I. Iwanowski

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.

Sound attenuation, shear viscosity, and mutual diffusivity behavior in the nitroethane-cyclohexane critical mixture

The shear viscosity eta(s), mutual diffusion coefficient D, and ultrasonic attenuation spectra of the nitroethane-cyclohexane mixture of critical composition have been measured at various temperatures near the critical temperature T(c). The relaxation rate of order parameter fluctuations resulting from a combined evaluation of the eta(s) and D data follows power law behavior with the theoretical exponent and with the large amplitude Gamma(o)=(156+/-2)x10(9) s(-1). The ultrasonic spectra have been evaluated in terms of a critical contribution and a noncritical background contribution. The amplitude of the former exhibits a temperature dependence, in conformity with a temperature dependence in the adiabatic coupling constant (|g| = 0.064 near T(c) and 0.1 at T-T(c)=3 K). If the variation of the critical amplitude with T is taken into account the experimental attenuation coefficient data display a scaling function which nicely fits to the theoretical prediction from the Bhattacharjee-Ferrell dynamic scaling model [R. A. Ferrell and J. K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)].

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.

Bulk viscosity universality and scaling function near the binary liquid consolute point

The hydrodynamical equations and the notion of a frequency dependent complex specific heat near the critical point of binary liquids are used to obtain an expression for the low-frequency bulk viscosity. In this way the interrelations between different theoretical models, treating the critical sound attenuation from either a specific heat or a bulk viscosity approach, are made evident. The general structure of the bulk viscosity relation agrees with that of Onuki [Phys. Rev. E 55, 403 (1997)] but a universal number emerges only if a normalization to the critical point value is done.

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.