Long-range Bond-orientational Order Research Articles

Green-Kubo stress correlation function at the atomic scale and a long-range bond-orientational ordering in a model liquid

Recently there have been several considerations by different authors of viscosity and the Green-Kubo stress correlation function from the microscopic perspective. In most of these and earlier works the atomic level stress is the minimal element of stress. It is also possible to consider, for pairwise interaction potentials, as the minimal elements of stress, the stress tensors associated with the pairs of interacting particles. From this perspective, the atomic level stress is not the minimal stress element, but a sum of all pair stress elements in which involved a selected particle. In this paper, we consider the Green-Kubo stress correlation function from a microscopic perspective using the stress tensors of interacting pairs as the basic stress elements. The obtained results show the presence of a long-range bond-orientational order in the studied model liquid and naturally elucidate the connection of the bond-orientational order with viscosity. It turns out that the long-range bond-orientational order is more clearly expressed in the pairs' stress correlation function than in the atomic-stress correlation function. On the other hand, previously observed stress waves are much better expressed in the atomic-stress correlation functions. We also address the close connection of our approach with the previous bond-orientational order considerations. Finally, we consider the probability distributions for the bond-stress and atomic-stress correlation products at selected distances. The character of the obtained probability distributions raises questions about the meaning of the average correlation functions at large distances.

CdSe nanoparticles dispersed in ferroelectric smectic liquid crystals: Effects upon the smectic order and the smectic-Ato chiral smectic-Cphase transition

Spherical CdSe nanoparticles, surface-treated with oleylamine and tri-octylphosphine, dispersed in ferroelectric liquid crystals, can efficiently target disclination lines, substantially altering the macroscopic properties of the host compound. Here we present an ac calorimetry and x-ray diffraction study demonstrating that for a large range of nanoparticle concentrations the smectic-A layer thickness increases monotonically. This provides evidence for enhanced accumulation of nanoparticles at the smectic layers. Our results for the Smectic-A (SmA) to chiral smectic-C (SmC) phase transition of the liquid crystal S-(+)4-(2'-methylbutyl)phenyl-4'-n-octylbiphenyl-4-carboxylate (CE8) reveal that the character of the transition is profoundly changed as a function of the nanoparticle concentration. Large transition temperature shifts are recorded. Moreover, the heat-capacity peaks exhibit a crossover trend to a step-like anomaly. This behavior may be linked to the weakening of the SmA and SmC order parameter coupling responsible for the observed near-tricritical, mean-field character of the transition in bulk CE8. At lower temperatures, the presence of nanoparticles disrupts the phase sequence involving the tilted hexatic phases most likely by obstructing the establishment of long-range bond-orientational order.

Can elemental bismuth be a liquid crystal?

A number of anomalies have been reported in molten Bi, including a first-order liquid–liquid transition at 1010 K and ambient pressure, which is irreversible at cooling rates of several degrees per minute. An interpretation of these effects as due to long-range bond-orientational order is suggested. Significant evidence for directionality in liquid Bi, albeit only at temperatures close to melting, is available in experiments made circa 1930. Further experimentation is called for.

Observation of a Hexatic Columnar Liquid Crystal of Polydisperse Colloidal Disks

We report the observation of a new type of columnar liquid crystal phase, which is formed by thin hard colloidal disks in a dense suspension. High-resolution small-angle x-ray diffraction reveals a combination of long-range bond-orientational order and short-range translational order between the columns, the hallmark of the hexatic phase. Our results imply that geometric frustration related to the size polydispersity of the particles destroys long-range translational order and therefore promotes the formation of this novel phase.

Epitaxial Film Growth of Au–Al Alloy on a Quasiperiodic Surface of Icosahedral Al72Pd19.5Mn8.5

We have found that an epitaxial film of Au–Al alloy can be formed on a quasiperiodic surface of icosahedral Al72Pd19.5Mn8.5. Depositions of Au onto the quasiperiodic surface, which is perpendicular to one of the fivefold axes of Al72Pd19.5Mn8.5, were attempted in order to create a quasicrystal of a single element as an epitaxial film. Although the desired film was not obtained on the clean surface, an ordered layer of Au–Al alloy with icosahedral symmetry was formed in the presence of predeposited In, which worked as a surfactant. X-ray photoelectron diffraction (XPD) images for Au 4f and Al 2s emissions from the ordered layer indicate clear fivefold symmetric patterns which are coherent with the symmetry of the substrate. In addition, symmetric elements specific to the icosahedral symmetry are clearly recognized in these patterns, indicating that both Au and Al atoms are located in an icosahedral environment with long-range bond-orientational order.

Layer-Dependent Surface-Induced Tilt, Hexatic, and Positional Orders in Free-Standing 7O.7 Films

Electron diffraction in free-standing films of 4-n-heptyloxybenzylidene-4-n-heptylaniline of up to 25 molecular layers has revealed the coexistence, as a function of distance from the surface, of three distinct phases: an outermost smectic-I layer, several layers of a middle phase, and a smectic-A interior. The middle phase is an unusual highly-correlated tilted liquid, with hexaticlike positional correlations but no long-range bond-orientational order, which transforms to the smectic-I at a lower temperature. The discovery of this unusual middle phase also represents the possibility of a novel layer-dependent two-stage tilt-induced surface-freezing transition.

Helix configurations in chiral hexatic liquid crystals

In the hexatic-${B}^{*}$ phase the bonds defined by the long-range bond-orientational order are spiraling about the axis normal to the smectic layers. Apart from the bond ordering for the mass centers, a helical alignment of the molecular long axes characterized by a director field exists in some hexatic phases with tilted molecules. A continuum elastic distortion theory of liquid crystals predicts the existence of two possible configurations. If the commensurate configuration is stable, the director and the bond field are locked together, forming a common helix for both degrees of freedom. In the incommensurate state the director alignment differs from the alignment of the bonds so that two different helices occur. A phase diagram is proposed that includes three commensurate phases ${I}^{*},$${F}^{*},$${L}^{*}$ and the incommensurate state. The incommensurate state becomes stable if the coupling between the director and the bond field is sufficiently small.

Bond orientational order, molecular motion, and free energy of high-density DNA mesophases.

By equilibrating condensed DNA arrays against reservoirs of known osmotic stress and examining them with several structural probes, it has been possible to achieve a detailed thermodynamic and structural characterization of the change between two distinct regions on the liquid-crystalline phase diagram: (i) a higher density hexagonally packed region with long-range bond orientational order in the plane perpendicular to the average molecular direction and (ii) a lower density cholesteric region with fluid-like positional order. X-ray scattering on highly ordered DNA arrays at high density and with the helical axis oriented parallel to the incoming beam showed a sixfold azimuthal modulation of the first-order diffraction peak that reflects the macroscopic bond-orientational order. Transition to the less-dense cholesteric phase through osmotically controlled swelling shows the loss of this bond orientational order, which had been expected from the change in optical birefringence patterns and which is consistent with a rapid onset of molecular positional disorder. This change in order was previously inferred from intermolecular force measurements and is now confirmed by 31P NMR. Controlled reversible swelling and compaction under osmotic stress, spanning a range of densities between approximately 120 mg/ml to approximately 600 mg/ml, allow measurement of the free-energy changes throughout each phase and at the phase transition, essential information for theories of liquid-crystalline states.

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.

Observation of bond orientational order in floating and transferred monolayers with Brewster angle microscopy

Brewster angle microscopy facilitates the observation of optical anisotropy in monolayers and multilayers of long-chain amphiphilic molecules. With new model calculations based on the 4 × 4 matrix formulation of Berreman we were able to distinguish between optical anisotropy induced by chain tilt and that caused by orthorhombic lattices. Thus long-range bond orientational order in monolayers and multilayers in a range of 100 microm could be identified.

Bond-orientational order in liquid Si

We study bond-orientational order in liquid Si via Monte Carlo simulation in conjunction with empirical two- and three-body potentials of the form proposed by Stillinger and Weber. Bond-orientational order (BOO) is described in terms of combinations of spherical harmonic functions. Liquid Si is found to have pronounced short-range BOO corresponding to l=3, as expected for a structure with local tetrahedral order. No long-range BOO is found either in the equilibrium or the supercooled liquid. When the three-body potential is artificially removed, the tetrahedral bond-orientation order disappears and the liquid assumes a close-packed structure.

Observation of bond-orientational order in the incommensurate fluid phase of potassium chemisorbed on nickel (111).

Low-energy electron diffraction measurements for incommensurate potassium chemisorbed on Ni(111) indicate that at coverages between 0.17 and 0.22, the overlayer disorders into a fluid phase which has long-range bond-orientational order. The transition temperature depends on the mean density of the overlayer and varies from approximately 130 K at 0.17 monolayers to 230 K at 0.21 monolayers. The diffraction data for this orientationally ordered phase are consistent with the predictions made by the Kosterlitz-Thouless-Halperin-Nelson-Young theory for the intermediate hexatic phase in two-dimensional melting, but substrate effects or other intrinsic effects cannot be ruled out as the source of the orientational order. The orientationally ordered fluid exists over a very wide temperature range, and the transition is reversible and apparently continuous. Bond-orientational order is still observed as high as 50 K above the onset of the transition; an isotropic fluid is never observed at these coverages.

Faceting in bond-oriented systems with icosahedral and decagonal symmetry.

The recent discoveries of large facets in Al-Li-Cu and other icosahedral quasicrystals, as well as the observation of spatial disorder in these systems, show that disordered systems with long-range bond-orientational order can have growth facets. A fundamental question which naturally arises is whether such systems have equilibrium facets. In this paper, we study the conditions under which a perfect bond-oriented system can facet at T=0. The T=0 equilibrium shapes of bond-oriented systems with icosahedral and decagonal bond-orientational order are discussed. An explicit example is presented to show that disordered systems can have equilibrium facets at T=0. We also give detailed derivation of the surface energy of quasicrystals.

Disclinations in quasicrystals.

The most significant feature in the transition from the quasicrystalline to the amorphous state is the loss of long-range bond-orientational order. Disclinations are candidates for elementary excitations which destroy angular correlations. Generalizing the topological defect classification, we investigate point singularities in two-dimensional pentagonal quasicrystals and construct disclinations, dislocations, and disclination dipoles.

Evidence for smectic order in a fluid of hard parallel spherocylinders.

We present Monte Carlo simulations on systems of parallel spherocylinders with length-to-width ratios $\frac{L}{D}$ between 0.25 and 5. We have determined the solid-liquid coexistence points in these systems by computing the absolute free energy of the solid and fluid phases. In addition we find that for $\frac{L}{D}>0.5$ a thermodynamically stable smectic phase is formed at densities well below the thermodynamic melting point. The transition from nematic to smectic appears to be continuous. We find no evidence for long-range bond-orientational order in the smectic phase.

Two-Dimensional Order in Liquid Crystals: a Phenomenological Approach

The two-dimensional ordering reported for a number of smectic and discotic phases is discussed in the framework of the Landau theory. It is shown that, within a phenomenological approach, distinction should be made between the longrange bond-orientational order, the in-plane positional order, and the orientational (tilting) ordering of the molecules. Accordingly, the configuration of the smectic liquid crystal phases BH, C, F, and smectic crystal phases I, J, G, K, E are shown to be related to irreducible degrees of freedom of definite parent smectic phases. Along the same line, discotic phases are shown to be induced by specific irreducible representations of the nematic phase.

Characterization of the Hexatic B and Crystal B phases by Optical Microscopy

Abstract Recent investigations concerning the structure of the B Phase have unearthed a variety of packing arrangements of the molecular layers for this semctic modification. Two general structures have been discovered; one in which the B Phase has three-dimensional crystalline order (crystal B), and one that is characterized by short-range in-plane positional ordering of the constituent molecules, and long-range bond orientational order, both within and between the layers (heatic B). In this present study n-hexyl 4′-n-pentyloxybiphenyl-4-carboxylated (650BC) has been synthesized and its smectic phases charaterized. Typically, this ester exhibits an A, B,E, phase sequence, with the B Phase being of the hexactic type. The Synthesis, microscopic textures, and miscibility studise ar reported here. The results show that while the two types of B phase appear co-miscibly by conventional optical mehtods, in fact X-ray diffraction studies show that a transition occurs between the two phases in certain binary mixt...