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.

FLOCKING OF A THERMODYNAMIC CUCKER-SMALE MODEL WITH LOCAL VELOCITY INTERACTIONS

In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.

Thermodynamic simulation of stepwise precipitation of NH_4VO_(3)and NaHCO_(3)from carbonating Na_(3)VO_(4)solution

Thermodynamic simulation was conducted to design a new process of stepwise precipitating NH_4VO_(3)and NaHCO_(3)from regulating the CO_(2)carbonation of Na_(3)VO_(4)solution.Firstly,a new V(V)speciation model for the aqueous solution containing vanadate and carbonate is established by using the Bromley-Zemaitis activity coefficient model.Subsequently,thermodynamic equilibrium calculations are conducted to clarify the behavior of vanadium,carbon,sodium,and impurity species in atmospheric or high-pressure carbonation.To ensure the purity and recovery of vanadium products,Na_(3)VO_(4)solution is initially carbonated to the pH of 9.3-9.4,followed by precipitating NH_4VO_(3)by adding(NH_4)_(2)CO_(3).After vanadium precipitation,the solution is deeply carbonated to the final pH of 7.3-7.5 to precipitate NaHCO_(3),and the remaining solution is recycled to dissolve Na_(3)VO_(4)crystals.Finally,verification experiments demonstrate that 99.1%of vanadium and 91.4%of sodium in the solution are recovered in the form of NH_4VO_(3)and NaHCO_(3),respectively.

Parameterization, sensitivity, and uncertainty of 1-D thermodynamic thin-ice thickness retrieval

Retrieval of Thin-Ice Thickness(TIT)using thermodynamic modeling is sensitive to the parameterization of the independent variables(coded in the model)and the uncertainty of the measured input variables.This article examines the deviation of the classical model’s TIT output when using different parameterization schemes and the sensitivity of the output to the ice thickness.Moreover,it estimates the uncertainty of the output in response to the uncertainties of the input variables.The parameterized independent variables include atmospheric longwave emissivity,air density,specific heat of air,latent heat of ice,conductivity of ice,snow depth,and snow conductivity.Measured input parameters include air temperature,ice surface temperature,and wind speed.Among the independent variables,the results show that the highest deviation is caused by adjusting the parameterization of snow conductivity and depth,followed ice conductivity.The sensitivity of the output TIT to ice thickness is highest when using parameterization of ice conductivity,atmospheric emissivity,and snow conductivity and depth.The retrieved TIT obtained using each parameterization scheme is validated using in situ measurements and satellite-retrieved data.From in situ measurements,the uncertainties of the measured air temperature and surface temperature are found to be high.The resulting uncertainties of TIT are evaluated using perturbations of the input data selected based on the probability distribution of the measurement error.The results show that the overall uncertainty of TIT to air temperature,surface temperature,and wind speed uncertainty is around 0.09 m,0.049 m,and−0.005 m,respectively.

Thermodynamic limit of the XXZ central spin model with an arbitrary central magnetic field

The U(1)symmetry of the X X Z central spin model with an arbitrary central magnetic field B is broken,since its total spin in the z-direction is not conserved.We obtain the exact solutions of the system by using the off-diagonal Bethe ansatz method.The thermodynamic limit is investigated based on the solutions.We find that the contribution of the inhomogeneous term in the associated T-Q relation to the ground state energy satisfies an N^(-1)scaling law,where N is the total number of spins.This result makes it possible to investigate the properties of the system in the thermodynamic limit.By assuming the structural form of the Bethe roots in the thermodynamic limit,we obtain the contribution of the direction of B to the ground state energy.It is shown that the contribution of the direction of the central magnetic field is a finite value in the thermodynamic limit.This is the phenomenon caused by the U(1)symmetry breaking of the system.

Thermodynamic consistent phase field model for sintering process with multiphase powders

A thermodynamic consistent phase field model is developed to describe the sintering process with multiphase powders. In this model, the interface region is assumed to be a mixture of different phases with the same chemical potential, but with different compositions. The interface diffusion and boundary diffusion are also considered in the model. As an example, the model is applied to the sintering process with Fe-Cu powders. The free energy of each phase is described by the well-developed thermodynamic models, together with the published optimized parameters. The microstructure and solute distribution during the sintering process can both be obtained quantitively.

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.

Crystallization thermodynamics of 2,4(5)-dinitroimidazole in binary solvents

2,4(5)-Dinitroimidazole(2,4(5)-DNI)is an important organic intermediate,and itself can also be used for energetic material.In this work,the solubility of 2,4(5)-DNI in(methanol+water,acetonitrile+water,acetone+water)binary solvents were measured by using a dynamic test method from 278.15 K to 323.15 K under 101.1 k Pa.The Jouyban–Acree model,van't Hoff–Jouyban–Acree model,Apelblat–Jouyb an–Acree model,Ma model,and Sun model were used to correlate the experimental data.The values of relative average deviation(RAD)and root-mean-square deviation(RMSD)were very small,indicating that the error between the experimental value and the correlated value was very small.The thermodynamic parameters such as dissolution enthalpy,dissolution entropy and Gibbs energy were calculated based on solubility data.High-purity of 2,4(5)-DNI was efficiently obtained by using cooling and dilution crystallization method.

Insights into the adsorption performance and mechanism of Cr(Ⅵ)onto porous nanocomposite prepared from gossans and modified coal interface:Steric,energetic,and thermodynamic parameters interpretations

Herein,iron oxide/hydroxides deposits(gossans)were utilized,for the first time,in the fabrication of magnetite nanoparticles(MNPs)to load modified coal(MC).The as-synthesized MNPs@MC composite was characterized via different techniques and utilized for the Cr(Ⅵ)remediation.Experimental studies supported by theoretical treatment were applied to offer a new overview of the Cr(Ⅵ)adsorption geometry and mechanism at 25-45℃.Experimental results suggested that the Cr(Ⅵ)uptake was mainly governed by adsorption-reduction coupled mechanism.The Langmuir model fitted well the Cr(Ⅵ)adsorption data with maximum adsorption capacities extended from 115.24 to 129.63 mg·g^(-1).Theoretical calculations indicated that Cr(Ⅵ)ions were adsorbed on the MNPs@MC following the theory of the advanced monolayer statistical model.The number of ions removed per site ranged from 1.88 to1.23 suggesting the involvement of vertical geometry and multi-ionic mechanism at all temperatures.The increment of the active sites density and the adsorption capacity at saturation with improving temperature reflected an endothermic process.Energetically,the Cr(Ⅵ)adsorption was controlled by physical forces as the adsorption energies were less than 40 kJ·mol^(-1).The calculated free enthalpy,entropy.and internal energy explained the spontaneous nature and the viability of Cr(Ⅵ)adsorption on the MNPs@MC adsorbent.These results offer a new approach in utilizing the iron-rich deposits as gossans in the preparation of magnetic and low-cost adsorbents for wastewater remediation.

Solubility measurement,correlation and thermodynamic properties of 2,3,4-trichloro-1,5-dinitrobenzene in fifteen mono-solvents at temperatures from 278.15 to 323.15 K

The solubility of 2,3,4-trichloro-1,5-dinitrobenzene(TCDNB) was measured by a laser dynamic method over the temperature range from 278.15 K to 323.15 K under 0.1 MPa in fifteen mono-solvents(methanol,ethanol,isopropanol,n-butanol,toluene,dichloromethane,chloroform,tetrachloromethane,1,2-dichloroethane,acetone,ethyl acetate,acetonitrile,N-methylpyrrolidone(NMP),N,Ndimethylformamide dimethyl sulfoxide(DMF),dimethyl sulfoxide(DMSO).The solubility of TCDNB could be increased with increasing temperature in fifteen mono-solvents.TCDNB solubility is in the following order at 298.15 K:NMP>DMF>DMSO>toluene>acetone>ethyl acetate>dichloromethane>1,2-dich loroethane>chloroform>acetonitrile>tetrachloromethane>methanol>ethanol>n-butanol>isopropanol.The KAT-LSER model was used to investigate the solvent effect,which revealed that the hydrogen bond acidity of solvents has a greater effect on TCDNB solubility.The van't Hoff model,the modified Apelblat model,theλh model,and the non-random two liquid(NRTL)model were used to correlate the solubility of TCDNB.The calculated solubility data agreed well with the experimental data,and the modified Apelblat model fit best.Furthermore,the van't Hoff and Gibbs equations were also used to calculate the dissolution thermodynamic properties of TCDNB in various solvents.TCDNB dissolution could be an enthalpy-driven,non-spontaneous,and endothermic process in fifteen mono-solvents.The determination and fitting solubility of TCDNB,as well as the calculation of its thermodynamic properties,would be critical in the purification and crystallization of its preparation process research.

Design and Numerical Simulation of an Arctic Ocean Circulation and Thermodynamic Sea－Ice Model

In this paper, the first version of a new Arctic Ocean circulation and thermodynamic sea-ice model is presentedby the authors based on the framework of a twenty-layer World Oceanic general circulation model developed byZhang et al. in 1994. The model's domain covers the Arctic Ocean and Greenland-Norwegian Seas with the horizontal resolution of 200 km×200 km on a stereographic projection plane. In vertical, the model uses the Eta-coordinate(Sigma modified to have quasi-horizontal coordinate surfaces) and has ten unevenly-spaced layers to cover the deepest water column of 3000 m. Two 150-year integrations of coupling the ocean circulation model with the sea-icemodel have been performed with seasonally cyclic surface boundary conditions. The only difference between the tWoexperiments is in the model's geography. Some preliminary analyses of the experimental results have been done focused on the following aspects: (1) surface layer temperature, salinity and current; (2) the' Atlantic Layer'; (3)sea-ice cover and its seasonal variation. In comparison with the available observational data, these results are acceptable with reasonable accuracy.

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 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.

Inter-comparisons of thermodynamic sea-ice modeling results using various parameterizations of radiative flux

Radiative fluxes are of primary importance in the energy and mass balance of the sea-ice cover. Various parameterizations of the radiative fluxes are studied in a thermodynamic sea-ice model. Model outputs of the surface radiative and heat fluxes and mass balance are compared with observations. The contribution of short-wave radiation is limited to a long part of winter. Therefore, simple schemes are often sufficient. Errors in estimations of the short-wave radiation are due mainly to cloud effects and occasionally to multi-reflection between surface and ice crystals in the air. The long-wave radiation plays an important role in the ice surface heat and mass balance during most part of a winter. The effect of clouds on the accuracy of the simple radiative schemes is critical, which needs further attention. In general, the accuracy of an ice model depends on that of the radiative fluxes.

Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

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 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.