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The blinking-checkers model [F. Caupin and M. A. Anisimov, Phys. Rev. Lett, 127,185701 (2021)] is a minimal lattice model which has demonstrated that, in the meanfield approximation, it can reproduce the phenomenon of fluid polyamorphism. This model is a binary lattice-gas, in which each site has three possible states: empty, occupied with particles of type 1, and occupied with particles of type 2. Additionally, the two types of particles may interconvert from one to another. Equilibrium interconversion imposes a constraint that makes this model thermodynamically equivalent to a single-component system. In this work, Monte-Carlo simulations of the blinking-checkers model are performed, demonstrating polyamorphic phase behavior. The locations of the liquid-liquid and liquid-gas critical points are found to be different from the meanfield predictions for this model with the same interaction parameters, as the phase behavior is significantly affected by critical fluctuations. Based on the computed values of the critical exponents of the order parameter, susceptibility, correlation length, and surface tension, we confirm that the blinking-checkers model, for both liquid-gas and liquid-liquid equilibria, belongs to the three-dimensional Ising class of critical-point universality., Comment: Submitted to Molecular Physics as a part of the Rull-Abascal special issue for statistical physics in Spain

It has been hypothesized that liquid polyamorphism, the existence of multiple amorphous states in a single component substance, may be caused by molecular or supramolecular interconversion. A simple microscopic model [Caupin and Anisimov, Phys. Rev. Lett., 127, 185701, (2021)] introduces interconversion in a compressible binary lattice to generate various thermodynamic scenarios for fluids that exhibit liquid polyamorphism and/or water-like anomalies. Using this model, we demonstrate the dramatic effects of interconversion on the interfacial properties. In particular, we find that the liquid-vapor surface tension exhibits either an inflection point or two extrema in its temperature dependence. Correspondingly, we observe anomalous behavior of the interfacial thickness and a significant shift in the location of the concentration profile with respect to the location of the density profile., Comment: This manuscript has been submitted to the Journal of Physical Chemistry B, as a part of the special issue, "Pablo G. Debenedetti Festschrift."

Critical fluctuations in fluids and fluid mixtures yield a nonanalytic asymptotic Ising-like critical thermodynamic behavior in terms of power laws with universal exponents. In polymer solutions, the amplitudes of these power laws depend on the degree of polymerization. Nonasymptotic behavior (upon the departure from the critical point) is particularly interesting in the case of polymer solutions, where it is governed by a competition between the correlation length of the critical fluctuations and the radius of gyration of the polymer molecules. If the correlation length is the dominant length scale, Ising-like critical behavior is observed. If, however, the radius of gyration exceeds the correlation length, tricritical behavior with mean-field critical exponents is observed. The Ising-like critical region shrinks with the increase of the polymer molecular weight. In the limit of an infinite degree of polymerization, the Ising-like critical region vanishes, yielding to theta-point tricriticality., Comment: Chapter intended for "50 years of the renormalization group/Dedicated to the memory of Michael E. Fisher", edited by A. Aharony, O. Entin-Wohlman, D. Huse, and L. Radzihovsky

The separation of substances into different phases is ubiquitous in nature and important scientifically and technologically. This phenomenon may become drastically different if the species involved, whether molecules or supramolecular assemblies, interconvert. In the presence of an external force large enough to overcome energetic differences between the interconvertible species (forced interconversion), the two alternative species will be present in equal amounts, and the striking phenomenon of steady-state, restricted phase separation into mesoscales is observed. Such microphase separation is one of the simplest examples of dissipative structures in condensed matter. In this work, we investigate the formation of such mesoscale steady-state structures through Monte Carlo and Molecular Dynamics simulations of three physically distinct microscopic models of binary mixtures that exhibit both equilibrium (natural) interconversion and a nonequilibrium source of forced interconversion. We show that this source can be introduced through an internal imbalance of intermolecular forces or an external flux of energy that promotes molecular interconversion, possible manifestations of which could include the internal nonequilibrium environment of living cells or a flux of photons. The main trends and observations from the simulations are well captured by a non-equilibrium thermodynamic theory of phase transitions affected by interconversion. We show how a nonequilibrium bicontinuous microemulsion or a spatially modulated state may be generated depending on the interplay between diffusion, natural interconversion, and forced interconversion., Comment: Manuscript submitted as a contributed article to PNAS

Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid-fluid phase transition in high-pressure hydrogen between insulating and conducting high-density fluids. This transition is induced by the reversible dimerization/dissociation of the molecular and atomistic states of hydrogen. In this work, we present the first attempt to thermodynamically model the fluid-fluid phase transition in hydrogen at extreme conditions. Our predictions for the phase coexistence and the reaction equilibrium of the two alternative forms of fluid hydrogen are based on experimental data and supported by the results of simulations. {Remarkably, we find that the law of corresponding states can be utilized to construct a unified equation of state combining the available computational results for different models of hydrogen and the experimental data., Comment: Manuscript intended for JCP

We suggest a simple model to describe polyamorphism in single-component fluids using a maximum-valence approach. The model contains three types of interactions: i) atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, ii) atoms may form covalent bonds that induce association, and iii) bonded atoms attract or repel each other stronger than non-bonded atoms, thus generating liquid-liquid separation. As an example, we qualitatively compare this model with the behavior of liquid sulfur and show that condition (iii) generates a liquid-liquid phase transition in addition to the liquid-gas phase transition., Comment: Manuscript intended for PRE

Using a modified Cahn-Hilliard-Cook theory for spinodal decomposition in a binary mixture that exhibits both diffusion and interconversion dynamics, we derive the time-dependent structure factor for concentration fluctuations. We compare the theory and obtain a qualitative agreement with simulations of the temporal evolution of the order parameter and structure factor in a nonequilibrium Ising/lattice-gas hybrid model in the presence of an external source of forceful interconversion. In particular, the characteristic size of the steady-state phase domain is predicted from the lower cut-off wavenumber of the amplification factor in the generalized spinodal-decomposition theory., Comment: Intended for J. Non Cryst. Solids: X

Liquid-liquid phase separation of liquids exhibiting interconversion between alternative states has been proposed as an underlying mechanism for fluid polyamorphism, and may be of relevance to protein function and intracellular organization. However, molecular-level insight into the interplay between competing forces that can drive or restrict phase separation in interconverting fluids remains elusive. Here, we utilize an off-lattice model of enantiomers with tunable chiral interconversion and interaction properties to elucidate the physics underlying the stabilization and tunability of phase separation in fluids with interconverting states. We show that introducing an imbalance in the intermolecular forces between two enantiomers results in nonequilibrium, arrested phase separation into microdomains. We also find that in the equilibrium case, when all interaction forces are conservative, the growth of the phase domain is restricted only by system size. In this case, we observe phase amplification, in which one of the two alternative phases grows at the expense of the other. These findings provide novel insights on how the interplay between dynamics and thermodynamics defines the equilibrium and steady-state morphologies of phase transitions in fluids with interconverting molecular or supramolecular states., Comment: Intended for JCP

Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Unveiling the phase diagram of the non-interconverting binary mixture gives unprecedented insight on the phase behaviors accessible to the interconverting fluid, such as a liquid-liquid transition with a critical point, or a singularity-free scenario, exhibiting thermodynamic anomalies without polyamorphism. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with water-like anomalies., Comment: 15 pages, 11 figures

If a binary liquid mixture, composed of two alternative species with equal amounts, is quenched from a high temperature to a low temperature, below the critical point of demixing, then the mixture will phase separate through a process known as spinodal decomposition. However, if the two alternative species are allowed to interconvert, either naturally (e.g. the equilibrium interconversion of enantiomers) or forcefully (e.g. via an external source of energy or matter), then the process of phase separation may drastically change. In this case, depending on the nature of interconversion, two phenomena could be observed: either phase amplification, the growth of one phase at the expense of another stable phase, or microphase separation, the formation of nongrowing (steady-state) microphase domains. In this work, we generalize the Cahn-Hilliard theory of spinodal decomposition to include molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed theory to describe the simulation results of three atomistic models which demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Lastly, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation., Comment: Accepted for publication at JCP

A fluid composed of two molecular species may undergo phase segregation via spinodal decomposition. However, if the two molecular species can interconvert, e.g. change their chirality, then a phenomenon of phase amplification, which has not been studied so far, emerges. As a result, eventually, one phase will completely eliminate the other one. We model this phenomenon on an Ising system which relaxes to equilibrium through a hybrid of Kawasaki-diffusion and Glauber-interconversion dynamics. By introducing a probability of Glauber-interconversion dynamics, we show that the particle conservation law is broken, thus resulting in phase amplification. We characterize the speed of phase amplification through scaling laws based on the probability of Glauber dynamics, system size, and distance to the critical temperature of demixing., Comment: 6 pages, 5 figures

Materials with low electron work function are of great demand in various branches of science and technology. LaB6 is among the most effective electron-beam sources with one of the highest brightness of thermionic emission. A deep understanding of the physical mechanisms responsible for the extraordinary properties of LaB6 is required in order to optimize the parameters and design of thermionic elements for application in various electron-beam devices. Motivated by recent experiments on rare earth borides indicating a strong coupling of conduction electrons to the crystal lattice and rare earth ions, we have studied the state of electrons in the conduction band of lanthanum hexaboride by performing infrared spectroscopic, DC resistivity and Hall-effect studies of LaB6 single crystals with different ratios of 10B and 11B isotopes. We find that only a small amount of electrons in the conduction band behave as Drude-type mobile charge carriers while up to 70% of the electrons are far out of equilibrium and involved in collective oscillations of electron density coupled to vibrations of the Jahn-Teller unstable rigid boron cage and rattling modes of La-ions that are loosely bound to the lattice. We argue that exactly these non-equilibrium (hot) electrons in the conduction band determine the extraordinary low work function of thermoemission in LaB6. Our observation may guide future search for compounds with possibly lower electron work function., Comment: 15 pages, 3 figures

Based on accurate X-ray structure analysis of GdB6 over the temperature range 85-300 K it has been shown that anomalously strong charge carrier scattering in the quantum diffusion regime of charge transport in this compound arises due to the formation of (i) dynamically coupled Gd3+ dimers of about 3.3 {\AA} in size with an energy of quasi-local oscillations ~ 7 - 8 meV and (ii) dynamic charge stripes along the [001] direction of the cubic lattice. It has been revealed that anharmonic approximation is useful when analyzing the static and dynamic components of the atomic displacement parameters of gadolinium. The barrier height of double-well potential of Gd3+ ions was determined both from low-temperature heat capacity measurements and from the electron density distribution reconstructed from X-ray data., Comment: 13 pages, 5 figures

Critical fluctuations are known to induce a collapse of polymer chains in a mixed solvent upon approaching its liquid-liquid critical point, as originally predicted by Brochard and de Gennes. Recently, we have found that closer to the critical point this collapse is followed by a reswelling of the polymer coils well beyond the original dimensions, a phenomenon not predicted by the theory of Brochard and de Gennes. We submit that upon approaching the critical temperature more closely, the correlation length of the critical fluctuations inside the polymer coils can no longer further increase due to the finite size of the coils, resulting in the appearance of large critical Casimir forces that cause a significant expansion of the polymer coils. Eventually, micro-phase separation inside the coils will appear and the coils will reshrink. This entire process takes place while the bulk solution is still in the one-phase region.

We have discovered unusual behavior of polymer coils in a binary solvent (nitroethane+isooctane) near the critical temperature of demixing. The exceptionally close refractive indices of the solvent components make the critical opalescence relatively weak, thus enabling us to simultaneously observe the Brownian motion of the polymer coils and the diverging correlation length of the critical fluctuations. The polymer coils exhibit a collapse-reswelling-expansion-collapse transition upon approaching the critical temperature. While the first stage (collapse-reswelling) can be explained by the theory of Brochard and de Gennes, the subsequent expansion-collapse transition is a new unexpected phenomenon that has not been observed so far. We believe that this effect is generic and attribute it to micro-phase separation of the solvent inside the polymer coil., Comment: 6 pages, 4 figures, 24 references

"Fluid polyamorphism" is the existence of different condensed amorphous states in a single-component fluid. It is either found or predicted, usually at extreme conditions, for a broad group of very different substances, including helium, carbon, silicon, phosphorous, sulfur,tellurium, cerium, hydrogen and tin tetraiodide. This phenomenon is also hypothesized for metastable and deeply supercooled water, presumably located a few degrees below the experimental limit of homogeneous ice formation. We present a generic phenomenological approach to describe polyamorphism in a single-component fluid, which is completely independent of the molecular origin of the phenomenon. We show that fluid polyamorphism may occur either in the presence or the absence of fluid phase separation depending on the symmetry of the order parameter. In the latter case, it is associated with a second-order transition, such as in liquid helium or liquid sulfur. To specify the phenomenology, we consider a fluid with thermodynamic equilibrium between two distinct interconvertible states or molecular structures. A fundamental signature of this concept is the identification of the equilibrium fraction of molecules involved in each of these alternative states. However, the existence of the alternative structures may result in polyamorphic fluid phase separation only if mixing of these structures is not ideal. The two-state thermodynamics unifies all the debated scenarios of fluid polyamorphism in different areas of condensed-matter physics, with or without phase separation, and even goes beyond the phenomenon of polyamorphism by generically describing the anomalous properties of fluids exhibiting interconversion of alternative molecular states., Comment: 56 pages, including 39 pages of main text with 7 figures and 117 references, and 17 pages of supplemental material with 12 figures and 19 references

One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecular water models. However, existing TSEOSs were not designed to describe the negative pressure region and do not account for the stability limit of the liquid state with respect to the vapor. While experimental data on supercooled water at negative pressures may shed additional light on the source of the anomalies of water, such data are very limited. To fill this gap, we have analyzed simulation results for TIP4P/2005, one of the most accurate classical water models available. We have used recently published simulation data, and performed additional simulations, over a broad range of positive and negative pressures, from ambient temperature to deeply supercooled conditions. We show that, by explicitly incorporating the liquid-vapor spinodal into a TSEOS, we are able to match the simulation data for TIP4P/2005 with remarkable accuracy. In particular, this equation of state quantitatively reproduces the lines of extrema in density, isothermal compressibility, and isobaric heat capacity. Contrary to an explanation of the thermodynamic anomalies of water based on a "retracing spinodal", the liquid-vapor spinodal in the present TSEOS continues monotonically to lower pressures upon cooling, influencing but not giving rise to density extrema and other thermodynamic anomalies., Comment: 11 pages, 9 figures. Supplementary Materials (2 pages, 2 figures) in anc subdirectory. Changes from previous version: Corrected misprint of values of S1 and S2 in Table I. Results unchanged. Supersedes arXiv:1605.05993

One of the most promising frameworks for understanding the anomalies of cold and especially supercooled water is that of two-structure thermodynamics, in which water is viewed as a non-ideal mixture of two interconvertible local structures. The non-ideality of this mixture may give rise, at very low temperatures, to a liquid-liquid phase transition (LLPT) and a liquid-liquid critical point (LLCP), at which thermodynamic response functions diverge. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data in real water and simulation results. However, recent experiments probing supercooled water at negative pressures reveal the inadequacy of extrapolations of equations of state developed for positive pressures, and have begun to shed additional light on the source of the anomalies of supercooled water. We have analyzed simulation results for the TIP4P/2005 model over a broad range of positive and negative pressures from ambient temperature to deep supercooling. We find that by explicitly incorporating a liquid-vapor spinodal into a two-structure equation of state, we are able to match the simulation data in TIP4P/2005 with striking accuracy. In particular, our equation of state reproduces the observed lines of minima and maxima in the density, isothermal compressibility, and isobaric heat capacity. Contrary to scenarios in which a retracing spinodal accounts for the thermodynamic anomalies of water, we find that the liquid-vapor spinodal in this model continues monotonically to lower pressures as temperature is decreased, influencing but not giving rise to the locus of density maxima and other thermodynamic anomalies. We explain the behavior of TIP4P/2005 in terms of two phenomena: the competition between two local structures and a monotonic liquid-vapor spinodal., Comment: 18 pages, 8 figures. This paper has been withdrawn by the authors because it is superseded by arXiv:1611.00443

Water shows intriguing thermodynamic and dynamic anomalies in the supercooled liquid state. One possible explanation of the origin of these anomalies lies in the existence of a metastable liquid-liquid phase transition (LLPT) between two (high and low density) forms of water. While the anomalies are observed in experiments on bulk and confined water and by computer simulation studies of water-like models, the existence of a LLPT in water is still debated. Unambiguous experimental proof of the existence of a LLPT in bulk supercooled water is hampered by fast ice nucleation which is a precursor of the hypothesized LLPT. Moreover, the hypothesized LLPT, being metastable, in principle cannot exist in the thermodynamic limit (infinite size, infinite time). Therefore, computer simulations of water models are crucial for exploring the possibility of the metastable LLPT and the nature of the anomalies. In this work, we present new simulation results in the NVT ensemble for one of the most accurate classical molecular models of water, TIP4P/2005. To describe the computed properties and explore the possibility of a LLPT we have applied two-structure thermodynamics, viewing water as a non-ideal mixture of two interconvertible local structures ("states"). The results suggest the presence of a liquid-liquid critical point and a LLPT in this model for the simulated length and time scales. We have compared the behavior of TIP4P/2005 with other popular water-like models, namely mW and ST2, and with real water, all of which are well described by two-state thermodynamics. In view of the current debate involving different studies of TIP4P/2005, we discuss consequences of metastability and finite size in observing the liquid-liquid separation. We also address the relationship between the phenomenological order parameter of two-structure thermodynamics and the microscopic nature of the low-density structure., Comment: 12 pages, 8 figures New version changed to clarify simulation details and, add references, and fix typographical errors; results unchanged. Supplementary material added with simulation details

Hydrotropes are substances consisting of amphiphilic molecules that are too small to self assemble in equilibrium structures in aqueous solutions, but can form dynamic molecular clusters H bonded with water molecules. Some hydrotropes, such as low molecular weight alcohols and amines, can solubilize hydrophobic compounds in aqueous solutions at a mesoscopic scale, around 100 nm, with formation of long lived mesoscale droplets. In this work, we report on the studies of near critical and phase behavior of binary, 2,6-lutidine - H2O, and quasibinary, 2,6-lutidine - H2O - D2O, and tert-butanol - 2-butanol - H2O solutions in the presence of a solubilized hydrophobic impurity, cyclohexane. In additional to visual observation of fluid phase equilibria, two experimental techniques were used - light scattering and small - angle neutron scattering. It was found that the increase of the tert-butanol to 2-butanol ratio affects the liquid - liquid equilibria in the quasi-binary system at ambient pressure in the same way as the increase of pressure modifies the phase behavior of binary 2-butanol - H2O solutions. The correlation length of critical fluctuations near the liquid-liquid separation and the size of mesoscale droplets of solubilized cyclohexane were obtained by dynamic light scattering and by small - angle neutron scattering. It is shown that the effect of the presence of small amounts of cyclohexane on the near - critical phase behavior is twofold - the transition temperature changes towards increasing the two-phase domain, and long-lived mesoscopic inhomogeneities emerge in the macroscopically homogeneous domain. These homogeneities remain unchanged upon approach to the critical point of macroscopic phase separation and do not alter the universal nature of criticality. However, a larger amount of cyclohexane generates additional liquid-liquid phase separation at lower temperatures.