Electron-diffraction study of free-standing liquid-crystal films

Observation of a Dynamical Sliding Phase Superfluid with P-Band Bosons

Sliding phases have been long sought after in the context of coupled XY models, as they are of relevance to various many-body systems such as layered superconductors, freestanding liquid-crystal films, and cationic lipid-DNA complexes. Here we report an observation of a dynamical sliding phase superfluid that emerges in a nonequilibrium setting from the quantum dynamics of a three-dimensional ultracold atomic gas loaded into the P band of a one-dimensional optical lattice. A shortcut loading method is used to transfer atoms into the P band at zero quasimomentum within a very short time duration. The system can be viewed as a series of "pancake"-shaped atomic samples. For this far-out-of-equilibrium system, we find an intermediate time window with a lifetime around tens of milliseconds, where the atomic ensemble exhibits robust superfluid phase coherence in the pancake directions, but no coherence in the lattice direction, which implies a dynamical sliding phase superfluid. The emergence of the sliding phase is attributed to a mechanism of cross-dimensional energy transfer in our proposed phenomenological theory, which is consistent with experimental measurements. This experiment potentially opens up a novel venue to search for exotic dynamical phases by creating high-band excitations in optical lattices.

Monolayer-to-thin-film transition in supramolecular assemblies: the role of topological protection

The ability to control the transition from a two-dimensional (2D) monolayer to the three-dimensional (3D) molecular structure in the growth of organic layers on surfaces is essential for the production of functional thin films and devices. This has, however, proved to be extremely challenging, starting from the currently limited ability to attain a molecular scale characterization of this transition. Here, through innovative application of low-dose electron diffraction and aberration-corrected transmission electron microscopy (acTEM), combined with scanning tunneling microscopy (STM), we reveal the structural changes occurring as film thickness is increased from monolayer to tens of nanometers for supramolecular assembly of two prototypical benzenecarboxylic acids - terephthalic acid (TPA) and trimesic acid (TMA) - on graphene. The intermolecular hydrogen bonding in these molecules is similar and both form well-ordered monolayers on graphene, but their structural transitions with film thickness are very different. While the structure of TPA thin films varies continuously towards the 3D lattice, TMA retains its planar monolayer structure up to a critical thickness, after which a transition to a polycrystalline film occurs. These distinctive structural evolutions can be rationalized in terms of the topological differences in the 3D crystallography of the two molecules. The templated 2D structure of TPA can smoothly map to its 3D structure through continuous molecular tilting within the unit cell, whilst the 3D structure of TMA is topologically distinct from its 2D form, so that only an abrupt transition is possible. The concept of topological protection of the 2D structure gives a new tool for the molecular design of nanostructured films.

Kosterlitz-Thouless physics: a review of key issues

This article reviews, from a very personal point of view, the origins and the early work on transitions driven by topological defects such as vortices in the two dimensional planar rotor model and in (4)Helium films and dislocations and disclinations in 2D crystals. I cover the early papers with David Thouless and describe the important insights but also the errors and oversights since corrected by other workers. I then describe some of the experimental verifications of the theory and some numerical simulations. Finally applications to superconducting arrays of Josephson junctions and to recent cold atom experiments are described.

Liquid crystal quenched orientational disorder at an AFM-scribed alignment surface

A polyimide substrate was scribed using the stylus of an atomic force microscope, then covered with a nematic liquid crystal. The fiber from a near field scanning optical microscope was immersed into the liquid crystal and rastered approximately 80 nm above the surface, thereby obviating smearing effects that occur in thicker samples. By appropriate averaging of multiple data sets, a histogram of the "frozen-in" director deviation Δφ from the average easy axis was obtained, having a full-width-half-maximum of ∼0.02 rad. Additionally, the spatial autocorrelation function of Δφ was extracted, where the primary correlation length was found to be comparable to, but larger than, the liquid crystal's extrapolation length. A secondary characteristic length scale of a few μm was observed, and is thought to be an artifact due to material ejection during the scribing process. Our results demonstrate the utility of nanoscale imaging of the interface behavior inside the liquid crystal.

Sixfold bond orientational properties of a model liquid crystal in the dimensional crossover of B phases: A computer simulation study

A wide range of NPT simulations of a bead necklace liquid crystal model in the crystal B, smectic B, smectic A, and nematic phases have been performed. Systems with up to 21 600 molecules have been studied to observe the behavior of slowly decaying spatial correlation functions. The pair correlation function and its in-plane restriction are consistent with a crystalline phase made of independent two-dimensional crystalline layers. Smectic B phase is studied by the bond orientational pair correlation functions g(6) and its extension g(6ext). The first reaches a constant value, which seems to rule out a classical hexatic phase. The latter shows a power-law decay within the layers: its typical decay exponent (eta(6ext)) is evaluated. Relationships between multiple harmonics of the C(6n) order parameter have been evaluated through the whole range of existence of B phases (crystalline and smectic): the extension to the crystalline phase holds and provides an excellent fit of the simulation data.

Multiple electron diffraction and two-dimensional crystalline order in liquid-crystal thin films

Electron diffraction in freestanding thin films in the crystal-B phase reveals extensive multiple diffraction in films of 14S5 but not of 4O.8, suggesting an important difference in the structural order in these films despite the similarities in their positional correlations found in earlier experiments. The result in a two-layer 14S5 film indicates surprisingly that secondary diffraction can occur in a crystal with only pseudo-long-range positional order.

Two-stage surface freezing of a single top layer in a smectic-A membrane

The crystallization of a single liquid top layer of smectic membranes of the compound 4O.8 has been studied with grazing-incidence x-ray diffraction. As this process takes place in two steps, involving an intermediate hexatic smectic-B layer before the final crystalline-B surface structure is reached, it provides a model for melting in two dimensions. The positional order has been investigated quantitatively by measuring the scattering profiles and the associated correlation lengths. The surface liquid-hexatic phase transition is found to be continuous, while the hexatic-crystal transition is weakly first order with an abrupt change of the in-plane positional correlations. The surface phase transitions do not modify the liquid in-plane structure of the interior layers.

Direct layer-by-layer freezing of a smectic liquid-crystal surface into the crystalline phase

Electron diffraction and optical reflectivity have provided the direct confirmation of the existence of layer-by-layer surface transitions from the smectic-A immediately to the crystal-B phase in a liquid-crystal material, without going through an intermediate hexatic phase. The molecular interactions are found to be through retarded van der Waals forces. Our results suggest that a smectic-A film can transform into a crystal-B through three possible scenarios.

Structural characterization of surface hexatic behavior in free-standing 4O.8 liquid-crystal films

Electron diffraction in free-standing liquid-crystal films of N-(4-n-butoxybenzylidene)-4-n-octylaniline between 3 and 12 molecular layers thick reveals the unusual occurrence of the smectic-A' phase, a highly correlated isotropic liquid, on the surface of smectic-A films. The surface smectic-A-smectic-A' transition is found to be first order. Surprisingly, the temperature range of the subsequent surface hexatic-B phase is reduced with decreasing film thickness.

Crystalline transitions in free-standing films of 4-n-heptyloxybenzylidene-4-n-heptylaniline

Free-standing films of 4-n-heptyloxybenzylidene-4-n-heptylaniline are known to exhibit multiple smectic-I surface layers in the presence of a smectic-A interior. The phase transitions leading to the crystallization of these films have been studied using electron diffraction. Our data are consistent with the scenario of the smectic-I surface layers first developing a crystal-B outermost layer before transforming entirely into the crystal-B phase, to be followed by the freezing of the smectic-A interior. The adjacent crystal-B and smectic-I layers show evidence of orientational epitaxy.

Refusing to twist: demonstration of a line hexatic phase in DNA liquid crystals

We report conclusive high resolution small angle x-ray scattering evidence that long DNA fragments form an untwisted line hexatic phase between the cholesteric and the crystalline phases. The line hexatic phase is a liquid-crystalline phase with long-range hexagonal bond-orientational order, long-range nematic order, but liquidlike, i.e., short-range, positional order. So far, it has not been seen in any other three dimensional system. By line-shape analysis of x-ray scattering data we found that positional order decreases when the line hexatic phase is compressed. We suggest that such anomalous behavior is a result of the chiral nature of DNA molecules.

Reaction diffusion models in one dimension with disorder

We study a large class of one-dimensional reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g., of several species) undergo diffusion with random local bias (Sinai model) and may react upon meeting. We obtain a detailed description of the asymptotic states (i.e., attractive fixed points of the RSRG), such as the large time decay of the density of each specie, their associated universal amplitudes, and the spatial distribution of particles. We also derive the spectrum of nontrivial exponents which characterize the convergence towards the asymptotic states. For reactions which lead to several possible asymptotic states separated by unstable fixed points, we analyze the dynamical phase diagram and obtain the critical exponents characterizing the transitions. We also obtain a detailed characterization of the persistence properties for single particles as well as more complex patterns. We compute the decay exponents for the probability of no crossing of a given point by, respectively, the single particle trajectories (theta) or the thermally averaged packets (theta). The generalized persistence exponents associated to n crossings are also obtained. Specifying to the process A+A--> or A with probabilities (r,1-r), we compute exactly the exponents delta(r) and psi(r) characterizing the survival up to time t of a domain without any merging or with mergings, respectively, and the exponents deltaA(r) and psiA(r) characterizing the survival up to time t of a particle A without any coalescence or with coalescences, respectively. theta, psi, and delta obey hypergeometric equations and are numerically surprisingly close to pure system exponents (though associated to a completely different diffusion length). The effect of additional disorder in the reaction rates, as well as some open questions, are also discussed.

Multiple-step melting in two-dimensional hexatic liquid-crystal films

An unexpected three-stage melting transition has been observed in two-dimensional (2D) free-standing liquid-crystal films by in situ electron-diffraction and optical-reflectivity measurements. These data suggest the existence of two phases between the 2D solid and liquid: a hexatic phase and, at a higher temperature, an intermediate liquid phase with hexatic-like positional correlations ( approximately 40 angstroms) but no long-range orientational order. Previous high-resolution heat-capacity measurements have revealed a divergent-like anomaly at the hexatic-liquid transition that sharply contradicts the predictions of 2D melting theories. The observation of an intermediate isotropic phase may alter our understanding of 2D melting and lead to reconciliation between current experiments and theories.

Liquid to hexatic to crystalline order in Langmuir-Blodgett films

Atomic force microscope images of zinc arachidate (ZnA2) Langmuir-Blodgett films show that three- and five-layer films are "hexatic," with long-range bond-orientational order and short-range positional correlations of three to five lattice repeats. The monolayer in contact with the substrate is disordered. Films of seven or more layers of ZnA2 are crystalline. A population of dislocations, most likely originating at the substrate, disrupts the positional but not the orientational order of the lattice, leading to hexatic layers intermediate between crystal and liquid. The influence of the substrate propagates farther into ZnA2 films than into cadmium arachidate films because the molecular cohesion is much weaker in ZnA2 than in cadmium arachidate, as evidenced by a less dense molecular packing.

Molecular organization in phospholipid monolayer domains by correlative fluorescence microscopy and electron diffraction

Lipid monolayer is a half leaflet model for lipid bilayer, which forms the basis of biological membranes. Within a certain range of surface area per molecular of phospholipid monolayers at the air-water interface, where the compressibility was nearly infinite, two phases with different molecular packings were observable by fluorescence microscopy. Mixed-phase monolayers of L-1,2-dipalmitoyl-N-monomethyl-3-phosphatidylethanolamine [DP(Me)PE] or L-1,2-dipalmitoyl-N-dimethyl-3-phosphatidyl-ethanolamine [DP(Me)2PE] were deposited on marker grids coated with Formvar films. The molecular organization in the dark and bright fluorescent areas on the grids was investigated by low dose, selected area electron diffraction. Sharp reflection arcs, at a spacing of 4.2A and arranged in a hexagon pattern, were detected from dark domains of both lipids. A diffuse reflection ring at a spacing of 4.6A was derived from the bright background areas. Diffraction patterns were obtained from neighboring areas along selected dark domains of both lipids. The orientations of diffraction patterns from areas along smooth and curving boundaries of DP(Me)2PE domains were found to turn with the boundaries. In the branching domains of DP(Me)PE, the orientations of diffraction patterns indicated that the branches were formed by twinning. Electron diffraction thus provides an unique way to sample the local molecular packing order and orientation within individual domains in phospholipid monolayers.

Electron diffraction studies of molecular ordering and orientation in phospholipid monolayer domains

The molecular order and orientation of phase separated domains in monolayers of DP(Me)PE and DP(Me)2PE were determined by electron diffraction. Dark and bright fluorescent domains at the air-water interface were observed by fluorescence microscopy. The monolayers were transferred to Formvar coated electron microscope grids for electron diffraction studies. The positions of domains on the marker grids were recorded in fluorescence micrographs, which were used as guide maps to locate these domains in the electron microscope. Selected area electron diffraction patterns were obtained from predetermined areas within and outside the dark domains. Sharp hexagonal diffraction patterns were recorded from dark domains, and diffuse diffraction rings from bright areas in between dark domains. The diffraction results indicated that the dark domains and bright areas were comprised of lipid molecules in solid and fluid states, respectively. The orientation of diffraction patterns from adjacent locations within a dark domains changed gradually, indicating a continuous bending of the molecular packing lattice vector within these domains. Orientation directors in U-shaped DP(Me)2PE domains followed the turn of the arm; no vortex nor branching was indicated by electron diffraction. Directors branching from the "stem" of highly invaginated DP(Me)PE domains usually occurred at twinning angles of n pi/3 from the stem director, which would minimize packing defects in the development of thinner branches. Electron diffraction from local areas of individual domains proved that dark fluorescent domains were solid ones, and that pseudo-long range order existed in these solid domains.

Electron diffraction and diffraction contrast imaging of thin organic films

The applications of electron diffraction and diffraction contrast electron microscopy with which to study the structure and dynamics of organic thin films are discussed. The techniques of making thin film deposits on substrates and of forming free-standing thin films over holes on the substrate are described. Selected area electron diffraction and diffraction contrast imaging techniques for thin film studies are elaborated, and examples are given. Methods to reduce radiation damage and environmental protection of the thin film specimen are outlined. The interpretation of electron diffraction and imaging data is given for three cases: 1) The effects of film tilting and molecular tilting (with respect to the film plane) are examined. 2) The detection of phase transition is illustrated. 3) The use of labels to mark film domains is shown together with the measurement of dynamic movement.