Predict Phase Separation Research Articles

Towards a thermodynamics of active matter

Self-propulsion allows living systems to display self-organization and unusual phase behavior. Unlike passive systems in thermal equilibrium, active matter systems are not constrained by conventional thermodynamic laws. A question arises, however, as to what extent, if any, can concepts from classical thermodynamics be applied to nonequilibrium systems like active matter. Here we use the new swim pressure perspective to develop a simple theory for predicting phase separation in active matter. Using purely mechanical arguments we generate a phase diagram with a spinodal and critical point, and define a nonequilibrium chemical potential to interpret the "binodal." We provide a generalization of thermodynamic concepts like the free energy and temperature for nonequilibrium active systems. Our theory agrees with existing simulation data both qualitatively and quantitatively and may provide a framework for understanding and predicting the behavior of nonequilibrium active systems.

Thermodynamic study of the Ge–Mn–Si system

Among the potential materials for thermoelectric applications, higher manganese silicides (HMS) MnSix (with x around 1.75) exhibit interesting figures-of-merit at intermediate temperatures (573–873K). Moreover it appears that the figure-of-merit can be improved by germanium doping. The optimization of the elaboration of such alloys needs the knowledge of the ternary Ge–Mn–Si system.The solid–solid equilibrium in the ternary system seems to be highly driven by the D88 phase an isostructural form of Mn5Si3 and Mn5Ge3. However, the existence of a complete solid solution between these two compounds is not clearly established in the literature. First principles calculations are performed to clarify the mixing enthalpies in this potential solid solution. The predicted phase separation at low temperature is then experimentally confirmed by metallographic examinations on 3 annealed samples.On the basis of these new data, a thermodynamic description of the ternary system is performed using the Calphad method.

Scalar φ4 field theory for active-particle phase separation

Recent theories predict phase separation among orientationally disordered active particles whose propulsion speed decreases rapidly enough with density. Coarse-grained models of this process show time-reversal symmetry (detailed balance) to be restored for uniform states, but broken by gradient terms; hence, detailed-balance violation is strongly coupled to interfacial phenomena. To explore the subtle generic physics resulting from such coupling, we here introduce 'Active Model B'. This is a scalar φ(4) field theory (or phase-field model) that minimally violates detailed balance via a leading-order square-gradient term. We find that this additional term has modest effects on coarsening dynamics, but alters the static phase diagram by creating a jump in (thermodynamic) pressure across flat interfaces. Both results are surprising, since interfacial phenomena are always strongly implicated in coarsening dynamics but are, in detailed-balance systems, irrelevant for phase equilibria.

Phase Separation Dynamics in Isotropic Ion-Intercalation Particles

Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase transformations coupled to ion-intercalation reactions. Using the recently developed Cahn--Hilliard reaction (CHR) theory, we investigate a simple mathematical model of ion intercalation in a spherical solid nanoparticle, which predicts transitions from solid-solution radial diffusion to two-phase shrinking-core dynamics. This general approach extends previous lithium-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler--Volmer kinetics, formulated in terms of diffusional chemical potentials, and the model consistently links the evolving concentration profile to the battery voltage. We examine sources of charge/discharge asymmetry, such as asymmetric charge transfer and surface “wetting" by ions within the solid, which can lead to three distinct phase regions. In order to solve the fourth-order nonlinear CHR initial-boundary-value problem, a control-volume discretization is developed in spherical coordinates. The basic physics are illustrated by simulating many representative cases, including a simple model of the popular cathode material, lithium iron phosphate (neglecting crystal anisotropy and coherency strain). Analytical approximations are also derived for the voltage plateau as a function of the applied current.

The Effect of Membrane-To-Domain Thickness Mismatch in Phase Separation Ternary Lipid Systems as a Function of Vesicle Size

Cellular membranes are no longer viewed as a homogeneous mix of lipids and proteins, but rather as having distinct lipid domains, so-called “rafts”, which are key for many biological processes. Much work devoted to understanding the actual mechanisms that drives lateral organization in cell membranes has been done on model membrane systems. This approach has given great insight into the formation of lipid rafts because in simple ternary mixtures with a saturated lipid, an unsaturated lipid and cholesterol, a region of liquid-liquid coexistence was found, with one of the liquid phases rich in cholesterol and saturated lipids, the finger-print of rafts. However, there is still no clear understanding of the molecular parameters that drives phase separation. Recently a new curvature hypothesis proposed a correlation between composition, leaflet coupling and emulsion-like induced curvature to predict phase separation and the formation of domains. To explore these ideas, we recently studied the phase behavior of well-researched phase separating ternary mixtures: dDPPC-DOPC-Cholesterol (1:1:1) and dDMPC-DOPC-Cholesterol (1:1:1), in 30nm vesicles using Small Angle Neutron Scattering. dDMPC is a 14-carbon long lipid while dDPPC is 16-carbon long lipid. As temperature was lowered, the system with dDPPC showed excess scattering, whereas the system with dDMPC showed no scattering even below its melting temperature. These results are interesting when compared to the previously established work where both systems show phase separation in GUVs as seen by fluorescent microscopy. Phase separation behavior differences as a result of variations to the tail length of the saturated lipids in our vesicles with high curvature gives insight into the role of local curvature (emulsion-like effects) at the domain-membrane interface.

Free-radical polymerization induced macrophase separation in poly(methyl methacrylate)/dimethacrylate blends: Experiment and modeling

This work presents the analysis of a polymerization-induced macrophase separation taking place during free-radical copolymerization of styrene and dimethacrylate in the presence of poly(methyl methacrylate) (PMMA) as a modifier. The PMMA does not participate in the polymerization but induces phase separation in the course of the reaction. An experimental study based on real-time static light scattering measurements with the aim of monitoring the phase behavior during the isothermal copolymerization is firstly presented. Then, an original and innovative contribution is made by modeling the evolution of the unstable region of the phase diagram as a function of conversion and by predicting phase separation in spinodal condition. The analysis is performed using an expression for the free energy of a reactive network-forming mixture based on the Flory–Rehner lattice model for swollen gels. The accuracy of the proposed model is verified by the good agreement found between its predictions and the experimental results.

Cahn-Hilliard Reaction Model for Isotropic Li-ion Battery Particles

ABSTRACTUsing the recently developed Cahn-Hilliard reaction (CHR) theory, we present a simple mathematical model of the transition from solid-solution radial diffusion to two-phase shrinking-core dynamics during ion intercalation in a spherical solid particle. This general approach extends previous Li-ion battery models, which either neglect phase separation or postulate a spherical shrinking-core phase boundary under all conditions, by predicting phase separation only under appropriate circumstances. The effect of the applied current is captured by generalized Butler-Volmer kinetics, formulated in terms of the diffusional chemical potential in the CHR theory. We also consider the effect of surface wetting or de-wetting by intercalated ions, which can lead to shrinking core phenomena with three distinct phase regions. The basic physics are illustrated by different cases, including a simple model of lithium iron phosphate (neglecting crystal anisotropy and coherency strain).

Effect of Polymer Compatibility on the Binder Migration during Spray Drying and Compaction Behavior

Granular feedstock for dry pressing is prepared by spray drying oxide powders with polymeric additives. The interactions between polymeric additives in suspension or during drying are usually considered negligible. However, recent studies demonstrate that interactions between polymers usually do occur and can adversely affect product performance. Flory-Huggins calculations predict phase separation of Na-PMAA and Na-PAA with PVA and homogeneous mixing of Na-silicate with PVA. These predictions were confirmed by the light scattering studies on polymer solutions and morphology studies on dried polymer solutions. This reveals that the interaction between polymers can lead to either a homogeneous or phase-separated solution, depending on the functional groups and chain length of polymers. PVA binder in spray-dried granules is stained and its location within the spray dried granule is observed verifying the effect of other polymers on binder migration and case-hardening of spray dried granules. The results indicate polymeric additives that prevent binder migration, potentially eliminating case-hardening in spray dried granules and the subsequent problems observed during compaction.

Experimental and computational study on structure development of PMMA/SAN blends

Structure development in PMMA/SAN28 blends was studied experimentally with small-angle light scattering (SALS) and computationally with a diffuse-interface model based on the Cahn–Hilliard theory. All three stages of phase separation were observed with SALS. The diffusion coefficient was derived from the initial stage, while the evolution of the interface thickness was derived from all stages. The coarsening kinetics is more dominated by hydrodynamics in the late stage than in the intermediate stage of the phase separation. This is confirmed by the computational study which revealed that the coarsening becomes dominated by hydrodynamics when the capillary number is reduced from 10 to 0.5. A quantitative comparison between the experimental and numerically predicted phase separation kinetics is presented.

Transmission electron microscopy of Co 2(Cr 1−xFe x)Al sputtered films and their magnetic tunneling junctions

The microstructures of Co 2FeAl and Co 2(Cr 0.4Fe 0.6)Al sputtered films and of their magnetic tunnel junctions (MTJs) have been investigated to discuss the possible reasons for an unexpectedly low tunneling magnetoresistance (TMR). The structure of the Co 2FeAl film changed from B2 to L2 1 with increasing substrate temperature, while that of the Co 2(Cr 0.4Fe 0.6)Al film remained B2 up to 500 °C. The thermodynamically predicted phase separation was not observed in the films. The low TMR values obtained from the MTJs using the Co 2FeAl and Co 2(Cr 0.4Fe 0.6)Al films are attributed to the low-spin polarization expected from the low degree of order in these films. The TMR values depend sensitively on the interfacial structure of the tunnel junctions when the degree of order of the film is low.

Prediction of activity coefficients in liquid aerosol particles containing organic compounds, dissolved inorganic salts, and water—Part 3: Organic compounds, water, and ionic constituents by consideration of short-, mid-, and long-range effects using X-UNIFAC.3

X-UNIFAC.3, a group contribution method for estimating activity coefficients of neutral and ionic components in liquid mixtures of organic compounds, inorganic salts, and water, is presented here. It is an extended UNIFAC method, in that traditional UNIFAC terms for short-range energetic interaction effects are extended to include ions as mixture components, and are combined with a Debye–Hückel long-range effect term and a second virial coefficient-type mid-range effect term. The method is formulated for application in modeling the formation of liquid aerosol particles consisting of general organic+inorganic salt+water solutions in which phase separation is likely to occur. Existing extended UNIFAC activity coefficient estimation methods can be problematic in modeling phase separation, since they require independent reference state corrections that may introduce significant errors. In X-UNIFAC.3, this problem is avoided by selecting appropriate reference states for all solution components, and imposing additional constraints on method parameters, when necessary, by inclusion of reference state correction terms within the activity coefficient expressions. Interaction parameters in the X-UNIFAC.3 equations are optimized for 12 different chemical groups (CH 3–, –CH 2–, - C | H - , - C | | - , −OH, −COOH, H 2O, NH 4 +, Na +, Cl −, NO 3 - , and SO 4 2 - ) using available data for systems containing multi-functional oxygenated organic compounds and/or inorganic salts that are relevant to atmospheric aerosol applications. Estimations of water activities and mean ionic activity coefficients using X-UNIFAC.3 are compared with those of other extended UNIFAC methods. To demonstrate the use of X-UNIFAC.3 in predicting phase separation, the method is also applied to the butanoic acid+NaCl+water system, for which experimental liquid–liquid equilibrium data is available. The method performs well for aqueous salt solutions with salt concentrations within 30 mol kg −1 and for organic+inorganic salt+water solutions with salt concentrations less than or equal to 10 mol kg −1. Suggestions are proposed for improving the predictive capabilities of the method in future work.

Prediction of Phase Separation in Silicate Glass for the Creation of Value-added Materials from Waste Slag

A thermodynamic evaluation was performed to predict phase separation in multi-component oxide glasses. Composition ranges for metastable liquid–liquid immiscibility and spinodal decomposition in a SiO2–CaO–MgO–Na2O quaternary system were calculated on the assumption that glasses in the oxide system can be regarded as super-cooled liquid phases. Some experimental studies on two-phase separation of glasses were carried out to confirm the thermodynamic evaluation of the phase separation. Microstructures in heat-treated glass samples were observed by transmission electron microscopy, to investigate the development of interconnected microstructures in the glass with increased heating temperatures and holding times, and spinodal decomposition of glass was indicated.

Liquid water model: Predicting phase separation and phase characteristics

A model of liquid water that considers the presence of intact, distorted and broken H-bonds in the liquid predicts the anomalous density variation at around 277 K and a liquid–liquid phase separation at around 223 K under 1 atm pressure. The liquid phases at 223 K have densities of around 0.97 (phase I) and 0.92 g/mL (phase II) with very high and very low viscosities, and may represent phases with glassy and superfluid characteristics, respectively. The superfluid phase II terminates at around 219 K with the formation of ice Ih, and the glassy phase I, if it avoids conversion to phase II (at 223 K) in ultra-fast cooling, may remain in the glassy state until its termination at around 150 K with the formation of ice Ic.

Phase separation inLixFePO4induced by correlation effects

We report on a significant failure of the local density approximation (LDA) and the generalized gradient approximation (GGA) to reproduce the phase stability and thermodynamics of mixed-valence ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ compounds. Experimentally, ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ compositions $(0<~x<~1)$ are known to be unstable and phase separate into ${\mathrm{LiFePO}}_{4}$ and ${\mathrm{FePO}}_{4}.$ However, first-principles calculations with LDA/GGA yield energetically favorable intermediate compounds and hence no phase separation. This qualitative failure of LDA/GGA seems to have its origin in the LDA/GGA self-interaction which delocalizes charge over the mixed-valence Fe ions, and is corrected by explicitly considering correlation effects in this material. This is demonstrated with LDA+U calculations which correctly predict phase separation in ${\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ for $U\ensuremath{-}J\ensuremath{\gtrsim}3.5\mathrm{eV}.$ The origin of the destabilization of intermediate compounds is identified as electron localization and charge ordering at different iron sites. Introduction of correlation also yields more accurate electrochemical reaction energies between ${\mathrm{FePO}}_{4}/{\mathrm{Li}}_{x}{\mathrm{FePO}}_{4}$ and $\mathrm{Li}/{\mathrm{Li}}^{+}$ electrodes.

Calculated phase diagrams for cellulose/ammonia/ammonium thiocyanate solutions in comparison to experimental results

Flory's lattice theory for rigid rod molecules and Kuhn chains is used to calculate phase diagrams for cellulose/ammonia/ammonium thiocyanate solutions. Persistence length values measured by light scattering and reported previously are used as rod length values. Variations in the phase diagram based on varying rod length/solvent composition and cellulose molecular weight are explored. Spinodal curves are calculated in a region of the phase diagram predicting phase separation between two anisotropic solutions. Finally, calculated phase diagrams are compared to published data for the system. Discrepancies between theory and data may be accounted for by soft interactions between cellulose molecules and solvent which are not incorporated into the lattice theory.

Giant fluctuations at a granular phase separation threshold.

We investigate a phase separation instability that occurs in a system of nearly elastically colliding hard spheres driven by a thermal wall. If the aspect ratio of the confining box exceeds a threshold value, granular hydrostatics predict phase separation: the formation of a high-density region coexisting with a low-density region along the wall that is opposite to the thermal wall. Event-driven molecular dynamics simulations confirm this prediction. The theoretical bifurcation curve agrees with the simulations quantitatively well below and well above the threshold. However, in a wide region of aspect ratios around the threshold, the system is dominated by fluctuations, and the hydrostatic theory breaks down. Two possible scenarios of the origin of the giant fluctuations are discussed.

Modelling of annular flow through pipes and T-junctions

This paper describes a computational model for the prediction of isothermal annular two-phase flow in vertical and horizontal intersecting pipes and presents the results of its application to predict phase separation in a horizontal T-junction. The method is based on computational fluid dynamics techniques (CFD) to compute the dispersed core flow simultaneously with the flow of the liquid film along the walls. The core is represented as a dispersed two-phase mixture in which the droplets are tracked using a Lagrangian technique; the wall liquid film is modelled as a thin boundary layer. Full account is made of the interaction between the wall-film and the droplet flow in the core through mass and momentum transfer mechanisms. The method has already been validated against experimental data for fully developed annular flow in vertical and horizontal pipes; there, the predicted film thickness was found to be in satisfactory agreement with data obtained from the literature. The method is now applied to the phenomenon of phase separation occurring in T-junctions where it is found that the predictions for phase split agree quite well with measurements from an independent experiment for a range of phase split ratios. The predictions for wall-film thickness also exhibit similar trends to the data but do not quite match the locations where wall-film thickness peaks occur.

Solubility and Solution Structure of Cellulose Derivatives

Strongly interacting solvents are needed to dissolve cellulose; therefore, in the past the interpretation of the uncommon solution behavior of cellulose and its derivatives was based mainly on energetic (enthalpic) considerations, for example, hydrogen bonding. These attempts have not been very successful. The present paper demonstrates that entropic effects influence the solution behavior much stronger than hitherto supposed. In the well-known Flory–Huggins theory the driving force for dissolution of flexible chains is the configurational entropy of mixing. This large entropy is strongly reduced by the chain stiffness of the cellulose backbone and by the strictly regular primary structure of this polysaccharide. It strongly reduces the driving force for dissolution. The entropy of mixing becomes largely increased again by the attachment of long side chains and causes solubility with surprising efficiency (hairy rod principle). This effect is demonstrated with several examples. Among others, the surprising insolubility of short, regular-selectively substituted cellulose chains is explained, although long chains of the same substitution pattern are soluble. The striking behavior of cellulose ethers in water is based on the hydrophobic effect, which causes an increased order of the polymer surrounding water molecules. The induced order results in a very pronounced decrease of entropy of mixing that overcompensates the positive configurational entropy of mixing. Common rules of basic thermodynamics now predict phase separation on heating, contrary to the Flory–Huggins theory, which can only predict phase separation on cooling.

Electronic, magnetic, and structural properties of L10FePtxPd1−x alloys

We present theoretical and experimental results on the electronic, magnetic, and structural properties of L10 FePd, FePt, and FePtxPd1−x alloys. These alloys have large magnetizations and magnetocrystalline anisotropies and as such are potentially technologically important for applications as permanent magnets or high-density storage media. Results of first principles electronic structure calculations show that the system is a strong ferromagnet with an almost full majority Fe band, and that magnetization and magnetocrystalline anisotropy remain large over the range of composition. Total energy calculations predict phase separation on the disordered Pd/Pt layer at low temperatures. Experimental studies using energy dispersion x-ray line scans confirm regions that are Pt rich and Pd rich forming at low temperatures.

Simulation of enzymatic cellular reactions complicated by phase separation.

We present two-dimensional Monte Carlo simulations of enzymatic cellular reaction occurring via the Michaelis-Menten scheme in the case of attractive interactions between the reaction products. The model employed predicts phase separation in the cell provided that the reaction is relatively fast. The shape of the corresponding patterns varies from a few separate islands to a large patch located in the center of the cell. The fluctuations of the reaction rate during such regimes are found to be much higher than those predicted by the Poissonian distribution.