Sirojiddin Z. Mirzaev

Sound attenuation near the demixing point of binary liquids: interplay of critical dynamics and noncritical kinetics

The nature and origin of sound attenuation due to critical fluctuations near the liquid consolute point are discussed. Starting from basic principles, the background of critical phenomena is reviewed and the conceptions of theoretical approaches to describe the critical contributions to the propagation of sound are analysed. Experimental broadband spectra of suitable binary systems are evaluated jointly with results from quasi-elastic light scattering, shear viscosity and heat capacity measurements to verify or disprove theoretical predictions. It is shown that spectra of systems without or with only small-amplitude ultrasonic contribution from noncritical relaxation processes can be represented by theory with the asymptotic high-frequency sonic attenuation coefficient as a simple adjustable parameter. As a result, sonic spectra of more complex systems, exhibiting significant contributions from noncritical ultrasonic relaxations, are discussed assuming the critical part to be known from theory and auxiliary data. This modus operandi allows for a clear extraction of parameters relevant to the noncritical elementary processes in liquid mixtures, such as conformational changes, protolysis and hydrolysis reactions, monomer exchange from micelles and rotational isomerizations of membrane molecules. The influence of the critical dynamics on the noncritical kinetics is disclosed for some topical examples.

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.

Supramolecular structure fluctuations of an imidazolium-based protic ionic liquid

At 20, 25, 30, and 40 °C, the ultrasonic absorption spectra of the protic ionic liquid 3-(butoxymethyl)-1H-imidazol-3-ium salicylate have been measured between 0.6 and 900 MHz. Below 250 MHz, the absorption coefficient decreases with temperature, potentially indicating a major effect of the viscosity and/or a relaxation time. Essentially the broad spectra can be favorably represented by two relaxation terms in addition to an asymptotic high-frequency contribution. One term reflects an asymmetric relaxation time distribution. It is described by a model of noncritical fluctuations in the structure and thermodynamic parameters of the liquid in order to yield the fluctuation correlation length and the mutual diffusion coefficient. Applying the Stokes-Einstein-Kawasaki-Ferrell relation, these quantities can be used to show that the effective shear viscosity controlling the fluctuations is substantially smaller than the steady-state shear viscosity. This result is consistent with dispersion in the shear viscosity as revealed by viscosity measurements at 25, 55, and 81 MHz. The other term can be well described by a Debye-type relaxation function. It has been tentatively assigned to a structural isomerization of the butoxymethyl chain of the imidazole molecule. However, it cannot be completely excluded that this term reflects, at least in parts, a Brønstedt acid-base equilibrium or a specific association process.

Does shear viscosity relaxation control the dynamics of critical fluctuations in polystyrene-cyclohexane?

Between 20 and 90 MHz frequency-dependent shear viscosities of the polystyrene-cyclohexane mixture of critical composition have been measured at polymer molar weight Mw = 30,000. The viscosity data reveal dispersion, in conformity with relaxation characteristics in the non-critical background contributions to the ultrasonic attenuation, i.e., in the longitudinal viscosity of the critical system. The dispersion behavior is discussed with a view to its effect on the critical dynamics of the liquid near its consolute point. Attention is especially given to the relaxation rates of fluctuations of that system. The data as resulting from ultrasonic attenuation spectroscopy on the one hand and from quasi-elastic light scattering and viscosity measurements on the other hand differ near the critical temperature. It is concluded that likely an additional dispersion exists in the shear viscosity at frequencies below the presently available frequency range of measurement.

Relaxation rate and scaling function of the critical system 3-methylpentane-nitroethane-cyclohexane

The critical system 3-methylpentane-nitroethane-cyclohexane (3-MP-NE-CH) has been investigated and compared to the limiting binary systems 3-MP-NE as well as NE-CH in order to study the degree of renormalization in the critical exponents of the ternary system. The solubility curves of the 3-MP-NE-CH system have been determined at various molar ratios of the nonpolar constituents in order to obtain the plait points as a function of mixture composition. At the col point (the mixture with the lowest transition temperature) and two further plait point compositions shear viscosity, dynamic light scattering, and frequency-dependent ultrasonic attenuation coefficient measurements have been performed as a function of temperature near the critical temperatures. The fluctuation correlation length and the relaxation rate of fluctuations display power law behavior as a function of reduced temperature, with universal critical exponents nu = 0.63 and nuZ(0) = 1.928, respectively, as characteristic for binary critical mixtures. In conformity with the 3-MP-NE and NE-CH critical mixtures the scaling function in the ultrasonic spectra nicely agrees with the empirical scaling function of the Bhattacharjee-Ferrell dynamic scaling theory. Hence with respect to power laws and scaling the 3-MP-NE-CH system behaves like a quasibinary mixture. The individual amplitudes of the relaxation rate show a minimum at the col point composition, corresponding with a maximum in the background viscosity of the liquids. The amount of the adiabatic coupling constant g, derived from the amplitudes in the ultrasonic spectra, increases monotonously when going from NE-CH (/g/ = 0.1) to 3-MP-NE (/g/ = 0.26).

Dynamic scaling of the critical mixture perfluoromethylcyclohexane-carbon tetrachloride

Ultrasonic attenuation, specific heats at constant pressure, static and dynamic light scattering as well as shear viscosity data of the perfluoromethylcyclohexane–carbon tetrachloride critical system have been re-evaluated in the light of the Bhattacherjee–Ferrell dynamic scaling model. The experimental sonic attenuation coefficients yield the theoretical form of the scaling function if a noncritical relaxation term is assumed to contribute to the total spectra in addition to the critical contribution. Evidence from noncritical ultrasonic spectra suggests the noncritical relaxation to be due to rotational isomerization of the perfluoromethylcyclohexane molecule. The amplitudes in the power laws of the fluctuation correlation length, the mutual diffusion coefficient and the relaxation rate of concentration fluctuations are ξ0 = (0.228 ± 0.021) nm, D0 = (1.24 ± 0.04) × 109 m2 s−1, and Γ0 = (47.5 ± 13) × 109 s−1, respectively. The amplitude of the critical term in the heat capacity is Cpc = (0.093 ± 0.002) J g−1 K−1 and the adiabatic coupling constant results as g = 0.126.

Dynamic scaling in the ultrasonic attenuation spectra of critical binary mixtures

Abstract 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.

Sound attenuation in the critical region of the ionic binary mixture ethylammonium nitrate/n‐octanol

Ultrasonic attenuation spectra (100 kHz<f<4 MHz) of the ionic mixture ethylammonium nitrate/n‐octanol of critical composition and also of the ethylammonium nitrate itself (100 kHz <f< 400 MHz) are discussed at different temperatures. The measured spectra are evaluated in terms of the Bhattacharjee–Ferrell dynamic scaling theory. Using literature data for the amplitude of the fluctuation correlation length, the background and critical part of the heat capacity, the sonic attenuation spectrum as predicted by the Bhattacharjee‐Ferrell model has been calculated for the critical mixture at the critical temperature. Again following this theoretical model, the contribution due to concentration fluctuations has been subtracted from the measured spectra at the temperatures of measurement and also subtracted has been the high‐frequency asymptotic background contribution. The measured data are consistent with the Bhattacharjee–Ferrell theory of critical concentration fluctuations but show an additional frequency dep...