Unusual Lower Critical Solution Temperature Phase Behavior of Poly(benzyl methacrylate) in a Pyrrolidinium-Based Ionic Liquid

Polymer/ionic liquid systems are being increasingly explored, yet those exhibiting lower critical solution temperature (LCST) phase behavior remain poorly understood. Poly(benzyl methacrylate) in certain ionic liquids constitute unusual LCST systems, in that the second virial coefficient (A2) in dilute solutions has recently been shown to be positive, indicative of good solvent behavior, even above phase separation temperatures, where A2 < 0 is expected. In this work, we describe the LCST phase behavior of poly(benzyl methacrylate) in 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide for three different molecular weights (32, 63, and 76 kg/mol) in concentrated solutions (5–40% by weight). Turbidimetry measurements reveal a strong concentration dependence to the phase boundaries, yet the molecular weight is shown to have no influence. The critical compositions of these systems are not accessed, and must therefore lie above 40 wt% polymer, far from the values (ca. 10%) anticipated by Flory-Huggins theory. The proximity of the experimental cloud point to the coexistence curve (binodal) and the thermo-reversibility of the phase transitions, are also confirmed at various heating and cooling rates.

Thermodynamic Derivation of Scaling at the Liquid–Vapor Critical Point

With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid–vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion of the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and the number of particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that, while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.

Phase Transition of the Horava-Lifshitz AdS Black Holes

Some ones have showed the first-order phase transition of the Horava-Lifshitz (HL) AdS black holes has unique characters from other AdS black holes. While the coexistence zone of the first-order phase transition was not exhibited. As well known the coexistence curve of a black hole carries a lot of information about black hole, which provides a powerful diagnostic of the thermodynamic properties on black hole. We study the first-order phase transition coexistence curves of the HL AdS black holes by the Maxwell’s equal-area law, and give the boundary of two-phase coexistence zone. It is very interesting that the first-order phase transition point is determined by the pressure F on the surface of the HL AdS black hole’s horizon, instead of only the pressure P (or the temperature T). This unique property distinguishes the HL AdS black hole from the other AdS black hole systems. Furthermore, this black hole system have the critical curves, and on which every point stands for a critical point.

Automated discovery of a robust interatomic potential for aluminum

Machine learning, trained on quantum mechanics (QM) calculations, is a powerful tool for modeling potential energy surfaces. A critical factor is the quality and diversity of the training dataset. Here we present a highly automated approach to dataset construction and demonstrate the method by building a potential for elemental aluminum (ANI-Al). In our active learning scheme, the ML potential under development is used to drive non-equilibrium molecular dynamics simulations with time-varying applied temperatures. Whenever a configuration is reached for which the ML uncertainty is large, new QM data is collected. The ML model is periodically retrained on all available QM data. The final ANI-Al potential makes very accurate predictions of radial distribution function in melt, liquid-solid coexistence curve, and crystal properties such as defect energies and barriers. We perform a 1.3M atom shock simulation and show that ANI-Al force predictions shine in their agreement with new reference DFT calculations.

Numerical and Experimental Study of Abnormal Thermo-Mechanical Effects in Supercritical Fluid

At least three regions can be distinguished on the phase diagram where one-phase fluid has abnormal thermo-mechanical properties: (1) the region above the thermodynamic critical point, strictly the supercritical fluid (SCF); (2) the region close to the coexistence curve; and (3) the region where (d2p/dv2)S&lt;0. This chapter is devoted to the experimental and numerical study of abnormal effects in (1) and (3) regions. The calculations are carried out with the use of equations of Navier-Stokes, mass conservation, energy balance, and van der Waals or perfect gas equation of state. Two basic characteristic features of the SCF near the critical point, the accelerated temperature rise in the bulk heated from boundaries (so-called “piston effect”) and very slow relaxation of the generated inhomogeneities of thermodynamic parameters are studied. For region (3) the abnormal regimes of propagation of the shock and rarefaction waves after decay of a discontinuity are found.

Atomistic modeling of the parameters of the critical region of gold using the liquid-vapor coexistence curve

The liquid-vapor coexistence curve for gold was obtained by molecular dynamics (MD) modeling and the critical parameters were determined: temperature, density and pressure. The interaction potential of particles of the “embedded atom” family EAM is used. The critical temperature Tcr was determined from the results of MD simulation using the method of the average cluster size in the critical region. To clarify the value of the critical density, the empirical rule of the rectilinear diameter was used. The comparison of the simulation results of this work with the results of the assessment of the critical parameters of gold by other authors using different approaches.

The Maxwell crossover and the van der Waals equation of state

The well-known Maxwell construction1 (the equal-area rule, EAR) was devised for vapor liquid equilibrium (VLE) calculation with the van der Waals (vdW) equation of state (EoS)2. The EAR generates an intermediate volume between the saturated liquid and vapor volumes. The trajectory of the intermediate volume over the coexistence region is defined here as the Maxwell crossover, denoted as the M-line, which is independent of EoS. For the vdW or any cubic3 EoS, the intermediate volume corresponds to the “unphysical” root, while other two corresponding to the saturated volumes of vapor and liquid phases, respectively. Due to it’s “unphysical” nature, the intermediate volume has always been discarded. Here we show that the M-line, which turns out to be strictly related to the diameter4 of the coexistence curve, holds the key to solving several major issues. Traditionally the coexistence curve with two branches is considered as the extension of the Widom line5,6-9. This assertion causes an inconsistency in three planes of temperature, pressure and volume. It is found that the M-line is the natural extension of the Widom line into the vapor-liquid coexistence region. As a result, the united single line coherently divides the entire phase space, including the coexistence and supercritical fluid regions, into gas-like and liquid-like regimes in all the planes. Moreover, along the M-line the vdW EoS finds a new perspective to access the second-order transition in a way better aligning with observations and modern theory10. Lastly, by using the feature of the M-line, we are able to derive a highly accurate and analytical proximate solution to the VLE problem with the vdW EoS.

On the Singularity of the Liquid-Gas Coexistence Curve Diameter

A simplified Anisimov–Wang variant of the complete scaling approach makes it possible to determine the amplitudes of singularities for the diameter of the phase coexistence curve (CXC) on the basis of the coefficients in the power series expansion of the mean-field free energy in the reduced temperature and pressure near the critical point. This method is applied to obtain the amplitudes for the leading critical singularities of the CXC diameter in the case of a fluid described in the framework of the mesoscopic mean-field model. The results obtained demonstrate that the amplitudes of leading singularities of the CXC diameter are determined by the mesoscopic asymmetry parameters of the heterophase fluid.

Reimagining Third Phase Formation as the Miscibility Gap of a Molecular Solution

Liquid/liquid phase transitions are inherent to multicomponent solutions, which often contain a diversity of intermolecular interactions between their molecular constituents. In one such example, a phase transition is observed in liquid/liquid extraction where the nonpolar organic phase separates into two phases under sufficiently high metal and acid extraction by the amphiphilic extractant molecule. This deleterious phenomenon, known as third phase formation, complicates processing and limits efficiency. While empirically well documented, the molecular origin of this phenomenon is not understood. The prevailing conceptualization of the organic phase treats it as a microemulsion where extractant molecules form reverse micelles that contain the extracted aqueous solutes in their polar cores. Yet recent studies indicate that a microemulsion paradigm is insufficient to describe molecular aggregation in some solvent extraction systems, implying that an alternative description of aggregation, and explanation for third phase formation, is needed. In this study, we demonstrate that the formation of a third phase is consistent with crossing the liquid-liquid miscibility gap for a molecular solution rather than a Winsor II to Winsor III transition as presumed in the microemulsion paradigm. This insight is provided by using a graph theoretic methodology, generalizable to other complex multicomponent molecular solutions, to identify the onset of phase splitting. This approach uses connectivity obtained from molecular dynamics simulation to correlate the molecular-scale association of extractants and extracted solutes to the solution phase behavior using percolation theory. The method is applied to investigate a solvent extraction system relevant to ore purification and used nuclear fuel recycling: tri-n-butyl phosphate/uranyl nitrate/water/nitric acid/n-dodecane. In analogy to a molecular solution, immediately preceding the liquid-liquid coexistence curve from the single phase region, the metal-ligand complexes percolate. This demonstrates that describing this solution with microemulsion chemistry is neither applicable nor broadly required to explain third phase formation. Additionally, the method developed herein can predict third phase formation phase boundaries from simulation for this and potentially other solvent extraction systems.