Thermodynamic Description Research Articles

Revisiting thermodynamics in (LiF, NaF, KF, CrF2)–CrF3 by first-principles calculations and CALPHAD modeling

The thermodynamic description of the (LiF, NaF, KF, CrF2)–CrF3 systems has been revisited, aiming for a better understanding of the effects of Cr on the FLiNaK molten salt. First-principles calculations based on density functional theory (DFT) were performed to determine the electronic and structural properties of each compound, including the formation enthalpy, volume, and bulk modulus. DFT-based phonon calculations were carried out to determine the thermodynamic properties of compounds, for example, enthalpy, entropy, and heat capacity as functions of temperature. Phonon-based thermodynamic properties show a good agreement with experimental data of binary compounds LiF, NaF, KF, CrF3, and CrF2, establishing a solid foundation to determine thermodynamic properties of ternary compounds as well as to verify results estimated by the Neumann-Kopp rule. Additionally, DFT-based ab initio molecular dynamics (AIMD) simulations were employed to predict the mixing enthalpies of liquid salts. Using DFT-based results and experimental data in the literature, the (LiF, NaF, KF, CrF2)–CrF3 system has been remodeled in terms of the CALculation of PHAse Diagrams (CALPHAD) approach using the modified quasichemical model with quadruplet approximation (MQMQA) for liquid. Calculated phase stability in the present work shows an excellent agreement with experiments, indicating the effectiveness of combining DFT-based total energy, phonon, and AIMD calculations, and CALPHAD modeling to provide the thermodynamic description in complex molten salt systems.

Cosmological FLRW phase transitions and micro-structure under Kaniadakis statistics

This article studies the thermodynamics phase transitions and critical phenomena of an FLRW cosmological model under truncated Kaniadakis's statistics. The EoS is derived from the corrected Friedmann field equations and the thermodynamics unified first law. To approach thermodynamics, we use an approximation for KSAH≪1, on the cosmological equation, and also check the validity of our approximation. Then for different values from Kaniadakis parameter K, order O(10−37) for the relic-abundance, O(10−84) for 7Li-abundance and O(10−125) in the recombination era, the EoS reveals non-trivial critical points where a first-order phase transition occurs a sort of a van der Waals fluid. Interestingly, the numerical values of the critical exponents are the same as those of the van der Waals system. Besides, to obtain more insights into the thermodynamics description, the so-called Ruppeiner's geometry is studied through the normalized scalar curvature, disclosing this invariant zone where the system undergoes repulsive/attractive interactions. Near the critical point, this curvature provides again the same critical exponent and universal constant value as for van der Waals fluid. Despite the similarity, both systems are quite different because the present one considers a relativistic entropy (Kaniadakis entropy) while the Van der Waals gas responds to a classical entropy (Maxwell-Boltzmann).

A quantitative description of barite thermodynamics, nucleation and growth for reactive transport modelling.

A quantitative description of barite thermodynamics, nucleation and growth for reactive transport modelling.

Generic low-density corrections to the equation of state of chain molecules with repulsive intermolecular forces.

Molecular-based equations of state for describing the thermodynamics of chain molecules are often based on mean-field like arguments that reduce the problem of describing the interactions between chains to a simpler one involving only nonbonded monomers. While for dense liquids such arguments are known to work well, at low density they are typically less appropriate due to an incomplete description of the effect of chain connectivity on the local environment of the chains' monomer segments. To address this issue, we develop three semi-empirical approaches that significantly improve the thermodynamic description of chain molecules at low density. The approaches are developed for chain molecules with repulsive intermolecular forces; therefore, they could be used as reference models for developing equations of the state of real fluids based on perturbation theory. All three approaches are extensions of Wertheim's first-order thermodynamic perturbation theory (TPT1) for polymerization. The first model, referred to as TPT1-v, incorporates a second-virial correction that is scaled to zero at liquid-like densities. The second model, referred to as TPT1-y, introduces a Helmholtz-energy contribution to account for correlations between next-nearest-neighbor segments within chain molecules. The third approach, called TPT-E, directly modifies TPT1 without utilizing an additional Helmholtz energy contribution. By employing TPT1 at the core of these approaches, we ensure an accurate description of mixtures and enable a seamless extension from chains of tangentially bonded hard-sphere segments of equal size to hetero-segmented chains, fused chains, and chains of soft repulsive segments (which are influenced by temperature). The low-density corrections implemented in TPT1 are designed to preserve these good characteristics, as confirmed through comparisons with novel molecular simulation results for the pressure of various chain fluids. TPT1-v exhibits excellent transferability across different chain types, but it relies on knowing the second virial coefficient of the chain molecules, which is non-trivial to obtain and determined here using Monte Carlo simulation. The TPT1-y model, on the other hand, achieves comparable accuracy to TPT1-v while being fully predictive, requiring no input besides the geometry of the chain molecules.

Experimental determination and thermodynamic optimization of the Nb–V–Zr system

A comprehensive thermodynamic description for each phase is essential for designing of the novel Zr-based nuclear materials. The construction of the experimental liquidus surface projection and isothermal section of the Nb–V–Zr system was established through analyzing solidification microstructures and phase constituents. The stability of the τ phase with C14-structure was established by investigating the composition range of Nb in τ, which was measured to be between 19.8 and 40.5 at. % at 1473 K. The solubility of Nb in λ2 with the C15-type was ∼ 16.9 at. % at 1473 K. The liquidus surface projection showed primary solidification areas of bcc(Nb,V,Zr), λ2 and τ. The thermodynamic parameters were derived combining the CALPHAD method with experimental results from phase diagram data in this work and the literatures. Solution phases, including liquid, bcc, and hcp, were regarded as substitutional solutions. Considering the crystal structures and solid solubility of intermetallic compounds, λ2 and τ were modeled as (Nb,V,Zr)2(Nb,V,Zr) using two-sublattice model. A set of self-consistent thermodynamic parameters of the Nb–V–Zr system was obtained, which will provide theoretical guidance for the design of Zr-based nuclear materials.

Microstructural characterisation and compound formation in rapidly solidified SiGe alloy

Severe Ge segregation to grain boundaries was observed in a Si–14.2 at% Ge thermoelectric alloy rapidly solidified using a drop-tube facility, manifesting itself as a series of regions with uniform stoichiometric compositions. The step change in composition at the interface between adjacent regions was ascribed to the formation of different SiGe pseudocompounds and contradicted the accepted thermodynamic description of the SiGe system as a continuous random solid solution. Rapid solidification increased, rather than decreased, the inhomogeneity degree of the solid product, and the Ge content of the most Ge-rich regions was positively correlated with the cooling rate, which suggested the absence of solute trapping. The transmission electron microscopy/selected area electron diffraction analysis of the most Ge-rich regions revealed superlattice spots indicative of chemical ordering. However, simple chemical ordering within a single diamond cubic unit cell could not explain the fact that most stoichiometries had compositions that were multiples of 5 at% Ge, which indicated the presence of superstructural ordering.

Improved Thermodynamic Descriptions of Carbides in Ni-Based Superalloys

The Ni-based superalloy René 41 has sparked recent interest for applications in next-generation aircraft engines due to its high-temperature strength that is superior to all similar grades. These desirable properties are achieved by careful control of the microstructure evolution during thermomechanical processing, and this is commonly informed by simulations. In particular, the grain boundary carbides M6C and M23C6 play an essential role in controlling the grain size and strength of the final product. Therefore, a solid understanding of the thermodynamic stability and thermokinetic evolution of these carbides is essential. However, thermokinetic simulations using existing thermodynamic databases have been demonstrated to have discrepancies between thermodynamic stabilities and experimental observations. Here, we collected a new experimental time–temperature–precipitation diagram. In conjunction with improved crystallographic descriptions, these experimental results are used to modify a CALPHAD database for M6C and M23C6. The modified database correctly identifies temperature regions with rapid carbide precipitation kinetics. Further, kinetic simulations and strengthening models successfully predict the hardness increase due to γ′ precipitation. The modified database has been applied to Udimet 700, Waspaloy, and Haynes 282, demonstrating improved results. These updates will facilitate more accurate simulations of the microstructure evolution during thermomechanical processing of advanced Ni-based superalloys for aerospace and other applications.

Thermodynamically consistent modeling of gas flow and adsorption in porous media

In modeling of gas flow through porous media width adsorption, the thermodynamic properties of the adsorbed phase are usually approximated by those of the bulk liquid. Using non-isothermal, gaseous transport of moist air through a porous insulation material as example, we show that this leads to violation of the second law of thermodynamics and a negative entropy production. To resolve this violation, we use information about the adsorption and thermodynamic properties of bulk fluids to derive consistent thermodynamic properties of the adsorbed phase, such as the chemical potential, enthalpy and entropy. The resulting chemical potential of the adsorbed phase is a starting point for rate-based models for adsorption based on non-equilibrium thermodynamics. Incorporating the consistent thermodynamic description into the energy, entropy and momentum balances restores agreement with the second law of thermodynamics. We show that the temperature evolution in the porous medium from the consistent description differs from the standard formulation only if the adsorption depends explicitly on temperature. This highlights the importance of characterizing the temperature dependence of the adsorption with experiments or molecular simulations for accurate non-isothermal modeling of porous media.

Thermodynamic Assessment of the Mo–Si System

The binary system Mo–Si is reassessed based on previously reported findings that the phase shows a deficiency in Si and to take into account experimental data on the heat capacities of the Mo silicides. The last aspect in particular has been neglected in previous assessments of the system. Experimental studies are carried out which confirm that the phase is deficient in Si in every alloy analyzed, with an average Si content of 23 at%. The thermodynamic description of this phase is adjusted accordingly and the parameters of the system are optimized. Two alternative possible descriptions are presented for the phase . It is shown that the calculated binary phase diagram agrees well with experimental data, like liquidus and solidus temperatures as well as homogeneity ranges of the phases, where applicable, for both datasets. Likewise, thermophysical data like enthalpies of the formation of the silicides are adequately described.

High-throughput determination of the interdiffusion coefficients and atomic mobilities in bcc Ti–Fe–V alloys

A comprehensive understanding of diffusion kinetics of the Ti–Fe–V system is crucial for elucidating the solidification process in high-strength titanium alloys. In this paper, ten sets of diffusion couples within bcc Ti–Fe–V alloys that underwent annealing at temperatures of 1273K, 1323K, and 1373K were prepared. Composition-distance curves were determined using the electron probe microstructure analysis technique. Atomic mobility parameters and interdiffusion coefficients were obtained using the numerical inverse method with the assistance of HitDIC software. It should be noted that the atomic mobility parameters for Ti–Fe and Ti–V were reoptimized using the most up-to-date thermodynamic descriptions. This approach enables the acquisition of comprehensive data regarding the temperature-composition relationship in diffusion. D˜FeFeTi exhibits a markedly greater value compared to D˜VVTi. Both D˜FeFeTi and D˜VVTi demonstrate an increase with the increase of temperature. Furthermore, the Arrhenius equation can be applied to solve for the variation in frequency factors and activation energies concerning temperature and composition.

Thermodynamic modeling of the Ti–Al–V system over the entire composition and a wide temperature range

Ti–Al–V alloys have received considerable attention owing to their excellent high-temperature mechanical properties. After conducting a critical review of the available experimental data for the ternary Ti–Al–V system, a thermodynamic assessment of the system was carried out over the entire composition and a wide temperature range utilizing the CALPHAD method. The extensive homogeneity ranges of the α2 and γ phases were satisfactorily reproduced. Of particular significance was the first accurate description of the phase equilibria at 1573 K. The model parameters obtained in this study well represented the thermochemical properties and phase equilibria of the experimental data. Furthermore, the enthalpies of the widely used Ti alloy Ti–6Al–4V were reproduced using the thermodynamic description established in this study. Thus, this study provides a reliable basis for guiding the development and design of Ti–Al–V alloys.

Thermodynamic Study of N-Methylformamide and N,N-Dimethyl-Formamide.

An extensive thermodynamic study of N-methylformamide (CAS RN: 123-39-7) and N,N-dimethylformamide (CAS RN: 68-12-2), is presented in this work. The liquid heat capacities of N-methylformamide were measured by Tian-Calvet calorimetry in the temperature interval (250-300) K. The vapor pressures for N-methylformamide and N,N-dimethylformamide were measured using static method in the temperature range 238 K to 308 K. The ideal-gas thermodynamic properties were calculated using a combination of the density functional theory (DFT) and statistical thermodynamics. A consistent thermodynamic description was developed using the method of simultaneous correlation, where the experimental and selected literature data for vapor pressures, vaporization enthalpies, and liquid phase heat capacities and the calculated ideal-gas heat capacities were treated together to ensure overall thermodynamic consistency of the results. The resulting vapor pressure equation is valid from the triple point to the normal boiling point temperature.

Innovative thermodynamic modeling for enhanced yeast dough mixing: energy perspectives and applications

A thermodynamic model for the calculation of energy exchange in the chamber of a new mixer with effective use of structural and technological parameters of the mixing process without the necessary introduction of experimental data correlations in the distribution of fluid velocities is proposed, which determines the relevance of this direction of calculation with the perspective of its development. The purpose of the presented work is to determine the specific power by substantiating the effective mode parameters of the preparation of the mixture (dough) as a result of evaluating the thermodynamic energy parameters of the kneading process. The assessment was carried out by developing a methodology for determining specific costs for creating a viscous medium when mixing components, which allows you to establish the required power depending on the design and technological parameters of the new mixer. The considered principle of the proposed open-type thermodynamic system of the description of the working process of mixing made it possible to reveal and determine the ways of converting energy into useful work of interphase heat and mass transfer of a heterogeneous medium. In the conditions of circulation mixing with multiple mechanical effects on the mixture of components in the closed circuit of the cylindrical working chamber, which is an effective way to achieve homogeneity of the environment, it was possible to obtain an analytical determination of the specific work and power of the drive in the absence of a clear description of the model of the interconnection of components. The proposed thermodynamic description of the system's energy balance allows to perform only a few experiments.  In general, the practical value of the given calculations is of practical importance for improving productivity and efficiency and minimizing energy consumption for the process while reducing the dynamic loads of the designed mixer.

Thermodynamic description for magneto-plastic coupling in electrical steel sheets

The purpose of the study is to propose a thermodynamic description of the full magneto-mechanical coupling in electrical steel sheets, including both elasticity and plasticity influence. Kinematic and isotropic hardening are considered as state variables and included to a second-order magneto-elastic energy written as a function of cubic invariants. The simulation of magnetic behaviour of plastified samples subjected to several elastic stresses reproduce the general trends of measurements carried out on non-oriented Fe-3%Si sheets.

Experimental Investigation and Thermodynamic Modeling of the Li2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O–Al2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document} System

In the present work, phase equilibria in the Li2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O–Al2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document} system were experimentally studied and calorimetric measurements were performed. Based on obtained results and data from literature, thermodynamic parameters of the system were assessed. The solid solution phases were modeled using Compound Energy Formalism (CEF) and liquid phase was described by two-sublattice partially ionic liquid model. The experimental investigations for selected compositions of isothermally heat-treated samples were performed using x-ray Diffraction (XRD) and Scanning Electron Microscopy (SEM). Differential Thermal Analysis (DTA) and Differential Scanning Calorimetry (DSC) were used to measure the temperature of the reactions as well as the heat capacities, respectively. After DTA, the microstructure was analyzed using SEM. Temperature of peritectic melting of h-LiAl5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_5$$\\end{document}O8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_8$$\\end{document} was determined to be 2222 K and temperature of eutectic reaction Liq ↔\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\leftrightarrow$$\\end{document}γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-LiAlO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} + h-LiAl5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_5$$\\end{document}O8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_8$$\\end{document} to be 1965 K. Heat capacity of LiAlO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} and LiAl5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_5$$\\end{document}O8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_8$$\\end{document} was measured in the temperature range of 100-1300 K. The degree of inversion of spinel phase (Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document}, Li+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+1}$$\\end{document})1T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_1^T$$\\end{document}:(Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document}, Li+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+1}$$\\end{document}, Va)2O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2^O$$\\end{document}:O4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_4$$\\end{document} was modelled assuming Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document} and Li+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+1}$$\\end{document} can occupy tetrahedral (T) and octahedral (O) cationic sublattices while its composition extension in Al2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_3$$\\end{document} enriched region was described by introducing vacancies in octahedral sites. Thermodynamic description derived in the present study reproduces the degree of inversion close to that of the high-temperature spinel phase, which means that Al+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+3}$$\\end{document} ions preferentially occupy the tetrahedral sites. The calculated phase diagram satisfactorily agrees with the experimental results. Available experimental thermodynamic data are also reproduced within uncertainty limits.

Molecular simulations of doxorubicin complexed with native and modified cyclodextrins in water

In this study, all-atom molecular dynamics simulations have been performed to investigate from a nanoscopic point of view the interactions in supramolecular complexes formed between doxorubicin and cyclodextrins in an aqueous phase at a temperature of 310 K. All the simulations are on the time scales of microseconds and are carried out on High Performance Computing resources provided by the Greek Supercomputer ARIS. Doxorubicin, which is a well-known anticancer drug belonging to the class of anthracyclines, is simulated with two cyclodextrins of broad utilization in drug delivery, i.e.: γ-cyclodextrin and 2-hydroxypropyl-β-cyclodextrin. In both cases, the complexation process takes place spontaneously during the course of the simulations and a detailed analysis of the formed complexes is conducted in terms of structural, dynamical and thermodynamic properties. In addition, we present a quantitative analysis of how doxorubicin affects, upon complexation, the geometry, the hydrogen bonding network and the hydration of the selected cyclodextrins. Special attention is paid to the thermodynamic description of the simulated systems. More specifically, the standard binding free energy is calculated with an extended version of the linear interaction energy method. The presented in silico approach reveals that doxorubicin forms stable complexes with the chosen cyclodextrin molecules, there is a water solubility enhancement of the drug with respect to its unbound state and also cyclodextrins act protectively to the drug preventing undesired effects, such as the glycosidic degradation. Excellent agreement is found between the presented results and published in silico and experimental findings.

Heavy metal decontamination by ion exchange polymers for water purification: counterintuitive cation removal by an anion exchange polymer

Ion exchange polymers were used for mercury and lead ions removal in water. The heavy metal ion concentration was analyzed by two independent methods: inductively coupled plasma–optical emission spectroscopy (ICP-OES) and gravimetry. The studied cation exchange polymer (CEP) was sulfonated poly(ether ether ketone) (SPEEK), and the anion exchange polymer (AEP) was poly(sulfone trimethylammonium) chloride (PSU-TMA). The removal capacity was connected with the ion exchange capacity (IEC) equal to 1.6 meq/g for both polymers. The concentration ranges were 0.15–0.006 mM for Hg2+ and 10.8–1.0 mM for Pb2+. SPEEK achieved 100% removal efficiency for mercury and lead if the concentration was below the maximum sorption capacity (Qmax), which was about 210 mg/g for Pb2+ with SPEEK. For PSU-TMA, the surprising removal efficiency of 100% for Hg2+, which seemed incompatible with ion exchange, was related to the formation of very stable complex anions that can be sorbed by an AEP. Langmuir adsorption theory was applied for the thermodynamic description of lead removal by SPEEK. A second-order law was effective to describe the kinetics of the process.

Thermodynamic description of active brownian particle driven by fractional gaussian noise

As a natural extension of the recent results on the thermodynamics of an active Brownian particle (self-propelled), we study the thermodynamics of an active Brownian particle (ABP) driven by fractional Gaussian noise (FGN). To serve as a prelude of the main results, we start from the conventional Markov process but with time dependent diffusion coefficient, where deviation in integral fluctuation relation (IFR) for total entropy production requires a general definition of the temperature, following the same case for a Brownian particle. In other words, the general temperature definition for this case is independent to the statistics of the rotational motion. We then proceed with the main problem of the paper, which is an active Brownian particle driven by fractional Gaussian noise. Under the assumption that self-propulsion is even under time-reversal, temperature is defined as well as the distance on how far the IFR for total entropy production deviates from the standard definition by adopting the standard definition of trajectory-level entropy and the joint probability of ABP. Furthermore, second law-like concept based on the found deviation is derived, as well as a generalized Clausius inequality. Lastly, magnitude of this deviation diminishes in the case of pure white noise.

Thermodynamics of quark matter with multiquark clusters in an effective Beth-Uhlenbeck type approach

We describe multiquark clusters in quark matter within a Beth-Uhlenbeck approach in a background gluon field coupled to the underlying chiral quark dynamics using the Polyakov gauge. An effective potential for the traced Polyakov loop is used to establish the center symmetry of the SU(3) color which suppresses colored states and its dynamical breaking as an aspect of the confinement/deconfinement transition. Quark confinement is modeled by a large quark mass in vacuum which is motivated by a confining density functional approach. A multiquark cluster containing n quarks and antiquarks is described as a binary composite of smaller subclusters n1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_1$$\\end{document} and n2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_2$$\\end{document} (n1+n2=n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_1+n_2=n$$\\end{document}). It has a spectrum consisting of a bound state and a scattering state continuum. For the corresponding cluster-cluster phase shifts we use simple ansätze that capture the Mott dissociation of clusters as a function of temperature and chemical potential. We go beyond the simple “step-up-step-down” model that ignores continuum correlations and introduce an improved model that includes them in a generic form. In order to explain the model, we restrict ourselves here to the cases where the cluster size is 1≤n≤6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1 \\le n \\le 6$$\\end{document}. A striking result is the suppression of the abundance of colored multiquark clusters at low temperatures by the coupling to the Polyakov loop and their importance for a quantitative description of lattice QCD thermodynamics at non-vanishing baryochemical potentials. An important ingredient are Polyakov-loop generalized distribution functions of n-quark clusters which are derived here for the first time. Within our approach we calculate thermodynamic properties such as baryon density and entropy. We demonstrate that the limits of a hadron resonance gas at low temperatures and O(g2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(g^2)$$\\end{document} perturbative QCD at high temperatures are correctly reproduced. A comparison with lattice calculations shows that our model is able to give a unified, systematic approach to describe properties of the quark-gluon-hadron system.

Soot formation in combustion of spherically symmetric isolated fuel droplets with different initial diameters

Spherically-symmetric, isolated droplets are ideal systems to investigate the physics and the chemistry of combustion of liquid fuels. Despite their simplicity, most phenomena involved in spray combustion are still accounted for: evaporation and diffusion-induced transport, complex liquid thermodynamics, radiation, aerosol chemistry. In this work we analyzed the formation and evolution of soot particles and aggregates from the combustion of n-heptane isolated droplets. A 1D mathematical model including detailed description of thermodynamics and transport properties of liquid and gaseous phases, radiative heat transfer, and detailed homogeneous chemistry is adopted. Soot formation and evolution is described via a discrete sectional method, accounting for nucleation, surface growth, coagulation, aggregation, and oxidation.The mathematical model was utilized in this study to investigate how the initial diameter of droplets affects their tendency to form soot. The simulations were specifically designed to examine the experimental findings of Choi et al. (2001), which indicated that droplets with intermediate diameters (∼ 1.9 mm) result in the highest soot volume fraction. The numerical results reveal that this maximum is due to a competition between two phenomena: (i) increasing droplet diameter leads to a longer lifetime, thereby promoting soot formation, but (ii) larger diameters cause more radiative losses, lower flame temperatures, and subsequently, a decrease in soot formation.