Stable Lattices Research Articles

Emulsion copolymerization of styrene and acrylated methyl oleate

In this work, the emulsion copolymerization of styrene and acrylated methyl oleate (AMO), a monomer derived from oleic acid (OA), has been evaluated. Reactions exhibiting high monomers conversions were successfully performed, leading to the formation of very stable polymer lattices, whose average particle size is kept unchanged for relatively high storage times. The average molar masses determined by gel permeation chromatography showed to be very dependent on the amount of AMO in the reaction medium, presenting experimental values within the range from 280 000 to 39 000 g mol−1 with molar mass dispersity ranging from 4 to 2 when the AMO fraction in the reaction medium was increased to 40 wt%. The nucleation rate was affected by AMO in such way that an increase in AMO concentration must be accompanied by an increase in initiator concentration, which leads to the reduction of the average molar masses of the copolymer. The thermal analyses of the polymer materials showed that the glass transition temperature decreased with increasing amount of AMO in the copolymer chains.Practical applications: The use of vegetable oils and their derivatives as precursor monomers in polymerization reactions has increased each day due to their renewable origin. Among them, OA deserves special attention due to the high availability and ease of chemical modification, mainly when the double bounds are considered. Results showed that AMO could be incorporated at high ratios in emulsion polymerization reducing the glass transition temperatures of the copolymer. The polymer lattices also showed good storage stability.

A surface-patterned chip as a strong source of ultracold atoms for quantum technologies

Laser-cooled atoms are central to modern precision measurements. They are also increasingly important as an enabling technology for experimental cavity quantum electrodynamics, quantum information processing and matter-wave interferometry. Although significant progress has been made in miniaturizing atomic metrological devices, these are limited in accuracy by their use of hot atomic ensembles and buffer gases. Advances have also been made in producing portable apparatus that benefits from the advantages of atoms in the microkelvin regime. However, simplifying atomic cooling and loading using microfabrication technology has proved difficult. In this Letter we address this problem, realizing an atom chip that enables the integration of laser cooling and trapping into a compact apparatus. Our source delivers ten thousand times more atoms than previous magneto-optical traps with microfabricated optics and, for the first time, can reach sub-Doppler temperatures. Moreover, the same chip design offers a simple way to form stable optical lattices. These features, combined with simplicity of fabrication and ease of operation, make these new traps a key advance in the development of cold-atom technology for high-accuracy, portable measurement devices.

Evidence of Cationic Pt Active for Water–Gas Shift Reaction: Pt-Doped BaCeO3 Perovskite

Precious metal incorporated into stable lattices like perovskites can be envisaged as an alternative catalysts to address deactivation problems. Here we report the barium cerate perovskite doped with varying amounts of Pt as catalysts for the water–gas shift reaction whereby ionic Pt is evidenced to be active. It is found that maximum CO conversion occurs above 325 °C and increases more than 2-fold after the first cycle. XPS analysis shows that after the first cycle, more ionic Pt species are present on the surface of the catalyst. X-ray and neutron diffraction studies also indicate the presence of oxygen vacancies that increases with increasing Pt substitution.

The stability and the nonlinear elasticity of 2D hexagonal structures of Si and Ge from first-principles calculations

By using the first-principles calculations based on the density-functional theory (DFT), we study the stability and the nonlinear elasticity of two-dimensional (2D) hexagonal structures of Si and Ge. The reproduced structure optimization and phonon–dispersion curves demonstrate that Si and Ge can form stable 2D hexagonal lattices with low-buckled structures, and provide a good agreement with the previous DFT calculations. The second- and third-order elastic constants are calculated by using the method of homogeneous deformation. The present results of the linear elastic moduli agree well with the previous results. In comparison with the linear approach, the nonlinear effects really matter while strain is larger than approximately 3.5%. The force–displacement behaviors and the breaking strength of 2D hexagonal Si and Ge are discussed using the nonlinear stress–strain relationship. By using the available results of graphene, we reasonably demonstrate that the radius of the atom increases and breaking strength of this element decreases for 2D hexagonal structures of group IV-elements.

Réseaux dʼinduction des représentations elliptiques de Lubin–Tate

Let K be a complete local field which residual field is finite of characteristic p and let l be a prime number not equal to p. Given a Q ¯ l -irreducible cuspidal integral representation π, we describe, for all s ⩾ 1 , the irreducible sub-quotients of the reduction modulo l of the generalized Steinberg representation St s ( π ) . By induction and with the use of the parabolic induction, we construct then stable lattices of St s ( π ) and describe a filtration of their reduction modulo l which appears, cf. Boyer (in preparation) [4], in the description of the l-torsion of the p+-intermediate extensions of the local systems of Harris–Taylor.

Failure tolerance of load-bearing hierarchical networks

We investigate the statistics and dynamics of failure in a two-dimensional load-bearing network with branching hierarchical structure, and its variants. The variants strengthen the original lattice by using connectivity strategies which add new sites to the maximal cluster in top-to-bottom or bottom-to-top versions. We study the load-bearing capacity and the failure tolerance of all versions, as well as that of the strongest realization of the original lattice, the V lattice. The average number of failures as a function of the test load shows power-law behavior with power 5/2 for the V lattice, but sigmoidal behavior for all other versions. Thus the V lattice turns out to be the critical case of the load-bearing lattices. The distribution of failures is Gaussian for the original lattice, the V lattice, and the bottom-to-top strategy, but is non-Gaussian for the top-to-bottom one. The bottom-to-top strategy leads to stable and strong lattices, and can resist failure even when tested with weights which greatly exceed the capacity of its backbone. We also examine the behavior of asymmetric lattices and discover that the mean failure rates are minimized if the probability of connection p is symmetric with respect to both neighbors. Our results can be of relevance in the context of realistic networks.

Nonadditive Hard-Sphere Reference Model for Ionic Liquids

A nonadditive hard-sphere (NAHS) reference model for ionic liquids with truncated ion−ion pair interaction potentials represented by collision diameters defined as σij=σ(1+δijε)(using the Kroneckerδ) is investigated. In a reference 1:1 ionic salt (e.g., AB = NaCl), the nonadditivity parameter (ε) is positive; hence, like ions interact with a larger diameter than unlike ions; that is, σAA=σBB=(1+ε)σAB The NAHS model is found to show remarkable similarity of structure to the full-Hamiltonian for electrostatic charged ion models of ionic liquids, their crystalline phases, and freezing properties. Molecular dynamics computations are used to show that the structures of ionic liquids and crystals are determined mainly by short-range geometric and symmetry effects rather than the long-range electrostatic potentials. A preliminary phase diagram for nonadditive hard spheres has been determined for the range of positive nonadditivity for stable cubic lattices CsCl (body-centered), rock salt, NaCl (simple cubic), and sphelerite ZnS (tetrahedral). Model NAHS ionic liquids obey a scaling law for the freezing temperature Tf = T0(1 + ε)3, where T0 is the HS freezing temperature. NAHS is an effective reference model, analogous to the HS model for molecular and atomic liquids, as a starting point for describing the structures and phase diagrams of ionic liquids and crystals.

Galois representations and Lubin-Tate groups

Using Lubin-Tate groups, we develop a variant of Fontaine's theory of (\varphi, \Gamma) -modules, and we use it to give a description of the Galois stable lattices inside certain crystalline representations.

Soft magnetic lithography and giant magnetoresistance in superconducting/ferromagnetic hybrids

We demonstrate an approach to create a tunable pinning potential in a superconducting/ferromagnetic (SC/FM) hybrid, allowing the switching of their electronic properties through the application of a small magnetic field. Using direct magneto-optical imaging, macroscopic transport, and magnetic measurements, we show that the alignment of stripe domains in the ferromagnet provides a remarkable directionality for the superconducting vortex motion. An analysis of the anisotropic flux motion demonstrates a substantial critical current anisotropy in the superconductor. The possibility of aligning stable lattices of stripe domains in select directions using in-plane magnetic fields allows the realization of soft magnetic lithography for efficient manipulation of supercurrent flow in SC/FM bilayers. Furthermore, in our samples we observed a pronounced magnetoresistance effect yielding 4 orders of magnitude resistivity change in a few millitesla in-plane field.

VORTEX LATTICE STATE OF A SUPERFLUID FERMI GAS IN THE UNITARY REGION

In this paper, we study the structure of vortex lattices in a trapped superfluid Fermi gas in the unitary region near the superfluid transition temperature. A phenomenological approach based on the Ginzburg-Landau theory is used. Two types of stable triangular vortex lattices are found numerically at the same rotation frequency. In type (A), the trap center is occupied by a vortex; in type (B), there are three vortices closest to the trap center which is unoccupied. The lattice structures at different rotation frequencies and temperatures are analyzed. The vortex density increases linearly with the rotation frequency, very close to the analytical estimation. The superfluid and type-(B) vortex lattice do not disappear together. At high rotation frequencies, the vortex lattice disappears, but there exists a localized superfluid state near the trap center. The superfluid vanishes at a critical rotation frequency consistent with the theory for the upper critical magnetic field of type-II superconductors.

Controlled/living photopolymerization of methyl methacrylate in miniemulsion mediated by HTEMPO

Controlled/living photopolymerization of methyl methacrylate (MMA) in miniemulsion mediated by 4-hydroxy-2,2,6,6-tetramethyl-piperidinyloxy (HTEMPO) was carried out at ambient temperatures. MMA miniemulsion was prepared by using an anionic surfactant with cetylalcohol as a co-stabilizer. The photopolymerization led to stable lattices and they were obtained with no coagulation during synthesis and no destabilization over time. It was found that the obtained MMA homopolymers exhibited relatively narrow molecular weight distribution (PDI = 1.27 − 1.36) which was characterized by GPC. The plots of number-average molecular weight in (M n) vs. conversion and ln([M0]/[M]) vs. time both were linear indicating that the reaction was a controlled/living free radical polymerization.

Simulations of the effects of 1-d interstitial diffusion on void lattice formation during irradiation

This paper describes the use of simulation techniques to examine some of the processes involved in the alignment of voids under the influence of one-dimensional self interstitial atom (1-d SIA) transport. The work follows the paper of Heinisch and Singh [1] on this topic but a different and simpler methodology is used. Besides repeating the scenarios studied by Heinisch and Singh, the effects of re-nucleation and the influence of vacancies have been introduced. One of the important processes that emerged from the results was the barrier to precise void alignment caused by the SIA-induced coalescence of aligned voids. This appears to prevent the formation of stable void lattices by any 1-d SIA transport mechanism, a point supported by the initial void alignment in the mechanism requiring swelling values well above those found experimentally. A full consideration of the void lattice phenomenon shows that the one-dimensional diffusion of self-interstitials central to the production bias model of irradiation damage cannot be the only mode of anisotropic diffusion available under irradiation.

Synthesis of Ethyl Acrylate-Methyl Acrylate Copolymers via Emulsion Polymerization

ABSTRACT A series of methyl acrylate-ethyl acrylate copolymers were prepared via emulsion polymerization using a batch reactor. Some reaction parameters, such as composition and temperature, were varied in order to determine their influence on the polymerization rate. A high exothermic behavior (Trommsdorf effect) was observed when the temperature was increased. Very stable lattices were obtained and characterized by gravimetry, infrared spectroscopy, quasi-elastic light scattering (QELS), differential scanning calorimetry, and transmission electron microscopy methods. In all cases, monodispersed, small sized particles were obtained. The position annihilation parameters τ3 and I 3 of all the copolymers were also measured and related with their glass transition temperatures.

Superfluidlike Motion of Vortices in Light Condensates

We demonstrate, through numerical simulations, the generation of stable vortex lattices in light condensates. This can be achieved by propagating several concentric laser beams with nested vortices of different topological charges in an optical material with a cubic-quintic nonlinearity. We have considered several initial conditions, and in all the cases the net topological charges of the resulting lattice is equal to the topological charge of the initial outer vortex. The lattice exhibits rotation similar to vortex motion in superfluids. These vortex arrays could be used to implement all-optical photonic crystal fibers. Our results also apply to Bose-Einstein condensates in the presence of three-body elastic interactions.

Charged colloids and polyelectrolytes: from statics to electrokinetics

A review is given on recent studies of charged colloidal suspensions and polyelectrolytes both in static and non-equilibrium situations. As far as static equilibrium situations are concerned, we discuss three different problems: 1) Sedimentation density profiles in charged suspensions are shown to exhibit a stretched non-bariometric wing at large heights and binary suspensions under gravity can exhibit an analog of the brazil-nut effect known from granular matter, i.e. the heavier particles settle on top of the lighter ones. 2) Soft polyelectrolyte systems like polyelectrolyte stars and microgels show an ultra-soft effective interaction and this results into an unusual equilibrium phase diagram including reentrant melting transitions and stable open crystalline lattices. 3) The freezing transition in bilayers of confined charged suspensions is discussed and a reentrant behaviour is obtained. As far as nonequilibrium problems are concerned, we discuss an interface instability in oppositely driven colloidal mixtures and discuss possible approaches to simulate electrokinetic effects in charged suspensions.

Crystal structures of two-dimensional magnetic colloids in tilted external magnetic fields.

The stability of different crystal lattices of two-dimensional superparamagnetic suspensions that are confined to a planar liquid-gas interface and exposed to a tilted external magnetic field is studied theoretically by lattice sum minimizations. The magnetic field induces magnetic dipoles onto the colloidal particles along its direction, whose strength can be controlled by the amplitude of the external field. The mutual interaction between the colloids is governed by dipole-dipole forces and a short-ranged repulsion having its physical origin at the presence of the colloidal cores. If the direction of the magnetic field is perpendicular to the liquid-gas interface, there is a purely repulsive interaction leading to stable triangular crystals. By tilting the external field, the interaction becomes anisotropic and a mutual attraction appears upon a threshold tilt angle. We have calculated the full phase diagram at zero temperature varying the tilt angle, the colloidal density, and the strength of the magnetic field. Apart from the triangular lattice we find a variety of stable crystal lattices including rectangular, oblique, chainlike oblique, and rhombic structures. We also present the accurate derivation of the Hamiltonian of two polarizable particles of finite arbitrary geometries in external magnetic and electric fields.

Kinetic Monte Carlo simulations of void lattice formation during irradiation

Over the last decade, molecular dynamics simulations of displacement cascades have revealed that glissile clusters of self-interstitial crowdions are formed directly in cascades and that they migrate one-dimensionally along close-packed directions with extremely low activation energies. Occasionally, under various conditions, a crowdion cluster can change its Burgers vector and glide along a different close-packed direction. The recently developed production bias model (PBM) of microstructure evolution under irradiation has been structured specifically to take into account the unique properties of the vacancy and interstitial clusters produced in the cascades. Atomic-scale kinetic Monte Carlo (KMC) simulations have played a useful role in understanding the defect reaction kinetics of one-dimensionally migrating crowdion clusters as a function of the frequency of direction changes. This has made it possible to incorporate the migration properties of crowdion clusters and changes in reaction kinetics into the PBM. In the present paper we utilize similar KMC simulations to investigate the significant role that crowdion clusters can play in the formation and stability of void lattices. The creation of stable void lattices, starting from a random distribution of voids, is simulated by a KMC model in which vacancies migrate three-dimensionally and self-interstitial atom (SIA) clusters migrate one-dimensionally, interrupted by directional changes. The necessity of both one-dimensional migration and Burgers vectors changes of SIA clusters for the production of stable void lattices is demonstrated, and the effects of the frequency of Burgers vector changes are described.

Stability of driven Josephson vortex lattice in layered superconductors revisited

We analytically study stability of sliding lattice of Josephson vortices driven by a transport current in the stack direction in strong in-plane magnetic field. In contrast to recent findings we obtain that there are no diverse configurations of stable vortex lattices, and, hence, the stable sliding vortex lattice can not be selected by boundary conditions. We find that only the triangular (rhombic) lattice can be stable, its stability being limited by a critical velocity value. At higher velocities there are no simple stable lattices with single flux line per unit cell. Oblique sliding lattices are found to be never stable. Instability of such lattices is revealed beyond the linear approximation in perturbations of the lattice.

Duality relations for elastic constants of the classical Gaussian core model.

The many-body Gaussian core model involves a potential energy function that consists of a sum of repelling pair interactions, each of which is a simple Gaussian function of distance. This paper examines the linear elastic response of the model for its stable lattices at absolute zero temperature, in D=1, 2, and 3 dimensions. Owing to the fact that the Gaussian function is self-similar under Fourier transformation, exact relations exist connecting each elastic constant at number density rho to a partner at dual density rho(') in the reciprocal lattice, where rhorho(')=pi(-D). By using these identities, it has been possible to show that shear elastic constants in D=2 and 3 tend strongly to zero in the asymptotic high density limit.

Decoration lattices of colloids adsorbed on stripe-patterned substrates.

The equilibrium structure of decoration lattices composed of colloidal particles adsorbed on periodic stripe-patterned substrates is calculated as a function of the stripe width and separation and for different interparticle interactions. Due to a competition of length scales, a wealth of different stable decoration lattices occurs such as triangular, quadratic, rhombic, kitelike, and sheared honeycomb lattices, triangular slices as well as triangle superlattices. This is of relevance for constructing templates that enforce crystal growth of unusual solid structures.