Interfacial Properties of Fluids Exhibiting Liquid Polyamorphism and Water-Like Anomalies.

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. 2021, 127, 185701] 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.

Chemically Fueled Dissipative Cross-Linking of Protein Hydrogels Mediated by Protein Unfolding.

Cells assemble dynamic protein-based nanostructures far from equilibrium, such as microtubules, in a process referred to as dissipative assembly. Synthetic analogues have utilized chemical fuels and reaction networks to form transient hydrogels and molecular assemblies from small molecule or synthetic polymer building blocks. Here, we demonstrate dissipative cross-linking of transient protein hydrogels using a redox cycle, which exhibit protein unfolding-dependent lifetimes and mechanical properties. Fast oxidation of cysteine groups on bovine serum albumin by hydrogen peroxide, the chemical fuel, formed transient hydrogels with disulfide bond cross-links that degraded over hours by a slow reductive back reaction. Interestingly, despite increased cross-linking, the hydrogel lifetime decreased as a function of increasing denaturant concentration. Experiments showed that the solvent-accessible cysteine concentration increased with increasing denaturant concentration due to unfolding of secondary structures. The increased cysteine concentration consumed more fuel, which led to less direction oxidation of the reducing agent and affected a shorter hydrogel lifetime. Increased hydrogel stiffness, disulfide cross-linking density, and decreased oxidation of redox-sensitive fluorescent probes at a high denaturant concentration provided evidence supporting the unveiling of additional cysteine cross-linking sites and more rapid consumption of hydrogen peroxide at higher denaturant concentrations. Taken together, the results indicate that the protein secondary structure mediated the transient hydrogel lifetime and mechanical properties by mediating the redox reactions, a feature unique to biomacromolecules that exhibit a higher order structure. While prior works have focused on the effects of the fuel concentration on dissipative assembly of non-biological molecules, this work demonstrates that the protein structure, even in nearly fully denatured proteins, can exert similar control over reaction kinetics, lifetime, and resulting mechanical properties of transient hydrogels.

Formation of dissipative structures in microscopic models of mixtures with species interconversion.

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 nonequilibrium 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.

Thermodynamic modeling of fluid polyamorphism in hydrogen at extreme conditions.

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 (FFPT) 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 FFPT 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.

Modeling fluid polyamorphism through a maximum-valence approach.

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) atoms with maximal valence attract or repel each other stronger than other 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.

Phase transitions affected by natural and forceful molecular interconversion.

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 phenomenologically generalize the Cahn-Hilliard theory of spinodal decomposition to include the molecular interconversion of species and describe the physical properties of systems undergoing either phase amplification or microphase separation. We apply the developed phenomenology to accurately describe the simulation results of three atomistic models that demonstrate phase amplification and/or microphase separation. We also discuss the application of our approach to phase transitions in polyamorphic liquids. Finally, we describe the effects of fluctuations of the order parameter in the critical region on phase amplification and microphase separation.

Interconversion-controlled liquid-liquid phase separation in a molecular chiral model.

Liquid-liquid phase separation of fluids exhibiting interconversion between alternative states has been proposed as an underlying mechanism for fluid polyamorphism and may be of relevance to the 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 the 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.

Dataset for the interfacial tension and phase properties of the ternary system water - 2-butoxyethanol - toluene.

Two-phase samples containing water, 2-butoxyethanol, and toluene in the different mass ratios were gravimetrically prepared in the jacketed cells at T=293.15 K and p=0.100 MPa and equilibrated for 24 h. The samples were volumetrically titrated until homogeneous. Then new samples were prepared in the two-phase region with compositions in the immediate proximity to the expected separation boundary and titrated until homogeneous. The critical point was located, keeping the phase ratio of 1:1 during the titration. The density of homogeneous samples obtained during titration was measured using the density meter. These data were used to construct an interpolation of the density along the separation boundary. New two-phase samples were prepared; the interfacial tension, density, and viscosity were measured. Thus, interfacial tension isotherm and viscosity isotherm were obtained using density interpolation to determine the composition of the equilibrated phases. The obtained data can be used to prepare the two-phase samples with desired properties, design the oil-water separation processes, and develop new oil spill dispersants containing 2-butoxyethanol. This article is a co-submission with a paper [1].

Minimal Microscopic Model for Liquid Polyamorphism and Waterlike Anomalies.

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 noninterconverting 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 waterlike anomalies.

Phase amplification in spinodal decomposition of immiscible fluids with interconversion of species.

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 to our best knowledge, 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.

Effects of Protein Unfolding on Aggregation and Gelation in Lysozyme Solutions.

In this work, we investigate the role of folding/unfolding equilibrium in protein aggregation and formation of a gel network. Near the neutral pH and at a low buffer ionic strength, the formation of the gel network around unfolding conditions prevents investigations of protein aggregation. In this study, by deploying the fact that in lysozyme solutions the time of folding/unfolding is much shorter than the characteristic time of gelation, we have prevented gelation by rapidly heating the solution up to the unfolding temperature (~80 °C) for a short time (~30 min.) followed by fast cooling to the room temperature. Dynamic light scattering measurements show that if the gelation is prevented, nanosized irreversible aggregates (about 10-15 nm radius) form over a time scale of 10 days. These small aggregates persist and aggregate further into larger aggregates over several weeks. If gelation is not prevented, the nanosized aggregates become the building blocks for the gel network and define its mesh length scale. These results support our previously published conclusion on the nature of mesoscopic aggregates commonly observed in solutions of lysozyme, namely that aggregates do not form from lysozyme monomers in their native folded state. Only with the emergence of a small fraction of unfolded proteins molecules will the aggregates start to appear and grow.

Generic Nature of Interfacial Phenomena in Solutions of Nonionic Hydrotropes.

Nonionic hydrotropes (low-molecular-weight amphiphiles) demonstrate striking dual actions in bulk solutions and interfaces, exhibiting both surfactant-like and co-solvent properties. We report on peculiar, strongly affected by this duality, liquid-liquid and air-liquid-liquid interfacial behavior in aqueous ternary systems, containing hydrotropes and hydrocarbons, in a broad range of compositions and at various temperatures. Phase diagrams of the studied systems, containing tertiary butanol (TBA), as a hydrotrope, are of Type 1: the hydrotrope, at the experimental conditions, is completely miscible with water and with all investigated hydrocarbons [cyclohexane (CHX), toluene (TOL), and n-decane (DEC)], whereas the ternary mixtures exhibit liquid-liquid phase separation terminated at corresponding critical points. The shape and location of the phase separation boundary are only weakly dependent on temperature and the hydrocarbon's nature; however, the critical point in the water-TBA-DEC system is significantly shifted toward a higher TBA concentration. For the experimentally studied systems and for available data reported in the literature, we confirmed an apparently generic (for nonionic hydrotropes) phenomenon of a dual action at water-oil interfaces (earlier found in water-TBA-CHX [J. Phys. Chem. C 2017, 121, 16423]): at low concentrations, hydrotropes saturate the water-oil interface like a surfactant, whereas at higher concentrations they act as co-solvents, resulting in vanishing interfacial tension at the liquid-liquid critical point. We suggest a universal crossover function that accurately interpolates the two theoretically based limits of interfacial behavior. This crossover function also accounts for earlier deviations from Langmuir-von Szyszkowski limiting behavior in the water-TBA-DEC system, caused by lower solubility (relative to other studied hydrocarbons) of DEC in water. An intriguing correlation between the dual action of hydrotropes at the water-oil interface and the behavior of the liquid-air interfaces is also discussed.

Thermodynamics of supercooled and stretched water: Unifying two-structure description and liquid-vapor spinodal.

We have applied a two-structure approach to the description of the thermodynamic properties of supercooled and stretched water, metastable toward vapor, ice, or both, by incorporating the stability limit of liquid with respect to vapor at negative pressures. In addition to the properties of water considered in previous studies, we include new data recently obtained in deeply supercooled and stretched regions. Our model reproduces the experimentally observed anomalies in metastable water up to 400 MPa and down to -140 MPa, and can provide a physically based extrapolation in regions where no measurements are available yet. Moreover, we are able to elucidate the thermodynamic nature of the alternative "states" of liquid water, namely, high-temperature denser water (state A) and "mother-of-ice" lighter water (state B). Based on the internal consistency of the described anomalies and new data on the isothermal compressibility, we exclude the critical-point-free scenario in which the first-order liquid-liquid transition line would continue into the stretched liquid state (doubly metastable) crossing the vapor-liquid spinodal. A "singularity-free" scenario remains an option for explaining supercooled water's anomalies within the framework of two-state thermodynamics; however, the extreme case of the singularity-free scenario, ideal mixing of A and B, seems improbable. We have also clarified the concept of fast interconversion of alternative states in supercooled water as a phenomenological representation of distribution of short-ranged local structures.

Pattern of property extrema in supercooled and stretched water models and a new correlation for predicting the stability limit of the liquid state.

Water exhibits anomalous behavior in its supercooled region. A widely invoked hypothesis to explain supercooled water's thermodynamic anomalies is the existence of a metastable liquid-liquid transition terminating at a critical point. In this work, we analyze previously published and new simulation results for three commonly used molecular water models (ST2, TIP4P/2005, and TIP5P) that support the existence of the metastable liquid-liquid transition. We demonstrate that a corresponding-states-like rescaling of pressure and temperature results in a significant degree of universality in the pattern of extrema loci of the density, isothermal compressibility, and isobaric heat capacity. We also report, for the first time, an intriguing correlation between the location of the liquid-liquid critical point, the rescaled locus of density extrema, and the stability limit of the liquid state with respect to the vapor. A similar correlation is observed for two theoretical models that also exhibit a second (liquid-liquid) critical point, namely, the van der Waals and lattice-gas "two-structure" models. This new correlation is used to explore the stability limit of the liquid state in simultaneously supercooled and stretched water.

Unusual Transformation of Polymer Coils in a Mixed Solvent Close to the Critical Point.

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-reshrinking transition upon approaching the critical temperature. While the first stage (collapse) can be explained by the theory of Brochard and de Gennes, the subsequent expansion-reshrinking transition is a new unexpected phenomenon that has not been observed so far. We believe that this effect is generic and attribute it to microphase separation of the solvent inside the polymer coil.

Mesoscopic Diffusion of Poly(ethylene oxide) in Pure and Mixed Solvents.

We present results from an experimental dynamic light-scattering study of poly(ethylene oxide) (PEO) in both a pure solvent (water) and a mixed solvent (tert-butanol + water). The concentration dependence of the diffusive relaxation of the PEO molecules is found to be typical of polymers in a good solvent. However, the mesoscopic diffusive behavior of PEO in the mixed solvent is very different, indicating an initial collapse and subsequent reswelling of PEO caused by co-nonsolvency. Furthermore, in the solutions of PEO with very large molecular weights, we found additional hydrodynamic modes indicating the presence of PEO clusters and aggregates similar to those found by some other investigators.

Two-structure thermodynamics for the TIP4P/2005 model of water covering supercooled and deeply stretched regions.

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.

Two-state thermodynamics and the possibility of a liquid-liquid phase transition in supercooled TIP4P/2005 water.

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 different 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 are consistent with the existence of 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.