Showing papers on "Phase transition published in 1987"

Cosmology for Grand Unified Theories With Radiatively Induced Symmetry Breaking

Abstract: The treatment of first-order phase transitions for standard grand unified theories is shown to break down for models with radiatively induced spontaneous symmetry breaking. It is argued that proper analysis of these transitions which would take place in the early history of the universe can lead to an explanation of the cosmological homogeneity, flatness, and monopole puzzles.

Fluctuation effects in the theory of microphase separation in block copolymers

Abstract: The effect of composition fluctuations on the microphase separation transition in diblock copolymers is investigated. Such fluctuation corrections, which were neglected in the mean field treatment of Leibler, are found to be significant for the molecular weights usually encountered. The analysis is facilitated by reducing the block copolymer Hamiltonian to a form previously studied by Brazovskii. Our principal results are the following: (i) A symmetric diblock copolymer is predicted to undergo a first order phase transition at a larger value of χN than the second order transition found by Leibler. The Flory interaction parameter is denoted χ and N is the number of statistical segments per chain. The location of the transition is predicted to be at (χN)t=10.495+41.022 N−1/3, where the peak in the scattering function attains its maximum value of 0.12328 N1/3. (ii) We find windows in composition, with finite width, through which it is possible to pass from the disordered phase to each of the ordered micropha...

Theory of first-order phase transitions

Abstract: An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order are discussed, as well as exceptions to these rules. Attention is drawn to the rounding of first-order transitions due to finite-size or quenched impurities. Computational methods to calculate phase diagrams for simple model Hamiltonians are also described. Particular emphasis is laid on metastable states near first-order phase transitions, on the 'stability limits' of such states (e.g. the 'spinodal curve' of the gas-liquid transition) and on the dynamic mechanisms by which metastable states decay (nucleation and growth of droplets of a new phase, etc.).

Volume‐phase transitions of ionized N‐isopropylacrylamide gels

Abstract: Equilibrium swelling curves of N‐isopropylacrylamide (NIPA) gel and a series of its ionized counterparts were measured as a function of temperature. Nonionic NIPA gels underwent a sharp yet continuous volume change, whereas incorporation of a small amount of ionizable groups into the gel network drives the transition toward a discontinuous one. The critical ionic concentration and polymer network density at which the get undergoes a critical phase transition were determined. The results were analyzed using a mean field theory. Discrepancy between experimental data and theory is nontrivial, and may require the formulation of a more elaborate theory.

Phase equilibria of fluid interfaces and confined fluids

Abstract: Phase transitions at fluid interfaces and in fluids confined in pores have been investigated by means of a density functional approach that treats attractive forces between fluid molecules in mean-field approximation and models repulsive forces by hard-spheres. Two types of approximation were employed for the hard-sphere free energy functional: (a) the well-known local density approximation (LDA) that omits short-ranged correlations and (b) a non-local smoothed density approximation (SDA) that includes such correlations and therefore accounts for the oscillations of the density profile near walls. Three different kinds of phase transition were considered: (i) wetting transition. The transition from partial to complete wetting at a single adsorbing wall is shifted to lower temperatures and tends to become first-order when the more-realistic SDA is employed. Comparison of the results suggests that the LDA overestimates the contact angle γ in a partial wetting situation. (ii) capillary evaporation of a fluid...

Resonating-valence-bond theory of phase transitions and superconductivity in La 2 CuO 4 -based compounds

Abstract: We identify the mysterious high-T ``twitch'' transition in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ with the mean-field resonating-valence-bond transition of the Heisenberg model of Baskaran, Zou, and Anderson. The structure distortions are caused by Coulomb correlations of the pair wave function. In the pure compound the pseudo-Fermi surface of the spin soliton nests and antiferromagnetism occurs at 240 K. We discuss briefly superconductivity and the nature of excitations in the system.

Supercooled Phase Transitions in the Very Early Universe

Abstract: The universe might have had a prolonged exponentially expanding phase caused by its being stuck in a metastable state of the grand unified phase transition. The only way that it could exit from this exponential expansion without introducing too much inhomogeneity or spatial curvature would be through a homogeneous “bubble” solution in which quantum tunnelling occured everywhere at the same time. This would produce more baryons than the conventional scenarios.

Mechanical instability of gels at the phase transition

Abstract: Polymer gels, consisting of a cross-linked polymer network immersed in liquid, undergo a volume phase transition: when external conditions such as temperature or solvent composition change, a gel reversibly swells or shrinks, but does so discontinuously1–5. The volume change at the transition can be as large as a factor of one thousand2, and the phenomenon occurs in all gels6,7. The equilibrium aspects of the phase transition have been extensively studied, but its kinetics have not yet been fully explored. In particular, the appearance of patterns on the originally smooth surface of a gel during the transition makes the kinetic process difficult to understand. Here we elucidate the physical basis underlying the formation and evolution of the pattern.

Quantized vortices in superfluid He-3

Abstract: The first measurements on vortices in rotating superfluid $^{3}\mathrm{He}$ have been conducted in the Low Temperature Laboratory at Helsinki University of Technology during the past five years. These experiments have revealed unique vortex phenomena that are not observed in any other known superfluids. In this review, the concept of broken symmetry is applied to investigate the quantized vortex lines in superfluid $^{3}\mathrm{He}$. In the superfluid $A$ phase, vorticity can be supported by a continuous winding of the order parameter; this gives rise to continuous "coreless" vortices with two flow quanta. Novel vortices with a half-integer number of circulation quanta may also exist in $^{3}\mathrm{He}$-$A$ due to a combined symmetry of the superfluid state. In the superfluid $B$ phase, the vortices have a complicated core structure. The vortex-core matter is ferromagnetic and superfluid, and it displays broken parity. The ferromagnetism of the core is observed in NMR experiments due to a gyromagnetic effect. The calculated core structures exhibit an experimentally observed first-order phase transition. This vortex-core transition in rotating $^{3}\mathrm{He}$-$B$ may be understood in terms of a change in the topology for flaring-out of the vortex singularity into higher dimensions; the topological identification further suggests that the phase transition manifests a spontaneous bifurcation of vorticity---involving half-quantum vortices in $^{3}\mathrm{He}$-$B$. These recent advances of interest in quantum liquids are also of general relevance to a wide range of fields beyond low-temperature physics.

Constant thermodynamic tension Monte Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers

Abstract: A constant thermodynamic tension Monte Carlo method is introduced and applied studies of the elastic properties of a two-dimensional system of hard cyclic hexamers. Elastic compliances and elastic constants are determined at a number of different values of the pressure. The existence of the phase transition between a tilted and a straight phase is confirmed. The results obtained strongly suggest that the Poisson modulus can be negative in the tilted phase.

Determination of Oxygen Nonstoichiometry in a High-Tc Superconductor Ba2YCu3O7-δ

Abstract: In order to elucidate the correlations between composition, structure and electrical properties of a high-Tc superconductor Ba-Y-Cu-O system, thermogravimetric measurement and chemical analysis of oxygen nonstoichiometry were made at a temperature range of 350 to 1000°C and under the oxygen partial pressure of 10-4 to 1 atm. Within a stability range of the composition Ba2YCu3O7-δ, the oxygen deficiency, δ, was found to vary approximately from zero to 0.9, with associated mean valence of copper ions varying from 2.33 to 1.73. At a possible phase boundary region of tetragonal to orthorhombic crystal structures, no sign of discontinuity in δ was observed, suggesting its phase transition was of higher than a first order.

Observation of a phase transition of stored laser-cooled ions.

Abstract: Clouds of two to about fifty simultaneously stored, laser-cooled ${\mathrm{Mg}}^{+}$ ions in a Paul trap were observed in two phases, which are clearly distinguishable by their excitation spectra. Transitions between these phases can be induced either by a variation of the power of the laser radiation used to cool the ions or by a change of the size of the radio-frequency voltage applied to the trap. Transitions between a "crystalline" phase and a "gaseous" phase can be repeatedly observed by variation of the appropriate parameters. The two phases and the transitions between them have also been recorded by a photon-counting image system.

Statistical Macrodynamics of Large Dynamical Systems. Case of a Phase Transition in Oscillator Communities

Abstract: A model dynamical system with a great many degrees of freedom is proposed for which the critical condition for the onset of collective oscillations, the evolution of a suitably defined order parameter, and its fluctuations around steady states can be studied analytically. This is a rotator model appropriate for a large population of limit cycle oscillators. It is assumed that the natural frequencies of the oscillators are distributed and that each oscillator interacts with all the others uniformly. An exact self-consistent equation for the stationary amplitude of the collective oscillation is derived and is extended to a dynamical form. This dynamical extension is carried out near the transition point where the characteristic time scales of the order parameter and of the individual oscillators become well separated from each other. The macroscopic evolution equation thus obtained generally involves a fluctuating term whose irregular temporal variation comes from a deterministic torus motion of a subpopulation. The analysis of this equation reveals order parameter behavior qualitatively different from that in thermodynamic phase transitions, especially in that the critical fluctuations in the present system are extremely small.

Dynamics of the structural glass transition and the p-spin-interaction spin-glass model.

Abstract: The mathematical structure of the dynamical theory for the soft-spin version of the $p$-spin-interaction ($pg2$) spin-glass model is related to that for the dynamical theories of the structural glass transition. The phase transitions predicted by both theories are discussed. The spin-glass transition predicted by the dynamical theory is related to a broken-replica-symmetry equilibrium calculation.

A differential scanning calorimetric study of the thermotropic phase behavior of model membranes composed of phosphatidylcholines containing linear saturated fatty acyl chains.

Abstract: The thermotropic phase behavior of a series of 1,2-diacylphosphatidylcholines containing linear saturated acyl chains of 10-22 carbons was studied by differential scanning calorimetry. When fully hydrated and thoroughly equilibrated by prolonged incubation at appropriate low temperatures, all of the compounds studied form an apparently stable subgel phase (the Lc phase). The formation of the stable Lc phase is a complex process which apparently proceeds via a number of metastable intermediates after being nucleated by incubation at appropriate low temperatures. The process of Lc phase formation is subject to considerable hysteresis, and our observations indicate that the kinetic limitations become more severe as the length of the acyl chain increases. The kinetics of Lc phase formation also depend upon whether the acyl chains contain an odd or an even number of carbon atoms. The Lc phase is unstable at higher temperatures and upon heating converts to the so-called liquid-crystalline state (the L alpha phase). The conversion from the stable Lc to the L alpha phase can be a direct, albeit a multistage process, as observed with very short chain phosphatidylcholines, or one or more stable gel states may exist between the Lc and L alpha states. For the longer chain compounds, conversions from one stable gel phase to another become separated on the temperature scale, so that discrete subtransition, pretransition, and gel/liquid-crystalline phase transition events are observed.(ABSTRACT TRUNCATED AT 250 WORDS)

Phase transitions in Langmuir monolayers of polar molecules

Abstract: Insoluble Langmuir monolayers are investigated in the presence of dipolar forces which can have two origins: permanent dipoles in neutral monolayers and induced dipoles in charged monolayers. The main effect of the additional long‐range repulsive interactions is to stabilize undulating phases at thermodynamic equilibrium. Phase diagrams are obtained in two limits: close to the liquid–gas critical point via a Ginzburg–Landau expansion of the free energy (mainly within a mean‐field approximation), and at low temperatures by free energy minimization. Possible applications of this theory to experiments at the liquid–gas, liquid expanded–liquid condensed, and solid–liquid transitions are discussed.

Mixed valence as an almost broken symmetry.

Abstract: By using a generalized version of the infinite-$U$ Anderson model, strong-coupling properties of mixed-valence systems are modeled by means of an expansion about a broken-symmetry mean-field theory. A renormalized Fermi liquid, with heavy-fermion bands in the lattice is an intrinsic feature of this mean-field theory. Strong-coupling divergence of the Kondo coupling constant arises as a direct consequence of the zero-mode fluctuations about the broken-symmetry state. In the large-degeneracy limit these fluctuations vanish and the broken-symmetry state is an exact solution, explicitly confirmed for the single-impurity case by a new Bethe-ansatz solution. The crossover to strong coupling is a vestige of the phase transition into the broken-symmetry state. Landau parameters, charge and spin correlations of the heavy Fermi liquid are directly related to the fluctuations about the broken-symmetry state. The general approach presented is applicable to an arbitrary number of impurities or a lattice. Analytic results are presented for the Landau parameters, the dynamical charge and spin correlations in the one- and the two-impurity models, and the one-impurity $f$ spectral function.

Phase transitions in a cylindrical pore

Abstract: We report adsorption isotherms for a Lennard-Jones fluid confined in a cylindrical pore with attractive walls at temperatures above the wetting temperature. A low temperature isotherm exhibited two branches with metastable states and hysteresis. The grand potential of the system was calculated and the thermodynamic transition between the two branches of the isotherm was found. This transition is shifted to lower pressures than the bulk transition; the Kelvin equation was found not to predict accurately the shift. A higher temperature isotherm, still below the bulk critical point, was continuous and reversible and no hysteresis was found. This confirms the existence of a capillary critical point for the confined fluid. The mean field density functional theory which has been used to study confined fluids is found to give the correct qualitative features of the phase behaviour, in agreement with other studies.

Reentrant phase transition of N‐isopropylacrylamide gels in mixed solvents

Abstract: Reentrant volume–phase transitions are observed in N‐isopropyoacrylamide gels in the methanol–water mixtures. When the solvent composition is varied systematically, the gel undergoes two transitions: a discontinuous collapsing followed by a discontinuous swelling. The reentrant transition defines a closed‐loop instability phase boundary having both upper and lower critical points. The closed‐loop phase boundary depends on temperature and diminishes to a point at approximately 0 °C. A simple mean field theory is presented to describe the phenomenon, which reveals an alteration of free energy of alcohol–water interaction by presence of polymer network. In the case of ethanol–water mixtures, there appear two closed‐loop phase boundaries, whose physico‐chemical basis are not yet clear.

The phase transition in a general class of Ising-type models is sharp

Abstract: For a family of translation-invariant, ferromagnetic, one-component spin systems—which includes Ising and ϕ4 models—we prove that (i) the phase transition is sharp in the sense that at zero magnetic field the high- and low-temperature phases extend up to a common critical point, and (ii) the critical exponent β obeys the mean field bound β⩽1/2. The present derivation of these nonperturbative statements is not restricted to “regular” systems, and is based on a new differential inequality whose Ising model version isM⩽βhχ+M3+ βM2∂M/∂β. The significance of the inequality was recognized in a recent work on related problems for percolation models, while the inequality itself is related to previous results, by a number of authors, on ferromagnetic and percolation models.

Phase transitions in flexible polymeric surfaces.

Abstract: The statistical mechanics of polymerized surfaces with a finite bending rigidity \ensuremath{\kappa}' is studied via the Monte Carlo method. The model system consists of a hexagon, L atoms across, excised from a triangular lattice embedded in three-dimensional space. Nearest-neighbor atoms interact via an infinite-square-well potential, while the bending energy is proportional to the (negative) scalar product of unit normals to adjacent triangles. Self-avoiding interactions are not included. The largest hexagon considered (L=19) consists of 271 atoms. Unlike linear polymers or liquid membranes, these surfaces undergo a remarkable finite-temperature crumpling transition, with a diverging specific heat. For small \ensuremath{\kappa}=\ensuremath{\kappa}'/${k}_{B}$T, the surface is crumpled, and the radius of gyration ${R}_{g}$ grows as \ensuremath{\surd}lnL . For large \ensuremath{\kappa} we find that the surface remains flat, i.e., ${R}_{g}$\ensuremath{\sim}L. Our results demonstrate the presence of a finite-temperature (second-order) crumpling transition, and provide a lower bound on a related transition in real self-avoiding membranes.

Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability

Abstract: For the motion of a one-dimensional viscoelastic material of rate type with a non-monotonic stress-strain relation, a mixed initial boundary value problem is considered. A simple existence theory is outlined, based on a novel transformation of the equation into the form of a degenerate reaction-diffusion system. This leads to new results characterizing the regularity of weak solutions. It is shown that each solution tends strongly to a stationary state asymptotically in time. Stable stationary states are characterized. Stable states may contain coexistent phases, i.e. they may have discontinuous strain. They need not be minimizers of energy in the strong sense of the calculus of variations; “metastable” and “absolutely stable” phases may coexist in a stable state. Furthermore, such states do arise as long-time limits of smooth solutions. Beyond the above, “hysteresis” and “creep” phenomena are exhibited in a model of a loaded viscoelastic bar. Also, a viscosity criterion is proposed for the admissibility of propagating waves in the associated purely elastic model. This criterion is then applied to describe the formation of some propagating phase boundaries in a loaded elastic bar.

Phase Transition of a Polymer Gel in Pure and Mixed Solvent Media

Abstract: A volume phase transition of poly-N-isopropylacrylamide (NIPA) gel immersed in some pure and mixed solvents has been investigated experimentally. A slightly discontinuous transition of NIPA get in water changed to a more distinctly first-order transition on adding a small amount (<20%) of alcohols to water. As the concentration of alcohols in the mixed solvent increased further, the volume transition blurred and eventually disappeared. Analyzing the experimental results on the basis of the mean field theory of polymer solution, it has been shown that the polymer-solvent interaction parameter χ exhibits a drastic change at the volume transitions. This indicates that the enthalpy and entropy of solution depend strongly on polymer concentration.