Equation of state and stability of the helium-hydrogen mixture at cryogenic temperature

The equation of state and the stability of the helium-molecular hydrogen mixture at cryogenic temperature up to moderate pressure are studied by means of current molecular physics methods and statistical mechanics perturbation theory. The phase separation, segregation and hetero-coordination are investigated by calculating the Gibbs energy depending on the mixture composition, pressure and temperature. Low temperature quantum effects are incorporated via cumulant approximations of the Wigner-Kirkwood expansion. The interaction between He and H₂ is determined by Double Yukawa potentials. The equation of state is derived from the hard sphere system by using the scaled particle theory. The behavior of the mixture over a wide range of pressure is explored with the excess Gibbs energy of mixing and the concentration fluctuations in the long wavelength limit. The theory is compared to cryogenic data and Monte-Carlo calculation predictions. Contrary to previous similar works, the present theory retrieves the main features of the mixture below 50 K, such as the critical point and the condensation-freezing curve, and is found to be usable well below 50 K. However, the method does not distinguish the liquid from the solid phase. The binary mixture is found to be unstable against species separation at low temperature and low pressure corresponding to very cold interstellar medium conditions, essentially because H₂ alone condenses at very low pressure and temperature, contrary to helium.     

Phase transitions of fluids confined in porous silicon: A differential calorimetry investigation

The phase transitions of non-polar organic fluids and of water, confined in the pores of porous silicon samples, were investigated by Differential Scanning Calorimetry (DSC). Two types of PS samples (p^- and p⁺ type) with different pore size and morphology were used (with spherical pores with a radius of about 1.5 nm and cylindrical shape with a radius of about 4 nm respectively). The DSC results clearly show that the smaller the pores are, the larger is the decrease in the transition temperature. Moreover, a larger hysteresis between melting and freezing is observed for p⁺ type than for p^- type samples. A critical review of the thermodynamical properties of small particles and confined fluids is presented and used to interpret and discuss our DSC results. The effects of the chemical dissolution as well as the influence of anodization time are presented, showing that thick p⁺ type porous silicon layers are non-homogeneous. The DSC technique which was used for the first time to investigate fluids confined in porous silicon, enables us to deduce original information, such as the pore size distribution, the decrease in the freezing temperature of confined water, and the thickness of non-freezing liquid layer at the pore wall surface. Received: 11 May 1998 / Revised and Accepted: 29 July 1998     

Phase transitions in simple models of rod-like and disc-like micelles

The interplay of interactions between micelles, and the aggregation of these micelles into large, highly anisotropic micelles, is studied. Simple, hard-body, models of rod-like and disc-like micelles are used, which allows us to apply fundamental measure theory to determine the free energy. Then we study the phase transition from the fluid phase to a liquid crystalline phase. We find that aggregation induces a strongly first order transition from a fluid phase of small micelles to a close packed liquid crystalline phase of infinitely large micelles. Received: 3 December 1997     

Critical fluctuations of a binary fluid mixture confined in a porous medium

We have performed small angle neutron scattering experiments on the binary fluid mixture n-C₆H₁₄+n-C₈F₁₈ imbibed inside porous Vycor glass in the thermodynamic region corresponding to the bulk critical one. The resulting structure can be represented as the sum of a temperature dependent Lorentzian term and a term describing the interference between the porous matrix, a shell part richer in one component coating the glass surface, and a core part richer in the other component. We observe critical fluctuations extending over distances markedly larger than the mean pore size. Received 20 May 1999     

Cluster description of water-in-oil microemulsions near the critical and percolation points

The three-component ionic microemulsion system consisting of AOT/water/decane shows an unusual phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40 degrees centigrades and 10% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to high volume fraction side at progressively lower temperatures. In this paper we review the evidence that allows to interpret the phase behavior of our system in terms of interacting spherical droplets. We also investigate the dynamics of droplets, below and approaching the critical point by dynamic light scattering. The first cumulant and time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction. The relaxation phenomena observed in an extensive set of measurements of electrical conductivity and permittivity close to percolation is also reviewed and interpreted through the same cluster-forming mechanism, which reproduces the most relevant features of the frequency-dependent complex dielectric constant of this system. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Probing the material properties and phase transitions of ferroelectric liquid crystals by determination of the Landau potential

The full Landau potential of several, widely varying ferroelectric liquid-crystalline materials has been experimentally determined. Tilt angle and polarisation data is analysed across the SmA to SmC transition for varying applied electric-field amplitudes, allowing the determination of all the coefficients of the generalised Landau model of ferroelectric liquid crystals. The materials investigated encompass different materials, including low-polarisation mixtures to high-polarisation single-component materials. The materials also possess a variation in the order of the SmA to SmC phase transition from strongly first order to strongly second order. The effects of both the polarisation and order of phase transition of the system are discussed with respect to the various terms of the generalised Landau model. Further, the mechanisms behind the difference between a first- and second-order phase transition are discussed with respect to the Landau potential and the second Landau coefficient b .     

Correlation effects,image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders. Electronic supplementary material  Supplementary material in the form of a doc file available from the journal web page at and are accessible for authorised users.     

Stabilization of the long-range magnetic ordering by dipolar and magnetoelastic interactions in two-dimensional ferromagnets

The possibility of the long-range magnetic order stabilization in two-dimensional ferromagnets with the account of dipolar and magnetoelastic interactions is investigated. The mechanisms of the magnetic order stabilization by both types of interactions are studied. The Curie temperature is estimated. The comparisons with experimental data are made. Received 22 June 2001 and Received in final form 17 January 2002     

Electric permittivity anomaly close to the critical mixing point: An improved method of estimation of the exponent describing a weak critical anomaly

A critical anomaly of electric permittivity in the vicinity of the consolute critical point of an ethanol and dodecane mixture has been measured and analyzed. A method of analysing the permittivity anomaly, which enhances the credibility of the fitting, has been proposed. We have found out that the exponent predicted in theoretical expectations, 1-α = 0.89, describes the anomaly correctly. However, in spite of the application of the improved method, it is not possible to obtain the value of the fitted critical exponent with satisfying precision.     

Phase transitions induced by thermal fluctuations

The present study generalizes the model of extended stochastic systems with a field-dependent kinetic coefficient [M. Ibanes, J. Garcia-Ojalvo, R. Toral, J.M. Sancho, Phys. Rev. Lett. 87, 020601 (2001)] to systems with symmetric and asymmetric bistable potentials. It is found that in systems with a relaxational flow and a symmetric local potential, reentrant phase transitions can be observed. In the case of an asymmetric local potential, a hysteresis-like behaviour in the order parameter appears. It is shown that such phase transitions can be controlled by the constant that governs relaxation flow, noise intensity and spatial coupling intensity.     

Phase behavior and structure of an ABC triblock copolymer dissolved in selective solvent

A mean-field lattice theory is applied to predict the self-assembly into ordered structures of an ABC triblock copolymer in selective solvent. More specifically, the composition-temperature phase diagram has been constructed for the system (C)₁₄(PO)₁₂(EO)₁₇/water, where C stands for methylene, PO for propylene oxide and EO for ethylene oxide. The model predicts thermotropic phase transitions between the ordered hexagonal, lamellar, reverse hexagonal, and reverse cubic phases, as well as the disordered phase. The thermotropic behavior is a result of the temperature dependence of water interaction with EO- and PO-segments. The lyotropic effect (caused by changing the solvent concentration) on the formation of different structures has been found weak. The structure in the ordered phases is described by analyzing the species volume fraction profiles and the end segment and junction distributions. A “triple-layer” structure has been found for each of the ordered phases, with each layer rich in C-, PO-, and EO-segments, respectively. The blocks forming the layers are not stretched. The dependence of the domain spacing on polymer volume fraction and temperature is also considered. Received 17 April 2002 Published online: 21 January 2003     

Critical dynamics of lateral and transversal phase separations in bilayer biomembranes and surfactants

We consider bilayer biomembranes or surfactants made of two chemically incompatible amphiphile molecules, which may laterally or transversely phase separate into macrodomains, upon variation of some suitable parameter (temperature, lateral pressure, etc.). The purpose is an extensive study of the dynamics of both lateral and transverse phase separations, when the bilayer is suddenly cooled down from a high initial temperature towards a final one very close to the spinodal point. The critical dynamics are investigated through the partial dynamic structure factors of different species. Using a two-order parameter field theory, where the two fields are the composition fluctuations of one component in the leaflets of the bilayer, combined with an extended van Hove approach that is based on two coupled Langevin equations (with noise), we exactly compute these dynamic structure factors. We first find that the dynamics is governed by two time scales. The longest one, , can be related to the thermal correlation length, | T - T _c|^-1/2 , by , with the dynamic critical exponent z = 4 , where is an atomic length scale, T the absolute temperature, and T_c its critical value. The characteristic time can be interpreted as the time required for the formation of the final macrophase domains. The second time scale is rather shorter, and can be viewed as the short time during which the unlike phospholipids execute local motion. Second, we demonstrate that the dynamic structure factors obey exact scaling laws, and depend on three lengths, namely the wavelength q^-1 (q is the wave vector modulus), the correlation length , and a length scale R(t) t ^1/z (z = 4representing the size of macrophase domains at time t . Of course, the two lengths and R(t) coincide at the final time at which the bilayer reaches its final equilibrium state. Finally, the present work must be considered as a natural extension of our previously published one dealing with the study of lateral and transverse phase separations from a static point of view.     

Structural analysis of the Γ phase in cholesterol-distearoylphosphatidylcholine multilamellar vesicles

Summary The interaction of cholesterol with membranes is particularly interesting as the cholesterol concentration influences membrane stability and permeability by inducing changes in the structure and dynamics of the constituent lipid molecules. On the other hand, cholesterol is present in the atherosclerotic plaques and in some skin diseases, like xanthomas and xantelasmas. An investigation was performed on the Γ phase in a cholesterol-distearoyl phosphatidyl choline (DSPC) mixture by using X-ray diffraction and differential scanning calorimetry. The cholesterol/DSPC molar ratio was 35/65 and DSPC-to-water weight ratio was 1/3. The Γ phase appears at sufficiently high concentration of cholesterol and it is characterized by interchain positional order considerably lower than in theL _β′ andP _β′ phases but higher than in theL _∝ liquid crystalline phase of pure lecithin in excess water. The results suggest that a lateral phase separation exists in the temperature range of existence of the Γ phase. The other phase Γ′ appears to be richer in cholesterol. The (Γ+Γ′) toL _∝ phase transition was investigated and the temperature dependence of the in-plane correlation length in the Γ phase was determined. A very weak enthalpy peak was observed at the chain melting transition, confirming the highly disordered nature of phases Γ and Γ′. Work presented at the First USSR-Italy Bilateral Meeting on Liquid Crystals held in Portonovo, Ancona (Italy), September 30–October 2, 1987.     

Phase transitions in generalized chiral or Stiefel's models

We study the phase transition in generalized chiral or Stiefel's models using Monte Carlo simulations. These models are characterized by a breakdown of symmetry O(N)/O(N-P). We show that the phase transition is clearly first order for when P=N and P=N-1, contrary to predictions based on the renormalization group in expansion but in agreement with a recent non perturbative renormalization group approach. Received 7 October 1999     

Field-theoretical Renormalization-Group approach to critical dynamics of crosslinked polymer blends

We consider a crosslinked polymer blend that may undergo a microphase separation. When the temperature is changed from an initial value towards a final one very close to the spinodal point, the mixture is out equilibrium. The aim is the study of dynamics at a given time t, before the system reaches its final equilibrium state. The dynamics is investigated through the structure factor, S(q, t), which is a function of the wave vector q, temperature T, time t, and reticulation dose D. To determine the phase behavior of this dynamic structure factor, we start from a generalized Langevin equation (model C) solved by the time composition fluctuation. Beside the standard de Gennes Hamiltonian, this equation incorporates a Gaussian local noise, ζ. First, by averaging over ζ, we get an effective Hamiltonian. Second, we renormalize this dynamic field theory and write a Renormalization-Group equation for the dynamic structure factor. Third, solving this equation yields the behavior of S(q, t), in space of relevant parameters. As result, S(q, t) depends on three kinds of lengths, which are the wavelength q ⁻¹, a time length scale R(t) ∼ t ^1/z , and the mesh size ξ ^*. The scale R(t) is interpreted as the size of growing microdomains at time t. When R(t) becomes of the order of ξ ^*, the dynamics is stopped. The final time, t ^*, then scales as t ^* ∼ ξ ^{* z}, with the dynamic exponent z = 6−η. Here, η is the usual Ising critical exponent. Since the final size of microdomains ξ ^* is very small (few nanometers), the dynamics is of short time. Finally, all these results we obtained from renormalization theory are compared to those we stated in some recent work using a scaling argument.     

Phase transitions of a spin-one alternating magnetic superlattice

We examine the critical behavior of a magnetic superlattice which made up of two magnetic materials, A and B. Using the effective field theory with a probability distribution technique that accounts for the single-site spin correlation, we derive the analytical equation for the Curie temperature of the superlattice which alternates as ABAB...AB. The dependence of the Curie temperature on the interface coupling strength J_ab and the layer number of the finite superlattice was calculated. The effects of the surface modification are also studied. Received 2 March 2001     

Study of temperature dependence of crystallisation transitions of a symmetric PEO-PCL diblock copolymer using simultaneous SAXS and WAXS measurements with synchrotron radiation

The reversible transitions of the lamellae of a crystalline-crystalline diblock copolymer from the melt to crystallites were studied using simultaneous small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) measurements with synchrotron radiation. A symmetric poly(ethylene oxide)-poly( -caprolactone) diblock copolymer was chosen for this study. We showed in the course of the block copolymer crystallisation that the time-resolved integrated intensity I _int was proportional to the product of the volume fractions of the PEO and PCL phases and the scattering contrast due to the electron density difference. These results demonstrated that simultaneous SAXS/WAXS measurements could be used to monitor the crystallisation process in two domains of different sizes at the same time.     

Molecular-dynamics simulation of a glassy polymer melt: Incoherent scattering function

We present simulation results for a model polymer melt, consisting of short, nonentangled chains, in the supercooled state. The analysis focuses on the monomer dynamics, which is monitored by the incoherent intermediate scattering function. The scattering function is recorded over six decades in time and for many different wave-vectors which range from the size of a chain to about three times the maximum position of the static structure factor. The lowest temperatures studied are slightly above , the critical temperature of mode-coupling theory (MCT), where was determined from a quantitative analysis of the - and -relaxations. We find evidence for the space-time factorization theorem in the -relaxation regime, and for the time-temperature superposition principle in the -regime, if the temperature is not too close to . The wave-vector (q-) dependence of the nonergodicity parameter, of the critical amplitude, and the -relaxation time are in qualitative agreement with calculations for hard spheres. For q larger than the maximum of the structure factor the -relaxation time already agrees fairly well with the asymptotic MCT-prediction . The behavior of the relaxation time at small q can be rationalized by the validity of the Gaussian approximation and the value of the Kohlrausch stretching exponent, as suggested in neutron-scattering experiments. Received 30 October 1998