Heat Capacity Difference Research Articles

Semi-empirical estimation of organic compound fugacity ratios at environmentally relevant system temperatures

Fugacity ratios of organic compounds are used to calculate (subcooled) liquid properties, such as solubility or vapour pressure, from solid properties and vice versa. They can be calculated from the entropy of fusion, the melting temperature, and heat capacity data for the solid and the liquid. For many organic compounds, values for the fusion entropy are lacking. Heat capacity data are even scarcer. In the present study, semi-empirical compound class specific equations were derived to estimate fugacity ratios from molecular weight and melting temperature for polycyclic aromatic hydrocarbons and polychlorinated benzenes, biphenyls, dibenzo[ p]dioxins and dibenzofurans. These equations estimate fugacity ratios with an average standard error of about 0.05 log units. In addition, for compounds with known fusion entropy values, a general semi-empirical correction equation based on molecular weight and melting temperature was derived for estimation of the contribution of heat capacity differences to the fugacity ratio. This equation estimates the heat capacity contribution correction factor with an average standard error of 0.02 log units for polycyclic aromatic hydrocarbons, polychlorinated benzenes, biphenyls, dibenzo[ p]dioxins and dibenzofurans.

Solubility and limiting activity coefficient of simvastatin in different organic solvents

Equilibrium mole fraction solubility of Zocor ® (simvastatin) a pharmaceutically important compound, was measured between 279 and 315 K, in fifteen different industrial-relevant organic solvents including: methyl acetate, ethyl acetate, propyl acetate, iso-propyl acetate, butyl acetate, iso-butyl acetate, sec-butyl acetate, tert-butyl acetate, and ethanol, propanol, 1-butanol, 2-butanol, 1-pentanol, 1-hexanol, and 1-octanol. Fusion enthalpy, Δ fus H, melting point temperature, T m , were measured to be 32,169 J/mol, 412.6 K, respectively; and the difference in the molar heat capacity (at constant pressure) of the liquid, and solid form of simvastatin, Δ C P , was approximated (by extrapolation) to be 230 J/mol K. Dissolution of simvastatin was found to be endothermic, and entropically favorable. The activity coefficient at infinite dilution of simvastatin in each solvent was calculated from the experimental data, then fitted to Gibbs–Helmholtz equation to estimate the limiting partial molar excess enthalpies, H ¯ E , ∞ , and the limiting partial molar excess entropies, S ¯ E , ∞ . The data was also fitted to the non-random-two-liquid (NRTL) activity coefficient equation to generate the model interaction parameters for dissolution of simvastatin in the organic solvents studied here.

Vapor pressures and standard molar enthalpies, entropies, and Gibbs free energies of sublimation of 2,4- and 3,4-dinitrobenzoic acids

The vapor pressures of the solid and liquid 2,4- and 3,4-dinitrobenzoic acids were determined by torsion–effusion and thermogravimetry under both isothermal and non-isothermal conditions, respectively. From the temperature dependence of vapor pressure derived by the experimental torsion–effusion and thermogravimetry data the molar enthalpies of sublimation Δ cr g H m ∘ (〈 T〉) and vaporization Δ l g H m ∘ (〈 T〉) were determined, respectively, at the middle 〈 T〉 of the respective temperature intervals. The melting temperatures and the molar enthalpies of fusion of these compounds were measured by d.s.c. Finally, the results obtained by all the methods proposed were corrected at the reference temperature of 298.15 K using the estimated heat capacity differences between gas and liquid for vaporization experiments and the estimated heat capacity differences between gas and solid for sublimation experiments. Therefore, the averages of the standard ( p° = 0.1 MPa) molar enthalpies, entropies and Gibbs free energies of sublimation at 298.15 K, have been derived: Compound Δ cr g H m ∘ ( 298.15 K ) /(kJ · mol –1) Δ cr g S m ∘ ( 298.15 K ) /(J · mol –1 · K –1) Δ cr g G m ∘ ( 298.15 K ) /(kJ · mol –1) 2,4-Dinitrobenzoic acid 134 ± 3 244 ± 8 61 ± 5 3,4-Dinitrobenzoic acid 129 ± 3 234 ± 8 59 ± 5

Prigogine−Defay Ratio for an Ionic Glass-Former: Molecular Dynamics Simulations

The pressure dependence of the glass-transition temperature, Tg(P), of the ionic glass-former 2Ca(NO3)2 x 3KNO3, CKN, has been obtained by molecular dynamics (MD) simulations The liquid-glass difference of thermal expansivity, deltaalpha, heat capacity, deltaCp, and isothermal compressibility, deltak, have been calculated as a function of pressure. It has been found that the Ehrenfest relation dTg/dP = TVdeltaalpha/deltaCp predicts the pressure dependence of Tg, but the other Ehrenfest relation, dTg/dP = deltakappa/deltaalpha, does not. Consequently, the Prigogine-Defay ratio, pi = deltaCpdeltakappa/TVdeltaalpha2, is n pi approximately 1.2 at low pressures, but increases 1 order of magnitude at high pressures. The pressure dependence of the Prigogine-Defay ratio is interpreted in light of recent explanations for the finding pi > 1.

Vapor pressures and standard molar enthalpies, entropies and Gibbs energies of sublimation of three 4-substituted acetanilide derivatives

The vapor pressures of three 4-substituted acetanilide derivatives (namely, 4-ethoxyacetanilide, 4-hydroxyacetanilide and 4-bromoacetanilide) were measured above their liquids using the mass loss rates determined by thermogravimetry under both isothermal and nonisothermal diffusion-controlled conditions. The coefficient used to convert mass loss rates in vapor pressures showed a slight increase with increasing temperature. Therefore, the small deviations observed from the mean value enable the use of a single calibration value to be considered reasonable. From the temperature dependence of the vapor pressure estimated using a calibration constant for each technique the molar enthalpies of vaporization Δ l g H m ° ( T ) were determined, respectively, at the middle 〈 T〉 of the respective temperature intervals. The melting temperatures and the molar enthalpies of fusion of these compounds were measured by differential scanning calorimetry. Finally, the standard molar enthalpies of sublimation Δ cr g H m ° ( 298.15 K ) were obtained at the reference temperature of 298.15 K using the standard molar enthalpies of vaporization Δ l g H m ° ( T ) , the molar enthalpies of fusion, the heat capacity differences between gas and liquid and the heat capacity differences between gas and solid, Δ l g C p,m ° and Δ cr g C p,m ° , respectively, both estimated by applying a group additivity procedure. Therefore, the averages of the standard ( p° = 0.1 MPa) molar enthalpies, entropies and Gibbs energies of sublimation at 298.15 K, have been derived: Compound Δ cr g H m ° ( 298.15 K ) (kJ mol −1) Δ cr g S m ° ( 298.15 K ) (J mol −1 K −1) Δ cr g G m ° ( 298.15 K ) (kJ mol −1) 4-Ethoxyacetanilide 120 ± 3 232 ± 9 52 ± 5 4-Hydroxyacetanilide 138 ± 3 245 ± 9 65 ± 5 4-Bromoacetanilide 110 ± 4 204 ± 10 49 ± 6

Thermodynamic properties of the Pd 77.5Cu 6Si 16.5 undercooled liquid

Proper understanding of glass formation implies the knowledge of the thermodynamics of the undercooled melts. Specifically, high values of the excess specific heat of the liquid are expected for good glass-formers. Extending the work of Gillessen and Herlach [F. Gillessen, D.M. Herlach, J. Non-Cryst. Solids 117–118 (1990) 555–558], we re-propose a calculation of the temperature dependence of entropy difference between amorphous-liquid and crystal states. An amorphous Pd 77.5Cu 6Si 16.5 alloy has been produced by injection casting in a cylindrical copper mould. DSC measurements in the liquid, amorphous and crystalline states were performed with samples sliced from the cylinder to determine the heat of fusion, of crystallization and the difference in specific heat capacity between amorphous-liquid and crystal phases. These thermodynamic quantities are used to calculate the thermodynamic functions of the liquid-glass with reference to the equilibrium crystal mixture. The data are compared to those of other bulk glass-formers in terms of fragility plots.

Estimation of the Molar Heat Capacity Change on Melting of Organic Compounds

A simple equation to predict the differential molar heat capacity (ΔCpm) of the solid and liquid forms for the organic compounds at their melting point (Tm) is developed. Only three parameters are used: the molecular flexibility number (τ), the molecular symmetry number (σ), and the hydrogen bond number (HBN). The results for more than 100 compounds show that the average absolute error of ΔCpm is 13.4 J/(mol K). This is less than the average absolute errors obtained by any of the three schemes proposed in a previous report [Pappa, G. D.; Voutsas, E. C.; Magoulas, K.; Tassios, D. P. Ind. Eng. Chem. Res. 2005, 44, 3799].

Enthalpy Relaxation of Photopolymerized Thiol−Ene Networks: Structural Effects

Physical aging behavior of photopolymerized thiol−ene networks was investigated by measuring the extent of enthalpy relaxation in terms of network density and molecular structure. The homogeneous network structure of the thiol−enes, having narrow glass transition temperature ranges, showed characteristic temperature and time dependency relationships for enthalpy relaxation. All thiol−ene films annealed at different temperatures (Ta) for 1 h according to the isochronal method showed maximum enthalpy relaxation peaks at approximately Tg − 10 °C by DSC. The extent of enthalpy relaxation as a function of annealing time (ta) was obtained by the isothermal aging method. Correlations between the extent of enthalpy relaxation and the heat capacity difference at Tg were made and related to thiol−ene chemical group rigidity and network linking density. Pendulum hardness values for a selected thiol−ene film showed a clear change in hardness upon aging, indicating sub-Tg mechanical relaxation, consistent with the related enthalpy relaxation process.

Interaction of fullerenol with lysozyme investigated by experimental and computationalapproaches

The potential biomedical applications of fullerenolC60(OH)x (x≈24) have been extensively studied. However, the structural information of the interaction offullerenol with the bio-system at the molecular level, which is essential for understandingits bioactivity and toxicity, is still missing. In this study, lysozyme was selected as a modelprotein to investigate the interaction between fullerenol and biomolecules. A stronginduced circular dichroism (CD) signal of achiral fullerenol was observed afterbinding with lysozyme. Activity assay shows that lysozyme activity is inhibitedsignificantly by fullerenol. No heat capacity difference between the folded andunfolded states of lysozyme was measured by differential scanning calorimetry (DSC)in the presence of fullerenol, indicating that fullerenol prefers to bind with thehydrophobic residues. Both experimental and Autodock computational resultssuggest that the binding site on lysozyme for fullerenol is close to Trp 62, and aπ–π stacking interaction might play an important role in binding.

Temperature dependence of the Kováts retention index: Convex or concave curves

The non-linearity in the temperature dependence of the Kováts index, I (the formation of convex or concave curves) was characterized by the second derivative, d 2 I/d T 2. The expression deduced on a purely mathematical–physicochemical basis is d 2 I/d T 2 = [2 TΔ S(CH 2)d I/d T − 100 δΔ C p]/ TΔ G(CH 2). The solute-dependent factor for d I/d T, d 2 I/d T 2, and the extreme temperature in the I vs. T relationship is δΔ C p, which is the molar solvation heat capacity difference between the solute and a hypothetical n-alkane which elutes at the same time as the given solute, while the solvent-dependent factors are the solvation entropy and free energy of the methylene unit, Δ S(CH 2) and Δ G(CH 2). Experimentally, convex I vs. T curves with a minimum are formed when δΔ C p ≫ 0, while concave ones with a maximum are observed when δΔ C p ≪ 0. In the event of a linear temperature dependence, the former equation can be simplified: d I/d T = 100 δΔ C p/2 TΔ S(CH 2) . The deviation from linearity (higher d 2 I/d T 2) increases with increasing δΔ C p values. The model equations were tested from the dataset published by the Kováts group on C78 (19,24-dioctadecyldotetracontane), POH (18,23-dioctadecyl-1-untetracontenol), PCN (1-cyano-18,23-dioctadecyluntetracontane) and TMO (1,38-dimethoxy-17,22-bis-(16-methoxyhexadecyl)-octatriacontane) and by present measurements on the Innowax phase.

Determination of the activity of a molecular solute in saturated solution

Prediction of the solubility of a solid molecular compound in a solvent, as well as, estimation of the solution activity coefficient from experimental solubility data both require estimation of the activity of the solute in the saturated solution. The activity of the solute in the saturated solution is often defined using the pure melt at the same temperature as the thermodynamic reference. In chemical engineering literature also the activity of the solid is usually defined on the same reference state. However, far below the melting temperature, the properties of this reference state cannot be determined experimentally, and different simplifications and approximations are normally adopted. In the present work, a novel method is presented to determine the activity of the solute in the saturated solution (=ideal solubility) and the heat capacity difference between the pure supercooled melt and solid. The approach is based on rigorous thermodynamics, using standard experimental thermodynamic data at the melting temperature of the pure compound and solubility measurements in different solvents at various temperatures. The method is illustrated using data for ortho-, meta-, and para-hydroxybenzoic acid, salicylamide and paracetamol. The results show that complete neglect of the heat capacity terms may lead to estimations of the activity that are incorrect by a factor of 12. Other commonly used simplifications may lead to estimations that are only one-third of the correct value.

Surface and volume superconductivity of Pb embedded in nanopores

The heat capacity of lead embedded in glass nanopores (7 nm in diameter) and bulk lead was studied in the temperature range 2–40 K without a magnetic field and in magnetic fields of 1–8 T. The properties of lead nanoparticles and bulk lead were compared. The results obtained allowed us to separate the surface superconductivity from the volume superconductivity. The temperature dependence of the heat capacity of lead nanoparticles was shown to exhibit two superconducting transitions above and below the transition temperature for bulk lead (Tc = 7.2 K), which are associated with the surface and volume superconductivity. The upper critical fields Hc3 for the surface superconductivity and Hc2 for the volume superconductivity were determined. It turned out that these fields for Pb nanoparticles are two orders of magnitude higher than those for bulk lead. The “superconductor-normal metal” phase diagrams were constructed for lead nanoparticles. The study established an increase in the density of low-frequency excitations in Pb nanocrystals as compared to bulk Pb and a difference in the electronic heat capacity of Pb nanoparticles as compared to bulk Pb.

Thermochemical and thermophysical study of 2-thiophenecarboxylic acid hydrazide and 2-furancarboxylic acid hydrazide

The standard ( p ∘ = 0.1 MPa) molar energies of combustion, Δ c U m ∘ , for the crystalline 2-thiophenecarboxylic acid hydrazide and 2-furancarboxylic acid hydrazide were determined, at the temperature of 298.15 K, by rotating bomb and static bomb combustion calorimetry, respectively. For these compounds, the standard molar enthalpies of sublimation, Δ cr g H m ∘ , at T = 298.15 K, were derived by the Clausius–Clapeyron equation, from the temperature dependence of the vapour pressures of these compounds, measured by the Knudsen effusion mass-loss technique. The results were as follows: - Δ c U m ∘ ( cr ) / ( kJ · mol - 1 ) - Δ f H m ∘ ( cr ) / ( kJ · mol - 1 ) Δ cr g H m ∘ / ( kJ · mol - 1 ) 2-Thiophenecarboxylic acid hydrazide 3359.4 ± 1.1 63.9 ± 1.3 113.3 ± 0.5 2-Furancarboxylic acid hydrazide 2620.8 ± 0.6 205.5 ± 0.9 99.0 ± 0.7 These values were used to derive the standard molar enthalpies of formation of the title compounds in their gaseous phases and the results are discussed in terms of energetic effects of the introduction of the –CONHNH 2 group in the thiophene and furan rings. Using estimated values for the heat capacity differences between the gas and the crystal phases of the studied compounds, the standard ( p ∘ = 0.1 MPa) molar enthalpies, entropies, and Gibbs energies of sublimation, at T = 298.15 K, were derived.

Effect of Dilution, Pressure, and Velocity on Smoke Point in Laminar Jet Flames

Smoke point measurements of diluted methane and ethylene flames were made in a co-flowing laminar jet diffusion flame at pressures up to 8 atm. The smoke point corresponds to the fuel flow rate where the soot production is exactly offset by the soot oxidation, and as such is sensitive to changes in rates of production or oxidation. Flame height in these flames was measured as a function of pressure, diluent, and dilution level as well as both fuel exit velocity profile (i.e., plug or parabolic) and fuel/air velocity ratio. As pressure increases, the smoke point became less sensitive to diluent or dilution level. In addition to heat capacity and thermal diffusivity differences between CO2 and He for example, the large differences in kinematic viscosity was shown to play an important role in the diluent's ability to suppress the fuel's propensity to form soot.

Solubility of lovastatin in a family of six alcohols: Ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, and 1-octanol

Accurate experimental determination of solubility of active pharmaceutical ingredients (APIs) in solvents and its correlation, for solubility prediction, is essential for rapid design and optimization of isolation, purification, and formulation processes in the pharmaceutical industry. An efficient material-conserving analytical method, with in-line reversed HPLC separation protocol, has been developed to measure equilibrium solubility of lovastatin in ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol, and 1-octanol between 279 and 313 K. Fusion enthalpy Δ H fus, melting point temperature, T m, and the differential molar heat capacity, Δ C P, were determined by differential scanning calorimetry (DSC) to be 43,136 J/mol, 445.5 K, and 255 J/(mol K), respectively. In order to use the regular solution equation, simplified assumptions have been made concerning Δ C P, specifically, Δ C P = 0, or Δ C P = Δ S. In this study, we examined the extent to which these assumptions influence the magnitude of the ideal solubility of lovastatin, and determined that both assumptions underestimate the ideal solubility of lovastatin. The solubility data was used with the calculated ideal solubility to obtain activity coefficients, which were then fitted to the van’t Hoff-like regular solution equation. Examination of the plots indicated that both assumptions give erroneous excess enthalpy of solution, H ∞, and hence thermodynamically inconsistent activity coefficients. The order of increasing ideality, or solubility of lovastatin was butanol > 1-propanol > 1-pentanol > 1-hexanol > 1-octanol.

Solubilities of Adamantane and Diamantane in Pressurized Hot Water

Aqueous solubilities of lower diamondoid hydrocarbons, adamantane (C10H16) and diamantane (C14H20), were measured along the 5 MPa isobar at temperatures between 313 K and the solid–liquid–vapor triple-point temperature of the solute. The activity coefficients of the individual diamondoids in saturated aqueous solutions were estimated from the solubility data employing two different approximations of the pure-solute heat capacity difference ΔCP2. The aqueous solubilities and activity coefficients of diamondoids were compared with those of polycyclic aromatic hydrocarbons with the same carbon numbers. Depending on temperature and on the approximation of ΔCP2, the activity coefficient of adamantane in saturated aqueous solution exceeds that of naphthalene by a factor ranging within 70 to 150, whereas the activity coefficient of diamantane in saturated aqueous solution exceeds that of anthracene by a factor ranging within 10 to 50.

Solid Polymer Electrolytes from Crosslinked PEG and Dilithium N,N'-Bis(trifluoromethanesulfonyl)perfluoroalkane-1,ω-disulfonamide and Lithium Bis(trifluoromethanesulfonyl)imide Salts

The present work consists of a series of studies with regard to the structure and charge transport in solid polymer electrolytes (SPE) prepared using various new bis(trifluoromethanesulfonyl)imide (TFSI)-based dianionic dilithium salts in crosslinked low-molecular-weight poly(ethylene glycol). Some of the thermal properties (glass transition temperature, differential molar heat capacity) and ionic conductivities were determined for both diluted (EO/Li = 30:1) and concentrated (EO/Li = 10:1) SPEs. Trends in ionic conductivity of the new SPEs with respect to anion structure revealed that while for the dilute electrolytes ionic conductivity is generally rising with increased length of the perfluoroalkylene linking group in the dianions, for the concentrated electrolytes the trend is reversed with respect to dianion length. This behavior could be the result of a combination of two factors: on one hand a decrease in dianion basicity that results in diminished ion pairing and an enhancement in the number of charge carriers with increasing fluorine anion content, thereby increasing ionic conductivity while on the other hand the increasing anion size and concentration produce an increase in the friction/entanglements of the polymeric segments which lowers even more the reduced segmental motion of the crosslinked polymer and decrease the dianion contribution to the overall ionic conductivity. DFT modeling of the same TFSI-based dianionic dilithium salts reveals that the reason for the trend observed is due to the variation in ion dissociation enthalpy, derived from minimum-energy structures, with respect to perfluoroalkylene chain length.

Numerical Simulation of Influence of Urban Heat Release into Osaka Bay

The stratification of upper layer of coastal water can be regarded as an unused energy source in summer. Moreover, the coastal water has capability to store the urban heat owing to the heat capacity difference to the atmosphere. The numerical simulation of the urban heat release into coastal zone is performed. The estimated urban heat along Osaka Bay is 1kGJ/h within the distance from 500 m to 5000 m from the coastal line. The urban heat released with 2000 m from the coastal line had little influence on the sea surface temperature of Osaka Bay.

Glass transformation studies in Ge-Se-Bi system

The thermal behavior of bulk glasses in the Ge20Se80 − x Bi x (x = 2.5, 4.0, 6.0 at %) system is studied using modulated differential scanning calorimetry (MDSC). All samples have the same thermal history as a result of heating to a temperature above the glass transition point, equilibrating, and then cooling. The total heat flow, modulated heat flow, reversing heat flow, and nonreversing heat flow under heating and cooling schedules are measured. The glass transition temperature T g , the relaxation enthalpy ΔH, the specific capacity C p , and the specific heat capacity difference ΔC p = C pl − C pg , which characterize the thermal events in the glass transition region, are also determined. These parameters reveal an increase with x, which can be attributed to the increase in the average coordination number with an increase in the bismuth content (at %) in the composite. The ratio of heat capacities C pl /C pg , the width of the glass transition temperature range ΔT g , and the activation enthalpy for glass transition ΔH Tg are also studied. The values of the ratio C pl /C pg vary in the range between 1.038 and 1.112. The activation energy of crystallization is evaluated using the Kissinger, modified JMA, and Matusita equations, which is found to be in the range of 100.92 kJ/mol.

Solubilities of Triptycene, 9-Phenylanthracene, 9,10-Dimethylanthracene, and 2-Methylanthracene in Pressurized Hot Water at Temperatures from 313 K to the Melting Point

Aqueous solubilities of two C20H14 isomers, triptycene (9,10-o-benzeno-9,10-dihydroanthracene) and 9-phenylanthracene, were measured at temperatures from 313 K to the solute melting point and pressures close to 5 MPa by a dynamic method combined with gas chromatography/mass spectrometry. In addition, aqueous solubilities of 2-methylanthracene and 9,10-dimethylanthracene were also obtained. The curvature of the temperature dependence of triptycene solubility differs distinctly from those for the other solutes. Although no data on aqueous solubilities of the solutes at T > 323.15 K were found in the literature, the results for methylanthracenes at the lower limit of the temperature range of the present measurements compare favorably with previous reports. The activity coefficients of triptycene in saturated aqueous solutions were estimated from the measured solubilities employing two different approximations for the pure solute heat capacity difference ΔCP2.