Binodal Research Articles

Phase properties of the mean-field Ising model with three-spin interaction

The equilibrium and phase properties of the Ising model with three-spin interaction and an external field are studied within the framework of mean-field approximation. The thermodynamic properties of the model reveals two coexistence curves, signifying two distinct second-order phase transitions, dependent on the domain of the interaction parameter. The critical exponents of the magnetic order parameter are calculated in all directions of the phase space and show their agreement with the mean-field universality class.

Nonuniversal aging during phase separation with long-range interaction.

Issues concerning the kinetics of phase transitions are not well established for the cases where the order parameter remains conserved with time, particularly when the interatomic interactions are long-range in nature.Here we present results on structure, growth, and aging from Monte Carlo simulations of the two-dimensional long-range Ising model. In our computer simulations, random initial configurations, for 50:50 compositions of up and down spins, mimicking high-temperature equilibrium states, have been quenched to temperatures inside the coexistence curve. Our analyses of the simulation data, for such a protocol, show interesting dependence of the aging exponent, λ, on σ, the parameter, within the Hamiltonian, that controls the range of interaction. These nonuniversal values of λ are compared with a theoretical result for lower bounds. For this purpose, we extracted information on relevant aspects of structural properties during the evolution. To estimate λ, as is necessary, we also calculated the average domain size and analyzed its time dependence to obtain the growth exponent α which also is nonuniversal. The trends in the values of λ and α, as well as an anomaly in structure, suggest that a crossover from the long-range to the short-range variety occurs at σ≃1. The location of this boundary and the nonuniversality provide a picture that is surprisingly different from that of the corresponding static critical phenomena. Furthermore, our results suggest an important scaling law combining α and λ.

Thermodynamic Geometry and coexistence curves of ferrofluids

The Thermodynamic Geometry (TG) for a particular equation of state of a ferrofluid is studied. The R-crossing method of TG is applied to reproduce the coexistence curves related to the dense and diluted phases of the ferrofluid in the limits, zero magnetic field and infinite magnetic field. For both limits, each phase is modeled by a separate equation of state. The phase diagram of the fluid does not have a critical point but dense and dilute phases are clearly separated by coexistence curves. In the framework of TG, each phase is represented by a particular metric tensor and hence, two different curvature scalars are obtained. It is verified that the coexistence curves can be accurately reproduced with a modified version of the R-crossing method of TG, namely using the equality between the two curvatures corresponding to the two separated dense and diluted phases.

Engineering Mixing Properties of Fluids by Spatial Modulations.

We propose a method to change the effective interaction between two fluids by modulation of their local density distributions with external periodic potentials, whereby the mixing properties can be controlled. This method is applied to a mixture of dilute bosonic gases, and binodal and spinodal curves emerge in the phase diagram. Spinodal decomposition into a mixed-bubble state becomes possible, in which one of the coexisting phases has a finite mixing ratio. A metastable mixture is also realized, which undergoes phase separation via nucleation.

Using the Zeno line to assess and refine molecular models.

The Zeno line is the locus of points on the temperature-density plane where the compressibility factor of the fluid is equal to one. It has been observed to be straight for a broad variety of real fluids, although the underlying reasons for this are still unclear. In this work, a detailed study of the Zeno line and its relation to the vapor-liquid coexistence curve is performed for two simple model pair-potential fluids: attractive square-well fluids with varying well-widths λ and Mie n-6 fluids with different repulsive exponents n. Interestingly, the Zeno lines of these fluids are curved, regardless of the value of λ or n. We find that for square-well fluids, λ ≈ 1.8 presents a Zeno line, which is the most linear over the largest temperature range. For Mie n-6 fluids, we find that the straightest Zeno line occurs for n between 8 and 10. Additionally, the square-well and Mie fluids with the straightest Zeno line showed the closest quantitative agreement with the vapor-liquid coexistence curve for experimental fluids that follow the principle of corresponding states (e.g., argon, xenon, krypton, methane, nitrogen, and oxygen). These results suggest that the Zeno line can provide a useful additional feature, in complement to other properties, such as the phase envelope, to evaluate molecular models.

A multidimensional examination of phase separation in single-component fluids

A thermodynamic instability in a homogeneous fluid can lead to spontaneous formation of distinct domains within the fluid. This process involves not only the spatial redistribution of fluid density but also transient exchanges of pressure, temperature, and energy. However, classical theoretical frameworks, such as the Ginzburg–Landau and Cahn–Hilliard models, lack incorporation of these essential thermodynamic aspects. To investigate the dynamics of multiple physical fields during phase separation, we numerically solve a two-dimensional van der Waals fluid model. Thermodynamic consistency is demonstrated by verifying the coexistence curve. While the equilibrium pressure remains similar across the unstable region of the isotherm, we demonstrate that the energy in the system depends on the initial density. Although the majority of energy is stored as heat at typical values of the heat capacity, high-density domains contain less specific energy compared to their low-density counterparts due to interparticle attraction. Consequently, the transition of low-density domains into high-density through the process of coalescence releases excess energy, which redistributes in the form of longitudinal waves and heat. We also highlight the role of parameters, such as heat capacity and thermal conductivity, in less intuitive phenomena, including elevated temperature fluctuations and memory preservation.

Practical deployment of automation to expedite aqueous two-phase extraction

The feasibility of bioprocess development relies heavily on the successful application of primary recovery and purification techniques. Aqueous two-phase extraction (ATPE) disrupts the definition of "unit operation" by serving as an integrative and intensive technique that combines different objectives such as the removal of biomass and integrated recovery and purification of the product of interest. The relative simplicity of processing large samples renders this technique an attractive alternative for industrial bioprocessing applications. However, process development is hindered by the lack of easily predictable partition behaviours, the elucidation of which necessitates a large number of experiments to be conducted. Liquid handling devices can assist to address this problem; however, they are configured to operate using low viscosity fluids such as water and water-based solutions as opposed to highly viscous polymeric solutions, which are typically required in ATPE. In this work, an automated high throughput ATPE process development framework is presented by constructing phase diagrams and identifying the binodal curves for PEG6000, PEG3000, and PEG2000. Models were built to determine viscosity- and volume-independent transfer parameters. The framework provided an appropriate strategy to develop a very precise and accurate operation by exploiting the relationship between different liquid transfer parameters and process error. Process accuracy, measured by mean absolute error, and device precision, evaluated by the coefficient of variation, were both shown to be affected by the mechanical properties, particularly viscosity, of the fluids employed. For PEG6000, the mean absolute error improved by six-fold (from 4.82% to 0.75%) and the coefficient of variation improved by three-fold (from 0.027 to 0.008) upon optimisation of the liquid transfer parameters accounting for the viscosity effect on the PEG-salt buffer utilising ATPE operations. As demonstrated here, automated liquid handling devices can serve to streamline process development for APTE enabling wide adoption of this technique in large scale bioprocess applications.

Phase diagram of a rigid rod system with attractive end groups

We present a molecular dynamics study into the thermotropic liquid crystalline phase behaviour of a coarse-grained model of a rigid bolaamphiphilic molecule. The model consists of 11 spherical beads held in a fixed linear arrangement, where the two opposing terminal beads are self-attracting, mimicking hydrophilic segments and the remaining internal beads, as well as cross-bead interactions, are softly repulsive, mimicking hydrophobic organic segments. The effect of the model’s end bead self-attraction strength on liquid crystalline phase behaviour is studied. Coexistence points between the smectic A, nematic and isotropic phases exhibited by the model are determined following a thermodynamic integration pathway, using equations of state constructed by multiple histogram reweighting of simulation data. Variants of Gibbs–Duhem integration are used to trace pressure–temperature coexistence curves. Under isobaric conditions, the effect of increasing the end-group self-attraction on the nematic–isotropic coexistence temperature is relatively small; however, the nematic phase stability is reduced at the expense of a significant increase in the smectic A–nematic coexistence temperature. Lower temperature simulations show the approximate smectic A–crystalline transition temperature to be only weakly dependent on the strength of the end-group self-attraction.

Triple points and phase transitions of D-dimensional dyonic AdS black holes with quasitopological electromagnetism in Einstein–Gauss–Bonnet gravity

By considering the negative cosmological constant Λ as a thermodynamic pressure, we study the thermodynamics and phase transitions of the D-dimensional dyonic AdS black holes (BHs) with quasitopological electromagnetism in Einstein–Gauss–Bonnet (EGB) gravity. The results indicate that the small/large BH phase transition that is similar to the van der Waals (vdW) liquid/gas phase transition always exists for any spacetime dimensions. Interestingly, we then find that this BH system exhibits a more complex phase structure in 6-dimensional case that is missed in other dimensions. Specifically, it shows for D = 6 that we observed the small/intermediate/large BH phase transitions in a specific parameter region with the triple point naturally appeared. Moreover, when the magnetic charge turned off, we still observed the small/intermediate/large BH phase transitions and triple point only in 6-dimensional spacetime, which is consistent with the previous results. However, for the dyonic AdS BHs with quasitopological electromagnetism in Einstein–Born–Infeld (EBI) gravity, the novel phase structure composed of two separate coexistence curves observed by Li et al. [Phys. Rev. D 105 104048 (2022)] disappeared in EGB gravity. This implies that this novel phase structure is closely related to gravity theories, and seems to have nothing to do with the effect of quasitopological electromagnetism. In addition, it is also true that the critical exponents calculated near the critical points possess identical values as mean field theory. Finally, we conclude that these findings shall provide some deep insights into the intriguing thermodynamic properties of the dyonic AdS BHs with quasitopological electromagnetism in EGB gravity.

Thermodynamics and Phase Transitions of Dyonic AdS Black Holes in Gauss-Bonnet-Scalar Gravity

In this paper, by treating the cosmological constant as a thermodynamic pressure, we study the thermodynamics and phase transitions of the dyonic AdS black holes in Gauss-Bonnet-Scalar gravity, where the conformal scalar field is considered. In a more general extended phase space, we first verified the first law of black hole thermodynamics, and find that it is always true. Meanwhile, the corresponding Smarr relation is also obtained. Then, we found that this black hole exhibits interesting critical behaviors in six dimensions, i.e., two swallowtails can be observed simultaneously. Interestingly, in a specific parameter space, we observed the small/intermediate/large black hole phase transitions, with the triple point naturally appearing. Additionally, the small/large black hole phase transition, similar to the liquid/gas phase transition of the van der Waals fluids, can also be found in other parameter regions. Moreover, we note that the novel phase structure composed of two separate coexistence curves discovered in the dyonic AdS black holes in Einstein-Born-Infeld gravity disappears in Gauss-Bonnet-Scalar gravity. This suggests that this novel phase structure may be related to gravity theory, and importantly, it is generally observed that the triple point is a universal property of dyonic AdS black holes. On the other hand, we calculated the critical exponents near the critical points and found that they share the same values as in mean field theory. Finally, it is true that these results will provide some deep insights into the interesting thermodynamic properties of the dyonic AdS black holes in the background of conformal scalar fields.

The Influence of Wettability Effect and Adsorption Thickness on Nanoconfined Methane Phase Behavior: Vapor-Liquid Co-Existence Curves and Phase Diagrams

Research interest in the behavior of methane inside nanopores has been growing, driven by the substantial geological reserves of shale gas and coalbed methane. The phase diagram of methane in nanopores differs significantly from its bulk state, influencing its existing form and pertinent physical properties—such as density and viscosity—at specific pressures and temperatures. Currently, there is a lack of effort to understand the nanoconfinement effect on the methane phase diagram; this is a crucial issue that needs urgent attention before delving into other aspects of nanoconfined methane behavior. In this study, we establish a fully coupled model to predict the methane phase diagram across various scales. The model is based on vapor-liquid fugacity equilibrium, considering the shift in critical pressure and temperature induced by pore size shrinkage and adsorption-phase thickness. Notably, our proposed model incorporates the often-overlooked factor of capillary pressure, which is greatly amplified by nanoscale pore size and the presence of the adsorption phase. Additionally, we investigated the impact of surface wettability, correlated to capillary pressure and the shift in critical properties, on the methane phase diagram. Our results indicate that (a) as pore size decreases, the methane phase diagram becomes more vertical, suggesting a transition from a gaseous to a liquid state for some methane molecules, which is contrary to the conventional phase diagram; (b) enhancing surface wettability results in a more vertical phase diagram, with the minimum temperature corresponding to 0 MPa pressure on the phase diagram, increasing by as much as 87.3%; (c) the influence of capillary pressure on the phase diagram is more pronounced under strong wettability conditions compared to weak wettability, and the impact from the shift in critical properties can be neglected when the pore size exceeds 50 nm.

Predicting polymer solubility from phase diagrams to compatibility: a perspective on challenges and opportunities.

Polymer processing, purification, and self-assembly have significant roles in the design of polymeric materials. Understanding how polymers behave in solution (e.g., their solubility, chemical properties, etc.) can improve our control over material properties via their processing-structure-property relationships. For many decades the polymer science community has relied on thermodynamic and physics-based models to aid in this endeavor, but all rely on disparate data sets and use-case scenarios. Hence, there are still significant challenges to predict a priori the solubility of a polymer, whether it is for selecting sustainable solvents, obtaining thermodynamic parameters for phase separation, or navigating the coexistence curve. This perspective aims to discuss the different approaches of applying computational tools to predict polymer solubility, with a significant focus on machine learning techniques to capture the rapid progress in that space. We examine challenges and opportunities that remain for creating a comprehensive solubility toolset that can accelerate the design of a broad range of applications including films, membranes, and pharmaceuticals.

Phase Equilibria and Interdiffusion in the Ternary System Epoxy Oligomer-Polysulfone-Alkyl Glycidyl Ether.

Phase equilibria, interdiffusion and structure in the initial uncured mixtures of epoxy oligomer-polysulfone-alkyl glycidyl ether were studied. Binodal curves were constructed on isothermal sections of the ternary phase diagram. Thermodynamic mixing parameters were calculated and spinodal curves were plotted. The interdiffusion coefficients of components, establishing the technological modes of mixing the components, were determined. To validate the phase diagram, the phase structure of mixtures, the composition of which at a temperature of 40 °C corresponds to heterogeneous and homogeneous regions, was studied.

Liquid-liquid phase of imidazolium-based ionic liquids in n-butyl acetate + n-butanol mixtures: Experimental measurements, quality testing, phase stability, thermodynamic modeling

The ester n-butyl acetate is an important chemical compound produced by esterification with n-butanol and used as solvent for pigments, vegetable oils and fats, and in the production of varnishes, coatings, waxes and resins. This work investigated the use of ionic liquids (ILs) as solvents in separation processes involving these substances. The ionic liquid 1-butyl-3-methylimidazolium chloride ([BMIM][Cl]) was synthesized, while 1-ethyl-3-methylimidazolium ethyl sulfate ([EMIM][EtSO4]) and 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]) were purchased. The liquid–liquid equilibrium (LLE) was analyzed based on the experimental measurements (binodal curve, tie-lines), σ-profiles analysis (COSMOTherm), experimental data quality tests, phase stability and thermodynamic modeling with NRTL for the n-butyl acetate + n-butanol + IL ([BMIM][Cl], [EMIM][EtSO4], [EMIM][BF4]) systems at 298.15 K and 101.3 kPa. Experimental results indicated that the studied systems had the LLE phase behavior of type I. Experiments and calculations showed that [EMIM][EtSO4] and [BMIM][Cl] had the best capacities to separate the azeotrope n-butanol and n-butyl acetate. All systems showed separation factors values higher than unity. Low deviations, in the compositions of both liquid phases, indicate that the NRTL model was able to analyze the phase stability and model the phase behavior of the n-butyl acetate + n-butanol + IL systems using gamma-gamma approach.

Onset of heterogeneous nucleation in pool boiling of HFE-7100 following rapid heating on a microscale heater

Effective thermal management of electronics is crucial for maintaining their reliability, longevity, and optimal performance. As electronic devices become increasingly compact and powerful, the need to explore new and innovative methods for thermal management becomes ever more critical. Rapid transitions of power lead to temperature spikes (hotspots) of up to 100 K, and thus can dramatically increase the failure occurrence of chips. Power spikes imply that heterogeneous nucleation occurs due to rapid heating, which can vary between 104 – 106 K/s, and hence the coolant is in its metastable region under various degrees of superheating. Gaining ONB data with respect to the heating rate holds significance for diverse applications including nuclear installations, engines, inkjet printers, and laser-based systems.In the present paper, we have refined the definition to a heterogeneous nucleation event due to a rapid heating process, that occurs when the timescale for the wall heating is shorter than the critical bubble’s significant growth time. Data pertaining to the dependence of the onset of nucleate boiling (ONB) on the heating rate is presented for the first time. Experiments are performed with HFE-7100 fluid that is rapidly heated using a uniquely designed micro-heater, 122 × 234 μm2 in size.The newly designed and constructed system facilitates precise measurements of fast heating processes. In this study, we conducted a series of experiments spanning heating rates from 104 to ∼106 K/s. This range of heating rates was identified in our previous studies as an intermediate regime for water. The region of intermediate heating rates was previously proved in our research to be challenging to attain, due to the varying stability of the metastable zone; it is primarily attributed to pre-existing nucleation sites. Consequently, this led to a notable gap in the experimental results for water, within this particular region, in the literature. Notably, in the current study, we were able to achieve a maximum superheating degree of 14 K at a heating rate of 2.2·106 K/s. Preheated liquids reach the same superheating degree with different heating rates, depending on the coexistence and spinodal curves. It was found that water and HFE-7100 differ significantly in their metastable zone, and that the first zone, for slower heating rates, spans approximately 12 K for water, but only 4 K for HFE-7100.

Coexistence curve diameter and slope of vapor pressure: “universal” relation in the critical region

We have (i) discovered a universal dependence of the coexistence curve diameter, related through the exponent of critical isotherm to vapor pressure slope in the vicinity of the critical point; (ii) proved that the dimensionless diameter of the coexistence curve cannot be less than 1; (iii) obtained the universal strength of the Yang-Yang anomaly with a value of 0.62±0.01; (iv) calculated the critical amplitude of isothermal compressibility for a number of fluids using the previously unknown universal ratio.

Smoothed particle hydrodynamics simulations of the evaporation of suspended liquid droplets

The ordinary evaporation and explosive vaporization of equilibrium, van der Waals, liquid drops subjected to uniform heating at supercritical temperatures are investigated by means of numerical simulations with the aid of a modified version of the DualSPHysics code. The models include the effects of surface tension, thermocapillary forces, mass transfer across the interface, and liquid–vapor interface dynamics by means of a diffuse-interface description. In contrast to previous simulations in this line, a new non-classical source term has been added to the internal energy equation to deal with the vaporization rate through the diffuse interface. This term is related to the diffusion of the latent heat in the interface zone and is, therefore, necessary for a correct physical description of the liquid–vapor interface structure. As the heating temperature increases the drops undergo surface evaporation, nucleation of an interior vapor bubble, nucleation followed by fragmentation of the liquid, and explosive vaporization. Heating at supercritical temperatures brings the drop out of equilibrium and forces it to rapid quenching into either the miscibility gap, where it undergoes surface evaporation by spinodal decomposition, or the metastable region bounded by the binodal and spinodal curves, where it nucleates a vapor bubble. The results also indicate that at comparable heating, drops of lower density experience faster evaporation rates than drops of higher density.

Binodal and spinodal curves of ternary systems containing lignin using the NRTL and UNIQUAC models

Binodal and spinodal curves of ternary systems containing lignin using the NRTL and UNIQUAC models

Structure and Dynamic Inhomogeneity of Liquids on the Liquid–Gas Coexistence Curve Near the Triple Point

Structure and Dynamic Inhomogeneity of Liquids on the Liquid–Gas Coexistence Curve Near the Triple Point

Influence of the temperature and type of macromolecule on phase diagrams of aqueous two-phase systems

Phase diagrams for aqueous two-phase systems formed by L64 + Na2SO3 + H2O, F68 + Na2SO3 + H2O, polyethylene glycol 10,000 g·mol–1 (PEG10k) + Na2SO3 + H2O and PEG 35,000 g·mol–1 (PEG35k) + Na2SO3 + H2O were determined experimentally at temperatures of 278.15, 288.15 and 298.15 K, at 0.09 MPa. The binodal curve is not significantly shifted with varying temperature, indicating a small change on the system enthalpy during the phase separation process, but an increase in the temperature promoted an increase in the slope of tie-line. The effectiveness of macromolecules in promoting phase separation occurs in the following order: PEG35k > PEG10k ≈ F68 > L64. An increase in molar mass requires lower concentrations to induce phase separation, due to the decrease of configurational entropy of the solution. When comparing macromolecules with similar molar masses, PEG10k required slightly lower concentrations than F68 to induce phase segregation. Although PEG10k has a higher molar mass, the structure of F68 contains hydrophobic groups (poly(propylene glycol)) that compensate for its lower molar mass, which generates similar phase segregation induction capabilities. Therefore, new aqueous two-phase systems have been characterized by extending the range of systems available for applications.