Temperature-dependent solubility of Rebaudioside A in methanol/ethanol and ethyl acetate mixtures:Experimental measurements and thermodynamic modeling

The equilibrium solubility of Rebaudioside A(Reb A)FormⅡin binary mixtures of methanol/ethanol and ethyl acetate was quantitatively determined within the temperature range of 283.15—328.15 K at ambient pressure.The experimental findings indicate a positive correlation between the solubility of Reb A(FormⅡ)and both the temperature and the methanol/ethanol content in the solvent system.To describe the solubility data,six distinct models were employed:the modified Apelblat equation,theλh model,the combined nearly ideal binary solvent/Redlich—Kister(CNIBS/R—K)model,the van't HoffJouyban-Acree(VJA)model,the Apelblat-Jouyban-Acree(AJA)model,and the non-random two-liquid(NRTL)model.The combined nearly ideal binary solvent/Redlich—Kister model exhibited the most precise fit for solubility in methanol+ethyl acetate mixtures,reflected by an average relative deviation(ARD)of 0.0011 and a root mean square deviation(RMSD)of 12×10^(-7).Conversely,for ethanol+ethyl acetate mixtures,the modified Apelblat equation provided a superior correlation(ARD=0.0014,RMSD=4×10^(-7)).Furthermore,thermodynamic parameters associated with the dissolution of Reb A(FormⅡ),including enthalpy,entropy,and the Gibbs energy change,were inferred from the data.The findings underscore that the dissolution process is predominantly endothermic across the solvent systems examined.Notably,the entropy changes appear to have a significant influence on the Gibbs free energy associated with the dissolution of Reb A(FormⅡ),suggesting that entropic factors may play a pivotal role in the studied systems.

Local structure of calcium silicate melts from classical molecular dynamics simulation and a newly constructed thermodynamic model

The distributions of local structural units of calcium silicate melts were quantified by means of classical molecular dynamics simulation and a newly constructed structural thermodynamic model. The distribution of five kinds of Si-O tetrahedra Qi from these two methods was compared with each other and also with the experimental Raman spectra, an excellent agreement was achieved. These not only displayed the panorama distribution of microstructural units in the whole composition range, but also proved that the thermodynamic model is suitable for the utilization as the subsequent application model of spectral experiments for the thermodynamic calculation. Meanwhile, the five refined regions mastered by different disproportionating reactions were obtained. Finally, the distributions of two kinds of connections between Qi were obtained, denoted as Qi-Ca-Qj and Qi-[Ob]-Qj, from the thermodynamic model, and a theoretical verification was given that the dominant connections for any composition are equivalent connections.

A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in aqueous solutions and its applications in binary and ternary aqueous solutions

A universal thermodynamic model of calculating mass action concentrations for structural units or ion couples in ternary and binary strong electrolyte aqueous solution was developed based on the ion and molecule coexistence theory and verified in four kinds of binary aqueous solutions and two kinds of ternary aqueous solutions. The calculated mass action concentrations of structural units or ion couples in four binary aqueous solutions and two ternary solutions at 298.15 K have good agreement with the reported activity data from literatures after shifting the standard state and concentration unit. Therefore, the calculated mass action concentrations of structural units or ion couples from the developed universal thermodynamic model for ternary and binary aqueous solutions can be applied to predict reaction ability of components in ternary and binary strong electrolyte aqueous solutions. It is also proved that the assumptions applied in the developed thermodynamic model are correct and reasonable, i.e., strong electrolyte aqueous solution is composed of cations and anions as simple ions, H2O as simple molecule and other hydrous salt compounds as complex molecules. The calculated mass action concentrations of structural units or ion couples in ternary and binary strong electrolyte aqueous solutions strictly follow the mass action law.

Thermodynamic model of lead oxide activity in PbO-CaO-SiO_2-FeO-Fe_2O_3 slag system

According to the ion and molecule coexistence theory, a thermodynamic model of lead oxide activity in PbO-CaO-SiO2-FeO-Fe2O3 slag system was established at the temperature of 1273-1733 K. The activities of Pb O in slag were calculated, and their equal activity curves were plotted. The influences of slag basicity Q, iron oxide rate R and temperature T on activity NPb O and activity coefficient γPbO were also investigated. Results show that the calculated values of γPb O are in good agreement with the reported experimental data, showing that the model can wholly embody the slag structural characteristics. NPbO departures positively from Raoult values, and increases with increasing Pb O content in slag but changes little with T. γPbO increases with increasing Q, and goes through the maximum with increasing R for basic slag（Q0.3）. Results can be applied to the thermodynamic research and operational optimization of modern lead smelting technologies.

Thermodynamic modeling and phase diagram prediction of salt lake brine systems.Ⅰ. Aqueous Mg^2+–Ca^2+–Cl^- binary and ternary systems

Salt lake brine is a complex salt-water system under natural environment.Although many models can express the thermodynamic properties and phase equilibrium of electrolyte aqueous solution,the multi-temperature characteristics and predictability are still the goals of model development.In this study,a comprehensive thermodynamic model system is re-established based on the eNRTL model and some improvements:(1) new expression of long-range electrostatic term with symmetrical reference state is proposed to handle the electrolyte solution covering entire concentration range;(2) the temperature dependence of the binary interaction parameters is formulated with a Gibbs Helmholtz expression containing three temperature coefficients,the liquid parameters,which associated with Gibbs energy,enthalpy,and heat capacity contribution;and(3) liquid parameters and solid species data are regressed from properties and solubility data at full temperature range.Together the activity coefficient model,property models and parameters of liquid and solid offer a comprehensive thermodynamic model system for the typical bittern of MgCl2-CaCl2-H2 O binary and ternary systems,and it shows excellent agreement with the literature data for the ternary and binary systems.The successful prediction of complete phase diagram of ternary system shows that the model has the ability to deal with high concentration and high non-idealitv system,and the ability to extrapolate the temperature.

A general thermodynamic model for the long-period stacking ordered phases in magnesium alloys

A thermodynamic model Mg x(Xs,Mg)6(Xl,Mg)8(Xs and Xl are elements smaller and larger than Mg)for long-period stacking ordered phases(LPSOs)was proposed based on two key factors:the Xs 6 Xl 8-type L12 clusters and the variation of chemical compositions.In general,all available LPSOs can be described with this model.As a representative system,Mg-Y-Zn with three LPSOs was investigated using the CALPHAD(calculation of phase diagram)approach aided with first-principles calculations.Two new three-phase equilibria were predicted and were validated by key experiments.The model-based descriptions will be the basis for the research and development of magnesium alloys.

Thermodynamic modeling and phase diagram prediction of salt lake brine systemsⅡ.Aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems

It is still a challenging task to accurately and temperature-continuously express the thermodynamic properties and phase equilibrium behaviors of the salt-lake brine with multi-component,multitemperature and high concentration.The essential subsystem of sulfate type brine,aqueous Li^(+)-Na^(+)-K^(+)-SO_(4)^(2-) and its subsystems across a temperature range from 250 K to 643 K are investigated with the improved comprehensive thermodynamic model.Liquid parameters(Δg_(IJ),Δh_(IJ),and ΔC_(p,IJ))associated with the contributions of Gibbs energy,enthalpy,and heat capacity to the binary interaction parameters,i.e.the temperature coefficients of eNRTL parameters formulated with a Gibbs Helmholtz expression,are determined via multi-objective optimization method.The solid constantsΔ_(f)G_(k)°^((298.15))andΔ_(f)H_(k)°^((298.15))of11 solid species occurred in the quaternary system are rebuilt from multi-temperature solubilities.The modeling results show the accurate representation of(1)solution properties and binary phase diagram at temperature ranges from eutectic points to 643 K;(2)isothermal phase diagrams for Li_(2)SO_(4)-Na_(2)SO_(4)-H_(2)O,Li_(2)SO_(4)-K_(2)SO_(4)-H_(2)O and Na_(2)SO_(4)-K_(2)SO_(4)-H_(2)O ternary systems.The predicted results of complete structure and polythermal phase diagram of ternary systems and the isothermal phase diagrams of quaternary system excellently match with the experimental data.

Thermodynamic Modeling of Wax Precipitation in Crude Oils

Most of the crude oils contain waxes which precipitate when temperature drops, resulting in deposition in pipelines and production equipment. It is necessary to set up a model which can predict the wax appearance tem-perature and the amount of solid precipitated in the different conditions. A modified thermodynamic solid-liquid equilibrium model to calculate wax precipitation in crude oil systems has been developed recently. The assumption that precipitated waxes consist of several solid phases is adopted in this research, and the solid-solid transition is also considered in the modified model. The properties of the pseudo-components are determined by using empirical correlations. New correlations for properties of solid-solid and solid-liquid transitions are also established in this work on the basis of the data from the literature. The results predicted by the proposed model for three crude oil systems are compared with the experimental data and the calculated results from the literature, and good agreement is observed.

A novel hybrid thermodynamic model for pore size distribution characterisation for shale

Scholars often see the gas adsorption technique as a straight-to-interpret technique and adopt the pore size distribution(PSD)given by the gas adsorption technique directly to interpret pore-structure-related issues.The oversimplification of interpreting shale PSD based on monogeometric thermodynamic models leads to apparent bias to the realistic pore network.This work aims at establishing a novel thermodynamic model for shale PSD interpretation.We simplified the pore space into two geometric types—cylinder-shaped and slit-shaped.Firstly,Low-temperature Nitrogen Adsorption data were analyzed utilizing two monogeometric models(cylindrical and slit)to generate PSD_(cyl).and PSD_(slit);Secondly,pore geometric segmentation was carried out using Watershed by flooding on typical SEM images to obtain the ratio of slit-shaped(∅_(s))and cylinder-shaped pores(∅_(c)).Combining the results of the two,we proposed a novel hybrid model.We performed pyrolysis,XRD,FE-SEM observation,quantitative comparison with the results obtained by the DFT model,and fractal analysis to discuss the validity of the obtained PSD_(Hybrid).The results showed that:the hybrid model proposed in this work could better reflect the real geometry of pore space and provide a more realistic PSD;compared with thermodynamic monogeometric models,PSD obtained from the hybrid model are closer to that from the DFT model,with an improvement in the deviation from the DFT model from 5.06%to 68.88%.The proposed hybrid model has essential application prospects for better interpretation of shale pore space.It is also worth noting that we suggest applying the proposed hybrid model for PSD analysis in the range of 5-100 nm.

Thermodynamic modeling of the La-Mg-Y system and Mg-based alloys database

As an example of the La-Mg-Y system, the method how to set up the themaodynamic model of individual phases was introduced in the process of thermodynamic optimization. The solution phases （liquid, body-centered cubic, face-centered cubic, hexagonal close-packed and double hexagonal close-packed） were modeled with the Redlich-Kister equation. The compound energy model has been used to describe the thermodynamic functions of the intermetallic compounds in the La-Mg-Y systems. The compounds Mg2Y, Mg24Y5, Mg12La, Mg17La2, Mg41Las, Mg3La and Mg2La in the La-Mg-Y system were treated as the formulae （Mg,Y）2（La,Mg,Y）, Mg24（La,Mg,Y）4Y, Mg12（La, Y）, Mg17（La,Y）2, Mg41（La,Y）5, Mg3（La,Mg,Y） and Mg2（La, Y）, respectively. A model （La, Mg,Y）0.5（La,Mg,Y）0.5 was applied to describe the compound MgM formed by MgLa and MgY in order to cope with the order-disorder transition between body-centered cubic solution （A2） and MgM with CsCl-type structure （B2） in the La-Mg-Y system. The Gibbs energies of individual phases were optimized in the La-Mg, La-Y and La-Mg-Y systems by CALPHAD technique. The projection of the liquidus surfaces for the La-Mg-Y system was predicted. The Mg-based alloys database including 36 binary and 15 ternary systems formed by Mg, Al, Cu, Ni, Mn, Zn and rare earth elements was set up in SGTE standard.

A Molecular Thermodynamic Model for Interfacial Tension in Surfactant-Oil-Water System

An interfacial equation of state based on perturbation theory for surfactant-oil-water system has been developed. By combining the interfacial equation of state with Boudh-Hir and Mansoori's model, a molecular ther-modynamic model has been proposed. The interfacial tension of surfactant-oil-water systems can be calculated from the surface tensions of pure oil and water by this model. The interfacial tension data for sodium dodecyl sulphate-heptane-water system, polyoxyethylene n-octylphenol-heptane-water system and hexadecyl trimethyl ammonium bromide-heptane-water system have been correlated. By using the adjustable parameters obtained, the interfacial tensions of these systems at other temperatures have been predicted. Both the correlated and the predicted values are satisfactory.

A thermodynamic model of calculating mass action concentrations for structural units or ion couples in NaClO_4-H_2O and NaF-H_2O binary solutions and NaClO_4-NaF-H_2O ternary solution

A thermodynamic model of calculating mass action concentrations for structural units or ion couples in NaClO4-H2O and NaF-H2O binary solutions and NaClO4-NaF-H2O ternary strong electrolyte aqueous solutions was developed based on the ion and molecule coexistence theory （IMCT）. A transformation coefficient was needed to compare the calculated mass action concentration and the reported activity, because they were usually obtained at different standard states and concentration units. The results show that transformation coefficients between the calculated mass action concentrations and the reported activities of the same components change in a very narrow range. The transformed mass action concentrations of structural units or ion couples in NaClO4-H2O and NaF-H2O binary solutions agree well with the reported activities. The transformed mass action concentrations of structural units or ion couples in NaClO4-NaF-H2O ternary solution are also in good agreement with the reported activities in a total ionic strength range from 0.1 to 0.9 mol/kg H2O by the 0.1 mol/kg step with different ionic strength fractions of 0, 0.2, 0.4, 0.5, 0.6, 0.8, and 1, respectively. The results indicate that the developed thermodynamic model can reveal the structural characteristics of binary and ternary strong electrolyte aqueous solutions, and the calculated mass action concentrations of structural units or ion couples also strictly follow the mass action law.

Multi-stage rodingitization of ophiolitic bodies from Northern Apennines(Italy): Constraints from petrography, geochemistry and thermodynamic modelling

The investigated mantle bodies from the External Ligurians(Groppo di Gorro and Mt.Rocchetta)show evidences of a complex evolution determined by an early high temperature metasomatism,due to percolating melts of asthenospheric origin,and a later metasomatism at relatively high temperature by hydrothermal fluids,with formation of rodingites.At Groppo di Gorro,the serpentinization and chloritization processes obliterated totally the pyroxenite protolith,whereas at Mt.Rocchetta relics of peridotite and pyroxenite protoliths were preserved from serpentinization.The rodingite parageneses consist of diopside+vesuvianite+garnet+calcite+chlorite at Groppo di Gorro and garnet+diopside+serpentine±vesuvianite±prehnite±chlorite±pumpellyite at Mt.Rocchetta.Fluid inclusion measurements show that rodingitization occurred at relatively high temperatures(264-334℃ at 500 bar and 300-380℃ at 1 kbar).Garnet,the first phase of rodingite to form,consists of abundant hydrogarnet component at Groppo di Gorro,whereas it is mainly composed of grossular and andradite at Mt.Rocchetta.The last stage of rodingitization is characterized by the vesuvianite formation.Hydrogarnet nucleation requires high Ca and low silica fluids,whereas the formation of vesuvianite does not need CO2-poor fluids.The formation of calcite at Groppo di Gorro points to mildly oxidizing conditions compatible with hydrothermal fluids;the presence of andradite associated with serpentine and magnetite at Mt.Rocchetta suggests Fe^3+-bearing fluids with fO2 slightly higher than iron-magnetite buffer.We propose that the formation of the studied rodingite could be related to different pulses of hydrothermal fluids mainly occurring in an oceancontinent transitional setting and,locally,in an accretionary prism associated with intra-oceanic subduction.

Thermodynamic modeling and elemental migration for the early stage of rodingitization:An example from the Xialu massif of the Xigaze ophiolite,southern Tibet

The analysis of early stage rodingite from the ultramafic rocks of the Xialu Massif in the Xigaze Ophiolite,Tibet,in China shows that the rodingitization involved continuous changes in fluid composition during different stages of subduction.The early stage prehnite-bearing rodingite was produced at low pressures and temperatures along extensional fractures.Samples of rodingite were collected along a profile from the center to the margin of a rodingitized intrusive igneous rock(^10 m×30 m),and they record wide variations in bulk composition,mineralogy,and texture.The mineral assemblages,from center to margin,vary from(1)relics of primary clinopyroxene(Cpx_(r))and primary amphibole(Amp_(r))+newly formed late amphibole(Act)+primary plagioclase(Pl_(r))+clinozoisite+prehnite+albite+chlorite+titanite+ilmenite(R1 rodingite),through(2)relics of primary clinopyroxene(Cpx_(r))+newly formed late clinopyroxene(Cpx_(n))+primary and late amphiboles(Amp_(r)+Act)+clinozoisite+prehnite+albite+chlorite+titanite(R2 rodingite),to(3)newly formed late clinopyroxene(Cpx_(n))and amphibole(Act)+clinozoisite+prehnite+albite+chlorite+titanite(R3 rodingite).As a result of the metasomatic process of rodingitization,the content of CaO in the whole rock chemical composition from R1 to R3 increases,SiO_(2) decreases,and Na_(2)O+K_(2)O is almost completely removed.Massbalance diagrams show enrichments in large ion lithophile elements such as Rb,Cs,Ba,and Pb as well as Ni during rodingitization.The central part of the rodingitized intrusion(R1 rodingite)was only slightly affected by metasomatism.On the other hand,the contents of the rare earth elements(REEs),high field strength elements(HFSEs;e.g.Zr,Nb,Ta,Hf,and Y),and some highly compatible elements such as Cr and Sc decreased slightly during rodingitization.Thermodynamic modeling based on equilibrium mineral assemblages indicates that the rodingite of the Xialu Massif formed in an H_(2)O-saturated,CO_(2)-rich environment.The estimated conditions of metamorphism were-281-323℃and 0.4-3.9 kbar,representing the subgreenschist facies.In this environment,REEs and HFSEs were soluble in the fluids and partly removed.Moreover,these prehnite rodingites formed in a progressively reducing and less alkaline environment,as indicated by decreases in f(O_(2))and bulk-rock Fe^(3+)/Fe^(2+) ratios,and the records of fluidΔpH from the center to the margin of the studied rodingitized intrusion.

Simplified Thermodynamic Model for Pro-Eutectoid Ferrite Formation in Multicomponent Structural Steel

By introducing aparameter of difference in ferrite formation temperature between binary Fe-C and multicomponent system,and referring to the thermodynamic model for Fe-C binary system,a simplified thermodynamic model for pro-eutectoid ferrite formation in Fe-ΣXiC multicomponent structural steels(Xi=Mn,Si,Mo,Cr,Ni or Ti,etc)was suggested.The comparison of the calculated Ae3 temperatures with the measured data of steels 42 shows that the relative standard deviation and root-mean-square(RMS)error between them are only 0.71% and 8.92 K,respectively.However,the deviations between the same measured data and the values calculated from the superelement model are as high as 1.86% and 23.83 K,respectively.It can be concluded that the simplified thermodynamic model for pro-eutectoid ferrite formation in multicomponent structural steels is acceptable and the calculated Ae3 temperatures are in good agreement with the experimental data.

Thermodynamic model for glass forming ability of ternary metallic glass systems

The thermodynamic model of multicomponent chemical short range order (MCSRO) was established in order to evaluate the glass forming ability (GFA) of ternary alloys. Comprehensive numerical calculations using MSCRO software were conducted to obtain the composition dependence of the MCSRO undercooling in Zr Ni Cu, Zr Si Cu and Pd Si Cu ternary systems. By the MCSRO undercooling principle, the composition range of Zr Ni Cu system with optimum GFA is determined to be 62.5 ～ 75 Zr, 5～ 20 Cu, 12.5 ～ 25 Ni ( n (Ni)/ n (Cu)=1～5). The TTT curves of Zr Ni Cu system were also calculated based on the MCSRO model. The critical cooling rates for Zr based alloy with deep MSCRO undercooling are estimated to be as low as 100?K/s, which is consistent with the practical cooling rate in the preparation of Zr based bulk metallic glass (BMG). The calculation also illustrates that the easy glass forming systems such as Pd based alloys exhibit an extraordinary deep MCSRO undercooling. It is shown that the thermodynamic model of MCSRO provides an effective method for the alloy designing of BMG.

Thermodynamic Model of Uranium and Arsenic Accumulation in Saline Lakes

1 Introduction The attractiveness of Shaazgai-Nuur Soda Lake(pH9.2-9.4)as an alternative metal source is explained by the high concentration of dissolved uranium(~1 mg/l)due to the location of water drainage territory within the Tsagan-

Molecular Thermodynamic Model for Polyelectrolyte Solutions with Added Salts

A molecular thermodynamic model of polyelectrolyte developed previously was extended to polyelectrolyte solutions with added salts.Thermodynamic properties,such as activity coefficients of polyelectrolytes or added salts and osmotic coefficients of solvent, of a number of aqueous mixtures of polyelectrolytes and salts are analyzed with the proposed model.Successful correlation is obtained in the range of moderate or higher polyion concentration.For the same sample,thermodynamic properties of polyelectrolytes with and without simple electrolytes can be predicted mutually using parameters from regression data.

Thermodynamic modeling of gas solubility in aqueous sodium chloride solution

An electrolyte Equation of State is presented by combining the Cubic Plus Association Equation of State,Mean Spherical Approximation and the Born equation.This new model uses experimental relative static permittivity,intend to predict well the activity coefficients of individual ions(ACI)and liquid densities of aqueous solutions.This new model is applied to model water+Na Cl binary system and water+gas+Na Cl ternary systems.The cation/anion-water interaction parameters of are obtained by fitting the experimental data of ACI,mean ionic activity coefficients(MIAC)and liquid densities of water+Na Cl binary system.The cation/anion-gas interaction parameters are obtained by fitting the experimental data of gas solubilities in aqueous Na Cl solutions.The modeling results show that this new model can correlate well with the phase equilibrium and volumetric properties.Without gas,predictions for ACI,MIAC,and liquid densities present relative average deviations of 1.3%,3.6%and 1.4%compared to experimental reference values.For most gas-containing systems,predictions for gas solubilities present relative average deviations lower than 7.0%.Further,the contributions of ACI,and salting effects of Na Cl on gases are analyzed and discussed.

Experimental measurement and thermodynamic modeling of binary and ternary solid–liquid phase equilibrium for the systems formed by L-arabinose,D-xylose and water

Solid–liquid phase equilibrium data for binary(L-arabinose–water) and(D-xylose–water) systems at temperatures from(269.85–298.05) K and ternary(L-arabinose–D-xylose–water) system at temperatures of 273.85 K,278.85 K and 284.45 K were measured at atmospheric pressure.The ternary phase diagrams of the systems were constructed on the base of the measured solubility.Two pure solid phases were formed at given temperatures,including pure L-arabinose and pure D-xylose,which were con firmed and determined by the method of Schreinemakers' wet residue.At the same temperature,the crystallization region of L-arabinose was larger than D-xylose's.The acquired solubility data were then correlated using the NRTL model,Wilson model and Xu model.The calculated solubility with the three models agreed well with the experimental values.