Spinodal Limit Research Articles

Strain pseudospins with power-law interactions: Glassy textures of a cooled coupled-map lattice

We consider a spin-1 model of strain pseudospins $S(\stackrel{P\vec}{r})=0,\ifmmode\pm\else\textpm\fi{}1$ that arise from a triple-well Landau free energy for a square/rectangle or ``austenite-martensite'' structural transformation of a two-dimensional lattice. The pseudospin model has elastic-compatibility-induced power-law anisotropic (PLA) interactions and no quenched disorder. The iteratively solved local mean-field equations for $⟨S(\stackrel{P\vec}{r},t)⟩$ form a temperature-dependent PLA-coupled nonlinear-map lattice, where $t$ is the iteration ``time.'' On cooling at a constant rate, the excess entropy shows a weak roll-off near a temperature $T={T}_{g}$ and a sharper elbow at a lower ${T}^{\ensuremath{\ast}}$, just above a Kauzmann-type ${T}_{K}$ where the excess entropy would have become negative. The crossover temperatures ${T}_{g},{T}^{\ensuremath{\ast}}$ decrease logarithmically with cooling rate and mark stability changes in spatiotemporal attractors of the cooled PLA-coupled map. Three phases in $⟨S(\stackrel{P\vec}{r},t)⟩$ are found, with textures of the martensitic-variant domain walls as ``inherent structures.'' There is a high-temperature $(Tg{T}_{g})$ fine scale phase of feathery domain walls and an intermediate temperature $({T}_{g}gTg{T}^{\ensuremath{\ast}})$ phase of mazelike domain walls, with both showing square-wave oscillations as predominantly period-two attractors but with minority-frequency subharmonic clusters. Finally, there is a low-temperature freezing $({T}^{\ensuremath{\ast}}gT)$ to a static fixed point or period-one attractor of coarse, irregular bidiagonal twins, as in a strain glass. A Haar-wavelet analysis is used to identify the local attractor dynamics. A central result is that dynamically heterogeneous and mobile low-strain droplets act as catalysts, and can form correlated chains or transient ``catalytic corrals'' to incubate an emerging local texture. The hotspot lifetime vanishes linearly in $T\ensuremath{-}{T}_{K}$, suggesting that ${T}_{K}$ is a dynamic spinodal limit for generating the ``austenitic'' catalyst, the disappearance of which drives a trapping into one of many bidiagonal glassy states. The model has relevance to martensitic or complex-oxide textures, coupled-map lattices, and configurational-glass transitions.

Prediction of micro-explosion delay of emulsified fuel droplets

Burning a water-in-oil emulsion enables reduction in solid and gaseous pollutants in comparison with neat oil. In the emulsion, Heavy Fuel-Oil and water lie in distinct phases, having a high difference in boiling point (up to 200 K). In an emulsion droplet injected and subsequently heated inside a flame, the internal water droplets are enclosed inside the emulsion and do not systematically vaporise at boiling point. They are known to reach a metastable state, breaking up at a temperature below the spinodal limit of water. From this moment, the surrounding Fuel-Oil is fragmented into numerous faster and smaller droplets by the suddenly expanding steam. This physical phenomenon is called “micro-explosion”. This work demonstrates a numerical modelisation of unsteady heat and mass transfer at the surface and inside of the emulsion droplet, and provides a prediction of its micro-explosion delay, using homogeneous nucleation hypothesis. This assumption of homogeneous nucleation for internal water droplets matches the use of a “drop tower” experimental facility. Finally, comparisons between predicted ranges for micro-explosion delays and experimental delays from literature are discussed, along with combustion parameters (ambient temperature, relative velocity) and combustible emulsion parameters. As a result, the experimental and numerical micro-explosion delays decrease with liquid or ambient temperature and relative velocity, and increase with water content and radius of emulsion droplet. Their low average deviation reveals the accuracy of the assumption of homogeneous nucleation in the considered situations.

Molecular dynamics study of a simple liquid at negative pressures

We investigate the effect of isochoric cooling of the Lennard–Jones liquid at the triple point i.e. ρ ⁎ = 1.20 r 0, T ⁎ = 0.70 into the negative pressure region of crystal + vapor phase with temperatures varying from T ⁎ = 1.00 to 0.0001. Along this line, initially, the liquid remains stable with respect to its crystallization, and is metastable with respect to liquid-vapor nucleation. The objective is to determine the limits of metastability extrapolated to sub-triple point temperatures along the line of crystal-liquid coexistence, and to explore the mechanism of return to thermodynamic equilibrium, i.e. crystal + vapor stability. It is found that a transient unstable phase is encountered at the reduced temperature T ⁎ = 0.3250 for a N = 4000 atom system, and T ⁎ = 0.45 for N = 32,000. The results indicate that T ⁎ = 0.35 and T ⁎ = 0.50 are the spinodal limits for simple liquids at the triple point density ρ ⁎ = 1.2 for both systems respectively. The pressure line changes its slope from negative to positive as the new phase i.e. crystal + hole (vapor) begins to form. The transformation mechanism from supercooled liquid to crystal + vapor is two-stage; first “metastable liquid” at negative pressure to “liquid + hole” at zero pressure, then from “liquid + hole” to “crystal + hole”.

Femtosecond laser ablation of metals and crater formation by phase explosion in the high-fluence regime

This work presents a two-dimensional theoretical model for numerical simulation of femtosecond laser ablation of metals and crater formation, based on the phase explosion mechanism. Parametric studies are carried out to reveal the ablation phenomena with emphasis on the topography formation by a laser pulse. Experiments are also conducted for fs laser ablation of Ni. The results show that the phase explosion model can effectively predict the crater shape as well as the ablation rate in the high-fluence regime where the lattice temperature approaches the spinodal limit.

Fluctuation induced first-order phase transitions in a dipolar Ising ferromagnetic slab

We investigate the competition between the dipolar and the exchange interaction in a ferromagnetic slab with finite thickness and finite width. From an analytical approximate expression for the Ginzburg-Landau effective Hamiltonian, it is shown that, within a self-consistent Hartree approach, a stable modulated configuration arises. We study the transition between the disordered phase and two kinds of modulated configurations, namely, striped and bubble phases. Such transitions are of the first-order kind and the striped phase is shown to have lower energy and a higher spinodal limit than the bubble one. It is also observed that striped configurations corresponding to different modulation directions have different energies. The most stable are the ones in which the modulation vanishes along the unlimited direction, which is a prime effect of the slab's geometry together with the competition between the two distinct types of interaction. An application of this model to the domain structure of MnAs thin films grown over GaAs substrates is discussed and general qualitative properties are outlined and predicted, like the number of domains and the mean value of the modulation as functions of temperature.

More about Rotons in Superfluid Helium 4

In a recent paper1 it was argued that rotons in superfluid helium 4 are the soft modes announcing a charge density wave that leads to the crystal: rotons are a normal state property. A small superfluid condensate acts to hybridize quasiparticles and soft density fluctuations - hence a level repulsion that lowers the energy: superfluidity is energetically favourable. A shallow roton implies a very small condensate density, as found in He4: what we need is a saturation mechanism. The clue is depletion due to quantum fluctuations. In (1) we assumed that such a depletion was drawn from the condensate itself: superfluidity then disappears in the liquid if the roton gap is too small. Here we explore an alternate possibility: quantum fluctuations are drawn from the normal fluid. We reach the opposite conclusion: superfluidity persists down to the spinodal limit where the roton gap vanishes, with an unusual power law dependence. We briefly mention the possible extension of that argument to a frozen charge density wave: in a toy 1d model it might shed light on the features that favour supersolids.

Determining the nucleation rate from the dimer growth probability

A new method is proposed for the determination of the stationary one-component nucleation rate J with the help of data for the growth probability P2 of a dimer which is the smallest cluster of the nucleating phase. The method is based on an exact formula relating J and P2, and is readily applicable to computer simulations of nucleation. Using the method, the dependence of J on the supersaturation s is determined by kinetic Monte Carlo simulations of two-dimensional (2D) nucleation of monolayers on the (100) face of Kossel crystal. The change of J over nearly 11 orders of magnitude is followed and it is found that the classical nucleation theory overestimates the simulation J values by an s-dependent factor. The 2D nucleus size evaluated via the nucleation theorem is described satisfactorily by the classical Gibbs-Thomson equation and its corrected version accounting for the spinodal limit of 2D nucleation.

Growth below and above the spinodal limit: The cholesteric-nematic front

In classical crystal growth, the solid propagates into its metastable liquid, even in the fast-dynamics regime in which kinetic effects dominate the diffusive effects. In usual experiments, the liquid is always very far from its spinodal limit below which it becomes unstable. For that reason, very little is known about crystal growth just below and above the spinodal limit of the liquid. In order to tackle this problem, we have performed an experiment about the propagation of the cholesteric-nematic front in directional melting. We show experimentally that, in this system, it is possible to reach and pass the spinodal limit. We show the existence of many morphological transitions at increasing velocities which lead to the formation of metastable or unstable phases. A complete phase diagram is drawn up as a function of the front velocity and the sample thickness. In particular, the crossing of the spinodal limit is clearly identified by comparison with the morphologies observed in free growth (i.e., at a homogeneous temperature). We show that this passage is accompanied by a reversal (pi rotation) of the structure in thin samples only. This spectacular effect resembles a "cell-to-dendrite" transition and is chirality induced. The importance of the first-order character of the transition is also emphasized.

Spinodal and ideal glass limits for metastable liquids.

A spinodal line provides a high-temperature limit to the stability of a superheated liquid and a line of ideal glass transitions may provide a low-temperature limit for a supercooled liquid. For models in which the thermodynamic properties depend on only one independent external variable the line of ideal glass transition can be viewed as a second-order transition between two equilibrated phases and it meets the spinodal with the same slope at the maximum tension a stretched liquid can sustain. For real materials there are two independent external variables, temperature and pressure; the line of ideal glass transitions cannot be viewed as a second-order phase transition and the two lines need not have the same slope where they meet.

Phase separation of off‐critical polymer blends of poly(styrene‐co‐maleic anhydride) and poly(methyl methacrylate). I. Kinetics of spinodal decomposition

AbstractThe kinetics of phase separation via the spinodal decomposition of poly(styrene‐co‐maleic anhydride)/poly(methyl methacrylate) from a delay time period to late stages were investigated with a light scattering technique. The standard procedure for identifying four stages of spinodal decomposition, based on the characteristics of concentration fluctuations, was clearly introduced with the light scattering method. The spinodal limits were divided into four stages: the delay time, the early stage, the intermediate stage, and the late stage. The validity of the linearized theory was reviewed because it was used as an indicator of the limit of the early stage of spinodal decomposition, which divided the delay time period from the early stage and the early stage from the intermediate stage. The linearized theory fit the experimental results very well after the delay time. The scaled structure function of the melt‐mixed blend was analyzed. The universality of the scale structure function, F(x) = S(q,t)qm3(t) (where S is the structure function, x is equal to q/qm, q is the scattering wave vector, qm is the maximum wave vector, and t is the time in seconds), indicated the late stage of phase separation and divided the late stage from the intermediate stage. The simple normalized scaling function profile for the cluster region proposed by Furukawa described the experimental data very well, whereas the profile for deep quenching, which was recently suggested, showed some discrepancies. As a result of the phase separation, the processing of this blend may be able to be developed to provide the most suitable morphology. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 871–885, 2004

Spinodal Shifts of a Polymeric Blend Film on an Interacting Surface

We use the Gaussian chain model in half-space, to study surface interacting binary polymer blends for a system that is not laterally incompressible. We derive the partition function of the system to all orders of the surface interaction parameters and find the spinodal limits. Surface-spinodal lines are shifted from those of the bulk on changing the thickness of the film or surface interactions, due to the change of the average number of heterocontacts between the units of different kind. These heterocontacts generally decrease for opposite surface interactions of the two species and contribute to the stability of the blend while they increase for surface interactions of the same kind, leading to destabilization. We thus explain quantitatively the experimental observations of both positive and negative shifts of the spinodals of polymeric films. For large confinements, an increase of the stability of a film is seen. This agrees with what is found in polymer blends and mixtures of smaller molecules between...

Limits of metastability of liquid helium

Helium can remain in a metastable liquid state at a pressure below its saturated vapour pressure or above its melting pressure. This metastability can reach high degrees in helium because of its purity. We review the present knowledge of the stretched liquid state; experiments on cavitation are interpreted in relation to the existence of a liquid–gas spinodal limit. In view of recent experiments, we also consider overpressurized liquid helium 4 and address the question of the stability of the superfluid phase against the solid.

Cavitation pressure in liquid helium

Recent experiments have suggested that, at low enough temperature, the homogeneous nucleation of bubbles occurs in liquid helium near the calculated spinodal limit. This was done in pure superfluid helium 4 and in pure normal liquid helium 3. However, in such experiments, where the negative pressure is produced by focusing an acoustic wave in the bulk liquid, the local amplitude of the instantaneous pressure or density is not directly measurable. In this article, we present a series of measurements as a function of the static pressure in the experimental cell. They allowed us to obtain an upper bound for the cavitation pressure ${P}_{\mathrm{cav}}$ (at low temperature, ${P}_{\mathrm{cav}}<\ensuremath{-}2.4 \mathrm{bar}$ in helium 3, ${P}_{\mathrm{cav}}<\ensuremath{-}8.0 \mathrm{bar}$ in helium 4). From a more precise study of the acoustic transducer characteristics, we also obtained a lower bound (at low temperature, ${P}_{\mathrm{cav}}>\ensuremath{-}3.0 \mathrm{bar}$ in helium 3, ${P}_{\mathrm{cav}}>\ensuremath{-}10.4 \mathrm{bar}$ in helium 4). In this article we thus present quantitative evidence that cavitation occurs at low temperature near the calculated spinodal limit $(\ensuremath{-}3.1 \mathrm{bar}$ in helium 3 and $\ensuremath{-}9.5 \mathrm{bar}$ in helium 4). Further information is also obtained on the comparison between the two helium isotopes. We finally discuss the magnitude of nonlinear effects in the focusing of a sound wave in liquid helium, where the pressure dependence of the compressibility is large.

Nature of the liquid crystalline phase transitions in the cesium pentadecafluorooctanoate (CsPFO)-water system: the nematic-to-isotropic transition.

Deuterium NMR spectroscopy of 2H2O has been used to monitor the magnetic-field-induced order on approaching a transition to a nematic phase in isotropic solutions of disklike micelles of cesium pentadecafluorooctanoate. Highly accurate data on the phase boundaries and spinodals have been obtained for solutions with volume fraction concentration straight phi between 0.078 and 0.201. The quantity TIN-T*, where T* is the spinodal limit of the isotropic phase and TIN is the temperature at which the nematic phase first appears on cooling, decreases linearly with decreasing concentration, extrapolating to zero only at zero concentration. Thus, there is no evidence to support the presence of a Landau point along the transition line as has previously been conjectured. The values for (TIN-T*)/TIN are in the range 10(-5)-10(-4), up to two orders of magnitude smaller than corresponding values reported for calamitic thermotropic nematics. The transition gap (phiNI-phiIN)/phiIN approximately 0.33% for phi<0.20 is also very small, although finite as required for a first-order phase transition. These data, when combined with previously measured properties, present an intriguing picture of the isotropic-to-nematic phase transition in a paradigmatic system of self-assembled diskotic particles. However, it is not completely clear, within the context of current theoretical understanding, whether the behavior of this system is explicable by hard-particle models, or if the self-assembly plays a crucial role in weakening the phase transition.

Acoustic Nucleation of Solid Helium 4 on a Clean Glass Plate

We have used a focused acoustic wave to nucleate solid helium 4 on a clean glass plate. From the reflectance of light at the glass/helium interface, we measured the amplitude of the acoustic wave in the focal region. Nucleation was found to be stochastic, occurring 4.3±0.2 bar above the equilibrium melting pressure. This overpressure is 2 to 3 orders of magnitude larger than found in previous nucleation studies where favorable defects or impurities must have been present. From the statistics of nucleation and its temperature dependence above 300 mK, we have estimated the activation energy E for the nucleation on the glass plate; we have found E/k B T=10. This value is consistent with a thermally activated nucleation on a single site at the glass/helium interface. We also found a crossover to a quantum nucleation regime below 300 mK. We focally discuss some implications of these results for the homogeneous nucleation of solid helium and the search of a liquidsolid spinodal limit.

Effect of director fluctuations on the surface tension of nematic liquid crystals

We discuss the surface tension of a thermotropic nematic liquid crystal near the nematic-isotropic temperature. We find that certain experimentally observed features of the temperature trend that present difficulties to mean-field theoretical approaches can be attributed to director fluctuations. Our main result is the possibility of a minimum below T(NI) if the anchoring extrapolation length scales with reduced temperature in the spinodal limit as tx, with x<1. We also show in the case of partial nematic wetting that dampening of director fluctuations at the surface by anchoring at the nascent interface can reverse the sign of the surface tension discontinuity at T(NI).

Looped finger transformation in frustrated cholesteric liquid crystals.

Localized structures named "fingers" form in the vicinity of the unwinding transition of a cholesteric liquid crystal subjected to an electric field and to homeotropic boundary conditions. Several types of fingers exist, with different static and dynamic properties. For instance, cholesteric fingers of the second species (CF-2) can drift perpendicular to their axes and form spirals in ac electric fields, whereas fingers of the first species (CF-1) crawl along their axes. In this article we show that CF-2's are much easier to nucleate in thick samples (with respect to the pitch) than in thin ones and may form loops like the CF-1's, with or without defects. We show that looped CF-1's always collapse in thick samples at increasing voltage, whereas they can form cholesteric bubbles in thin samples. By contrast, we never observe the formation of a bubble from a loop of a CF-2 except when it possesses a point defect. We also recall that CF-1 segments always collapse at increasing voltage, whereas CF-2 segments systematically give cholesteric bubbles in similar conditions. To qualitatively explain these transformations, we use a simplified representation on the unit sphere S2 of the director field within the fingers. While the CF-1's are described within the standard model of Press and Arrot, we use for the CF-2's a recent model of Gil and Gilli, which we prove to explain most observations. We also describe the growth and collapse dynamics of a loop of a CF-2 in close connection with the spiral dynamics. Finally, we show experimentally and numerically that the CF-2's get abruptly thinner when the electric field exceeds the spinodal limit of the CF-1's. This transformation is reversible, but strongly hysteretic.

Cavitation in Normal Liquid Helium 3

We have studied cavitation, i.e. bubble nucleation, by focusing ultrasound hurts in normal liquid helium 3 at temperatures down to 40 mK. As in helium 4, cavitation is found to be stochastic, with a cavitation probability 0.5 at a given value of the sound amplitude, which we define as a “cavitation threshold”. This threshold is found significantly lower in helium 3 than in helium 4, a result which agrees with theoretical predictions of a spinodal limit at - 3.1 bar in helium 3 instead of- 9.5 bar in helium 4- We also measured the temperature variation of this cavitation threshold; it decreases with temperature as expected for a thermally activated nucleation process. We have not yet found any evidence for a crossover toward cavitation by quantum tunneling below 120 mK as predicted by several authors; if confirmed, it might indicate that the superfluid coherence plays a role in quantum cavitation.

Isotropic and Anisotropic Composition Fluctuations Close to the Order-to-Disorder Transition in an Asymmetric Diblock Copolymer Melt Subjected to Reciprocating Shear Fields

An asymmetric poly(ethylene-propylene)-poly(ethylethylene) (PEP-PEE) diblock copolymer was examined near the order-to-disorder transition temperature, TODT, by small-angle neutron scattering as a function of shear rate, $\dot{\gamma}$. Heating in the absence of shear disorders the material from a hexagonal structure at TODT=155±1 ○C. Application of a reciprocating simple shear field markedly influences the phase behavior near the ODT. Application of shear while heating increases TODT consistent with the theoretical prediction, $T_{\rm ODT}\sim\dot{\gamma}^{2} $. During fast cooling studies we observe an additional characteristic temperature, TS, at which the material spontaneously orders, which we interpret as a stability (i.e., spinodal) limit. this result also agrees with the theoretical prediction, $\tau_{\rm S}\sim\dot{\gamma}^{-1/3}$. Upon cessation of shear at temperatures close to but above the quiescent TODT a transient phase is observed before the system macroscopically disorders. The transient structure has a symmetry compatible with spheres arranged on a body centered cubic (BBC) space lattice, or undulating cylinders of the minority component (PEE). Anisotropic (i.e. lattice pinned) fluctuations can also be observed close to, but below, TODT upon heating the hexagonal structure under shear free conditions.

Ion dynamics studies of liquid and glassy silicates, and gas-in-liquid solutions

We give a brief review of ion dynamics studies of liquid and glassy states of SiO2 and silicate colutions which have been carried out in recent years in this laboratory. We summarize studies on SiO2, Na+ migration in Na2O·SiO2 in the “glassy state”, and ionic coordination in multicomponent framework silicates. We present new results on the coordination of Al3+ in albite as a function of pressure and show that it is consistent with results of laboratory studies on albite glasses formed at high pressure. We compare calculated PVT data for jadeite, albite and diopside and relate the behavior of the low pressure compressibility to the spinodal limit at negative pressures. Some preliminary studies of inert gas solution in jadeite and of CO2 solution in a glass having a composition of approximately Na2O·3SiO2 are described.