Crossover parametric equation of state for Ising-like systems

Phase transitions affected by natural and forceful molecular interconversion

If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g., the equilibrium interconversion of enantiomers) or forcefully (e.g., via an external source of energy or matter), then the process of phase separation may drastically change. In this case, depending on the nature of interconversion, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of another stable phase, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we phenomenologically generalize the Cahn–Hilliard theory of spinodal decomposition to include the molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed phenomenology to accurately describe the simulation results of three atomistic models that demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Finally, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation.

Liquid-vapor rectilinear diameter revisited

In the modern theory of critical phenomena, the liquid-vapor density diameter in simple fluids is generally expected to deviate from a rectilinear law approaching the critical point. However, by performing precise scannerlike optical measurements of the position of the SF_{6} liquid-vapor meniscus, in an approach much closer to criticality in temperature and density than earlier measurements, no deviation from a rectilinear diameter can be detected. The observed meniscus position from far (10K) to extremely close (1mK) to the critical temperature is analyzed using recent theoretical models to predict the complete scaling consequences of a fluid asymmetry. The temperature dependence of the meniscus position appears consistent with the law of rectilinear diameter. The apparent absence of the critical hook in SF_{6} therefore seemingly rules out the need for the pressure scaling field contribution in the complete scaling theoretical framework in this SF_{6} analysis. More generally, this work suggests a way to clarify the experimental ambiguities in the simple fluids for the near-critical singularities in the density diameter.

Weightless experiments to probe universality of fluid critical behavior

Near the critical point of fluids, critical opalescence results in light attenuation, or turbidity increase, that can be used to probe the universality of critical behavior. Turbidity measurements in SF6 under weightlessness conditions on board the International Space Station are performed to appraise such behavior in terms of both temperature and density distances from the critical point. Data are obtained in a temperature range, far (1 K) from and extremely close (a few μK) to the phase transition, unattainable from previous experiments on Earth. Data are analyzed with renormalization-group matching classical-to-critical crossover models of the universal equation of state. It results that the data in the unexplored region, which is a minute deviant from the critical density value, still show adverse effects for testing the true asymptotic nature of the critical point phenomena.

Master crossover functions for one-component fluids

By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.

Nature of vapor-liquid asymmetry in fluid criticality

We have investigated the nature and experimental consequences of vapor-liquid asymmetry in near-critical fluids within the framework of "complete scaling" [M. E. Fisher and G. Orkoulas, Phys. Rev. Lett. 85, 696 (2000); Y. C. Kim, Phys. Rev. E 67, 061506 (2003)]. We used the thermodynamic freedom for a choice of the critical-entropy value to simplify "complete scaling" to a form with only two independent parameters, responsible for two different sources of the asymmetry. We then developed a procedure to obtain these two parameters from mean-field equations of state. By combining accurate liquid-vapor coexistence and heat-capacity data, we have unambiguously separated two nonanalytic contributions from the two sources of vapor-liquid asymmetry and proved the validity of "complete scaling." Since the nonanalytic asymmetry effects in the critical region are fully determined by the Ising critical exponents for the symmetric lattice-gas model, there is no need for a special renormalization-group theoretical treatment of "non-Ising" asymmetry in fluid criticality.

Mean crossover functions for uniaxial three-dimensional Ising-like systems

We give simple expressions for the mean of the max and min bounds of the critical-to-classical crossover functions, previously calculated [Bagnuls and Bervillier, Phys. Rev. E 65, 066132 (2002)] within the massive renormalization scheme of the Phi(d)4(n) model in three dimensions (d = 3) and scalar order parameter (n = 1) of the Ising-like universality class. The mean functions are determined relying on the properties of the theoretical functions in the two limiting three-dimensional (3D) Ising-like and mean-field-like descriptions close to the Wilson-Fisher fixed point and to the Gaussian fixed point, respectively. Such descriptions correspond to the preasymptotic domains near each fixed point where a Wegner expansion restricted to two terms (leading and first confluent terms) is valid. The Ising-like preasymptotic domain description includes the correlations between parameters due to the error-bar determination of the exponents and amplitude combinations very close to the Wilson-Fisher fixed point. Adding the equivalent description of the mean field preasymptotic domain close to the Gaussian fixed point leads to define each mean crossover function with three calculated parameters. Fixing a unique value of one parameter whatever the selected mean crossover function, we use this parameter as a relative sensor to estimate the dominant nature, either (Ising-like) critical, or (mean-field-like) classical, of the crossover behavior. Finally, we obtain an explicit criterion to measure the extension of the Ising-like preasymptotic domain which can then permit to coherently account for measurements performed in systems where the asymptotical approach to the critical point remains finite, using a well-controlled number of system-dependent parameters (like in the subclass of one-component fluids).

Universality and quantum effects in one-component critical fluids

Nonuniversal scale transformations of the physical fields are extended to pure quantum fluids and used to calculate the susceptibility, the specific heat, and the order parameter density along the critical isochore of near its liquid-vapor critical point. Within the so-called preasymptotic domain, where the Wegner expansion restricted to the first term of confluent corrections to scaling is expected to be valid, the results are in agreement with the experimental measurements and recent predictions, either based on the minimal-substraction renormalization and the massive renormalization schemes within phi (4)(d = 3) (n = 1)the model, or based on the crossover parametric equation of state for Ising-like systems.

Bulk viscosity of stirred xenon near the critical point

We deduce the thermophysical properties of near-critical xenon from measurements of the frequencies and half-widths of the acoustic resonances of xenon maintained at its critical density in centimeter-sized cavities. In the reduced temperature range 1 x 10-3<(T-Tc)/Tc<7 x 10 (-6), we measured the resonance frequency and quality factor (Q) for each of six modes spanning a factor of 27 in frequency. As Tc was approached, the frequencies decreased by a factor of 2.2 and the Q's decreased by as much as a factor of 140. Remarkably, these results are predicted (within +/-2% of the frequency and within a factor of 1.4 of Q) by a model for the resonator and a model for the frequency-dependent bulk viscosity zeta(omega) that uses no empirically determined parameters. The resonator model is based on a theory of acoustics in near-critical fluids developed by Gillis, Shinder, and Moldover [Phys. Rev. E 70, 021201 (2004)]. In addition to describing the present low-frequency data (from 120 Hz to 7.5 kHz), the model for zeta(omega) is consistent with ultrasonic (0.4--7 MHz) velocity and attenuation data from the literature. However, the model predicts a peak in the temperature dependence of the dissipation in the boundary layer that we did not detect. This suggests that the model overestimates the effect of the bulk viscosity on the thermal boundary layer. In this work, the acoustic cavities were heated from below to stir the xenon, thereby reducing the density stratification resulting from Earth's gravity. The stirring reduced the apparent equilibration time from several hours to a few minutes, and it reduced the effective temperature resolution from 60 mK to approximately 2 mK, which corresponds to (T-Tc)/Tc approximately =7 x 10(-6).

Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions

The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.

Comparison of theoretical models of crossover behavior near the 3He liquid-vapor critical point

Parametric expressions, based on three different theoretical models, are used to calculate the isothermal susceptibility, specific heat, and order parameter along the critical isochore and coexistence curve from the asymptotic region to the crossover region. These models are (i) the minimal-subtraction renormalization scheme, (ii) the massive renormalization scheme within the phi(4) model, and (iii) the crossover parametric model based on the crossover Landau model. We fit these theories globally to experimental measurements of the isothermal susceptibility and specific heat along the critical isochore and coexistence curve, and to the coexistence curve of 3He near its liquid-vapor critical point. All of the theories provide good agreement with the experimental measurements within the reduced temperature range |t| < or =2 x 10(-2) . The differences in the fits between the theories and the correlations between the adjustable model parameters are discussed.

Criticality in aqueous solutions of 3-methylpyridine and sodium bromide

We address a controversial issue regarding the nature of critical behavior in ternary electrolyte solutions of water, 3-methylpyridine, and sodium bromide. Earlier light-scattering studies showed an anomalous critical behavior in this system that was attributed to the formation of a microheterogeneous phase associated with ion-molecule clustering [M.A. Anisimov, J. Jacob, A. Kumar, V.A. Agayan, and J. V. Sengers, Phys. Rev. Lett. 85, 2336 (2000)]], while some other investigators subsequently found this system to exhibit ordinary Ising-like critical behavior. This contradiction forced us to revisit the problem and perform an accurate and comprehensive study of light scattering in this system paying attention to the achievement of thermodynamic equilibrium, hysteresis effects, aging, and prehistory of the samples, and a possible role of impurities. We show that properly aged, equilibrium samples of aqueous solutions of 3-methylpyridine with NaBr exhibit universal Ising-like critical behavior, typical for other aqueous solutions. No evidence for an equilibrium microheterogeneous phase was found. We have been able to reproduce anomalous behavior (similar to that reported initially) in a fast run on a freshly prepared sample. We attribute the observed anomalies to mesoscopic nonequilibrium aggregates, possibly associated with supramolecular restructuring in aqueous solutions. To support this conclusion we performed a study of aqueous solutions of 3-methylpyridine without NaBr and have found long-living nonequilibrium states in aqueous solutions of 3-methylpyridine.

Thermoacoustic boundary layers near the liquid-vapor critical point

We measure and calculate the sound attenuation within thermoacoustic boundary layers between solid surfaces and xenon at its critical density rhoc as the reduced temperature tau identical with (T- Tc)/Tc approaches zero. (Tc is the critical temperature.) Using the known thermophysical properties of xenon, we predict that the attenuation at the boundary first increases approximately as tau(-0.6) and then saturates when the effusivity of the xenon exceeds that of the solid. [The effusivity is epsilon identical with (rhoCPlambdaT)(1/2), where CP is the isobaric specific heat and lambdaT is the thermal conductivity.] The model correctly predicts (+/-1.0%) the quality factors Q of resonances measured in a stainless steel resonator (epsilon(ss) =6400 kg K(-1) s(-5/2)); it also predicts the observed increase of the Q, by up to a factor of 8, when the resonator is coated with a polymer (epsilon(pr) =370 kg K(-1) s(-5/2)). The test data span the frequency range 0.1<f<7.5 kHz and the reduced temperature range 10(-3) <tau< 10(-1). We also predict that the thickness deltaT of the thermal boundary layer in the xenon decreases approximately as tau(0.4) until 2pifgammazeta/(rhoc2) approximately 0.5. (zeta is the bulk viscosity, gamma is the heat capacity ratio, and c is the speed of sound.) Still closer to Tc, deltaT becomes complex and its magnitude increases. These predictions concerning deltaT have not yet been tested. We deduce accurate values for the heat capacity CV and thermal conductivity lambdaT for xenon in the range 10(-3) <tau< 10(-1).

Application of minimal subtraction renormalization to crossover behavior near the 3He liquid-vapor critical point

Parametric expressions are used to calculate the isothermal susceptibility, specific heat, order parameter, and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region. These expressions are based on the minimal-subtraction renormalization scheme within the phi(4) model. Using two adjustable parameters in these expressions, we fit the theory globally to recently obtained experimental measurements of isothermal susceptibility and specific heat along the critical isochore and coexistence curve, and early measurements of coexistence curve and light scattering intensity along the critical isochore of 3He near its liquid-vapor critical point. The theory provides good agreement with these experimental measurements within the reduced temperature range |t|<or=2x10(-2).

Competition of mesoscales and crossover to tricriticality in polymer solutions

We show that the approach to asymptotic fluctuation-induced critical behavior in polymer solutions is governed by a competition between a correlation length diverging at the critical point and an additional mesoscopic length-scale, the radius of gyration. Accurate light scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 200 000 up to 11.4x10(6) clearly demonstrate a crossover between two universal regimes: a regime with Ising asymptotic critical behavior, where the correlation length prevails, and a regime with tricritical theta-point behavior determined by a mesoscopic polymer-chain length.

Crossover phenomena in spin models with medium-range interactions and self-avoiding walks with medium-range jumps

We study crossover phenomena in a model of self-avoiding walks with medium-range jumps, which corresponds to the limit N-->0 of an N-vector spin system with medium-range interactions. In particular, we consider the critical crossover limit that interpolates between the Gaussian and the Wilson-Fisher fixed point. The corresponding crossover functions are computed by using field-theoretical methods and an appropriate mean-field expansion. The critical crossover limit is accurately studied by numerical Monte Carlo simulations, which are much more efficient for walk models than for spin systems. Monte Carlo data are compared with the field-theoretical predictions for the critical crossover functions, finding good agreement. We also verify the predictions for the scaling behavior of the leading nonuniversal corrections. We determine phenomenological parametrizations that are exact in the critical crossover limit, have the correct scaling behavior for the leading correction, and describe the nonuniversal crossover behavior of our data for any finite range.