Thermodynamic Phase Equilibria Research Articles

Protein viscoelastic dynamics: a model system.

A model system inspired by recent experiments on the dynamics of a folded protein under the influence of a sinusoidal force is investigated and found to replicate many of the response characteristics of such a system. The essence of the model is a strongly overdamped oscillator described by a harmonic restoring force for small displacements that reversibly yields to stress under sufficiently large displacement. This simple dynamical system also reveals unexpectedly rich behavior-exhibiting a series of dynamical transitions and analogies with equilibrium thermodynamic phase transitions. The effects of noise and of inertia are briefly considered and described.

RNA transcription modulates phase transition-driven nuclear body assembly.

Nuclear bodies are RNA and protein-rich, membraneless organelles that play important roles in gene regulation. The largest and most well-known nuclear body is the nucleolus, an organelle whose primary function in ribosome biogenesis makes it key for cell growth and size homeostasis. The nucleolus and other nuclear bodies behave like liquid-phase droplets and appear to condense from the nucleoplasm by concentration-dependent phase separation. However, nucleoli actively consume chemical energy, and it is unclear how such nonequilibrium activity might impact classical liquid-liquid phase separation. Here, we combine in vivo and in vitro experiments with theory and simulation to characterize the assembly and disassembly dynamics of nucleoli in early Caenorhabditis elegans embryos. In addition to classical nucleoli that assemble at the transcriptionally active nucleolar organizing regions, we observe dozens of "extranucleolar droplets" (ENDs) that condense in the nucleoplasm in a transcription-independent manner. We show that growth of nucleoli and ENDs is consistent with a first-order phase transition in which late-stage coarsening dynamics are mediated by Brownian coalescence and, to a lesser degree, Ostwald ripening. By manipulating C. elegans cell size, we change nucleolar component concentration and confirm several key model predictions. Our results show that rRNA transcription and other nonequilibrium biological activity can modulate the effective thermodynamic parameters governing nucleolar and END assembly, but do not appear to fundamentally alter the passive phase separation mechanism.

Kinetic evidence for the effect of salts on the oxygen solubility using laboratory prototype aeration system

This study is dedicated to an accurate evaluation of thermodynamic and kinetic aspects in the oxygenation process of water/salt solutions. Oxygenation has been analyzed by means of kinetic study of oxygen dissolution from the oxygen mass transfer coefficient (KLa) and oxygen transfer rate (SOTR). A stirred, submerged aerated 4-liter system has been designed and the operational conditions have been optimized by studying the influence of hydraulic head, air flow and salinity of water using an optical oxygen sensor. Concerning the thermodynamic phase equilibria, experimental and modeling results are obtained from different binary systems (water/air) and ternary systems (water/air/salts). This information is necessary to predict the composition of the gas phase during the process and is also important for an implementation in a process simulation. The oxygen mass transfer coefficients were firstly measured, by monitoring in the time the oxygen concentration in various synthetic liquid phases containing different salts (NaCl, KCl, LiCl). When compared to clean water, noticeable increase of KLa was observed; the variation of KLa and SOTR with the solution salinity was modeled and found dependent on the nature of cation in the salt added. For all cases, an increase of KLa with increasing salinity was observed but, when the results are correlated with salt molar concentration, very important relation attributed to different salts has been obtained. The present study clearly confirmed the importance to define the experimental conditions before to describe and to model appropriately the gas–liquid mass transfer phenomena.

Analysis of countercurrent membrane vapor extraction of a dilute aqueous biosolute

Removal of dilute bioproducts from fermenter broths is a major challenge both to avoid microbe inhibition and to recover solutes economically without water loss. We analyze a proposed new process, membrane vapor extraction (MVE), where semi‐volatile dilute aqueous solutes vaporize at the upstream side of an omniphobic, microporous membrane and dissolve into a nonpolar solvent highly favorable to the solutes but not to water. A new membrane‐process analysis is outlined and applied to the countercurrent recovery of 2 wt % aqueous butanol by a prototype solvent (dodecane) at 40°C. Thermodynamic phase equilibria, pioneered by the Prausnitz school, are crucial to MVE process design. Over 90% of the feed butanol is recovered with essentially no water loss giving a separation factor of over 1000. Energy requirements in MVE are low. Our design calculations demonstrate that MVE is a viable separation process to remove and recover dilute aqueous biosolutes. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2795–2809, 2015

Carbon deposition on iron surfaces in CO–CO2 atmosphere

Thermodynamic calculations and thermogravimetric (TG) analysis were performed in order to understand the mechanism of carbon deposition on the surfaces of iron particles during the reduction of iron ore in a CO–CO2 atmosphere. The results of the thermodynamic equilibrium phase analysis indicate that the phases of the carbon deposition process can be predicted on the basis of the carbon potential, reaction temperature and gas pressure. The optimal thermodynamic conditions for carburisation are a low temperature (T < Tm) and a high carbon potential (αc>1). TG analysis is performed in a gas mixture of 65 vol.-% CO and 35 vol.-% CO2 at 650, 706 and 750°C. Cementite (Fe3C) is generated as an intermediate product, which acts as a catalyst for carbon deposition. Carbon deposition is inhibited at high temperatures (T>791°C) owing to the high stability of Fe3C. When the reaction temperature is higher than the thermodynamic limit for the formation of Fe3C, carbon deposition cannot occur. A mechanism for carbon deposition is proposed based on the experimental results.

Influence of Hetero Grain Boundaries on Oxygen Exchange Activity: Investigation of Two-Phase (La,Sr)CoO3-δ / (La,Sr)2CoO4+δ Cathode Materials

Recent investigations indicated that oxygen reduction is accelerated at hetero-contacts between perovskite (La,Sr)CoO3- d (LSC) and Ruddlesden-Popper phase (La,Sr)2CoO4+ d(LSC-RP) [1-3]. In the present study, we want to quantify the activity of triple phase boundaries (TPB) and distinguish it from the activity of the pure LSC and LSC-RP phases, and evaluate under which conditions LSC/LSC-RP composites could be more active cathode materials compared to pure LSC. Dense thin films of LSC/LSC-RP composites on single crystalline YSZ were prepared by a single PLD run from a two-phase PLD target with overall Sr content z=nSr/(nLa+nSr) of 0.3 and phase ratio w=nLSC-RP/(nLSC+nLSC-RP) of 0.25-0.75. On the heated substrate, the incoming material from the plasma plume crystallizes into a two-phase mixture (miscibility gap between LSC and LSC-RP). The resulting dense films are a nanocomposite of LSC and LSC-RP phases. For comparison, films of pure LSC and LSC-RP only were deposited under identical conditions. Furthermore, composite samples were deposited as amorphous films on unheated substrates, and crystallized by subsequent annealing. XRD shows crystalline LSC and/or LSC-RP phases in the single-phase and composite films deposited at 770 °C. The amorphous films developed crystal-like morphology (SEM) at annealing temperatures >500 °C. The SEM images in Fig. 1 show a crystallite size of 50-100 nm for films deposited at 770 °C, and 5-10 nm for amorphously deposited, post-annealed films. The area specific resistance of oxygen reduction (ASR, measured by impedance spectroscopy on microelectrodes) of single phase samples and composites is shown as a function of the volumetric LSC-RP content. The lines show the expected behavior of the ASR under the assumption that TPB effects are negligible. The grey line assumes a Sr content of 30% in both phases, the red curve takes into account that LSC and LSC-RP phases in thermodynamic equilibrium exhibit different Sr content (Sr accumulation in LSC-RP, for overall Sr content up to 40%). This Sr distribution can happen during the PLD films growth, and was evidenced by TEM. Its quantification by XRD on powder samples (glycine-nitrate process, annealed at 1200 °C) is shown in Fig. 2. Since the oxygen exchange activity of LSC decreases more steeply with decreasing Sr content than the activity of LSC-RP increases [4,5], the expected overall ASR of composite films is higher considering this distribution. The post-annealed sample with high TPB length (about 106 cm/cm2) showed the lowest ASR of all composites, but also deactivated most quickly (under morphological changes such as coarsening). The composites deposited at high T with shorter TPB lengths (105 cm/cm2 or less) exhibit a higher ASR, and after initial deactivation most of them are situated at or above the red curve. XRD/TEM indicated formation of a higher-order Ruddlesden-Popper phase at expense of LSC in some samples, which could explain an activity below the red curve. Taking the red curve as reference ASR (absence of TPB effects) for the two most active composites, their length specific resistance was in the range of 1-2 MΩ∙cm. At 500-600 °C their ASR is lower than the values obtained in [3] for a slightly larger overall Sr content. To summarize: dense composite films can be deposited in a single PLD run, with crystallite sizes down to 5-10 nm. The effects of Sr distribution increase the overall ASR compared to single phases with same overall Sr content, and unless very high TPB lengths are achieved (or high overall Sr/La ratios are used which diminish this effect) this effect prevails over the small activity enhancement which is specifically caused by the LSC/LSC-RP hetero-contacts. [1] M. Sase, K. Yashiro, K. Sato, J. Mizusaki, T. Kawada, N. Sakai, K. Yamaji, T. Horita, H. Yokokawa, Solid State Ionics 178 (2008) 1843. [2] E.J. Crumlin, E. Mutoro, S.-J. Ahn, G. Jose la O', D.N. Leonard, A. Borisevich, M.D. Biegalski, H.M. Christen, Y. Shao-Horn, J. Phys. Chem. Lett. 1 (2010) 3149. [3] W. Ma, J.J. Kim, N. Tsvetkov, T. Daio, Y. Kuru, Z. Cai, Y. Chen, K. Sasaki, H.L. Tuller, B. Yildiz, J. Mater. Chem. A 3 (2015) 207 [4] A.V. Berenov, A. Atkinson, J.A. Kilner, E. Bucher, W. Sitte, Solid State Ionics 181 (2010) 819 [5] F. Zhao, X. Wang, Z. Wang, R. Peng, C. Xia, Solid State Ionics 179 (2008) 1450 Figure 1

Thermodynamic Study of Ag-Au-Gd, Tb Ternary Systems

The addition of the rare earth elements into the Ag-based filler alloy, which is typical and important, can control and eliminate the negative effect of impurity elements, and furthermore, it improves the spreading property of the Ag-based filler alloy. Phase diagram provides an important direction for materials design of the Ag-based filler alloy. Thus it is necessary to investigate the phase diagrams and construct the thermodynamic database. On the basis of this background, thermodynamic assessments of the Au-Gd, Tb binary systems were carried out by using the CALPHAD (Calculation of Phase Diagrams) method based on the experimental data including thermodynamic properties and phase equilibrium. The Gibbs free energies of the solution phases were described by sub-regular solution models with the Redlich-Kister equation, while all of the intermetallic compounds were described by sub-lattice models. A consistent set of thermodynamic parameters was derived from describing the Gibbs free energies of each solution phase and intermetallic compound. The calculated phase diagram achieved consistency with the available experiments. Then combined with the assessed relevant binary systems, the Ag-Au-Gd, Tb ternary systems have been predicted. The thermodynamic database of these ternary systems has been developed to present the significant information for the design of Ag-based filler alloys.

Thermodynamic effects of calcium and iron oxides on crystal phase formation in synthetic gasifier slags containing from 0 to 27 wt.% V2O3

Thermodynamic phase equilibria in synthetic slags (Al2O3–CaO–FeO–SiO2–V2O3) were investigated with 0–27wt.% vanadium oxide corresponding to industrial coal–petroleum coke (petcoke) feedstock blends in a simulated gasifier environment. Samples encompassing coal–petcoke mixed slag compositions were equilibrated at 1500°C in a 64vol.% CO/36vol.% CO2 atmosphere (Po2≈10−8atm at 1500°C) for 72h, followed by rapid water quench, then analyzed by inductively coupled plasma optical emission spectrometry, X-ray diffractometry, and scanning electron microscopy with wavelength dispersive spectroscopy. With increasing CaO content, FeO content, or both; the slag homogeneity region expanded and a composition range exhibiting crystals was reduced. The mullite (Al6Si2O13) crystalline phase was not present in the slags above 9wt.% FeO while the karelianite (V2O3) crystalline phase was always present in compositions studied if a sufficient amount of vanadium existed in the slag. Based on the present experimental equilibrium evaluation, a set of isothermal phase diagrams showing effects of CaO and FeO on thermodynamic phase stabilities in the vanadium-bearing slags is proposed. Some uses of the diagrams for potential industrial practice are discussed.

Liquid-Liquid Extraction of Acids and Water by a Malonamide: I-Anion Specific Effects on the Polar Core Microstructure of the Aggregated Malonamide

In a solvent extraction process, the compositions of the phases in thermodynamic equilibrium (described as a Winsor-II regime) must be determined to obtain the extraction isotherms of ions as well as co-extracted water. By comparing the extractions of a series of acids by the malonamide DMDOHEMA (N,N’-dimethyl-N,N’-dioctyl hexylethoxy malonamide) in n-heptane, the specific anion effects regarding third phase formation and the strength of the acid-extractant interaction were investigated. It is shown that third phase formation is driven by hydration enthalpy of acid, while the polar core microstructure is controlled by the pKa of the acids. Upon acid extraction, the promotion of third phase formation follows the series H2SO4 ≈ H3PO4 ≈ HClO4 > HNO3 > HCl > HCOOH, which correlates to hydration enthalpy of acid in the case of monoacids. The combination of IR spectroscopy and DFT calculations revealed two different modes of acid extraction, either by hydrogen bonding (extraction of non-dissociated acid: HA) or by protonation of the extractant (extraction of dissociated acid: H+A−). The strength of the amide-acid interaction (protonation vs. hydrogen bonding) is correlated to the pKa of the acid and is responsible for the microstructure of the solution.

Polymorphism and thermodynamic ground state of silver fulminate studied from van der Waals density functional calculations.

Silver fulminate (AgCNO) is a primary explosive, which exists in two polymorphic phases, namely, orthorhombic (Cmcm) and trigonal (R3) forms at ambient conditions. In the present study, we have investigated the effect of pressure and temperature on relative phase stability of the polymorphs using planewave pseudopotential approaches based on Density Functional Theory (DFT). van der Waals interactions play a significant role in predicting the phase stability and they can be effectively captured by semi-empirical dispersion correction methods in contrast to standard DFT functionals. Based on our total energy calculations using DFT-D2 method, the Cmcm structure is found to be the preferred thermodynamic equilibrium phase under studied pressure and temperature range. Hitherto Cmcm and R3 phases denoted as α- and β-forms of AgCNO, respectively. Also a pressure induced polymorphic phase transition is seen using DFT functionals and the same was not observed with DFT-D2 method. The equation of state and compressibility of both polymorphic phases were investigated. Electronic structure and optical properties were calculated using full potential linearized augmented plane wave method within the Tran-Blaha modified Becke-Johnson potential. The calculated electronic structure shows that α, β phases are indirect bandgap insulators with a bandgap values of 3.51 and 4.43 eV, respectively. The nature of chemical bonding is analyzed through the charge density plots and partial density of states. Optical anisotropy, electric-dipole transitions, and photo sensitivity to light of the polymorphs are analyzed from the calculated optical spectra. Overall, the present study provides an early indication to experimentalists to avoid the formation of unstable β-form of AgCNO.

Steady-state dynamical phase diagram calculation of U–Nb binary system under irradiation: Ballistic effect

A kinetic model involved in ballistic effects has been used for studying the steady-state configuration under irradiation, with considering the irradiation-enhanced diffusion. By applying this model to all the solid phases, the dynamical phase diagram of U–Nb system under irradiation is calculated and critically compared with the assessed thermodynamic equilibrium phase diagram. The calculated results indicate that the irradiation has little effect on the phase relationships of U–Nb system at high temperatures. However, it leads to the close of the miscibility gap of U–Nb system at relatively low temperatures. Meanwhile, the high-temperature stable γ(U,Nb) phase is stabilized by the irradiation, which is in agreement with the available experimental results.

Phase equilibria and thermodynamics of Mn–C, Mn–Si, Si–C binary systems and Mn–Si–C ternary system by critical evaluation, combined with experiment and thermodynamic modeling

Critical evaluation and thermodynamic optimization of Mn–C, Mn–Si, Si–C binary systems and Mn–Si–C ternary system were carried out over the whole composition range from room temperature to above the liquidus temperature. In order to provide critical experimental input for the thermodynamic modeling, some key experiments were carried out in the present study. The liquid solution was modeled using the Modified Quasichemical Model (MQM) in the pair approximation in order to take into account the Short-Range Ordering (SRO) exhibited in the solution. In particular, the SRO observed in the Mn–C binary liquid was reasonably accounted for by the present thermodynamic model, while the conventional random mixing model was not able to properly describe the SRO. All solid solutions were modeled using the Compound Energy Formalism (CEF). Model parameters were optimized to best reproduce the important thermodynamic properties and phase equilibrium data in three binary systems. By taking a reasonable interpolation method for Gibbs free energy of the liquid solution in the ternary Mn–Si–C system, it was shown that the present model successfully reproduced thermodynamic and phase equilibrium data in the ternary system without any adjustable ternary parameter. The present database can be used as a part of larger thermodynamic database for the ferromanganese alloy.

Phase Stability Analysis using a Polarization Technique and the Randomness of a Stochastic Method in an Unconstrained Optimization Framework

This article deals with the phase stability analysis of multicomponent systems via the determination of all the stationary points of the so-called tangent plane distance function, which is known as an important but difficult problem of the thermodynamics of phase equilibrium, where high nonlinearities are inherent aspects of the different thermodynamic models commonly used in the description of this distance function. To analyze phase stability described from different models, we combine three basic procedures here that were selected in order to attack points that we deem of relevant difficulty. To this end, we encapsulate in a single iterative algorithm the following steps: (i) polarization of a merit function associated with first-order stationary conditions of the phase stability problem, in order to avoid (or at least minimize) the repetition of stationary points previously calculated; (ii) a stochastic optimization method, which (at each iteration of the encapsulation algorithm) minimizes m times the same merit function polarized with the predetermined stationary points, using m different seeds for a reliable random number generator (where m is a given integer), in order to calculate new stationary points; (iii) a change of variables designed to allow the numerical method to work in the unconstrained optimization framework, providing the location of stationary points near the boundary of the original feasible set. Using the NRTL and UNIQUAC models for liquid–liquid equilibria at low pressures and the Soave–Redlich–Kwong and Peng–Robinson cubic equations of state for vapor–liquid equilibria at high pressures, we analyze 9 multicomponent systems studied in the literature, equipped with different feed compositions, totaling 32 tested mixtures, whose component numbers ranged between 3 and 12. We show 14 new stationary points obtained here that were not detected by methods previously used by other authors.

Construction of Solidus Lines of Binary Metal Systems Having a Low Solubility of Components in the Solid Phase

The paper presents the calculation results on the construction of solidus lines of phase diagrams for some binary metal systems based on cadmium, zinc and tellurium. The investigations have been carried out using the phase equilibrium thermodynamics and known liquidus lines. By the calculation method the solidus lines of phase diagrams of the Cd-Na, Cd-Tl, Te-Ga, Te-As, Te-Cu and Zn-Sn systems were constructed in the temperature range from the base component melting point to the eutectic transformation temperature. In the Cd-Tl, Te-As, Te-Cu and Zn-Sn systems a retrograde solubility of the second component in the solid phase was observed. The temperature and maximum solubility values at the retrograde behavior of solidus lines, as well as, the limiting solubility values of components at eutectic transformation in the systems based on Cd, Zn and Te were determined.

Thermodynamic assessment of the Mg-Pb and Mg-Bi systems using substitutional solution and associate models for the liquid phase

By means of CALPHAD approach, thermodynamic assessments of the Mg-Pb and Mg-Bi systems were carried out based on the available experimental data including thermodynamic properties and phase equilibrium data. The liquid phase was described with both the substitutional solution model and the associate model, and two sets of self-consistent thermodynamic parameters for the Mg-Pb and Mg-Bi systems were obtained, respectively. It was found that the associate model can account for the experimental data more satisfactorily than the substitutional solution one, especially for the liquid phase with the short-range order behavior.

A modified MMM EOS for high-pressure PVT calculations of heavy hydrocarbons

A theoretical based cubic equation of state has been proposed (MMM EOS) by Mohsen-Nia (Mohsen-Nia et al., 1995) for calculation of pure fluid and mixture properties Z=(v+1.3191b)/(v−b)−a/[RT1.5(v+b)] In previous works, the superiority of the MMM has been shown over the vdW family of EOSs for PVT and VLE calculations. In this work, a new simple functional form for its attractive and repulsive parameters [a(T) and b(T)] is introduced. The proposed EOS is applied to vapor pressure and saturated density calculations of different pure fluids. Then, the proposed equation is used to calculate high-pressure PVT of heavy hydrocarbons. The performance of the proposed EOS for VLE calculations is examined against the corresponding experimental measurements for a number of binary mixtures and the results are compared with those obtained from the cubic EOSs frequently used for thermodynamic and fluid phase equilibrium calculations. The comparisons indicate the modified MMM EOS is quite suitable for property predictions of gas and liquid systems, especially for high-pressure PVT of heavy hydrocarbon systems of interest in the oil and gas industries.

Simulating Flow of CO2 with Impurities in OLGA; Dealing with Narrow Phase-envelopes and the Critical Point

The dynamic multiphase flow simulator OLGA [1–4] uses pressure (P), temperature (T), and fluid composition, as independent variables, meaning that all thermodynamic and transport properties for the fluid are given as functions of P and T. Although this is a good approximation for typical multicomponent oil and gas systems, several problems are being faced using the same formulation for pure CO2 and for CO2 containing small amounts of impurities. A better approach is then to use pressure and enthalpy (H) as independent variables for thermodynamic equilibrium calculations and phase properties. This change in formulation is critical for accurate modelling of single component and near single component systems.A prototype P-H formulation has been implemented in OLGA as part of the R&D project CO2-VIP [5].The new calculation scheme is presented here, demonstrated through simple examples, and validated against experimental results. It has proven to give increased simulation accuracy and stability.

Modeling weak acids' reactive transport in reverse osmosis processes: A general framework and case studies for SWRO

Despite appearing at relatively low concentrations, weak acids of various types have a significant impact on the design, operation and the quality of the product water in many RO (reverse osmosis) applications. During the RO process, weak acid species are simultaneously involved in interconnected transport and chemical reactions. This complex behavior requires the use of a “reactive transport” modeling approach. In this paper we present a systematic method for combining commonly used cross-membrane transport and concentration polarization models with thermodynamic aqueous phase equilibrium models. The new approach can be used for the prediction of the acid–base thermo-chemical condition that develop within the membrane module affecting the final permeate and brine characteristics in a variety of RO applications. A computerized algorithm was developed, described and applied for simulating two case studies. The case study results demonstrate the practical significance of the approach in the context of boron removal and chemical scaling control within seawater RO applications.

A simple thermo-physical model for vapor–liquid equilibrium of the reactive HIx (HI–H2O–I2–H2) system

Thermodynamic phase equilibrium of the reactive HIx system encountered in the sulfur-iodine (SI) cycle has been identified as a basic research need for the hydrogen economy. In this communication, a simple NRTL (nonrandom two-liquid)-based vapor–liquid equilibrium (VLE) model is devised for the HIx system considering the HI decomposition reaction in the gas phase only. We propose a new set of NRTL binary interaction parameters as well as a new expression for the HI decomposition chemical equilibrium constant as a function of temperature. This simple VLE model with the use of only one set of NRTL binary parameters is capable of reproducing the Larousse et al. (Int. J. Hydrogen Energy 34 (2009) 3258–3266) experimental data for a wide range of pressures (1–24bar) and HI concentrations beyond the azeotrope.

The precipitation behavior of an Al–Cu–Mg–Ag alloy under ECAP

The changes in the dispersions of secondary phases during equal channel angular pressing (ECAP) at 250°C were studied in an Al–Cu–Mg–Ag alloy initially processed in a supersaturated solid solution (QA, quenched alloy), on coherent plates of the Ω-phase (OA, over-aged alloy) and on coarse particles of phases in thermodynamic equilibrium (HA, heterogenized alloy). In the QA, the decomposition of the supersaturated solid solution and the precipitation of nanoscale coherent plates of the Ω-phase begin to occur under soaking before ECAP. During ECAP, a shearing offset leads to the fragmentation of the Ω-phase into nanoscale spherical particles followed by their direct allotropic transformation to θ-phase dispersoids with an equiaxed shape. The S-phase (Al2CuMg) particles also nucleate and rapidly grow. In the OA the precipitation behavior is essentially the same. At ε≥4, a dispersion of incoherent particles with an average size of ~30nm evolves in the QA and the OA. Therefore, a dispersion of thermodynamically metastable phases with coherent interfaces is replaced by a dispersion of phases with incoherent interfaces during ECAP at over-aged temperatures. These phases can be different from those precipitated during static artificial aging. Insignificant changes in the dispersion of secondary phases take place in the HA during ECAP.