Fluid-fluid Phase Transition Research Articles

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.

On $$\varGamma $$-Convergence of a Variational Model for Lithium-Ion Batteries

A singularly perturbed phase field model used to model lithium-ion batteries including chemical and elastic effects is considered. The underlying energy is given by $$I_\epsilon [u,c ] := \int_\Omega \left( \frac{1}{\epsilon} f(c) + \epsilon\|\nabla c\|^2 + \frac{1}{\epsilon}\mathbb{C} (e(u)-ce_0) : (e(u)-ce_0)\right) dx, $$ where $f$ is a double well potential, $\mathbb{C}$ is a symmetric positive definite fourth order tensor, $c$ is the normalized lithium-ion density, and $u$ is the material displacement. The integrand contains elements close to those in energy functionals arising in both the theory of fluid-fluid and solid-solid phase transitions. For a strictly star-shaped, Lipschitz domain $\Omega \subset \mathbb{R}^2,$ it is proven that $\Gamma - \lim_{\epsilon\to 0} I_\epsilon = I_0,$ where $I_0$ is finite only for pairs $(u,c)$ such that $f(c) = 0$ and the symmetrized gradient $e(u) = ce_0$ almost everywhere. Furthermore, $I_0$ is characterized as the integral of an anisotropic interfacial energy density over sharp interfaces given by the jumpset of $c.$

A homogenization result in the gradient theory of phase transitions

A variational model in the context of the gradient theory for fluid-fluid phase transitions with small scale heterogeneities is studied. In particular, the case where the scale \varepsilon of the small homogeneities is of the same order of the scale governing the phase transition is considered. The interaction between homogenization and the phase transitions process will lead, in the limit as \varepsilon \to 0 , to an anisotropic interfacial energy.

Entropic colloidal crystallization pathways via fluid–fluid transitions and multidimensional prenucleation motifs

Complex crystallization pathways are common in protein crystallization, tetrahedrally coordinated systems, and biomineralization, where single or multiple precursors temporarily appear before the formation of the crystal. The emergence of precursors is often explained by a unique property of the system, such as short-range attraction, directional bonding, or ion association. But, structural characteristics of the prenucleation phases found in multistep crystallization remain unclear, and models are needed for testing and expanding the understanding of fluid-to-solid ordering pathways. Here, we report 3 instances of 2-step crystallization of hard-particle fluids. Crystallization in these systems proceeds via a high-density precursor fluid phase with prenucleation motifs in the form of clusters, fibers and layers, and networks, respectively. The density and diffusivity change across the fluid-fluid phase transition increases with motif dimension. We observe crystal nucleation to be catalyzed by the interface between the 2 fluid phases. The crystals that form are complex, including, notably, a crystal with 432 particles in the cubic unit cell. Our results establish the existence of complex crystallization pathways in entropic systems and reveal prenucleation motifs of various dimensions.

Fluid-fluid phase behaviour in the explicit solvent ionic model: Hard spherocylinder solvent molecules

We study a fluid-fluid phase transition of the explicit solvent model represented as a mixture of the restricted primitive model (RPM) of ionic fluid and neutral hard spherocylinders (HSC). To this end, we combine two theoretical approaches, i.e., the scale particle theory (SPT) and the associative mean spherical approximation (AMSA). Whereas the SPT is sufficient to provide a rather good description of a reference system taking into account hard-core interactions, the AMSA is known to be efficient in treating the Coulomb interactions between the ions. Alternatively, we also use the mean spherical approximation (MSA) for comparison. We restrict our attention to the HSC with aspect ratios L2/σ2 = 5 and 10, when the diameter of RPM particles is set to σ1 = σ2. We find the conditions at which the fluid-fluid phase transition is accompanied by the isotropic-nematic phase transition occurring in the solvent component. Furthermore, the effect of asphericity of solvent molecules on the fluid-fluid phase transition is studied by considering an “equivalent” mixture in which the HSC particles are replaced by hard spheres (HS) of the same volume. We discuss an importance of accounting for the association effects which appear between oppositely charged ions.

Virial coefficients, equation of state, and demixing of binary asymmetric nonadditive hard-disk mixtures

Values of the fifth virial coefficient, compressibility factors, and fluid-fluid coexistence curves of binary asymmetric nonadditive mixtures of hard disks are reported. The former correspond to a wide range of size ratios and positive nonadditivities and have been obtained through a standard Monte Carlo method for the computation of the corresponding cluster integrals. The compressibility factors as functions of density, derived from canonical Monte Carlo simulations, have been obtained for two values of the size ratio (q = 0.4 and q = 0.5), a value of the nonadditivity parameter (Δ = 0.3), and five values of the mole fraction of the species with the biggest diameter (x1 = 0.1, 0.3, 0.5, 0.7, and 0.9). Some points of the coexistence line relative to the fluid-fluid phase transition for the same values of the size ratios and nonadditivity parameter have been obtained from Gibbs ensemble Monte Carlo simulations. A comparison is made between the numerical results and those that follow from some theoretical equations of state.

Lipid Phase Control and Secondary Structure of Viral Fusion Peptides Anchored in Monoolein Membranes.

The fusion of lipid membranes involves major changes of the membrane curvatures and is mediated by fusion proteins that bind to the lipid membranes. For a better understanding of the way fusion proteins steer this process, we have studied the interaction of two different viral fusion peptides, HA2-FP and TBEV-FP, with monoolein mesophases as a function of temperature and pressure at limited hydration. The fusion peptides are derived from the influenza virus hemagglutinin fusion protein (HA2-FP) and from the tick-borne encephalitis virus envelope glycoprotein E (TBEV-FP). By using synchrotron X-ray diffraction, the changes of the monoolein phase behavior upon binding the peptides have been determined and the concomitant secondary structures of the peptides have been analyzed by FTIR spectroscopy. As main results we have found that the fusion peptides interact differently with monoolein and change the pressure and temperature dependent lipid phase behavior to different extents. However, they both destabilize the fluid lamellar phase and favor phases with negative curvature, i.e. inverse bicontinuous cubic and inverse hexagonal phases. These peptide-induced phase changes can partially be reversed by the application of high pressure, demonstrating that the promotion of negative curvature is achieved by a less dense packing of the monoolein membranes by the fusion peptides. Pressure jumps across the cubic-lamellar phase transition reveal that HA2-FP has a negligible effect on the rates of the cubic and the lamellar phase formation. Interestingly, the secondary structures of the fusion peptides appear unaffected by monoolein fluid-fluid phase transitions, suggesting that the fusion peptides are the structure dominant species in the fusion process of lipid membranes.

Fluid–fluid–solid triple point on melting curves at high temperatures

An analysis is presented of experimental data where fluid-fluid phase transitions are observed for different substances at high temperatures with triple points on melting curves. Viscosity drops point to the structural character of the transition, whereas conductivity jumps remind of both semiconductor-to-metal and plasma nature. The slope of the phase equilibrium dependencies of pressure on temperature and the consequent change of the specific volume, which follows from the Clapeyron-Clausius equation, are discussed. P(V, T) surfaces are presented and discussed for the phase transitions considered in the vicinity of the triple points. The cases of abnormal P(T) dependencies on curves of phase equilibrium are in the focus of discussion. In particular, a P(V, T) surface is presented when both fluid-fluid and melting P(T) curves are abnormal. Particular attention is paid to warm dense hydrogen and deuterium, where remarkable contradictions exist between data of different authors. The possible connection of the P(V, T) surface peculiarities with the experimental data uncertainties is outlined.

Optimization of crystal nucleation close to a metastable fluid-fluid phase transition.

The presence of a metastable fluid-fluid critical point is thought to dramatically influence the crystallization pathway, increasing the nucleation rate by many orders of magnitude over the predictions of classical nucleation theory. We use molecular dynamics simulations to study the kinetics of crystallization in the vicinity of this metastable critical point and throughout the metastable fluid-fluid phase diagram. To quantitatively understand how the fluid-fluid phase separation affects the crystal nucleation, we evaluate accurately the kinetics and reconstruct the thermodynamic free-energy landscape of crystal formation. Contrary to expectations, we find no special advantage of the proximity of the metastable critical point on the crystallization rates. However, we find that the ultrafast formation of a dense liquid phase causes the crystallization to accelerate both near the metastable critical point and almost everywhere below the fluid-fluid spinodal line. These results unveil three different scenarios for crystallization that could guide the optimization of the process in experiments

The fourth virial coefficient of a nonadditive hard-disc mixture

The fourth virial coefficient of symmetric nonadditive hard-disc mixtures is calculated over a wide range of nonadditivity. The irreducible cluster integrals were evaluated numerically using a standard Monte Carlo method. The coexistence line relative to the fluid-fluid phase transition, calculated through two equations of state built using the new virial coefficients, is compared with some numerical simulation results.

Higher-order phase transitions with line-tension effect

The behavior of energy minimizers at the boundary of the domain is of great importance in the Van de Waals-Cahn-Hilliard theory for fluid-fluid phase transitions, since it describes the effect of the container walls on the configuration of the liquid. This problem, also known as the liquid-drop problem, was studied by Modica in [Ann. Inst. Henri Poincare, Anal. non lineaire 4 (1987) 487–512], and in a different form by Alberti et al. in [Arch. Rational Mech. Anal. 144 (1998) 1–46] for a first-order perturbation model. This work shows that using a second-order perturbation Cahn-Hilliard-type model, the boundary layer is intrinsically connected with the transition layer in the interior of the domain. Precisely, considering the energies where u is a scalar density function and W and V are double-well potentials, the exact scaling law is identified in the critical regime, when .

Heat capacity anomalies along the critical isotherm in fluid-fluid phase transitions

The behavior of the isochoric heat capacity of pure fluids and the isobaric heat capacity at constant composition of binary mixtures along isothermal paths of approach to liquid-gas and liquid-liquid critical points is studied. From the complete scaling formulation of fluid-fluid criticality, explicit expressions for the critical amplitudes of the leading /Y-Y(c)/(-alpha/beta) (where Y can be the density or the mole fraction) contributions are found to reveal previously discovered features of the scaling function, whereas the nature of the most important asymmetry-related terms is characterized. Data for pure toluene and for the binary mixture nitromethane-isobutanol are described within experimental uncertainty using the /Y-Y(c)/(-alpha/beta) singularity plus a linear term. Extensive data for mixtures allow proper visualization of the topological features of the heat capacity-density-temperature surface in the critical region.

Formation of lamellar structures from spherical particles

We report disorder to lamellar transition in a system of spherically symmetric particles where the interparticle potential consists of a short-ranged attraction and a longer-ranged repulsion. The system provides a simplified model for aqueous dispersions of colloidal particles and globular proteins that may exhibit stable/metastable clusters or microscopic phases. By using a non-mean-field density functional theory, we predict that under appropriate conditions, a lamellar phase with alternating condensed and dilute layers of particles is thermodynamically more stable than a uniform disordered phase at the same temperature and molecular number density. Formation of the lamellar structure may prohibit the macroscopic fluid-fluid phase transition. At a given condition, the width of the condensed lamellar layers increases with the overall particle density but the trend is opposite for the dilute lamellar layers. A minimal lamellar periodicity is obtained when the condensed and dilute layers have approximately the same thickness.

Phase equilibria in polydisperse nonadditive hard-sphere systems

Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter Delta the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. NPT Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with Delta>0 are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich, Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter Delta > 0 is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter sigmac of the Schulz distribution, and three-phase equilibria can occur for large values of sigmac.

Reversible Phase Transition of Colloids in a Binary Liquid Solvent

We report fluid-fluid and fluid-solid phase transitions of charge-stabilized polystyrene particles suspended in a binary liquid mixture of 3-methylpyridine and water. These thermally reversible phase transitions occur in the homogeneous phase of the binary liquid mixture below the coexistence temperature of the two liquids. Close density matching of the particles and the solvent allows us to follow the phase behavior until complete coexistence of macroscopic phases with temperature as the control parameter. We use small angle x-ray scattering to characterize these phases as colloidal gas, liquid, fcc crystal, and glass.

Influence of interaction energy in fluid-fluid phase transitions on Langmuir monolayers

A pure lattice model for Langmuir monolayers is presented where only nearest neighbor interactions are considered. The flexibility of hydrophobic tails laying on the surface is taken into account but the segments above the surface are taken as upstanding rigid rods without contribution to the entropy. The numerical calculations show that to obtain more than one phase transition the flexibility of these tails has to be taken into account.

Effect of the range of attractive interactions on crystallization, metastable phase transition, and percolation in colloidal dispersions.

The equilibrium as well as nonequilibrium phase behaviors of colloidal dispersions have been investigated using statistical-mechanical theories of fluids and solids in complement with the renormalization-group (RG) theory. It is shown that the osmotic second virial coefficient at the critical point of the fluid-fluid transition varies with the range of attractions and is sensitive to specific forms of the attractive potential in contrast to a common speculation that it remains practically constant. However, for colloids with short-ranged forces, the critical temperature of the fluid-fluid phase transition is well correlated with the range of attractions in good agreement with an earlier empirical correlation based on simulation results. A comparison of the relative positions of the fluid-fluid coexistence curve, freezing, melting, and percolation lines in the phase diagram indicates that the gelation in colloidal systems has significant effects on the equilibrium phase transitions and crystallization, especially when the attractions between colloidal particles are short ranged.

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in three dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature (London) 409, 692 (2001)] that, even with no evidence of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas-low-density-liquid (LDL) critical point, and the other in a gas-high-density-liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the three-parameter space of the soft-core potential and perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram, we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.

Simple model of liquid-liquid phase transitions

In recent years, a second fluid-fluid phase transition has been reported in several materials at pressures far above the usual liquid-gas phase transition. In this paper, we introduce a new model of this behavior based on the Lennard-Jones interaction with a modification to mimic the different kinds of short-range orientational order in complex materials. We have done Monte Carlo studies of this model that clearly demonstrate the existence of a second first-order fluid-fluid phase transition between high- and low-density liquid phases.

Wetting-induced effective interaction potential between spherical particles

Using a density-functional-based interface displacement model, we determine the effective interaction potential between two spherical particles which are immersed in a homogeneous fluid such as the vapor phase of a one-component substance or the A-rich liquid phase of a binary liquid mixture composed of A and B particles. If this solvent is thermodynamically close to a first-order fluid-fluid phase transition, the spheres are covered with wetting films of the incipient bulk phase, i.e., the liquid phase or the B-rich liquid, respectively. Below a critical distance between the spheres their wetting films snap to a bridgelike configuration. We determine phase diagrams for this morphological transition, and analyze its repercussions on the effective interaction potential. Our results are accessible to various types of force microscopy and scattering experiments, and may be relevant to flocculation in colloidal suspensions.