Critical Concentration Fluctuations Research Articles

Decomposition of liquid-liquid extraction organic phase structure into critical and pre-peak contributions

Solution nanostructure induced by amphiphile self-association plays an important role in various chemical and physical processes, including liquid-liquid extraction (LLE). Small angle scattering techniques are an essential means of probing this structure, but, due to non-uniqueness of scattering patterns, their interpretation is not trivial. Here, we decompose small angle x-ray scattering (SAXS) patterns for a range of binary LLE organic phases into two components: Ornstein-Zernike and pre-peak contributions resulting from, respectively, critical concentration fluctuations and packing of the amphiphilic extractant molecules in the nonpolar aliphatic diluent. While we previously applied Ornstein-Zernike scattering models to similar organic phases, including the pre-peak explicitly in the fit allows us to measure weak fluctuations at high extractant concentration and simultaneously obtain information on the position and intensity of the correlation peak related to amphiphile packing. Scattering patterns and partial structure factors calculated from molecular dynamics simulations support this interpretation. We demonstrate how this minimal scattering model describes nanostructuring for a large number of extractant types over their entire extractant/diluent composition ranges, suggesting simple and universal behavior. The straightforward assignment of these structural contributions facilitates the comparison of these features between different classes of extractant molecules and will enable further studies of organic phase aggregation. Applicability to more complex, process-relevant organic phases is illustrated with post-contact organic phases containing significant quantities of extracted lanthanide nitrate salt, which we find are readily described by this model.

Phase diagram in cyclopentanone + water + secondary butyl alcohol and light scattering investigations near the LCST

We report light scattering investigations and study of phase diagram in the system cyclopentanone (CP) + water (W) + secondary butyl alcohol (sBA), a more promising system for exploring the Quadruple Critical Point (QCP) as compared to methyl ethyl ketone (MEK) + W + sBA. Unlike in MEK + W + sBA [A. P. Naseer and P. K. M. Unni, J. Mol. Liq., 296, 111,776 (2019)], the diameter of the tunnel D≡TU-TL decreases from 66.626 K at XCP≡Xketone = 0.1000 to 24.926 K at Xketone = 0.2500 without addition of a fourth component. Our studies indicate that addition of only 0.0018 weight fraction of KSCN (i.e., 5% of the concentration of KSCN required in case of the system MEK + W + sBA), is sufficient to split the tunnel-like portion into two paraboloids with an intervening one-phase region in between. The tunnel-like feature in the phase diagram of CP + W + sBA occurs for 0.1000≤XCP≤0.2000 and for XCP>0.2000, the tunnel is open towards higher water weight fractions, though the critical line of UCSTs and LCSTs is continuous. Light scattering investigations show Fisher renormalization of the susceptibility exponent γ for 0.1750≤Xketone≡XCP≤0.2500 with a near complete renormalization observed for Xketone≡XCP = 0.2500 and normal Ising exponents observed for the region 0.1750>Xketone≡XCP>0.2500. Similarly, Ising-like behavior is observed at both low and high XCP weight-fractions while a tendency for mean-field behavior is observed for Xketone = 0.2500. Both these features appear generic to ternary systems involving (ketone + water + secondary butyl alcohol). The correlation length amplitude of critical concentration fluctuation ξ0 starts from a value of 6.5Å for XCP = 0.15 and saturates at 8.5Å in the range 0.175≤XCP≤0.350.

Critical fluctuations in liquid-liquid extraction organic phases controlled by extractant and diluent molecular structure.

Extractant aggregation in liquid-liquid extraction organic phases impacts extraction energetics and is related to the deleterious efficiency-limiting liquid-liquid phase transition known as third phase formation. Using small angle X-ray scattering, we find that structural heterogeneities across a wide range of compositions in binary mixtures of malonamide extractants and alkane diluents are well described by Ornstein-Zernike scattering. This suggests that structure in these simplified organic phases originates from the critical point associated with the liquid-liquid phase transition. To confirm this, we measure the temperature dependence of the organic phase structure, finding critical exponents consistent with the 3D Ising model. Molecular dynamics simulations were also consistent with this mechanism for extractant aggregation. Due to the absence of water or any other polar solutes required to form reverse-micellar-like nanostructures, these fluctuations are inherent to the binary extractant/diluent mixture. We also show how the molecular structure of the extractant and diluent modulate these critical concentration fluctuations by shifting the critical temperature: critical fluctuations are suppressed by increasing extractant alkyl tail lengths or decreasing diluent alkyl chain lengths. This is consistent with how extractant and diluent molecular structure are known to impact metal and acid loading capacity in many-component LLE organic phases, suggesting phase behavior of practical systems may be effectively studied in simplified organic phases. Overall, the explicit connection between molecular structure, aggregation and phase behavior demonstrated here will enable the design of more efficient separations processes.

The pervasive impact of critical fluctuations in liquid-liquid extraction organic phases.

Liquid-liquid extraction is an essential chemical separation technique where polar solutes are extracted from an aqueous phase into a nonpolar organic solvent by amphiphilic extractant molecules. A fundamental limitation to the efficiency of this important technology is third phase formation, wherein the organic phase splits upon sufficient loading of polar solutes. The nanoscale drivers of phase splitting are challenging to understand in the complex hierarchically structured organic phases. In this study, we demonstrate that the organic phase structure and phase behavior are fundamentally connected in a way than can be understood with critical phenomena theory. For a series of binary mixtures of trialkyl phosphate extractants with linear alkane diluents, we combine small angle x-ray scattering and molecular dynamics simulations to demonstrate how the organic phase mesostructure over a wide range of compositions is dominated by critical concentration fluctuations associated with the critical point of the third phase formation phase transition. These findings reconcile many longstanding inconsistencies in the literature where small angle scattering features, also consistent with such critical fluctuations, were interpreted as reverse micellar-like particles. Overall, this study shows how the organic phase mesostructure and phase behavior are intrinsically linked, deepening our understanding of both and providing a new framework for using molecular structure and thermodynamic variables to control mesostructure and phase behavior in liquid-liquid extraction.

Impact of the prequench state of binary fluid mixtures on surface-directed spinodal decomposition

Using lattice Boltzmann simulations we investigate the impact of the amplitude of concentration fluctuations in binary fluid mixtures prior to demixing when in contact with a surface that is preferentially wet by one of the components. We find a bicontinuous structure near the surface for an initial, prequench state of the mixture close to the critical point where the amplitude of concentration fluctuations is large. In contrast, if the initial state of the mixture is not near the critical point and concentration fluctuations are relatively weak, then the morphology is not bicontinuous but remains layered until the very late stages of coarsening. In both cases, it is the morphology of a depletion layer rich in the nonpreferred component that dictates the growth exponent of the thickness of the fluid layer that is in direct contact with the substrate. In the early stages of demixing, we find a growth exponent consistent with a value of 1/4 for a prequench state away from the critical point, which is different from the usual diffusive scaling exponent of 1/3 that we recover for a prequench state close to the critical point. We attribute this to the structure of a depletion layer that is penetrated by tubes of the preferred fluid, connecting the wetting layer to the bulk fluid even in the early stages if the initial state is characterized by concentration fluctuations that are large in amplitude. Furthermore, we find that in the late stages of demixing the flow through these tubes results in significant in-plane concentration variations near the substrate, leading to dropletlike structures with a concentration lower than the average concentration in the wetting layer. This causes a deceleration in the growth of the wetting layer in the very late stages of the demixing. Irrespective of the prequench state of the mixture, the late stages of the demixing process produce the same growth law for the layer thickness, with a scaling exponent of unity usually associated with the impact of hydrodynamic flow fields.

Volume phase transition of a polymer gel induced by phase separation of mixed solvents of water and 2‐butoxyethanol

ABSTRACTThe occurrence of the volume phase transition triggered by the phase separation of mixed solvents is investigated using polyacrylamide gels in mixtures of water and 2‐butoxyethanol. When the water content of the mixtures is lower than that of the critical composition, the temperature‐dependent swelling curves show a steep change around the phase separation temperatures but remain continuous, although the solvent inside the gel undergoes a discontinuous composition change. This continuous change originates from the critical concentration fluctuation below the spinodal temperature. Hysteresis‐like behavior is also observed for the heating and cooling curves. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46366.

Hydrodynamic effects on concentration fluctuations in multicomponent membranes

We investigate the hydrodynamic effects on the dynamics of critical concentration fluctuations in multicomponent fluid membranes. Two geometrical cases are considered; (i) confined membrane case and (ii) supported membrane case. We numerically calculate the wavenumber dependence of the effective diffusion coefficient by changing the temperature and/or the thickness of the bulk fluid. For some limiting cases, the result is compared with the previously obtained analytical expression. An analogy of the multicomponent membrane to 2D microemulsions is explored for the confined membrane geometry.

Micro-phase separation explains the abrupt structural change of denatured globular protein gels on varying the ionic strength or the pH

Aqueous solutions of globular proteins gel after heat-induced denaturation. The structure of β-lactoglobulin gels was studied as a function of the pH (2–8) and the NaCl concentration (0–1 M) over a wide range of length scales (1 nm-100 µm) using a combination of scattering techniques and microscopy. The gel structure depended on the strength of the electrostatic interaction that was varied by changing the charge density of the proteins (pH) or the screening length (ionic strength). Homogeneous so-called finely stranded gels were formed at strong interaction, while more heterogeneous so-called particulate gels were formed at weak interaction. It is shown that phase separation of growing irreversibly bound protein aggregates explains the abrupt transition between the two structures for small changes of the ionic strength or the pH. Phase separation was limited to the formation of protein rich domains with a radius of several microns that associated into the particulate gels. The structure of homogeneous gels is shown to be determined by the amplitude of the (critical) concentration fluctuations of protein aggregates that were frozen-in by gelation. The characteristic length scales of the homogeneous gels varied between about 20 nm and 1 µm.

Pluronic L64 Micelles near Cloud Point: Investigating the Role of Micellar Growth and Interaction in Critical Concentration Fluctuation and Percolation

The structure and the properties of the (Ethylene Oxide)(13)(Propylene Oxide)(30)(Ethylene Oxide)(13) (Pluronic L64, MW approximately 2900) micelles have been studied in the aqueous medium by small angle neutron scattering (SANS), dynamic light scattering (DLS) and viscometry measurements. The aqueous solutions of this triblock copolymer are unique among the pluronic solutions in showing critical concentration fluctuations and a concomitant enhancement in viscosity on approaching their cloud point. So far these results have been attributed solely to the presence of attractive interaction between the spherical L64 micelles. Recent theoretical studies, on the other hand, suggest that L64 micelles prefer a prolate ellipsoidal structure to sphere (Bedrov et al. Langmuir 2007, 23, 12032) and have a predominantly repulsive intermicellar interaction. A comparative analysis of our SANS data based on the spherical and prolate ellipsoidal structure shows that the L64 micelles can be best described by a prolate ellipsoidal structure, the aspect ratios of which increase progressively with increase in temperature. This, together with our viscosity and DLS studies, suggests that the enhanced viscosity of the copolymer solution near the cloud point arises largely due to the anisotropic growth of the micelles to the worm-like structures. The role of the intermicellar attractive interaction has thus been limited to the observed critical concentration fluctuation, and its effect decreases progressively with increase in copolymer concentration. It has also been shown that the water structure making salts like NaCl reduces the micellar growth temperature and helps in forming worm-like micelles at the room temperature. These studies thus identify the effect of micellar growth and interaction in determining the properties of the copolymer solution near the cloud point, which are the first of its kind in the case of the pluronics.

Heat capacity close to the unattainable critical layering point

An analysis of the literature data on the heat capacity of aqueous low-concentration solutions of tert-butanol at several temperatures showed that the heat capacity peak in this concentration region was largely related to critical concentration fluctuations close to the binodal, which appeared because of microlayering on the network of H-bonds in solutions of hydrophobic nonelectrolyte molecules.

Concentration Fluctuation in a Two-Component Fluid Membrane Surrounded with Three-Dimensional Fluids

We calculate the relaxation rate of the critical concentration fluctuation in a two-component fluid membrane by considering hydrodynamics of the surrounding fluids. Results are compared with the previous results obtained by Seki, Komura, and Imai (2007), who treated the momentum flux from the membrane to its environments using the friction coefficient.

Dynamics of critical fluctuations in polymer solutions

Using dynamic light scattering we have investigated the time dependence of fluctuations near the critical point of phase separation in solutions of polystyrene in cyclohexane with polymer molecular weights ranging from 196,000 to 11.4 x 10(6) g mol(-1). At the lowest polymer molecular weight the dynamic correlation function follows a single-exponential decay with a decay rate that can be represented by the mode-coupling theory of critical dynamics but with a mesoscopic viscosity that characterizes the hydrodynamic environment of the polymers in the solution. At all higher polymer molecular weights two distinct dynamic modes are observed, a slow and a fast mode, that originate from a coupling of the critical concentration fluctuations with viscoelastic relaxation of the polymer chain in solutions. This coupling causes an additional slowing down of the fluctuations on top of the well-known critical slowing down expected in the absence of a coupling between the two modes. From an analysis of the time dependence of the experimental dynamic correlation functions in terms of a theory of coupling of dynamic modes we are able to determine the viscoelastic properties of the polymers in the solution. These viscoelastic properties diverge in the theta-point limit of infinite polymer molecular weight.

Ion-induced multiply reentrant liquid-liquid transitions and the nature of criticality in ethanol-water mixture

We report a quite unusual feature of four liquid-liquid reentrant transitions in ethanol (E)+water (W)+ammonium sulfate mixture by meticulous tuning of the ammonium sulfate concentration in a narrow range, as a function of temperature, at atmospheric pressure. Detailed exploration of the intricate phase behavior in terms of E/W sections shows that the range of triple reentrance shrinks with increasing E/W. The behavior of osmotic susceptibility is investigated by light scattering, near the critical point, in the one-phase region by varying the temperature at fixed concentration of the components, in a particular E/W section. The critical exponent of susceptibility (gamma) and correlation length (nu) are observed to have Fisher renormalized Ising values [Phys. Rev. 176, 237 (1968)], with gamma(r)=1.41 and nu(r)=0.718. The effective susceptibility exponent, gamma(eff), exhibits a sharp, nonmonotonic crossover from Ising to mean-field critical behavior, which is completed outside the critical regime. The amplitude of the correlation length, xi(o)(=21.2+/-0.4 A), deduced from light scattering experiment, is an order of magnitude larger than the typical values in usual aqueous electrolyte systems. This value of xi(o) is further verified from small-angle x-ray scattering (SAXS) experiments and found to be consistent. SAXS experiments on the critical sample reveal the presence of long-ranged intermolecular correlations, leading to supramolecular structuring, at a temperature far away from the critical point. These results convincingly demonstrate that the finite length scale arising due to the structuring competes with the diverging correlation length of critical concentration fluctuations, which influences the nonasymptotic critical behavior in this aqueous electrolyte system. The sulphate ions play a dominant role in both structuring and the complex phase behavior.

Long-range periodic structure induced by coupling of the solvation effect and concentration fluctuation in water and 3-methylpyridine with salts

Small-angle neutron scattering (SANS) experiments were performed on mixtures of 3-methylpyridine, D 2O, and salts to investigate concentration fluctuations and structures in the vicinity of the critical point. The temperature-dependence of the SANS profile of a mixture without salt showed critical phenomena that were consistent with 3D-Ising behavior. On the other hand, the SANS profiles with salt added mixtures could not be explained solely in terms of critical scattering, because they include both the concentration fluctuation and a periodic structure. The periodic structure could be induced by the coupling of solvation and a critical concentration fluctuation.

Shear-Induced Phase Separation in Solutions of Wormlike Micelles

Polymer solutions in the vicinity of the theta-point are known to undergo shear-induced turbidity or phase separation. The present study shows that a similar phenomenon also occurs for certain wormlike micellar solutions. Wormlike micelles are the self-assembled counterparts of polymers and are characterized by their ability to reversibly break and recombine. In the system of interest, the micelles are formed by the cationic surfactant erucyl bis(hydroxyethyl)methylammonium chloride (EHAC), in conjunction with a salt such as sodium chloride (NaCl) or sodium salicylate (NaSal). Micellar samples that become turbid under shear show evidence of critical concentration fluctuations and may contain predominantly branched micelles. The shear-induced turbidity in these samples correlates with the appearance of flow-dichroism in rheooptic experiments and with an increase in low-q scattering in small-angle light scattering under flow (flow-SALS) experiments. The characteristic "butterfly" pattern, with enhanced scattering in the flow direction and a dark streak perpendicular to the flow direction, is typically observed in flow-SALS. The results suggest that the turbidity is due to a shear-induced growth of concentration fluctuations, which in turn manifests as large anisotropic domains, typically oriented along the vorticity axis.

Crossover behavior in micellar solutions with lower critical demixing point: broadband ultrasonic spectrometry of the isobutoxyethanol-water system.

The aggregation kinetics of isobutoxyethanol-water mixtures with lower critical demixing point has been investigated. Two types of kinetics have been observed, a diffusion-controlled formation of micellar species and the formation of a microheterogeneous liquid structure, governed by fluctuations in the local concentration. Ultrasonic attenuation spectra of isobutoxyethanol-water mixtures have been measured between 100 kHz and 2 GHz at 25 degrees C and at several concentrations, covering the complete composition range. With the mixture of critical composition measurements have been performed at some temperatures near the critical temperature (T(c)=299.51 K). In addition to the asymptotic high frequency background contribution, the broadband spectra reveal a Bhattacharjee-Ferrell relaxation term due to critical concentration fluctuations, a restricted Hill term reflecting the monomer exchange between micelles and the suspending phase, and two Debye-type relaxation terms that are assigned to chemical relaxations. The relaxation rates of the Bhattacharjee-Ferrell term exceed those from static and dynamic light scattering (amplitude Gamma(0)=5.3 x 10(9) s(-1)), likely due to the effect of a second parallel pathway of relaxation in the ultrasonic field. The adiabatic coupling constant following from the amplitude in the ultrasonic spectrum agrees with that from a thermodynamic relation (g=1.3). The restricted Hill term displays the features of an extended Teubner-Kahlweit-Aniansson-Wall model of the micelle formation and decay kinetics in surfactant solutions with high critical micelle concentration (C=0.6 mol/l). The idea of a fluctuation controlled monomer exchange in aqueous solutions of poly(ethylene glycol) monoalkyl ether-water mixtures near the critical point is briefly discussed.

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.

Cloud-Point Phenomena in Wormlike Micellar Systems Containing Cationic Surfactant and Salt

Cationic surfactants with an erucyl (C22, monounsaturated) tail display unusual phase behavior in aqueous solution as a function of temperature and added salt concentration. Low amounts of salts with binding counterions such as sodium tosylate (NaTos) lead to highly viscoelastic wormlike micellar solutions. With further addition of salt, the viscosity decreases, and the solutions cloud on heating (i.e., exhibit lower consolute phase behavior). The cloud-point temperature and the zero-shear viscosity η0 pass in parallel through minima as a function of NaTos concentration. Cloud-point behavior is seen over a wider range of salt concentrations in the case of sodium salicylate (NaSal), which has an even stronger binding counterion. In the case of a weakly binding salt (NaCl), phase transitions are observed only at much higher salt contents, and the phase behavior is predominantly of the upper consolute type. Light and neutron scattering data show evidence of critical concentration fluctuations near the cloud ...

Nonuniversal nature of dynamic critical anomaly in polymer solutions.

Critical anomaly of viscosity has been studied for ideal polymer solutions, focusing on its dependence on the molecular weight of polymer M(w). According to the conventional understanding that polymer solutions should belong to the same dynamic universal class as classical fluids, the critical exponent of viscosity y(c) should be a universal constant (approximately 0.04). Contrary to this, we find that y(c) significantly decreases with increasing M(w). This unusual behavior can be explained by the dynamic coupling of critical concentration fluctuations with an additional slow viscoelastic mode intrinsic to polymer solutions. Our dynamic light scattering measurements support this picture.

Ultrasonic studies of dynamics of critical concentration fluctuations in benzonitrile–isooctane mixture

This paper presents results of the ultrasonic velocity measurements in the temperature range 291–303 K and absorption coefficient measurements in the frequency range 5–43 MHz and temperature range 0.15⩽ T− T c⩽20 K in the benzonitrile–isooctane critical mixture. Ferrell and Bhattacharjee dynamic scaling theory which predicts a linear dependence between α c/ f 2 and f −1.06 was chosen for data analysis. This relation was confirmed by experimental data. The results of acoustic attenuation were also compared with the scaling function of Shiwa–Kawasaki mode-coupling theory, Kroll–Ruhland renormalization-group theory, and Ferrell–Bhattacharjee dynamic scaling theory.