intermediate frequencies, T u (q) interpolates smoothly between these two limiting behaviours 12 .The behaviour seen in Fig. 2 is consistent with KTB dynamics, if we identify the crossover with T KTB of an isolated bilayer. Above T KTB , the conductivity is predicted to scale according to 13±15 :The scaling function S(q/) is constrained by the physics of the high-and low-frequency limits. As q= !`, S must approach i/q in order for j to assume its superconducting form, equation (1). At low frequencies, S approaches a real constant S 1 (0) which characterizes the d.c. conductivity of the normal state. By comparing the measured complex conductivity to equation (2), we can extract both the phase stiffness and correlation time at each temperature. To analyse the experimental data in terms of equation (2), we note that the phase angle of the complex conductivity, J [ tan 2 1 j 2 =j 1 , equals the phase angle of S(q/). Therefore J depends only on the single parameter , and is independent of T 0 u . With the appropriate choice of (T), all the measured values of J should collapse to a single curve when plotted as a function of the normalized frequency q/. Knowing (T), T 0 u is obtained from a collapse of the normalized conductivity magnitude, (~=k B T 0 v jjqj=j Q , to jSq=j. Figure 3 shows the collapse of the data to the phase angle and magnitude of S. As anticipated, S approaches a real constant in the limit q= ! 0, and approaches i/q as q= !`.When analysed further, the data reveal a con®rmation of thermal generation of vortices in the normal state. In the KTB picture we expect that the d.c. conductivity will equal k B T/n f D© 2 0 , which is thè¯u x-¯ow' conductivity of n f free vortices with quantized¯ux © 0 , and diffusivity D (ref. 16). Together with equation (2), this implies that is a linear function of n f , that is, 0 n f a vc =£, where a vc is the area of a vortex core, £ [ T=T 0 u is the reduced temperature, and 0 [ p 2 S 1 0D=a vc . Moreover, we expect that n f will be a thermally activated function, except for T very close to T KTB . The activation energy is simply Ck B T 0 u , where C is a non-universal constant of order unity. It follows that the¯uctuation frequency depends exponentially on the reciprocal of the reduced temperature, 0 =£exp 2 2C=£. The inset to Fig. 3 is a plot of log(£) versus 1/£ which shows that the exponential relation is observed over nearly four orders of magnitude. This is direct evidence that vanishing of phase coherence in our samples re¯ects the dynamics of thermally generated vortices. From the slope and intercept of a straight-line ®t we obtain C 2:23 and 0 1:14 3 10 14 s 2 1 .In Fig. 4 we present the behaviour of the bare stiffness and phasecorrelation time obtained from our measurement and modelling of j(q). The main panel contrasts T 0 u with the dynamical stiffness T u (q) measured at 150 and 400 GHz. The inset shows t as a function of temperature together with hatching that highlights the region where t ,~=k B T.The parameters displayed in Fig. 4 suggest that while phase ...

High-resolution calorimetric studies have been made of the liquid crystal phase transitions for several dispersions of 70-Å-diam silica spheres ͑aerosil͒ in octylcyanobiphenyl ͑8CB͒ as a function of silica density S. The excess specific heat peaks associated with the nematic-isotropic (N-I) and the nematic-smectic-A (N-SmA) transitions both exhibit shifts to lower temperatures, decreases in the specific heat maximum values, and decreases in the transition enthalpies as S is increased. Two distinct regimes of S-dependent behaviors are observed with a crossover between them at S Х0.1 g cm Ϫ3. For lower silica densities, sharp second-order C p peaks are observed at the N-SmA transitions, characterized by effective critical exponents that decrease monotonically with S from the pure 8CB value toward the three-dimensional XY value, and two closely spaced but distinct first-order C p features are observed at the N-I transition. For higher silica densities, both the N-SmA and the N-I transitions exhibit a single rounded C p peak, shifting in temperature and decreasing in total enthalpy in a manner similar to that observed in 8CBϩaerogel systems. Small angle x-ray scattering data are qualitatively aerogel-like and yield temperature-independent mass-fractal dimensionalities for aerosil aggregates that differ for samples with silica densities above and below the crossover density.

Three different water−alcohol cosolvent systems were used to assemble mesoporous molecular sieve silicas with wormhole framework structures (previously denoted HMS silicas) from an electrically neutral amine surfactant (S°) and a silicon alkoxide precursor (I°). The fundamental particle size and associated textural (interparticle) porosity of the disordered structures were correlated with the solubility of the surfactant in the water−alcohol cosolvents used for the S°I° assembly process. Polar cosolvents containing relatively low volume fractions of C n H2 n +1OH alcohols (n = 1−3) gave heterogeneous surfactant emulsions that assembled intergrown aggregates of small primary particles with high textural pore volumes (designated HMS−HTx). Conversely, three-dimensional, monolithic particles with little or no textural porosity (designated HMS−LTx) were formed from homogeneous surfactant solutions in lower polarity cosolvents. Aluminum substituted Al-HMS−HTx analogues with high textural porosity and improved framework accessibility also were shown to be much more efficient catalysts than Al-HMS−LTx or monolithic forms of hexagonal Al-MCM-41 for the sterically demanding condensed phase alkylation of 2,4-di-tert-butylphenol with cinnamyl alcohol. Transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) studies verified the textural differences between wormhole HMS and electrostatically assembled hexagonal MCM-41 and SBA-3 molecular sieves. Power law fits to the scattering data indicated a surface fractal (D s = 2.76) for HMS−HTx, consistent with rough surfaces. A second power law at lower-q indicated the formation of a mass fractal (D m = 1.83) consistent with branching of small fundamental particles. Hexagonal MCM-41 and SBA-3 silicas, on the other hand, exhibited scattering properties consistent with moderately rough surfaces (D s = 2.35 and 2.22, respectively) and large particle diameters (≫1 μm). HMS−LTx silicas showed little or no mass fractal character (D m = 2.87), and no surface fractal scattering.

High-resolution x-ray scattering studies of thin smectic-C (SmC) samples prepared between solid plates by cooling from the smectic-^ phase reveal a surprising "chevron" structure of tilted layers. This structure is formed as a response to the shrinking of the SmC layers while anchored to the solid plates. The layer tilt is independent of surface treatment. Our results provide fundamental new information on the structure and surface interactions of SmC layers and provide evidence for a new SmC defect.