Hexatic Phase Research Articles

Melting transition in a two-dimensional complex plasma heated by driven acoustic instability

The melting transition in a two-dimensional complex (dusty) plasma is studied experimentally. A system consisting of ≈3900 microspheres is heated by amplitude modulating the rf discharge power with a square wave at the vertical resonance frequency. The vertical motion couples to an in-plane dust-acoustic instability at one-half the modulation frequency, thereby increasing the complex plasma’s effective temperature. The “thermodynamic” phase of the system is characterized for increasing levels of amplitude modulation at constant neutral pressure (35mTorr Ar) and average rf power using the Lindemann ratio, defect density, bond-orientational correlation function, and pair correlation function. A melting transition showing evidence for an intermediate hexatic phase is observed.

Fabrication of Well-Organized and Densely Packed Si Nanopillars Containing SiGe Nanodots by Using Block Copolymer Templates

We present a method to obtain a dense array of well-organized SiGe quantum dots in Si nanopillars on a large substrate area by using a PS-b-PMMA block copolymer template. First, the 2D order of the template is evaluated using a pair correlation function and a bond-orientational correlation function. It is shown that the holes contained in the polystyrene template form a structure presenting a hexatic order. This template is then used to fabricate the nanopillars using the following method: in a first step, the copolymer template serves as a deposition mask to fabricate a hexagonal array of Pt dots. In a second step, the Pt dot pattern is transferred to an alternation of Si and SiGe layers on a silicon substrate with an anisotropically etching using Cl2/O2 plasma.

Polycrystalline solidification in a quenched 2D colloidal system

We investigate a two-dimensional colloidal system when quenched from the isotropic fluidphase into the crystalline phase. In thermal equilibrium one finds two continuous phasetransitions with a hexatic phase in between the fluid and the crystalline phase. Here, noindications of this anisotropic fluid are observed if the system is driven out of equilibrium.Therefore we investigate whether a nucleation process may describe the scenario. Toidentify the crystallites a criterion based on the local bond-order field is introduced. Withthis at hand the growth of the crystallites is investigated. At early times, small crystallitesstart to grow in the supercooled isotropic phase and later, when the crystallites start totouch each other, the small ones are merged into the bigger crystallites due to a ripeningprocess.

Competition between Pomeranchuk instabilities in the nematic and hexatic channels in a two-dimensional spinless Fermi fluid

We study the competition between the nematic and the hexatic phases of a two-dimensional spinless Fermi fluid near Pomeranchuk instabilities. We show that the general phase diagram of this theory contains a bicritical point where two second-order lines and a first-order nematic/hexatic phase transition meet together. We found that at criticality and deep inside the associated symmetry broken phases, the low energy theory is governed by a dissipative cubic mode, even near the bicritical point where nematic and hexatic fluctuations cannot be distinguished due to very strong dynamical couplings.

Coexistence of hexatic and isotropic phases in two-dimensional Yukawa systems

We performed Brownian-dynamics simulations on the melting of two-dimensional colloidalcrystals in which particles interact via a Yukawa potential. A stable hexatic phase was found inthe Yukawa systems, but we also found that the melting of Yukawa systems is a two-stagemelting, which is inconsistent with the Kosterlitz–Thouless–Halperin–Nelson–Young(KTHNY) theory. A two-phase coexistence region between the stable hexatic phase and theisotropic liquid phase was found. The behavior of point defects in the coexistence region isvery complicated. The emergence of some unstable free disclinations and grainboundaries was a characteristic representative of the isotropic liquid phase, and alarge number of free dislocations indicated the existence of a hexatic phase. Thisindicates the existence of a phase of hexatic–isotropic liquid phase coexistence.The big picture in the melting of a two-dimensional Yukawa system is that firstthe system undergoes a transition induced by the formation of free dislocations,then it goes through a phase coexistence, and finally, it comes into an isotropicfluid phase. This melting process is consistent with experiments and simulations.

Orientationally correlated colloidal polycrystals without long-range positional order

We probe the local and global structure of spin-coated colloidal crystals via laser diffraction measurements and scanning electron and atomic force microscopies, and find that they are unique three-dimensional orientationally correlated polycrystals, exhibiting short-range positional order but long-range radial orientational correlations, reminiscent of-but distinct from-two-dimensional colloidal hexatic phases. Thickness and symmetries are controllable by solvent choice and spin speed. While the polycrystallinity of these colloidal films limits their applicability to photonics, we demonstrate their feasibility as templates to make crack-free magnetic patterns.

Effect of multilactate chiral part of liquid crystalline molecule on mesomorphic behaviour

Mesomorphic behaviour of several series of materials derived from the lactic acid has been studied and their physical properties have been compared and summarized. These compounds with the same molecular core differing by the linkage group of the non-chiral chain possess a broad variety of liquid crystalline phases: the paraelectric SmA, the ferroelectric SmC ∗, the antiferroelectric SmC ∗ A, the re-entrant SmC ∗ re, the ferroelectric hexatic phases and a monotropic low temperature phase. The antiferroelectric phase occurs in materials with two lactate groups only, where the ether or the keto group is used as linkage between the non-chiral chain and molecular core. The studied homologues with one, three or even four lactate groups do not exhibit the antiferroelectric phase, but possess a broad range of the SmA and SmC ∗ phases down to room temperatures. The presence of the keto group increases the temperature range and values of the spontaneous polarisation of polar liquid crystalline phases. Molecules with the ether or keto group have a different distribution of electron densities, which seems to be responsible for the difference in the mesomorphic properties. The relationship between the molecular chain structure and mesomorphic properties of lactic acid derivatives with particular molecular core forming the polar mesophases are discussed.

Melting of two-dimensional tunable-diameter colloidal crystals

Melting of two-dimensional colloidal crystals is studied by video microscopy. The samples were composed of microgel spheres whose diameters could be temperature tuned, and whose pair potentials were measured to be short ranged and repulsive. We observed two-step melting from the crystal to a hexatic phase and from the hexatic to the liquid phase as a function of the temperature-tunable volume fraction. The translational and orientational susceptibilities enabled us to definitively determine the phase transition points, avoiding ambiguities inherent in other analyses and resolving a "dislocation precursor stage" in the solid phase that some of the traditional analyses may incorrectly associate with the hexatic phase. A prefreezing stage of the liquid with ordered patches was also found.

Synthesis and Characterization of Branched Mesogen-Jacketed Liquid Crystal Polymers Based on 2,5-Bis[(4‘-methoxyphenyl)oxycarbonyl]styrene and 4-Chloromethylstyrene

A series of branched mesogen-jacketed liquid crystal polymers were synthesized via atom transfer radical copolymerization of mesogenic 2,5-bis[(4‘-methoxyphenyl)oxycarbonyl]styrene (MPCS) and nonmesogenic 4-chloromethylstyrene (CMS) catalyzed by the CuCl/CuCl2/bipyridine complex in anisole solution at 110 °C. During the early period of polymerization, CMS acted mainly as an initiator to induce the polymerization of MPCS. The molecular weights (MWs) of the resultant polymers increased linearly with monomer conversion and showed a symmetrical and relatively narrow distribution. With the proceeding of polymerization, MWs changed from monomodal to multimodal distribution, indicating the formation of branched structure through the action of vinyl group of CMS. This mechanism was also supported by the increased chain density estimated by a combination of gel permeation chromatography and laser light scattering, end-group analysis, and the reactivity ratios of two monomers (rMPCS = 0.71, rCMS = 0.10). The thermotropic properties of the copolymers strongly relied on the feed ratio of MPCS to CMS and MW. The feed ratio of MPCS to CMS should be at least 30 with high enough MW. For the copolymer obtained at the feed ratio of 32, the minimum Mn,GPC was 1.21 × 104 Da to achieve a mesophase. Although linear poly{2,5-bis[(4‘-methoxyphenyl)oxycarbonyl]styrene} displayed columnar nematic phase (ΦN) and hexatic columnar nematic phase (ΦHN) depending on MW, the branched polymer showed just a ΦN phase, indicating the remarkable depressing effect of the branched structure on the mesomorphic property.

Implicit-solvent mesoscale model based on soft-core potentials for self-assembled lipid membranes

An efficient implicit-solvent model for self-assembled lipid bilayers is presented and analyzed using Langevin molecular dynamics simulations. The model is based on soft interactions between particles and short-range attractive interaction between lipid tails, leading for the self-assembly of a lipid bilayer without an explicit solvent. This allows for efficient simulations of large membranes over long times. The model exhibits a fluid phase at high temperatures and a gel phase at low temperatures, identified with the Lbeta-phase. The melting transition is investigated via analysis of the diffusivity of the lipid molecules, the chain-orientational order parameter, the sixfold bond-orientational order parameter, and the positional and bond-orientational correlation functions. The analysis suggests the existence of a hexatic phase over a narrow range of temperatures around the melting transition. The elastic properties of the membrane in the fluid phase are also investigated.

Temperature and bias electric field dependence of dielectric parameters of ( S )-(+)-4-(1-methylheptyloxycarbonyl) phenyl-4’-(3-butanoiloxyprop-1-oxy)biphenyl-4’-carboxylate

Temperature and bias electric field-dependent dielectric behaviour of an antiferroelectric liquid crystal compound was investigated in the frequency range 1 Hz to 10 MHz. The investigated compound possessed paraelectric (SmA*) and antiferroelectric () phases, in addition to a monotropic hexatic antiferroelectric smectic () phase. The dielectric study showed the presence of a soft mode in the SmA* phase. In the phase, two weak relaxation modes were observed for a planar orientation of molecules. These two modes were related to antiferroelectric ordering and the helical structure of the phase. Two modes, related to the hexatic order of the phase, were also observed and characterized in terms of bond-orientational order and coupling to the molecular tilt direction. With respect to non-collective modes, rotation around the short axis of molecules was detected in the SmA* and phases for a homeotropic alignment.

Ferroelectricity of Hexatic Phases

Two fluorinated compounds: 3-(2-fluoroctyloxy)-6-(4octyl-phenyl) pyridine (FOOPP) and 3-(fluornonyl)-6-(4-heptyloxy-phenyl)pyridine (FNHPP), synthesized by E. Merck Company in earlier 1990s, which show a pronounced increase of spontaneous polarization at the SmC*-hexatic SmI* transition have been reinvestigated. In this contribution we shall present calorimetric, dielectric and electro-optic behavior of two perfluorinated compounds which display enhanced high spontaneous polarization in enantiotropic hexatic phases. Phase transitions have been studied by DSC, polarizing microscopy, X-ray diffraction, and reversal current method, and molecular and collective dynamics – by dielectric spectroscopy. Spontaneous polarization measurements vs. temperature show that the SmI* phase of FOOPP exhibits almost 3 times larger spontaneous polarization than the high temperature ferroelectric SmC* phase.

Rheooscillations of a Bottlebrush Polymer Solution Due to Shear-Induced Phase Transitions between a Shear Molten State and a Line Hexatic Phase

Time-resolved small-angle X-ray scattering (SAXS) experiments were carried out on concentrated solutions of bottlebrush polymers exposed to an external shear flow. We followed the rheological response of the sample online. If the experiment is performed in the strain-controlled mode, the rheological response of the bottlebrush polymer solution to the rotational shear shows oscillations with changes in viscosity of almost 2 orders of magnitude. The SAXS data reveal that this oscillatory response is due to a reentrant phase transition between a shear molten phase and a line hexatic phase. It is not due to shear-induced phase separation leading to shear band formation. The in-situ rheological SAXS measurements allow a detailed description of the structural changes occurring in the sample during structural buildup and breakdown.

Molecular dynamics study of two-dimensional melting transition in copper via the embedded atom method

We report detailed molecular dynamics results for the two-dimensional (2D) melting transition using embed atomic method. The simulations are performed in the $NPT$ ensemble. Under different temperatures, the orientational correlation functions ${g}_{6}(r)$ and the pair distribution functions are measured and compared with the prediction of KTHNY theory. The size effect of distribution of the second moment of the local bond-orientational order parameter ${\ensuremath{\mid}{\ensuremath{\psi}}_{6,i}\ensuremath{\mid}}^{2}$ is studied. All results prove the existence of an intermediate hexatic phase during 2D melting. The dependence of average potential energy per atom on temperature and evidences from observations on the global bond-orientational order parameter and global translational order parameter show that the melting contains two stages and is a first-order transition as a whole. By exploring the evolution of topological defects, along with observations on the distributions of defects in inherent structures of typical crystalline phase, hexatic liquid, and isotropic liquid, we find that, instead of disclinations, the formation of defect chains and the correlation between them play an important role in both steps, which is rather different from the prediction of KTHNY theory.

Stability of Nematic and Smectic Phases in Rod-Like Mesogens with Orientation−Dependent Attractive Interactions

The stability of isotropic (I), nematic (N), smectic A (Sm A), and hexatic (Hex) liquid crystalline phases is studied for a fluid of molecules with a rod-like shape and dispersive interactions dependent on orientation. The fluid is modeled with the spherocylindrical Gay-Berne-Kihara interaction potential proposed in a recent work, with parameters favoring parallel pair orientations. The liquid crystal phase diagram is characterized for different molecular aspect ratios by means of Monte Carlo simulations in the isobaric-isothermal ensemble. Three types of triple points are observed, namely, I-Sm A-Hex, I-N-Sm A, and N-Sm A-Hex, leading to island-shape domains for the smectic A phase. The resulting phase diagrams are compared with those derived previously for prolate fluids of ellipsoidal and spherocylindrical symmetry. It is concluded that the stability of the layered phases with respect to the nematic phase is enhanced in the spherocylindrical fluids due to geometrical constraints. Furthermore, the anisotropy of the dispersive interactions induces a stronger dependence of the overall phase diagram on temperature and aids in the energetic stabilization of the hexatic crystalline phase with respect to the fluid smectic A phase.

Frank’s constant in the hexatic phase

Using videomicroscopy data of a two-dimensional colloidal system the bond-order correlation function G{6} is calculated and used to determine both the orientational correlation length xi{6} in the liquid phase and the modulus of orientational stiffness, Frank's constant F{A}, in the hexatic phase. The latter is an anisotropic fluid phase between the crystalline and the isotropic liquid phase. F{A} is found to be finite within the hexatic phase, takes the value 72/pi at the hexatic<-->isotropic liquid phase transition, and diverges at the hexatic<-->crystal transition as predicted by the Kosterlitz-Thouless-Halperin-Nelson-Young theory. This is a quantitative test of the mechanism of breaking the orientational symmetry by disclination unbinding.

Adsorption and phase transitions in adsorbed systems: structural properties of CCl4 layers adsorbed on a graphite surface

We present the results of simulations of a CCl(4) monolayer adsorbed on a graphite surface. The CCl(4) molecule was represented either by a shapeless superatom or by its atomic sites. The simulations were carried out over a large range of temperatures, from 20 K up to 340 K. We address the following problems: (1) the influence of molecular shape on the structure and stability of phases (particularly at low temperatures), and (2) the influence of the graphite corrugation on layer stability and mechanism of phase transitions. In particular, we discuss the possibility and conditions of the appearance of hexatic phase in the system.

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.

Phase transitions in two-dimensional colloidal particles at oil/water interfaces

Enhanced digital video microscopy is applied to study the equilibrium structure of a two-dimensional charged sulfate-polystyrene particle (2 mum in diameter) monolayer at decane/water interfaces. When the surface density is decreased, a sequential phase transition, pure solid phase-->pure hexatic phase-->liquid-hexatic-coexisting phase-->pure liquid phase, is observed. In addition, the transition between liquid and hexatic phases is first order, while the solid-hexatic phase transition is second order. The temperature effect on this two-dimensional melting transition is discussed by performing the experiments at three different temperatures. The Voronoi [J. Reine Angew. Math. 134, 198 (1908)] construction is applied to analyze the defect structure in the two-dimensional particle monolayer. The pair interaction potential of the two-dimensional colloidal particles is found to be a very long range repulsion and to decay with distance to the power of -3.

Surface effects on the relaxation dynamics of hexatic-Bliquid-crystal films

Based in a linearized hydrodynamic model, we study the relaxation dynamics of hexatic-B liquid-crystal films in two distinct cases. First, we investigate the hexatic order relaxing through a purely diffusive process for which the particles velocity field is assumed to be negligible. In this case, the asymptotic relaxation of deformations in the hexatic order presents a pronounced dependence on the boundary conditions. We found that a surface tilted order is enough to drive the slowest relaxation mode from an acoustic to an optic character. Second, we study the viscous case which is characterized by the coupling between the particles velocity field and the bond orientational order. In this case, underdamped modes with oscillatory-exponential relaxation are obtained on a narrow range of wave vectors. Further, the viscous relaxation of surface and inner layers deformations display distinct scaling behaviors under a surface tilted order.