Reentrant Order Research Articles

Melting, reentrant ordering and peak effect for Wigner crystals with quenched and thermal disorder

We consider simulations of Wigner crystals in solid state systems interacting with random quenched disorder in the presence of thermal fluctuations. When quenched disorder is absent, there is a well defined melting temperature determined by the proliferation of topological defects, while for zero temperature, there is a critical quenched disorder strength above which topological defects proliferate. When both thermal and quenched disorder are present, these effects compete, and the thermal fluctuations can reduce the effectiveness of the quenched disorder, leading to a reentrant ordered phase in agreement with the predictions of Nelson (1983 Phys. Rev. B 27 2902–14). There are two competing theories for the low temperature behavior, and our simulations show that both capture aspects of the actual response. The critical disorder strength separating ordered from disordered states remains finite as the temperature goes to zero, as predicted by Cha and Fertig (1995 Phys. Rev. Lett. 74 4867–70), instead of dropping to zero as predicted by Nelson. At the same time, the critical disorder strength decreases with decreasing temperature, as predicted by Nelson, instead of remaining constant, as predicted by Cha and Fertig. The onset of the reentrant phase can be deduced based on changes in the transport response, where the reentrant ordering appears as an increase in the mobility or the occurrence of a depinning transition. We also find that when the system is in the ordered state and thermally melts, there is an increase in the effective damping or pinning. This produces a drop in the electron mobility that is similar to the peak effect phenomenon found in superconducting vortices, where thermal effects soften the lattice or break down its elasticity, allowing the particles to better adjust their positions to take full advantage of the quenched disorder.

Blunt-End Driven Re-entrant Ordering in Quasi Two-Dimensional Dispersions of Spherical DNA Brushes.

We investigate the effects of crowding on the conformations and assembly of confined, highly charged, and thick polyelectrolyte brushes in the osmotic regime. Particle tracking experiments on increasingly dense suspensions of colloids coated with ultralong double-stranded DNA (dsDNA) fragments reveal nonmonotonic particle shrinking, aggregation, and re-entrant ordering. Theory and simulations show that aggregation and re-entrant ordering arise from the combined effect of shrinking, which is induced by the osmotic pressure exerted by the counterions absorbed in neighbor brushes and of a short-range attractive interaction competing with electrostatic repulsion. An unconventional mechanism gives origin to the short-range attraction: blunt-end interactions between stretched dsDNA fragments of neighboring brushes, which become sufficiently intense for dense and packed brushes. The attraction can be tuned by inducing free-end backfolding through the addition of monovalent salt. Our results show that base stacking is a mode parallel to hybridization to steer colloidal assembly in which attractions can be fine-tuned through salinity and, potentially, grafting density and temperature.

Beyond the “Coffee Ring”: Re-entrant Ordering in an Evaporation-Driven Self-Assembly in a Colloidal Suspension on a Substrate

We study the phenomenon of evaporation-driven self-assembly of a colloid suspension of silica microspheres in the interior region and away from the rim of the droplet on a glass plate. In view of the importance of achieving a large-area, monolayer assembly, we first realize a suitable choice of experimental conditions, minimizing the influence of many other competing phenomena that usually complicate the understanding of fundamental concepts of such self-assembly processes in the interior region of a drying droplet. Under these simplifying conditions to bring out essential aspects, our experiments unveil an interesting competition between ordering and compaction in such drying systems in analogy to an impending glass transition. We establish a re-entrant behavior in the order-disorder phase diagram as a function of the particle density, such that there is an optimal range of the particle density to realize the long-range ordering. The results are explained with the help of simulations and phenomenological theory.

Coil fraction-dependent phase behaviour of a model globular protein–polymer diblock copolymer

The self-assembly of the model globular protein-polymer block copolymer mCherry-b-poly(N-isopropyl acrylamide) is explored across a range of polymer coil fractions from 0.21 to 0.82 to produce a phase diagram for these materials as a function of molecular composition. Overall, four types of morphologies were observed: hexagonally packed cylinders, perforated lamellae, lamellae, and disordered nanostructures. Across all coil fractions and morphologies, a lyotropic re-entrant order-disorder transition in water was observed, with disordered structures below 30 wt% and above 70 wt% and well-ordered morphologies at intermediate concentrations. Solid state samples prepared by solvent evaporation show moderately ordered structures similar to those observed in 60 wt% solutions, suggesting that bulk structures result from kinetic trapping of morphologies which appear at lower concentrations. While highly ordered cylindrical nanostructures are observed around a bioconjugate polymer volume fraction of 0.3 and well-ordered lamellae are seen near a volume fraction of 0.6, materials at lower or higher coil fractions become increasingly disordered. Notable differences between the phase behaviour of globular protein-polymer block copolymers and coil-coil diblock copolymers include the lack of spherical nanostructures at either high or low polymer coil fractions as well as shifted phase boundaries between morphologies which result in an asymmetric phase diagram.

A scheduling algorithm for the reentrant shop: an application in semiconductor manufacture

This paper addresses a heuristic algorithm that minimizes total weighted tardiness for reentrant flow shop problems with sequence-dependent set up time. The proposed algorithm consists of three phases: prior plan phase, initial solution generation phase and solution improvement phase. In the first phase, a reentrant order with cyclic process is divided into a number of jobs. An initial solution is obtained by a RATCS (revised apparent tardiness cost with setups) rule in the second phase, and the last phase employs a RHTS (rolling horizon tabu search) to improve the solution. The experimental results show that the proposed algorithms give very efficient schedules in terms of total weighted tardiness and computational effort.

Charge and salt-driven reentrant order–disorder and gas–solid transitions in charged colloids

Monte Carlo simulations have been performed for aqueous charged colloidal suspensions as a function of effective charge density ( σ) on the particles and salt concentration C s . We vary the effective charge density in our simulations over a range where a reentrant solid–liquid transition in suspensions of silica and polymer latex particles has been reported by Yamanaka et al. (Phys. Rev. Lett. 80 (1998) 5806). We show that at low ionic strengths a homogeneous liquid-like ordered suspension undergoes crystallization upon increasing σ. Further increase in σ resulted once again in a disordered state, which is in agreement with experimental observations. In addition to this reentrant order–disorder transition, we observe an inhomogeneous-to-homogeneous transition in our simulations when salt is added to the disordered inhomogeneous state. This inhomogeneous-to-homogeneous disordered transition is analogous to the solid–gas transition of atomic systems and has not yet been observed in charged colloids. The reported experimental observations on charged colloidal suspensions are discussed in the light of present simulation results.

Off-Diagonal Long-Range Order in a Harmonically Confined Two-Dimensional Bose Gas

We investigate the presence of off-diagonal long-range order in a harmonically confined two-dimensional Bose gas. In the noninteracting case, an analytical calculation of the the finite-temperature one-particle density matrix provides an exact description of the spatial correlations known to be associated with the existence of a Bose–Einstein condensate below the transition temperature T(0) c. We treat the effects of repulsive interactions within the semiclassical Hartree–Fock–Bogoliubov approximation and find that even though the system remains in the same uncondensed phase for all T≥0, there appears to be a revival of off-diagonal long-range order for temperatures T<T(0) c. We suggest that this re-entrant order is related to a phase transition in the system which is not the BEC state.

Reentrant Order−Disorder Transition in Ionic Colloidal Dispersions by Varying Particle Charge Density

The influence of the effective particle surface charge density, σ e , on the order-disorder phase transition was examined for aqueous dispersions of charged colloidal silica and polymer latex particles (diameters = 0.11-0.13 μm). The σ e value of the silica particle was continuously tuned by changing the concentration of added NaOH. The three-dimensional phase diagram of the order-disorder transition for the silica system was determined as a function of σ e , particle volume fraction Φ, and salt concentration C s , by observing iridescence due to Bragg diffraction from the ordered structure, and further by applying an ultra-small-angle X-ray scattering method. With increasing σ e , the disordered dispersion became ordered and thereafter reentered into the disordered state. The presence of the reentrant disordered phase at high σ e conditions was observed for ionic polymer latex systems. The reentrant phase transition was not explainable in terms of the Yukawa potential and charge renormalization model.

Transitions between Ordered and Disordered Phases and Their Coexistence in Dilute Ionic Colloidal Dispersions

Order−disorder transitions in dilute aqueous dispersions of ionic colloids were studied experimentally in colloidal silica and polymer latex systems. A three-dimensional phase diagram of the silica system was determined by treating the particle density, the effective surface charge number, and the ionic strength as variables. On the basis of the phase diagram, the structures of the dispersions were studied by means of ultrasmall-angle X-ray scattering and confocal laser scanning microscopy. The results clearly revealed the presence of a reentrant order−disorder transition with increasing charge number, and a wide biphasic region where ordered and disordered phases coexist. The nearest interparticle distance 2Dexp was almost equal to that calculated assuming a homogeneous particle distribution, 2D0, in the ordered single-phase region, while 2Dexp was smaller than 2D0 under the biphasic condition. Further studies concerning the crystallization process of the dispersion in the biphasic region demonstrated the development of disordered liquidlike regions inside the space-filling crystalline grains which was induced by lattice contraction. The results suggest that the commonly held view based on a Yukawa-type potential, in which only repulsive interparticle interactions are considered, cannot explain the phase behavior of the dilute ionic colloids.

Thermodynamical properties of the random field Ising model

The random field Ising model is studied within the differential operator method. The phase diagrams were obtained for coordination numbers z = 4 and z = 6. They show several interesting behaviours, presenting tricritical points (only for z = 6), and re-entrant order parameters in either of the two distribution functions studied. The influence of the re-entrant behaviour on the thermodynamical properties is also investigated.