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

Advancing Chemical Separations: Unraveling the Structure and Dynamics of Phase Splitting in Liquid-Liquid Extraction

Liquid-liquid extraction (LLE), the go-to process for a variety of chemical separations, is limited by spontaneous organic phase splitting upon sufficient solute loading, called third phase formation. In this study we explore the applicability of critical phenomena theory to gain insight into this deleterious phase behavior with the goal of improving separations efficiency and minimizing waste. A series of samples representative of rare earth purification were constructed to include each of one light and one heavy lanthanide (cerium and lutetium) paired with one of two common malonamide extractants (DMDOHEMA and DMDBTDMA). The resulting postextraction organic phases are chemically complex and often form rich hierarchical structures whose statics and dynamics near the critical point were probed herein with small-angle X-ray scattering and high-speed X-ray photon correlation spectroscopy. Despite their different extraction behaviors, all samples show remarkably similar critical behavior with exponents well described by classical critical point theory consistent with the 3D Ising model, where the critical behavior is characterized by fluctuations with a single diverging length scale. This unexpected result indicates a significant reduction in relevant chemical parameters at the critical point, indicating that the underlying behavior of phase transitions in LLE rely on far fewer variables than are generally assumed. The obtained scalar order parameter is attributed to the extractant fraction of the extractant/diluent mixture, revealing that other solution components and their respective concentrations simply shift the critical temperature but do not affect the nature of the critical fluctuations. These findings point to an opportunity to drastically simplify studies of liquid-liquid phase separation and phase diagram development in general while providing insights into LLE process improvement.

Nanoscale Critical Phenomena in a Complex Fluid Studied by X-Ray Photon Correlation Spectroscopy

The advent of high-speed x-ray photon correlation spectroscopy now allows the study of critical phenomena in fluids to much smaller length scales and over a wider range of temperatures than is possible with dynamic light scattering. We present an x-ray photon correlation spectroscopy study of critical fluctuation dynamics in a complex fluid typical of those used in liquid-liquid extraction (LLE) of ions, dodecane-DMDBTDMA with extracted aqueous Ce(NO_{3})_{3}. We observe good agreement with both static and dynamic scaling without the need for significant noncritical background corrections. Critical exponents agree with 3D Ising values, and the fluctuation dynamics are described by simple exponential relaxation. The form of the dynamic master curve deviates somewhat from the Kawasaki result, with a more abrupt transition between the critical and noncritical asymptotic behavior. The concepts of critical phenomena thus provide a quantitative framework for understanding the structure and dynamics of LLE systems and a path forward to new LLE processes.

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.

Broadband ultrasonic spectrometry of polystyrene-cyclohexane critical mixtures

Mutual diffusion coefficients, shear viscosities, and broadband ultrasonic attenuation spectra in the frequency range 100 kHz to 300 MHz have been measured for solutions of polystyrene in cyclohexane at two degrees of polymerization N and various temperatures near the critical. The exponent y(η) in the power law representation of the critical part in the viscosity deviates substantially from the universal value y(η) = 0.0435: y(η) = 0.028 (N = 288) and y(η) = 0.014 (N = 6242). Also, the adiabatic coupling constant g and the amplitudes ξ(0) and Γ(0) in the power laws of the correlation length and the relaxation rate of fluctuations, respectively, depend on N. This is especially obvious with the relaxation rates, for which Γ(0) = 5.8×10(9) at N = 288 and Γ(0) = 6.1×10(7) with the larger polymer results. A noteworthy feature is the difference between the relaxation rates from the diffusion coefficients and shear viscosities on the one hand and from the ultrasonic spectra on the other. Near the critical temperatures the latter Γ values deviate from power law behavior, indicating a coupling between the concentration fluctuations and structural isomerizations of the polymers.

Ultrasonic spectrometry of aqueous solutions of alkyl maltosides: kinetics of micelle formation and head-group isomerization

At frequencies between 100 kHz and 400 MHz, ultrasonic attenuation spectra are measured at 25 degrees C for aqueous solutions of hexyl-, heptyl-, octyl-, nonyl-, and decyl-beta-D-maltopyranoside as well as of decyl-alpha-D-maltopyranoside. The spectra with surfactant concentration c above the relevant critical micelle concentration (cmc) display three relaxation terms with discrete relaxation times. That with a relaxation time between 0.1 and 1.2 micros is due to exchange of monomers between micelles and the suspending phase. It is discussed in the light of the Teubner-Kahlweit-Aniansson-Wall model of the formation/decay kinetics of systems with Gaussian size distribution of micelles. The relaxation parameters are compared to those for solutions of other non-ionic surfactants, such as alkyl monoglycosides and poly(ethylene glycol) monoalkyl ethers. At c < cmc this low-frequency relaxation term is missing and at c approximately = cmc it is broadened, as is characteristic of solutions of oligomeric molecular structures rather than proper micelles. The relaxation terms with relaxation times between 6 and 15 ns and 0.7 and 2.3 ns reveal head-group rotations around glycosidic angles and isomerization of the exocyclic hydroxymethyl group, respectively. These unimolecular reactions are also examined with a view to solutions of alkyl monoglycosides as well as of glucose and maltose.

Critical behavior on approaching a special critical point in a complex fluid

The critical behavior of osmotic susceptibility is investigated in the re-entrant complex mixture 1-propanol (P)+water (W)+potassium chloride (KCl) through light-scattering measurements. The measurements are performed on approaching a special critical point [i.e., the double critical point (DCP)] in this mixture, along the line of upper critical solution temperatures (T(U)'s), by varying t from the high temperature one-phase region. The light-scattering data analysis emphasizes the need for corrections to the asymptotic Ising behavior and yields very large magnitudes for the correction-to-scaling amplitudes A(1) and A(2), with the first-correction amplitude A(1) being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the T(U) closest to the DCP, the effective susceptibility exponent gamma(eff) displays a nonmonotonic crossover from its nearly doubled three dimensional (3D)-Ising value toward its nearly double mean-field value with an increase in t. While for that far away from the DCP, it displays a nonmonotonic crossover from its single-limit Ising value toward a value slightly lower than its mean-field value of 1 with an increase in t. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic high t region. The renormalized Ising regime extends over a larger t range for the sample (or T(U)) closest to the DCP when compared to that far away from it. The in-between T(U)'s display a trend toward shrinkage in the renormalized Ising regime as T(U) shifts away from the DCP. Nevertheless, the crossover to the mean-field behavior is completed only beyond t>10(-2) for the T(U)'s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover behavior is discussed in terms of the varying influence of the DCP on the critical behavior along the T(U) line. The crossover behavior for the T(U)'s is pronounced and more sharp compared to the T(L)'s (lower critical solution temperatures) [U. K. Pradeep, J. Chem. Phys. 129, 134506 (2008)] in this mixture, although there exists no difference in the growth of the mesoscale clusters in the lower and upper one-phase regions in this mixture. Our observations suggest the need to look at the crossover behavior probably from two perspectives, namely, the dielectric effect and the clustering effect. The effective susceptibility exponent as a function of the field variable t(UL), instead of the conventional variable t, displays a sharp nonmonotonic crossover from its asymptotic 3D-Ising value ( approximately 1.24) toward a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis for the T(U) far away from the influence of the DCP.