Effect of ion impurities on a binary mixture of isobutyric acid and water

Anomalous Solubility of an Inert Solid in a Binary Liquid Mixture with a Critical Point of Solution

We consider the dissolution of a chemically inert solid in a binary liquid mixture with a critical point of solution. When the mixture, acting as the solvent, has come to equilibrium with the solid, the state of the system is completely described by the temperature, pressure, and a concentration variable formed by dividing the molar amount of one solvent component by that of the other. Under conditions of fixed pressure, the principle of critical point isomorphism predicts that the slope of a van't Hoff plot of the solubility of the solid should diverge toward infinity as the temperature enters the critical region. The sign of the divergence is negative when the dissolution is endothermic, whereas it is positive when the dissolution is exothermic. In experiments where excess solid phenolphthalein dissolves in a binary mixture of nitrobenzene + dodecane, we have observed exothermic dissolution concurrently with a positive divergence of the van't Hoff slope. The data are insufficiently precise to compute an accurate numerical value for the exponent of the temperature power law expected to govern this divergence; nevertheless, on the basis of Widom scaling theory, we argue that the exponent should be equal to 0.326, which is identical to the value of the exponent that governs the temperature dependence of the shape of the liquid-liquid coexistence curve. Being entirely physical in nature, the anomalous solubility effect should be observable in the case of any chemically inert solid dissolving in any one of the more than 1000 liquid pairs known to have a critical point of solution.

Ion exchange at the critical point of solution

A mixture of isobutyric acid (IBA)+water has an upper critical point of solution at 26.7°C and an IBA concentration of 4.40M. We have determined the Langmuir isotherms for the hydroxide form of Amberlite IRN-78 resin in contact with mixtures of IBA+water at temperatures, 27.0, 29.0, 31.0 and 38.0°C, respectively. The Langmuir plot at 38.0°C forms a straight line. At the three lower temperatures, however, a peak in the Langmuir plot is observed for IBA concentrations in the vicinity of 4.40M. We regard this peak to be a critical effect not only because it is located close to 4.40M, but also because its height becomes more pronounced as the temperature of the isotherm approaches the critical temperature. For concentrations in the vicinity of the peak, the data indicate that the larger isobutyrate ion is rejected by the resin in favor of the smaller hydroxide ion. This reversal of the expected ion exchange reaction might be used to separate ions according to size. Using the Donnan theory of ion exchange equilibrium, we link the swelling pressure to the osmotic pressure. We show that the peak in the Langmuir plot is associated with a maximum in the "osmotic" energy. This maximum has its origin in the concentration derivative of the osmotic pressure, which goes to zero as the critical point is approached.

A study of the conformational changes of β-lactoglobulin in the vicinity of critical point of binary mixed solvents

Most of the protein is entangled in the upper IB rich phase.

A chemical test of critical point isomorphism: reactive dissolution of ionic solids in isobutyric acid + water near the consolute point

Binary liquid mixtures having a consolute point can be used as solvents for chemical reactions. When excess cerium(IV) oxide is brought into equilibrium with a mixture of isobutyric acid + water, and the concentration of cerium in the liquid phase is plotted in van't Hoff form, a straight line results for temperatures sufficiently in excess of the critical solution temperature. Within 1 K of the critical temperature, however, the concentration becomes substantially suppressed, and the van't Hoff slope diverges toward negative infinity. According to the phase rule, one mole fraction can be fixed. Given this restriction, the temperature behavior of the data is in exact agreement with the predictions of both the principle of critical point isomorphism and the Gibbs-Helmholtz equation. In addition, we have determined the concentration of lead in the liquid phase when crystalline lead(II) sulfate reacts with potassium iodide in isobutyric acid + water. When plotted in van't Hoff form, the data lie on a straight line for all temperatures including the critical region. The phase rule indicates that two mole fractions can be fixed. With this restriction, the data are in exact agreement with the principle of critical point isomorphism.

Shift of the critical mixing temperature in strong electric fields. Theory and experiment

We study the shift in the critical temperature T(c) in binary mixtures in strong electric fields. In experiments we measure the nonlinear dielectric effect (NDE) in a mixture of nitrobenze and n-octane and calculate Piekara's factor. We find that the critical anomaly of Piekara's factor is a function of an electric field strength. We propose to explain this observation as a result of a downward shift of T(c), and this allows us to calculate (∂T(c)/∂E(2)) = (-22 ± 10) × 10(-16) (K m(2))/V(2). In the theoretical part we amend Landau and Lifshitz's formula and show that the downward shift of Tc can be estimated from a simple mean-field theory taking into account the linear and quadratic terms in an expansion of the constitutive relation ε(x) between the electric constant ε and mixture composition x.

Nonasymptotic Critical Behavior of a Ternary Ionic System

Refractive indices n and salt concentrations ms of coexisting phases of the ternary system 1,4-dioxane + water + potassium chloride were measured along the liquid-liquid-solid coexistence curve near the liquid-liquid critical end point. Refractive index measurements were carried out in the range 0.689 x 10-3 < t = (T - Tc)/Tc < 0.118 while salt concentrations were determined for the temperature range 1.84 x 10-3 < t < 8.07 x 10-2. From these experimental results, compositions fD (mass fraction of dioxane on a salt-free basis) and densities rho of coexisting phases were obtained. The shape of the coexistence curve was analyzed using alternatively n, ms, fD, and rho as order parameters. In all cases, the obtained coexistence curve displays, asymptotically, Ising behavior. Outside the asymptotic critical domain, n, ms, and rho show significant deviations of the effective critical exponent from its Ising value, while the concentration variable fD requires no corrections to simple scaling. On the basis of the present results, we conclude that this system shows no indication of multicritical behavior.

Polymer Modifies the Critical Region of the Coexisting Liquid Phases

Several recent conceptual advances, which take advantage of the polymer conformation in the near critical point of coexisting liquid phases and practical techniques of some unique molecular interactions between polymer chain and the solvent molecules, have been made to allow the investigation of the effect of the well-defined polymer in phase separation of binary mixtures. The behavior of a flexible linear or branched chain polymer (polyethylene oxide, PEO, MW = 9 x 10(5), as an impurity) in the critical binary mixture of isobutyric acid (I) + water (W) was studied by the refractive index (n) measurements using a very accurate and sensitive refractometer. The refractive index in each phase of IW as well as three different PEO concentrations (C = 0.395, 0.796, and 1.605 mg/cm(3)) in the near critical composition of IW have been measured at temperatures below the system's upper critical point. We observed that the polymer was significantly affected in the critical region of IW and these various concentrations of PEO show an important behavior on the critical exponents (beta), the critical temperatures (T(c)), and critical composition (phi(c)), which are depicting the shape of the coexistence curve. The phase-transition region of coexisting phases of IW shifts down with the addition of PEO and T(c) decreases linearly with increasing PEO concentrations. This may indicate that the polymer chain entangles with each phase, thereby the polymer monomers strongly interact with neighbor solvent particles and also intrachain interaction between the polymer segments. At such conditions, the collapse of polymer chain is possible in the vicinity of the critical point. At temperatures T close enough to T(c), the critical exponent beta (defined by the relation (n(1) - n(2)) proportional, variant (T(c) - T)(beta), with n(1) and n(2) being the refractive indices of the coexisting phases) was found to decrease from 0.382 to 0.360 when the PEO concentration changes from 0.395 to 1.605 mg/cm(3). These values are higher than that of 0.326 +/- 0.005 of pure IW, which is compatible with the three-dimensional Ising value beta = 0.325. The observed critical exponents for the PEO in IW are fully renormalized Ising critical exponents. Besides, the phi(c) values decrease with increasing the C values in the mixture of IW. It appears that the shape of the PEO in IW coexistence curves is similar from that of pure IW.

Evidence for the existence of an effective interfacial tension between miscible fluids: isobutyric acid-water and 1-butanol-water in a spinning-drop tensiometer

We report definitive evidence for an effective interfacial tension between two types of miscible fluids using spinning-drop tensiometry (SDT). Isobutyric acid (IBA) and water have an upper critical solution temperature (UCST) of 26.3 degrees C. We created a drop of the IBA-rich phase in the water-rich phase below the UCST and then increased the temperature above it. Long after the fluids have reached thermal equilibrium, the drop persists. By plotting the inverse of the drop radius cubed (r(-)(3)) vs the rotation rate squared (omega(2)), we confirmed that an interfacial tension exists and estimated its value. The transition between the miscible fluids remained sharp instead of becoming more diffuse, and the drop volume decreased with time. We observed droplet breakup via the Rayleigh-Tomotika instability above the UCST when the rotation rate was decreased by 80%, again demonstrating the existence of an effective interfacial tension. When pure IBA was injected into water above the UCST, drops formed inside the main drop even as the main drop decreased in volume with time. We also studied 1-butanol in water below the solubility limit. Effective interfacial tension values measured over time were practically constant, while the interface between the two phases remains sharp as the volume of the drop declines. The effective interfacial tension was found to be insensitive to changes in temperature and always larger than the equilibrium interfacial tension. Although these results may not apply to all miscible fluids, they clearly show that an effective interfacial tension can exist and be measured by SDT for some systems.

Effect of polymer chain in coexisting liquid phases by refractive index measurements

The behavior of polyethylene oxide (PEO, molecular weight, M(w) = 9 x 10(5), as an impurity) was studied in the critical binary mixture of nitroethane (NE) + 3-methylpentane (MP) by refractive index measurements. The measurements were performed at three different PEO concentrations (C = 0.373, 0.759, and 1.509 mg/cc) in the near critical composition of NEMP. We observed that the coexisting phase region shifts down with increasing PEO concentration and the critical temperature (T(c)) decreases linearly with C. At temperatures T close enough to T(c), the critical exponent beta [defined by the relation (n1-n2) proportional (T(c)-T)beta, with n1 and n2 being the refractive indices of the coexisting phases] was found to decrease from 0.456 to 0.372 when the PEO concentration changes from 0.373 to 1.509 mg/cc. These values are higher than that of 0.345+/-0.015 of pure NEMP, which is compatible with the three-dimensional Ising value beta = 0.325. It appears that the shape of the PEO in NEMP coexistence curves is similar from that of pure NE + MP.

Critical phenomenon of nonaqueous microemulsion (AOT/DMA/decane)

The critical phenomenon of nonaqueous microemulsion was studied for the first time. The coexistence curves of (T,n), (T,phi), and (T,psi) (n and phi are refractive index and volume fraction, respectively; psi is defined as psi=phi/[phi+phi(c)(1-phi)/(1-phi(c))]) for a ternary microemulsion [phi (AOT-DMA)+(1-phi) decane] at constant pressure and a constant molar ratio (omega=2.86) of DMA to AOT have been determined within about 7 K from the critical temperature T(c) by measurements of refractive index. The critical exponent beta has been deduced from (T,n), (T,phi), and (T,psi) coexistence curves within 1 K below T(c). They all were 0.329+/-0.005 and were consistent with the 3D Ising value. The experimental results in a temperature range of (T(c)-T)<7 K also have been analyzed to obtain critical amplitudes and the Wegner correction terms, to examine the diameters of the coexistence curves.

Coexistence curve exponent of a binary mixture with a high molecular weight polymer

We studied the effects of a high molecular weight polymer (polyacrylic acid, PAA, M(w)=7.5 x 10(5)) on the coexistence curve of a binary liquid mixture (2,6-lutidine + water, LW). A high precision refractometer was built to measure the temperature dependence of the refractive indexes of the two coexisting phases of phase separated LW samples containing less than 1 mg/cc of PAA. From the refractive indexes we mapped out the coexistence curve and obtained the refractive index difference triangle upn between the two coexisting phases. At temperature T close to the critical temperature T(c), the critical exponent beta such that triangle n inversely proportional to (T-T(c))(beta) was found to be 0.41+/-0.02 which is higher than (0.31+/-0.01) that of pure LW.