Showing papers on "Phase transition published in 1993"

Volume phase transition and related phenomena of polymer gels

Abstract: This review covers the recent advances in studies of the volume phase transition and critical phenomena of polymer gels mostly carried out in our group from 1973 to the present. We aimed here to discuss intensively (i) the basic understanding of the transition from the viewpoints of structure, dynamics, kinetics, and equilibrium thermodynamics, (ii) technological applications of the volume transition, and (iii) the relation between the phase transition and biological interactions.

Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations.

Abstract: We use the zero-temperature random-field Ising model to study hysteretic behavior at first-order phase transitions. Sweeping the external field through zero, the model exhibits hysteresis, the return-point memory effect, and avalanche fluctuations. There is a critical value of disorder at which a jump in the magnetization (corresponding to an infinite avalanche) first occurs. We study the universal behavior at this critical point using mean-field theory, and also present results of numerical simulations in three dimensions.

Sodium chloride-induced phase transition in nonionic poly(N-isopropylacrylamide) gel

Abstract: A nonionic poly(N-isopropylacrylamide) hydrogel, which exhibits a temperature-dependent volume phase transition (lower critical solution temperature, LCST) behavior in aqueous solution, demonstrates an unusual NACl-induced phase transition phenomenon as well. The gel collapses sharply at critical NaCl concentration, which depends on the temperature. Other salts tested show no such behavior, and typical salting-out behaviors (the gradual gel collapse with increasing their concentration) were observed. It appear that chloride ions play a major role in this phase transition

Statistical mechanics of classical particles with logarithmic interactions

Abstract: The inhomogeneous mean-field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions. The results apply to various physical models of translation invariant plasmas, gravitating systems, as well as to planar fluid vortex motion. For attractive interactions a critical behavior occurs which can be classified as an extreme case of a second-order phase transition. To include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic-geometric mean inequality. The method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions. In addition, it also provides us with a new proof of the Trudinger-Moser inequality known from differential geometry – in its sharp form.

Random-field induced antiferromagnetic, ferroelectric and structural domain states

Abstract: The occurrence of metastable or stable domain states on mesoscopic length scales seems to be a widespread property of many solids undergoing phase transitions in the presence of quenched random fields A survey is given on the experimental evidence of domain states in various magnetic, ferroelectric and structural systems In particular we discuss phenomena like the excess magnetization of field-cooled diluted uniaxial antiferromagnets and its relaxation The domain state of the relaxor ferroelectric PbMg1/3Nb2/3O3 is due to the random distribution of B site cations, whereas dipolar quenched impurities give rise to mesoscopic disorder in K1−xLixTaO3 and Sr1−xCaxTiO3 Spontaneously relaxing quadrupolar domain states are observed in KTa1−xNbxO3 They are probably caused by random strain fields due to ionic size mismatch The same type of random fields determines the critical behavior of the Jahn-Teller compound DyAsxV1−xO4 but merely causes roughening of the natural ferroeleastic twin domain walls

Superfluid and insulating phases in an interacting-boson model: mean-field theory and the RPA

Abstract: The bosonic Hubbard model is studied via a simple mean-field theory. At zero temperature, in addition to yielding a phase diagram that is qualitatively correct, namely a superfluid phase for non-integer fillings and a Mott transition from a superfluid to an insulating phase for integer fillings, this theory gives results that are in good agreement with Monte Carlo simulations. In particular, the superfluid fraction obtained as a function of the interaction strength U for both integer and non-integer fillings is close to the simulation results. In all phases the excitation spectra are obtained by using the random phase approximation (RPA): the spectrum has a gap in the insulating phase and is gapless (and linear at small wave vectors) in the superfluid phase. Analytic results are presented in the limits of large U and small superfluid density. Finite-temperature phase diagrams and the Mott-insulator-normal-phase crossover are also described.

A continuum model of a thermoelastic solid capable of undergoing phase transitions

Abstract: We construct explicitly a Helmholtz free energy, a kinetic relation and a nucleation criterion for a one-dimensional thermoelastic solid, capable of undergoing either mechanically- or thermally-induced phase transitions. We study the hysteretic macroscopic response predicted by this model in the case of quasistatic processes involving stress cycling at constant temperature, thermal cycling at constant stress, or a combination of mechanical and thermal loading that gives rise to the shape-memory effect. These predictions are compared qualitatively with experimental results.

1/f NOISE IN A TRAFFIC MODEL

Abstract: One-dimensional traffic flow is simulated by a cellular-automaton-type discrete model. As we increase the car density, the model shows a phase transition between a jam phase and a non-jam phase. By adding random perturbations we found a 1/f power spectrum in the jam phase, whereas a white noise is observed in the non-jam phase.

Optical, dielectric and polarization studies of the electric field-induced phase transition in Pb(Mg1/3Nb2/3)O3 [PMN]

Abstract: Single crystals of PMN have been studied between 10 and 300 K by means of dielectric, polarization and poling/depoling current measurements, associated with optical domain observations under bias field. Evidence for a first order electric field-induced phase transition, from the mean cubic phase to a macroscopically polar phase, has been disclosed by studying, as a function of temperature, the dielectric anomalies, the establishment of induced polarization, the onset of poling current and the appearance of the birefringence and phase boundary. By means of combined optical and domain switching analysis, the symmetry of the induced phase has been deduced to be trigonal 3m. The induced macropolarization Pind can be switched by a field of opposite polarity. The thermal depoling under a bias field takes place at a temperature depending on the field strength, whereas the zero-field depoling of an induced state occurs always at T do = 213 K, independently of the initial poling field. An electric field/t...

Phase transition in PbTiO3 ultrafine particles of different sizes

Abstract: The size effect on the ferroelectric phase transition in PbTiO3 ultra-fine particles is reported. Samples with particle sizes from 20 to 200 nm were prepared by a sol-gel process followed by calcining at different temperatures. The particle size was determined by X-ray diffraction from the integrated width of diffractions. The soft-mode frequency at room temperature was measured by Raman scattering. It decreases with decreasing particle size. The ferroelectric phase transition was traced by specific-heat measurement. The transition temperature decreases and the transition becomes diffused as the particle size decreases. The size dependence of TC can be described by TC(D)=766-256/(D-8.8) (K), where 766 K is the TC for bulk PbTiO3 and D (nm) is the particle size. This equation gives a critical size of 9.1 nm below which ferroelectricity disappears.

Volume-fraction dependence of elastic moduli and transition temperatures for colloidal silica gels.

Abstract: Colloidal silica spheres bearing grafted octadecyl chains dispersed in hexadecane undergo a sol-gel transition with decreasing temperature. The gelation temperature depends on the volume fraction \ensuremath{\varphi} and, perhaps, the particle size. For \ensuremath{\varphi}g${\mathrm{\ensuremath{\varphi}}}_{gel}$(T), the value at the transition, the elastic modulus varies as (\ensuremath{\varphi}-${\mathrm{\ensuremath{\varphi}}}_{gel}$${)}^{\mathit{s}}$ with the prefactor and exponent independent of temperature. This form resembles prediction from static percolation theories, but the exponent s=3.0\ifmmode\pm\else\textpm\fi{}0.5 lies significantly below those expected and the transition volume fraction varies with temperature. The relationship of the gelation transition to dynamic percolation and phase transitions predicted by equilibrium statistical mechanics has also been addressed. Matching the calculated structure factor for adhesive spheres with that measured by static light scattering yields the unknown strength of the interparticle attraction as a function of temperature. Though an imperfect fit introduces considerable uncertainty, this empirical relationship distinguishes the gel transition from both the dynamic percolation threshold and the spinodal associated with the fluid-fluid transition for adhesive spheres. Thus we conclude that gelation in this colloidal dispersion corresponds to a metastable state lying between the fluid-solid phase boundary and the spinodal.

Pressure-induced phase transition in SiC.

Abstract: X-ray diffraction studies have been made of cubic (3C) and hexagonal (6H) polytypes of SiC under pressures to 105 and 95 GPa, respectively, using a diamond-anvil cell and an imaging plate technique. 3C-SiC undergoes a phase transition into the rocksalt-type structure at 100 GPa or higher accompanied by a volume reduction of 20.3%. The 6H polytype of SiC remains stable to the highest pressure studied, with a premonition of a phase transition above 90 GPa. Equation-of-state data for the two polytypes have been found to be essentially the same to 95 GPa, yielding the bulk modulus 260(9) GPa and its pressure derivative 2.9(0.3).

Phase transitions in anisotropically confined ionic crystals.

Abstract: Crystalline, confined ionic systems exhibit well defined phase transitions as a function of the anisotropy of the confining potential. The transitions from one to two dimensions, from two to three, and back from three to two have been investigated as a function of this anisotropy with molecular dynamics simulations. The anisotropy at which such transitions occur seems to be proportional to a power of the number of confined ions.

Shear-induced isotropic-to-lamellar transition.

Abstract: Reciprocating shear is found to increase the isotropic-to-lamellar transition temperature in a symmetric diblock copolymer melt. The temperature at which the isotropic state becomes unstable rapidly approaches the ordering transition as the shear rate increases. Shear-induced ordering results in lamellae orientation with wave vectors directed normal to the shear and velocity gradient directions. These results are anticipated by a recent theory that accounts for the suppression of fluctuations by a symmetry breaking field in this class of weakly first-order phase transitions.

Large $N$ Phase Transition in Continuum QCD$_2$

Abstract: We compute the exact partition function for pure continuous Yang-Mills theory on the two-sphere in the large $N$ limit, and find that it exhibits a large $N$ third order phase transition with respect to the area $A$ of the sphere. The weak coupling (small A) partition function is trivial, while in the strong coupling phase (large A) it is expressed in terms of elliptic integrals. We expand the strong coupling result in a double power series in $e^{-g^2 A}$ and $g^2 A$ and show that the terms are the weighted sums of branched coverings proposed by Gross and Taylor. The Wilson loop in the weak coupling phase does not show the simple area law. We discuss some consequences for higher dimensions.

Volume-fraction dependence of elastic moduli and transition temperatures for colloidal silica gels

Abstract: Colloidal silica spheres bearing grafted octadecyl chains dispersed in hexadecane undergo a sol-gel transition with decreasing temperature. The gelation temperature depends on the volume fraction O and, perhaps, the particle size. For O>O gel (T), the value at the transition, the elastic modulus varies as (O-O gel ) s with the prefactor and exponent independent of temperature. This form resembles prediction from static percolation theories, but the exponent s=3.0±0.5 lies significantly below those expected and the transition volume fraction varies with temperature. The relationship of the gelation transition to dynamic percolation and phase transitions predicted by equilibrium statistical mechanics has also been addressed

Transitions and instabilities in liquid crystal elastomers

Abstract: Solid nematic liquids, formed by cross-linking polymer liquid crystals into elastomers, are shown to display novel and complex elasticity. The internal (nematic) direction suffers a barrier to its rotation and this couples to standard elasticity. By considering imposed strains we illuminate this elasticity and also demonstrate an entirely new nematic phase transition. At a critical strain there is a discontinuity of director rotation.

Isotropic-nematic phase separation of a dispersion of organophilic boehmite rods

Abstract: An isotropic-nematic phase separation is observed in dispersions of sterically stabilized rodlike boehmite particle. The phase separation process is studied with polarization microscopy. Also, the phase volumes and particle concentrations in the coexisting phases are determined. The dependence of these quantities on the total concentration of the dispersion is analyzed in terms of the Onsager theory for the isotropic-nematic phase transition extended to bidisperse mixture of rodlike particles. Qualitative agreement between theory and experiment is obtained. The triphasic isotropic-nematic-nematic equilibrium as predicted by the theory is observed after 6 months

Two-dimensional vortex lattice melting.

Abstract: We report on a Monte Carlo study of two-dimensional Ginzburg-Landau superconductors in a magnetic field. We find evidence suggestive of a first-order phase transition between a low-temperature state characterized by power-law positional correlations in the superfluid density and a high-temperature vortex-fluid state. A key aspect of our study is the introduction of a quantity proportional to the Fourier transform of the superfluid density which can be sampled efficiently in Landau gauge Monte Carlo simulations and which satisfies a useful sum rule.

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

Abstract: We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq≧3, with the correlation length ξ of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL≫ξ by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest are calculated straight-forwardly. In particular, it is shown that forL exceeding a characteristic minimum sizeL min the forthorder cumulantg L (T) exhibits a minimum atT min>T c, withT min−T c∝L −d and the value of the cumulant and the minimum (g(T min)) behaving asg(T min)∝L −d. All cumulantsg L (T) forL≫ξ approximately intersect at a common crossing pointT cross∝L −2d, with a universal valueg(T cross)=1−n/2q, wheren is the order parameter dimensionality. By searching for such a behavior in numerical simulation data, the first order character of a phase transition can be asserted. The usefulness of this approach is shown using data for theq=3,d=3 Potts ferromagnet.

Extraordinary pressure dependence of the metal-to-insulator transition in the charge-transfer compounds NdNiO 3 and PrNiO 3

Abstract: The pressure dependence of the metal-to-insulator transition in NdNiO${}_{3}$ and PrNiO${}_{3}$ has been studied up to applied hydrostatic pressures of 16 kbar In both cases the first-order metal-to-insulator phase transition is extremely sensitive to pressure, with 151 kbar suppressing the transition from 196 to 103 K in NdNiO${}_{3}$ and 141 kbar suppressing the transition from 130 to below 15 K in PrNiO${}_{3}$ Analysis of the data within the framework of charge-transfer gap insulators leads to the prediction that the primary effect of pressure is to straighten the Ni-O-Ni bond angle, leading to a broadening of the lower, oxygenlike valence band