Critical Mixing Point Research Articles

Purified myelin lipids display a critical mixing point at low surface pressure

Lipids extracted from Purified Myelin Membranes (LPMM) were spread as monomolecular films at the air/aqueous interface. The films were visualized by Brewster Angle Microscopy (BAM) at different lateral pressures (π) and ionic environments. Coexistence of Liquid-Expanded (LE) and cholesterol-enriched (CE) rounded domains persisted up to π ≈ 5 mN/m but the monolayers became homogeneous at higher surface pressures. Before mixing, the domains distorted to non-rounded domains. We experimentally measured the line tension (λ) for the lipid monolayers at the domain borders by a shape relaxation technique using non-homogeneous electric fields. Regardless of the subphase conditions, the obtained line tensions are of the order of pN and tended to decrease as lateral pressure increased toward the mixing point. From the mean square displacement of nested trapped domains, we also calculated the dipole density difference between phases (μ). A non-linear drop was detected in this parameter as the mixing point is approached. Here we quantitively evaluated the π-dependance of both parameters with proper power laws in the vicinity of the critical mixing surface pressure, and the exponents showed to be consistent with a critical phenomenon in the two-dimensional Ising universality class. This idea of bidimensionality was found to be compatible only for simplified lipidic systems, while for whole myelin monolayers, that means including proteins, no critical mixing point was detected.Finally, the line tension values were related with the thickness differences between phases (Δt) near the critical point.

A molecular dynamics study of fuel droplet evaporation in sub- and supercritical conditions

Evaporation processes of a fuel droplet under sub- and supercritical ambient conditions have been studied using molecular dynamics (MD) simulations. Suspended n-dodecane droplets of various initial diameters evaporating into a nitrogen environment are considered. Both ambient pressure and temperature are varied from sub- to supercritical values, crossing the critical condition of the chosen fuel. Temporal variation in the droplet diameter is obtained and the droplet lifetime is recorded. The time at which supercritical transition happens is determined by calculating the temperature and concentration distributions of the system and comparing with the critical mixing point of the n-dodecane/nitrogen binary system. The dependence of evaporation characteristics on ambient conditions and droplet size is quantified. It is found that the droplet lifetime decreases with increasing ambient pressure and/or temperature. Supercritical transition time decreases with increasing ambient pressure and temperature as well. The droplet heat-up time as well as subcritical to supercritical transition time increases linearly with the initial droplet size d0, while the droplet lifetime increases linearly with d02. A regime diagram is obtained, which indicates the subcritical and supercritical regions as a function of ambient temperature and pressure as well as the initial droplet size.

Electric Conductivity of Delaminated AgI + NaCl Mixture

The liquid–liquid phase equilibrium for the melted AgI + NaCl mixture was studied by the impedance method over a wide range of temperatures along the saturation line to correlate the charge transfer in two-phase ion systems with the nature of the chemical bond. The temperature dependences of the specific electric conductivity κ of the coexisting phases have opposite signs because of the superposition of the temperature and concentration factors that act in the same or opposite directions. The difference between the κ values for the equilibrium phases decreases with increasing temperature, becoming zero at 1064 K. Near the critical mixing point, the temperature dependence of the difference between the conductivities of the coexisting phases is described by the exponential equation with a critical exponent of 0.91, which is 8% smaller than that found for alkali metal halides with primarily Coulomb forces acting between the ions.

Galvani potential at liquid–liquid interfaces for dissolving AgBr + LiCl and AgI + LiCl melts

An electrochemical method was used to study the Galvani potential between two coexisting equilibrium phases of molten AgI + LiCl and AgBr + LiCl systems. The method measures the electromotive force (emf) of a cell with two silver electrodes: Ag | x ′ AgI (or AgBr) + (1 − x ′ ) LiCl | x ″ AgI (or AgBr) + (1 − x ″ ) LiCl | Ag. The measurement was performed beginning with the melting point of the mixtures until reaching the temperature of full mixing, T c , to establish the Galvani potential magnitude and its temperature dependence near the critical point of mixing. It is shown that in the temperature range of 200 K below the critical mixing point, the temperature dependence of the Galvani potential for both systems is described by a universal equation, ∆E ≈ τ n , where τ = (T c − T)/T c , with the critical exponent n = 1.228.

Sound Wave Propagation in Immiscible AgBr+LiCl Melts

Abstract The velocity of sound wave propagation was measured for the biphasic region of AgBr+LiCl melts using the pulse method at temperatures from melting point to mixing temperature. It was found that temperature dependences of sound velocities on the saturation lines have opposite signs because of the different effect of thermal motion of the particles and the phases’ composition at the sound velocity. The difference between the sound velocities in the coexisting phases, Δu, is described by the exponential equation Δu≈(Tc−T)θ where the exponent is 0.865. This index is close to the values found in salt families formed with silver iodide and lithium and sodium halides but occurs at a lower value than that found for alkali halide melts between each other. The sound velocities in the phases take the same value 1612 m s−1 at the upper critical consolute temperature Tc=843 K. For a family of stratified silver halide containing melts, the versatility of the temperature dependence of the sound velocity near the critical point of mixing is declared. The sound velocity is discussed from the viewpoint of the different character of chemical bonds of salts.

Phase-boundary potential in the two-liquid-phase (AgI + NaCl) system

An electrochemical method has been developed for studying the Galvanic potential between two coexisting equilibrium phases of the molten (0.5 AgI+0.5 NaCl) system. The method measures the electromotive force (emf) of a cell with two silver electrodes:Ag|x′AgI+(1-x′)NaCl|x″AgI+(1-x″)NaCl|Ag.The measurement was carried out from the melting point of the mixture to T=1067K to establish the Galvanic potential magnitude and its temperature dependency near the critical point of mixing. The behavior of the Galvanic potential in the vicinity of the critical temperature corresponded to those found for the interfacial tension between coexisting phases.

Investigation on Deformation of an Evaporating Droplet in Convective Transcritical Environments

An investigation of the dynamic deformation for an individual droplet under convective transcritical conditions is conducted with a developed deformation model. This model takes account of gas solubility in liquid phase, variable thermophysical properties, the effective conductivity accounting for convective heat and mass transfer and liquid phase internal circulation, and the disappearance of surface tension at the critical mixing point. The results show that (1) at higher ambient pressures, surface tension decreases more smoothly with the reduction of fuel mole fraction but more rapidly with the droplet surface temperature; (2) as time elapses, the drop is continuously oscillating, together with the decreasing oscillation amplitude; (3) at high ambient pressures and temperatures the maximum drop deformation occurs in the late stage of the evaporation process, while at low pressures and temperatures, it occurs in the initial stage. In addition, the drop deformation and Weber number are initially quite insensitive to the ambient temperature.

Molecular dynamics simulation of the reciprocal fused LiF–KBr mixture: local structure and self-diffusion coefficients

This paper describes the molecular dynamics simulation of the reciprocal fused LiF–KBr mixture, which is located above the critical mixing point, in the temperature range 1280–1450 K. The first coordination sphere is found to form as follows: a smaller ion is formed around a smaller counter-ion, and a larger ion is formed around a larger counter-ion. The calculated concentration dependence of the self-diffusion coefficients and the radial distribution functions of all ion pairs indicate that the degree of association of the Li–F pair increases as the lithium fluoride fraction in the mixture decreases.

Liquid gallium-lead mixture phase diagram, surface tension near the critical mixing point, and prewetting transition

Quite recently, we reported a semianalytical equation of state (EOS) for the Ga-Pb alloy [Phys. Rev. B 78, 024205 (2008)], which was based on the first-order perturbation theory of fluid mixtures, within the simplified random phase approximation, in conjunction with the Grosdidier et al. model pair potentials for Ga-Ga and Pb-Pb with a suitable nonadditive pair potential between Ga-Pb unlike pairs. In the present work, we employ the present EOS to calculate the Ga-Pb phase diagram along the immiscibility gap region. The accuracy of the EOS is tested by consulting the empirical binodal curve. A statistical-mechanical-based theory for the surface tension is employed to obtain an analytical expression for the alloy surface tension. We calculated the surface tension along the bimodal curve and at extreme conditions of temperatures and pressures. The surface tension exhibits reasonably well the prewetting transition of Pb atoms at the surface of the Ga-rich liquid alloy and could qualitatively explain the prewetting phenomena occurring in the Ga-rich side of the phase diagram. The predicted prewetting line and wetting temperature qualitatively agree with the empirical measurements.

Liquid + liquid equilibrium in mixtures of lithium fluoride with potassium and rubidium halides

The liquid+liquid phase equilibrium of molten mixtures of lithium fluoride with potassium and rubidium halides was investigated over an extended temperature range in the two-phase region along the saturation line by the electrical conductivity method. In the overwhelming majority of mixtures, the electrical conductivity for coexisting equilibrium phases increased when the temperature increased. For mixtures with only potassium bromide, it decreased because of the extensive solubility of potassium bromide in lithium fluoride. The electrical conductivity for the light phase was half the value of the conductivity of the pure lithium fluoride. The electrical conductivity of the heavy phase did not differ enough from the conductivity of the pure heavy alkali halides. At the same time, the solubility of the heavy component in LiF was many times less than the lithium fluoride solubility in the lower phase. This contradiction points to essential reorganisation of the structure of the light phase. The difference between the conductivities of the coexisting phases at equal temperatures increased as the radius of the halide anion or alkali cation grew. The temperature growth led to the increase in the conductivity difference along the saturation line for mixtures of LiF with RbI. For mixtures of LiF with lighter alkali halides, it decreased up to zero at the critical mixing point for LiF+KBr mixtures as the temperature increased. Between the coexisting equilibrium phases, a transient layer was revealed, where a conductivity gradient exists. The thickness of this layer decreased as the temperature decreased and the sum of the ionic radii of the mixtures increased.

Molecular characteristics and antioxidant activity of polyethylene glycols modified by sterically hindered phenols

Chemical modification of polyethylene glycols by antioxidants belonging to the class of sterically hindered phenols is used to obtain water-soluble conjugates differing in the structure of the joined antioxidant and molecular weight. The inclusion of hydrophobic end groups in polyethylene glycol molecules leads to a decrease in the lower critical mixing point of the solution as compared to the original polymer. Dilute solution viscometry and light scattering are used to determine the molecular-mass characteristics of the polymers and the hydrodynamic radii of single conjugate molecules. The mass fraction of single molecules in aqueous solutions of the conjugates is greater than 95%. The aggregates are micellar-type particles whose core is formed by the hydrophobic moieties of sterically hindered phenols. It is shown that the antiradical activity of the antioxidants 3-(3-tert-butyl-4-hydroxy-5-methylphenyl)-propionic acid and 3- (3,5-di-tert-butyl-4-hydroxyphenyl)-propionic acid, which are used for the modification, differs only slightly, whereas the activity of the relevant conjugates increases significantly.

Ultrasound velocity in dissolving alkali halide melts

Ultrasound velocities in the molten exsolving mixtures (LiF + CsCl, LiF + KBr, LiF + RbBr, LiF + CsBr, LiF + KI, LiF + RbBr, and LiF + CsBr) were obtained along the saturation line over a wide temperature range using the acoustic method. The temperature dependences of properties far away from the critical temperature are close to linear and the temperature and composition factors are highly correlated. The difference between the magnitudes of sound velocity for the coexisting phases increases with the radii of ions in the mixtures. The linearity of the temperature dependence of the velocity, which is typical for all systems at relatively low temperatures, is violated when approaching the critical point of mixing, mainly due to sharp changes of the light phase state. Our results suggested a classical (mean-field) critical behavior of ionic melts.

Pressure-coupled vaporization response of n-pentane fuel droplet at subcritical and supercritical conditions

The dynamic response of a liquid fuel droplet to externally impressed pressure oscillations is studied comprehensively over a wide range of mean pressures. Both subcritical and supercritical conditions are considered. The formulation treats a complete set of conservation equations and incorporates real fluid thermodynamics and transport theories. As a specific example, the situation with isolated n-pentane droplets in nitrogen is studied at various forcing frequencies. Results are correlated with the liquid thermal inertial time, instantaneous droplet radius, and oscillation frequency. The magnitude of the vaporization response increases with increasing pressure, mainly due to the decreased enthalpy of vaporization at high pressures. The increased sensitivity of droplet thermophysical properties to ambient flow variations at high pressures also plays a role. The phase angle of the vaporization response function, however, appears to be independent of the ambient pressure. An abrupt increase in the response function takes place when the droplet surface reaches its critical mixing state. A major factor contributing to this phenomenon is the abnormal variations of fluid thermophysical properties near the critical mixing point.

Calculation of the sound velocity in LiF-KBr salt mixtures with a miscibility gap

A model is proposed for an ionic melt with many kinds of ions. It uses the Debye-Huckel theory to take into account the Coulomb interaction and the van der Waals approach to consider the direct contribution of the excluded volume forces. For LiF-KBr salt melts with a miscibility gap, the immiscibility dome, density, isothermal compressibility, and the sound velocity above and below the critical mixing point are calculated. The calculation results are compared with recent experimental data.

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.

Fluids near a critical point obey a generalized Cox–Merz rule

Upon approaching the liquid–vapor critical point, the spontaneous density fluctuations in a small-molecule fluid increase in both size and lifetime. Similar increases of the concentration fluctuations occur near the critical mixing point of a binary liquid mixture. The presence of these large fluctuations leads to an increase of the zero-shear viscosity, and their persistence in time leads to viscoelasticity and shear thinning. These rheological phenomena, which are already supported by theory and experiment, are shown here to obey a generalized form of the Cox–Merz rule. This relation formally equates the shear viscosity η(γ̇) measured at shear rate γ̇ with the magnitude of the linear complex viscosity η*(ω) measured at frequency ω. Comparisons of theoretical results and experimental data obtained elsewhere demonstrate that fluids near a critical point obey the somewhat generalized form η(kCMγ̇=ω)=|η*(ω)|, with kCM=0.4. The demonstration is simplified by showing that the Carreau–Yasuda model in the form (1+bAγ|γ̇τ|)−p represents the theories for η(γ̇) and |η*(ω)| near critical points. (The product bAγτ is a time constant, and p=0.022 is a universal critical exponent.).

Thermal conductivity, thermal effusivity, and specific heat capacity near the lower critical point of the binary liquid mixture n-butoxyethanol-water.

Experimental investigations on binary liquid mixtures near the critical mixing point are presently leading to a controversy about the anomaly in the thermal conductivity. A photopyroelectric technique is used to determine the thermal conductivity and the effusivity of the binary liquid mixture n-butoxyethanol-water at its critical concentration near the critical mixing point. It is proven that, contrary to previous reports, there is no critical enhancement in the thermal conductivity. The specific heat capacity is calculated from these results and compared with the results from measurements performed by adiabatic scanning calorimetry.

Annihilation of o-Positronium in the Vicinity of the Critical Mixing Point

Let us consider a liquid mixture of two-component mutually soluble in high temperatures and forming saturated phases in low ones. At the temperature and the concentration of maximum of the coexistence curve, the phase transition is classified as continuous and belongs to (3, 1) universality class. The critical anomaly of second derivatives of the Gibbs free energy (heat capacity, isothermal compressibility, osmotic compressibility, etc.) results in large and long-living concentration fluctuations impeding most of macroscopic properties of such binary mixtures. Some of the quantities, as light scattering [1-5], non-linear dielectric effect [6-8], absorption of ultrasonic waves [9-11] exhibit strong critical anomalies while others, as density [12] or electric permittivity [13, 14] — weak ones. Many critical properties could be qualitatively predicted when regarding a mixture in the vicinity of critical point as an inhomogeneous one. This attempt was successively used in understanding of critical phenomena of low frequency electric permittivity and conductivity [15-20], as well as in nonlinear dielectric effect [21]. It has to be pointed out that formal similarities between critical mixtures and real inhomogeneous mixtures (for example emulsions) are true only very close to the critical point, where concentration fluctuations are long-range and long-living. Positron annihilation measurements are a suitable experimental technique for investigation of solid minerals [22], polymers [23], as well as for investigation of clathrate-like structures in diluted aqueous mixtures of non-electrolytes [24-26].

Experimental investigation of the behavior of the specific heat in finite systems in the vicinity of the critical mixing point

The specific heat of a 2,6-lutidine-water mixture is measured in the vicinity of the lower critical mixing point in the bulk and in porous media. The results of the measurements are interpreted by finite-size scaling. In particular, a universal function of the ratio t/t* [t is the dimensionless deviation of the temperature from the specific-heat maximum T m (L), and t* is the characteristic dimensionless temperature, which depends on the pore size] describing the behavior of the specific heat in the vicinity of the critical point in porous media with different pore sizes is obtained. The results obtained are consistent with the predictions of finite-size scaling and with the data from a numerical calculation of the specific heat of the finite three-dimensional Ising model.

Phase separation kinetics in a binary mixture of polyethylene glycol and polypropylene glycol studied by light scattering after a pressure jump: Pinning of domain growth by hydrogen bond structures

The phase separation kinetics of fluid mixtures of polyethylene glycol/polypropylene glycol (a system with an upper critical mixing point) is studied after a pressure jump from the homogeneous one-phase region into the two-phase region of the phase diagram. The growth of the emerging domains of the coexisting phases is observed by small angle laser light scattering. In additional measurements the pressure dependence of the phase separation temperature is analyzed. In the kinetic experiments the time-dependent structure function is detected for a mixture with near-critical as well as for a mixture with off-critical composition. For the near-critical mixture an increase of the maximum of the scattering intensity with time has been found, which qualitatively is typical for the intermediate to late stages of spinodal decomposition. A closer analysis of the late stages reveals two maxima in the structure factor with their own set of growth exponents for the scattering vector and for the intensity. The data of the low q maximum are compatible with a two-dimensional growth process which is interpreted as a demixing process in a wetting layer. The data of the high q maximum are according to a three-dimensional process. It is assumed that this maximum reflects the demixing process in the bulk phase. The values of the three-dimensional growth exponents, which are considered to be late stage values, are not compatible with observations on other fluid systems but are close to those for solid systems or, in general, for systems with suppressed hydrodynamic interactions. For the mixture with an off-critical composition the structure function remains constant for larger times (pinning effect). The occurrence of a pinning effect in samples of relatively low molecular weight Mw (Mw⩽1019 g/mol) and the apparently suppressed hydrodynamic interactions in a fluid sample are explained with specific interactions caused by hydrogen bonding (i.e., transient entanglement or a dynamic network).