Entropy Of Fusion Research Articles

Solubility of cefoxitin acid in different solvent systems

Cefoxitin acid is one kind of important pharmaceutical intermediate. Its solubility is crucial for designing and optimizing the crystallization processes. In this work, the solubility of cefoxitin acid in organic solvents (methanol, acetonitrile, ethanol, isopropanol, n-propanol and ethyl acetate), water and water-methanol mixtures was measured spectrophotometrically using a shake-flask method within the temperature range 278.15–303.15K. PXRD data and the Karl Fischer method were used to verify the crystal form stability of cefoxitin acid in the solubility measuring process. The melting points, the enthalpy and entropy of fusion were estimated. Results showed that the solubility of cefoxitin acid increases with the increasing temperature in all tested solvents in this work, and the solubility of cefoxitin acid increases with the increasing methanol concentration in water-methanol mixtures. The experimental solubility values were well correlated using the modified Apelblat equation, NRTL model and CNIBS/R-K model. An equation proposed by Williamson was adopted to calculate the molar enthalpy during the dissolution process.

Glass formability in medium-sized molecular systems/pharmaceuticals. I. Thermodynamics vs. kinetics.

Scrutinizing critical thermodynamic and kinetic factors for glass formation and the glass stability of materials would benefit the screening of the glass formers for the industry of glassy materials. The present work aims at elucidating the factors that contribute to the glass formation by investigating medium-sized molecules of pharmaceuticals. Glass transition related thermodynamics and kinetics are performed on the pharmaceuticals using calorimetric, dielectric, and viscosity measurements. The characteristic thermodynamic and kinetic parameters of glass transition are found to reproduce the relations established for small-molecule glass formers. The systematic comparison of the thermodynamic and kinetic contributions to glass formation reveals that the melting-point viscosity is the crucial quantity for the glass formation. Of more interest is the finding of a rough correlation between the melting-point viscosity and the entropy of fusion normalized by the number of beads of the pharmaceuticals, suggesting the thermodynamics can partly manifest its contribution to glass formation via kinetics.

Phase behavior and heat capacities of the 1-benzyl-3-methylimidazolium ionic liquids

The thermal behavior, solid and liquid heat capacities of the 1-benzyl-3-methylimidazolium, [Bzmim]+, based ionic liquid series with Cl−, PF6−, BF4−, CHF2CF2SO3− and NTf2− as anions were used to evaluate the effect of the insertion of an aromatic character (benzyl group) and the expected increase of the π–π interactions as well as the impact in the cation–anion hindrance and charge delocalization in the ionic liquid properties. It was found that the molar liquid heat capacities of [Bzmim][X] are in the same order as the 1-pentyl-3-methylimidazolium, [C5C1im][X] analogs. A good correlation between the molar (solid and liquid) heat capacity and the number of atoms of the anion was found. Two different crystalline forms for [Bzmim][BF4] differing by 10K in the melting temperature and about 10% in the heat capacity were found. The crystallization behavior, melting temperatures, and enthalpies and entropies of fusion show that the insertion of an aromatic character (benzyl group) in the imidazolium cation leads to a significant and systematic change of the thermophysical properties of the ionic liquids associated with an increase of the glass transition and melting temperatures arising from the additional π–π interactions.

Experimental Solubility Approach to Determine PDMS-Water Partition Constants and PDMS Activity Coefficients.

Freely dissolved aqueous concentration and chemical activity are important determinants of contaminant transport, fate, and toxic potential. Both parameters are commonly quantified using Solid Phase Micro-Extraction (SPME) based on a sorptive polymer such as polydimethylsiloxane (PDMS). This method requires the PDMS-water partition constants, KPDMSw, or activity coefficient to be known. For superhydrophobic contaminants (log KOW >6), application of existing methods to measure these parameters is challenging, and independent measures to validate KPDMSw values would be beneficial. We developed a simple, rapid method to directly measure PDMS solubilities of solid contaminants, SPDMS(S), which together with literature thermodynamic properties was then used to estimate KPDMSw and activity coefficients in PDMS. PDMS solubility for the test compounds (log KOW 7.2-8.3) ranged over 3 orders of magnitude (4.1-5700 μM), and was dependent on compound class. For polychlorinated biphenyls (PCBs) and polychlorinated dibenzo-p-dioxins (PCDDs), solubility-derived KPDMSw increased linearly with hydrophobicity, consistent with trends previously reported for less chlorinated congeners. In contrast, subcooled liquid PDMS solubilities, SPDMS(L), were approximately constant within a compound class. SPDMS(S) and KPDMSw can therefore be predicted for a compound class with reasonable robustness based solely on the class-specific SPDMS(L) and a particular congener's entropy of fusion, melting point, and aqueous solubility.

Fusion and Thermal Degradation Behavior of Symmetric Sulfur-Containing Quaternary Ammonium Bromides.

Quaternary ammonium salts are widely used in consumer products and industrial processes, where their instability at elevated temperatures limits their range of applications. In this work, the thermal behavior of a new class of quaternary ammonium salts was investigated using differential scanning calorimetry. These salts contain a sulfur atom in each chain at the fourth position from the central nitrogen and are thus termed thiaquats. The temperatures at which these salts melt and thermally degrade were determined, and enthalpies and entropies of fusion were evaluated. Their melting points increase with chain lengths, in contrast to the behavior of traditional quaternary ammonium salts. Furthermore, they exhibit enthalpies and entropies of fusion significantly lower than corresponding tetraalkyl analogues. These trends provide physical insight into the molecular-level behavior of these salts, suggesting that they do not fully dissociate upon melting. The thiaquats also exhibit thermal stability to markedly higher temperatures than traditional quaternary ammonium bromides, a phenomenon that can be explained in by strong pairing between the quaternary cation and bromide anion, which inhibits possible decomposition mechanisms. This enhanced thermal stability may enable applications of these salts in processes where traditional salts are not viable, such as phase-transfer-catalyzed systems performed at elevated temperatures.

Calorimetric Properties and Solubility in Five Pure Organic Solvents of N-Methyl-d-Glucamine (Meglumine)

The solid–liquid solubility of the title compound has been measured by a gravimetric method in five pure organic solvents over the temperature range (283 to 323) K. The melting temperature and associated enthalpy of fusion have been determined by differential scanning calorimetry (DSC), and the heat capacity of the solid and the melt have been determined over a range of temperatures by means of temperature-modulated DSC. Melting data and the extrapolated difference in heat capacity between the melt and the solid have been used to calculate the Gibbs energy, enthalpy, and entropy of fusion and the ideal solubility from below ambient temperature to the melting point. On the basis of estimated activity coefficients at equilibrium, solutions in all the five solvents are shown to exhibit positive deviation from Raoult’s law. The highest mole fraction solubility is observed in methanol, and all van’t Hoff solubility curves are nonlinear. Solubility data is well correlated by a recently proposed semiempirical re...

Theoretical Considerations of the Prigogine–Defay Ratio with Regard to the Glass-Forming Ability of Drugs from Undercooled Melts

Drug behavior in undercooled melts is highly important for pharmaceutics with regard to amorphous solid dispersions, and therefore, categories were recently introduced that differentiate glass formers (GFs) from other drugs that are nonglass formers (nGFs). The present study is based on the assumption that molecular properties relevant for the so-called Prigogine-Defay (PD) ratio would be indicative of a drug's glass-forming ability. The PD ratio depends in theory on the entropy of fusion and molar volume. Experimental data were gathered from a broad set of pharmaceutical compounds (n = 54) using differential scanning calorimetry. The obtained entropy of fusion and molar volume were indeed found to significantly discriminate GFs from nGFs. In a next step, the entropy of fusion was predicted by different in silico methods. A first group contribution method provided rather unreliable estimates for the entropy of fusion, while an alternative in silico approach seemed more promising for drug categorization. Thus, a significant discrimination model employed molar volume, a so-called effective hydrogen bond number, and effective number of torsional bonds (or torsional units) to categorize GFs and nGFs (p ≤ 0.0000). The results led to new insights into drug vitrification and to practical rules of thumb. The latter may serve as guidance in pharmaceutical profiling and early formulation development with respect to amorphous drug formulations.

Phase diagram and thermal properties of organic analogues of nonmetal–nonmetal systems

The solid–liquid phase equilibrium data on three binary organic systems, namely 4-hydroxy benzaldehyde (HB)–2-methyl-4-nitro aniline (MNA), 3-hydroxy-4-methoxybenzaldehyde (HMB)–2-chloro-4-nitroaniline (CNA) and 4-aminobenzophenone (ABP)–m-nitrobenzoic acid (NBA), determined by the thaw-melt method, show the formation of a eutectic at 0.60 mol fraction of HB, 0.48 mol fraction of HMB and 0.51 mol fraction of ABP. These systems are organic analogue of nonmetal–nonmetal system. The values of enthalpy of fusion of eutectics and parent components were determined by the DSC method. Using the heat of fusion values, entropy of fusion, heat of mixing, excess thermodynamic functions and Jackson’s roughness parameter were calculated. The negative values of enthalpy of mixing in each case suggest the associative interaction between the molecules of the eutectic melt. The positive value of excess free energy for HB–MNA system indicates the associative interaction between like molecules, while the negative values of excess free energy for HMB–CNA and ABP–NBA indicate the associative interaction between unlike molecules.

Synthesis and thermodynamic properties of a novel pyridinium-based asymmetrical gemini ionic liquid

A novel asymmetrical gemini ionic liquid (GIL), [1-(1-pyridinium-yl-hexyl)-6-methylpiperidinium] dihexafluorophosphate ([PyC6MPi][PF6]2) combined with pyridine, 1-methylpiperidine by 1,6-dibromohexane with PF6− as anion, was synthesized and characterized by 1H NMR and IR. The molar heat capacity of the GIL was measured via differential scanning calorimetry from 298.15 K to 448.15 K under atmospheric pressure. No phase transition or other thermal anomaly was observed in the solid-phase region (298.15 K to 358.15 K) and liquid-phase region (403.15 K to 448.15 K). The basic properties and thermodynamic functions of the GIL, such as melting point, molar enthalpy and entropy of fusion, heat capacity, enthalpy HT-H298.15 K, and entropy ST-S298.15 K, were also determined from the experimental data. Thermal decomposition kinetics of [PyC6MPi][PF6]2 were investigated by using non-isothermal thermogravimetric analysis in pure nitrogen atmosphere at various heating rates. Thermal decomposition data were, respectively, correlated with Friedman method, Ozawa-Flynn-Wall equation, and ASTM model. The activation energy (E) and pre-exponential factor (logA) values were obtained by using the above three methods.

Thermal properties and solubility of methyl α-d-glucopyranoside in methanol at different temperatures

Heat capacity of methyl α-d-glucopyranoside (α-MeG) was measured by differential scanning calorimetry at the temperatures ranging from 298.15 to 513.15 K. Melting point, enthalpy and entropy of fusion, enthalpy HT–H298.15 K, and entropy ST-S298.15 K were determined. Thermal decomposition of α-MeG was investigated using thermogravimetric analysis under pure nitrogen atmosphere. Ozawa-Flynn-Wall and ASTM models were used to calculate the activation energy and pre-exponential factor. Solubilities of α-MeG in methanol were measured within the temperature range of 293.15–318.15 K by using a synthetic method under atmospheric pressure. The modified Apelblat, λh, Wilson and NRTL models were applied to correlate the experimental data. The calculated results show good agreement with the experimental data and Wilson model is slightly more accurate than modified Apelblat, λh and NRTL models. The dissolution enthalpy, entropy, and Gibbs free energy were calculated by the Van't Hoff equation. The excess enthalpy of the solution can be evaluated by the λh model.

Термодинамическое моделирование поверхности ликвидус диаграммы состояния системы Cu2O–Al2O3–ZrO2

Calculations of the liquidus lines for the phase diagrams of the Cu2O–Al2O3, Cu2O–ZrO2 and Al2O3–ZrO2 binary systems were made as well as the calculations of liquidus surface for the phase diagram of the Cu2O–Al2O3–ZrO2 ternary system. The theory of subregular ionic solutions was used in thermodynamic modeling. The values of the theory parameters Q, thermodynamic characteristics (melting temperature, heat of fusion, and entropy of fusion) for CuAlO2 compound were determined. The values of the equilibrium constants of the transition from solid to liquid for Cu2O, Al2O3, ZrO2 and CuAlO2 were defined. Calculations of activity of Cu2O, Al2O3, and ZrO2 in the oxide melt for Cu2O–Al2O3 and Cu2O–ZrO2 diagrams show that a(Cu2O) , a(Al2O3 ) and a(ZrO2 ) have negative deviation from Raoult’s law. The calculated activity of the aluminium oxide has good agreement with the literature. Construction of the liquidus surface for the Cu2O–Al2O3–ZrO2 ternary system allows to define the points of the nonvariant transformation. Results of the thermodynamic modeling of the Cu2O–Al2O3–ZrO2 ternary system show that equilibrium “oxide melt–pure solid copper oxide–pure solid aluminium oxide” is realized in this system. This equilibrium is not characteristic for Cu2O–Al2O3 binary system. Results of this work can be used for the analysis of the bronze production and for the analysis of slag behavior for the copper and copper-based alloys industries.

The influence of the halogen atoms and acetyl group on vapour pressures and related properties of the p-haloacetophenones

This work reports experimental vapour pressures at different temperatures of four halogenated acetophenones. The liquid phase vapour pressures of p-fluoro and p-chloro acetophenones were measured, respectively, across the temperatures ranges (255.1 to 310.2)K and (271.6 to 335.0)K, using a static method based on capacitance diaphragm manometers. This experimental technique was also used to measure the vapour pressures of both (crystalline and liquid) condensed phases of p-bromo- and p-iodoacetophenones, respectively, through the temperature intervals (295.3 to 378.4)K and (313.1 to 402.0)K. The temperatures and molar enthalpies and entropies of fusion of the four p-halogenated acetophenones were determined using differential scanning calorimetry. The standard molar enthalpies, entropies and Gibbs energies of sublimation and of vaporisation, at selected reference temperatures, were derived from the experimental results. The contributions of the acetyl group and of the constituent halogen atoms to these thermodynamic properties were also predicted through correlation equations.

Determination of thermodynamic properties of aluminum based binary and ternary alloys

In the present work, the Gibbs–Thomson coefficient, solid–liquid and solid–solid interfacial energies and grain boundary energy of a solid Al solution in the Al–Cu–Si eutectic system were determined from the observed grain boundary groove shapes by measuring the thermal conductivity of the solid and liquid phases and temperature gradient. Some thermodynamic properties such as the enthalpy of fusion, entropy of fusion, the change of specific heat from liquid to solid and the electrical conductivity of solid phases at their melting temperature were also evaluated by using the measured values of relevant data for Al–Cu, Al–Si, Al–Mg, Al–Ni, Al–Ti, Al–Cu–Ag, Al–Cu–Si binary and ternary alloys.

Effect of Core Crystallization and Conformational Entropy on the Molecular Exchange Kinetics of Polymeric Micelles.

Here we systematically study the equilibrium molecular exchange kinetics of a series of amphiphilic n-alkyl-poly(ethylene oxide) (Cn-PEO) micelles containing partly crystallized cores. Using differential scanning calorimetry (DSC), we determined the melting transition and extracted the enthalpy of fusion, ΔHfus, of the n-alkyl chains inside the micellar core. Molecular exchange kinetics was measured below the melting point using a time-resolved small-angle neutron scattering technique (TR-SANS) based on mixing deuterated and proteated but otherwise identical micelles. Comparing both kinetic and thermodynamic data, we find that crystallinity within the micellar cores leads to significant enthalpic and the entropic contributions to the activation barrier for molecular exchange. While the former leads to an enhanced stability, the positive entropic gain favors the process. Interestingly, the entropic term contains an excess term beyond what is expected from the measured entropy of fusion. Based on calculations using the Rotational Isomeric State (RIS) model, we suggest that the excess entropy is due to the gain in conformational entropy upon releasing the chain from the confined state in the core. The study thus provides deep insight into the fundamental processes of micellar kinetics and which might be relevant also to other semicrystalline soft matter and biological systems including lipid membranes.

An experimental verification of a criterion for forming metastable phases in containerless solidification

On the thermodynamic condition for forming a metastable phase from undercooled melt in a containerless state, we had proposed a criterion that crystals will preferentially form if they have a smaller entropy of fusion than the entropy of fusion of equilibrium crystals (Kuribayashi et al., Mater. Sci. Eng., A 449–451, 675 (2007)). This criterion is proposed for being applied to materials that exhibit a faceted interface, such as semiconductors and oxides. However, no experimental data that support this criterion have been obtained. From this point, we used an aerodynamic levitator as a tool for forming metastable phases from undercooled melt and verified the above-mentioned criterion using LnFeO3 (Ln: lanthanide and Y) as the model material. In addition, the condition for double recalescence, which corresponds to forming metastable phases and stable phases, was discussed in terms of competitive 2D isomorphic nucleation of the metastable phase and 3D polymorphic nucleation of the stable phase.

Thermodynamic properties of 4-tert-butyl-diphenyl oxide

The main thermodynamic functions (changes of the entropy, enthalpy, and Gibbs free energy) and functions of formation at T=298.15K of 4-tert-butyl-diphenyl oxide in condensed and ideal gas states were computed on the basis of experimental results obtained. The heat capacities of 4-tert-butyl-diphenyl oxide was measured by vacuum adiabatic calorimetry over the temperature range (8 to 371)K. The temperature, the enthalpy and the entropy of fusion were determined. The energy of combustion of the sample was determined by static-bomb combustion calorimetry. The saturation vapor pressures of the substance were measured by dynamic transpiration method over the temperature and pressure intervals (298 to 325)K and (0.05 to 1.2)Pa. The enthalpy of sublimation at T=298.15K was derived. The contribution of O-(2Cb) group (where Cb is the carbon atom in a benzene ring) into the absolute entropies of diphenyl oxide derivatives was assessed.

Synthesis, crystal growth and physicochemical studies on a novel organic inter-molecular compound; 3,5-dinitrobenzoic acid and salicylamide system

The phase diagram of salicylamide (SAM) and 3,5-dinitrobenzoic acid (DNBA) system was determined by the thaw-melt method. Results show the formation of an inter-molecular compound and two eutectics. The values of heat of mixing, entropy of fusion, roughness parameter, interfacial energy, and the excess thermodynamic functions were calculated from the enthalpy of fusion data determined by the differential scanning calorimetric (DSC) method. The spectroscopic investigations (IR and NMR) suggest the presence of hydrogen bonding between the components of the compound. A single crystal of the inter-molecular compound was grown using slow cooling technique from the mixed solvent of ethanol and triple distilled water in 2:1 volume ratio. The single crystal analysis and the atomic packing pattern of the grown crystal confirm the monoclinic crystal structure with P21/c space group. The solubility of the inter-molecular compound was determined in the mixed solvent at different temperatures. Using solubility and entropy of fusion data, the entropy of dissolution and heat of mixing were calculated. The optical transmittance spectra of the crystal of the inter-molecular compound show 75% transmittance and the band gap of the crystal was found to be 3.00eV. The refractive index of the crystal was computed to be 2.50 at the cut off wavelength.

Thermodynamics of 4’-bromomethyl-2-cyanobiphenyl in different solvents

The melting properties and the heat capacity of the solid state and the melt state 4’-bromomethyl-2-cyanobiphenyl (OTBNBr) were determined. The enthalpy, entropy and Gibbs free energy of fusion were also calculated. The solubility of OTBNBr in eight organic solvents was experimentally measured at temperatures from (283.15 to 323.15)K by using a static method. The reasons for the differences of the solubility of OTBNBr in various solvents are discussed by using the intermolecular interaction. Furthermore, the experimental solubility values were well correlated by the modified Apelblat equation, the λh equation, the Wilson model and the van’t Hoff equation. Finally, the temperature dependence of the activity coefficient and the van’t Hoff enthalpy in the tested solutions was investigated and is discussed.

Low-temperature heat capacities and thermodynamic properties of ethyl 4-dimethylaminobenzoate (C11H15NO2)

Molar heat capacities of ethyl 4-dimethylaminobenzoate were measured by a high precision automated adiabatic calorimeter over the temperature range from 79 to 397 K. The melting temperature, the molar enthalpy and entropy of fusion were determined to be (336.818 ± 0.017) K, (20.761 ± 0.345) kJ mol−1 and (61.64 ± 1.03) J K−1 mol−1. It has a great potential in the use of the substance as solid–liquid phase change material based on large enthalpy of solid–liquid phase transition and moderate melting temperature. The thermodynamic functions (HT−H298.15 K) and (ST−S298.15 K) were calculated in the temperature range from 80 to 400 K with the interval of 5 K. The mass fraction purity of the sample was determined to be (1−N) = 0.99514 (mol fraction) by the fractional melting method. The constant-volume energy and standard molar enthalpy of combustion were determined, ΔcU (C11H15NO2, s) = −(6,161.73 ± 5.19) kJ mol−1 and Δc\( H_{\text{m}}^{0} \) (C11H15NO2, s) = −(6,167.31 ± 5.19) kJ mol−1, by means of a precision oxygen-bomb combustion calorimeter at T = 298.15 K. At last, the standard molar enthalpy of formation was derived, Δf\( H_{\text{m}}^{0} \) (C11H15NO2, s) = −(305.03 ± 6.92) kJ mol−1.

Melting curves and entropy of melting of iron under Earth’s core conditions

The melting curves of iron are determined up to 365GPa via molecular dynamic (MD) simulations combining with the embedded atom model (EAM) potential developed by Ackland et al. We simulated the melting with three approaches, the hysteresis, two-phase and recently modified Z methods. All three techniques can produce satisfying results, consistent well with most of static compression measurements and shock experiments. Hence, we recommend that these three techniques and this EAM potential are reliable techniques and potential for simulating melting properties of iron. Fitting the well-known Simon equation to our two-phase data we yield the analytical melting curve for iron: 1825(1+P/57.723)0.654, which gives a melting point at the inner core boundary of 6345K, very close to the recent diamond anvil cell (DAC) extrapolated value and other ab initio calculations. Furthermore, the analyses of our entropy of melting and solid–liquid interfacial energy γsl indicate that at high pressure, the entropy of fusion shows weak pressure effect. The γsl increases monotonically with pressure, and can be described as a second-order polynomial relation.