Slowing Down in Chemical Reactions. The Isobutyric Acid/Water System in the Critical Region

Carboxylic acids in aqueous solutions: Hydrogen bonds, hydrophobic effects, concentration fluctuations, ionization, and catalysis

In the frequency range between 100 kHz and 2 GHz, ultrasonic absorption spectra have been measured for a series of carboxylic acids from formic to enanthic acid, including constitutional isomers. Also investigated have been the spectra for mixtures with water of short-chain formic, acetic, propionic, butyric, and isobutyric acid, in each case covering the complete composition range. The neat carboxylic acids feature two Debye-type relaxation terms with relaxation times between 5.6 and 260 ns as well as 0.14 and 1.4 ns, respectively, at room temperature. Depending on the composition, mixtures with water reveal an additional Debye relaxation term in the intermediate frequency range (acetic acid) or a term subject to a relaxation time distribution (propionic, butyric, and isobutyric acid). The relaxations of the neat acids are assigned to the equilibrium between monomers and single-hydrogen-bonded linear dimers and between linear and twofold-hydrogen-bonded cyclic dimers. The latter equilibrium is considerably catalyzed by hydronium and carboxylate ions. Several mixtures with water indicate one of the up to three Debye relaxations to reflect the protolysis of the organic acid. The term with underlying relaxation time distribution is due to noncritical fluctuations in the local concentrations. The Debye relaxations are evaluated to yield the parameters of the relevant elementary chemical reactions, such as the rate and equilibrium constants and the isentropic reaction volumes. A comparison of the correlation length of concentration fluctuations with data for other aqueous systems confirms the idea that the hydrophobic part of the organic constituent promotes the formation of a micro-heterogeneous liquid structure, whereas the hydrophilic moiety is of minor importance in this respect. The high-frequency limiting absorption suggests the equilibrium between conformers of linear dimers to contribute to the spectra well above the frequency range of measurements.

Dynamic Scaling and Slowing Down in Chemical Reactions of the Critical Triethylamine−Water System

Between 100 kHz and 1 MHz, special ultrasonic attenuation measurements of the triethylamine-water mixture of critical composition have been performed for the determination of the Bhattacharjee-Ferrell scaling function. The experimental data are evaluated considering two noncritical Debye-type relaxation terms as revealed by broadband ultrasonic spectra. Shear viscosity and dynamic light scattering data from the literature are re-evaluated to yield the relaxation rate of order parameter fluctuations of the critical system as a function of temperature. The power law behavior found for the relaxtion rate fits to the scaling function in the ultrasonic spectra. The relaxation times of the noncritical Debye terms display a non-Arrhenius temperature dependence, pointing at effects of slowing in the chemical reactions associated with the relaxations.

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.

Critical fluctuations of the micellar triethylene glycol monoheptyl ether-water system

Using the equal volume criterion and also the pseudospinodal conception the critical demixing point of the triethylene glycol monoheptyl ether/water system (C7E3H2O) has been determined as Ycrit=0.1 and Tcrit=296.46 K (Y, mass fraction of surfactant). From density measurements the critical micelle concentration (cmc) followed as Ycmc=0.007 at 288.15 K and Ycmc=0.0066 at 298.15 K. The (static) shear viscosity etas and the mutual diffusion coefficient D of the C7E3H2O mixture of critical composition have been evaluated to yield their singular and background parts. From a combined treatment of both quantities the relaxation rate Gamma of order parameter fluctuations has been derived. Gamma follows power law with universal critical exponent and amplitude Gamma0=3.1 x 10(9) s(-1). Broadband ultrasonic spectra of C7E3H2O mixtures exhibit a noncritical relaxation, reflecting the monomer exchange between micelles and the suspending phase, and a critical term due to concentration fluctuations. The former is subject to a relaxation time distribution that broadens when approaching the critical temperature. The latter can be well represented with the aid of the dynamic scaling model by Bhattacharjee and Ferrell (BF) [Phys. Rev. A. 31, 1788 (1985)]. The half-attenuation frequency in the scaling function of the latter model is noticeably smaller (Omega12 (BF) approximately 1) than the theoretically predicted value Omega12 (BF)=2.1. This result has been taken as an indication of a coupling between the fluctuations in the local concentration and the kinetics of micelle formation, in correspondence with the idea of a fluctuation controlled monomer exchange [T. Telgmann and U. Kaatze, Langmuir 18, 3068 (2002)].

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.

Critical concentration fluctuations of the ionic binary mixture ethylammonium nitrate-n-octanol: an ultrasonic spectrometry study

Between 200 kHz and 130 MHz, the ultrasonic attenuation spectrum of the ionic ethylammonium nitrate--n-octanol mixture of critical composition has been measured at various reduced temperatures (1.5 x 10(-4)<or= t <or=5.7 x 10(-2)). Using static and dynamic light scattering data as well as viscosity and heat capacity data from the literature, the experimental spectra have been evaluated to yield the scaling function, with the background contribution to the spectra as the only adjustable parameter. Agreement, within the limits of experimental error, of the measured scaling function with that of the nonionic binary system ethanol--dodecane and with the theoretical predictions of the Bhattacharjee-Ferrell dynamic scaling model is found. The amplitude of the fluctuation correlation length xi(o) (=0.47 nm) and the amount of the coupling constant /g/ (=1.3) are rather high as compared to nonionic binary critical mixtures. The amplitude of the relaxation rate of order parameter fluctuations Gamma(o)(=2.6 x 10(8) s(-1)) exhibits an unusual small value, likely to the most part a reflection of the high viscosity and thus small diffusion coefficient of the ionic liquid.