Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is on the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures

Length and time scale divergences at the magnetization-reversal transition in the Ising model

The divergences of both the length and time scales, at the magnetization- reversal transition in Ising model under a pulsed field, have been studied in the linearized limit of the mean field theory. Both length and time scales are shown to diverge at the transition point and it has been checked that the nature of the time scale divergence agrees well with the result obtained from the numerical solution of the mean field equation of motion. Similar growths in length and time scales are also observed, as one approaches the transition point, using Monte Carlo simulations. However, these are not of the same nature as the mean field case. Nucleation theory provides a qualitative argument which explains the nature of the time scale growth. To study the nature of growth of the characteristic length scale, we have looked at the cluster size distribution of the reversed spin domains and defined a pseudo-correlation length which has been observed to grow at the phase boundary of the transition.Comment: 9 pages Latex, 3 postscript figure

Growth, microstructure, and failure of crazes in glassy polymers

We report on an extensive study of craze formation in glassy polymers. Molecular dynamics simulations of a coarse-grained bead-spring model were employed to investigate the molecular level processes during craze nucleation, widening, and breakdown for a wide range of temperature, polymer chain length $N$, entanglement length $N_e$ and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at constant drawing stress. The extension ratio is determined by the entanglement length, and the characteristic length of stretched chain segments in the polymer craze is $N_e/3$. In the craze, tension is mostly carried by the covalent backbone bonds, and the force distribution develops an exponential tail at large tensile forces. The failure mode of crazes changes from disentanglement to scission for $N/N_e\sim 10$, and breakdown through scission is governed by large stress fluctuations. The simulations also reveal inconsistencies with previous theoretical models of craze widening that were based on continuum level hydrodynamics

Spatiotemporal Stochastic Resonance in Fully Frustrated Josephson Ladders

We consider a Josephson-junction ladder in an external magnetic field with half flux quantum per plaquette. When driven by external currents, periodic in time and staggered in space, such a fully frustrated system is found to display spatiotemporal stochastic resonance under the influence of thermal noise. Such resonance behavior is investigated both numerically and analytically, which reveals significant effects of anisotropy and yields rich physics.Comment: 8 pages in two columns, 8 figures, to appear in Phys. Rev.

Stationary State Solutions of a Bond Diluted Kinetic Ising Model: An Effective-Field Theory Analysis

We have examined the stationary state solutions of a bond diluted kinetic Ising model under a time dependent oscillating magnetic field within the effective-field theory (EFT) for a honeycomb lattice $(q=3)$. Time evolution of the system has been modeled with a formalism of master equation. The effects of the bond dilution, as well as the frequency $(\omega)$ and amplitude $(h/J)$ of the external field on the dynamic phase diagrams have been discussed in detail. We have found that the system exhibits the first order phase transition with a dynamic tricritical point (DTCP) at low temperature and high amplitude regions, in contrast to the previously published results for the pure case \cite{Ling}. Bond dilution process on the kinetic Ising model gives rise to a number of interesting and unusual phenomena such as reentrant phenomena and has a tendency to destruct the first-order transitions and the DTCP. Moreover, we have investigated the variation of the bond percolation threshold as functions of the amplitude and frequency of the oscillating field.Comment: 8 pages, 4 figure

Spreading Dynamics of Polymer Nanodroplets

The spreading of polymer droplets is studied using molecular dynamics simulations. To study the dynamics of both the precursor foot and the bulk droplet, large drops of ~200,000 monomers are simulated using a bead-spring model for polymers of chain length 10, 20, and 40 monomers per chain. We compare spreading on flat and atomistic surfaces, chain length effects, and different applications of the Langevin and dissipative particle dynamics thermostats. We find diffusive behavior for the precursor foot and good agreement with the molecular kinetic model of droplet spreading using both flat and atomistic surfaces. Despite the large system size and long simulation time relative to previous simulations, we find no evidence of hydrodynamic behavior in the spreading droplet.Comment: Physical Review E 11 pages 10 figure

Morphologies of poly(cyclohexadiene) diblock copolymers: Effect of conformational asymmetry

Concerted experimental and theoretical investigations have been carried out to understand the microphase separation in diblock copolymer melts containing poly (1,3-cyclohexadiene), PCHD, as one of the constituents. In particular, we have studied diblock copolymer melts containing polystyrene (PS), polybutadiene (PB), and polyisoprene (PI) as the second block. We have systematically varied the ratio of 1,2-/1,4-microstructures of poly (1,3-cyclohexadiene) to tune the conformational asymmetry between the two blocks and characterized the effects of these changes on the morphologies using transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS). Our experimental investigations reveal that the melts of PCHD-b-PB, PCHD-b-PS and PCHD-b-PI containing nearly equal fractions of each component and high percentage of 1,4-microstructures in the PCHD block form cylindrical rather than lamellar morphologies as expected in symmetric diblock copolymers. In contrast, the morphologies of PCHD-b-PB, PCHD-b-PS and PCHD-b-PI containing PCHD block with higher 1,2-microstructure are found to be disordered at 110 °C. The change in the morphological behavior is in good agreement with our numerical calculations using the random phase approximation and self-consistent field theory for conformationally asymmetric diblock copolymer melts. Also, the effects of composition fluctuations are studied by extending the Brazovskii-Leibler-Fredrickson-Helfand (J. Chem. Phys. 87, 697 (1987)) theory to conformationally asymmetric diblock copolymer melts. These results allow the understanding of the underlying self-assembly process that highlights the importance of the conformational asymmetry in tuning the morphologies in block copolymers. © 2012 Elsevier Ltd. All rights reserved

Morphologies of ABC triblock terpolymer melts containing poly(Cyclohexadiene): Effects of conformational asymmetry

We have synthesized linear ABC triblock terpolymers containing poly(1,3-cyclohexadiene), PCHD, as an end block and characterized their morphologies in the melt. Specifically, we have studied terpolymers containing polystyrene (PS), polybutadiene (PB), and polyisoprene (PI) as the other blocks. Systematically varying the ratio of 1,2- /1,4-microstructures of poly(1,3-cyclohexadiene), we have studied the effects of conformational asymmetry among the three blocks on the morphologies using transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and self-consistent field theory (SCFT) performed with PolySwift++. Our work reveals that the triblock terpolymer melts containing a high percentage of 1,2-microstructures in the PCHD block are disordered at 110 C for all the samples, independent of sequence and volume fraction of the blocks. In contrast, the triblock terpolymer melts containing a high percentage of 1,4-microstructure form regular morphologies known from the literature. The accuracy of the SCFT calculations depends on calculating the χ parameters that quantify the repulsive interactions between different monomers. Simulations using χ values obtained from solubility parameters and group contribution methods are unable to reproduce the morphologies as seen in the experiments. However, SCFT calculations accounting for the enhancement of the χ parameter with an increase in the conformational asymmetry lead to an excellent agreement between theory and experiments. These results highlight the importance of conformational asymmetry in tuning the χ parameter and, in turn, morphologies in block copolymers. © 2012 American Chemical Society

Effects of polydispersity on the order-disorder transition of diblock copolymer melts

The effect of polydispersity on an AB diblock copolymer melt is investigated using latticebased Monte Carlo simulations. We consider melts of symmetric composition, where the B blocks are monodisperse and the A blocks are polydisperse with a Schultz-Zimm distribution. In agreement with experiment and self-consistent field theory (SCFT), we find that polydispersity causes a significant increase in domain size. It also induces a transition from flat to curved interfaces, with the polydisperse blocks residing on the inside of the interfacial curvature. Most importantly, the simulations show a relatively small shift in the order-disorder transition (ODT) in agreement with experiment, whereas SCFT incorrectly predicts a sizable shift towards higher temperatures