Mixture Of Critical Composition Research Articles

Thermodynamic aspects of phase equilibrium in binary water–organic solvent mixtures

It is shown that the boundary curves of liquid equilibria in binary systems characterize the temperature–concentration boundary of the existence of homogeneous mixtures whose formation is not accompanied by changes in the Gibbs energy of the system and are a combination of two branches that do not convert into each other but intersect at the temperature of homogenization of a mixture of critical composition. The phase diagrams of a number of water–organic solvent systems are analyzed to determine the thermodynamic particularities of the latter.

The Effect of Alkali Halides on the Critical Exponents of the 2,6-Dimethylpyridine-Water System.

The diffusion coefficients and shear viscosities of 2,6-dimethylpyridine-water mixtures of critical composition have been measured without and with small amounts of alkali halides added. The data have been analyzed in terms of power law behavior. Deviations from power law behavior indicate a coupling between the critical fluctuations in the local concentrations and the formation of mesoscopic molecular aggregates. The critical exponent of the fluctuation correlation length, the shear viscosity exponent, and the critical exponent of the relaxation rate of fluctuations have been evaluated to show noticeable influences from the salts. The correlation length exponent indicates a suppression of the critical fluctuations, whereas the viscosity exponent rather points at the activation of some extra fluctuations. No clear evidence has been obtained that the added salts affect the critical behavior, and thus cause the opposed effects in the exponents, directly by the long-range ionic fields. Alternatively, the ions may have an influence on the aggregate formation which in turn could modify the critical fluctuations either by reducing the region of true critical exponents or by affecting the critical behavior due to the presence as well as the formation and disintegration kinetics of the multimolecular structures.

Adiabatic Coupling Constant of Nitrobenzene–n-Alkane Critical Mixtures. Evidence from Ultrasonic Spectra and Thermodynamic Data

Ultrasonic spectra of mixtures of nitrobenzene with n-alkanes, from n-hexane to n-nonane, are analyzed. They feature up to two Debye-type relaxation terms with discrete relaxation times and, near the critical point, an additional relaxation term due to the fluctuations in the local concentration. The latter can be well represented by the dynamic scaling theory. Its amplitude parameter reveals the adiabatic coupling constant of the mixtures of critical composition. The dependence of this thermodynamic parameter upon the length of the n-alkanes corresponds to that of the slope in the pressure dependence of the critical temperature and is thus taken another confirmation of the dynamic scaling model. The change in the variation of the coupling constant and of several other mixture parameters with alkane length probably reflects a structural change in the nitrobenzene–n-alkane mixtures when the number of carbon atoms per alkane exceeds eight.

Relaxation rate in the critical dynamics of the micellar isobutoxyethanol-water system with lower consolute point

For the isobutoxyethanol-water mixture of critical composition acoustical scaling function measurements have been performed at frequencies between 200 kHz and 3 MHz. Using the relaxation rates of concentration fluctuations as resulting from dynamic light scattering and shear viscosity measurements, the acoustical data can be well represented by the Bhattacharjee-Ferrell empirical scaling function. The theoretically predicted scaled half attenuation frequency Omega(BF)(1/2)=2.1 follows from the experiments. However, the adiabatic coupling constant, derived from the amplitude of the Bhattacharjee-Ferrell critical term, displays an unreliably strong temperature dependence. It is shown that this dependence upon temperature likely reflects a hidden low-frequency and low amplitude relaxation term in the acoustical spectra of the mixture of critical composition.

Critical behavior of 2,6-dimethylpyridine-water: Measurements of specific heat, dynamic light scattering, and shear viscosity

The specific heat C(p) at constant pressure, the shear viscosity eta(s), and the mutual diffusion coefficient D of the 2,6-dimethylpyridine-water mixture of critical composition have been measured in the homogeneous phase at various temperatures near the lower critical demixing temperature T(c). The amplitude of the fluctuation correlation length xi(0)=(0.198+/-0.004) nm has been derived from a combined evaluation of the eta(s) and D data. This value is in reasonable agreement with the one obtained from the amplitude A(+)=(0.26+/-0.01) J(g K) of the critical term in the specific heat, using the two-scale-factor universality relation. Within the limits of error the relaxation rate Gamma of order parameter fluctuations follows power law with the theoretical universal exponent and with the amplitude Gamma=(25+/-1)x10(9) s(-1). No indications of interferences of the critical fluctuations with other elementary chemical reactions have been found. A noteworthy result is the agreement of the background viscosity eta(b), resulting from the treatment of eta(s) and D data, with the viscosity eta(s)(nu=0) extrapolated from high-frequency viscosity data. The latter have been measured in the frequency range of 5-130 MHz using a novel shear impedance spectrometer.

Dynamic scaling of the critical binary mixture methanol-hexane

Acoustical attenuation spectrometry, dynamic light scattering, shear viscosity, density, and heat capacity measurements of the methanol/n-hexane mixture of critical composition have been performed. The critical part in the sonic attenuation coefficients nicely fits to the empirical scaling function of the Bhattacharjee-Ferrell [Phys. Rev. A 24, 1643 (1981)] dynamic scaling model if the theoretically predicted scaled half-attenuation frequency Omega(12) (BF)=2.1 is used. The relaxation rates of order parameter fluctuations, as resulting from the acoustical spectra, within the limits of experimental error agree with those from a combined evaluation of the light scattering and shear viscosity measurements. Both series of data display power law with amplitude Gamma(0)=44x10(9) s(-1). The amplitude of the fluctuation correlation length follows as xi(0)=0.33 nm from the light scattering data and as xi(0)=0.32 nm from the amplitude of the singular part of the heat capacity if the two-scale factor universality relation is used. The adiabatic coupling constant g=0.11 results from the amplitude of the critical contribution to the acoustical spectrum near the critical point, in conformity with g=0.12 as following from the variation of the critical temperature with pressure along the critical line and the thermal expansion coefficient.

Critical Dynamics of the Binary System Nitroethane/3-Methylpentane: Relaxation Rate and Scaling Function

Shear viscosity and dynamic light scattering measurements as well as ultrasonic spectrometry studies of the nitroethane/3-methylpentane mixture of critical composition have been performed at various temperatures near the critical temperature, T(c). A combined evaluation of the shear viscosity and mutual diffusion coefficient data yielded the amplitude, xi(0), of the fluctuation correlation length, xi, assumed to follow power law, and the relaxation rate, Gamma, or order parameter fluctuations. The latter was found to follow power law with the theoretical universal exponent. The amplitudes xi(0) = 0.23 +/- 0.02 nm and Gamma(0) = (125 +/- 5) x 10(9) s(-1) nicely agree with literature values. Using the relaxation rates resulting from the viscosity and diffusion coefficient data, the scaling function has been calculated assuming the ultrasonic spectra to be composed of a critical part and a noncritical background contribution. The experimental scaling function fits well to the predictions of the Bhattacharjee-Ferrell dynamic scaling model with scaled half-attenuation frequency, Omega(BF)1/2= 2.1. The amplitude of the sonic spectra yields the amount |g| = 0.26 of the adiabatic coupling constant, g, in fair agreement with -0.29 from another thermodynamic relation.

Critical fluctuations near the consolute point of n-pentanol-nitromethane. An ultrasonic spectrometry, dynamic light scattering, and shear viscosity study.

Ultrasonic attenuation spectra, the shear viscosity, and the mutual diffusion coefficient of the n-pentanol-nitromethane mixture of critical composition have been measured at different temperatures near the critical temperature. The noncritical background contribution, proportional to frequency, to the acoustical attenuation-per-wavelength spectra has been determined and subtracted from the total attenuation to yield the critical contribution. When plotted versus the reduced frequency, with the relaxation rate of order-parameter fluctuations from the shear viscosity and diffusion coefficient measurements, the critical part in the sonic attenuation coefficient displays a scaling function which nicely fits to the data for the critical system 3-methylpentane-nitromethane and also to the empirical scaling function of the Bhattacharjee-Ferrell dynamic scaling theory. The scaled half-attenuation frequency follows from the experimental data as Omega(1/2)emp= 1.8+/-0.1. The relaxation rate of order-parameter fluctuation shows power-law behavior with the theoretically predicted universal exponent and the extraordinary high amplitude Gammao= (187+/-2) x 10(9) s(-1). The amount of the adiabatic coupling constant /g/= 0.03, as estimated from the amplitude of the critical contribution to the acoustical spectra, is unusually small.

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.

Phase behaviour of mixtures of polyethylene glycol and polypropylene glycol: Influence of hydrogen bond clusters on the phase diagram

The phase behaviour of a binary polymer blend of polyethylene glycol (PEG600) and polypropylene glycol (PPG1000) of low polydispersity was investigated. The coexistence curves of five different compositions, including the critical composition, were measured by differential refractometry. From the coexistence curves, the critical exponents of the order parameter could be determined. The order parameter of the coexistence curve of the critical composition was β = 0.357, near to the Ising value. The measured coexistence curves for different compositions were different to each other and to the cloud point curve measured by small angle light scattering. These differences are explained by clusters built of intermolecular hydrogen bonds which lead to a broad effective molar mass distribution of the mixture. Two of the investigated mixtures, the mixture of critical composition (yPPG = 0.46, yPPG: mass fraction of polypropylene glycol) and a mixture of non-critical composition (yPPG = 0.365) were also measured by static and dynamic light scattering. The measurements were carried out in the homogeneous one-phase region (above the critical temperature TC) and in the two-phase region in both coexisting phases. The light scattering measurements showed, additionally to the composition fluctuations due to the phase transition of demixing, a contribution of larger objects, which could be attributed to hydrogen bonded clusters. The size of these clusters was estimated to be 250 nm to 550 nm.

Heat capacity behavior in the critical region of the ionic binary mixture ethylammonium nitrate-n-octanol

At temperatures between 30 degrees C and 58 degrees C we have recorded the heat capacity of the ionic ethylammonium nitrate-n-octanol mixture of critical composition and also of the constituents. Different samples of the binary mixture have been measured with its upper critical demixing temperature T(c) varying between 41.04 degrees C and 46.87 degrees C, depending on small traces of water within the liquid under test. Almost identical heat capacity profiles result if the data are displayed as a function of the temperature distance to the actual T(c) value. In the homogeneous phase the critical contribution exhibits power-law behavior with the critical exponent alpha=0.11 as theoretically predicted for nonionic liquids and in conformity with our understanding of the ionic criticality as being asymptotically Ising like. The noncritical background part of the heat capacity can be related to the heat capacities of the constituents using a simple mixture relation. In the two-phase regime a series of almost perfectly reproducible events is found which may be taken to indicate the existence of nonequilibrium intermediate states in the ethylammonium nitrate-n-octanol system.

Dynamic scaling in the ultrasonic attenuation spectra of critical binary mixtures

A broadband (30 kHz to 3 GHz) ultrasonic spectrum for the aniline/cyclohexane mixture of critical composition is reported to show that, in addition to the critical contribution and the asymptotic high frequency contribution, there exist three further contributions to the attenuation coefficient. These additional contributions tend to mask the critical part in the spectrum. Here we calculate the critical contribution from the Bhattacharjee–Ferrell dynamic scaling model in order to enhance the significance in the determination of the relaxation terms with discrete relaxation times.

Dynamic scaling of the critical ultrasonic attenuation in binary liquids: evidence from broadband spectrometry

Between 200 kHz and 500 MHz, the ultrasonic attenuation spectrum of the ethanol/dodecane mixture of critical composition has been measured at various temperatures near the critical one. The measured broadband spectra are evaluated in light of the Ferrell-Bhattacharjee dynamic scaling theory. The experimental findings largely fit the theoretical spectral function if suitable crossover corrections are made using dynamic light-scattering data. The measured scaling function follows the predictions of the recent Folk-Moser renormalization-group theory even better. Combining our ultrasonic attenuation coefficient data with density data from the literature, the asymptotic critical behavior of the thermal expansion coefficient and of the specific heat has been determined and found consistent with the two-scale factor universality. The sonic attenuation data have also been evaluated to yield the adiabatic coupling constant g of the dynamic scaling theory. The unusually small absolute value |g|=0.1 resulted, in fairly good agreement with |g|=0.13 as following from thermodynamic data.

Static and dynamic light scattering experiments with an iso-butoxyethanol/water mixture of critical composition

Abstract Results of static and dynamic light scattering as well as of viscosity measurements are reported. They are carried out with an i-C 4 E 1 /water mixture of critical composition in the vicinity of its lower critical point (y c = 0.3180, mass fraction of i-C 4 En 1 ; Tc = 26.450 °C). This point is approached from temperatures T c . The value of the critical amplitude ξ o of the correlation length of local concentration fluctuations obtained from static light scattering experiments is combined with the known values of the critical amplitude σ o of the liquid/liquid interfacial tension and the critical amplitude A o,v the heat capacity at constant pressure per unit volume c p to calculate the values of the universal amplitude ratios R ( σ , ξ ) and R (c p , ξ ). The critical amplitudes are material-dependent quantities. The calculated values of R ( σ , ξ ) and R (c p , ξ ) are consistent with their theoretical predictions. The “hydrodynamic” correlation length ξ hd of concentration fluctuations is obtained by combining experimental viscosity and mutual diffusion coefficient data. The ξ hd values are in agreement with the corresponding values of ξ obtained from static light scattering experiments. The calculation of ξ hd is based on an equation analogous to the Stokes-Einstein relation. The data of the diffusion coefficient are obtained from dynamic light scattering experiments. The material dependent critical amplitude Q o of the viscosity is found to have a value typical of simple binary mixtures of low molar mass components. It is concluded that formation of aggregates of i-C 4 E 1 molecules and/or i-C 4 E 1 and water molecules in an i-C 4 E 1 /water mixture of critical composition does not influence the critical properties of this system. The properties are in agreement with that predicted by the universality concept of critical phenomena.

The near-critical microscopic viscosity of binary liquid mixtures: 2-butoxyethanol + water at the lower critical endpoint

The decay of the fluorescence anisotropy for a dye molecule derived from the Bodipy fluorophore has been measured in the binary liquid mixture 2-butoxyethanol + water near its lower critical endpoint. Results are presented for a mixture of critical composition both in the single-phase and in the lower water-rich phase of the two-phase mixture as the critical temperature is approached in each case. The results indicate that the enhanced viscosity near a critical point can be detected by the rate of decay of the fluorescence anisotropy, and that the behaviour of the viscosity at the microscopic level shows an anomaly comparable with that already observed for the macroscopic shear viscosity.

Raman investigation of the supercritical mixture He-H2

We investigated the vibrational Raman spectrum of H2 in the binary mixture He-H2. The Q1-line was measured between 150 and 350 K for two isobars in the gigapascal region in a mixture of critical composition. The results indicate a broadening of the spectrum due to critical concentration fluctuations.

Temperature Dependence of the Specific Heat Capacity of a Succinonitrile/Water Mixture of Critical Composition

Temperature Dependence of the Specific Heat Capacity of a Succinonitrile/Water Mixture of Critical Composition

Temperature Dependence of Liquid/Liquid Interfacial Tension of a Succinonitrile/Water Mixture of Critical Composition in the Vicinity of a Temperature of Equal Density of the Coexisting Phases

Article Temperature Dependence of Liquid/Liquid Interfacial Tension of a Succinonitrile/Water Mixture of Critical Composition in the Vicinity of a Temperature of Equal Density of the Coexisting Phases was published on January 1, 1995 in the journal Zeitschrift für Physikalische Chemie (volume 189, issue 1).

Diffusivity in a non-ionic surfactant/water mixture of critical composition

Results of measurements of the temperature dependence of the mutual diffusion coefficient D of a tetraethyleneglycoloctylether (abbreviated C8E4) /water mixture of critical composition are reported (lower critical point, visually determined critical temperature Tc(vis)=40.587 °C; critical composition, mass fraction yc(C8E4)=0.071). The critical micelle concentration of C8E4 is smaller than the critical concentration, so that micelles are expected to be present in the mixture of critical composition. The reduced diffusion coefficients D*(=6πηξ/(kBT)⋅D) calculated from static and dynamic light scattering and viscosity data scale when plotted as function of the scaling variable x (=qξ) (η, shear viscosity; ξ, correlation length; D, diffusion coefficient; q, absolute value of scattering vector; kB, Boltzmann constant; T, temperature). They can be represented by the approximant of the dynamic scaling function proposed by Burstyn et al. [Phys. Rev. A 28, 1567 (1983)] assuming that the measured diffusion coefficient can be identified with the singular contribution (i.e., D=Dc). The influence of micelles on the critical properties of the system does not show up in the D* versus x plot.

Ultrasonic absorption of nitrobenzene–isooctane mixtures of non-critical composition

The dynamic scaling theory of Ferrell and Bhattacharjee (Phys. Rev. A, 1985, 31, 1788) has been used to analyse ultrasonic absorption data of two nitrobenzene–isooctane mixtures of non-critical composition. The measurements were carried out as a function of temperature [1 ⩽(T–Tp)/K ⩽ 20; Tp, temperature of phase separation] and frequency (3 ⩽f/MHz ⩽ 57). The data describing the temperature- and frequency-dependent contributions of composition fluctuations to the ultrasonic absorption follow a single curve. The data can be represented by a modified dynamic scaling function similar to that proposed by Ferrell and Bhattacharjee to describe the ultrasonic absorption of a mixture of critical composition. The temperature dependence of the scaling variable Ωnc for the mixtures of non-critical compostion is calculated by replacing the critical temperature Tc by an empirical pseudospinodal temperature Tps or the temperature of phase separation Tp of the mixture of non-critical composition. The frequency- and temperature-independent parameter ω0, nc of the scaling variable Ωnc is used as the only free parameter of the fit of the scaling function F(Ωnc) to the experimental data. The value of ω0 is found to be composition dependent.