High-resolution calorimetric study of the nematic to smectic-A transition in aligned liquid crystal-aerosil gels.

High-resolution ac calorimetry has been used to study the nematic to smectic- A (N-SmA) phase transition in the liquid crystal octylcyanobiphenyl (8CB) confined in aligned colloidal aerosil gels. A stable and robust nematic alignment was achieved by repeated thermal cycling of the samples in the presence of a strong uniform magnetic field. In some ways (such as transition temperature and integrated enthalpy), the dependence of the specific heat peak associated with the N-SmA transition on the aerosil density for aligned gels is consistent with that observed in unaligned (random) gel samples. However, a power-law analysis reveals that the behavior of the critical exponent alpha is quite different. For random gels, alpha varies gradually with aerosil density, whereas we find that alpha for aligned gels shifts abruptly to an XY -like value for the lowest aerosil density studied and remains essentially constant as the sil density increases. This aerosil density independence of alpha is consistent with the critical behavior of the smectic correlation lengths obtained from an x-ray scattering study of 8CB in aligned aerosil gels. The combined calorimetric and x-ray results indicate that the role of quenched randomness in aligned gels of 8CB+sils differs significantly from that in random gels.

Slow, nondiffusive dynamics in concentrated nanoemulsions.

Using multispeckle x-ray photon correlation spectroscopy, we have measured the slow, wave-vector-dependent dynamics of concentrated, disordered nanoemulsions composed of silicone oil droplets in water. The intermediate scattering function possesses a compressed exponential line shape and a relaxation time that varies inversely with wave vector. We interpret this dynamics as strain in response to local stress relaxation. The motion includes a transient component whose characteristic velocity decays exponentially with time following a mechanical perturbation of the nanoemulsions and a second component whose characteristic velocity is essentially independent of time. The steady-state characteristic velocity is surprisingly insensitive to the droplet volume fraction in the concentrated regime, indicating that the strain motion is only weakly dependent on the droplet-droplet interactions.

Wrinkling of a bilayer membrane.

The buckling of elastic bodies is a common phenomenon in the mechanics of solids. Wrinkling of membranes can often be interpreted as buckling under constraints that prohibit large-amplitude deformation. We present a combination of analytic calculations, experiments, and simulations to understand wrinkling patterns generated in a bilayer membrane. The model membrane is composed of a flexible spherical shell that is under tension and that is circumscribed by a stiff, essentially incompressible strip with bending modulus B . When the tension is reduced sufficiently to a value sigma , the strip forms wrinkles with a uniform wavelength found theoretically and experimentally to be lambda=2pi(B/sigma)(1/3). Defects in this pattern appear for rapid changes in tension. Comparison between experiment and simulation further shows that, with larger reduction of tension, a second generation of wrinkles with longer wavelength appears only when B is sufficiently small.

Microscopic dynamics of recovery in sheared depletion gels.

We report x-ray photon correlation spectroscopy and diffusing wave spectroscopy studies of depletion gels formed from nanoscale silica colloids in solutions of nonabsorbing polymer following the cessation of shear. The two techniques provide a quantitatively coherent picture of the dynamics as ballistic or convective motion of colloidal clusters whose internal motion is arrested. While the dynamics possesses features characteristic of nonergodic soft solids, including a relaxation time that grows linearly with the time since shear, comparison with behavior of quenched supercooled liquids indicates that this evolution is not directly related to traditional aging phenomena in glasses.

Phase behavior and local dynamics of concentrated triblock copolymer micelles.

We report a neutron-scattering study to characterize the ordering and local dynamics of spherical micelles formed by the triblock copolymer polyethylene oxide (PEO)--polypropylene oxide (PPO)--polyethylene oxide (Pluronic) in aqueous solution. The study focuses on two Pluronic species, F68 and F108, that have the same weight fraction of PEO but that differ in chain length by approximately a factor of 2. At sufficiently high concentration, both species undergo a sequence of phase changes with increasing temperature from dissolved chains to micelles with liquid-like order to a cubic crystal phase and finally back to a micelle liquid phase. A comparison of the phase diagrams constructed from small-angle neutron scattering indicates that crystallization is suppressed for shorter chain micelles due to fluctuation effects. The intermediate scattering function I(Q,t)I(Q,0) determined by neutron spin echo displays a line shape with two distinct relaxations. Comparisons between I(Q,t)I(Q,0) for fully hydrogenated F68 chains in D2O and for F68 with deuterated PEO blocks reveal that the slower relaxation corresponds to Rouse modes of the PPO segments in the concentrated micelle cores. The faster relaxation is identified with longitudinal diffusive modes in the PEO corona characteristic of a polymer brush.

Evolution of particle-scale dynamics in an aging clay suspension.

Multispeckle x-ray photon correlation spectroscopy was employed to characterize the slow dynamics of a suspension of highly charged, nanometer-sized disks. At wave vectors q corresponding to interparticle length scales, the dynamic structure factor follows a form f(q,t) approximately exp([-(t/tau)(beta)], where beta approximately 1.5. The relaxation time tau increases with the sample age t(a) approximately as tau approximately t(1.8)(a) and decreases with q as tau approximately q(-1). Such behavior is consistent with models that describe the dynamics in disordered elastic media in terms of strain from random, local structural rearrangements. The measured amplitude of f(q,t) varies with q in a manner that implies caged particle motion. The decrease in the range of this motion and an increase in suspension conductivity with increasing t(a) indicate a growth in interparticle repulsion as the mechanism for internal stress development implied by these models.

Elastic torque and the levitation of metal wires by a nematic liquid crystal.

Anisotropic particles suspended in a nematic liquid crystal disturb the alignment of the liquid crystal molecules and experience small forces that depend on the particles' orientation. We have measured these forces using magnetic nanowires. The torque on a wire and its orientation-dependent repulsion from a flat surface are quantitatively consistent with theoretical predictions based on the elastic properties of the liquid crystal. These forces can also be used to manipulate submicrometer-scale particles. We show that controlled spatial variations in the liquid crystal's alignment convert the torque on a wire to a translational force that levitates the wire to a specified height.

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.

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.

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.

Evidence for Glass and Spin-Glass Phase Transitions From the Dynamic Susceptibility.

We present evidence that there is a phase transition, with a diverging static susceptibility, underlying the transformation of a liquid into a glass. The dielectric susceptibility, at frequencies above its characteristic value, shows a power-law tail extending over many decades to higher frequencies. An extrapolation of this behavior to the temperature where the dynamics becomes arrested indicates a diverging susceptibility. We present evidence for analogous behavior in the magnetic susceptibility of a paramagnet approaching the spin-glass transition. The similarity of the response in these two glassy systems suggests that some conventional lore, such as that the spin glass shows evidence for a diverging correlation length only in a nonlinear but not in the linear susceptibility, may be invalid.