Interaction Parameters Of Model Research Articles

Vapor-liquid equilibrium data for the binary system isopropanol+water at 60 kPa and 80 kPa

In this work, experimental Vapor-Liquid Equilibrium (VLE) data for the Isopropanol + Water system under vacuum conditions at 60 kPa and at 80 kPa, for which no experimental evidences have been found in the literature, are reported. The experimental investigation of the isobaric equilibrium has been carried out by GASP at the Process Thermodynamics laboratory (PT lab) of Politecnico di Milano by employing an all-glass dynamic recirculation still. The collected experimental data, together with those already available in the literature at other conditions, have been used for the evaluation of the thermodynamic model that best fits the data. Four different models have been considered and their performances have been checked through the calculation of the Absolute Average Deviation (AAD%). The lowest AAD% has been found for the UNIFAC model only for isobaric data, not for the isothermal points. The regression tool available in Aspen Plus® V14 has been used to fit the binary interaction parameters of the NRTL activity model.

Development of the NRTL functional activity coefficient (NRTL-FAC) model using high quality and critically evaluated phase equilibria data. 2

One of the most significant models based on the local composition concept in advanced thermodynamics, is the non-random two-liquid (NRTL) model. Many studies have been conducted to enhance its applicability to various systems. Among these studies, the development of the NRTL model for electrolytic systems, polymer systems, and systems containing special chemical associations has been particularly significant. However, the NRTL model and its developed forms are based on the concept of local composition, and the dependency of these models on the experimental data for regressing NRTL interaction parameters limits their applicability of the NRTL model. Accordingly, to overcome this limitation, the NRTL functional activity coefficient model (NRTL-FAC), which is a group contribution model, was developed (https://doi.org/10.1016/j.fluid.2021.113088). The current study aims to extend the NRTL-FAC model. To achieve this, 15 new main groups have been added to the previous ones, and 266 new interaction parameters have been optimized. A total of 374 isothermal/isobaric VLE data sets, including 7115 data points, were used. The quality of the experimental VLE data was assessed using various thermodynamic consistency tests, including the Herington test, Van Ness test, point test, infinite dilution test, EoS test, and endpoint test. The NRTL-FAC model can accurately predict the VLE of binary systems, with results in good agreement with experimental data at different temperature and pressure ranges. This accuracy was observed for both azeotrope systems and ideal systems with positive or negative deviation from Raoult's law. Unlike the UNIFAC-DMD model, which restricts a portion of its interaction parameters to consortium members, the NRTL-FAC model interaction parameters are publicly accessible. Therefore, the NRTL-FAC model can be confidently used as a preliminary estimate to predict VLE behavior in process design when experimental data is not available.

The Influence of the Scalar and Vector Anomalous Couplings on the Z-production at ILC in the Randall - Sundrum Model

An attempt is made to present the effect of the scalar and vector anomalous couplings on scattering process with polarized initial beams in the Randall-Sundrum model. We have studied the contribution of radion, Higgs and gauge bosons on the Z-production cross-section at International Linear Colliders (ILC). The cross-section depends strongly on the polarization of initial beams, the center of mass energy and model interaction parameters. The obtained results indicate that with the vector anomalous couplings included Z boson and photon, the cross-sections for the Z production are much larger than that with the scalar couplings included radion and Higgs under the same conditions.

An Experimental and Numerical Study for Discrete Element Model Parameters Calibration: Gluten Pellets

Discrete element method (DEM) simulation is widely used to calculate the flow characteristics of particles under certain conditions. DEM input parameters are the prerequisite for the accurate modeling and simulation of particles. In order to explore the mechanical properties and breaking behavior of gluten pellets, the pellet material property, the interaction parameters of pellet–stainless steel and pellet–pellet (multi-spheres autofill model), and the bonding parameters (bonded particle model) were calibrated by experiments and simulations. The relative error of the angle of repose, the breaking displacement, and the breaking force between simulated and experimental values were 0.28%, 0.66%, and 1.09%, respectively. Based on the regression analysis in the Design-Expert 12.0 software, the relationships among evaluating indicators (angle of repose, breaking displacement, and breaking force) and their corresponding influencing factors were established, respectively. Meanwhile, the feasibility of applying the interaction parameters of the multi-spheres autofill model to the bonded particle model was verified through the free fall test, the inclined plane sliding test, and the inclined plane tumbling time test. This work can provide a reference for the design of pellet feed processing and transportation machinery.

Experimental Study and Modeling of Solid-liquid Equilibrium for Binary and Ternary Pharmaceutical and Food Systems

Background: The experimental measurement of the solubility of a solute in a given solvent is a difficult task; hence, there is a need for reliable thermodynamic models for its prediction. However, these models require either molecular or group interaction parameters, which are not always available. Objective: The objective of the present study is to measure experimentally the solubility of different solutes in solvents selected from pharmaceutical or food fields on the basis that not all the required model interaction parameters are available to use the obtained experimental data for their determination. Methods: The experimental study of solid-liquid equilibrium for chosen binary and ternary systems at different temperatures was carried out using differential scanning calorimetry to determine the essential thermophysical properties like melting temperature and enthalpy. The modeling of these phase equilibrium data was performed using thermodynamic models like Random Two Liquids (NRTL) and Universal Functional Activity Coefficient (UNIFAC). The required NRTL interaction parameters were determined by minimizing a well-defined objective function using the simplex method. Results: The solubilities of the solutes in the different considered solvents at different temperatures obtained experimentally provided the required NRTL molecular interaction parameters. Solute solubilities were obtained using NRTL, UNIFAC, and ideal models. The comparisons showed an excellent agreement between the experimental values and the NRTL results, contrary to UNIFAC and ideal case models. Conclusion: This study shows the importance of thermodynamic modeling to predict solubility data that may be difficult, time-consuming, and costly to obtain experimentally.

Study of Thermodynamic Properties of l-Serine and l-Threonine in Aqueous Solutions of 1-(2-Carboxyethyl)-3-methylimidazolium Chloride [HOOCEMIM][Cl

The stability of amino acids in solutions containing electrolytes and the effect of ambient pH on their biological activity is an important research area. In this research work, the volumetric and transport properties of ionic liquid (IL) aqueous solution with special performance of 1-(2-carboxyethyl)-3-methylimidazolium chloride ([HOOCEMIM][Cl]) were studied. The selected IL acts as an electrolyte and allows the study of systems containing amino acids at acidic pH. In this work, the density, speed of sound and viscosity of binary and ternary solutions of IL in aqueous solution of amino acids in the structure of proteins, namely l-serine and l-threonine within IL molality range of (0.05, 0.07 and 0.09 mol·kg−1) were measured at 298.15 K. From these quantities, apparent molar volume, limiting apparent molar volume, apparent molar isentropic compression, limiting apparent molar isentropic compression, transfer standard volumes for amino acids from water to the aqueous IL solutions and viscosity B-coefficients were calculated using the equations of Redlich–Meyer and Jones–Dole. Close examination of literature indicates that there is no data for water activity for solution of l-serine + H2O at 308.15 and 318.15 K. In this way water activity, osmotic coefficient and vapor pressure were measured and using the interaction parameters of Wilson, NRTL, NRF-NRTL and UNIQUAC models, activity coefficient values of l-serine calculated.

Vapor pressure and vapor-liquid equilibrium data for eugenol/caryophyllene binary system at low pressures by experimental and predictive methods

The main objective of this study was to determine the vapor-liquid equilibrium of the binary mixture eugenol/caryophyllene at reduced pressures and to obtain pure compounds vapor pressure data in the same low-pressure condition. Isobaric vapor–liquid equilibrium (VLE) data have been measured in a Fischer ebulliometer at 5.0, 10.0, and 20.0 kPa. The vapor pressure of the pure compounds was determined by direct measurement of the equilibrium temperature at different pressures. The extended Antoine equation and the Clarke and Glew equation were fitted to the experimental data and compared with a predictive method. The thermodynamic consistency of the VLE experimental data was checked using the Redlich-Kister area test and the Van Ness point test. The binary interaction parameters of NRTL, Wilson, and UNIQUAC activity coefficient models were fitted from regression of experimental data. The average absolute deviation of the temperature (AAD(T)) and vapor-phase molar fraction (AAD(y)) are less than 0.22 K and 0.0119, respectively, proving a good adherence of the models for the calculation of the VLE system. The COSMO-SAC model was used to predict activity coefficients, compared with classic thermodynamic models, and was able to represent the azeotrope presented by the mixture.

Measurement and correlation of the vapor-liquid equilibria related to the extraction of phenols from tar with mono-ethanolamine

Extracting phenol from coal tar has great economic significance. In this paper, a process for separating phenol from coal tar using mono-ethanolamine (MEA) as extractant was proposed, the conceptual design and optimized of the process was carried out by using Aspen Plus software. To ensure the accuracy of simulation, the vapor-liquid equilibrium data of MEA + phenol binary system were measured under different pressures. The binary interaction parameters of NRTL model, Wilson model and UNIQUAC model were fitted with the experimental data by data regression system. The results show that the deviation of NRTL model is less than that of Wilson model and UNIQUAC model. Considering that the boiling point difference between MEA and phenol is only 10°, two energy-saving schemes of double effect distillation are introduced into the conceptual process proposed in this paper, which can save 20% and 44.8% respectively compared with the traditional single tower distillation process. This paper provides reference for the industrial application of MEA in the extraction of phenol from coal tar.

Recommendations for simplified yet robust assessments of atomic mobilities and diffusion coefficients of ternary and multicomponent solid solutions

This study extends a 1-parameter Z-Z-Z binary diffusion coefficient model to ternary and multicomponent systems. The cross-binary and ternary interaction parameters in atomic mobility (diffusion coefficient) assessments were systematically tested on 4 ternary solid solutions: fcc Ag-Au-Cu, fcc Co-Fe-Ni, fcc Cu-Fe-Ni, and bcc Nb-Ti-V. A simple combination of the Z-Z-Z binary model parameters without any additional fitting parameters already provides impressive predictions of the ternary diffusion coefficients when the 3 cross-binary parameters are set to be the corresponding binary Z-Z-Z model interaction parameters, leading to a robust Z-Z-ternary diffusion model. Employment of 3 independent cross-binary fitting parameters leads to an even better binary and cross-binary parameters only (BCBPO) model. Recommendations are rendered based upon the amount of available experimental ternary diffusion coefficients. These recommendations will substantially reduce the number of fitting parameters and improve the robustness of the resultant atomic mobility and diffusion coefficient databases for computational materials design.

Research on separation of aromatics from FCC diesel using organic solvent: A combination of experiments and quantum chemical calculations

Fluid catalytic cracking (FCC) diesel is the main contributor of polycyclic aromatic hydrocarbons (PAHs) in diesel, so reducing the content of PAHs in FCC diesel is of great significance to environmental protection and high-value utilization of FCC diesel. To understand the potential separation of dicyclic aromatic from FCC diesel, dimethyl sulfoxide (DMSO), 2-methoxyethanol (EGME), and N,N-dimethylformamide (DMF) were selected as extracting solvents. The liquid-liquid phase behavior of the dodecane + 1-methylnaphthalene + solvent systems was determined to investigate the solvent extraction ability, the values of S were calculated and the high selectivity of DMSO could be confirmed. Then, the quantum chemical calculation found that the extraction mechanism of DMSO and DMF was weak H-bond and van der Waals (VDW) forces, while that of EGME was only VDW force. Additionally, the structure-activity relationship between solvent molecular structure and solvent selectivity was obtained by combining the experimental results and the quantum chemical calculations, which could provide theoretical guidance for the selection of high separation performance solvents in the future. Finally, the binary interaction parameters of NRTL and UNIQUAC models were obtained with the root-mean-square deviation (RMSD) values all less than 0.60%, which provide basic data for the further simulation of aromatics extraction of FCC diesel.

Influence of solvent structure on the extraction of aromatics from FCC diesel and computational thermodynamics study

The separation of aromatics from fluid catalytic cracking (FCC) diesel is of great significance for environmental protection. The extraction ability of 1-methyl-2-pyrrolidinone (NMP), sulfolane (SUL), and 4-formylmorpholine (NFM) were studied by the liquid-liquid equilibrium (LLE) experimental, and the corresponding LLE data of NMP/SUL/NFM + 1-methylnaphthalene + dodecane systems were obtained. The calculated distribution coefficients and separation factors showed that the solubility of 1-methylnaphthalene was the highest in NMP and the selectivity of SUL to 1-methylnaphthalene was the strongest. The effects of solvent structures were investigated by a combination of experiments and quantum chemical calculations. The 1-methylnaphthalene is more soluble in solvents with planar molecular structure because the steric hindrance between the two molecules is smaller, and the group with more electronegative has higher selectivity for 1-methylnaphthalene. Moreover, the reduced density gradient (RDG) and atoms in molecules (AIM) analyzed found that the main extraction mechanism of the three solvents was van der Waals (VDW) and weak hydrogen bond, in which VDW was dominant. Finally, the binary interaction parameters of NRTL and UNIQUAC models were obtained, which make up for the blank in Aspen simulation for the separation of FCC diesel by organic solvents.

Isobaric vapor–liquid equilibria and distillation process design for separating ketones in biomass pyrolysis oil

Biomass pyrolysis oil is a renewable resource and some of compounds (such as ketones, phenols and furans) in biomass pyrolysis oil are very useful compounds that can be used as raw materials for production of fine chemicals. Vapor-liquid equilibrium (VLE) data are critical and fundamental for designing distillation separation process. The VLE experiment and calculation of ketone-related binary systems (2-butanone + cyclopentanone, 2,3-butanedione + cyclopentanone) at atmospheric pressure are studied in this work. Binary interaction parameters of activity coefficient models (NRTL, Wilson and UNIQUAC) are obtained by correlating VLE experimental data. The new group CH2COCH2 is defined and the new group interaction parameters are presented and used to predict VLE data by UNIFAC-DMD model. The distillation separation process of ketones is designed and simulated based on VLE results. This work will provide theoretical basis and technical guidance for industrial separation process of biomass pyrolysis oil.

Estimation of interaction parameters of electrolyte NRTL model based on NaCN and Na2CO3 solubility in water–ethanol mixed solvent and process simulation for separation of NaCN/Na2CO3

The solubility of NaCN and Na2CO3 in the water–ethanol mixture was determined through experiments. Also the polynomial fit was used to lead to the relationship between the solubility of NaCN/Na2CO3 and the solvent composition. In the meantime, the solvent molecular-electrolyte pair interaction parameters of electrolyte NRTL (eNRTL) model were estimated by using the data regression function of Aspen Plus software from solubility data of NaCN and Na2CO3 in water–ethanol mixed solvent. The process simulation for separation and purification of NaCN and Na2CO3 in water–ethanol mixed solvent was carried out by using Aspen Plus software. During the simulation, electrolyte equilibrium system in water–ethanol mixed solvent was observed by using eNRTL model property method, and the influence of several factors on the separation efficiency of NaCN was examined.

Constrained random phase approximation of the effective Coulomb interaction in lattice models of twisted bilayer graphene

Recent experiments on twisted bilayer graphene show the urgent need for establishing a low-energy lattice model for the system. We use the constrained random phase approximation to study the interaction parameters of such models, taking into account screening from the moir\'e bands left outside the model space. Based on an atomic-scale tight-binding model, we numerically compute the polarization function and study its behavior for different twist angles. We discuss an approximation scheme which allows us to compute the screened interaction, in spite of the very large number of atoms in the unit cell. We find that the polarization has three different momentum regimes. For small momenta, the polarization is quadratic, leading to a linear dielectric function expected for a two-dimensional dielectric material. For large momenta, the polarization becomes independent of the twist angle and approaches that of uncoupled graphene layers. In the intermediate-momentum regime, the dependence on the twist angle is strong. Close to the largest magic angle the dielectric function peaks at a momentum of $1/(4\phantom{\rule{4.pt}{0ex}}\text{nm})$, attaining values of 18--25, depending on the exact model, meaning very strong screening at intermediate distances. We also calculate the effective screened Coulomb interaction in real space and give estimates for the on-site and extended interaction terms for the recently developed hexagonal-lattice model. For freestanding twisted bilayer graphene, the effective interaction decays slower than $1/r$ at intermediate distances $r$, while it remains essentially unscreened at large enough $r$.

Von Neumann Entropy Distribution with Influence Factors in Matrix Product States

Different kinds of description and measure of multispin quantum correlation (MSQC) and the corresponding influence factors investigation not only advance the understanding of MSQC organization and structure, but also concern different kinds of specific potential applications with the superiorities compared to the corresponding classical ones. The previous conventional condensed matter theory approach researches all focused on some existing kinds of MSQC description and measure on the concrete interaction-model parameters based on a few ground-state solvable models. Here by using Matrix Product States (MPSs), we not only investigate the MSQC varying with the concrete interaction model parameters, but also investigate other influence factors including the total spin number (TSN) and the characteristic parameters of the MSQC concrete description and measure, starting with Von Neumann Entropy (VNE) distribution with influence factors. The long-wavelength VNE behavior is also investigated and analyzed. We then further study their physical mechanisms, especially for long-range MSQC beyond our previous cognition.

Molecular Force Field Development for Aqueous Electrolytes: 2. Polarizable Models Incorporating Crystalline Chemical Potential and Their Accurate Simulations of Halite, Hydrohalite, Aqueous Solutions of NaCl, and Solubility.

The current state-of-the-art force fields (FFs) for Na+ and Cl- ions are not capable of simultaneously predicting the thermodynamic properties of the aqueous solution and the crystalline phase. This is primarily due to an oversimplification of the interaction models used but partially also due to the insufficient parametrization of the FFs. We have devised a straightforward and simple parametrization procedure for determining the ion-ion interaction parameters in complex molecular models of NaCl electrolytes which involves fitting the density, lattice energy, and chemical potential of crystalline NaCl at ambient conditions. Starting from the AH/BK3 and MAH/BK3 FFs, the parametrization approach is employed to develop a complex and accurate polarizable molecular model for the NaCl electrolyte by parametrizing the ion-ion interactions. The performance of the refined polarizable NaCl FF is assessed by evaluating the different thermodynamic and mechanical properties of the crystal, density of crystalline and molten NaCl, along with the melting temperature, properties of aqueous solutions, and the structure and stability of hydrohalite. The simulation results confirm the superiority of the refined FF in comparison with the existing state-of-the-art FFs to accurately predict a wide range of system properties in different NaCl phases, including NaCl aqueous solubility. The refined FF may find applications in the accurate simulations of NaCl electrolytes including inhomogeneous environment, phase equilibria and interfaces, and metastable states. Finally, the parametrization strategy is robust and general and can be used to devise molecular models for other electrolytes.

Comparison of MOSCED (NRTL) model results with regular correlative and predictive models based on vapor-liquid equilibrium calculations for azeotropic systems

The Modified Separation of Cohesive Energy Density (MOSCED) model is an attractive and accurate engineering tool for process design and modeling. MOSCED is able to make qualitative as well as precise quantitative predictions of principal molecular-level interactions. However, the capability of this model in predicting Vapor-Liquid Equilibrium (VLE) of different azeotropic systems has not yet been fully assessed, when compared with the conventional methods. In this study, the ability of MOSCED model to predict the binary interaction parameters of NRTL model has been evaluated by comparing the obtained isobaric phase diagrams of the experimental sets of data for 11 binary isobaric systems. In order to better evaluate the performance of MOSCED model, the same calculations were performed via correlative (Wilson and NRTL) and predictive (UNIFAC) models. The values of statistical parameters have demonstrated acceptable predictions for the studied systems. Overall, the MOSCED model has provided an Average Absolute Relative Deviation(s) (AARD %) of 0.1978% and 4.3239% for temperature and K-value, respectively; which illustrate excellent performance of this model in spite of no dependence on experimental data, which is a big advantage over other methods.

Liquid-liquid Equilibrium Determination and Data Correlation for 2,2,4-trimethyl Pentane - tripropylene Glycol Binary System

Liquid-liquid equilibrium at temperatures between 293.16K and 353.1K for the mixture of 2,2,4-trimethylpentane + 2- [2- (2-Hydroxypropoxy) propoxy] -1-propanol was determined using the cloud point method. The measured data was used to estimate the binary interaction parameters of NRTL thermodynamic model, through non-linear regression using MATLAB� software. The binary interaction parameters resulting from regression were used further in a chemical simulation software (PRO/II 9.3) to determine the LLE for the studied mixture. The LLE calculation results obtained with the NRTL model were compared with the results of LLE calculations using the predictive thermodynamic model-UNIFAC. It was determined that the results of the calculation of the LLE using binary interaction parameters obtained through regression have a smaller deviation from the experimental data than the results of the calculation performed using the UNIFAC model. Moreover, the binary interaction parameters obtained from regression were utilized for the estimation of the solvency properties of tripropylene glycol considering the extraction of C8 aromatics from a mixture containing 2,2,4-trimethyl pentane, ethylbenzene and xylenes.

A Gibbs free energy minimization based model for liquid–liquid equilibrium calculation of a system containing oil, brine, and surfactant

Accurate and reliable phase equilibrium calculations of microemulsion systems are of great importance. This study deals with the thermodynamic modeling of Liquid–Liquid Equilibrium (LLE) of a system including oil (n-decane), brine (containing CaCl2 salt), and ionic surfactant (sodium dodecyl sulfonate). Two models of UNIQUAC and UNIQUAC + Debye–Hückel were used for thermodynamic calculations. The LLE experimental data were utilized to estimate the binary interaction parameters of UNIQUAC model and the adjustable parameter, b, of the Debye–Hückel model. The thermodynamic model calculates the microemulsion phase’s compositions by minimizing the Gibbs free energy of the LLE system using a combination of genetic algorithm and fmincon function in order to prevent local minima. The thermodynamic modeling results show an appropriate agreement with the experimental data. Accordingly, the presented model of this study can be used as a suitable method to investigate the liquid–liquid equilibrium of systems containing oil, water, and surfactant.

Phase equilibrium modeling for methane solubility in aqueous sodium chloride solutions using an association equation of state

A new formulation for the fraction of electron acceptor sites of methane (CH4) of cubic-plus-association couple with Huron-Vidal (CPA-HV) model is presented, and a combine rule is used to calculate the cross-associating strength of CH4-water (H2O) binary system. Meanwhile, the interaction parameters (Eij, Eji and F) of CPA-HV model are regressed for CH4–H2O binary and CH4–H2O–NaCl ternary systems. The predictions of CPA-HV model are consistent with a lot of binary and ternary experimental data of these systems. Compared with CPA-vdW and SRK-HV models, the accuracy of CPA-HV model is the best for vapor-liquid equilibria of CH4–H2O system. The average absolute relative deviations of the predicted CH4 solubility in H2O and aqueous sodium chloride solutions for CPA-HV model are respectively 5.84% and 6.91%.