Macroscopic Order Research Articles

Void lattice formation in electron irradiated CaF2: Statistical analysis of experimental data and cellular automata simulations

Calcium fluoride (CaF2) is an important optical material widely used in both microlithography and deep UV windows. It is known that under certain conditions electron beam irradiation can create therein a superlattice consisting of vacancy clusters (called a void lattice). The goal of this paper is twofold. Firstly, to perform a quantitative analysis of experimental TEM images demonstrating void lattice formation, we developed two distinct image filters. As a result, we can easily calculate vacancy concentration, vacancy cluster distribution function as well as average distances between defect clusters. The results for two suggested filters are similar and demonstrate that experimental void cluster growth is accompanied by a slight increase of the void lattice constant. Secondly, we proposed a microscopic model that allows us to reproduce a macroscopic void ordering, in agreement with experimental data, and to resolve existing theoretical and experimental contradictions. Our computer simulations demonstrate that macroscopic void lattice self-organization can occur only in a narrow parameter range. Moreover, we studied the kinetics of a void lattice ordering, starting from an initial disordered stage, in a good agreement with the TEM experimental data.

Studies of optical texture, birefringence, order parameter, normalized polarizability and validation of the four-parameter model of a thermotropic mesogen 7OAOB

Study of optical texture of different mesophases and phase transition temperatures of the liquid crystal compound 4,4′-di-n-heptyloxy-azoxy benzene has been carried out by using optical polarizing microscope. Enthalpy values and the phase transition temperatures have also been conducted by DSC studies. The variation of refractive indices with temperature has been measured by a thin prism technique using He–Ne laser and temperature dependent birefringence is calculated which shows a moderate value. Validation of the modified four-parameter model based on Vuks approximation has been carried out and reported in this article. The most important characteristics of LC compound namely macroscopic and microscopic order parameter have been evaluated by using direct extrapolation method and modified Vuks method based on Haller's extrapolation respectively. Temperature gradients of refractive indices have also been calculated. Further the normalized polarizabilities for extraordinary and ordinary rays and their ratio have been reported in this paper.

Ferroelectric domain formation in discotic liquid crystals: Monte Carlo study on the influence of boundary conditions.

The realization of a spontaneous macroscopic ferroelectric order in fluids of anisotropic mesogens is a topic of both fundamental and technological interest. Recently we demonstrated that a system of dipolar achiral disklike ellipsoids can exhibit long-searched ferroelectric liquid crystalline phases of dipolar origin. In the present work, extensive off-lattice Monte Carlo simulations are used to investigate the phase behavior of the system under the influences of the electrostatic boundary conditions that restrict any global polarization. We find that the system develops strongly ferroelectric slablike domains periodically arranged in an antiferroelectric fashion. Exploring the phase behavior at different dipole strengths, we find existence of the ferroelectric nematic and ferroelectric columnar order inside the domains. For higher dipole strengths, a biaxial phase is also obtained with a similar periodic array of ferroelectric slabs of antiparallel polarizations. We have studied the depolarizing effects by using both the Ewald summation and the spherical cutoff techniques. We present and compare the results of the two different approaches of considering the depolarizing effects in this anisotropic system. It is explicitly shown that the domain size increases with the system size as a result of considering a longer range of dipolar interactions. The system exhibits pronounced system size effects for stronger dipolar interactions. The results provide strong evidence to the novel understanding that the dipolar interactions are indeed sufficient to produce long-range ferroelectric order in anisotropic fluids.

Thermoelectric spin transport through ferromagnetic heterostructures

We study how spin is transferred by ferromagnetic dynamics in a charge insulator in response to a thermoelectric bias, which is established by supplying heat and/or spin accumulation via normal leads. At zero temperature, magnetic anisotropies pin the macroscopic order, which necessitates a finite threshold bias to induce a spin current in a steady state of unpinned dynamics. At finite temperatures, however, thermal spin waves provide a spin transport channel in response to a linear thermoelectric bias. The theoretical description is rooted in the Landau–Lifshitz–Gilbert phenomenology both for the macroscopic dynamics of the magnetic order and quantum kinetics of thermal magnons. In this paper we connect the classical and quantum aspects of the underlying magnetic dynamics and spin transport, as well as provide a unified view of the exchange mediated bias of spin See-beck physics of the magnetic interface and bulk.

Macroscopic ordering of helical pores for arraying guest molecules noncentrosymmetrically.

Helical nanostructures have attracted continuous attention, not only as media for chiral recognition and synthesis, but also as motifs for studying intriguing physical phenomena that never occur in centrosymmetric systems. To improve the quality of signals from these phenomena, which is a key issue for their further exploration, the most straightforward is the macroscopic orientation of helices. Here as a versatile scaffold to rationally construct this hardly accessible structure, we report a polymer framework with helical pores that unidirectionally orient over a large area (∼10 cm2). The framework, prepared by crosslinking a supramolecular liquid crystal preorganized in a magnetic field, is chemically robust, functionalized with carboxyl groups and capable of incorporating various basic or cationic guest molecules. When a nonlinear optical chromophore is incorporated in the framework, the resultant complex displays a markedly efficient nonlinear optical output, owing to the coherence of signals ensured by the macroscopically oriented helical structure.

Primary ferrotoroidicity in antiferromagnets

Antiferromagnetic ordering does not give rise to a measurable macroscopic symmetry-breaking order parameter such as the magnetization in a ferromagnet. An exception is the case of antiferromagnets with a vortexlike toroidal alignment of the magnetic moments in the unit cell because this gives rise to the formation of a spontaneous macroscopic toroidal moment which can be measured as a magnetoelectric effect. It is a long-standing question whether the toroidal moment is merely a side effect of the antiferromagnetic state or whether it can become the primary order parameter in a ferroic phase transition. Here we report the magnetoelectric properties of ${\mathrm{LiFeSi}}_{2}{\mathrm{O}}_{6}$ and show that they point to the role of the toroidal vector moment as the primary order parameter. Based on Landau theory we distinguish it from primary antiferromagnetic order. We thus justify the proposal that along with ferromagnets, ferroelectrics, and ferroelastics the ferrotoroidics constitute a new class of primary ferroics.

Dinitroxide biradical crystals with polar order

A dinitroxide biradical (dCdO) has the peculiar tendency to crystallize in non-centrosymmetric polar space groups either as a stable dichloromethane solvate or as a pure phase. The molecules arrange with no compensation of their dipolar moment resulting in net macroscopic polar order.

Macroscopic degeneracy and order in the 3D plaquette Ising model

The purely plaquette 3D Ising Hamiltonian with the spins living at the vertices of a cubic lattice displays several interesting features. The symmetries of the model lead to a macroscopic degeneracy of the low-temperature phase and prevent the definition of a standard magnetic order parameter. Consideration of the strongly anisotropic limit of the model suggests that a layered, “fuki-nuke” order still exists and we confirm this with multi-canonical simulations. The macroscopic degeneracy of the low-temperature phase also changes the finite-size scaling corrections at the first-order transition in the model and we see this must be taken into account when analyzing our measurements.

Wrinkles of graphene on Ir(1 1 1): Macroscopic network ordering and internal multi-lobed structure

The large-scale production of graphene monolayer greatly relies on epitaxial samples which often display stress-relaxation features in the form of wrinkles. Wrinkles of graphene on Ir(111) are found to exhibit a fairly well ordered interconnecting network which is characterized by low-energy electron microscopy (LEEM). The high degree of quasi-hexagonal network arrangement for the graphene aligned to the underlying substrate can be well described as a (non-Poissonian) Voronoi partition of a plane. The results obtained strongly suggest that the wrinkle network is frustrated at low temperatures, retaining the order inherited from elevated temperatures when the wrinkles interconnect in junctions which most often join three wrinkles. Such frustration favors the formation of multi-lobed wrinkles which are found in scanning tunneling microscopy (STM) measurements. The existence of multiple lobes is explained within a model accounting for the interplay of the van der Waals attraction between graphene and iridium and bending energy of the wrinkle. The presented study provides new insights into wrinkling of epitaxial graphene and can be exploited to further expedite its application.

Macroscopic order in a nematic liquid crystal: Perturbation by spontaneous director fluctuations.

The dynamic alignment of the nematic director by near-orthogonal electric and magnetic fields has been investigated. The intermediate states during the relaxation process were found, with the aid of time-resolved deuterium NMR spectroscopy, to be markedly nonuniform. The macroscopic order was perturbed, although the initial and final states of the director appear to be essentially uniform. However, the initial state does have a profound influence on the uniformity of the director in the intermediate states. We have developed a fundamental model based on the effect of spontaneous director fluctuations to explain these unusual NMR observations.

Cluster and constraint analysis in tetrahedron packings.

The disordered packings of tetrahedra often show no obvious macroscopic orientational or positional order for a wide range of packing densities, and it has been found that the local order in particle clusters is the main order form of tetrahedron packings. Therefore, a cluster analysis is carried out to investigate the local structures and properties of tetrahedron packings in this work. We obtain a cluster distribution of differently sized clusters, and peaks are observed at two special clusters, i.e., dimer and wagon wheel. We then calculate the amounts of dimers and wagon wheels, which are observed to have linear or approximate linear correlations with packing density. Following our previous work, the amount of particles participating in dimers is used as an order metric to evaluate the order degree of the hierarchical packing structure of tetrahedra, and an order map is consequently depicted. Furthermore, a constraint analysis is performed to determine the isostatic or hyperstatic region in the order map. We employ a Monte Carlo algorithm to test jamming and then suggest a new maximally random jammed packing of hard tetrahedra from the order map with a packing density of 0.6337.

Light and thermal responses of liquid-crystal-network films: A finite element study.

As a polymeric system incorporating rigid molecules within its structure, the liquid-crystal network (LCN) has been envisaged as a novel heterogeneous material. Under the influence of external stimuli, the orientational order of the liquid-crystalline phase becomes dilute and overall anisotropy is hence decreased; the actinic light absorbed by photochromic molecules, for example, induces the geometric isomerization and subsequently yields internal stress within the local network. In this study we investigate light- and temperature-induced spontaneous deformations of the LCN structure via a three-dimensional finite element model that incorporates geometric nonlinearity with a photomechanical constitutive model. We first examine the bending behavior and its nonlinearity and then parametrically study the various behaviors that stem from different origins ranging from the microscale to the macroscale: (i) the geometry of the LCN film, (ii) the macroscopic global order, (iii) the distorted mesogenic orientation due to the Fredericks distortion, and (iv) defect-induced instability. These interrelated behaviors demonstrate both the simulation capability and the necessity of the presenting framework. By employing a nonlinear consideration along with a microscopic shape parameter r the present approach facilitates further understanding of photomechanical physics such as the deconvolution of various stimuli and the deformed shape obtained due to snap-through instability. Furthermore, this study may offer insight into the design of light-sensitive actuation systems by deepening our knowledge and providing an efficient measure.

Valley order and loop currents in graphene on hexagonal boron nitride

In this letter, we examine the role of Coulomb interactions in the emergence of macroscopically ordered states in graphene supported on hexagonal boron nitride substrates. Due to incommensuration effects with the substrate, graphene can develop gapped low energy modes that spatially conform into a triangular superlattice of quantum rings. In the presence of these modes, we show that Coulomb interactions lead to spontaneous formation of chiral loop currents in bulk and to macroscopic spin-valley order at zero temperature. We show that this exotic state breaks time reversal symmetry and can be detected with interferometry and polar Kerr measurements.

Microscopic instability in recurrent neural networks.

In a manner similar to the molecular chaos that underlies the stable thermodynamics of gases, a neuronal system may exhibit microscopic instability in individual neuronal dynamics while a macroscopic order of the entire population possibly remains stable. In this study, we analyze the microscopic stability of a network of neurons whose macroscopic activity obeys stable dynamics, expressing either monostable, bistable, or periodic state. We reveal that the network exhibits a variety of dynamical states for microscopic instability residing in a given stable macroscopic dynamics. The presence of a variety of dynamical states in such a simple random network implies more abundant microscopic fluctuations in real neural networks which consist of more complex and hierarchically structured interactions.

Fabrication and optical testing of hybrid SiO2: azo-polymer based planar waveguides for NLO/SHG laser emission

Predesigned push-pull azo-dye polymers were homogeneously dispersed within a SiO2 sol-gel matrix synthesized via the sonogel (SG) route. High-quality spin-coated films were obtained with these hybrid structures in the liquid sol-phase. The spectroscopic UV- Vis analyses reveal the appropriate insertion of these organic compounds within the highly pure SG-environment whereas the thermal (DSC) analysis and photoacoustic measurements evidence the thermomechanical stability of the amorphous hybrid layers. As the optical attenuation, refractive index and film thickness values of the obtained films are adequate for opto-electronic applications; these hybrid films were implemented to fabricate optical waveguiding prototypes. In this sense, functional planar waveguides were fabricated for nonlinear optical (NLO) applications after performing a molecular ordering via a corona DC-poling procedure in order to achieve a macroscopic polar order (ferroelectric and noncentrosymmetric arrangement of the organic chromophores). The poled films were then able to exhibit stable NLO-waveguiding effects as excited with a Nd:YAG laser system in order to generate second harmonic waves travelling within the planar layer.

Keeping speed and distance for aligned motion.

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space and time we find that if two particles arrive symmetrically in a plane at a large angle, then (i) radial repulsion and (ii) linear self-propelling toward a fixed preferred speed are sufficient for them to depart at a smaller angle. For this local gain of momentum explicit velocity alignment is not necessary, nor are adhesion or attraction, inelasticity or anisotropy of the particles, or nonlinear drag. With many particles obeying these microscopic rules of motion we find that their spatial confinement to a square with periodic boundaries (which is an indirect form of attraction) leads to stable macroscopic ordering. As a function of the strength of added noise we see--at finite system sizes--a critical slowing down close to the order-disorder boundary and a discontinuous transition. After varying the density of particles at constant system size and varying the size of the system with constant particle density we predict that in the infinite system size (or density) limit the hysteresis loop disappears and the transition becomes continuous. We note that animals, humans, drones, etc., tend to move asynchronously and are often more responsive to motion than positions. Thus, for them velocity-based continuous models can provide higher precision than coordinate-based models. An additional characteristic and realistic feature of the model is that convergence to the ordered state is fastest at a finite density, which is in contrast to models applying (discontinuous) explicit velocity alignments and discretized time. To summarize, we find that the investigated model can provide a minimal description of flocking.

Insulated Polyacetylene Chains in an Inclusion Complex by Photopolymerization

ABSTRACTThe properties of a material often depend on the degree of order of their atomic, molecular, or crystalline domain components. This is expected to be especially true for the case of polyacetylene, whose properties are highly anisotropic. For many applications, it may be necessary to have macroscopic order but not necessarily crystalline order. Having polyacetyelene chains fully extended and aligned parallel to each other may be sufficient for these applications even without order of the chains around their long axis. We report here progress in the use of an inclusion crystal containing a photo-reactive precursor to prepare high molecular weight polyacetylene. Raman spectroscopy was performed to probe the resulting conjugated polyene chains. Ultraviolet irradiation of a 1,4-diiodo-1,3-butadiene/urea inclusion complex results in the appearance of new resonance-enhanced Raman modes at 1125 and 1509 cm-1. The Raman spectra of the resulting confined polyene chains are very similar to freestanding isolated trans-polyacetylene prepared by solution methods.

Ferroelastoelectric phase transition in (NH4)2CuCl4·2H2O single crystal

The (NH4)2CuCl4·2H2O crystal exhibits anomalous thermal, piezoelectric, dielectric and elastic properties in the vicinity of the ferroelastoelectric phase transition at TC = 200 K. Macroscopic order parameter is the h36 component of the spontaneous piezoelectric tensor connecting polarisation P3 and strain η6. The temperature change in h36 component was proportional to (TC − T)α, where α = 0.58 ± 0.05. Close to TC changes in dielectric permittivity were negligible. High value of ac conductivity in the high-temperature phase results from protons jumping between disordered ions NH4+ and between molecules of crystallisation water. Only longitudinal ultrasonic waves exhibited an abrupt change upon the phase transition. The relaxation time of the order parameter was determined from anomalous changes in attenuation of the longitudinal waves.

Bifurcation of learning and structure formation in neuronal maps

Most learning processes in neuronal networks happen on a much longer time scale than that of the underlying neuronal dynamics. It is therefore useful to analyze slowly varying macroscopic order parameters to explore a network's learning ability. We study the synaptic learning process giving rise to map formation in the laminar nucleus of the barn owl's auditory system. Using equation-free methods, we perform a bifurcation analysis of spatio-temporal structure formation in the associated synaptic-weight matrix. This enables us to analyze learning as a bifurcation process and follow the unstable states as well. A simple time translation of the learning window function shifts the bifurcation point of structure formation and goes along with traveling waves in the map, without changing the animal's sound localization performance.

Nanotube liquid crystal elastomers: photomechanical response and flexible energy conversion of layered polymer composites

Elastomeric composites based on nanotube liquid crystals (LCs) that preserve the internal orientation of nanotubes could lead to anisotropic physical properties and flexible energy conversion. Using a simple vacuum filtration technique of fabricating nanotube LC films and utilizing a transfer process to poly (dimethyl) siloxane wherein the LC arrangement is preserved, here we demonstrate unique and reversible photomechanical response of this layered composite to excitation by near infra-red (NIR) light at ultra-low nanotube mass fractions. On excitation by NIR photons, with application of small or large pre-strains, significant expansion or contraction of the sample occurs, respectively, that is continuously reversible and three orders of magnitude larger than in pristine polymer. Schlieren textures were noted in these LC composites confirming long range macroscopic nematic order of nanotubes within the composites. Order parameters of LC films ranged from Soptical = 0.51–0.58 from dichroic measurements. Film concentrations, elastic modulus and photomechanical stress were all seen to be related to the nematic order parameter. For the same nanotube concentration, the photomechanical stress was almost three times larger for the self-assembled LC nanotube actuator compared to actuator based on randomly oriented carbon nanotubes. Investigation into the kinetics of photomechanical actuation showed variation in stretching exponent β with pre-strains, concentration and orientation of nanotubes. Maximum photomechanical stress of ∼0.5 MPa W−1 and energy conversion of ∼0.0045% was achieved for these layered composites. The combination of properties, namely, optical anisotropy, reversible mechanical response to NIR excitation and flexible energy conversion all in one system accompanied with low cost makes nanotube LC elastomers important for soft photochromic actuation, energy conversion and photo-origami applications.