Continuous Crystallization in Hexagonally-Ordered Materials

We demonstrate that the phase transition from columnar-hexagonal liquid crystal to hexagonal-crystalline solid falls into an unusual universality class, which in three-dimensional allows for both discontinuous transitions as well as continuous transitions, characterized by a single set of exponents. We show by a renormalization group calculation (to first order in $\epsilon = 4-d$) that the critical exponents of the continuous transition are precisely those of the XY model, which gives rise to a continuous evolution of elastic moduli. Although the fixed points of the present model are found to be identical to the XY model, the elastic compliance to deformations in the plane of hexagonal order, $\mu$, is nonetheless shown to critically influence the crystallization transition, with the continuous transition being driven to first order by fluctuations as the in plane response grows weaker, $\mu \to 0$.Comment: 4 pages, 2 figures (revised version

Unified Hydrodynamic Theory for Crystals, Liquid Crystals, and Normal Fluids

A unified hydrodynamic theory is presented that is appropriate for crystals; smectic, cholesteric, and nematic liquid crystals; glasses; and normal fluids. In the theory, the increased spatial degeneracy as the system progresses from crystalline and mesomorphic phases to the isotropic fluid phase is marked by successive reductions in the number of firstorder elastic constants and in the number of transport coefficients. Distinction between local lattice dilations and local mass changes, and recognition of processes like vacancy diffusion that this difference makes possible, are crucial for understanding the connection between theories in different phases. Formulas are derived that give the number of hydrodynamic modes and the frequencies, lifetimes, and intensities of these modes in all of the above systems. In the nematic and cholesteric phases, the results agree with some found previously. In more complex systems, they are new. An attempt is made to explain the differences between the present hydrodynamic theory and other phenomenological proposals.Engineering and Applied Science

Surface Induced Order in Liquid Metals and Binary Alloys

Measurements of the surface x-ray scattering from several pure liquid metals (Hg, Ga, and In) and from three alloys (Ga-Bi, Bi-In, and K-Na) with different heteroatomic chemical interactions in the bulk phase are reviewed. Surface-induced layering is found for each elemental liquid metal. The surface structure of the K-Na alloy resembles that of an elemental liquid metal. Bi-In displays pair formation at the surface. Surface segregation and a wetting film are found for Ga-Bi.Comment: 10 pages, 3 fig, published in Journal of Physics: Condensed Matte

Sliding Phases in XY-Models, Crystals, and Cationic Lipid-DNA Complexes

We predict the existence of a totally new class of phases in weakly coupled, three-dimensional stacks of two-dimensional (2D) XY-models. These ``sliding phases'' behave essentially like decoupled, independent 2D XY-models with precisely zero free energy cost associated with rotating spins in one layer relative to those in neighboring layers. As a result, the two-point spin correlation function decays algebraically with in-plane separation. Our results, which contradict past studies because we include higher-gradient couplings between layers, also apply to crystals and may explain recently observed behavior in cationic lipid-DNA complexes.Comment: 4 pages of double column text in REVTEX format and 1 postscript figur

X-Ray Grazing Incidence Diffraction from Alkylsiloxane Monolayers on Silicon Wafers

X‐ray reflection (both specular and off‐specular) and grazing incidence diffraction (GID) have been used to study the structure of alkylsiloxane monolayers ($n‐C_{18}H_{37}SiO_{1.5}$) formed by self‐assembly from solution on silicon wafers. GID studies of complete monolayers reveal a single ring of scattering associated with the monolayer. The Lorentzian line shape of this ring indicates that the film is characterized by liquidlike order, with a typical translational correlation length of about 45 Å. The thermal coefficient of expansion of the monolayer, as determined from the GID peak position, is approximately equal to the value for liquid n‐alkanes. Upon either heating or cooling, the monolayer correlation lengths decrease, suggesting that the differential thermal‐expansion coefficients of the film and substrate figure prominently in thermal changes of the molecular ordering. GID data for incomplete monolayers also reveal a single ring of scattering associated with the monolayer. While both the translational correlation lengths and integrated peak areas are significantly reduced relative to complete monolayers, the peak positions of the incomplete monolayers are comparable to those of complete monolayers. Given the lower average areal density of incomplete monolayers, this finding implies that incomplete monolayers are inhomogeneous.Engineering and Applied Science

Capillary Filling of Anodized Alumina Nanopore Arrays

The filling behavior of a room temperature solvent, perfluoromethylcyclohexane, in approximately 20 nm nanoporous alumina membranes was investigated in situ with small angle x-ray scattering. Adsorption in the pores was controlled reversibly by varying the chemical potential between the sample and a liquid reservoir via a thermal offset, $\Delta$T. The system exhibited a pronounced hysteretic capillary filling transition as liquid was condensed into the nanopores. These results are compared with Kelvin-Cohan theory, with a modified Derjaguin approximation, as well as with predictions by Cole and Saam.Comment: 4 pages, 3 figures, pre-proof

Wetting Behavior at the Free Surface of a Liquid Gallium–Bismuth Alloy: An X-ray Reflectivity Study Close to the Bulk Monotectic Point

We present X-ray reflectivity measurements from the free surface of a liquid gallium–bismuth alloy (Ga–Bi) in the temperature range close to the bulk monotectic temperature $T_{mono}$=222$^\circ$C. Our measurements indicate a continuous formation of a thick wetting film at the free surface of the binary system driven by the first order transition in the bulk at the monotectic point. We show that the behavior observed is that of a complete wetting at a tetra point of solid–liquid–liquid–vapor coexistence.Engineering and Applied Science