Extension of the Wilson-NRF Gibbs Energy Model in Correlating Vapor-Liquid and Liquid-Liquid Phase Behavior of Polymer-Polymer Aqueous Two-Phase Systems

In this work, the proposed model by Pazuki et al. based on the Local Composition Concept (LCC), has been used in correlating the vapor-liquid phase behavior of polymer solutions and the liquid-liquid phase behavior of aqueous two-phase systems. The Flory-Huggins model has been used as the combinatorial part of the proposed model, as well as the model proposed by Pazuki et al. was considered as the residual term. The proposed model has been used in correlating the vapor-liquid phase behavior for a number of PEG-Water systems at constant temperature. The results obtained from the proposed model have been compared with those obtained from the Poly-NRTL and the Poly-Wilson models. The results showed that the proposed model can accurately correlate the VLE data for PEG-Water systems. Also, the proposed model has been used to obtain phase behavior of aqueous two-phase systems for PEG-DEX-Water systems. The results obtained from the proposed model have been compared with those obtained from the UNIQUAC and the UNIQUAC-NRF models. The results showed that the proposed model can accurately correlate liquid-liquid phase behavior of aqueous two-phase systems than the UNIQUAC and the UNIQUAC-NRF models.     

(Liquid + liquid) equilibrium for ternary mixtures of {heptane + aromatic compounds + [EMpy][ESO4]} at T = 298.15 K

(Liquid + liquid) equilibrium (LLE) data for the ternary systems (heptane + toluene + 1-ethyl-3-methylpyridinium ethylsulfate) and (heptane  + benzene + 1-ethyl-3-methylpyridinium ethylsulfate) were measured at T = 298.15 K and atmospheric pressure. The selectivity and aromatic distribution coefficients, calculated from the equilibrium data, were used to determine if this ionic liquid can be used as a potential extracting solvent for the separation of aromatic compounds from heptane. The consistency of tie-line data was ascertained by applying the Othmer–Tobias and Hand equations.     

Zhang's conjecture and squares of Abelian surfaces

We give in this Note some squares of Abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points.     

A New Gibbs Energy Model for Obtaining Thermophysical Properties of Aqueous Electrolyte Solutions

In this paper, a new Gibbs energy model is proposed to study the thermophysical properties of aqueous electrolyte solutions at various temperatures. The proposed model assumes that the electrolytes completely dissociate in solution. The model also has two temperature-independent adjustable parameters that were regressed using experimental values of the mean ionic activity coefficients (MIAC) for 87 electrolyte solutions at 298.15 K. Results from the proposed model for the MIAC were compared with those obtained from the E-Wilson, E-NRTL, Pitzer and the E-UNIQUAC models, and the adjustable model parameters were used directly to predict the osmotic coefficients at this temperature. The results showed that the proposed model can accurately correlate the MIAC and predict the osmotic coefficients of the aqueous electrolyte solutions better on the average than the other models studied in this work at 298.15 K. Also, the proposed model was examined to study the osmotic coefficient and vapor pressure for a number of aqueous electrolyte solutions at high temperatures. It should be stated that in order to calculate the osmotic coefficients for the electrolyte solutions, the regressed values of parameters obtained for the vapor pressure at high temperatures were used directly. The results obtained for the osmotic coefficients and vapor pressures of electrolyte solutions indicate that good agreement is attained between the experimental data and the results of the proposed model. In order to unequivocally compare the results, the same experimental data and same minimization procedure were used for all of the studied models.     

Modeling of Osmotic Pressure of Aqueous Poly(Ethylene Glycol) Solutions Using the Artificial Neural Network and Free Volume Flory Huggins Model

In this work, the modified Flory-Huggins coupled with the free-volume concept and the artificial neural network models were used to obtain the osmotic pressure of aqueous poly(ethylene glycol) solutions. In the artificial neural network, the osmotic pressure of aqueous poly(ethylene glycol) solutions depends on temperature, molecular weight and the mole fractions of poly(ethylene glycol) in aqueous solution. The network topology is optimized and the (3-1-1) architecture is found using optimization of an objective function with batch back propagation (BBP) method for 134 experimental data points. The results obtained from the neural network in obtaining of the osmotic pressure of aqueous poly(ethylene glycol) were compared with those obtained from the free volume Flory-Huggins model (FV-FH). The results showed that the modified Flory-Huggins model and also the artificial neural network can accurately predict the osmotic pressure of aqueous poly(ethylene glycol) solutions but the accuracy of ANN is much better than the modified Flory-Huggins model.     

Minoration de la hauteur de Néron-Tate sur les surfaces abéliennes

This paper contains results concerning a conjecture made by Lang and Silverman, predicting a lower bound for the canonical height on abelian varieties of dimension 2 over number fields. The method used here is a local height decomposition. We derive as corollaries uniform bounds on the number of torsion points on families of abelian surfaces and on the number of rational points on families of genus 2 curves.     

Correlation and prediction the activity coefficients and solubility of amino acids and simple peptide in aqueous solution using the modified local composition model

In this work, the modified Wilson model was used to obtain the activity coefficients of amino acids and simple peptides in non-electrolyte aqueous solutions. The Wilson model was modified using the new local mole fraction proposed by Zhao et al. and non-random case for the reference state. The binary interaction parameters (BIP) of the modified Wilson model for amino acid–water pairs were obtained using the experimental data of the activity coefficients for amino acids available in the literature. The modified Wilson model was also used to correlate the solubility of amino acids in water and the values of Δh/R, Δs/R, and Δg/R of the solutions studied were reported. The results obtained showed that the modified Wilson model can accurately correlate the activity coefficients as well as the solubility of amino acids and simple peptides in aqueous solutions. Also the modified Wilson model was coupled with the Pazuki–Rohani model to correlate the mean ionic activity coefficients of electrolytes in aqueous amino acid solutions. The results showed that the proposed model can accurately correlate the activity coefficients of the electrolytes in aqueous amino acid solution.     

On the prediction of equilibrium phase behavior of amino acids in aqueous and aqueous-electrolyte solutions using SAFT equation of state

We present an approach based on the statistical associating fluids theory (SAFT) to predict the solubility of amino acids in aqueous and aqueous-electrolyte solutions. This approach can describe the association interactions and their effects on the solubility of amino acids. Using the experimental data of activity coefficients of amino acids in water, the parameters of SAFT model for amino acids are obtained. The solubility of several amino acids in the temperature range of 273.15–373.15 K is predicted. Results obtained from the model are in a good accordance with the experimental data. Also, we examine the effect of pH on the solubility of dl-methionine. Addition of an extra amino acid to the binary solution of amino acid + water makes the system more complex. To check the accuracy of model, we study the ternary solution of dl-serine + dl-alanine + water and dl-valine + dl-alanine + water. Predicted results depict that the proposed model has the ability to describe the ternary solution of amino acids, accurately. Finally, the solubility of amino acids in aqueous-electrolyte solutions is investigated. The long-range interactions caused by the presence of ions affects the solubility of amino acids, leading them to be salted in or out. To treat this kind of interaction, the restrictive primitive mean spherical approximation (RP-MSA) is coupled with the SAFT equation of state. The proposed model can accurately predict the solubility of amino acids in aqueous-electrolyte solutions.     

Volumetric,Acoustic, Viscometric Properties,and Solute–Solvent Interactions of Metformin Hydrochloride in Aqueous Solution of Polyethylene Glycol (PEG 4000) at Different Temperatures (T = 288.15—318.15 K)

Journal of Solution Chemistry - An attempt to understand the interactions between metformin, a drug, and a water-soluble polymer, polyethylene glycol (PEG 4000) in aqueous solutions through...     

A Modified Local Composition-Based Model for Correlating the Vapor-Liquid and Liquid-Liquid Phase Equilibria of Aqueous Polymer-Salt Systems

In this research, a new local composition model has been proposed to study the vapor-liquid and liquid-liquid phase equilibria of polyelectrolyte solutions. The proposed model has been used in order to obtain the activity of water in polyethylene glycol (PEG) and polypropylene glycol (PPG) solutions. The interaction parameters introduced into the proposed model have been reported. The interaction parameters between the salt and water molecule have been estimated using the experimental mean ionic activity coefficients of aqueous electrolytes studied in this work. Also, the interaction parameters between the polymer and salt molecule, and the polymer and water molecule have been computed using the experimental activity of water data in aqueous polymer solutions. The results showed that the proposed model, segment-based Wilson and segment-based NRTL models have good accuracy in correlating the vapor-liquid phase equilibria of the water-polymer and water-polymer-salt systems. Also, the liquid-liquid phase behavior of the polymer-salt aqueous two-phase systems has been correlated using the proposed model. The results show that the proposed model can more accurately correlate the phase behavior of aqueous two-phase systems than the UNIQUAC and the modified Wilson models.