Showing papers on "Phase transition published in 1994"
TL;DR: Comparisons with the thermodynamic theory of phase transitions show that the lattice-Boltzmann-equation model can be made to correspond exactly to an isothermal process.
Abstract: We describe in detail a recently proposed lattice-Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey nonideal gas equations of state and can undergo a liquid-gas-type phase transition. The model is shown to be momentum conserving. From the microscopic mechanical stability condition, the densities in bulk liquid and gas phases are obtained as functions of a temperaturelike parameter. Comparisons with the thermodynamic theory of phase transitions show that the lattice-Boltzmann-equation model can be made to correspond exactly to an isothermal process. The density profile in the liquid-gas interface is also obtained as a function of the temperaturelike parameter and is shown to be isotropic. The surface tension, which can be changed independently, is calculated. The analytical conclusions are verified by numerical simulations.
1,222 citations
TL;DR: This work considers the stochastic background of gravity waves produced by first-order cosmological phase transitions from two types of sources: colliding bubbles and hydrodynamic turbulence and finds that the characteristic amplitude of the gravity wavesproduced is comparable to that from bubble collisions.
Abstract: We consider the stochastic background of gravity waves produced by first-order cosmological phase transitions from two types of sources: colliding bubbles and hydrodynamic turbulence. First we discuss the fluid mechanics of relativistic spherical combustion. We then numerically collide many bubbles expanding at a velocity v and calculate the resulting spectrum of gravitational radiation in the linearized gravity approximation. Our results are expressed as simple functions of the mean bubble separation, the bubble expansion velocity, the latent heat, and the efficiency of converting latent heat to kinetic energy of the bubble walls. A first-order phase transition is also likely to excite a Kolmogoroff spectrum of turbulence. We estimate the gravity waves produced by such a spectrum of turbulence and find that the characteristic amplitude of the gravity waves produced is comparable to that from bubble collisions. Finally, we apply these results to the electroweak transition. Using the one-loop effective potential for the minimal electroweak model, the characteristic amplitude of the gravity waves produced is h≃1.5×10^-27 at a characteristic frequency of 4.1 × 10^-3 Hz corresponding to Ω∼10^-22 in gravity waves, far too small for detection. Gravity waves from more strongly first-order phase transitions, including the electroweak transition in nonminimal models, have better prospects for detection, though probably not by LIGO.
738 citations
Book•
01 Dec 1994
TL;DR: In this paper, the authors present a survey of nonlinear optical properties observed in liquid crystals, including laser-induced nonelectronic optical nonlinearities in Liquid Crystals.
Abstract: Order Parameter, Phase Transition, and Free Energies. Nematic Liquid Crystals. Cholesteric, Smectic, and Ferroelectric Liquid Crystals. Light Scatterings. Laser--Induced Nonelectronic Optical Nonlinearities in Liquid Crystals. Thermal, Density, and Other Nonelectronic Nonlinear Mechanisms. Electronic Optical Nonlinearities. Introduction to Nonlinear Optics. Nonlinear Optical Phenomena Observed in Liquid Crystals. Index.
498 citations
TL;DR: High-pressure x-ray diffraction and optical absorption are used to study the wurtzite to rock salt structural transformation in CdSe nanocrystals, showing that both the thermodynamics and kinetics of this transformation are altered in finite size, as compared to bulk Cd Se.
Abstract: Measurements of the size dependence of a solid-solid phase transition are presented. High-pressure x-ray diffraction and optical absorption are used to study the wurtzite to rock salt structural transformation in CdSe nanocrystals. These experiments show that both the thermodynamics and kinetics of this transformation are altered in finite size, as compared to bulk CdSe. An explanation of these results in the context of transformations in bulk systems is presented. Insight into the kinetics of transformations in both bulk and nanocrystal systems can be gained.
487 citations
TL;DR: In this paper, the authors have suggested the pair formation of transverse dipole moments in adjacent smectic layers as the cause of antiferroelectricity in liquid crystals.
Abstract: In a brief history of the discovery of antiferroelectricity in liquid crystals, the important role played by tristable switching, i.e. an electric field induced phase transition from antiferroelectric SCA* to ferroelectric SC*, has been emphasised and the antiferroelectric herringbone structure of SCA* has been presented. Then we have explained how to identify the subphases in the SC* region, e.g. SCγ*, SCα*; the clarification of the subphase structures is essential for understanding antiferroelectricity in liquid crystals. After summarizing the evidence for the SCA* structure presented, we have suggested the pair formation of transverse dipole moments in adjacent smectic layers as the cause of its antiferroelectricity, showing that the smectic layer is much closer to the usual picture of molecules lying on equidistant planes; the packing entropy due to the sinusoidal density wave character stabilizes ferroelectric SC*. The competition between the interactions stabilizing SCA* and SC* is responsible for the occurrence of several varieties of ferrielectric and antiferroelectric subphases, which constitutes the Devil's staircase. We have further suggested that the essentials of the SCα* phase are its considerably reduced ability to form SCA* and SC*. At least when the spontaneous polarization is zero, SCα* is a smectic C-like phase with molecular tilting that is non-correlated on the visible wavelength scale When the spontaneous polarization is not zero, as suggested by Prost and Bruinsma recently, a novel type of Coulomb interaction between smectic layers due to the collective polarization fluctuations causes the antiferroelectricity in the high-temperature region of SCα*; the competition between this antiferroelectricity and the SC* ferroelectricity may form another staircase, causing the complexity in SCα*. Applications and some future problems have been described in the final section.
478 citations
TL;DR: In this paper, the size effects on the Curie temperature and spontaneous polarization in spherical particles are studied using Landau phenomenological theory and the extrapolation length is shown to be size dependent.
Abstract: Size effects on the Curie temperature and spontaneous polarization in spherical particles are studied using Landau phenomenological theory. The extrapolation length is shown to be size dependent. The spatial distribution of polarization is obtained. The size dependence of the polarization is calculated whereby a size-driven phase transition is demonstrated. The Curie temperature as a function of particle size is calculated. Theoretical results are compared with the experimental in the literature and good agreement is obtained.
454 citations
TL;DR: The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma.
Abstract: The properties of spin-1/2 antiferromagnetic chains with various types of random exchange coupling are studied via an asymptotically exact decimation renormalization-group transformation, which is a generalization of that introduced by Dasgupta and Ma. Random-singlet phases occur in which each spin is paired with one other spin that may be very far away; more exotic phases also occur. The behavior of typical and mean correlation functions is analyzed and found to be very different, with very small sets of spins dominating the latter at long distances as well as the low-temperature thermodynamics. Some of the phase transitions that occur between antiferromagnetically ordered phases and random singlet or other antiferromagnetic phases are also analyzed. For example, if a small uniaxial anisotropy perturbation is added to a random Heisenberg antiferromagnetic chain, a transition occurs from a random-singlet phase to an Ising antiferromagnetic phase, as the anisotropy changes sign from easy plane to easy axis. The staggered magnetization vanishes at the transition with critical exponent \ensuremath{\beta}=8/(1+ \ensuremath{\surd}7 ). Possible implications for the properties of random quantum magnetic systems in higher dimensions are briefly discussed.
453 citations
TL;DR: In this article, a first-principles scheme to study ferroelectric phase transitions for perovskite compounds was developed, which was applied to BaTi${\mathrm{O}}_{3}$, and the resulting Hamiltonian was studied using Monte Carlo simulations.
Abstract: We develop a first-principles scheme to study ferroelectric phase transitions for perovskite compounds. We obtain an effective Hamiltonian which is fully specified by first-principles ultrasoft pseudopotential calculations. This approach is applied to BaTi${\mathrm{O}}_{3}$, and the resulting Hamiltonian is studied using Monte Carlo simulations. The calculated phase sequence, transition temperatures, latent heats, and spontaneous polarizations are all in good agreement with experiment. The order-disorder versus displacive character of the transitions and the roles played by different interactions are discussed.
450 citations
TL;DR: In this article, a structural phase transition between the cubic and tetragonal phases in a zirconia-ceria solid solution (Zr1−xCexO2) has been observed by Raman spectroscopy.
Abstract: A structural phase transition between the cubic (space group, Fm3m) and tetragonal (space group, P42/nmc) phases in a zirconia–ceria solid solution (Zr1−xCexO2) has been observed by Raman spectroscopy. The cubic–tetragonal (c–t″) phase boundary in compositionally homogeneous samples exists at a composition X0 (0.8 < X0 < 0.9) at room temperature, where t″ is defined as a tetragonal phase whose axial ratio c/a equals unity. The axial ratio c/a decreases with an increase of ceria concentration and becomes 1 at a composition X′0 (0.65 < X′0 < 0.7) at room temperature. The sample with a composition between X0 and X′0 is t″ ZrO2. By Raman scattering measurements at high temperatures, the tetragonal (t″) → cubic and cubic → tetragonal phase transitions occur above 400°C in Zr0.2 Ce0.8O2 solid solution.
443 citations
TL;DR: In this paper, a CP-asymmetry is found in the reflection coefficients of quarks hitting the phase boundary created during the electroweak transition and a regular GIM behavior is found as intuitively expected.
Abstract: In CP arguments, we argue against a Standard Model explanation of the baryon asymmetry of the universe in the presence of a first order phase transition. A CP-asymmetry is found in the reflection coefficients of quarks hitting the phase boundary created during the electroweak transition. The problem is analyzed both in an academic zero temperature case and in the realistic finite temperature one. The building blocks are similar in both cases: Kobayashi-Maskawa CP-violation, CP-even phases in the reflection coefficients of quarks, and physical transitions due to fermion self-energies. In both cases an effect is present at order $\alpha_W^2 $ in rate. A regular GIM behavior is found as intuitively expected. In the finite temperature case, a crucial role is played by the damping rate of quasiparticles in a hot plasma, which is a relevant scale together with MW and the temperature. The effect is many orders of magnitude below what observation requires, and indicates that non-standard physics is indeed needed ...
430 citations
Book•
10 May 1994
TL;DR: In this paper, the International Temperature Scale (ITSS) was used to measure the thermal properties of pure substances and their properties associated with physical constants and phase behavior, such as heat capacity, phase transition, and surface tension.
Abstract: Symbols, Units, and Terminology Recommended Symbols for Thermodynamic and Transport Properties SI Units and Conversion Factors International Temperature Scale of 1990 Thermodynamic Properties of Pure Substances Physical Constants and Phase Behavior Volumetric Properties Calorimetric Properties Associated with Chemical Reactions Heat Capacity Phase Transition Properties Surface Tension Thermodynamic Properties of Mixtures Vapor-Liquid Equilibrium Volumetric Properties Calorimetric Properties Transport Properties Viscosity Thermal Conductivity Diffusion Coefficients Properties of Individual Substances Thermophysical Properties of Some Common Fluids Thermodynamic Properties of Air Properties of Liquid Water Density of Water Steam Tables Indexes Substance List Index
TL;DR: A Monte Carlo study of phase transitions in a finite two-dimensional system of charged classical particles which are confined by a circular parabolic or hard-wall well and the results are compared with Wigner crystallization in the infinite 2D system.
Abstract: We report a Monte Carlo study of phase transitions in a finite two-dimensional (2D) system of charged classical particles which are confined by a circular parabolic or hard-wall well. The ground-state configurations are found by static energy calculations and their structures are analyzed using the Voronoi constructions. A Mendeleev table for these classical 2D-like atoms is obtained. We calculate the radial and angular components of the displacements of the particles as functions of temperature and determine the critical temperatures for the order-disorder phase transitions. The intershell rotation and intershell diffusion transitions are investigated. The results are compared with Wigner crystallization in the infinite 2D system.
TL;DR: In this paper, the authors provided direct evidence for covalent bonding between neighboring C60 molecules through powder X-ray diffraction studies of RbC60 and KC60, which has been hypothesized to take place during photopolymerization of solid C60.
Abstract: NEARLY all of the molecular crystals containing C60, formed at ambient pressure1,2 have inter-fullerene separations of the order of 10 A — the expected distance based on the molecular van der Waals radii. The sole exceptions are the room-temperature phases of AC60 (where A denotes K, Rb or Cs), which are formed by reversible solid-state transformation from high-temperature (>150 °C) phases3. These phases have lattice parameters about 9% shorter in one direction, and in addition RbC60 has magnetic properties suggestive of a one-dimensional metal4. We suggested in ref. 4 that this short distance may be due to covalent bonding between neighbouring C60 molecules. Here we provide direct evidence for such bonding from powder X-ray diffraction studies of RbC60 and KC60 . The linkage is through a [2+2] cycloaddition, which has been hypothesized to take place during photopolymerization of solid C60 (ref. 5), and which has also been proposed6 for RbC60. Such inter-fullerene linkages are calculated7,8 to be the preferred mode of dimerization of C60. The AC60 phases thus provide an example of a thermal phase transition driven by the reversible formation and breaking of covalent bonds.
TL;DR: In this paper, the authors observed two coexisting liquid phases in the supercooled melt of AI2O3-Y2O 3 just above the glass transition at ambient pressure, both of which have the same composition.
Abstract: PHASE separation of liquid mixtures into two liquids with different compositions is a well-known phenomenon. It has been proposed1–9 that another type of liquid–liquid phase separation, driven by fluctuations in density rather than in composition, may occur in some elemental systems. Transitions between low- and high-density amorphous phases have been described for the one-component oxides H2O, SiO2and GeO2 (refs 10–17), and it has been suggested18–21 that a liquid–liquid phase transition might occur in supercooled water. If density-driven phase separation truly does occur in liquid mixtures, it should be possible to observe the coexistence of two liquids with the same composition but different density. Here we report the direct observation of such a situation. We observe two coexisting liquid phases in the supercooled melt of AI2O3–Y2O3 just above the glass transition at ambient pressure, both of which have the same composition. We propose that these two phases must differ solely in density, and that the transition is entropically driven. The occurrence of the phase transition in this system may explain why the crystallization of yttrium aluminium garnet, the host material for Nd3 +ions in YAG lasers, is sluggish22–25.
TL;DR: In this article, a simple model of a spatially distributed system subject to multiplicative noise, white in space and time, can undergo a nonequilibrium phase transition to a symmetry-breaking state, while no such transition exists in the absence of the noise term.
Abstract: We report on a simple model of a spatially distributed system which, subject to multiplicative noise, white in space and time, can undergo a nonequilibrium phase transition to a symmetry-breaking state, while no such transition exists in the absence of the noise term. The transition possesses features similar to those observed at second order equilibrium phase transitions: divergence of the correlation length and of the susceptibility, critical slowing down, and scaling properties. Furthermore, the transition is found to be reentrant: The ordered state appears at a critical value of the noise intensity but disappears again at a higher value of the noise strength.
TL;DR: Comparison of MD results with reliable experimental data showed that the simulations, especially the one in the liquid-crystalline phase, can serve as a realistic model for a phospholipid membrane, including full atomic detail.
Abstract: We present the results of molecular dynamics (MD) simulations of a phospholipid membrane in water, including full atomic detail The goal of the simulations was twofold: first we wanted to set up a simulation system which is able to reproduce experimental results and can serve as a model membrane in future simulations This goal being reached it is then further possible to gain insight in to those properties that are experimentally more difficult to access The system studied is dipalmitoylphosphatidylcholine/water, consisting of 5408 atoms Using original force field parameters the membrane turned out to approach a gel-like state With slight changes of the parameters, the system adopted a liquid-crystalline state Separate 80 ps runs were performed on both the gel and liquid-crystalline systems Comparison of MD results with reliable experimental data (bilayer repeat distance, surface area per lipid, tail order parameters, atom distributions) showed that our simulations, especially the one in the liquid-crystalline phase, can serve as a realistic model for a phospholipid membrane Further analysis of the trajectories revealed valuable information on various properties In the liquid-crystalline phase, the interface turns out to be quite diffuse, with water molecules penetrating into the bilayer to the position of the carbonyl groups The 10-90% width of the interface turns out to be 13 nm and the width of the hydrocarbon interior 30 nm The headgroup dipoles are oriented at a small angle with respect to the bilayer plane The resulting charge distribution is almost completely cancelled by the water molecules The electron density distribution shows a large dip in the middle of the membrane In this part the tails are more flexible The mean life time between dihedral transitions is 20 ps The average number of gauche angles per tail is 35 The occurrence of kinks is not a significant feature
TL;DR: In this article, a review of phase transitions in momentum-conserving lattice gases is presented, with particular attention given to the derivation of macroscopic constitutive equations from microscopic dynamics.
Abstract: Momentum-conserving lattice gases are simple, discrete, microscopic models of fluids. This review describes their hydrodynamics, with particular attention given to the derivation of macroscopic constitutive equations from microscopic dynamics. Lattice-gas models of phase separation receive special emphasis. The current understanding of phase transitions in these momentum-conserving models is reviewed; included in this discussion is a summary of the dynamical properties of interfaces. Because the phase-separation models are microscopically time irreversible, interesting questions are raised about their relationship to real fluid mixtures. Simulation of certain complex-fluid problems, such as multiphase flow through porous media and the interaction of phase transitions with hydrodynamics, is illustrated.
01 Jan 1994
TL;DR: A survey of the physical techniques used in the study of molecular dynamics can be found in this paper, where the authors present an overview of the most commonly used techniques in the literature.
Abstract: 1. A Comparative Survey of the Physical Techniques Used in Studies of Molecular Dynamics.- 1. Introduction.- 2. Molecular Motion in Liquid Crystals.- 3. Spectroscopy in Studies of Molecular Motion.- 4. Applications of Spectroscopy to the Study of Rotational Motion.- 5. Applications to Studies of Translational Diffusion.- 2. On the Description of Ordering in Liquid Crystals.- 1. Introduction.- 2. General Approach.- 3. Purely Positional Order.- 4. Orientational Order.- 5. Positional-Orientational Order in Uniaxial Phases.- 6. Rotameric Molecules.- 3. Diffusion Models for Molecular Motion in Uniaxial Mesophases.- 1. Diffusion Equations.- 2. Solution of the Diffusion Equation.- 3. Diffusion Across Potential Barriers.- 4. Dynamics of Chain Molecules.- 5. Diffusive Coupling with the Solvent.- 4. ESR and Liquid Crystals: Statistical Mechanics and Generalised Smoluchowski Equations.- 1. Introduction.- 2. Rotational and Translational Motion in Ordered Fluids.- 3. Symmetries of the Liquid-Crystalline Potential.- 4. Relative Translational Diffusion: The Pair Correlation Function.- 5. Fluctuating Torques and Slowly Relaxing Local Structures.- 5. Techniques and Applications of Langevin Dynamics Simulations.- 1. Introduction.- 2. Hydrodynamics.- 3. Algorithms and Errors.- 4. Barrier Crossing.- 5. Rotation.- 6. Application to Lipid Bilayers.- 7. Limitations and Extensions of Langevin Dynamics.- 8. Appendix.- 6. An Introduction to the Molecular Dynamics Method and to Orientational Dynamics in Liquid Crystals.- 1. Introduction.- 2. Equations of Motion.- 3. Integration of the Equations of Motion.- 4. Calculation of Static and Dynamic Properties.- 5. General Properties of Orientational Correlation Functions.- 6. Evaluation of Correlation Functions by Molecular Dynamics.- 7. Appendix.- 7. Nuclear Spin Relaxation Formalism for Liquid Crystals.- 1. Introduction.- 2. Spin Dynamics: Density Matrix Description of Relaxation.- 3. Molecular Dynamics.- 4. Cooperative Motion.- 5. Illustrative Experiments.- 6. Summarising Remarks.- 8. Nuclear Spin Relaxation and Molecular Motion in Liquid Crystals.- 1. Introduction.- 2. Experiments and Methods.- 3. Density Operator Theory.- 4. Conclusions.- 9. The Effects of Director Fluctuations on Nuclear Spin Relaxation.- 1. Introduction.- 2. Historical Background.- 3. Theory.- 4. Experiments.- 5. Conclusions.- 10. Nuclear Spin Relaxation Mechanisms in Liquid Crystals Studied By Field Cycling NMR.- 1. Introduction.- 2. Principles and Techniques of Field Cycling NMR.- 3.T1 Relaxation Dispersion in Nematic Mesophases.- 4.T1 Relaxation Dispersion in Smectic Mesophases.- 5. DeuteronT1 Relaxation Dispersion in Methyl Deuteriated MBBA.- 11. Probe Studies of Liquid Crystals.- 1. Introduction.- 2. Orientational Order.- 3. Tools for Molecular Ordering.- 4. Solute-Solvent Interactions.- 5. Interesting Complications.- 6. Conclusions.- 12. ESR and Molecular Motions in Liquid Crystals: Motional Narrowing.- 1. The ESR Spin Hamiltonian: g and A Tensors.- 2. Effective Spin Hamiltonian and Order Parameters.- 3. Spectral Densities and Linewidths.- 4. Rotational Dynamics in Liquid-Crystalline Phases.- 5. Translational Motion in Liquid Crystals.- 13. Thermodynamics of Liquid Crystals and the Relation to Molecular Dynamics: ESR Studies.- 1. Introduction.- 2. Smectic A-Nematic Tricritical Point and Crossover Behaviour.- 3. Universality in Nematic Ordering.- 4. Lipid-Cholesterol Mixtures.- 5. Dynamics: Thermotropics.- 6. Dynamics: Lyotropics.- 14. ESR Studies of Molecular Dynamics at Phase Transitions in Liquid Crystals.- 1. Introduction.- 2. Models of Collective Dynamics: Director Fluctuations.- 3. The Nematic-Isotropic Phase Transition.- 4. The Smectic A-Nematic Phase Transition.- 5. The Dynamic Cluster Model.- 6. Fast versus Slow Collective Motions.- 7. Treatment of Data.- 15. ESR and Slow Motions in Liquid Crystals.- 1. Introduction.- 2. ESR Lineshapes: The Stochastic Liouville Equation.- 3. Methods of Solution: Lanczos and Conjugate Gradient Methods.- 4. Relation to Mori's Method in Statistical Mechanics.- 5. Ordering and Thermodynamics: Behaviour of Large versus Small Probes.- 6. Dynamics in I, N, SA and NR Phases.- 7. Rotational Dynamics in Lyotropics: Lipid Multilayers.- 8. Experimental Techniques: Lineshapes in One and Two Dimensions.- 9. On Fitting the Data.- 16. Raman and IR Fluctuation Spectroscopy of Liquid Crystals.- 1. Introduction.- 2. Determination of Correlation Functions from IR and Raman Lineshapes.- 3. Fluctuation Raman and IR Spectroscopy in Liquid Crystals.- 4. Experimental Results.- 5. Conclusions.- 17. Dielectric Relaxation Behaviour of Liquid Crystals.- 1. Introduction.- 2. Phenomenological Aspects of Dielectric Relaxation.- 3. Measurement of Dielectric Permittivity.- 4. Molecular Aspects of the Dielectric Permittivity.- 5. Experimental Results.- 6. Conclusions.- 18. Neutron Scattering From Liquid Crystals.- 1. Introduction to the Neutron.- 2. Types of Neutron Scattering Experiments.- 3. Coherent and Incoherent Scattering.- 4. Examples of Neutron Diffraction from Liquid Crystals.- 5. Inelastic and Quasi-Elastic Scattering.- 6. Model Incoherent Scattering Laws.- 7. Experiments and Examples of Results.- 19. Molecular Order and Motion in Liquid Crystal Polymers Studied By Pulsed Dynamic NMR.- 1. Introduction.- 2. Experiments and Methods.- 3. Results and Discussion.- 4. Conclusions.- 20. Aggregates of Amphiphiles in Lyotropic Liquid Crystals.- 1. Aggregation of Amphiphiles.- 2. Structure and Aggregates.- 3. Within the Aggregates.- 21. Orientation and Frequency Dependent NMR Relaxation Studies of Bilayer Membranes: Characterisation of the Lipid Motions.- 1. Introduction.- 2. Experiments and Methods.- 3. Results and Discussion.- 4. Conclusions.- 22. Molecular Dynamics in Liquid-Crystalline Systems Studied By Fluorescence Depolarisation Techniques.- 1. Introduction.- 2. Principles of Fluorescence Spectroscopy.- 3. Instrumentation for Fluorescence Spectroscopy.- 4. Principles of Fluorescence Polarisation.- 5. Data Analysis.- 6. Order and Dynamics of DPH and TMA-DPH Molecules in Lipid Bilayer Configurations.- 23. Spectroscopic Studies on Structure and Dynamics of Lyotropic Liquid Crystals: Cubic and Reversed Hexagonal Phases and Lipid Vesicles.- 1. Introduction.- 2. Phase Equilibria and Structural Polymorphism.- 3. Theoretical Aspects on Lipid Self-Assembly.- 4. Nuclear Magnetic Resonance.- 5. Electron Spin Resonance.- 6. Time-Resolved Fluorescence Spectroscopy.- 7. Fluorescence Anisotropy.
TL;DR: These results identify block copolymers as model compounds for investigating the thermodynamics and dynamics of complex "soft" condensed matter.
Abstract: Small-angle neutron scattering experiments have revealed an epitaxial relationship between the hexagonal cylinder phase, and a bicontinuous cubic phase with $\mathrm{Ia}\overline{3}d$ space group symmetry, in a poly(styrene)-poly(2-vinylpyridine) diblock copolymer mixture. Proximity to the order-disorder transition and an inelastic low frequency rheological response suggest that the cubic phase is stabilized by fluctuations. These results identify block copolymers as model compounds for investigating the thermodynamics and dynamics of complex "soft" condensed matter.
01 Jan 1994
TL;DR: In this paper, the authors discuss the conditions under which the linearized (Cahn-like) theory of spinodal decomposition holds for block copolymer melts, where chains may stretch out in a dumbbell-like shape even in disordered phase, before the microphase separation transition.
Abstract: The classical concepts about unmixing of polymer blends (Flory-Huggins theory) and about mesophase ordering in block copolymers (Leibler's theory) are briefly reviewed and their validity is discussed in the light of recent experiments, computer simulations and other theoretical concepts. It is emphasized that close to the critical point of unmixing non-classical critical exponents of the Ising universality class are observed, in contrast to the classical mean-field exponents implied by the Flory-Huggins theory. The temperature range of this non-mean-field behavior can be understood by Ginzburg criteria. The latter are also useful to discuss the conditions under which the linearized (Cahn-like) theory of spinodal decomposition holds. While Flory-Huggins theory predicts correctly that the critical value of the Flory χ-parameter scales with chain length N (for symmetrical mixtures) χc ∝ 1/N, it strongly overestimates the prefactor and its use for fitting experimental data yields spurious concentration dependence. Also the chain radii depend on both χ and the composition of the mixture, thus invalidating the random phase approximation (RPA). Particular strong deviations from the RPA are predicted for block copolymer melts, where chains may stretch out in a dumbbell-like shape even in the disordered phase, before the microphase separation transition is approached. This review concludes with an outlook on interfacial phenomena and surface effects on these systems and other open problems in this field.
TL;DR: In this paper, a thermodynamically consistent continuum theory for solid-solid phase transitions is developed, in which deformation dominates heat and mass transfer, and the growth of one phase at the expense of another is modeled by configurational forces.
TL;DR: In this paper, the authors measured the sub-picosecond optical response of a solid-state, semiconductor-to-metal phase transition excited by femtosecond laser pulses.
Abstract: We have measured the subpicosecond optical response of a solid‐state, semiconductor‐to‐metal phase transition excited by femtosecond laser pulses. We have determined the dynamic response of the complex refractive index of VO2 thin films by making pump‐probe optical transmission and reflection measurements at 780 nm. The phase transition was found to be largely prompt with the optical properties of the high‐temperature metallic state being attained within 5 ps. The ultrafast change in complex refractive index enables ultrafast optical switching devices in VO2.
TL;DR: In this paper, a 3D model of mantle convection is presented, with cylindrical features and linear features that behave differently in their ability to penetrate the 670-km discontinuity.
Abstract: Numerical models of mantle convection that incorporate the major mantle phase changes of the transition zone reveal an inherently three-dimensional flow pattern, with cylindrical features and linear features that behave differently in their ability to penetrate the 670-km discontinuity. The dynamics are dominated by accumulation of cold linear downwellings into rounded pools above the endothermic phase change at 670 km depth, resulting in frequent “avalanches” of upper mantle material into the lower mantle. The effect of the exothermic phase transition at 400 km depth is to reduce the overall degree of layering by pushing material through the 670-km phase change, resulting in smaller and more frequent avalanches, and a wider range of morphologies. Large quantities of avalanched cold material accumulate above the coremantle boundary (CMB), resulting in a region of strongly depressed mean temperature at the base of the mantle. The 670-km phase change has a strong effect on the temperature field, with three-distinct regions being visible: (1) the upper mantle, containing linear downwellings and pools of cold material in the transition zone and characterized by a high amplitude long wavelength spectrum; (2) the midmantle, containing quasi-cylindrical avalanche conduits and characterized by a low amplitude, broad spectrum; and (3) the deep mantle, containing large pools of cold, avalanched material and characterized by a high amplitude, ultra-red (i.e., long wavelength) spectrum. The effect on the velocity field is very different. Flow penetration across the 670-km phase change is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. Thus, when comparing numerical models with long wavelength seismic tomography, diagnostics based on the density field, such as the radial correlation function, are much more sensitive to the effects of phase transitions than those based on the velocity field. The amplitude of the geoid is not significantly affected by the partial layering, because the contribution from the strong heterogeneity in the transition zone is almost perfectly balanced by the contribution from deflection of the 670-km discontinuity. Avalanches are associated with geoid lows. However, a more complex viscosity structure is required to correctly match the sign of the geoid over slabs in Earth.
TL;DR: The phase stability of Mg2SiO4, a major constituent in the Earth9s mantle, has been investigated experimentally by in situ observation with synchrotron radiation as discussed by the authors.
Abstract: The stability of Mg2SiO4, a major constituent in the Earth9s mantle, has been investigated experimentally by in situ observation with synchrotron radiation. A cubic-type high-pressure apparatus equipped with sintered diamond anvils has been used over pressures of 11 to 15 gigapascals and temperatures of 800° to 1600°C. The phase stability of α-Mg2SiO4 and β-Mg2SiO4 was determined by taking account of the kinetic behavior of transition. The phase boundary between α-Mg2SiO4 and β-Mg2SiO4 is approximated by the linear expression P = (9.3 ± 0.1) + (0.0036 ± 0.0002)T where P is pressure in gigapascals and T is temperature in degrees Celsius.
TL;DR: In this paper, the first calorimetric study of the normal alkanes CH3-n−2-CH3 (21≤n≤30) covering the temperature range of the five rotator phases with sufficient resolution to observe the various rotator to rotator transitions.
Abstract: We present the first calorimetric study of the normal alkanes CH3–(CH2)n−2–CH3 (21≤n≤30) covering the temperature range of the five rotator phases (whose structures were previously identified using x‐ray scattering) with sufficient resolution to observe the various rotator to rotator transitions. We find first‐order hexagonal–orthorhombic distortion transitions; second‐order azimuthal tilt‐angle rotation transitions, and two types of second‐order tilting transitions, one of which has the higher symmetry phase at low temperature. These transitions appear to be mean field in character, in that they are without significant pretransitional fluctuations. We discuss the calorimetric signatures for the transitions in terms of the order parameters obtained from x‐ray scattering data. In addition to the transitions, we find strong temperature variation of the heat capacity in the rotator phases not associated with the transitions.
TL;DR: In this paper, the authors developed a method for the construction of the effective potential at high temperatures, based on the effective field theory approach and renormalization group, which makes it possible to sum up the leading logarithms in all orders of perturbation theory.
TL;DR: In this paper, it is shown that a phase can appear and grow in a phase that is different from that in its state of ultimate stability, maintaining this in a metastable form when it may or may not transform into the ultimate stable state in the course of growth.
Abstract: This article aims to link the mainstream subject of chain-folded polymer crystallization with the rather speciality field of extended-chain crystallization, the latter typified by the crystallization of polyethylene (PE) under pressure. Issues of wider generality are also raised for crystal growth, and beyond for phase transformations. The underlying new experimental material comprises the prominent role of metastable phases, specifically the mobile hexagonal phase in polyethylene which can arise in preference to the orthorhombic phase in the phase regime where the latter is the stable regime, and the recognition of “thickening growth” as a primary growth process, as opposed to the traditionally considered secondary process of thickening. The scheme relies on considerations of crystal size as a thermodynamic variable, namely on melting-point depression, which is, in general, different for different polymorphs. It is shown that under specifiable conditions phase stabilities can invert with size; that is a phase which is metastable for infinite size can become the stable phase when the crystal is sufficiently small. As applied to crystal growth, it follows that a crystal can appear and grow in a phase that is different from that in its state of ultimate stability, maintaining this in a metastable form when it may or may not transform into the ultimate stable state in the course of growth according to circumstances. For polymers this intermediate initial state is one with high-chain mobility capable of “thickening growth” which in turn ceases (or slows down) upon transformation, when and if such occurs, thus “locking in” a finite lamellar thickness. The complete situation can be represented by a P, T, 1/l (l ≡ crystal thickness) phase-stability diagram which, coupled with kinetic considerations, embodies all recognized modes of crystallization including chain-folded and extended-chain type ones. The task that remains is to assess which applies under given conditions of P and T. A numerical assessment of the most widely explored case of crystallization of PE under atmospheric pressure indicates that there is a strong likelihood (critically dependent on the choice of input parameters) that crystallization may proceed via a metastable, mobile, hexagonal phase, which is transiently stable at the smallest size where the crystal first appears, with potentially profound consequences for the current picture of such crystallization. Crystallization of PE from solution, however, would, by such computations, proceed directly into the final stage of stability, upholding the validity of the existing treatments of chain-folded crystallization. The above treatment, in its wider applicability, provides a previously unsuspected thermodynamic foundation of Ostwald's rule of stages by stating that phase transformation will always start with the phase (polymorph) which is stable down to the smallest size, irrespective of whether this is stable or metastable when fully grown. In the case where the phase transformation is nucleation controlled, a ready connection between the kinetic and thermodynamic considerations presents itself, including previously invoked kinetic explanations of the stage rule. To justify the statement that the crystal size can control the transformation between two polymorphs, a recent result on 1 -4-poly-trans-butadiene is invoked. Furthermore, phase-stability conditions for wedge-shaped geometries are considered, as raised by current experimental material on PE. It is found that inversion of phase stabilities (as compared to the conditions pertaining for parallel-sided systems) can arise, with consequences for our scheme of polymer crystallization and with wider implications for phase transformations in tapering spaces in general. In addition, in two of the Appendices two themes of overall generality (arising from present considerations for polymers) are developed analytically; namely, the competition of nucleation-controlled phase growth of polymorphs as a function of input parameters, and the effect of phase size on the triple point in phase diagrams. The latter case leads, inter alia to the recognition of previously unsuspected singularities, with consequences which are yet to be assessed.
TL;DR: In this paper, an analysis based on the oscillator strength of the Bu mode at 580 cm-1 revealed that the t-m phase transition occurs discontinuously with a very narrow transition width of ∼2 K.
TL;DR: In this paper, it has been shown that a symmetry-breaking phase transition occurred via the Higgs mechanism about 10−34 after the Big Bang as the universe cooled through a critical temperature of 1027 K. This transition may have generated defects in the geometry of space-time (such as cosmic strings), which provided the inhomogeneities on which galaxies subsequently condensed.
Abstract: ALTHOUGH the birth of the Universe is inaccessible to experimental study, aspects of cosmological theories can nonetheless be explored in the laboratory. Tiny inhomogeneities in the mix of particles and radiation produced in the Big Bang grew into the clusters of galaxies that we see today, but how those inhomogeneities arose and grew is still unclear. Cosmologies based on grand unified theories suggest that a symmetry-breaking phase transition occurred via the Higgs mechanism about 10−34 after the Big Bang as the Universe cooled through a critical temperature of 1027 K. It has been proposed by Kibble1 that this transition may have generated defects in the geometry of space-time (such as cosmic strings), which provided the inhomogeneities on which galaxies subsequently condensed. Zurek2–4 has suggested that it might be possible to model this cosmological phase transition by a laboratory analogue, the superfluid transition of liquid 4He induced by fast adiabatic expansion through the critical density. Here we report the results of such an experiment. We observe copious production of quantized vortices5, the superfluid analogue of cosmic strings. These results support Kibble's contention that such defects were available in the early Universe to seed galaxy formation.