Mean Spherical Approximation Model Research Articles

A modified mean spherical approximation model for prediction of mean ionic activity coefficient in mixed electrolyte solution at different temperatures

In this work, the Dehghani–Modarress mean spherical approximation model has been modified and extended for prediction of the mean ionic activity coefficient in mixed aqueous electrolyte solutions at different temperatures. In the DM-MSA model the cationic diameter as well as the dielectric constant of water are considered to be concentration dependent. In order to make the DM-MSA model applicable in engineering applications, a binary interaction parameter has been introduced. Using these parameters, the mean ionic activity coefficient of electrolytes can be predicted applying a linear mixing rule. To calculate the activity coefficient of single electrolytes at different temperatures, a temperature dependency has been considered for cationic size as well as dielectric constant. Utilizing the obtained parameters for single electrolytes at different temperatures, the mean ionic activity coefficients of mixed electrolytes have been predicted. The accuracy of the model is also compared with those results produced by extended UNIQUAC model. In order to have a fair judgment, the same experimental data and minimization algorithm have been used for comparison.

Activity Coefficient Prediction for Binary and Ternary Aqueous Electrolyte Solutions at Different Temperatures and Concentrations

The mean spherical approximation (MSA) model, coupled with two hard sphere models, was used to predict the activity coefficients of mixtures of electrolyte solutions at different temperatures and concentrations. The models, namely the Ghotbi-Vera-MSA (GV-MSA) and Mansoori et al.-MSA (BMCSL-MSA), were directly used without introducing any new adjustable parameters for mixing of electrolyte solutions. In the correlation step, the anion diameters were considered to be constant, whereas the cation diameters were considered to be concentration dependent. The adjustable parameters were determined by fitting the models to the experimental mean ionic activity coefficients for single aqueous electrolytes at fixed temperature. The results showed that the studied models predict accurately the activity coefficients for single electrolyte aqueous solutions at different temperatures. In the systems of binary aqueous electrolyte solutions with a common anion, the GV-MSA model has slightly better accuracy in predicting the activity coefficients. Also, it was observed that the GV-MSA model can more accurately predict the activity coefficients for ternary electrolyte solutions with a common anion, especially at higher concentrations.

Effect of Disaccharides on Ion Properties in Milk-Based Systems

The mean spherical approximation (MSA) theory is used to explain the impact of sugars on ion properties in milk-based systems by taking into account electrostatic interactions and volume exclusion effects. This study first focuses on the changes in Ca(2+) activity and pH in a solution consisting of CaCl(2), KCl, and K(3)citrate, as a function of sucrose concentration. MSA model calculations were compared with experimental results, and the model satisfactorily describes the ion properties. The excluded volume effects appear to account for a considerable increase in activity coefficient of the ions. This offers a sufficient explanation for the increase in Ca(2+) activity and the decrease in pH in milk-based systems with added disaccharides. In addition, hydration of milk proteins seems to enhance ion pair formation in milk. All disaccharides lead to similar modification of the thermodynamic properties of milklike systems, confirming that the observed effects are primarily due to volume exclusion effects.

Application of the MSA-based models in correlating the surface tension for single and mixed electrolyte solutions

Experimental values for surface tension of single and mixed electrolyte solutions were correlated using the models based on the perturbation theory. The Mean Spherical Approximation (MSA) model, coupled with the Ghotbi–Vera (GV) and the Mansoori et al. (BMCSL) equations of state, were used to correlate the experimental values of the surface tension. The results showed that the models can favourably correlate the experimental values for single electrolyte solutions. However, it was observed that the GV–MSA model can more accurately predict the surface tension for single electrolytes, especially at higher concentrations. Two different expressions for concentration dependency of cation hydrated diameters were used. Therefore, in terms of such dependency different forms of the models, i.e., GV–MSA1, GV–MSA2, BMCSL–MSA1 and BMCSL–MSA2 were introduced. It should be stated that the prediction of the surface tension for the mixed electrolyte solutions were made without introducing any new adjustable parameters. The results showed that GV–MSA2 model can predict more accurately the surface tension of electrolyte mixtures particularly at higher concentrations. Finally, the GV–MSA model was directly used to correlate the experimental results for the surface tension for both single and mixed electrolyte solutions with 2 and 4 adjustable parameters. The results showed that both of the models can accurately predict the experimental data of surface tension. These models can favourably fit and also, predict the surface tension of single electrolyte solutions with less than 1% average absolute relative deviation (AARD). The prediction capability of the proposed models is also acceptable for mixtures of electrolytes.

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.

A new model in correlating the activity coefficients of aqueous electrolyte solutions with ion pair formation

In this work, the Ion Pair Modified Ghotbi-Vera Mean Spherical Approximation (IP-MGV-MSA) model was proposed to correlate the mean ionic activity coefficients (MIAC) for a number of symmetric and asymmetric aqueous electrolyte solutions at 25 °C. The new model is based on the recently proposed MGV-MSA model by Mortazavi-Manesh et al. In the IP-MGV-MSA model, the effects arising from the ion pair formation in the electrolyte solution was taken into account. Also, in the proposed model, while the cation diameter as well as the relative permittivity of water was considered to be dependent on electrolyte concentration, the anion diameter was independent of electrolyte concentration. The results obtained from the IP-MGV-MSA model showed that the model can accurately correlate the MIAC of single electrolyte solutions, in which ion pairs are formed. These results were also compared with those obtained from the GV-MSA and MGV-MSA models. The comparison showed that in the electrolyte solutions in which ion pairs are formed, the IP-MGV-MSA model can give more superior results than those obtained from the MGV-MSA and GV-MSA models. In the proposed model, the equilibrium constant of ion pair formation, K, is an adjustable parameter and can be obtained using the experimental data of the MIAC for electrolyte solutions. It should be noted that the values for the MIAC obtained from the IP-MGV-MSA model were converted from the McMillan–Mayer (MM) framework to that of the Lewis–Randall (LR) in order to be compatible with the experimental data.

Prediction of Hydrate Formation for the Systems Containing Single and Mixed Electrolyte Solutions

In this work the effect of electrolytes on hydrate formation was investigated. To do so, a new model was used in predicting the hydrate formation conditions in presence of both single and mixed electrolyte solutions. The new model is based on the van der Waals - Platteeuw hydrate equation of state. In order to evaluate the values for the activity of water in electrolyte solutions the simplified version of the Ghotbi-Vera Mean Spherical Approximation (SGV-MSA) model was used. According to the SGV-MSA model the ions in the solutions are considered as charged hard spheres with different sizes. The values of the parameters for the SGV-MSA model are independent of temperature and depend only on the nature as well as concentration of electrolytes studied in this work. These parameters were obtained using the experimental data for the mean ionic activity coefficient of the single electrolyte solutions at 298.15 K. In the case of the mixed electrolyte solutions a new mixing rule was introduced to obtain the activity of water in aqueous electrolyte solutions. The results show that the proposed model can predict the hydrate formation for the systems containing single or mixed electrolyte solutions with good accuracy compared to the experimental data available in the literature. In addition, the results obtained from the proposed model were favorably compared with those obtained from the previously used models.

Electrical Conductivity of Concentrated Al2(SO4)3−MgSO4−H2SO4 Aqueous Solutions up to 250 °C

The extended mean spherical approximation (MSA) model was applied to previously published electrical conductivity data for H2SO4−H2O, Al2(SO4)3−H2SO4−H2O, and MgSO4−H2SO4−H2O solutions. It was foun...

Prediction and correlation of osmotic coefficient and activity of water in electrolyte solution using a MSA model

In this work, a modified mean spherical approximation (MSA) model has been used to estimate osmotic coefficient and water activity in electrolyte solutions. The diameters of anion and cation are considered as linearly dependent on their densities. The results of this model show that it is suited for estimating the osmotic coefficient of electrolytes in aqueous solutions. Also, water activity in electrolyte solutions was calculated by the modified MSA model. The average absolute deviation error for estimated water activity shows the applicability of this model for estimating the water activity in aqueous solutions.

Modification of the GV-MSA model in obtaining the activity and osmotic coefficients of aqueous electrolyte solutions

In this work a modified form of the Ghotbi–Vera Mean Spherical Approximation model (MGV-MSA) has been used to correlate the mean ionic activity coefficients (MIAC) for a number of symmetric and asymmetric aqueous electrolyte solutions at 25 °C. In the proposed model the hard sphere as well as the electrostatic contributions to the MIAC and the osmotic coefficient of the previously GV-MSA model has been modified. The results of the proposed model for the MIAC of the electrolyte solutions studied in this work are used to directly calculate the values of the osmotic coefficients without introducing any new adjustable parameter. In the MGV-MSA model the cation diameter as well as the relative permittivity of water depends on the electrolyte concentration. Having considered such dependency for both cation and relative permittivity for water in an electrolyte solution the modification of the GV-MSA has been made. It should be stated that in the MGV-MSA model the anion diameter in the solution similar to that in the GV-MSA model remains constant and independent of the electrolyte concentration. The results obtained from the proposed model have been favorably compared with those of the GV-MSA model. The results showed that the MGV-MSA model can more accurately correlate the MIAC of the single electrolyte solutions than those of the GV-MSA model. The same comparison has been observed in case of the osmotic coefficients for the electrolyte solutions studied in this work. It should be noted that in order to do an unequivocal comparison between the results obtained from the models used in this work the same minimization procedure and the same experimental data for the MIAC and the osmotic coefficients have been used. Also it should be mentioned that in the MGV-MSA model the conversion from the McMillan–Mayer (MM) framework to that of the Lewis–Randall (LR) has been performed. It has been concluded that such transformation can affect the results in particular at higher electrolyte concentrations.

Experimental Determination of Water Activity for Binary Aqueous Cerium(III) Ionic Solutions: Application to an Assessment of the Predictive Capability of the Binding Mean Spherical Approximation Model

This work is aimed at a description of the thermodynamic properties of actinide salt solutions at high concentration. The predictive capability of the binding mean spherical approximation (BIMSA) theory to describe the thermodynamic properties of electrolytes is assessed in the case of aqueous solutions of lanthanide(III) nitrate and chloride salts. Osmotic coefficients of cerium(III) nitrate and chloride were calculated from other lanthanide(III) salts properties. In parallel, concentrated binary solutions of cerium nitrate were prepared in order to measure experimentally its water activity and density as a function of concentration, at 25 degrees C. Water activities of several binary solutions of cerium chloride were also measured to check existing data on this salt. Then, the properties of cerium chloride and cerium nitrate solutions were compared within the BIMSA model. Osmotic coefficient values for promethium nitrate and promethium chloride given by this theory are proposed. Finally, water activity measurements were made to examine the fact that the ternary system Ce(NO3)3/HNO3/H2O and the quaternary system Ce(NO3)3/HNO3/N2H5NO3/H2O may be regarded as "simple solutions" (in the sense of Zdanovskii and Mikulin).

Application of the GV-MSA model to the electrolyte solutions containing mixed salts and mixed solvents

In this work the Ghotbi–Vera mean spherical approximation (GV-MSA) model, coupled with two different expressions for the cation-hydrated diameters, was used in predicting the mean ionic activity coefficients (MIAC) of electrolytes for a number of the mixed-solvent and mixed-salt electrolyte solutions at 25 °C. In all cases the cation diameters in solutions changed with concentration of electrolyte while the anion diameters were considered to be constant and equal to the corresponding Pauling diameters. In application of the GV-MSA model to the electrolyte systems, two different expressions were used for concentration dependency of cation-hydrated diameters, i.e., the GV-MSA1 and GV-MSA2 models. In case of the electrolyte solutions containing the mixed-solvent of water and alcohol, the dielectric constants of the mixed solvents were obtained by simple regression of polynomial equations in terms of weight fraction of alcohol to the pertinent experimental data available in the literature. For the mixed-salt and mixed-solvent electrolyte solutions, in order to directly calculate the MIAC of electrolytes without introducing any new adjustable parameter, the values obtained in this work for the cation-hydrated diameters in the single aqueous electrolyte solutions were used. The results obtained in this work showed that the GV-MSA2 could more accurately correlate the MIAC of electrolytes in the single aqueous electrolyte solutions in comparison to those of the GV-MSA1 and Pitzer models. Also, the results showed that the GV-MSA-based models could accurately predict the MIAC of electrolytes in the mixed-solvent electrolyte solutions in comparison to those obtained from the model of Pitzer. In case of the mixed-salt electrolyte solutions the results of the two GV-MSA-based models studied in this work reasonably predict the MIAC of electrolytes in the mixed-salt electrolyte solutions without introducing any additional adjustable parameters compared to those obtained from the model of Pitzer with two adjustable parameters.

Lanthanide Salts Solutions: Representation of Osmotic Coefficients within the Binding Mean Spherical Approximation

Osmotic coefficients of aqueous solutions of lanthanide salts are described using the binding mean spherical approximation (BIMSA) model based on the Wertheim formalism for association. The lanthanide(III) cation and the co-ion are allowed to form a 1-1 ion pair. Hydration is taken into account by introducing concentration-dependent cation size and solution permittivity. An expression for the osmotic coefficient, derived within the BIMSA, is used to fit data for a wide variety of lanthanide pure salt aqueous solutions at 25 degrees C. A total of 38 lanthanide salts have been treated, including perchlorates, nitrates, and chlorides. For most solutions, good fits could be obtained up to high ionic strengths. The relevance of the fitted parameters has been discussed, and a comparison with literature values has been made (especially the association constants) when available.

Solvent influence on the conformational equilibrium of 2,2′-bipyridine

The relative energies and dipolar properties of two conformers of 2,2′-bipyridine ( 1) were calculated using AM1 and ab initio methods. Dipole moments of 1 and pyridine in many organic solvents were determined. On this basis, the Gibbs energy Δ G (s) for the conformational s-trans⇌ s-cis equilibrium of 1 was estimated. The solvent effect on Δ G (s) is discussed quantitatively using the reaction-field model for the continuum dielectric medium, in the framework of which both the dipolar and quadrupolar terms are considered. This simple model works very well when the adopted radius of the solvent cavity is that obtained from the apparent molar volume of 2,2′-bipyridine in solutions. It is also shown that the mean spherical approximation (MSA) model predicts a weaker dependence of Δ G (s) on the solvent's relative permittivity than the continuum model.

P.1.077 Escitalopram vs venlafaxine XR treatment ofmajor depressive disorder

In this study, twenty-five hard sphere equations of state (EOSs) were applied to evaluate the compressibility factor of fifty different single electrolyte solutions (Z1). Then by using two well-known mixing rules (Barrio Solana (BS) and Santos et al. (S)) the compressibility factor (Zm) was calculated for 1086 binary mixtures of electrolytes. The obtained results were compared with the simulation data and it was concluded that the Dehghani–Modarress (DM) EOS when applied along with the Santos et al. mixing rule has the highest accuracy (ARD%Z1DM=0.124 and ARD%ZmDM−S=0.466). Also, the mean ionic activity coefficients of a number of 1:1 electrolytes were calculated by applying the hard sphere EOSs with the mixing rules based on the mean spherical approximation (MSA) model where the concentration of cation was considered a function of electrolyte concentration. By comparing these results with reported experimental data it was found that the Ree–Hoover (RH) EOS with Santos et al. mixing rule predicts the mean ionic activity coefficients with the highest accuracy (ARD% γ(RH − S) = 0.206). In continuation of this study the compressibility factor and mean ionic activity coefficient were recalculated by means of the artificial neural network (ANN) method. The optimum architectures of ANN models for predicting the compressibility factor of single and binary mixtures of electrolytes as well as the mean ionic activity coefficient of 1:1 electrolytes were respectively obtained as 2:4:1, 3:3:1 and 3:5:1. The calculated error in the results showed that the mathematical models of the ANN method predicted the abovementioned parameters with better accuracy in comparison with the EOSs and MSA models (ARD%Z1ANN=0.047, ARD%ZmANN=0.022 and ARD % γ(ANN) = 0.014).

Effect of Arm Length on the Aggregation Structure of Fullerene-Based Star Ionomers

Using small angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS), we have studied aqueous solutions of a fullerene-based star ionomer−hexa(sulfobutoxypentylcarboxy)[60]fullerene (FC10S). With six sulfobutoxypentyl arms randomly bounded on the C60 cage, FC10S demonstrates a good solubility in water. The scattering results show that the water-soluble fullerene-based ionomers of a starlike molecular morphology form rodlike aggregates in water solutions. With the contrast provided by SAXS and SANS, we extract detailed structural information for the rodlike aggregates, including arm distribution, aggregation number ∼ 32, and the rod radius and length of 21 Å and 160 Å, respectively. We also extract an averaged ionization factor of ∼ 0.03 for the FC10S aggregates, using the structural factor derived from the mean spherical approximation model for the charge interacting aggregates. The aggregation structure changes little within the concentration range studied (0.5−4%). Compared to the aggregation characteristics of FC4S, a similar fullerene-based ionomer with six shorter sulfobutyl arms, FC10S, has a much higher aggregation tendency due to the longer sulfobutoxypentyl arms anchored on the C60 cage.

Application of the non-primitive MSA-based models in predicting the activity and the osmotic coefficients of aqueous electrolyte solutions

The non-primitive mean spherical approximation (NP-MSA) based models were used to correlate the individual and the mean ionic activity coefficients of the symmetric and asymmetric aqueous electrolyte solutions. The results of the models for the mean ionic activity coefficients were directly used to calculate the osmotic coefficient for the electrolyte solutions studied in this work. In the NP-MSA models, the Ghotbi–Vera and the Boublik–Mansoori–Carnahan–Starling–Leland hard sphere equation of state as the reference system coupled with the non-primitive mean spherical approximation model (NP-GV-MSA and NP-BMCSL-MSA models, respectively). In correlating the mean ionic activity coefficients of electrolyte solutions, while the hard sphere diameters for anion were treated as a concentration-independent adjustable parameter, the diameters for cation were assumed to be concentration dependent. In the use of the non-primitive MSA-based models in correlating the individual ionic activity coefficients of electrolyte solutions, both anion and cation diameters were considered to be concentration dependent. The results for the mean ionic activity coefficients obtained from the NP-GV-MSA model compared favorably with those of the NP-BMCSL-MSA model produced in this work and also with those of NP−BMCSL-MSA available in the literature. It was shown that the NP-GV-MSA model more accurately calculate the mean ionic activity and the osmotic coefficients than those obtained from the NP−BMCSL-MSA models.

Simplification and application of the mean spherical approximation (MSA) model for 1:1 electrolyte solution

Mean spherical approximation (MSA) model, is simplified, and used for the calculation of activity coefficients, for single 1:1 electrolyte solutions. By using constant anion diameter, the cation diameters are calculated as a function of concentration. The cation diameters obtained are compared with those calculated by other models. The capability of the simplified MSA model to represent the activity coefficients of single aqueous 1:1 electrolyte solution is demonstrated by application of the model to various kinds of single 1:1 electrolytes. The calculated results have negligible error, and indicate the accuracy of the simplified MSA model.

Modification and application of a non-primitive mean spherical approximation model for simple aqueous electrolyte solutions

In this study, the non-primitive mean spherical approximation (NPMSA) model has been modified and an equation is obtained for calculating the cationic diameter for single electrolyte solutions at various concentrations. Furthermore, based on this modification of the NPMSA model an equation for the Helmholtz energy is derived and the thermodynamic properties are calculated at various ionic strengths and dipole diameters. The results show that the pair potential and electrostatic forces play the main role in the obtained thermodynamic properties. Also, the calculated thermodynamic properties by the NPMSA model are compared with results from other models such as primitive mean spherical approximation (PMSA) and restricted mean spherical approximation (RMSA). The results indicate that the NPMSA model underestimates the thermodynamic properties due to the solvent effects in this model.

On the Correlation of the Activity Coefficients in Aqueous Electrolyte Solutions Using the K-MSA Model

The objective of this work is to extend the Kelvin mean spherical approximation (K-MSA) model to correlate the mean and individual ionic activity coefficients for symmetric and asymmetric electrolyte solutions at different concentrations and at different temperatures. Revised values of the parameters for the mean and individual ionic activity coefficients of 1:1 electrolytes and new values of the parameters for the mean ionic activity coefficients of asymmetric electrolytes are presented. The effect of the short-range electrostatic term (Pn) at different size ratios of the ions is examined. Assuming a constant anion diameter and a composition-dependent diameter for the cation, the K-MSA model gives realistic cation-hydrated diameters, in comparison with their crystallographic Pauling diameters. Notably, for both symmetric and asymmetric electrolytes, the like and unlike ionic radial distribution function at contact value are positive over all of the concentration and temperature ranges studied. The result...