Search Results (23 total)

Application of polymer scaling to the problem of Tolman’s length, a curvature correction coefficient in the interfacial tension, shows that Tolman’s length in polymer solutions may become as large as half of the thickness of the interface. Tolman’s length depends on the degree of polymerization N and the distance to the critical point of phase separation, ΔT̂. In the “critical” regime (N^1/2|ΔT̂|⪡1) Tolman’s length diverges upon approach to the critical temperature as ∼N^0.348|ΔT̂|^−0.304. In the “polymer” regime (N^1/2|ΔT̂|⪢1) Tolman’s length does not depend on N, but diverges more strongly, as ∼|ΔT̂|⁻¹, proportional to the thickness of the interface.

The extension of the principle of critical-point universality to binary fluid mixtures, known as isomorphism of critical phenomena, has been reformulated in terms of complete scaling, a concept that properly matches asymmetric fluid-phase behavior with the symmetric Ising model. The controversial issue of the proper definition of the order parameter in binary fluid mixtures is clarified. We show that asymmetry of liquid-liquid coexistence in terms of mole fractions originates from two different sources: one is associated with a correlation between concentration and entropy fluctuations, whereas the other source is the correlation between concentration and density fluctuations. By analyzing the coexistence curves of liquid solutions of nitrobenzene in a series of hydrocarbons (from n-pentane to n-hexadecane), we have separated these two sources of asymmetry and found that the leading nonanalytical contribution to the asymmetry correlates linearly with the solute-solvent molecular-volume ratio. Other thermodynamic consequences of complete scaling for binary mixtures, such as an analog of the Yang-Yang anomaly in the behavior of the heat capacity and a curvature correction to the interfacial tension, are also discussed.

Using dynamic light scattering we have investigated the time dependence of fluctuations near the critical point of phase separation in solutions of polystyrene in cyclohexane with polymer molecular weights ranging from 196  000  to  11.4×10⁶  g  mol⁻¹. At the lowest polymer molecular weight the dynamic correlation function follows a single-exponential decay with a decay rate that can be represented by the mode-coupling theory of critical dynamics but with a mesoscopic viscosity that characterizes the hydrodynamic environment of the polymers in the solution. At all higher polymer molecular weights two distinct dynamic modes are observed, a slow and a fast mode, that originate from a coupling of the critical concentration fluctuations with viscoelastic relaxation of the polymer chain in solutions. This coupling causes an additional slowing down of the fluctuations on top of the well-known critical slowing down expected in the absence of a coupling between the two modes. From an analysis of the time dependence of the experimental dynamic correlation functions in terms of a theory of coupling of dynamic modes we are able to determine the viscoelastic properties of the polymers in the solution. These viscoelastic properties diverge in the theta-point limit of infinite polymer molecular weight.

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.

The application of “complete scaling” [Kim , Phys. Rev. E 67, 061506 (2003); Anisimov and Wang, Phys. Rev. Lett. 97, 025703 (2006)] to the interfacial behavior of fluids shows that Tolman’s length, a curvature correction to the surface tension, diverges at the critical point of fluids much more strongly than is commonly believed. The amplitude of the divergence depends on the degree of asymmetry in fluid phase coexistence. In highly asymmetric fluids and fluid mixtures the Tolman length may become large enough to significantly affect the interfacial behavior.

We have developed a scaled parametric equation of state to describe and predict thermodynamic properties of supercooled water. The equation of state, built on the growing evidence that the critical point of supercooled liquid-liquid water separation exists, is universal in terms of theoretical scaling fields and is shown to belong to the Ising-model class of universality. The theoretical scaling fields are postulated to be analytical combinations of the physical fields, pressure, and temperature. The equation of state enables us to accurately locate the “Widom line” (the locus of stability minima) and determine that the critical pressure is considerably lower than predicted by computer simulations.

By combining accurate liquid-vapor coexistence and heat-capacity data, we have unambiguously separated two nonanalytical contributions of liquid-gas asymmetry in fluid criticality and showed the validity of “complete scaling” [Fisher , Phys. Rev. Lett. 85, 696 (2000); Phys. Rev. E 67, 061506 (2003)]. We have also developed a method to obtain two scaling-field coefficients, responsible for the two sources of the asymmetry, from mean-field equations of state. Since the asymmetry effects are completely determined by Ising critical exponents, there is no practical need for a special renormalization-group theoretical treatment of asymmetric fluid criticality.

We have studied isotropic-to-nematic pretransitional fluctuations in an aqueous solution of disodium cromoglycate (cromolyn) by static and dynamic light scattering. Cromolyn is a representative of lyotropic chromonic liquid crystals with building units being elongated rods formed by aggregates of disk-like molecules. By combining light-scattering and viscosity measurements we have determined the correlation length and relaxation time of the orientational order-parameter fluctuations and estimated the size of the cromolyn aggregates. The pretransitional behavior of light scattering does not completely follow the classic Landau–de Gennes model. This feature is most probably associated with the variable length of cromolyn aggregates. We have observed a dramatic increase of the shear viscosity near the transition to the nematic phase, the fact which correlates with the idea of growing supramolecular aggregates. The steep temperature dependence of the viscosity is accompanied by a practically temperature-independent translational diffusion coefficient.

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.

We have performed accurate dynamic light-scattering measurements near critical demixing points of solutions of polystyrene in cyclohexane with polymer molecular weight ranging from 200 000 to 11.4×10⁶. Two dynamic modes have been observed, “slow” and “fast,” which result from a coupling between diffusive relaxation of critical fluctuations of the concentration and viscoelastic relaxation associated with the entanglement network of the polymer chains. The coupling with the viscoelastic mode causes an additional slowdown of the critical mode on top of the uncoupled diffusion mode. By implementing crossover from the critical to the θ-point tricritical behavior for both static and dynamic properties, we are able to present a quantitative description of the phenomenon and obtain a scaling of the viscoelastic parameters as a function of the molecular weight.

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 11.4×10⁶ 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 θ-point behavior determined by a mesoscopic polymer-chain length.

We present a parametric equation for the thermodynamic properties in the critical region of three-dimensional Ising-like systems which include fluids and fluid mixtures. The equation of state incorporates a crossover from singular Ising behavior asymptotically close to the critical point to classical (mean-field) behavior further away from the critical point, characterized by two physical crossover parameters: a coupling constant related to the strength and range of molecular interactions and a “cutoff” wave number for the critical fluctuations. In the asymptotic Ising limit, the crossover equation reproduces the most recent theoretical estimates for the universal ratios of the leading and correction-to-scaling critical amplitudes. The equation has been tested by comparing it with recent experimental thermodynamic-property data for ³He near its vapor-liquid critical point.

We have discovered a mean-field multicritical point on the critical locus in an aqueous solution of 3-methylpyridine and sodium bromide. Light-scattering measurements indicate Ising-like asymptotic critical behavior at the lower salt concentrations. However, the temperature range of Ising critical behavior shrinks with increasing salt concentration and the critical behavior becomes mean-field-like at a concentration of about 17% mass fraction of NaBr. Emergence of a new characteristic length scale diverging at this point and a simultaneous pronounced increase in the background scattering suggests mean-field tricritical behavior associated with the formation of a microheterogeneous phase due to clustering of ions and molecules.

The near-critical behavior of the susceptibility deduced from light-scattering measurements in a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide has been determined. The measurements have been performed in the one-phase region near the lower consolute points of samples with different concentrations of sodium bromide. A crossover from Ising asymptotic behavior to mean-field behavior has been observed. As the concentration of sodium bromide increases, the crossover becomes more pronounced, and the crossover temperature shifts closer to the critical temperature. The data are well described by a model that contains two independent crossover parameters. The crossover of the susceptibility critical exponent γ from its Ising value γ=1.24 to the mean-field value γ=1 is sharp and nonmonotonic. We conclude that there exists an additional length scale in the system due to the presence of the electrolyte which competes with the correlation length of the concentration fluctuations. An analogy with crossover phenomena in polymer solutions and a possible connection with multicritical phenomena is discussed.

Two hydrodynamic relaxation modes associated with mass diffusion and thermal diffusion are present in binary fluids. In near-critical binary fluids a coupling between the two modes results in two characteristic relaxation times, neither of which is associated with pure mass diffusion or pure thermal diffusion. Instead, the relaxation times are inversely proportional to two effective diffusivities D₁ and D₂, which can be detected experimentally by dynamic light scattering. The physical meaning of D₁ and D₂ changes as one considers states in the vicinity of different points on the critical locus: in the infinite-dilution limit the diffusivity D₁ of the slow mode is associated with the thermal diffusivity and the diffusivity D₂ of the fast mode with the mutual mass diffusion coefficient, while in the “incompressible” liquid-mixture limit D₁ is associated with the mass diffusion coefficient and D₂ with the thermal diffusivity. In addition we have determined the intensities (amplitudes) of these relaxation modes, which can also be measured with light scattering. We discuss the conditions at which a two-exponential decay of the dynamic correlation function can be measured. As an example we consider mixtures of methane and ethane near the vapor-liquid critical line where the two exponential decays indeed have been observed.

The analogy with the liquid-gas critical point is analyzed to clarify the nature of the pretransitional behavior of physical properties in the vicinity of the Blue-Phase-III–isotropic transition in chiral liquid crystalline systems. The analogy is unusual: temperature serves as the ordering field and entropy plays the role of the order parameter. Both mean field and parametric equations of state are formulated in terms of scaling fields. The scaling fields are linear combinations of the physical fields, which are temperature and chirality. It is shown that mixing of the physical field variables naturally leads to a strong asymmetry with respect to the transition temperature in the behavior of the physical properties that cannot be described by simple power laws. While the mean field theory gives a good description of the experimental data, the scaling theory, if one incorporates mixing of the field variables, gives even better agreement with the experimental data, placing this transition in the same universality class as the three-dimensional Ising model.

We have observed a sharp and nonmonotonic crossover of the susceptibility (osmotic compressibility) from mean-field to Ising critical behavior in semidilute solutions of polystyrene in deuterocyclohexane as the temperature decreases from the Θ region down to the critical temperature of the phase separation. We describe this crossover in terms of a competition between the long-range but finite intramolecular correlations of monomers in the polymer chain and the diverging correlation length of concentration fluctuations.

A Reply to the Comment by C. Bagnuls and C. Bervillier.

An analysis of experimental data for the susceptibility of fluids and of liquid mixtures in the critical region has been performed to elucidate the character of the nonasymptotic critical behavior. While fluids and fluid mixtures exhibit an ultimate crossover to Ising-like asymptotic behavior, the effective susceptibility exponent γ_eff approaches the universal value γ≃1.24 either from above (A) or from below (B). We conclude that simple fluids belong to type B, whereas more complex systems may belong to type A and show a sharper nonmonotonic crossover from mean-field to Ising-like behavior.

The application of the principle of critical-point universality to fluid mixtures near plait points is generalized to encompass crossover between the one-component vapor-liquid critical limit and the liquid-liquid critical limit of incompressible liquid mixtures. This goal is accomplished by generalizing the scaling fields to linear combinations of three physical field variables related to the temperature and the chemical potentials of the two components. We show how one recovers from the general expressions for the scaling fields the limiting critical behavior of dilute mixtures near the vapor-liquid critical point and of weakly compressible liquid mixtures near the consolute point. In addition we elucidate the consequences for the critical behavior in some special cases, namely, near an azeotropic critical point, near a reentrant critical point, and when the critical temperature goes through a maximum or a minimum as a function of concentration.

In 1974, Halperin, Lubensky, and Ma (HLM) [Phys. Rev. Lett. 32, 292 (1974)] predicted that the nematic–smectic-A transition of pure compounds and their mixtures should be at least weakly first order. One way to obtain such a prediction is to treat the smectic order parameter as a constant and integrate out the director fluctuations. The coupling between the director fluctuations and the smectic order parameter then generates a cubic term in the effective free energy for the nematic–smectic-A(N–Sm-A) transition, which tends to drive the transition first order. So far, however, there has not been clear experimental evidence in support of this prediction: Some materials appear to exhibit a first-order transition but others a second-order transition. In this paper we introduce two new approaches to test the predictions of HLM. First, we note that if a cubic term in the effective free energy for the smectic order parameter is present, its effect is dominant near the Landau tricritical point (LTP), where the quartic term in the free energy vanishes.

In a mean-field approximation, a universal scaling form of the latent heat can then be derived close to the LTP. Its form depends sensitively on the presence of the cubic term. By reanalyzing earlier calorimetric measurements near the LTP, we find that these data yield evidence for the presence of the cubic term predicted by HLM. The second new approach to experimentally determine whether a transition is weakly first order or second order is a dynamical method. This general method is based on the observation that when a transition is (weakly) first order, the dynamics of interfaces are symmetric about T_c, so that an interface can propagate into both phases, depending on whether the sample is undercooled or overheated (corresponding to ‘‘melting’’ and ‘‘freezing’’). For a weakly first-order transition, a simple scaling relation for the interface speed can be derived. In contrast, the dynamics of propagating fronts close to a second-order transition are very asymmetric. Results of moving interfaces close to T_c in 8CB-10CB (where CB represents cyanobiphenyl) and 9CB-10CB mixtures are presented and shown to support both qualitatively as well as quantitatively the prediction that the transition is always at least weakly first order. For the N–Sm-A transition in these compounds, our comparison finds that the dynamic experiments are more sensitive than the adiabatic calorimetry experiments by about one order of magnitude and more sensitive than the x-ray-diffraction experiments by about two orders in detecting the phase-transition order.