The critical behavior of the refractive index near liquid-liquid critical points

Liquid-liquid criticality in the dielectric constant and refractive index: A perspective

The critical region in the phase diagram of condensed matter systems such as fluids or fluid mixtures is characterized by the anomalous behaviour of specific thermodynamic properties. Here, we discuss the progress of understanding the behaviour of two intimately related properties, the dielectric constant [Formula: see text] and the refractive index n, when approaching the liquid-liquid critical point in binary liquid mixtures. Phenomenological scaling approaches, in particular, complete scaling formulation, are highlighted. In addition, experimental evidence provided by dielectric spectroscopy and optical measurements supporting the asymmetry-related critical features in [Formula: see text] and n in the one- and two-phase regions is assessed. We revisit recent experimental data and point out peculiar patterns of behaviour of polar-polar liquid mixtures as compared to (much more frequently studied) polar-non-polar mixtures. We point the necessity of additional research efforts towards the study of polar-polar mixtures, which would shed light into the influence of (microscopic) system-dependent parameters on asymmetry-related features of liquid-liquid criticality.

Liquid-liquid phase equilibrium and the effect of a water-soluble polymer on the interaction between droplets in water-in-oil microemulsions

The liquid-liquid phase equilibria of {water/PEG200/sodium bis(2-ethylhexyl)sulfosuccinate (AOT)/n-decane} with the molar ratio of water to AOT being 37.9 and various concentrations cPEG of PEG in water were measured in this study. The critical exponent β corresponding to the width of the coexistence curve was determined, which showed good agreement with the 3D-Ising value and supported the proposal of the pseudo binary droplet solution for these multiple microemulsions. A previously developed thermodynamic approach based on the Carnahan-Starling-van der Waals type equation was improved and used to analyze the coexistence curve data of {water/PEG200/AOT/n-decane} microemulsions to deduce the interaction properties between droplets and further to investigate the effect of the additive PEG200 on these interactions. It was found that the addition of PEG200 into the {water/AOT/n-decane} microemulsion resulted in the decrease in the critical temperature and the interaction enthalpy and entropy. Both the interaction enthalpy and entropy decreased first, then increased with an increase of cPEG and had minimum values at cPEG = 25 g L-1, which showed the same tendency as the isothermal titration microcalorimetric results for the {water/PEG200/AOT/isooctane} microemulsion we reported very recently. The effects of the interaction enthalpy and the entropy on the phase separation and their dependences on cPEG were discussed and related to the effects of the additive on the rigidity of the interface layer of the microemulion droplet.

Critical universality and asymmetry of ionic solution {iodobenzene + 1-decyl-3-methyl-imidazolium bis(trifluorosulfonyl)imide}

The liquid-liquid coexistence curve, heat capacity in the critical and noncritical regions, and the turbidity in critical one-phase and two-phase regions of the binary solution {iodobenzene + 1-decyl-3-methylimidazolium bis(trifluorosulfonyl)imide ([C₁₀mim][NTf₂])} have been precisely measured. From the data collected in the critical region, the critical exponents α, β, γ and ν, as well as the universal critical amplitude ratios R_B and X were obtained and were shown to agree well with their theoretical values for the 3D-Ising universality class, which further confirmed the 3D-Ising criticality of ionic solutions even in a very low relative permittivity solvent. The coulombic character of the studied system was suggested by the small values of the RPM reduced critical temperature and density. Furthermore, it was found that both the asymmetric behaviors of the diameter of the coexistence curve and the osmotic compressibility could be well described using the complete scaling theory.

Compressible cell gas models for asymmetric fluid criticality

We thoroughly describe a class of models recently presented by Fisher and coworkers [Phys. Rev. Lett. 116, 040601 (2016)]PRLTAO0031-900710.1103/PhysRevLett.116.040601. The crucial feature of such models, termed compressible cell gases (CCGs), is that the individual cell volumes of a lattice gas are allowed to fluctuate. They are studied via the seldom-used (μ, p, T) ensemble, which leads to their exact mapping onto the Ising model. Remarkably, CCGs obey complete scaling, a formulation for the thermodynamic behavior of fluids near the gas-liquid critical point that accommodates features inherent to the asymmetric nature of this phase transition like the Yang-Yang (YY) and singular coexistence-curve diameter anomalies. The CCG_{0} models generated when volumes vary freely reveal local free volume fluctuations as the origin of these phenomena. Local energy-volume coupling is found to be another relevant microscopic factor. Furthermore, the CCG class is greatly extended by using the decoration transformation, with an interesting example being the Sastry-Debenedetti-Sciortino-Stanley model for hydrogen bonding in low-temperature water. The magnitude of anomalies is characterized by a single parameter, the YY ratio, which for the models so far considered here ranges from -∞ to 1/2.

Liquid-Liquid Phase Equilibria and Interactions between Droplets in Water-in-Oil Microemulsions

The liquid-liquid phase equilibria of [water/sodium bis(2-ethylhexyl)sulfosuccinate (AOT)/n-decane] with the molar ratio w₀ of water to AOT being 37.9 and [water/AOT/ethoxylated-2,5,8,11-tetramethyl-6-dodecyne-5,8-diol(Dynol-604)/n-decane] with w₀ = 37.9 and the mole fraction α of Dynol-604 in the total surfactants being 0.158 were measured in this study. From the data collected in the critical region, the critical exponent β corresponding to the width of the coexistence curve was determined, which showed good agreement with the 3D-Ising value. A thermodynamic approach based on the Carnahan-Starling-van der Waals type equation was proposed to describe the coexistence curves and to deduce the interaction properties between droplets in the microemulsions. The interaction enthalpies were found to be positive for the studied systems, which evidenced that the entropy effect dominated the phase separations as the temperature increased. The addition of Dynol-604 into the (water/AOT/n-decane) microemulsion resulted in the decrease in the critical temperature and the interaction enthalpy. Combining the liquid-liquid equilibrium data for (water/AOT/n-decane) microemulsions with various w₀ values determined previously, it was shown that the interaction enthalpy decreased with w₀ and tended to change its sign at low w₀, which coincided with the results from the isothermal titration calorimetry investigation. All of these behaviors were interpreted by the effects of entropy and enthalpy and their competition, which resulted from the release of solvent molecules entrapped in the interface of microemulsion droplets and were dependent on the rigidity of the surfactant layers and the size of the droplet.

Soluble Model Fluids with Complete Scaling and Yang-Yang Features

Yang-Yang (YY) and singular diameter critical anomalies arise in exactly soluble compressible cell gas (CCG) models that obey complete scaling with pressure mixing. Thus, on the critical isochore ρ=ρ(c), C(μ)≔-Td(2)μ/dT(2) diverges as |t|^(-α) when t∝T-T(c)→0^(-) while ρ(d)-ρ(c)∼|t|^(2β) where ρ(d)(T)=1/2[ρ(liq)+ρ(gas)]. When the discrete local CCG cell volumes fluctuate freely, the YY ratio R(μ)=C(μ)/C(V) may take any value -∞<R(μ)<1/2 but "anticorrelated" free volumes are needed for R(μ)>0. More general decorated CCGs, including "hydrogen bonding" water models, illuminate energy-volume coupling as relevant to R(μ).