Molar Entropy Research Articles

An Adventurous Journey Around the Thermodynamics of Liquid Chromatography

The characterization of the thermodynamics of separations, especially the calculation of the standard molar enthalpy and entropy through the van ’t Hoff plot, is a popular approach among chiral chromatographers, although it is already known that this representation was adopted into chromatography without real critical consideration. In our work, chiral chromatography is modeled with the column-coupling method to obtain the contribution of each adsorption site. Besides the original problems of the van ’t Hoff plot, it was found that the respective change in entropy (ΔS) and change in enthalpy (ΔH) values of each adsorption site differs significantly from the values obtained when both adsorption sites are present. The circumstances of the chromatographic adsorption were also examined to see whether the calculated values are important, or unique values are obtained for each system. Pressure especially affects the determined values, thus the chromatographic system used—high performance liquid chromatography (HPLC) or ultrahigh-pressure liquid chromatography (UHPLC)—has to be distinguished. We also have to ask: Is there any suitable equation that is less problematic to calculate thermodynamic quantities?

Solubility measurement, correlation, and dissolution thermodynamics of 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane · 1,3,5,7-tetranitro-1,3,5,7-tetrazocane (2HNIW·HMX) co-crystal in two binary solvent mixtures

The solubility of 2HNIW·HMX co-crystal in two binary solvent mixtures (ethanol + methyl acetate, and 1,2-dichloroethane + methyl acetate) was measured by gravimetric method at various temperatures (283.15, 288.15, 293.15, 298.15, 303.15, 308.15, 313.15 and 318.15 K) under atmospheric pressure (0.1 MPa). The experimental results revealed that the solubility for co-crystal in binary solvent mixtures is a simple function of ethanol (or 1,2-dichloroethane) mass fraction and temperature, which decreased with increasing temperature and mass fraction of ethanol (or 1,2-dichloroethane) in the binary solvent mixtures. The solubility of 2HNIW·HMX co-crystal was correlated with the modified Apelblat equation, CNIBS/R-K model, Jouyban-Acree-van't Hoff model, and Jouyban-Acree-Apelblat model. The fitting results demonstrate that the modified Apelblat model and CNIBS/R-K model provided a better correlation with the experimental results than the other models. Furthermore, the van’t Hoff equation was used to study the thermodynamic properties of the 2HNIW·HMX co-crystal dissolution process, including the apparent molar enthalpy change (ΔdisH°), the apparent molar entropy change (ΔdisS°), and the apparent molar Gibbs free energy change (ΔdisG°). The results show that the dissolution of the co-crystal in the selected binary solvent mixture is an exothermic process. The experimental and calculated solubility data and thermodynamic properties of the 2HNIW·HMX co-crystal would be helpful for selecting the appropriate solvent system for the reaction, crystallization, and purification of the 2HNIW·HMX co-crystal.

Study on macroscopic thermodynamic properties of ClO molecule based on the improved Hulburt–Hirschfelder potential energy function

AbstractThe improved Hulburt–Hirschfelder potential energy function is used as a proposal to emulate the behavior of intramolecular motion of a gas composed of diatomic molecules. In this work, the rovibrational energies of ClO molecule in the ground electronic state are obtained by solving the one‐dimensional Schrödinger equation with the improved Hulburt–Hirschfelder potential energy curve. And then, the molar heat capacities, molar entropies, molar enthalpies and reduced Gibbs free energies of ClO macroscopic gas are calculated by the quantum statistical ensemble theory. The results are compared with those calculated by using RKR potential energy curve from experiment and Morse potential energy function. It is found that the macroscopic thermodynamic properties of ClO calculated by the improved Hulburt–Hirschfelder potential energy function are closer to the experimental values, which provides a new way to calculate the macroscopic thermodynamic quantities of diatomic gas based on molecular microscopic information.

A combined experimental and computational thermodynamic study of fluoronitrophenol isomers

Combustion energies of the 5-fluoro-2-nitrophenol, 4-fluoro-2-nitrophenol, 3-fluoro-4-nitrophenol and 2-fluoro-4-nitrophenol isomers were obtained by means of a rotating-bomb combustion calorimeter. From these determinations, standard molar combustion enthalpies and standard molar formation enthalpies, at T = 298.15 K, in the crystalline state, were derived. The Knudsen mass-loss effusion technique was used to determine the standard molar enthalpies, entropies and Gibbs energies of sublimation, at T = 298.15 K, of the studied compounds. The standard molar enthalpies of sublimation of the four isomers were also measured by Calvet microcalorimetry. The gas-phase standard molar enthalpies of formation were derived from the experimental measurements, at T = 298.15 K, for the fluoronitrophenols studied.Additionally, the standard molar enthalpies of formation were estimated by means of computational methodology at the G3(MP2)//B3LYP level. The estimated values are in very good agreement with experimental data, giving us support to estimate the gas-phase enthalpies of formation of the remaining isomers whose values have not been determined experimentally.A simple group additivity scheme was successfully applied for prediction of molar enthalpies of formation.The computational study was also extended to the determination of OH bond dissociation enthalpies for all the isomers.

Influence of oxidative stress on drug-DNA binding: Microcalorimetric and mechanistic insights with anticancer drugs

Oxidative stress causing the chronic inflammation, mediates to deadly diseases such as cancer, diabetes, cardiovascular disease. Maintaining the ratio of reactive oxygen species generation to scavenging, thus the oxidative stress is important to have healthy cells. Oxidative stress not only causes the deadly diseases but also affect the conformation of biomolecules such as protein and DNA, even at lower concentrations. Binding of drugs to DNA is susceptible to these DNA structural or conformational changes. Here, we have reported the influence of oxidative stress on binding of anti-cancer drugsdoxorubicin hydrochloride (DOX),mitoxantrone dihydrochloride (MTX), capecitabine (CPT), and ethidium bromide (EtBr) with DNA. Quantitative insights of association of these anticancer drugs with DNA in presence of different environments, in vitro (pH – 7.4), cellular (100:1 ratio of GSH to GSSG) and oxidative stress condition (1:1 ratio of GSH to GSSG) have been compared. Microcalorimetry has been used for determination of thermodynamic parameters, binding constant Kb, molar enthalpy of interaction (ΔHm), molar entropy of interaction (ΔSm) & stoichiometry (n). Fluorescence spectroscopy has been used to illustrate the mode of drug-DNA binding and also to complement the ITC results. Insignificant changes in thermodynamic parameters for drug-DNA binding in in vitro and in presence of cellular condition were observed whereas significant decrease in binding affinity and stoichiometry was observed in the presence of oxidative stress conditions. Quantitative understanding of drug-DNA binding and influence of oxidative stress in terms of thermodynamic signature assists in the structure-based drug designing and development.

Comparative Thermal and Thermodynamic Study of Homologous series by Chromatography using Liquid Crystalline Stationary Phase

This work consisted in the preparation and the study of a new stationary phase based on liquid crystals for gas chromatography applications. Most of the synthesized compounds that have the character of liquid crystals in their constitution include aromatic molecules. In addition, there is little work that replaces this type of molecules with heterogeneous molecules that have a liquid crystalline character. This study constitutes an approach for the synthesis of a new molecule azoesters involves a 1,3,4-oxadiazole unit instead of aromatic rings, and which exhibits liquid crystalline characters. A liquid crystal has been prepared and characterized. The thermodynamic characteristics of the n-alkanes for the filled column were studied by reverse gas chromatography. The intermediate products, as well as the mesogens obtained, were characterized by various experimental analysis techniques such as infrared spectrometry (IR) and nuclear magnetic resonance (NMR). The thermal properties of synthesized liquid crystal require the use of DSC technique. Thermodynamic parameters such as enthalpies, partial solution molar entropy and infinite dilution, were determined for the liquid crystal-solvent system. The thermodynamic quantities show that these values depend on the number of carbon atoms of the CL phase terminal substituent. The transition temperatures obtained by gas chromatography are in good agreement with those found by DSC.

Non-ionic surfactants in drug delivery vehicles: Physicochemical insights with systems of drugs, Igepal CA-630, bovine serum albumin and hen egg-white lysozyme

Most of the synthetically developed drugs are hydrophobic in nature and hence possess low bioavailability. An efficient delivery of such drugs at the specific target site requires usage of suitable drug delivery vehicles. The quantitative aspects of drug partitioning into delivery vehicles, their release and binding of target protein are crucial for developing guidelines aimed at rational drug design. We have examined the partitioning of anti-thyroid, anti-inflammatory and anti-cancer drugs methimazole, naproxen, imatinib, and (s,s)-n,n′-bis(1-hydroxy-2-butyl)-ethylenediamine dihydrochloride in non-ionic self-assemblies of Igepal CA-630. The use of non-ionic surfactants in drug delivery is important because of their mild and harmless nature. The partitioning of drugs into surfactant micelles have been carried out using calorimetric and spectroscopic techniques. The quantitative details of partitioning mechanism have been investigated using parameters of their interaction such as change in Gibbs free-energy, standard molar enthalpy and entropy. These thermodynamic signatures have allowed us to develop relationships between structure-property and energetics which are very important in rational drug design. The results obtained were compared with different class of drugs having divergent nature to understand the key molecular features in the process of drug partitioning.

1.6-Hexanediol based deep eutectic solvent and their excess data at infinite dilution

For over two decades, deep eutectic solvents have offered pre-eminence characteristics with the purpose of improving the issues of both ionic liquids and traditional solvents. The affordability, ease of preparation, in-flammability, non-or low toxicity, biodegradability, and other environmental advantages of DESs make them more appealing as green solvents. In the present study, 1-ethyl-1-methylpyrrolidinium bromide, a hydrogen bond accepter (HBA), was paired with 1,6-hexanediol (1,6-HDO), a hydrogen bond donor (HBD), to produce a DES with a mole ratio of 1:2. With the use of gas liquid chromatography (GLC), the infinite dilution activity coefficients (IDACs) of 32 different solutes were measured at different temperatures (313.15–343.15) K and atmospheric pressures. The partial molar properties, i.e., enthalpy, entropy, and Gibbs free energy, were calculated from the IDAC values at a reference temperature of T = 313.15 K to give more details for molecular interaction interpretation. Lastly, the selectivity and capacity values of separation problems such as benzene/acetone, benzene/cyclohexane, and cyclohexane/acetone were calculated from the IDAC values. The investigated DES was discovered to have good performance and could be used in industrial processes such as petroleum distillation, separation, extraction, and so on.

Study on the volatility of four benzaldehydes

This work reports the experimental determination of relevant thermodynamic properties of four benzaldehydes. The vapor pressures of both crystalline and liquid phases (including supercooled liquid) of syringaldehyde, 3,4,5-trimethoxybenzaldehyde, 4-(dimethylamino)benzaldehyde and of the liquid phase of veratraldehyde were determined using a static method based on capacitance diaphragm manometers. Additionally, the sublimation vapor pressures of the four compounds were also determined at different temperatures, using the Knudsen mass-loss effusion method. The experimental results allowed accurate determination of the standard molar enthalpies, entropies and Gibbs energies of sublimation and of vaporization for the benzaldehydes studied, at reference temperatures, allowing phase diagram representations of the (p,T) results, in the neighborhood of the triple point of the four compounds. Their temperatures and molar enthalpies of fusion were determined using differential scanning calorimetry and were compared with the ones obtained indirectly through vapor pressure measurements. Using high-precision drop calorimetry, the standard isobaric molar heat capacities of the four crystalline benzaldehydes were determined at 298.15 K. The enthalpy of the intermolecular hydrogen bond OH…O in the crystalline phase of syringaldehyde was estimated.

Enthalpies of formation and standard entropies for some potassium Tutton salts

Differential scanning calorimetry (DSC) was used to measure the enthalpies of reaction for the dehydration of the potassium Tutton salts, K2M(SO4)2. 6 H2O with M = Mg, Co, Ni, Cu and Zn. The values determined ranged from 335 kJ mol−1 for K2Mg(SO4)2 6 H2O to 355 kJ mol−1 for K2Ni(SO4)2. 6 H2O with a measured standard deviation of ± 5 kJ mol−1. Although the information needed to obtain precise values for the enthalpies of formation is not available in the literature for all of these salts, values calculated by modeling the amorphous dehydrated compound as an ideal solid solution produced values within 10 kJ mol−1 of the values determined for K2M(SO4)2. 6 H2O (M= Mg, Cu, and Zn) where the information needed for this calculate was available. DSC was also used to determine the entropies of reaction for the dehydration of these salts. Since there is little information about the entropies of these compounds in the literature, the entropies of reaction were used with the ideal solution model for the amorphous compound to estimate the standard molar entropies for these salts. The values determined ranged from 490 J K−1 mol−1 for K2Cu(SO4)2. 6 H2O to 540 J K−1 mol−1 for K2Co(SO4)2. 6 H2O. Since these values are based upon estimated values, they have an estimated error of ± 5 percent.

On the Study of Thermal Transitions in Selected n-Paraffins Using Differential Scanning Calorimetry

The results obtained from a study of the thermal transformations of polymorphic long-chain normal paraffins (n-C32H66 and n-C36H74) are presented here. The research was performed using a power-compensated Differential Scanning Calorimeter (DSC). Both heating and cooling experiments were performed in dynamic nitrogen atmosphere. Thermodynamic data for both polymorphic transitions, as well as the fusion endotherms, were determined from the DSC thermal curves. Using the heats of transition (∆H), in Joules/gram, obtained from the data in the DSC thermal curves, molar heats of transition (∆H), in kJ/mol, were calculated and compared to previously published values. The molar entropy of transition (∆S) was then calculated for each of the observed thermal events. Additional information is given by the author on obtaining the best results from the use of DSC for the thermal behavior of n-paraffins. This manuscript opens with a review of most of the early work and the results it provided dealing with polymorphism of n-paraffin solids. Some of this referenced work was performed prior to the advent of computerized analytical instrumentation.

The Influence of Deuterium Isotope Effects on Structural Rearrangements, Ensemble Equilibria, and Hydrogen Bonding in Protic Ionic Liquids.

We report strong isotope effects for the protic ionic liquid triethylammonium methanesulfonate [TEA][OMs] by means of deuterium solid-state NMR spectroscopy covering broad temperature ranges from 65 K to 313 K. Both isotopically labelled PILs differ in non-deuterated and fully deuterated ethyl groups of the triethyl ammonium cations. The N-D bond of both cations is used as sensitive probe for hydrogen bonding and structural ordering. The 2 H NMR line shape analysis provides the deuteron quadrupole coupling constants and the characteristics of a broad heterogeneous phase with simultaneously present static and mobile states indicating plastic crystal behavior. The temperatures where both states are equally populated differ by about 80 K for the two PILs, showing that deuteration of the ethyl groups in the trialkylammonium cations tremendously shifts the equilibrium towards the static state. In addition, it leads to a significant less cooperative transition, associated with a significantly reduced standard molar transition entropy.

Synthesis and characterization of physicochemical properties of two new hydroxyl-functionalized ionic liquids

Two hydroxyl functionalized ionic liquids, 1-(2-hydroxyethyl)-3-methylimidazolium acetate [HEMIM][AC], and 1-(2-hydroxyethyl)-3-methylimidazolium propionate [HEMIM][Pro] ionic liquids were synthesized. The ionic liquids were characterized by 1H NMR and 13C NMR respectively. The density ρ, surface tension γ, and viscosity η of the two ionic liquids were measured in the temperature range (288.15–333.15 K). The contributions of anionic structure to molecular volume Vm, standard molar entropy S0 and the crystal energy UPOT, as well as the variation rules of surface entropy Sa, surface energy Ea and sound velocity W were calculated and discussed. In addition, according to Eyring viscosity equation and thermodynamic equation, the activation Gibbs energy of viscous flow activation ΔG≠ is calculated at different temperatures. And the influence of different anions on the thermodynamic properties of ionic liquids was discussed.

Crystallization Thermodynamics of α-Lactose Monohydrate in Different Solvents.

It is common to find that some of the lactose in dairy powders and pharmaceutical tablets is present in the unstable amorphous state. Therefore, their crystallization thermodynamics in different solvents are particularly important. In this paper, the solubility of α-lactose monohydrate (α-LM) in 15 mono-solvents such as ethanol, isopropanol, methanol, 1-propanol, 1-butanol, 2-butanol, isobutanol, 1-pentanol, isoamylol, 1-hexanol, 1-heptanol, 1-octanol, propanoic acid, acetonitrile, and cyclohexanone was evaluated by using the gravimetric method in the temperature ranges from 274.05 K to 323.05 K at constant pressure (1 atm). In the given temperature range, the solubility of α-LM in these solvents increased with the rising of temperature, the highest solubility of α-LM was found in methanol (2.37 × 104), and the lowest was found in 1-hexanol (0.80 × 105). In addition, the increase of α-LM solubility in isopropanol was the largest. The sequence at 298.15 K was: methanol > 1-butanol > isopropanol > ethanol > 1-propanol > 1-heptanol > isobutanol > propionic acid > 1-pentanol > 1-octanol > acetonitrile > isoamylol > 2-butanol > cyclohexanone > 1-hexanol. Solvent effect analysis shows that the properties of α-LM are more important than those of solvents. The Apelblat equation, λh equation, Wilson model, and NRTL model were used to correlate the experimental values. The root-mean-square deviation (RMSD) and relative average deviation (RAD) of all models were less than 2.68 × 10−2 and 1.41 × 10−6, respectively, implying that the fitted values of four thermodynamic models all agreed well with the experimental values. Moreover, the thermodynamic properties of the dissolution process (i.e., dissolution Gibbs free energy (ΔdisG), molar enthalpy (ΔdisH), and molar entropy (ΔdisS)) for α-LM in selected solvents were determined. The results indicate that ΔdisH/(J/mol) (from 0.2551 to 6.0575) and ΔdisS/(J/mol/K) (from 0.0010 to 0.0207) of α-LM in these solvents are all positive, and the values of ΔdisH and ΔdisS. ΔdisG/(J/mol) (from −0.0184 to −0.6380) are all negative. The values were observed to decrease with rising temperatures, implying that α-LM dissolution is an endothermic, entropy-driven, and spontaneous process. The solid–liquid equilibrium data and dissolution thermodynamics of α-LM were obtained, which provide a basis for industrial production.

Measurement and accurate prediction of surface tension for VOSO4-H2SO4-H2O ternary electrolyte system at high-concentration in vanadium redox flow batteries

Surface tension is an important thermodynamic parameter for vanadium redox flow battery (VRFB) however its related theoretical study for multicomponent systems containing sulfuric acid at high concentration is rare due to the complexity of ion interaction in the electrolyte. In this work, the surface tension and density of VOSO4-H2SO4-H2O electrolyte solution were firstly measured at different temperatures from 283.15 to 313.15 K over a wide range of solute concentration. The average molar volume (V) was calculated according to above experimental data, and then the new definition of molar surface Gibbs free energy (gs) and improved Eötvös equation for VOSO4-H2SO4-H2O ternary solution has been derived based on Li’s theory. Simultaneously, several thermodynamic data of this ternary solution were obtained, such as the value of molar surface entropy, s, molar surface enthalpy, h, and Eötvös empirical parameter. In addition, the high-accuracy and semi-empirical equation was established to predict the surface tension of the VOSO4-H2SO4-H2O ternary solution based on the new gs definition. The results revealed that predicted values are in good agreement with the experimental values and correlation coefficient is 0.9993. This work provides basic data for mass transfer and heat transfer analysis of the VRFB and it also provides convenience for evaluating the interface effect between the electrolyte and other components when optimizing the composition of electrolyte and improving battery performance.

Thermodynamics of trimethyltetradecylammonium bromide – Sodium deoxycholate binary mixed micelle formation in aqueous solution: Regular solution theory with mutual compensation of excess configurational and excess conformational entropy

A binary mixture of trimethyl(tetradecyl)ammonium bromide = TB-SD = sodium deoxycholate surfactants forms non-ideal binary mixed micelles that have molar excess Gibbs free energy described with the Margules function of the first order. Strong synergistic interactions exist between TB and SD particles (interaction coefficient with a magnitude of 10). Based on the temperature dependence of interaction coefficient and temperature dependence of TB and SD micellar molar fractions product logarithm, it follows that the molar excess entropy is zero. Therefore, although the surfactants TB and SD are structurally very different, their binary mixed micelles can still be described with regular solution theory (random mixing of TB and SD). However, the 2D ROESY spectrum indicates that the binary micellar pseudophase is not random in terms of the spatial distribution of TB and SD particles. Namely, intermolecular interactions between deoxycholic acid anions are missing in the binary mixed micelle. This results in the appearance of excess configuration entropy. However, a zero value of the total molar excess entropy and the existence of the first order Margules function for the molar excess Gibbs free energy means that the molar excess configurational entropy is compensated with the molar excess conformational entropy and that there are correlation effects between the excess configurational enthalpy and entropy as well as between the excess conformational enthalpy and entropy.

Physicochemical and excess properties of binary system mixtures of ether-functionalized ionic liquids with DMSO

In the full molar fraction range, the density, surface tension and viscosity of 1-(4-methoxybutyl)-3-methylimidazolium glycine ([COC4mim][Gly]), 1-(4-methoxybutyl)-3-methylimidazolium alanine ([COC4mim][Ala]) and 1-(4-methoxybutyl)-3-methylimidazolium threonine ([COC4mim][Thr]) with DMSO binary mixtures were determined. The variation trends of excess molar volume (VE), excess molar surface Gibbs energy (gsE), Gibbs energy of activation for viscous flow of the relative viscosity (ΔG≠r) and x1 of binary system mixture were systematically studied, and the interaction between ether-functionalized ionic liquids (ILs) and solvent molecules in binary system mixtures was studied. According to the molar surface Gibbs energy definition, excess molar surface Gibbs energy definition and Redlich-Kister empirical equation, the correlation between the predicted and experimental surface tension values of ILs + DMSO binary system mixtures was investigated. Furthermore, using the improved Eötvös empirical equation and thermodynamic formula, molar surface entropy and molar surface enthalpy of binary system mixture were calculated. The molar surface enthalpy of binary mixture was independent of temperature. This fact indicated that the process from the bulk to the surface of binary system mixture was an isocoulombic reaction.

Measuring and modeling the solubility of carbon dioxide in protic ionic liquids

The solubility of carbon dioxide (CO2) in three protic ionic liquids, namely N-Ethylmorpholine acetate ([NEMH][Ac]), N-Ethylmorpholine propionate ([NEMH][Pro]), and Triethylamine propionate ([TEAH][Pro]), was measured at temperatures from 298.15 to 338.15 K and pressures up to about 900 kPa. The solubility data were fitted by Pitzer's model and Soave-Redlich-Kwong (SRK) cubic equation of state. In the range of experimental uncertainty, both models can well correlate solubility data. Henry's law constants of CO2 in these three protic ionic liquids at zero pressure were estimated from the solubility data, and the partial molar Gibbs free energy, partial molar enthalpy, and partial molar entropy at infinite dilution were calculated.

Interaction between Triton X100 and Brij 58 in their binary mixed micelles: Micellization in aqueous solution and aqueous solution of Poloxamer 188 at the range of temperature T = (273.15–323.15) K

The micellization of the binary mixture of surfactants Triton X100 – Brij 58 in an aqueous solution (with and without Poloxamer 188) was investigated using a spectrofluorimetric method with pyrene as a probe molecule. There are synergistic interactions between the micellar building units in the binary mixed micelles Triton X100 – Brij 58, which increase with increasing temperature. The analyzed binary mixed micelles possess molar excess entropy. The molar excess Gibbs free energy is a first-order Margules function from the surfactant (Triton X100 or Brij 58) molar fraction in the binary mixed micelles Triton X100 – Brij 58. Poloxamer 188, in the temperature range T = (273.15–323.15) K, does not form micelles. Poloxamer 188 in an aqueous surfactant solution (0.01 w/w) reduces the thermodynamic stabilization of the binary mixed micelle Triton X100 – Brij 58 concerning the state of the same binary mixed micelle when this polymer is not present in an aqueous solution. In the presence of Poloxamer 188, the thermodynamic destabilization of the binary mixed micelle Triton X100 – Brij 58 increases with increasing temperature.

Prediction of thermal properties of phosphorus dimer – The analytical approach

In this study, modified hyperbolical-type oscillator was used to simulate the internal vibration of a diatomic molecule. By employing the expression of partition function of the system, new analytical equations for the prediction of molar entropy, enthalpy, Gibbs free energy, and isobaric specific heat capacity were derived. The thermodynamic equations were applied to ground-state phosphorus dimer. Average absolute deviations of 0.3795, 0.8939, 0.3895, and 0.6978% were obtained. The results are in good agreement with existing data on gaseous phosphorus molecules in the literature.