Λh Equation Research Articles

Uncover the effect of solvent and temperature on solid-liquid equilibrium behavior of 2-bromodibenzofuran

The effects of solvent properties and temperature on the solid–liquid equilibrium of 2-bromodibenzofuran (NSC 1735) were investigated for the first time in terms of temperature, solvent polarity, hydrogen bonding donor and acceptor tendency, as well as cohesive energy density. Firstly, the equilibrium solubility of 2-bromodibenzofuran in 12 mono-solvents, such as alcohol, ketone, nitrile and ester, was determined by gravimetric method ranging from 278.15 ∼ 343.15 K. The values of the mole fraction solubility of NSC 1735 in all the selected solvents increased with increasing temperature. Moreover, the statistical correlations between temperature and solubility were described by the modified Apelblat equation, λh equation, Van’t Hoff equation, and NRTL model. The calculated ARD% values show that the correlation results agree well with the experimental date and the modified Apelblat equation receives the best regression performance. Solvent polarity and cohesive energy density mainly determine the solubility of NSC 1735 in various solvents. Thermodynamic studies of dissolution have shown that the dissolution of NSC 1735 in selected solvents.is endothermic and enthalpy driven. The change of dissolution enthalpy is the main contributor to the molar Gibbs free energy during the dissolution process.

Thermodynamic analysis and molecular dynamic simulation of the solubility of risperidone (form I) in the pure and binary solvents

Risperidone is one of the second-generation anti-schizophrenia representative drugs, which is widely used in the treatment of acute and chronic schizophrenia. In this work, the solubility of risperidone (form I) in thirteen pure solvents and three binary solvent mixtures (ethanol + water, acetone + water and 2-propanol + water) was determined. The measured temperature range was 278.15–313.15 K and the measurement was accomplished by utilizing a gravimetric method under the barometric pressure. The experimental solubility data were correlated by the Apelblat equation, λh equation, NRTL model, UNIQUAC model, Jouyban-Acree model and CNIBS/R-K model with all the calculated solubility data dovetailing well with the experimental solubility data. The solubility of risperidone (form Ⅰ) in selected solvent systems was positively correlated with the temperature and the co-solvency phenomenon was observed in all the three binary solvent systems, which was different from the results obtained from the literature. The Hirshfeld surface (HS) analysis was applied to understand the intermolecular interaction of the crystal packing of risperidone (form I). The molecular dynamic simulation was then carried out and the Radial distribution function (RDF) analysis was employed to illustrate the intermolecular interaction between the solute and solvent molecules, and it turns out that the results of the RDF analysis can well explain the co-solvency phenomenon. In addition, based on the van’t Hoff equation, the apparent thermodynamic properties of risperidone (form I) in selected solvent systems were calculated and the results show that the dissolution of risperidone (form I) is a process of endothermic and entropy-driven.

Measurement and correlation of solubility data for albendazole in ten pure solvents and two binary solvent systems from 278.15 K to 323.15 K

The equilibrium solubility of albendazole (ABZ) in ten single solvents and two binary solvent mixtures of different ratio was measured by a typical static method combined with ultraviolet (UV) spectrophotometry within the temperature range from 278.15 K to 323.15 K. Meanwhile, the modified Apelblat model, Van't Hoff equation and λh equation were used to correlate the solubility data of ABZ in pure solvent, the modified Apelblat model, λh equation, Sun model, GSM equation and NRTL model were used to correlate the solubility data of ABZ in binary mixed solvent, the 100RD, 100ARD, 103RMSD and 103ORMSD values of the above models were calculated respectively. The results show that the experimental data of six models have a good correlation with the calculated data. Especially, the Van't Hoff equation in pure solvent has the best fitting effect, and the GSM equation in binary mixed solvent has the best fitting effect. Additionally, the Van't Hoff equation was used to calculate and evaluate the thermodynamic properties of the ABZ dissolution process, including enthalpy (ΔdisH), entropy (ΔdisS) and Gibbs free energy (ΔdisG).

Thermodynamic modelling, Hansen solubility parameter and solvent effect of palbociclib in fourteen pure solvents at different temperatures

The solubility of palbociclib in fourteen organic solvents (chlorobenzene (MCB), N,N-dimethylformamide (DMF), pyridine (Py), anisole (An), ethyl acetate (EA), dimethyl sulfoxide (DMSO), tetrahydrofuran (THF), acetone (DMK), water, toluene (PhMe), methanol (MeOH), o-xylene (OX), ethanol (EtOH) and m-xylene (MX)) was determined using a laser monitoring method at atmospheric pressure in this work. The measured temperature range for all selected solvents is 293.15 K to 333.15 K. The holistic solubility profile showed that palbociclib solubility in all measured solvents was proportional to the increasing of test temperature. It was also found that the mole-fraction solubility values of palbociclib in measured solvents exhibited a sequence of: Py > THF > DMSO > DMF > DMK > PhMe > MCB > MX > OX > EtOH > EA > An > MeOH > water. Four mathematical equations were employed to correlate the solubility data including the modified Apelblat equation, λh equation, NRTL equation and Wilson equation, with the modified Apelblat equation giving the best regression. Solubility order of palbociclib in fourteen solvents was analyzed by using the Hansen solubility parameter (HSP) and the solvent effect (solvent interaction) was investigated through correlating palbociclib solubility in selected solvents based on KAT-LSER model. Finally, the thermodynamic properties of ΔmixG, ΔmixH, ΔmixS, ΔdisH, ΔdisG and ΔdisS of palbociclib in different solvents were computed based on measured solubility values and Wilson equation. The results demonstrated that the dissolution process was entropy-driven and favorable process.

Correlation of solubility data and solution properties of chlorzoxazone in pure solvents

The accurate determination of solubility of an active pharmaceutical ingredient in a solvent is essential for the design and development of the purification process. The solubility of chlorzoxazone (CHZ) in the pure solvents such as isopropanol, ethyl acetate, 2-ethoxyethyl acetate, and toluene are determined in the temperature range of 278.15 to 333.15 K by shake-flask method at a pressure of 101.2 kPa. The solubility of CHZ in selected solvents is found to increase with temperature. The solubility of CHZ is maximum in 2-ethoxyethyl acetate and minimum in toluene. The mole fraction (x1) solubility of CHZ is correlated with four semi-empirical temperature dependent equations such as the modified Apelblat equation, λh equation, van’t Hoff equation, and non-random two liquid (NRTL) equation. The maximum root-mean-square deviation (RMSD) and relative average deviation (RAD) predicted via four thermodynamic models are 528.80 ×10−4 and 1.146 ×10−2 respectively. The modified Apelblat equation shows a better fit with experimental values for solubility of CHZ. The R2 value obtained from the modified Apelblat equation is >0.99 and the values of RMSD and RAD are smaller for all the selected solvents. The thermodynamic energy properties of the solution are calculated using the van't Hoff equation. The obtained values ΔHm, ΔSm and ΔGm are found to be positive which indicates the dissolution process is an endothermic and entropy-driven process.

Solubility, thermodynamic properties and molecular simulation of tinidazole in fourteen mono-solvents at different temperatures

The solubility properties of tinidazole (TNZ) in investigated fourteen mono-solvents were further studied at several temperature points (278.15 K ∼ 323.15 K) under 101.2 kPa using the laser monitoring technique. The selected solvents were acetone, methanol, ethanol, 2-methoxyethanol, 2-ethoxyethanol, 2-propoxyethanol, 2-butoxyethanol, methyl acetate, ethyl acetate, n-propyl acetate, n-butyl acetate, NMP, DMF, DMAC, respectively. The order of solubility of tinidazole in fourteen mono-solvents at 298.15 K is: NMP > DMAC > DMF > acetone > 2-methoxyethanol > methylacetate > 2-ethoxyethanol > ethyl acetate > 2-propoxyethanol > n-propyl acetate > 2-butoxyethanol > n-butyl acetate > methanol > ethanol. As shown by the solubility data of TNZ in chosen fourteen mono-solvents in this work, TNZ is more soluble in higher temperature. The KAT-LSER model and molecular dynamics simulation were adopted to probe the influence of solvent effects and solute–solvent interaction on TNZ solubility. The obtained solubility data of TNZ was fitted by (λh equation, NRTL model, NRTL-SAC model, two-Suffix Margules model, and UNIQUAC model). The results indicate that five models can fit the experimental values well, in which the NRTL-SAC model gives the best regression effect. Moreover, the apparent thermodynamic properties (△solG°, △solH° and △solS°) of TNZ in various solvents were calculated by Van’t Hoff equation. In accordance with the analysis and calculation of dissolution, the dissolution process is is entropy-motivated and endothermal.

Experimental Determination and Computational Prediction of Dehydroabietic Acid Solubility in (-)-α-Pinene + (-)-β-Caryophyllene + P-Cymene System.

The solubility of dehydroabietic acid in (−)-α-pinene, p-cymene, (−)-β-caryophyllene, (−)-α-pinene + p-cymene, (−)-β-caryophyllene + p-cymene and (−)-α-pinene + (−)-β-caryophyllene were determined using the laser monitoring method at atmospheric pressure. The solubility of dehydroabietic acid was positively correlated with temperature from 295.15 to 339.46 K. (−)-α-pinene, p-cymene, and (−)-β-caryophyllene were found to be suitable for the solubilization of dehydroabietic acid. In addition, the non-random two liquid (NRTL), universal quasi-chemical (UNIQUAC), modified Apelblat, modified Wilson, modified Wilson–van’t Hoff, and λh models were applied to correlate the determined solubility data. The modified Apelblat model gave the minor deviation for dehydroabietic acid in monosolvents, while the λh equation showed the best result in the binary solvents. A comparative analysis of compatibility between solutes and solvents was carried out using Hansen solubility parameters. The thermodynamic functions of ΔsolH0, ΔsolS0, ΔsolG0 were calculated according to the van’t Hoff equation, indicating that the dissolution was an entropy-driven heat absorption process. The Conductor-like Screening Model for Real Solvents (COSMO-RS) combined with an experimental value was applied to predict the reasonable solubility data of dehydroabietic acid in the selected solvents systems. The interaction energy of the dehydroabietic acid with the solvent was analyzed by COSMO-RS.

Solubility Measurement and Thermodynamic Correlation of Diacetone Acrylamide in 15 Pure Solvents from 272.05 to 323.65 K

For the design, optimization, and control of the solution crystallization process of diacetone acrylamide (DAAM), solid–liquid equilibrium data in various solvents are critical. In this work, the solubility of DAAM in 15 pure solvents, such as methanol, ethanol, n-propanol, isopropanol, n-butanol, 1-hexanol, isobutanol, n-pentanol, isopentanol, 2-butanone, acetone, ethyl acetate, 2-pentanone, acetonitrile, methyl acetate, and ethyl formate, is analyzed by a gravimetric method under ambient pressure and temperatures ranging from 272.05 to 323.65 K. The solubility values in all of the solvents are positively correlated with temperature. The solubility of DAAM can be satisfactorily correlated by the Apelblat equation, λh equation, nonrandom two-liquid (NRTL) model, and Wilson model, and the calculated solubility agrees well with the measured results. The obtained maximum relative average deviation (RAD) and root-mean-square deviation (RMSD) are 2.44 × 10–2 (n-propanol, NRTL model) and 2.40 × 10–2 (methanol, λh equation), respectively. The most suitable model is the Apelblat equation.

Experimental measurement and thermodynamic modeling of solubility of flufenamic acid in different pure solvents

Flufenamic acid (FFA) is a BCS II class drug having low solubility and high permeability in the gastrointestinal tract. The solubility enhancement techniques of BCS II class drugs such as co-crystallization, solid dispersion or fine particle generation by supercritical or liquid antisolvent method require the knowledge of solubility of API in the organic solvent. In the present work, the equilibrium solubility of FFA was determined in methanol, ethanol, 1-propanol and 2-propanol at a temperature ranging from 298 to 318 K. Different models such as the modified Apelblat equation, λh equation, NRTL and Wilson were used to correlate the experimental solubility of FFA in these solvents. The enthalpy of mixing (ΔmH), entropy of mixing (ΔmS) and Gibbs energy of mixing (ΔmG) were computed in the real binary mixture of FFA – solvent to examine the nature of mixing thermodynamically.

Measurement, correlation of solubility and thermodynamic properties analysis of 5,5′-bis(2,4,6-trinitrophenyl)-2,2′-bis(1,3,4-oxadiazole) in different mono solvents

In this paper, the solubility of 5,5′-bis(2,4,6-trinitrophenyl)-2,2′-bis(1,3,4-oxadiazole) (TKX-55) in methanol, ethanol, 1-propanol, 2-propanol, formic acid, acetic acid, propionic acid, acetonitrile, ethyl acetate, tetrahydrofuran, nitromethane, 1,2-dichloroethane, benzene and 1,4-dioxane was determined at T = (293.15–333.15) K under atmospheric pressure (P = 0.1 MPa) by a gravimetric method. The results showed that the solubility increases with rise of temperature in all selected solvents. Additionally, the solvent effect on TKX-55 solubility was investigated with Kamlet-Taft parameters. Moreover, Hansen solubility parameter was used for explaining the solubility order of TKX-55 in selected solvents, the consequences showed that solubility order of TKX-55 resulted from the comprehensive function of several solubility parameters. The solubility parameter of Δδt between TKX-55 and solvents reached from 0.17 MPa0.5 to 8.68 MPa0.5. The interaction energy (Einter) between TKX-55 and selected solvents was calculated by molecular simulation to explain the solubility behavior. Activity coefficient was to access the solute-solvent molecular interactions. Besides, the solubility values were correlated by the modified Apelblat equation, λh equation, the polynomial empirical equation, and ideal equation, and the results showed that all models can give a satisfactory correlation. The average root-mean-square deviation (106RMSD) values were 14.57, 33.08, 8.523 and 30.29, respectively. On the basis of the van’t Hoff and Gibbs equations, the thermodynamic properties exhibited by TKX-55 (i.e., standard dissolution enthalpy (ΔdisHo), standard dissolution entropy (ΔdisSo) and standard dissolution Gibbs free energy (ΔdisGo)) in the selected solvents were characterized and then discussed from the experiment data. As revealed from the result, TKX-55 in solvents selected showed a non-spontaneous process. The excess enthalpy of solution was estimated on the basis of λh equation. And solid-liquid surface tension (γ) and surface entropy factor (f) of TKX-55 were estimated by using the experimental solubility data. Furthermore, the experimental solubility values, model parameters, and thermodynamic properties of TKX-55 in different pure solvents will provide the necessary support for its preparation, crystallization process, and further theoretical studies.

Determination and modeling of binary solid-liquid equilibria of para-xylene/meta-xylene, para-xylene/ortho-xylene by DSC method

Solid-liquid equilibria of three binary mixtures consisting of para-xylene, ortho-xylene, meta-xylene and ethylbenzene were investigated in this study using differential scanning calorimetry (DSC) method, the mixtures were cooled to -120 °C and then heated to 20 °C at different heating rates, eutectic phase diagrams were observed for para-xylene/ortho-xylene and para-xylene/meta-xylene binary systems. The freezing point of pure ethylbenzene at atmospheric pressure is around -95 °C, but due to the effect of induction time, the observed freezing temperature is lower than -120 °C, the operation temperature of industrial xylene crystallization separation process is higher than -80 °C traditionally, therefore ethylbenzene will not crystallize in practical process, the phase diagram for para-xylene/ethylbenzene was not achieved. The experimental data were compared with data from other literatures and new features were found. The data were well correlated by Apelblat equation and λH equation, it is significative to provide important engineering data for the separation and purification of xylene mixtures.

Dl-isoprenaline hydrochloride solubility in four binary solvents at saturation: Thermodynamic analysis, Hansen solubility parameters and molecular simulation

The solubility properties of dl-isoprenaline hydrochloride (dl-IPN) in four kinds of binary-solvents systems {(n-propanol, n-butanol, 2-propoxyethanol and 2-butoxyethanol) + methanol} at temperature range of 278.15–323.15 K under 101.3 kPa was further investigated using the laser monitoring technique. According to the result about solubility of dl-IPN in these chosen binary solvents, it is obvious that dl-IPN is more soluble at higher temperature. Additionally, the solubility values of dl-IPN, in all the investigated binary solvent mixtures, is improved with increasing mass fraction of co-solvent (methanol). The Hansen solubility parameters (HSPs) interpretate reasonably the order of dl-IPN solubility in these binary-solvents systems. Furthermore, the molecular dynamic (MD) simulation is employed to describe the molecular interactions of the types solute–solvent and solvent–solvent, and the obtained results confirm that solute–solvent and solvent–solvent molecular interactions have deep impact on the solubility of dl-IPN. The obtained experimental data about the solubility of dl-IPN is fitted by five models (λh equation, Apelblat equation, Jouyban-Acree-Apelblat (J-A-A) model, Ma model and Sun model). The analysis of thermodynamic properties was based on the values of the calculated thermodynamic parameters. It can be concluded that the dl-IPN dissolution process is entropy-motivated and endothermal in all the investigated binary-solvents systems, and that the main contribution to ΔdisGo is due to enthalpy.

Solubility Determination, Solute–Solvent Interactions, and Model Correlation of Sorafenib in Twelve Pure Organic Solvents between T = 273.15 and 313.15 K

The isothermal saturation method was applied to study the solubility of sorafenib free base in 12 pure solvents in the temperature range from 273.15 to 313.15 K under atmospheric pressure. The solubility in selected solvents increased with the increasing temperature. The maximum mole solubility was in cyclohexanone (2.512 × 10–2) at 313.15 K, followed by in 2-butanone (1.334 × 10–2), acetone (5.577 × 10–3), toluene (4.282 × 10–3), ethyl acetate (2.930 × 10–3), n-propanol (2.067 × 10–3), 1-butanol (1.816 × 10–3), ethanol (1.554 × 10–3), isopropanol (1.385 × 10–3), isobutanol (1.256 × 10–3), methanol (0.848 × 10–3), and acetonitrile (0.678 × 10–3). The quantitative solubility data of sorafenib free base in some pure and mixed organic solvents have been reported in the literature. However, the results were not satisfactory. There is an increase of 12.06-fold between cyclohexanone and n-propanol at 313.15 K. Hence, for sorafenib free base, the solubility can be improved not only in the form of salt, but also by the selection of a good solvent. In addition, the results obtained in 12 pure solvents were correlated with the modified Apelblat equation and the λh equation. The maximum of relative average deviation was 1.62% and obtained using the λh equation, which indicated that two equations could give satisfactory results in selected pure solvents.

Solubility study of lamotrigine in the aqueous mixture of choline chloride based deep eutectic solvent at different temperatures

Solubility and thermodynamic properties of lamotrigine as a practically insoluble drug in binary mixtures of choline chloride / propylene glycol deep eutectic solvent and water are determined by shake-flask method followed by a spectrophotometric method at the temperature range of 293.2–313.2 K. The acquired molar data are correlated to the linear and non-linear solubility models including van’t Hoff, the mixture response surface, the Jouyban-Acree, the Jouyban-Acree-van’t Hoff, the modified Wilson and the λh equations. The accuracy of each model is tested by the mean relative deviation of the back-calculated solubility data. Moreover, the apparent thermodynamic properties of lamotrigine dissolution are also calculated based on the van't Hoff and Gibbs equations.

Solid–Liquid Phase Equilibrium of Isophthalonitrile in 16 Solvents from T = 273.15 to 324.75 K and Mixing Properties of Solutions

The solid–liquid equilibrium of isophthalonitrile (IPN) in 16 solvents (methanol, ethanol, n-propanol, isopropanol, acetone, ethyl acetate, acetonitrile, chloroform, cyclohexanone, cyclopentanone, methyl acetate, ethyl formate, 2-pentanone, tetrahydrofuran, toluene, and diethyl ether) was measured by using a static equilibrium method at temperatures T = 273.15–324.75 K under atmospheric pressure. The results demonstrated that the solubility of IPN in these 16 monosolvents increased with increasing temperature. The largest solubility values of IPN were found in cyclopentanone, and the lowest were in isopropanol. The values of solubility in ketones were much larger than those in esters and alcohols. In alcohols, the solubility ranked as methanol > ethanol > n-propanol > isopropanol, and the sequence was identical to that of the solvent polarities. The polarity of the solvent is an important factor influencing the solubility profiles of IPN in alcohols, despite that the conclusion is not supported by other kinds of solvents studied. Moreover, the Apelblat equation, λh equation, Wilson model, and nonrandom two-liquid model were used to correlate the experimental values. The calculated values of four models all provided good fitting results with the experimental data, and the values of root-mean-square deviation and relative average deviation (RAD) were no more than 6.84 × 10–4 and 6.84 × 10–3, respectively. Furthermore, the thermodynamic properties of the mixing process for IPN in selected solvents were calculated, that is, mixing Gibbs energy (ΔmixG), molar enthalpy (ΔmixH), and molar entropy (ΔmixS). The results indicated that the mixing process of IPN was a spontaneous and entropy-driven process. The solid–liquid equilibrium data and solution thermodynamics would be helpful for the synthesis and purification of IPN in the industry.

Thermodynamic analysis and molecular dynamic simulation of the solubility of 2,2-Bis(hydroxymethyl)propionic acid in 12 monosolvents

The solubility of 2,2-Bis(hydroxymethyl)propionic acid (DMPA) in 12 mono solvents (methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, methyl ethanoate, ethyl acetate, butyl acetate, N, N-dimethylformamide, water, and acetone) was determined by the gravimetric method at temperatures ranging from 288.15 to 328.15 K under atmospheric pressure (0.1 MPa). Solubility data were correlated by the Apelblat model, λh equation, and van’t Hoff model, and the Apelblat equation achieved the best fitting performance. Furthermore, the mixing thermodynamic functions were derived by NRTL model, which showed that the dissolution was a spontaneous and entropy-driven mixing process in solvents. Besides, the contributions of multiple physicochemical properties of solvents to the solubility of DMPA were evaluated. The results indicated that polarity and summation of the hydrogen bond acceptor propensities played crucial roles in determining DMPA solubility among all solvents. Molecular dynamic simulations were further employed to investigate solvent effect on the solubility of DMPA. Radial distribution function (RDF) analyses showed that the rank of solute-solvent interactions can be well correlated with solubility order of DMPA in the solvents. Moreover, the rank of solvation free energy of DMPA in different solutions is consistent with the order of solubility very well.

Uncovering solubility behavior of Prednisolone form II in eleven pure solvents by thermodynamic analysis and molecular simulation

Thermodynamic analysis and molecular simulation were used to investigate the solubility behavior of prednisolone (PDL) form II, which is a widely used corticosteroid. Solubility data were collected in eleven solvents (methanol, ethanol, n-propanol, i-propanol, n-butanol, methyl acetate, ethyl acetate, n-propyl acetate, acetone, tetrahydrofuran, and 1,4-dioxane) using a gravimetric method at temperatures from 283.15 K to 323.15 K. The modified Apelblat equation, λh equation, and Van't Hoff equation were employed to correlate the experimental solubility data. The dissolution process of PDL form II was endothermic and entropy-driven. The intermolecular interactions (PDL-PDL) were analyzed by molecular electrostatic potential surface and Hirshfeld surface analyses. The solvent properties, solvation free energy, and radial distribution function were investigated to explore the influence of intermolecular interactions (PDL-solvent and solvent–solvent) on the solubility. The solubility behavior of PDL form II is related to several solvent parameters, such as the hydrogen-bonding donor propensity and polarity. According to regression analyses, the PDL-solvent interactions play a crucial role in the dissolution process.

Measurement and Correlation of Solubility Behavior of Bisphenol A in Binary (Ethyl Acetate + n-Butanol, Ethyl Acetate + 2-Butanol, Ethanol + n-Butanol, and Ethanol + 2-Butanol) Solvents

The solubility of bisphenol A in binary solvents (ethyl acetate + n-butanol, ethyl acetate + 2-butanol, ethanol + n-butanol, and ethanol + 2-butanol) was measured by a laser dynamic method under p = 101.1 kPa at temperatures ranging from 273.15 to 313.15 K. The solubility increased with increasing temperature at a given solvent composition; the solubility also increased with increasing content of ethyl acetate or ethanol at a given temperature. The modified Apelblat equation, λh equation, and Sun model were used to correlate the experimental solubility data; the values of RD and rmsd indicated that these models fitted the solubility data well.

Solubility determination and correlation for 3-nitropyrazole in four binary solvents (water + methanol, ethanol, 1-propanol and acetone) from 283.15 K to 323.15 K

The solubility of 3-nitropyrazole in four binary solvents (water + methanol, ethanol, 1-propanol and acetone) was measured by a dynamic laser monitoring over the temperature range of 283.15 K, 288.15 K, 293.15 K, 298.15 K, 303.15 K, 308.15 K, 313.15 K, 318.15 K and 323.15 K at pressure of 0.1 MPa. The solubility of 3-nitropyrazole increased positively with increasing temperature, while increased with decreasing mass-fraction of water in each binary system. Moreover, the experimental solubility values of 3-nitropyrazole in this work were correlated well with four thermodynamic models namely “the modified Apelblat equation, λh equation, Jouyban-Acree model and CNIBS/R-K model” obtaining average relative deviations (104RMSD) lower than 4.79 for correlative studies, which shows that all the four models have a good correlation. Through the comparison of R2 and 104RMSD, it was found that the modified Apelblat equation can get more satisfactory results. In addition, Hansen solubility parameters were used to explain and predict the solubility behavior. Solute-solvent interaction was calculated by molecular simulation to investigate the solubility behavior deeply. Finally, the thermodynamic parameters (ΔdisGo, ΔdisHo, ΔdisSo) of 3-nitropyrazole dissolution processes in investigated four binary solvents were evaluated utilizing the van’t Hoff equation. The positive ΔdisHo and ΔdisSo, indicate that the dissolution processes of 3-nitropyrazole are endothermic and entropy-driven in all chosen binary solvents. And the main contributor of ΔdisGo is positive enthalpy. The solubility of 3-nitropyrazole in mixed solvents (water + methanol, water + ethanol, water + 1-propanol and water + acetone) will provide essential support for the further researches of crystallization and spheroidization of 3-nitropyrazole.

Systematic thermodynamic study of clorsulon dissolved in ten organic solvents: Mechanism evaluation by modeling and molecular dynamic simulation

The thermodynamic properties of clorsulon were systematically studied through solubility measurement, calculation with modeling and molecular dynamics simulations. The equilibrium solubility of clorsulon in ten organic solvents (methanol, ethanol, n-propanol, n-butanol, iso-butanol, ethylene glycol, dichloromethane, acetonitrile, methyl acetate, ethyl acetate) was measured by employing the dynamic method at the temperature from 293.15 to 333.15 K at 0.1 MPa. Especially, the solubility of clorsulon in ethylene glycol shows extreme sensitivity to temperature due to the dihydroxy structure, which was revealed via analysis of hydrogen bond formation between solvent molecules and solute molecules. Subsequently, the experimental solubility values were correlated well with four thermodynamic models, including the modified Apelblat model, λh equation, van't Hoff equation, and Wilson model, among which the modified Apelblat model gives the best fit. The miscibility of clorsulon-solvents and the solvent effect were explored by analyzing the polarity of solvents, Hansen solubility parameters and KAT-LSER model. The derived thermodynamic parameters showed an endothermic, entropy-driven, and non-spontaneous dissolution process of clorsulon via van't Hoff equation. Through molecular dynamic simulation based on the mechanism of intermolecular interaction, the optimized unit cell structure of clorsulon was established, and the solvation free energies were accurately calculated. The results show that the absolute value of calculated solvation free energy was positively correlated with solubility.