Crossover Theory Research Articles

Adsorption at the liquid-vapor surface of a binary liquid mixture

In a binary liquid mixture, the component possessing the lowest surface tension preferentially adsorbs at the liquid-vapor surface. In the past this adsorption behavior has been extensively investigated for critical binary liquid mixtures near the mixture's critical temperature T(c). In this fluctuation-dominated regime the adsorption is described by a universal function of the dimensionless depth zxi where xi is the bulk correlation length. Fewer studies have quantitatively examined adsorption for off-critical mixtures because, in this case, one must carefully account for both the bulk and surface crossover from the fluctuation-dominated regime (close to T(c)) to the mean-field dominated regime (far from T(c)). In this paper we compare extensive liquid-vapor ellipsometric adsorption measurements for the mixture aniline+cyclohexane at a variety of critical and noncritical compositions with the crossover theory of Kiselev and co-workers [J. Chem. Phys. 112, 3370 (2000)].

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐Tc superconductivity

AbstractIn this series of articles (I, II), N‐band Hubbard models have been considered for strongly correlated electron systems, which are realized in d–p, π–d, π–R, and σ–R conjugated systems. The magnetism and superconductivity of these systems have been elucidated in terms of effective exchange integrals (J), which are calculated by first‐principle methods. In part III of this series, the BCS–BEC crossover theory, has been introduced to elucidate the physical foundation of our J and JP model for the high‐Tc superconductivity (HTSC). The boson–fermion (BF) model for this theory is found useful for a reasonable explanation of the experimental phase diagrams of HTSC. The underlying physics of the BF model is different from that of the slave boson field‐theoretical model assuming spinon–holon condensations in the low dimension. The interaction boson model (IBM) for nuclear matter is also employed to describe the cooperative mechanisms of electron–phonon (EP), spin fluctuation (SF), charge fluctuation (CF), and many‐bands (MB) effects. This phenomenological model is useful for pictorial understanding and for the theoretical explanation of the cooperative mechanisms: (EP + SF), (SF + CF), (EP + SF + MB), etc. These are also investigated in analogy to BF model of fermionic gases, where the Feshbach resonance between boson and fermion is responsible for their coupling. The implications of these theoretical results are discussed in relation to recent ALPES and STM experiments for HTSC, which suggest the contributions of SF (J) and EP (P) interactions. The recently discovered superconductivity of boron‐doped diamond is examined as an example of two‐band sigma‐radical (σ–R) conjugated systems. Finally, the bipolaron model is briefly discussed in relation to boson–fermion model via EP interaction to superconductivity. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

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 between a diagrammatic theory for the BCS-BEC crossover and quantum Monte Carlo results

Predictions for the chemical potential and the excitation gap recently obtained by our diagrammatic theory for the BCS-BEC crossover in the superfluid phase are compared with novel Quantum Monte Carlo results at zero temperature now available in the literature. A remarkable agreement is found between the results obtained by the two approaches

Thermodynamic properties of ethane in the critical region

The thermodynamic properties of fluids are predicted using global equations of state. Among these thermodynamic properties, we consider the densities of the liquid and vapor phases, pressure, the caloric properties such as specific heat at constant volume and specific heat at constant pressure and the speed of sound. In the present work, we apply the crossover theory to these thermodynamic properties and give a comparison of the crossover model equation of state with the experimental thermodynamic property data of ethane.

Nature of superfluidity in ultracold Fermi gases near Feshbach resonances

We study the superfluid state of atomic Fermi gases using a BCS-BEC crossover theory. Our approach emphasizes non-condensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above $T_c$ and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity.

Application of Crossover Theory to the SAFT-VR Equation of State: SAFT-VRX for Pure Fluids

The molecular-based SAFT equation of state has proven to be very versatile in the prediction of fluid phase equilibria. However, in common with all analytic equations of state, SAFT exhibits classical behavior in the critical region rather than the nonanalytical, singular behavior seen in real fluids. As a result, accurate agreement over the whole phase diagram cannot be obtained and must be localized to either the critical or subcritical regions. To overcome this problem, we have combined the SAFT-VR equation of state with a crossover technique developed by Kiselev (Kiselev, S. B. Fluid Phase Equilib. 1998, 147, 7) to obtain the SAFT-VRX equation. We have applied SAFT-VRX to both associating and nonassociating pure fluids. Results are presented for n-alkanes, water, and carbon dioxide. Furthermore, by fitting to the phase diagram and PVT behavior for a small number of n-alkanes, we have developed simple expressions for the potential model parameters for the n-alkane homologous series. These prescriptions enable the accurate prediction of the thermodynamic properties, including the phase diagram, of n-alkanes without additional fitting to experimental data. Additionally, by combining density functional theory with SAFT-VRX we predict the surface tension of both low and high molecular weight n-alkanes.

Crossover critical phenomena in an aqueous electrolyte solution: Light scattering, density and viscosity of the 3-methylpyridine+water+NaBr system

We have measured the light scattered by critical mixtures of 3-methylpyridine+water+NaBr, at three different salt concentrations, as a function of temperature and wave vector, in the one-phase region. From the data, we have calculated the susceptibility χ and the correlation length ξ. We have also measured the density and the shear viscosity for the same critical mixtures over a broad temperature range. The analysis of the χ and ξ data in terms of the Wegner expansion lead to negative values for the amplitudes of the first correction-to-scaling terms. This is consistent with the nonmonotonic crossover from Ising to mean-field critical behavior. The analysis of the light scattering data in terms of the crossover theory of Anisimov et al. [Phys. Rev. Lett. 75, 3146 (1995)] leads to a good fit of the data, and allows one to describe accurately the behavior of the effective critical exponents γ and ν. The thermal expansivity calculated from the density measurements is consistent with a (1-α) critical anomaly, with α=0.11 for the three critical mixtures studied. Finally, the shear viscosity has been analyzed in terms of the dynamic crossover function and the ξ values calculated from the theory of Anisimov et al. [Phys. Rev. Lett. 75, 3146 (1995)]. The values of the critical exponent z are consistent with the theoretical predictions.

Scaling near the theta point for isolated polymers in solution.

Recently questions have been raised as to the conclusions that can be drawn from currently proposed scaling theory for a single polymer in various types of solution in two and three dimensions. Here we summarize the crossover theory predicted for low dimensions and clarify the scaling arguments that relate thermal exponents for quantities on approaching the theta point from low temperatures to those associated with the asymptotics in polymer length at the theta point itself.

Low-temperature behaviour of the transverse Ising model in the influence domain of the quantum critical point

The critical properties of the d-dimensional transverse Ising model in the influence domain of its quantum critical point are studied solving the one-loop renormalization group equations around and at d=3. Different critical regimes occur involving crossover behaviours which can be described in terms of effective exponents, consistently with the conventional crossover theory.

Density matrix renormalization group studies of the effect of constraint release on the viscosity of polymer melts.

The scaling of the viscosity of polymer melts is investigated with regard to the molecular weight. We present a generalization of the Rubinstein-Duke model, which takes constraint releases into account and calculates the effects on the viscosity by the use of the density matrix renormalization group algorithm. Using input from Rouse theory, the rates for the constraint releases are determined in a self-consistent way. We conclude that shape fluctuations of the tube caused by constraint release are not a likely candidate for improving Doi's crossover theory for the scaling of the polymer viscosity.

Stochastic renormalization group in percolation: I. fluctuations and crossover

A generalization of the Renormalization Group, which describes order-parameter fluctuations in finite systems, is developed in the specific context of percolation. This “Stochastic Renormalization Group” (SRG) expresses statistical self-similarity through a non-stationary branching process. The SRG provides a theoretical basis for analytical or numerical approximations, both at and away from criticality, whenever the correlation length is much larger than the lattice spacing (regardless of the system size). For example, the SRG predicts order-parameter distributions and finite-size scaling functions for the complete crossover between phases. For percolation, the simplest SRG describes structural quantities conditional on spanning, such as the total cluster mass or the minimum chemical distance between two boundaries. In these cases, the Central Limit Theorem (for independent random variables) holds at the stable, off-critical fixed points, while a “Fractal Central Limit Theorem” (describing long-range correlations) holds at the unstable, critical fixed point. This first part of a series of articles explains these basic concepts and a general theory of crossover. Subsequent parts will focus on limit theorems and comparisons of small-cell SRG approximations with simulation results.

STAR POLYMERS IN GOOD SOLVENTS FROM DILUTE TO CONCENTRATED REGIMES: CROSSOVER APPROACH

An introduction is given to the crossover theory of the conformational and thermodynamic properties of star polymers in good solvents. The crossover theory is tested against Monte Carlo simulation data for the structure and thermodynamics of model star polymers. In good solvent conditions, star polymers approach a ``universal'' limit as $Nto; however, there are two types of approach towards this limit. In the dilute regime, a critical degree of polymerization $N^*$ is found to play a similar role as the Ginzburg number in the crossover theory for critical phenomena in simple fluids. A rescaled penetration function is found to control the free energy of star polymer solutions in the dilute and semidilute regions. This equation of state captures the scaling behaviour of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer-monomer interactions become important.

Crossover behavior of linear and star polymers in good solvents

Monte Carlo simulation calculations for the mean-square end-to-end distance and second virial coefficient for model linear and star polymers composed of hard spheres with square-well attractions are presented. For these polymers, two types of crossover behavior are observed: (i) crossover from the Gaussian chain to the Kuhnian chain limits and (ii) crossover from the semiflexible chain to the Kuhnian chain limits. A crossover theory for the properties of dilute linear and star polymers under good solvent conditions is presented. This model directly relates the properties of the monomer–monomer interaction to the renormalized parameters of the theory. The predictions of the crossover theory are in good agreement with simulation data. A new equation of state for linear and star polymers in good solvents is presented. The equation of state captures the scaling behavior of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer–monomer interactions become important. This theory is compared to Monte Carlo simulation data for the volumetric behavior of tangent hard-sphere polymers.

Crossover behavior of star polymers in good solvents

We perform Monte Carlo calculations for the mean-square center-to-end distance, mean-square radius of gyration, and second virial coefficient of f=3 to 41 arm star polymers composed of rigidly bonded hard spheres of varying diameters. As with linear chains, there are two different crossover regimes: (i) crossover from the Gaussian chain to the Kuhnian chain limit, where the penetration function Ψ(f) increases monotonically with increasing polymer molecular weight, and (ii) crossover from the rigid-rod to the Kuhnian chain limit, where the penetration function decreases with increasing molecular weight. We propose a phenomenological approach for the extension of our previous crossover theory for linear polymers to star polymers. We show that the theoretical crossover function obtained earlier by Douglas and Freed [Macromolecules 16, 1854 (1984)] fails to reproduce the simulation data for the penetration function with f⩾6, while the phenomenological crossover model is in good agreement with the simulation data up to f⩽41. We also obtain a generalized crossover equation for the penetration function for linear and star polymers in good solvents. The crossover equation is able to accurately describe the variation of the infinite molecular weight limit of the penetration function Ψ*(f) with the number of arms f on the star polymer, and it predicts that Ψ*(f) approaches 2.39 in the limit f→∞.

Effective Landau theory for crossover from thermal hopping to quantumtunnelling

In this paper the decay rate is obtained accurately near thecrossover temperature. Because of the strong fluctuations near the crossovertemperature a method called the effective Landau theory beyond the Gaussiansemiclassical approximation is developed. We find that in the crossoverregion the transition rate of the first-order transition changes much moresharply than that of the second-order one. For both cases there is nodiscontinuity of transition rate for any of the order derivatives.

Scaling and crossover to tricriticality in polymer solutions

We propose a scaling description of phase separation of polymer solutions. The scaling incorporates three universal limiting regimes: the Ising limit asymptotically close to the critical point of phase separation, the “ideal gas” limit for the pure solvent phase, and the tricritical limit for the polymer-rich phase asymptotically close to the theta point. We have also developed a phenomenological crossover theory based on the near-tricritical-point Landau expansion renormalized by fluctuations. This theory validates the proposed scaled representation of experimental data and crossover to tricriticality.

Random resistor-diode networks and the crossover from isotropic to directed percolation

By employing the methods of renormalized field theory, we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic model from the general epidemic process by including a relevant isotropy-breaking perturbation. We present a two-loop calculation of the crossover exponent straight phi. Upon blending the varepsilon-expansion result with the exact value straight phi=1 for one dimension by a rational approximation, we obtain straight phi=1.29+/-0.05 for two dimensions. This value is in agreement with the recent simulations of a two-dimensional random diode network by Inui, et al. [Phys. Rev. E 59, 6513 (1999)], who found an order parameter exponent beta different from those of isotropic and directed percolation. Furthermore, we reconsider the theory of the full crossover from isotropic to directed percolation by Frey, Tauber, and Schwabl [Europhys. Lett. 26, 413 (1994); Phys. Rev. E 49, 5058 (1994)], and clear up some minor shortcomings.

Unusual thermodynamical and transport signatures of the BCS to bose-einstein crossover scenario below T(c)

In this paper we present predictions for thermodynamic and transport properties of a BCS to Bose-Einstein crossover theory, below T(c), which satisfies the reasonable constraints that it yields (i) the Leggett ground state and (ii) BCS theory at weak coupling and all temperatures T. The nature of the strong coupling limit is inferred, along with the behavior of the Knight shift, superfluid density, and specific heat. Comparisons with existing data on short coherence length superconductors, such as organic and high T(c) systems, are presented, which provide some support for the present picture.

Near-Critical Behavior of Mutual Diffusion Coefficients for Five Solutes in Supercritical Carbon Dioxide

The Taylor−Aris dispersion technique was employed to measure the binary diffusion coefficients of five solid solutes (phenanthrene, biphenyl, benzoic acid, 1,4-dichlorobenzene, and phenol) in supercritical carbon dioxide within the pressure range from 75 to 170 bar at 308.2 K. Measurements were made at very dilute concentrations, in the vicinity of the pure CO2 critical point and also near the solid/supercritical fluid lower critical end point. At 308.2 K (4 K above the critical temperature of the solvent), decreasing the pressure (density) of the fluid causes the binary diffusion coefficients to increase until a certain pressure is reached. With further decreases in pressure, approaching the critical pressure of CO2, the diffusion coefficients decrease sharply. The decrease in diffusion coefficient near the solvent critical point is discussed using the concept of the solvent density inhomogeneities in supercritical fluids. A crossover theory that considers both the critical singular contribution and background contribution of transport properties is used to describe semiquantitatively the observed decrease in the diffusion coefficient.