Relaxation processes and structural transitions in stretched films of polyvinylidene fluoride and its copolymer with hexafluoropropylene

Relaxation processes and structural transitions in nonstretched and uniaxially stretched films of poly(vinylidene fluoride-hexafluoropropylene) (P(VDF-HFP)) and its homopolymer polyvinylidene fluoride (PVDF) for comparison were investigated with the aim of understanding the electromechanical properties of this lower-modulus ferroelectric copolymer. The mechanical and the dielectric response at the glass transition (?? _a relaxation) exhibit similar temperature dependence of the relaxation time, whereas mechanical and dielectric processes above the glass transition are not related. They represent a continuous softening process within the amorphous phase and the dielectric ?? _c relaxation, respectively. The latter is attributed to conformational changes of VDF segments in lamellae of spherulites constituting the nonpolar crystalline ?? phase. Furthermore, there is a contribution from melting of secondary crystallites formed in the amorphous phase during annealing or storage. Mechanically, this transition appears in nonstretched and stretched films as an accelerated decrease of the elastic modulus that terminates the rubber plateau. Dielectrically, this transition becomes visible as a frequency-independent loss peak only in stretched films, because stretching removes the ?? _c relaxation, which superimposes the transition in nonstretched films. Melting of secondary crystallites is shown to appear in the homopolymer, too, though less pronounced because of more complete primary crystallisation. Stretching increases the modulus above the glass transition only slightly, and it does not significantly influence the softening process. On the other hand, stretching causes a spontaneous polarisation and introduces order within the amorphous phase, rendering it more polar. Melting of secondary crystallites provides an additional contribution to the polarisation. These findings may explain the relatively high electromechanical activity of P(VDF-HFP) but also its relatively low thermal stability. Moreover, they may be important for correct procedure and analysis of temperature-dependent dielectric measurements on partially crystalline polymers, in particular on those with less favourable sterical conditions for primary crystallisation.     

Low-frequency critical dynamics in (CnH2n+1NH3)2SnCl6 model biomembrane systems

Nuclear magnetic resonance has been employed as a probe for the collective hydrocarbon chain dynamics in the organic–inorganic model biomembranes (C_nH_2n+1NH₃)₂SnCl₆, undergoing order–disorder and conformational phase transitions. No anomalies were observed in the laboratory-frame spin–lattice relaxation measurements at the order–disorder phase transitions, whereas a discontinuity was manifest at the conformational phase transitions characteristic of a first-order phase transition. On the other hand, our rotating frame spin–lattice relaxation measurements revealed a low-frequency critical collective chain dynamics in the kilohertz regime associated with the order–disorder phase transition.     

H NMR study of the phase transitions of trissarcosine calcium chloride single crystals at low temperature

The ¹H NMR line-width and spin-lattice relaxation time T₁ of TSCC single crystals were studied. Variations in the temperature dependence of the spin-lattice relaxation time were observed near 65 and 130 K, indicating drastic alterations of the spin dynamics at the phase transition temperatures. The changes in the temperature dependence of T₁ near 65 and 130 K correspond to phase transitions of the crystal. The anomalous decrease in T₁ around 130 K is due to the critical slowing down of the soft mode. The abrupt change in relaxation time at 65 K is associated with a structural phase transition. The proton spin-lattice relaxation time of this crystal also has a minimum value in the vicinity of 185 K, which is governed by the reorientation of the CH₃ groups of the sarcosine molecules. From this result, we conclude that the two phase transitions at 65 and 130 K can be discerned from abrupt variations in the ¹H NMR relaxation behavior, and that ¹H nuclei play important roles in the phase transitions of the TSCC single crystal.     

Precursor phenomena in frustrated systems

To understand the origin of the dynamical transition, between high-temperature exponential relaxation and low-temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in the presence of disorder) or fully frustrated Ising (in the absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case.     

Transition order and dynamics of a model with competing exchange and dipolar interactions

We performed Monte Carlo simulation of phase transitions from isotropic stripe phase with short-range order to long-range stripe phase in a model with competing ferromagnetic exchange and antiferromagnetic dipolar interactions on triangular lattice. We calculated phase diagram for different values of exchange and dipolar interaction constants ratio, η. We also determined the order of the transitions to stripe phases AFh of different stripe widths h: first-order phase transition was found to transitions into AF1 and AF2 phases, while transitions to AF3 and AF4 phases were of the second order. In the phase diagram the tricritical point was determined at the AF2 and AF3 phase boundary. We observed the peak of nematic phase at the transition region to the AF1 phase, but found it metastable at low values of η. We have also found that in AF1 phase spin relaxation corresponds to the Ising model dynamics. In phases AF3 and AF4 the dynamics slows down, and stripe domain growth with time is proportional to logt.     

Phase transition and ferroelastic property studied by using the Cs nuclear magnetic resonance in a CsHSO4 single crystal

The ¹³³Cs spin-lattice relaxation time in a CsHSO₄ single crystal was measured in the temperature range from 300 to 450 K. The changes in the ¹³³Cs spin-lattice relaxation rate near T_c1 (=333 K) and T_c2 (=415 K) correspond to phase transitions in the crystal. The small change in the spin-lattice relaxation time across the phase transition from II to III is due to the fact that during the phase transition, the crystal lattice does not change very much; thus, this transition is a second-order phase transition. The abrupt change of T₁ around T_c2 (II-I phase transition) is due to a structural phase transition from the monoclinic to the tetragonal phase; this transition is a first-order transition. The temperature dependences of the relaxation rates in phases I, II, and III are indicative of a single-phonon process and can be represented by T₁⁻¹=A+BT. In addition, from the stress-strain hysteresis loop and the ¹³³Cs nuclear magnetic resonance, we know that the CsHSO₄ crystal has ferroelastic characteristics in phases II and III.     

Phase diagram of antiferromagnetic cobalt fluoride

The H-T phase diagram of antiferromagnetic cobalt fluoride in an external magnetic field H perpendicular to the easy magnetization axis A is completed and used to construct a phase diagram in the variables H _z and H _y . In this diagram, the lines corresponding to second-order phase transitions (between an angular phase and a phase with antiferromagnetic vector I ⊥ A) begin and end in fields of a spin-flip transition (i.e., in an exchange field). A peculiarity of these lines of phase transitions is that each of them has two tricritical points at which this line of second-order phase transitions transforms into a line of first-order phase transitions. A critical angle between the direction of the external magnetic field and the basal plane within which the first-order phase transition takes place is determined.     

Crystal-glass phase transitions in the adatom layers

Phase transitions in the two-dimensional crystalline films adsorbed onto an imperfect substrate (with impurities and defects) are analyzed. It is shown that the phase transition from the commensurate long-range-order (LRO) crystal to the glass state occurs with increase of impurity concentration. The orientational correlation function is shown to tend algebraically to zero at large distances in the glass state. The influence of defects on the phase transition from the LRO-commensurate crystal to the disordered state at the definite temperature T_m is considered.     

Phase transitions in ferroelectric polymer films

Phase transitions in ferroelectric films of vinylidene fluoride-trifluoroethylene (70/30) copolymer are studied by differential scanning calorimetry (DSC). Films 40 nm thick are prepared from solution by centrifugation. DSC thermograms reveal peaks typical of the first-order phase transition that are associated with heat absorption and heat release, and the enthalpies of the transitions are determined. Upon cooling, a kink in the slope of the DSC curve that determines the temperature of the glass transition is observed at T = ?30°C.     

Magnetic properties of Ising metamagnet in both external longitudinal and transverse fields

The phase diagrams of a two-sublattice Ising metamagnet at finite temperature in a mixed longitudinal field and a transverse magnetic field are investigated by the use of an effective-field theory (EFT) with correlations. In addition to the second-order transition lines, the first-order transition lines are also presented in the phase diagrams, since the Gibbs free energy can be calculated numerically. The results show that there is no fourth-order critical line in the phase diagrams given by using EFT as found by using mean-field theory (MFT). The tricritical lines and their projection in the t−h_x plane obtained by using EFT are also quite different from those by using MFT. Only one type of phase diagram is obtained by using EFT while three kinds of phase diagrams are obtained by using MFT, which indicates that only the first kind of phase diagrams obtained by using MFT is reliable. Furthermore, it is shown that the region of first-order transitions increases as the transverse magnetic field h_x decreases.     

Temperature Dependence of Structural Relaxation in Glass-Forming Liquids and Polymers

Understanding the microscopic mechanism of the transition of glass remains one of the most challenging topics in Condensed Matter Physics. What controls the sharp slowing down of molecular motion upon approaching the glass transition temperature T_g, whether there is an underlying thermodynamic transition at some finite temperature below T_g, what the role of cooperativity and heterogeneity are, and many other questions continue to be topics of active discussions. This review focuses on the mechanisms that control the steepness of the temperature dependence of structural relaxation (fragility) in glass-forming liquids. We present a brief overview of the basic theoretical models and their experimental tests, analyzing their predictions for fragility and emphasizing the successes and failures of the models. Special attention is focused on the connection of fast dynamics on picosecond time scales to the behavior of structural relaxation on much longer time scales. A separate section discusses the specific case of polymeric glass-forming liquids, which usually have extremely high fragility. We emphasize the apparent difference between the glass transitions in polymers and small molecules. We also discuss the possible role of quantum effects in the glass transition of light molecules and highlight the recent discovery of the unusually low fragility of water. At the end, we formulate the major challenges and questions remaining in this field.     

Nonequilibrium tricritical point in a system with long-range interactions

Systems with long-range interactions display a short-time relaxation towards quasistationary states whose lifetime increases with system size. With reference to the Hamiltonian mean field model, we here show that a maximum entropy principle, based on Lynden-Bell's pioneering idea of "violent relaxation," predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (nonzero magnetization) quasistationary states. When varying the initial condition within a family of "water bags" with different initial magnetization and energy, first- and second-order phase transition lines are found that merge at an out-of-equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.     

Investigation of polyamorphism in compressed B<Subscript>2</Subscript>O<Subscript>3</Subscript> glass by the direct measurement of the density

Precise measurements of the relative volume change of vitreous B₂O₃ have been performed by the strain-gauge technique at hydrostatic pressures up to 9 GPa. The features of the strain-gauge technique are analyzed and the specificity of the measurements of “relaxed” and “unrelaxed” bulk moduli is discussed. Smeared anomalies of compressibility (at P > 0.5 GPa and P > 5 GPa) and logarithmic relaxation of the glass density are observed. A significant (by several times!) difference has been revealed between the relaxed bulk modulus of glass obtained from the volume measurements and the unrelaxed modulus estimated from the Brillouin spectroscopic data. The measurements of the relative volume change under compression together with the previous structure investigations and computer simulation results reveal the basic features of the phase transitions in B₂O₃ glass. Both direct and reverse transitions are smeared in pressure. The residual densification in glass is not associated with change in the short-range order.     

Langevin dynamics of a π4-model with long range interactions

The Dominicis-Peliti generating functional (GF) method is used for the investigation of a Langevin dynamics of the π⁴-model: the symmetric double-well on-site potential and the infinite range interparticle interaction. We limit ourselves to the range above the temperature of the second order phase transition. The role of the 1/N-fluctuations (where N is the number of particles) is systematically investigated by using the steepest descent method. It is shown that the functional Legendre transformation directly results in the kinetic equation for the complete correlation function. Although this equation resembles the mode coupling equations used to describe the glass transition, it is qualitatively different. The solutions of this non-linear equation are investigated. It is shown that 1/N-fluctuations do not result in a breaking or ergodicity if the mean-field correlator is ergodic. On the other hand, if the mean-field correlator is nonergodic (e.g. if the time is much less than the inverse Kramers rate) then 1/N-fluctuations restore the ergodicity with characteristic relaxation time proportional to N.     

Thermomodulation experiments at the cubic-to-tetragonal phase transition in SrTiO3

After a brief comment on the important features of strontium titanate and a critical review of recent optical work in this material, thermoabsorption results at the cubic-to-tetragonal second-order phase transition are reported. Use of insulating samples has been possible by means of indirect heating. Optical evidence of the phase change is seen for the momentum-forbidden transitions starting at the indirect gap energy. This is discussed in terms of the relaxation of the momentum condition brought about by structural fluctuations near the transition temperature T₀. Part of the effect may be related to the increasing static distortion of the lattice in the tetragonal state. The results presented also confirm earlier pictures of the absorption threshold as due to LO-phonon-assisted Γ₁₅→X₃ transitions (with phonon energy equal to 52 meV). Furthermore, in the vicinity of T₀, an extra thermomodulation signal, corresponding to a weak absorption threshold ? 20 meV higher than the gap, becomes visible. This critical point is also particularly sensitive to the application of electric fields, as found by electroabsorption results obtained at liquid nitrogen temperature.     

Stretched exponential relaxation on the hypercube and the glass transition

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution p the form of the relaxation of the memory function q(t) can be accurately parametrized by a stretched exponential over several orders of magnitude in q(t). As the critical dilution for percolation is approached, the time constant tends to diverge and the stretching exponent drops towards 1/3. As the same pattern of relaxation is observed in a wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube appears to be a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition may be pictured as a percolation transition in phase space. Received 16 June 2000 and Received in final form 13 October 2000     

Thermoplastic Elastomer Phase Changing Materials for Stiffness Modulation

Abstract

Four natural rubber-based phase changing materials (PCMs) were synthesized and evaluated with the goal of achieving controlled stiffness modulation at elevated temperatures (～100-120?°C). The phase changing was achieved through either the glass transition or melt transition of one of four phase changing fillers: polystyrene, poly(methyl methacrylate), low density polyethylene, and indium tin alloy. The PCM stiffness was analyzed using dynamic mechanical analysis and the results showed that all four PCMs exhibited two thermal transitions: a low temperature transition at ?58?°C due to the glass transition of the natural rubber matrix and a high temperature transition at ～100-120?°C due to the thermal transitions in the four filler materials. The degree of stiffness change of all PCMs at 100-120?°C was found to be strongly influenced by the type of the phase changing filler as well as the type of thermal transition (glass transition versus melt transition). The compatibilities of the phase changing materials were analyzed using the Flory-Huggins interaction parameter and it was shown that natural rubber and low density polyethylene had the best compatibility. All systems exhibited effective stiffness modulation with the change in temperature, enabling them to be used for applications requiring variable stiffness control.     

Spectroscopy of electron subbands on Ge-(111)

We report on the resonant excitation of electronic surface subbands at far-infrared energies. Distinct lines for transitions from the lowest-lying n = 0 subband to the n = 1 and 2 states are observed. The transition energies are compared to a subband calculation. Typical linewidths are of order 2 meV and indicate an intersubband relaxation rate which is ～ $\text{1}\text{10}$ of the scattering rate derived from the surface mobility. The 0→ 1 transition shows additional structure on the low energy side.     

Effects of point defects on the phase diagram of vortex states in high- T(c) superconductors in the B parallel to c axis

The phase diagram for the vortex states of high- T(c) superconductors with point defects in the B--> parallel to c axis is drawn by large-scale Monte Carlo simulations. The vortex slush (VS) phase is found between the vortex glass (VG) and vortex liquid (VL) phases. The first-order transition between this novel normal phase and the VL phase is characterized by a sharp jump of the density of dislocations. The first-order transition between the Bragg glass (BG) and VG or VS phases is also clarified. These two transitions are compared with the melting transition between the BG and VL phases.     

Frustrated Blume-Emery-Griffiths model

A generalised integer S Ising spin glass model is analysed using the replica formalism. The bilinear couplings are assumed to have a Gaussian distribution with ferromagnetic mean . Incorporation of a quadrupolar interaction term and a chemical potential leads to a richer phase diagram with transitions of first and second order. The first order transition may be interpreted as a phase separation, and contrary to what has been argued previously, it persists in the presence of disorder. Finally, the stability of the replica symmetric solution with respect to fluctuations in replica space is analysed, and the transition lines are obtained both analytically and numerically. Received 13 January 1997