Critical Consolute Point Research Articles

Line Tension at Fluid Membrane Domain Boundaries Measured by Micropipette Aspiration

Line tension is a determinant of fluid phase domain formation kinetics and morphology in lipid bilayer membranes, which are models for biological membrane heterogeneity. We describe the first direct measurement of this line tension by micropipette aspiration. Our data are analyzed with a model that does not rely on independently measured (and composition dependent) secondary parameters, such as bending stiffness or membrane viscosities. Line tension is strongly composition dependent and decreases towards a critical consolute point in a quasiternary room temperature phase diagram.

Critical behaviour in nitrobenzene–hexane mixture by approaching the liquid–liquid critical line

The pressure dependence of the critical consolute temperature in nitrobenzene–hexane mixture has been studied in the −28 to +110 MPa range. The negative pressure part of the locus was determined by the extrapolation of the pretransitional anomaly of nonlinear dielectric effect and analyzed by a modified Simon–Glatzel type equation, which makes the extension into the P < 0 domain possible. This equation is parameterised by invariant coefficients and exhibits a negative power exponent. Our results proved that fluctuations can be important even far away from the critical consolute point.

Wetting transitions in a binary thin-film

The effect of finite thickness of a binary thin-film system exhibiting a consolute critical point on the wetting behavior at the planar film-substrate interface was examined by accounting for the short-range chemical interaction between the film and substrate. Owing to the limited amount of mass available within the film, the first-order adsorption transition obtained from the one-dimensional equilibrium analyses has a physical meaning only when the film is initially uniform in composition. The line of first-order adsorption transition is strongly affected by the finite film thickness, with the composition line shifting inward towards the bulk miscibility gap as the film thickness descreases. However, when the film is initially in a two-phase mixture state, two-dimension simulations showed that the wetting transition from partial to perfect wetting is hardly influenced by the film thickness. The results of the present study suggest that the wetting behavior of a thin film at a given film composition and temperature depends critically on the initial state of the film.

Demixing can occur in binary hard-sphere mixtures with negative nonadditivity

A binary fluid mixture of nonadditive hard spheres characterized by a size ratio gamma = sigma(2)/sigma(1) < 1 and a nonadditivity parameter Delta = 2 sigma(12)/(sigma(1) + sigma(2)) - 1 is considered in infinitely many dimensions. From the equation of state in the second virial approximation (which is exact in the limit d--> infinity) a demixing transition with a critical consolute point at a packing fraction scaling as eta approximately d2(-d) is found, even for slightly negative nonadditivity, if Delta >-1/8 (ln gamma)(2). Arguments concerning the stability of the demixing with respect to freezing are provided.

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.

Critical adsorption at chemically structured substrates

We consider binary liquid mixtures near their critical consolute points and exposed to geometrically flat but chemically structured substrates. The chemical contrast between the various substrate structures amounts to opposite local preferences for the two species of the binary liquid mixtures. Order parameter profiles are calculated for a chemical step, for a single chemical stripe, and for a periodic stripe pattern. The order parameter distributions exhibit frustration across the chemical steps which heals upon approaching the bulk. The corresponding spatial variation of the order parameter and its dependence on temperature are governed by universal scaling functions which we calculate within mean field theory. These scaling functions also determine the universal behavior of the excess adsorption relative to suitably chosen reference systems.

Rescaled density expansions and demixing in hard-sphere binary mixtures.

The demixing transition of a binary fluid mixture of additive hard spheres is analyzed for different size asymmetries by starting from the exact low-density expansion of the pressure. Already within the second virial approximation the fluid separates into two phases of different composition with a lower consolute critical point. By successively incorporating the third, fourth, and fifth virial coefficients, the critical consolute point moves to higher values of the pressure and to lower values of the partial number fraction of the large spheres. When the exact low-density expansion of the pressure is rescaled to higher densities as in the Percus-Yevick theory, by adding more exact virial coefficients a different qualitative movement of the critical consolute point in the phase diagram is found. It is argued that the Percus-Yevick factor appearing in many empirical equations of state for the mixture has a deep influence on the location of the critical consolute point, so that the resulting phase diagram for a prescribed equation has to be taken with caution.

Molecular dynamics simulations of a fluid near its critical point.

We present computer simulations for the static and dynamic behavior of a fluid near its consolute critical point. We study the Widom-Rowlinson mixture, which is a two component fluid where like species do not interact and unlike species interact via a hard core repulsion. At high enough densities this fluid exhibits a second order demixing transition that is in the Ising universality class. We find that the mutual diffusion coefficient DAB vanishes as DAB approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from renormalization-group and mode coupling theory predictions for model H, which are DAB approximately xi(-1.065) and DAB approximately xi(-1), respectively.

Critical behavior of dielectric permittivity and electric conductivity in temperature and pressure studies above and below the critical consolute point

Results of comprehensive temperature (T) and pressure (P) studies of static dielectric permittivity (ε′) and electric conductivity (σ) in the one- and two-phase regions of critical nitrobenzene–dodecane mixture are presented. A strong asymmetry of determined coexistence curves causes a strong violation of the law of rectilinear diameter. The obtained critical anomalies in the homogeneous phase [εhomo′(T),εhomo′(P),σhomo(P)] or the diameter of the binodal [εmean′(T),εmean′(P),σmean(T),σmean(P)] are associated with the same critical exponent φ=1−α ≈0.88, where α is the specific heat critical exponent. Critical anomalies for the isothermal, pressure path exhibit a set of favorite in comparison with results obtained in σ(T) and ε(T) tests. They are: the negligible influence of the critical Maxwell–Wagner effect, the hardly visible appearance of the correction-to-scaling term, a more pronounced manifestation of critical anomalies, and a reduced number of fitted parameters. Particularly noteworthy is the evidence for the σhomo(P) anomaly in the homogeneous phase, hardly obtained up to now in a mixture of a low electric conductivity. Results presented suggest the isomorphic behavior of ε′(T), σ(T) and ε′(P), σ(P) critical anomalies for the homogeneous phase and for the diameter of the binodal.

MONTE CARLO SIMULATION OF PHASE EQUILIBRIA IN ISING FLUIDS AND THEIR MIXTURES

The mean field theory for the pure Ising fluid was recently extended to binary mixtures of an Ising and a van der Waals fluid. Depending on the relative interaction strengths, their three dimensional phase diagrams show lines of tricritical consolute and plait points, lines of critical end points and magnetic consolute point lines. Our current efforts are to compare these mean field results with different Monte Carlo simulation techniques, investigating both first order (liquid-vapor and demixing) and second order (paramagneticferromagnetic) phase transitions. We show the resulting ρ, T phase diagrams of the pure Ising fluid for different magnetic interaction strengths R and constant pressure cross-sections of the x, T, p phase diagrams of Ising mixtures for different relative interaction strengths. The methods we have used include Gibbs Ensemble MC, Multihistogram Reweighting, Hyper-parallel Tempering, the cumulant intersection method and the newly developed Density of States MC technique.

The binary system triethylamine-water near its critical consolute point: An ultrasonic spectrometry, dynamic light scattering, and shear viscosity study

Ultrasonic attenuation spectra between 100 kHz and 500 MHz, mutual diffusion coefficients and shear viscosities of the triethylamine/water mixture of critical composition have been measured at various temperatures near the critical one. The broadband ultrasonic spectra reveal two relaxation terms with discrete relaxation time and a term that is subject to a broad relaxation time distribution. The former have been discussed to be due to a protolysis reaction and a structural isomerization. The latter term has been evaluated in the light of the Bhattacharjee–Ferrell dynamic scaling theory, relating the sonic spectrum to fluctuations in the local mixture concentrations. The relaxation rate of the Bhattacharjee–Ferrell term follows power law behavior. However, its amplitude (Γ0=45×109 s−1) is considerably smaller than that derived from the dynamic light scattering and shear viscosity measurements (Γ0=96×109 s−1). This result is assumed to be due to a shear viscosity relaxation. Using density and heat capacity measurements from the literature, the adiabatic coupling constant g of the triethylamine/water system has been derived from the amplitude of the Bhattacharjee–Ferrell term in the ultrasonic spectra and from a thermodynamic relation as well. Again, a discrepancy is found. The ultrasonic spectra yield g=0.19, whereas g=0.98 follows otherwise. This difference in the g values is taken as an indication of the limitations of the Bhattacharjee–Ferrell model. It had been derived assuming a small amplitude in the singular part of the heat capacity, a precondition which is clearly not fulfilled with the triethylamine/water system.

Density functional theory for a model colloid–polymer mixture: bulk fluidphases

We describe a density functional theory for mixtures of hard sphere (HS) colloids andideal polymers, the Asakura–Oosawa model. The geometry-based fundamentalmeasures approach which is used to construct the functional ensures the correctbehaviour in the limit of low density of both species and in the zero-dimensionallimit of a cavity which can contain at most one HS. Dimensional crossover isdiscussed in detail. Emphasis is placed on the properties of homogeneous (bulk)fluid phases. We show that the present functional yields the same free energy and,therefore, the same fluid–fluid demixing transition as that given by a differentapproach, namely the free-volume theory. The pair direct correlation functionscij(2)(r)of the bulk mixture are given analytically. We investigate the partial structure factorsSij(k)and the asymptotic decay, r → ∞, of the total pair correlationfunctions hij(r)obtained from the Ornstein–Zernike route. The locus in the phase diagram of the crossoverfrom monotonic to oscillatory decay of correlations is calculated for several size ratiosq = Rp/Rc, whereRp is the radius of thepolymer sphere and Rcthat of the colloid. We determine the (mean-field) behaviour of the partialstructure factors on approaching the fluid–fluid critical (consolute) point.

Diffusion and thermal diffusion of semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition.

The approaching glass transition in polystyrene/toluene solutions leads to a sharp decay of both the collective diffusion coefficient D and the thermal diffusion coefficient D(T) at concentrations above 0.2 g/cm(3). The Soret coefficient S(T) = D(T)/D follows power-law scaling from semidilute to concentrated and is not influenced by the slowing down of the dynamics associated with the glass transition. Both D and D(T) are governed by the same friction coefficient. The scaling behavior of S(T) with concentration on approach of the glass transition is compared to the divergence of S(T) near a consolute critical point.

Comment on “Self-diffusion near the liquid–vapor critical point” [J. Chem. Phys. 114, 4912 (2001)

Drozdov and Tucker [J. Chem. Phys. 114, 4912 (2001)] have computed the self-diffusion coefficient along a near-critical isotherm showing anomalous slowing of molecular motion near the critical density and cite some experiments in support. A considered examination of the best literature data shows no such anomaly near neat liquid critical or mixture consolute points.

Critical behavior in broad-band dielectric relaxation on approaching the critical consolute point in ethanol-dodecane mixture

We present a quantitative experimental evidence for the influence of critical fluctuations on the high frequency dielectric relaxation in a binary critical mixture. The analysis clearly shows the presence of critical anomaly both for the maxima (epsilon(")(p)) and frequencies (f(p)) of loss curves peaks. For the temperature evolution of epsilon(")(p) similar relation as for the static dielectric permittivity was obtained. The temperature dependence of relaxation times can be portrayed by using the Eyring-type equation remote from the critical consolute point and shows the unusual precritical speeding up. The obtained behavior resembles that found recently in the isotropic phase of nematic liquid crystals [A. Drozd-Rzoska and S. J. Rzoska, Phys. Rev. E 65, 041701 (2002)]. Results presented agree also with the recent theoretical suggestion [S. Goodyear and S. C. Tucker, J. Chem. Phys. 111, 9673 (1999)] that relaxation in supercritical fluids may exhibit glasslike features.

Critical Behavior of the Electrical Conductivity of Concentrated Electrolytes: Ethylammonium Nitrate in n-Octanol Binary Mixture

The electrical conductivity κ of highly concentrated binary ionic mixtures of ethylammonium nitrate in n-octanol at a critical salt mole fraction x = 0.766 and at an off-critical one x = 0.908 was measured over an extended temperature range above the critical consolute point. Far from the critical temperature Tc, the conductivity is accurately described by the Vogel–Fulcher–Tammann (VFT) law. However, in a temperature range ΔT = (T − Tc) ≤ 3 K, the conductivity exhibits a monotonous deviation from the VFT behavior. This anomaly is finite at Tc and, for the critical mixture, its amplitude is ≅ 0.23% of κ (Tc). The asymptotic behavior of the conductivity anomaly is described by a power law τ(1 − α), with τ = (T − Tc)/Tc, the reduced temperature, and α, the critical exponent of the specific heat anomaly at constant pressure. This critical anomaly is similar to the one observed in other highly concentrated critical electrolytes. The degree of dissociation of the salt for the critical mixture, αdiss ≅ 0.78 ± 0.04, is estimated from the value of the Walden product computed at Tc, and accounts for the effective free ion concentration in the reduced critical coordinates of the system.

On the critical behavior of linear and nonlinear dielectric permittivity on approaching the critical consolute point

Results are presented of the dielectric permittivity /spl epsi/ and nonlinear dielectric effects (NDE) in binary mixtures on approaching the critical consolute point (CCP), focusing first on Piekara's findings [Phys. Rev. Vol.42, pp. 445-447, 1932, and C. R. Acad. Sci. Paris Vol. 203, pp. 1058-1059, 1936]. The presented results cover changes in temperature and pressure. For NDE particular attention is given to complex liquid features of critical mixtures appearing in /spl epsi/ and NDE tests. The latter are presented for the stationary and dynamic (time-resolved NDE) behavior. New results for NDE in nitrobenzene, hexane mixture with the lowest measurement frequency ever applied and in benzonitrile-isooctane mixture for dielectric permittivity are also included. For the latter, the first test of the relation: d/spl epsi//dT /spl alpha/ (T - T/sub C/) /sup -/spl alpha// is shown.

Diameters of the liquid-liquid coexistence curves of aqueous solutions of tetrahydrofuran

The diameters of the coexistence curves of aqueous solutions of tetrahydrofuran and two quasibinary, isotopically related mixtures near their lower consolute points are analyzed in terms of different composition variables including mole, mass, and volume fractions, using various possible definitions of the reduced temperature. A (1−α) anomaly is observed for all choices of the temperature and concentration variables. In terms of mole fraction the diameters are free from a regular contribution as well as from a spurious 2β contribution arising from the inappropriate choice of the order parameter. The mass and volume fractions lead to an apparent symmetrization of the coexistence curve, but cause significant 2β contributions to the diameter that could mask the 1−α anomaly. A reduced temperature that accounts for the presence of both upper and lower critical consolute points is found to be preferable, although the second critical point is 80 K away.

Electrical conductivity of highly concentrated electrolytes near the critical consolute point: A study of tetra-n-butylammonium picrate in alcohols of moderate dielectric constant

The electrical conductivity of highly concentrated solutions of tetra-n-butylammonium picrate (TBAP) in 1-dodecanol (dielectric constant ε=4.6) and 1,4-butanediol (ε=25.9), and in mixtures of both alcohols, is measured in an extended temperature range ≈10−5&amp;lt;τ&amp;lt;≈10−1, where τ=(T−Tc)/Tc is the reduced temperature with Tc, the critical temperature. The electrical conductivity Λ(T) obeys the Vogel–Fulcher–Tammann (VFT) law for the temperatures far from the critical one. In the temperature range τ&amp;lt;10−2 a systematic deviation of the electrical conductivity from the regular VFT behavior is observed. This deviation is attributed to a critical anomaly. At the critical point the amplitude of the critical anomaly is finite with a value which varies between ≈0.4 and ≈2.7% of Λ(Tc), depending on the solvent. The (1−α) critical exponent describes well the conductivity anomaly, α being the exponent of the specific heat anomaly at constant pressure. The value of the Walden product (Λeqvη), with Λeqv, the equivalent conductivity and η, the shear viscosity, allows the degree of dissociation αdiss of TBAP to be determined at the critical point. αdiss becomes larger for increasing values of ε: for TBAP in 1-dodecanol αdiss≈0.25 and in 1,4-butanediol αdiss≈0.73. When the degree of dissociation of the salt is accounted for the Debye screening length is found almost independent on ε.

Critical anomaly of dielectric permittivity for the temperature and pressure paths on approaching the critical consolute point.

The experimental results of isothermal pressure dielectric permittivity epsilon studies in a critical mixture characterized by a negative shift of critical temperature induced by pressure (dT(C)/dP<0) are presented. The critical effect is portrayed by the same relation as in previous epsilon(T) and epsilon(P) studies, with the critical exponent alpha=0.12+/-0.03. The advantage of pressure studies is the negligible influence of the correction-to-scaling term and the low-frequency Maxwell-Wagner effect. This conclusion is supported by the distortion-sensitive derivative analysis of the experimental data. In contrast to previous epsilon(P) studies, carried out in mixtures with dT(C)/dP>0, the critical effect manifests by the bending-up behavior near the critical point. It is suggested that signs of the critical amplitudes of epsilon(P) and epsilon(T) anomalies may be related to the excess volume V(E) and the excess enthalpy H(E), respectively.