear forces can unlock the director and the layer normal in smectic-A elastomers, leading to a smectic-C like tilt analogous to the electroclinic effect of chiral SA* phases. In order to investigate this phenomenon, we present detailed X-ray investigations of SA elastomers under shear, comparing networks of different chemical constitution. Upon shear imposed in the layer planes, an induced SC like tilt is observed, which develops linearly with the applied shear angle. With decreasing layer compression modulus B of the smectic network, the effect becomes smaller, and additional layer rotations are found. For elastomers containing fluorinated mesogens, layer normal and director are rigidly locked, despite their large B modulus, and the phase structure remains unchanged under shear strain. The experimental results provide clear evidence for recent theoretical predictions.

THE EFFECT OF SURFACES ON THE ORIENTATIONAL PROPERTIES AND PHASE TRANSITIONS PECULIARITIES OF A NONPOLAR SMECTOGEN

The effect of thin films on the orientational and optical properties of nonpolar monolayer smectogen 4-butoxyphenyl-4′-decyloxybenzoate [Formula: see text] liquid crystal has been studied by polarizing microscopy and high-resolution photon transmission method. The uniform planar textures of [Formula: see text] on the surfaces coated with WO3, VO2, and WO3– VO2mixture thin films have been obtained. No significant shifts in the phase transition temperatures to lower values under the influence of the surfaces have been observed. We have also presented the new experimental data on the critical behavior of the layer compression modulus B near the nematic–smectic A transition. It was observed that the data in the vicinity of the transition can be described by a power law expression after the introduction of a first-order correction-to-scaling term within the limit of experimental error. The resulting critical exponent was found to be 0.34∓0.01 which is good agreement with the previously reported values for other investigated compounds in literature.

Poiseuille flow of a smectic A liquid crystal

This article considers the dynamics of smectic A liquid crystals subjected to Poiseuille flow. Linearised governing equations are constructed using a recent dynamic theory for Smectic A [36]. These equations are solved analytically and the consequent solutions are then calculated for some typical experimental data in order to determine the explicit flow behaviour. Stability of flow and layer structure solutions are proved. Results show how the response time for small perturbations to the smectic layers depends upon the permeation constant and the layer compression modulus.

Influence of phase sequence on focal conic domains in smectic films

We present a study of smectic focal conic domains in films of various liquid-crystal compounds on a solid substrate. Focal conic domains are generated as a result of the antagonistic anchoring conditions of the film surfaces, random planar at the substrate interface and homeotropic at the air interface. The curved arrangement of the smectic layers in focal conic domains leads to a depression in the film/air interface above each domain. Using atomic force microscopy, we determine the temperature dependence of the depth of the depressions in different smectic phases and at different phase transitions. In most cases, our results are not in accordance with the assumption of strictly incompressible smectic layers, and we discuss the observed behavior with respect to the known results on the layer compressibility modulus B .

Second sound in bursting freely suspended smectic-Afilms

We describe the bursting of macroscopic spherical bubbles formed by smectic liquid crystals. During rupture, strong light scattering is observed. It is suggested here that peristaltic undulations of the films are responsible for this scattering. This phenomenon distinguishes bursting smectic films from bursting soap films. The dynamics of these mechanical waves are strongly influenced by the internal layered structure of the smectic films, viz. by the elasticity of the molecular layers, expressed by the smectic layer compression modulus B. We study experimentally the optical properties of bursting smectic films by means of optical transmission measurements and laser scattering. The typical wavelength range of the propagating peristaltic waves is in the micrometer range. The wavelength spectrum rather is independent of the initial film thickness delta, but the scattering intensity strongly depends on delta.

Couette flow of a smectic A liquid crystal

This paper considers the dynamics of cylindrically arranged parallel layers of smectic Aliquid crystal subjected to Couette flow. Governing equations are constructed using arecently developed dynamic theory for smectic A (Stewart 2007 Contin. Mech. Thermodyn.18 343–60). These equations are solved to provide analytical solutions for thesmectic layer undulations and velocity profiles. Results show the dependence of theresponse time of the smectic layers upon the permeation constant and the layercompression modulus. The relaxation times for the flow profiles are shown todepend upon two viscosities; estimates for these times are shown to be shorterthan that for a typical approximation to the relaxation time of the smectic layerundulations.

Range of interlayer interactions in smectic-Cliquid crystals

The fact that the elastic constant for bending a layer of smectic- C liquid crystal along its c director differs from the value for bending in the perpendicular direction has recently been shown to give rise to interactions between distant layers. The effect of this entropy-induced interaction is to favor a parallel or antiparallel alignment of the c directors in these nonadjacent layers. We calculate in detail the range and strength of this interaction in both infinite and finite samples, and find the results to depend mainly on the ratio of the average layer bending elastic constant to the layer compression modulus. At low values of this ratio, the interlayer interaction is of long range in a bulk sample, while at high values of the ratio it decays as the inverse cube of the interlayer distance. For a sample confined between rigid substrates parallel to the layers, the interaction is greatly reduced. For a free-standing film the interaction may be enhanced if the surface tension is weak, but may be diminished if the surface tension is strong.

Calorimetric study of the nematic to smectic-Aand smectic-Ato smectic-Cphase transitions in liquid-crystal–aerosil dispersions

A high-resolution calorimetric study has been carried out on nanocolloidal dispersions of aerosils in the liquid crystal 4-n-pentylphenylthiol-4'-n-octyloxybenzoate (8S5) as a function of aerosil concentration and temperature spanning the smectic-C to nematic phases. Over this temperature range, this liquid crystal possesses two continuous XY phase transitions: a fluctuation-dominated nematic to smectic-A transition with alpha approximately alphaXY=-0.013 and a mean-field smectic-A to smectic-C transition. The effective critical character of the N-SmA transition remains unchanged over the entire range of the introduced quenched random disorder while the peak height and enthalpy can be well described by considering a cutoff length scale to the quasicritical fluctuations. The robust nature of the N-SmA transition in this system contrasts with cyanobiphenyl-aerosil systems and may be due to the mesogens being nonpolar and having a long nematic range. The character of the SmA-SmC transition changes gradually with increasing disorder but remains mean field like. The heat capacity maximum at the SmA-SmC transition scales as rho with an apparent evolution from tricritical to a simple mean-field step behavior. These results may be generally understood as a stiffening of the liquid crystal (both the nematic elasticity as well as the smectic layer compression modulus B) with silica density.

Behavior of the layer compression elastic modulus near, above, and below a smectic C?hexatic I critical point in binary mixtures

We present the first study of the layer compression modulus B carried out near, above and below the Smectic C-Hexatic I critical point in racemic mixtures of methylbutyl phenyl octylbiphenyl-carboxylate (8SI) and the octyloxy biphenyl analog (8OSI), at frequencies ranging from 0.2 Hz to 2 x 10(3) Hz. The behavior of B as a function of temperature shows a progressive evolution from a first order transition in 8SI to a continuous supercritical behavior in 8OSI. The latter is characterized by an increase in B, which appears above the transition, and which is followed by a leveling off when the temperature is decreased towards the transition. It is proposed that this behavior stems from the relaxation of the hexatic domains which are frozen in the frequency range studied. For the supercritical and near-critical compounds, B exhibits a small dip near the transition temperature, which is visible in the low frequency range only, indicating that the dynamics associated with the critical point is very slow. We also report measurements in the Crystal-J phase of the pure compounds, and show that 8SI behaves mechanically as a hexatic phase and 8OSI as a soft crystal phase.

Study of smectic elastomer films under uniaxial stress

We study the mechanical properties of free-standing films of smectic liquid crystalline elastomers. Macroscopically ordered elastomer films of submicrometer thickness are prepared from freely suspended smectic A polymer films by photo crosslinking. The deformation characteristics depend criticically on the sample composition, in particular on the density of mesogenic side chains at the siloxane backbone. In materials where the siloxane backbone is only partially substituted (dilute systems), a uniaxial stretching of the films in the layer plane is accompanied by a shrinkage of the smectic layers. This layer shrinkage is to only a minor extent achieved by the induction of a molecular tilt. We conclude that the layer compression modulus (enthalpic contribution to elasticity) in such materials is very weak. In materials with a fully substituted backbone (homopolymers), the smectic layer thickness is preserved under uniaxial stress in the layer planes.

Behavior of the layer compression modulus as a function of frequency near the nematic-smectic-A and re-entrant nematic-smectic-A phase transitions.

A progressive cross-over of the layer compression modulus B from a simple power law behavior to a saturation behavior when the frequency is increased from 1 Hz to 2 x 10(3) Hz is observed for the first time near the nematic-smectic-A and the re-entrant nematic-smectic-A phase transitions of a mixture of 4-cyano-4'-( n-hexyloxy)biphenyl and 4-cyano-4'-( n-octyloxy)biphenyl (6OCB-8OCB). This result shows that the saturation of B determined by second sound near the nematic-smectic-A phase transition of a similar mixture is dynamic in nature, and cannot be associated with the static saturation effect predicted by the dislocation loop model, as proposed previously.

Inter-lamellar interactions modulated by addition of guest components.

We have investigated the effects of a guest component (polymer or spherical colloidal particle) confined between flexible lamellar slits on the inter-lamellar interaction by means of a small-angle X-ray scattering technique and a neutron spin echo technique. The dominant interaction between flexible lamellar membranes without guest components is the Helfrich mechanism. The addition of a neutral polymer into the lamellar phase induces an attractive inter-lamellar interaction and finally destabilizes the lamellar phase. On the other hand, spherical colloidal particles confined between flexible lamellar membranes reduce the undulational fluctuations of lamellae and bring a repulsive inter-lamellar interaction. The behavior of the layer compression modulus of the lamellar membrane containing colloidal particles is well described by the entropical repulsive inter-lamellar interaction driven by steric hindrance.

Theory of layer structure in ferroelectric liquid crystal devices in applied electric fields.

We propose a model for the free energy of a ferroelectric liquid crystal formed by cooling a sample from the smectic-A phase between parallel substrates. Under these circumstances the smectic layers may deform into V-shaped structures known as chevrons. Application of a strong electric field causes the layers to return to a flat shape, but this can occur in a number of ways. In the model presented here, it is a parameter related to the layer compression modulus that is the principal factor in determining the nature of the field-induced transition from chevrons to flat layers. When this parameter is large, the transition is sudden, but when it is small the chevron first takes on a rounded form before flattening. At intermediate values the tip of the chevron first flattens, and then this flat region gradually grows to encompass the entire layer.

Undulation Properties of the Lamellar Phase of a Diblock Copolymer: SAXS Experiments

We report on X-ray scattering results on an oriented lamellar single crystal of a diblock copolymer melt of poly(dimethylsiloxane)-b-poly(ethylene propylene). From the Bragg peak position, q0, we calculate the temperature dependence of the lamellar period and show that it is in agreement with the values obtained using literature values of the Flory−Huggins parameter, χ. We observe the predicted diffuse scattering affecting the profile of the Bragg peak, which is related to the layer splay and compressional elasticity. We show that extremely small misalignments of the lamellar planes prevent a quantitative calculation of the layer compressibility modulus, B̄, and we explain this effect qualitatively using the mosaicity theory.