Equilibrium Properties Research Articles

Solid-liquid phase equilibrium and thermodynamic properties analysis of Bazedoxifene acetate in fifteen kinds of mono-solvents

Crystallization is widely used for the isolation and purification of active pharmaceutical ingredients (APIs) in the final manufacturing stage. Bazedoxifene (BZD) acetate, classified as a third-generation selective estrogen receptor modulator, is employed in the treatment of postmenopausal osteoporosis. This work reports the equilibrium solubility data of BZD acetate in fifteen different mono-solvents, including methanol, ethanol, n-propanol, i-propanol, n-butanol, ethyl formate, methyl acetate, ethyl acetate, acetone, 2-butanone, cyclohexanone, tetrahydrofuran (THF), 2-methyltetrahydrofurane (2-MeTHF), 1,4-dioxane and acetonitrile (ACN), within the temperature range “T = 283.15–323.15 K” under p = 0.1 MPa. The solubilities of BZD acetate in various solvents increase with increasing temperature. Among the alcoholic solvents, the solubility order is as follows: methanol > ethanol > n-propanol > n-butanol > i-propanol. In esters solvent, the solubility of BZD acetate decreases in the following order: methyl acetate > ethyl acetate > ethyl formate. For ketones solvent, the solubility decreases in the following order: cyclohexanone > acetone > 2-butanone. The maximum value of BZD acetate solubility was 0.011 mol·mol−1 in tetrahydrofuran at T = 323.15 K, but the least data was found in ethyl formate at 283.15 K. Four thermodynamic models, i.e., the Yaws model, modified Apelblat model, λh model, and Wilson model were applied to fit the solubility data of BZD acetate in different solvents. Among them, the Wilson model represents the most accurate fitting outcomes. Finally, the thermodynamic functions of mixing (including enthalpy, entropy, and Gibbs energy) were calculated, and the results indicate a mixing process that is both spontaneous and driven by entropy. The solubility data, correlated models, and derived thermodynamic functions present essential thermodynamic fundamentals for the industrial production of BZD acetate crystallization, facilitating efficient separation and purification.

Effects of sequence-dependent non-native interactions in equilibrium and kinetic folding properties of knotted proteins.

Determining the role of non-native interactions in folding dynamics, kinetics, and mechanisms is a classic problem in protein folding. More recently, this question has witnessed a renewed interest in light of the hypothesis that knotted proteins require the assistance of non-native interactions to fold efficiently. Here, we conduct extensive equilibrium and kinetic Monte Carlo simulations of a simple off-lattice C-alpha model to explore the role of non-native interactions in the thermodynamics and kinetics of three proteins embedding a trefoil knot in their native structure. We find that equilibrium knotted conformations are stabilized by non-native interactions that are non-local, and proximal to native ones, thus enhancing them. Additionally, non-native interactions increase the knotting frequency at high temperatures, and in partially folded conformations below the transition temperatures. Although non-native interactions clearly enhance the efficiency of transition from an unfolded conformation to a partially folded knotted one, they are not required to efficiently fold a knotted protein. Indeed, a native-centric interaction potential drives the most efficient folding transition, provided that the simulation temperature is well below the transition temperature of the considered model system.

Characterization of Liquid Adsorption Layers Formed from Aqueous Polymer–Surfactant Solutions—Significant Contributions by Boris A. Noskov

In many modern technologies, surface-active compounds, such as surfactants, polymers, proteins, particles and their mixtures, are essential components. They change the dynamic and equilibrium properties of the inherent interfaces, which is mostly visible in foams and emulsions. The interfacial dilational visco-elasticity is probably the most informative quantity due to its direct interrelation to the equation of state of the corresponding interfacial layers as well as the mechanisms governing the interfacial molecular dynamics. The scientific field of interfacial visco-elasticity, although quite young, has been inspired by the pioneering work of Marangoni, Levich, Lucassen, Lucassen-Reynders, Hansen, van den Tempel and Krotov, and during the last decades, also significantly by Boris Noskov. His contributions to the theoretical foundation and experimental analysis of polymer and mixed surfactant–polymer interfacial layers in particular are essential.

Bose Polaron in a One-Dimensional Lattice with Power-Law Hopping

Polarons, quasiparticles resulting from the interaction between an impurity and the collective excitations of a medium, play a fundamental role in physics, mainly because they represent an essential building block for understanding more complex many-body phenomena. In this manuscript, we study the spectral properties of a single impurity mixed with identical bosons in a one-dimensional lattice with power-law hopping. In particular, based on the so-called T-matrix approximation, we show the existence of well-defined quasiparticle branches for several tunneling ranges and for both repulsive and attractive impurity-boson interactions. Furthermore, we demonstrate the persistence of the attractive polaron branch when the impurity-boson bound state is absorbed into the two-body continuum and that the attractive polaron becomes more robust as the range of the hopping increases. The results discussed here are relevant for the understanding of the equilibrium properties of quantum systems with power-law interactions.

Thermodynamically consistent determination of free energies and rates in kinetic cycle models

Kinetic and thermodynamic models of biological systems are commonly used to connect microscopic features to system function in a bottom-up multiscale approach. The parameters of such models—free energy differences for equilibrium properties and in general rates for equilibrium and out-of-equilibrium observables—have to be measured by different experiments or calculated from multiple computer simulations. All such parameters necessarily come with uncertainties so that when they are naively combined in a full model of the process of interest, they will generally violate fundamental statistical mechanical equalities, namely detailed balance and an equality of forward/backward rate products in cycles due to Hill. If left uncorrected, such models can produce arbitrary outputs that are physically inconsistent. Here, we develop a maximum likelihood approach (named multibind) based on the so-called potential graph to combine kinetic or thermodynamic measurements to yield state-resolved models that are thermodynamically consistent while being most consistent with the provided data and their uncertainties. We demonstrate the approach with two theoretical models, a generic two-proton binding site and a simplified model of a sodium/proton antiporter. We also describe an algorithm to use the multibind approach to solve the inverse problem of determining microscopic quantities from macroscopic measurements and, as an example, we predict the microscopic pKa values and protonation states of a small organic molecule from 1D NMR data. The multibind approach is applicable to any thermodynamic or kinetic model that describes a system as transitions between well-defined states with associated free energy differences or rates between these states. A Python package multibind, which implements the approach described here, is made publicly available under the MIT Open Source license.

Adsorption Equilibrium Properties of Zn(II) on Activated Carbon Composite of Derived Empty Palm Oil Fruit Bunches with Metal Organic Frameworks Cu(TAC)

This study aims to determine the adsorption equilibrium of the activated carbon of empty palm oil fruit bunches and KA-Cu(TAC) on Zn(II). Oil palm empty fruit bunches are used as a biosorbent in making carbon at a temperature of 5000 C, the resulting carbon is activated using H3PO4 and modified into a composite with metal organic frameworks of Cu metal and terephthalic acid. MOFs and KA-Cu(TAC) composites were produced by reflux method. Activated carbon, MOFS and KA-Cu(TAC) were characterized using XRD. The adsorption process of Zn(II) metal was analyzed using AAS and determined the optimum conditions with various concentrations to determine the adsorption equilibrium. XRD characterization results show that activated carbon has an amorphous structure, while MOFs Cu(TAC) and KA-Cu(TAC) have a crystalline structure. The optimum condition of activated carbon and KA-Cu(TAC) at a concentration of 180 ppm with the appropriate adsorption isotherm model is the Langmuir isotherm.

Tautomeric equilibrium and spectroscopic properties of 8-azaguanine revealed by quantum chemistry methods.

8-azaguanine is a triazolopyrimidine nucleobase analog possessing potent antibacterial and antitumor activities, and it has been implicated as a lead molecule in cancer and malaria therapy. Its intrinsic fluorescence properties can be utilized for monitoring its interactions with biological polymers like proteins or nucleic acids. In order to better understand these interactions, it is important to know the tautomeric equilibrium of this compound. In this work, the tautomeric equilibrium of all natural neutral and anionic compound forms (except highly improbable imino-enol tautomers) as well as their methyl derivatives and ribosides was revealed by quantum chemistry methods. It was shown that, as expected, tautomers protonated at positions 1 and 9 dominate neutral forms both in gas phase and in aqueous solution. 8-azaguanines methylated at any position of the triazole ring are protonated at position 1. The computed vertical absorption and emission energies are in very good agreement with the experimental data. They confirm the validity of the assumption that replacing the proton with the methyl group does not significantly change the positions of absorption and fluorescence peaks.

Moisture-driven CO2 pump for direct air capture

Direct Air Capture, the chemical separation of carbon dioxide (CO2) from air, is considered a necessary approach to generate negative carbon emissions and in turn limit global warming, though energetic and monetary costs must continue to decline to meet the needed gigaton scale. The promise of energy-efficient and continuous carbon dioxide membrane separation has only recently been investigated with the development of facilitated chemical transport and novel electrochemically driven methods. This work demonstrates the potential for continuous pumping of CO2 from air using commercial anion exchange membranes driven solely by a water vapor gradient. A reactive transport model that couples ionic transport with moisture sensitive bicarbonate chemistry in charged polymers, also termed moisture swing sorption, was developed alongside experimentally measured equilibrium and transport properties of CO2 and water vapor in Fumasep FAA-3 to determine the mass transport limits of such a system. The results show that the commercial membrane is kinetically limited by the moisture sensitive chemistry, enabling a CO2 current of 1.1 μmol/m2∙ s. In diffusion limited materials, a CO2 pumping flux can reach 11 μmol/m2∙ s in and peak performance is expected with a dry air relative humidity around 50% pumping into a saturated water vapor permeate. In all configurations, water loss becomes the major cost in such a separation and must be managed through optimal polymer design or water recovery mechanisms. The work demonstrates the applicability of a new driving force, the evaporation of water, to meet the energetic demand of CO2 separation from air.

Ti, V, Cr, Mn, Co, and Ni substitution effect on structural, electronic, thermodynamic and magnetic properties of MgS and MgSe for spintronics

For the purposes of fitting the characteristics of the Magnesium sulfide (MgS) and, Magnesium selenide (MgSe) semiconductors in Spintronic applications, a theoretical ab-initio investigation of Transition metals (TM=Ti, V, Cr, Mn, Co, Ni) substitution is performed. The equilibrium properties have been studied in the zinc-blende phase of MgS and MgSe. The effects of temperature and pressure on the structural, electronic, thermodynamic, and magnetic properties of our systems are explored as well. It is found that the introduction of the TMs in MgS and MgSe brings out a half-metallic ferromagnetic behavior with 100% polarization around Fermi level in Ti, V, Cr, Co and Ni cases, contrary to the Mn case where the half-metallic feature does not appear. The double exchange mechanism was the mechanism responsible for magnetism in these systems. Finally, the high Curie Temperate (Tc) of the ferromagnetic systems reveals that Ti, Cr and V substitutions could play a significant role in spintronic applications.

Properties of Hot Nuclear Matter

A fully quantitative description of the equilibrium and dynamical properties of hot nuclear matter will be needed for the interpretation of the available and forthcoming astrophysical data, providing information on the post-merger phase of a neutron star coalescence. We discuss the results of a recently developed theoretical model, based on a phenomenological nuclear Hamiltonian including two- and three-nucleon potentials, to study the temperature dependence of average and single-particle properties of nuclear matter relevant to astrophysical applications. The potential of the proposed approach for describing dissipative processes leading to the appearance of bulk viscosity in neutron star matter is also outlined.

Analysis of the Dynamics of Tuberculosis in Algeria Using a Compartmental VSEIT Model with Evaluation of the Vaccination and Treatment Effects

Despite low tuberculosis (TB) mortality rates in China, Europe, and the United States, many countries are still struggling to control the epidemic, including India, South Africa, and Algeria. This study aims to contribute to the body of knowledge on this topic and provide a valuable tool and evidence-based guidance for the Algerian healthcare managers in understanding the spread of TB and implementing control strategies. For this purpose, a compartmental mathematical model is proposed to analyze TB dynamics in Algeria and investigate the vaccination and treatment effects on disease breaks. A qualitative study is conducted to discuss the stability property of both disease-free equilibrium and endemic equilibrium. In order to adopt the proposed model for the Algerian case, we estimate the model parameters using Algerian TB-reported data from 1990 to 2020. The obtained results using the proposed mathematical compartmental model show that the reproduction number (R0) of TB in Algeria is less than one, suggesting that the disease can be eradicated or effectively controlled through a combination of interventions, including vaccination, high-quality treatment, and isolation measures.

Carnot, Stirling, and Ericsson stochastic heat engines: Efficiency at maximum power.

This work uses the low-dissipation strategy to obtain efficiency at maximum power from a stochastic heat engine performing Carnot-, Stirling- and Ericsson-like cycles at finite time. The heat engine consists of a colloidal particle trapped by optical tweezers, in contact with two thermal baths at different temperatures, namely hot (T_{h}) and cold (T_{c}). The particle dynamics is characterized by a Langevin equationwith time-dependent control parameters bounded to a harmonic potential trap. In a low-dissipation approach, the equilibrium properties of the system are required, which in our case, can be calculated through a statelike equationfor the mean value 〈x^{2}〉_{eq} coming from a macroscopic expression associated with the Langevin equation.

Phase equilibrium of double-guest clathrates of methane and CO2, ethane, or propane as measured by high-pressure microcalorimetry

The world's increasing energy demand has led to considering methane hydrates as a promising alternative energy source to oil, gas, and coal. Due to the growing concerns about climate change, carbon capture via hydrate formation is considered a potential pathway for decarbonization. Understanding the phase equilibria is crucial for the development of these applications. This study presents new experimental data on the dissociation temperatures of double-guest clathrates at high pressure. Specifically, aqueous systems containing binary mixtures of methane and low-molecular-weight gases, such as ethane, propane, and carbon dioxide, were investigated. The experimental data were obtained using High-Pressure Microcalorimetry, covering pressures up to 100 MPa. The performance of a multicycle Differential Scanning Calorimetry (DSC) procedure was evaluated to determine the influence of the amount of non-clathrated water on the equilibrium properties of the binary guest systems. The experimental results were successfully modeled using the CSMGem and Multiflash software, demonstrating good agreement. The impact of the diffusivity and solubility of different guest species in water on the hydrate structure and its thermodynamic properties is discussed. The suitability of sI and sII clathrate structures to accommodate distinct molecules, the degree of cavity occupation, and the gas composition were evaluated to elucidate their effects on the dissociation temperatures.

Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge

Fear and prey refuges are two significant topics in the ecological community because they are closely associated with the connectivity of natural resources. The effect of fear on prey populations and prey refuges (proportional to both the prey and predator) is investigated in the nonlinear-type predator-harvested Leslie–Gower model. This type of prey refuge is much more sensible and realistic than the constant prey refuge model. Because there is less research on the dynamics of this type of prey refuge, the current study has been considered to strengthen the existing literature. The number and stability properties of all positive equilibria are examined. Since the calculations for the determinant and trace of the Jacobian matrix are quite complicated at these equilibria, the stability of certain positive equilibria is evaluated using a numerical simulation process. Sotomayor’s theorem is used to derive a precise mathematical confirmation of the appearance of saddle-node bifurcation and transcritical bifurcation. Furthermore, numerical simulations are provided to visually demonstrate the dynamics of the system and the stability of the limit cycle is discussed with the help of the first Lyapunov number. We perform some sensitivity investigations on our model solutions in relation to three key model parameters: the fear impact, prey refuges, and harvesting. Our findings could facilitate some biological understanding of the interactions between predators and prey.

Spatial metapopulation dynamics with local and global colonization

We revisit a spatial metapopulation model on continuous space as a stochastic point pattern dynamics. In the model, local patches as points are distributed with a certain spatial configuration and status of each patch changes stochastically between occupied and empty: an occupied patch becomes empty by local extinction and an empty patch becomes occupied both by local and global colonization. We carry out simulation analysis and derive an analytical model in terms of singlet, pair and triplet probabilities that describe the stochastic dynamics. Using a simple closure that approximates triplet probabilities by singlet and pair probabilities, we show that equilibrium singlet and pair probabilities can be analytically derived. The derived equilibrium properties successfully describe simulation results under a certain condition where the range of local colonization and the proportion of global colonization play key roles. Our model is an extension of the classical non-spatial Levins model to a spatially explicit metapopulation model. We appeal the advantage of point pattern approach to study spatial dynamics in general ecology and call for the need to deepen our understanding of mathematical tools to explore point pattern dynamics.

A class of mean‐field games with optimal stopping and its applications

AbstractThis paper studies the optimal stopping problem under the large‐population framework. In particular, two classes of optimal stopping problems are formulated by taking into account the relative performance criteria. It is remarkable that the relative performance criteria, also understood by the Joneses preference, habit formation utility, or relative wealth concern in economics and finance, play an important role in explaining various decision behaviors such as price bubbles. By introducing such criteria in large‐population setting, a given agent can compare his individual stopping rule with the average behaviors of its cohort. The associated mean‐field games are formulated in order to derive the decentralized stopping rules. The related consistency conditions are characterized via some coupled equation system and the ‐Nash equilibrium properties are also verified. In addition, some inverse mean‐field optimal stopping problem is also introduced and discussed.

Structural features and thermodynamic properties of Pr0.5Ba0.25Sr0.25MnO3–δ

The structure, oxygen non-stoichiometry, defect equilibrium, and thermodynamic properties of perovskite-type Pr0.5Ba0.25Sr0.25MnO3–δ manganite were studied. It was shown that the manganite can be air synthesized in one step at 1450 °C. Though having a disordered arrangement of Pr, Ba, and Sr atoms, the compound crystallizes with a tetragonal structure (S.G. I4/mcm) due to the regular tilts of MnO6 octahedra. The oxygen content in oxide as a function of oxygen partial pressure and temperature was measured by coulometric titration, and the data were used for the modeling of defect equilibrium. The oxygen content measurements show stability of the manganite at 973–1223 K and oxygen pressure decrease down to 10−16–10−12 atm. The equilibration of defects in Pr0.5Ba0.25Sr0.25MnO3-δ involves oxygen exchange with the gaseous ambient, intrinsic electron excitation, and oxygen disordering reactions. According to thermodynamic calculations, oxygen sites available for oxygen exchange are characterized by praseodymium-rich coordination. The disordering caused by the half substitution of barium by strontium leads to a lower energy of chemical bonding of the labile oxygen in Pr0.5Ba0.25Sr0.25MnO3–δ compared to the parent Pr0.5Ba0.5MnO3–δ manganite.

Optimized reaction coordinates for analysis of enhanced sampling.

Atomistic simulations of biological processes offer insights at a high level of spatial and temporal resolution, but accelerated sampling is often required for probing timescales of biologically relevant processes. The resulting data need to be statistically reweighted and condensed in a concise yet faithful manner to facilitate interpretation. Here, we provide evidence that a recently proposed approach for the unsupervised determination of optimized reaction coordinate (RC) can be used for both analysis and reweighting of such data. We first show that for a peptide interconverting between helical and collapsed configurations, the optimal RC permits efficient reconstruction of equilibrium properties from enhanced sampling trajectories. Upon RC-reweighting, kinetic rate constants and free energy profiles are in good agreement with values obtained from equilibrium simulations. In a more challenging test, we apply the method to enhanced sampling simulations of the unbinding of an acetylated lysine-containing tripeptide from the bromodomain of ATAD2. The complexity of this system allows us to investigate the strengths and limitations of these RCs. Overall, the findings presented here underline the potential of the unsupervised determination of reaction coordinates and the synergy with orthogonal analysis methods, such as Markov state models and SAPPHIRE analysis.

Do Financial Analysts Herd?

ABSTRACT Financial analysts may have strategic incentives to herd or to anti-herd when issuing forecasts of firms' earnings. This paper develops and implements a new test to examine whether such incentives exist and to identify the form of strategic behaviour. We use the equilibrium property of the finite-player forecasting game of Kim and Shim [2019. “Forecast Dispersion in Finite-Player Forecasting Games.” The B.E. Journal of Theoretical Economics 19 (1).] that forecast dispersion decreases (resp. increases) as the number of forecasters increases if and only if there is strategic complementarity (resp. substitutability) in their forecasts. Using the I/B/E/S database, we find strong evidence that supports strategic herding incentive of financial analysts through a plausible natural experiment setting of brokerage house mergers. We show further that this finding is robust to different forecast horizons and is more pronounced for firms with low initial coverage.

Bose-Einstein condensates with Raman-induced spin-orbit coupling: An overview

Since their first realization more than a decade ago spin-orbit-coupled Bose-Einstein condensates have been the subject of intense theoretical and experimental investigations. Spin-orbit coupling deeply modifies the equilibrium properties of the condensate, giving rise to novel configurations such as a supersolid stripe phase and a phase-separated plane-wave state. At the level of dynamics, both the frequency and the nature of the collective modes are significantly affected by the coupling with the spin degree of freedom. Here we review some of the most relevant advances in the field and provide our perspective on possible future research directions.