Gas-liquid Coexistence Research Articles

Continuum Theory of Phase Separation Kinetics for Active Brownian Particles

Active Brownian particles (ABPs), when subject to purely repulsive interactions, are known to undergo activity-induced phase separation broadly resembling an equilibrium (attraction-induced) gas-liquid coexistence. Here we present an accurate continuum theory for the dynamics of phase-separating ABPs, derived by direct coarse graining, capturing leading-order density gradient terms alongside an effective bulk free energy. Such gradient terms do not obey detailed balance; yet we find coarsening dynamics closely resembling that of equilibrium phase separation. Our continuum theory is numerically compared to large-scale direct simulations of ABPs and accurately accounts for domain growth kinetics, domain topologies, and coexistence densities.

Two-patch colloidal model with re-entrant phase behaviour

We propose a second-order thermodynamic perturbation theory for a hard-sphere patchy colloidal model with two doubly bondable patches of type A and B. AB bonding results in the formation of a three-dimensional network of the particles and AA and BB bonding promotes chain formation. The theory is applied to study the phase behaviour of the model at different values of the potential model parameters. Competition between network and chain formation gives rise to a re-entrant phase behaviour with upper and lower critical points. The model with an additional van der Waals type of interaction may have a re-entrant phase diagram with three critical points and two separate regions of the liquid-gas phase coexistence. We analyze our results in terms of the fractions of the particles in different bonding states and conclude that re-entrant phase coexistence can be seen as a coexistence between a gas phase rich in chain ends and a liquid phase rich in branch points.

Phase behavior and critical activated dynamics of limited-valence DNA nanostars

Colloidal particles with directional interactions are key in the realization of new colloidal materials with possibly unconventional phase behaviors. Here we exploit DNA self-assembly to produce bulk quantities of "DNA stars" with three or four sticky terminals, mimicking molecules with controlled limited valence. Solutions of such molecules exhibit a consolution curve with an upper critical point, whose temperature and concentration decrease with the valence. Upon approaching the critical point from high temperature, the intensity of the scattered light diverges with a power law, whereas the intensity time autocorrelation functions show a surprising two-step relaxation, somehow reminiscent of glassy materials. The slow relaxation time exhibits an Arrhenius behavior with no signs of criticality, demonstrating a unique scenario where the critical slowing down of the concentration fluctuations is subordinate to the large lifetime of the DNA bonds, with relevant analogies to critical dynamics in polymer solutions. The combination of equilibrium and dynamic behavior of DNA nanostars demonstrates the potential of DNA molecules in diversifying the pathways toward collective properties and self-assembled materials, beyond the range of phenomena accessible with ordinary molecular fluids.

Predicting crystals of Janus colloids

We present a numerical study on the phase diagram for a simple model of Janus colloids, including ordered and disordered structures. Using a range of techniques, we generate a set of crystal structures and investigate their relative stability field in the pressure-temperature and temperature-density planes by means of free-energy calculations and thermodynamic integration schemes. We find that despite the Janus colloids' simple architecture, they form stable crystal structures with complicated bond-topologies on an underlying face-centered-cubic or hexagonal-close-packed lattice. In addition, we find a phase consisting of wrinkled bilayer sheets, competing with both the fluid and the crystal phases. We detect a metastable gas-liquid coexistence which displays a micellization-driven re-entrant behavior.

Thermodynamic status of random close packing

An amorphous ground state reminiscent of random close packing (RCP) of spheres terminates a liquid phase that spans all temperatures. On the Gibbs density surface, the liquid phase has bounded by a supercritical percolation line, two-phase liquid–gas coexistence line, and below the triple point, the metastable liquid branch terminating at T = 0 K with the RCP state. There is no “continuity of gas and liquid phases”; they are separated by a supercritical mesophase bounded by percolation transitions. As a consequence, the gas phase cannot be a starting point for liquid-state theory. RCP has a thermodynamic status. For square-well model fluids, evidence from computer simulations shows that the amorphous ground state is the same RCP state of the hard-sphere model. The RCP limiting density state of the hard-sphere fluid, with its reproducible and well-characterized structure, can be obtained by well-defined irreversible and reversible processes which establish a thermodynamic status. Empirical results, within margins of numerical uncertainty, are that the amorphous ground state density corresponds to a packing fraction = 0.6366 ± 0.0005 (Buffon’s constant 2/π) and a residual entropy per sphere ΔS(0) ∼ kB (Boltzmann constant). We conclude that RCP of spheres is a well-defined state with a thermodynamic status, and a central role in the description of liquid phase equilibria, as originally suggested, 50 years ago, by J.D. Bernal. We postulate that the metastable RCP state is the starting point for a modern theory of the liquid state.

Gibbs Density Surface of Fluid Argon: Revised Critical Parameters

A phase diagram of simple fluids, based upon percolation transition loci determined from literature experimental density-pressure isotherms of argon, shows three fluid phases. The liquid phase spans all temperatures from a metastable amorphous ground state to supercritical temperatures. There is a supercritical mesophase of a colloidal nature between two percolation transition loci, PA and PB, that bound the existences of liquid and gas phases, respectively. There is no ‘critical point’ on the Gibbs density surface. When two percolation transitions have the same pressure, i.e., on intersection of the loci in the \(p\)–\(T\) plane, an equilibrium ‘line of critical states’ is thermodynamically defined. This description of criticality yields slightly different values of critical parameters than those hitherto obtained by interpolation of experimental \(p\)–\(\rho \)–\(T\) data from the coexistence region. Revised values of the critical temperature (\(T_\mathrm{c})\) and critical pressure (\(p_\mathrm{c})\) of argon can be obtained from the original high precision thermodynamic measurements for fluid argon, using only data from one-phase supercritical isotherms. Values of coexisting densities at \(T_\mathrm{c}\) and the density loci of the percolation transitions that bound the existence of supercritical gas and liquid phases for \(T>T_\mathrm{c}\) are also reported. Percolation loci, for \(T<T_\mathrm{c}\), extend into the gas–liquid coexistence region to become the spinodal lines that limit the existence of metastable gas and liquid phases.

Relationship between local molecular field theory and density functional theory for non-uniform liquids

The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical density functional theory (DFT). We show that the general LMF equation for the effective reference potential φ(R)(r) follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere reference fluid we determine φ(R)(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density "gas" layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non-DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one-dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.

Structure and phase behavior of colloidal dumbbells with tunable attractive interactions

We investigate thermodynamic and structural properties of colloidal dumbbells in the framework provided by the Reference Interaction Site Model (RISM) theory of molecular fluids and Monte Carlo simulations. We consider two different models: in the first one we set identical square-well attractions on the two tangent spheres constituting the molecule (SW-SW model); in the second scheme, one of the square-well interactions is switched off (HS-SW model). Appreciable differences emerge between the physical properties of the two models. Specifically, the k → 0 behavior of SW-SW structure factors S(k) points to the presence of a gas-liquid coexistence, as confirmed by subsequent fluid phase equilibria calculations. Conversely, the HS-SW S(k) develops a low-k peak, signaling the presence of aggregates; such a process destabilizes the gas-liquid phase separation, promoting at low temperatures the formation of a cluster phase, whose structure depends on the system density. We further investigate such differences by studying the phase behavior of a series of intermediate models, obtained from the original SW-SW by progressively reducing the depth of one square-well interaction. RISM structural predictions positively reproduce the simulation data, including the rise of S(k → 0) in the SW-SW model and the low-k peak in the HS-SW structure factor. As for the phase behavior, RISM agrees with Monte Carlo simulations in predicting a gas-liquid coexistence for the SW-SW model (though the critical parameters appear overestimated by the theory) and its progressive disappearance when moving toward the HS-SW model.

Effect of controlled corrugation on capillary condensation of colloid–polymer mixtures

We investigate with Monte Carlo computer simulations the capillary phase behaviour of model colloid–polymer mixtures confined between a flat wall and a corrugated wall. The corrugation is modelled via a sine wave as a function of one of the in-plane coordinates leading to a depletion attraction between colloids and the corrugated wall that is curvature dependent. We find that for an increased amplitude of corrugation the region of the phase diagram where capillary condensation occurs becomes larger. We derive a Kelvin equation for this system and compare its predictions to the simulation results. We find good agreement between the theory and simulation indicating that the primary reason for the stronger capillary condensation is an increased contact area between the fluid and the corrugated substrate. On the other hand, the colloid adsorption curves at colloid gas–liquid coexistence show that the increased area is not solely responsible for the stronger capillary condensation. Additionally, we analyse the dimensional crossover from a quasi-2D to a quasi-1D system and find that the transition is characterised by the appearance of a metastable phase.

Phase behavior and structure of a fluid confined between competing (solvophobic and solvophilic) walls

We consider a model fluid with long-range r(-6) (dispersion) interparticle potentials confined between competing parallel walls. One wall is solvophilic and would be completely wet at bulk liquid-gas coexistence μ(co)(-), whereas the other is solvophobic and would be completely dry at μ=μ(co)(+). When the wall separation L is large and the system is below the bulk critical temperature T(C) and close to bulk liquid-gas coexistence, a delocalized interface or soft-mode phase forms with a liquid-gas interface near the center of the slit; this interacts with the walls via the power-law tails of the interparticle potentials. We use a coarse-grained effective Hamiltonian approach to derive explicit scaling expressions for the Gibbs adsorption Γ, the surface tension γ, the solvation force f(s), and the total susceptibility χ. These quantities depend on the dimensionless scaling variable (L/σ)(3)βδμ, where β=(k(B)T)(-1), σ is the diameter of the fluid particles and δμ=μ-μ(co) is the chemical potential deviation from bulk coexistence. Using a nonlocal density functional theory, we calculate density profiles for the asymmetrically confined fluid at different chemical potentials and for sufficiently large L confirm the scaling predictions for the four thermodynamic quantities. Since the upper critical dimension for complete wetting with power-law potentials is less than 3, we argue that our (mean-field) scaling predictions should remain valid in treatments that incorporate the effects of interfacial fluctuations. As the wall separation L is decreased at μ(co), we predict a capillary evaporation transition from the delocalized interface phase to a dilute gas state with just a thin adsorbed film of liquidlike density next to the solvophilic wall. This transition is closely connected to the first-order prewetting transition that occurs at the solvophilic wall in the semi-infinite system. We compare the phase diagram for the competing walls system with the phase diagrams for the fluid confined between identical solvophilic and identical solvophobic walls. Comparisons are also made with earlier studies of asymmetric confinement for systems with short-range forces.

Properties of patchy colloidal particles close to a surface: A Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheim's first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime.

Chiral thermodynamics of nuclear matter

The free energy and the equation of state of isospin-asymmetric nuclear matter are calculated at finite temperature up to three loop order in the framework of in-medium chiral perturbation theory, systematically incorporating one- and two-pion exchange dynamics to this order. Effects from the two-pion exchange with explicit {\Delta}-isobar excitation are included, as well as three-body forces. We construct the phase diagram of nuclear matter for different proton fractions x_p and investigate the dependence of nuclear matter properties on the isospin-asymmetry. A detailed study of the liquid-gas phase transition is performed. For isospin-symmetric nuclear matter we find a critical temperature of 15.1 MeV; as the isospin-asymmetry is increased, the liquid-gas coexistence region decreases until it disappears at x_p \approx 0.05, while nuclear matter becomes unbound at x_p \approx 0.12. The quadratic expansion of the free energy in the asymmetry parameter {\delta} is a good approximation at low temperature even for large {\delta}. An estimate of chiral four-body correlations in nuclear and neutron matter is also performed and the corrections from such four-body interactions are found to be small.

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: Theory and experiments

Salt, glycerol, and dimethyl sulfoxide (DMSO) are used to modify the properties of protein solutions. We experimentally determined the effect of these additives on the phase behavior of lysozyme solutions. Upon the addition of glycerol and DMSO, the fluid-solid transition and the gas-liquid coexistence curve (binodal) shift to lower temperatures and the gap between them increases. The experimentally observed trends are consistent with our theoretical predictions based on the thermodynamic perturbation theory and the Derjaguin-Landau-Verwey-Overbeek model for the lysozyme-lysozyme pair interactions. The values of the parameters describing the interactions, namely the refractive indices, dielectric constants, Hamaker constant and cut-off length, are extracted from literature or are experimentally determined by independent experiments, including static light scattering, to determine the second virial coefficient. We observe that both, glycerol and DMSO, render the potential more repulsive, while sodium chloride reduces the repulsion.

1019 気液固混相反応に用いる触媒充填型ガラス製マイクロ流路デバイスの開発(OS8-2 オーガナイズドセッション《マイクロマシンとG-MEMS/N-MEMS》)

Hydrogen peroxide (H_2O_2) is a chemical which has a wide variety of applications. The direct synthesis of hydrogen peroxide from hydrogen and oxygen gas is a potential process which does not require complicated operations and much energy, moreover, the commercialization of the process has been strongly desired. Before this study, we have designed and fabricated a glass micro-channel reactor for the direct synthesis of hydrogen peroxide. Then in order to determine the flow of calm region, the climacteric region and the instability region when gas-liquid coexist on catalyst packed-bed, we observed the flow of gas-liquid (N_2-H_2O) coexistence in fabricated reactor (1 channel). Furthermore, the pressure drop of gas-liquid on catalytic packed-bed was measured.

Oscillatory shear-induced 3D crystalline order in colloidal hard-sphere fluids

We investigate with Monte Carlo computer simulations the capillary phase behaviour of model colloid-polymer mixtures confined between a flat wall and a corrugated wall. The corrugation is modelled via a sine wave as a function of one of the in-plane coordinates leading to a depletion attraction between colloids and the corrugated wall that is curvature dependent. We find that for increased amplitude of corrugation the region of the phase diagram where capillary condensation occurs becomes larger. We derive a Kelvin equation for this system and compare its predictions to the simulation results. We find good agreement between theory and simulation indicating that the primary reason for the stronger capillary condensation is an increased contact area between the fluid and the corrugated substrate. On the other hand, the colloid adsorption curves at colloid gas-liquid coexistence show that the increased area is not solely responsible for the stronger capillary condensation. Additionally, we analyse the dimensional crossover from a quasi-2D to a quasi-1D system and find that the transition is characterised by the appearance of a metastable phase.

No Evidence of Gas-Liquid Coexistence in Dipolar Hard Spheres

We report accurate calculations of the particle density of states in the dipolar hard-sphere fluid. Implementing efficient and tailored Monte Carlo algorithms, we are able to explore, in equilibrium, the low temperature region where a phase separation between a dilute gas of chain ends and a high-density liquid of chain junctions has been predicted to occur. Our data clearly show that the density of states remains always single peaked, definitively excluding the possibility of critical phenomena in the investigated temperature and density region. The analysis of the low temperature configurations shows that at low densities particles preferentially self-assemble into closed rings, strongly suppressing the chain ends concentration.

Third-order gas-liquid phase transition and the nature of Andrews critical point

The main objective of this article is to study the nature of the Andrews critical point in the gas-liquid transition in a physical-vapor transport (PVT) system. A dynamical model, consistent with the van der Waals equation near the Andrews critical point, is derived. With this model, we deduce two physical parameters, which interact exactly at the Andrews critical point, and which dictate the dynamic transition behavior near the Andrews critical point. In particular, it is shown that 1) the gas-liquid co-existence curve can be extended beyond the Andrews critical point, and 2) the transition is first order before the critical point, second-order at the critical point, and third order beyond the Andrews critical point. This clearly explains why it is hard to observe the gas-liquid phase transition beyond the Andrews critical point. Furthermore, the analysis leads naturally the introduction of a general asymmetry principle of fluctuations and the preferred transition mechanism for a thermodynamic system. The theoretical results derived in this article are in agreement with the experimental results obtained in (K. Nishikawa and T. Morita, Fluid behavior at supercritical states studied by small-angle X-ray scattering, Journal of Supercritical Fluid, 13 (1998), pp. 143-148). Also, the derived second-order transition at the critical point is consistent with the result obtained in (M. Fisher, Specific heat of a gas near the critical point, Physical Review, 136:6A (1964), pp. A1599-A1604).

Thermodynamics and diffusion in size-symmetric and asymmetric dense electrolytes

MD simulation results for model size-symmetric and asymmetric electrolytes at high densities and temperatures (well outside the liquid-gas coexistence region) are generated and analyzed focusing on thermodynamic and diffusion properties. An extension of the mean spherical approximation for electrolytes originally derived for charged hard sphere fluids is adapted to these systems by exploiting the separation of short range and Coulomb interaction contributions intrinsic to these theoretical models and is found to perform well for predicting equation of state quantities. The diffusion coefficients of these electrolytes can also be reasonably well predicted using entropy scaling ideas suitably adapted to charged systems and mixtures. Thus, this approach may provide an avenue for studying dense electrolytes or complex molecular systems containing charged species at high pressures and temperatures.

Gas-liquid phase coexistence and finite-size effects in a two-dimensional Lennard-Jones system

The gas-liquid phase coexistence in a two-dimensional Lennard-Jones system is investigated using Maxwell construction method together with molecular dynamics simulations. The results of phase coexistence in different truncations of the potential are compared with data obtained from the literature, and the corresponding critical properties calculated. The crossover from Ising-like to mean field behavior is observed and confirmed as the temperature approaches the critical point from below. Performing simulations on systems with different sizes, we find that a finite size effect is more significant than those shown in most of the previous results, and a lower critical temperature is obtained when the full extent of this finite size effect is considered.

Probing local structure of sub and supercritical CO 2 by using two-dimensional Raman correlation spectroscopy

Using two-dimensional correlation spectroscopy and curve fitting procedure, we analyzed the hypothesis that each of the two Raman Fermi dyad modes of CO 2 may be resolved in two contributions. The contribution to the highest frequency side of each vibration dyad mode of CO 2 is associated with molecules experiencing a low local density and the contribution to the lowest frequency side is associated with molecules experiencing a high local density. The Raman spectra were recorded along the liquid–gas coexistence curve of CO 2 in the temperature range between 250 K and 303 K, and along the critical isochore between 306 K and 320 K. The two-dimensional synchronous and asynchronous contour maps obtained by processing the dynamic spectra revealed that these two contributions undergo band shift, band width changes and intensity variation. Particularly, it was shown that the temperature affects in an asymmetric way the high and low frequency sides of the Fermi dyad centered at 1385 cm − 1 . The Fermi dyads were also decomposed into two Lorentzian components. The effect of temperature on the position, the width and the intensity of each of these components was quantified. The results show a systematic red shift of the two Fermi dyads along the coexistence curve and almost no dependence along the critical isochore. More interestingly, in the case of the Fermi dyad centered at 1280 cm − 1 , the width of these two contributions increases along the coexistence curve and remains almost constant along the critical isochore. This behavior was traced back to the increase of the heterogeneous distributions of CO 2 molecules and indicates that there are more different environment of individual CO 2 molecules when approaching the critical temperature. Finally, our results demonstrate the complementarities between two-dimensional spectroscopy and curve fitting procedure in order to analyze the Raman Fermi dyads and to characterize the changes in the local structure of sub and supercritical CO 2.