Driven Disordered Polymorphic Solids: Phases and Phase Transitions, Dynamical Coexistence and Peak Effect Anomalies

We study a model for the depinning and driven steady state phases of a solid tuned across a polymorphic phase transition between ground states of triangular and square symmetry. These include pinned states which may have dominantly triangular or square correlations, a plastically flowing liquid-like phase, a moving phase with hexatic correlations, flowing triangular and square states and a dynamic coexistence regime characterized by the complex interconversion of locally square and triangular regions. We locate these phases in a dynamical phase diagram. We demonstrate that the apparent power-law orientational correlations we obtain in our moving hexatic phase arise from circularly averaging an orientational correlation function with qualitatively different behaviour in the longitudinal (drive) and transverse directions. The intermediate coexistence regime exhibits several novel properties, including substantial enhancement in the current noise, an unusual power-law spectrum of current fluctuations and striking metastability effects. This noise arises from the fluctuations of the interface separating locally square and triangular ordered regions. We demonstrate the breakdown of effective ``shaking temperature'' treatments in the coexistence regime by showing that such shaking temperatures are non-monotonic functions of the drive in this regime. Finally we discuss the relevance of these simulations to the anomalous behaviour seen in the peak effect regime of vortex lines in the disordered mixed phase of type-II superconductors. We propose that this anomalous behavior is directly linked to the behavior exhibited in our simulations in the dynamical coexistence regime, thus suggesting a possible solution to the problem of the origin of peak effect anomalies.Comment: 22 pages, double column, higher quality figures available from author

Thermodynamic behaviour of two-dimensional vesicles revisited

We study pressurised self-avoiding ring polymers in two dimensions using Monte Carlo simulations, scaling arguments and Flory-type theories, through models which generalise the model of Leibler, Singh and Fisher [Phys. Rev. Lett. Vol. 59, 1989 (1987)]. We demonstrate the existence of a thermodynamic phase transition at a non-zero scaled pressure $\tilde{p}$, where $\tilde{p} = Np/4\pi$, with the number of monomers $N \rightarrow \infty$ and the pressure $p \rightarrow 0$, keeping $\tilde{p}$ constant, in a class of such models. This transition is driven by bond energetics and can be either continuous or discontinuous. It can be interpreted as a shape transition in which the ring polymer takes the shape, above the critical pressure, of a regular N-gon whose sides scale smoothly with pressure, while staying unfaceted below this critical pressure. In the general case, we argue that the transition is replaced by a sharp crossover. The area, however, scales with $N^2$ for all positive $p$ in all such models, consistent with earlier scaling theories.Comment: 6 pages, 4 figures, EPL forma

Glass formation in a lattice model for living polymers

We study glass formation in a lattice model for living, semiflexible polymers. Our model exhibits logarithmically slow relaxation out of quenched, metastable configurations, a frustration-driven glass to crystal transition, and an exotic lamellar glass. We propose a Monte Carlo analog of scanning calorimetry and use it to study these glasses. We discuss the relevance of our work to experiments and to some theories of the glass transition in model systems

Crystallization and vitrification of semiflexible living polymers: a lattice model

We study the systematics of a d-dimensional lattice model for melts of semiflexible living polymers. For d=2 and 3 our model, which includes vacancies, loops, and the possibilities of polymerization and polydispersity, exhibits both equilibrium crystallization and glass formation in the wake of a quench. We study these analytically, in some limits, and via extensive Monte Carlo simulations. A continuous Ising-type transition separates crystalline and disordered phases for the d=2 square lattice. If loop formation is favored in d=2, crossover effects lead to power-law decays of polymer-length distributions over large length scales, strong fluctuations in thermodynamic quantities, and slow relaxation. These crossover effects arise because of the proximity of a phase with an infinite correlation length in one limit of our model. For the d=3 simple cubic lattice our model has a first-order crystallization transition. Quenches from the disordered to the ordered phase yield glassy, metastable configurations for both d=2 and 3. We study the latter case in detail and find logarithmically slow relaxation out of these metastable configurations, a frustration-driven glass-crystal transition, and an exotic lamellar glass. We propose a Monte Carlo analog of scanning calorimetry and use it to study these glasses. We discuss the relevance of our work to experiments on different systems of living polymers, earlier studies of crystallization in polymeric melts, and some theories of the glass transition in model systems