Gibbs-Helmholtz Equation Research Articles

The Parallel between Boiling Point Elevation and Limit of Superheat for Polymer Solutions

The derivation for boiling point elevation (BPE) for polymer solutions goes back to mathematics of the Clausius-Clapeyron equation combined with Raoult's Law or the Gibbs-Helmholtz equation combined with Raoult's Law. BPE can be used to measure polymer molecular weight and is effective when the concentration of polymer approaches zero. The limit of superheat for polymer solutions formula (LSPS) was derived by (Jennings, 2012) [1], a complicated derivation involving the surface tension in particular. (Jennings and Middleman, 1985) [2] Published data that agrees with Jennings' formula. BPE and LSPS have various uses that will be discussed as will the parallel between the two equations.

Adsorption of copper(II) ions by zeolite modified with organosilicon thiosemicarbazide

The article is devoted to the calculation of the kinetics and thermodynamics of adsorption of copper(II) ions by zeolite activated with hydrochloric acid and modified 1-(3-triethoxysilylpropyl)thiosemicarbazide. For the calculation of the kinetic parameters, we used the Lagergren, Ho, and Mackay equation. The activation energy was found using the Arrhenius equation. For the calculation of thermodynamic parameters, the linearized Van't Hoff equation and the Gibbs-Helmholtz equation were used. A comparison of the determination coefficients of the pseudo-first (from 0.815 to 0.892) and pseudo-second (from 0.995 to 0.999) order models allowed choosing the latter as the leading model for the adsorption of Cu(II) ions. Pseudo-second order rate constants depending on temperature were in the range 0.201-3.915 g⋅mmol-1⋅min.-1. The determined value of the activation energy 42.3 kJ mol-1 was in the range of 40-120 kJ, which is typical for chemisorption of ions Cu(II). Adsorption isotherms were well described by the Langmuir model. Adsorption proceeded with the formation of sorbate monolayer on the outer surface. Adsorption limit values ranged from 0.0016 to 0.0039 mol g-1 depending on temperature from 238 to 309 K. The processes of adsorption of Cu(II) ions on the surface of the modified zeolite occurred spontaneously. A decrease in the Gibbs energy ΔG0 was observed (from -14.20 to -16.29 kJ mol-1) with increasing temperature. Positive enthalpy value Δ𝐻0 (3.6 kJ mol-1) indicated that the adsorption of Cu(II) ions occurred endothermically. Positive entropy value Δ𝑆0 (58.15 J mol-1) indicated an increase in randomness at the interface due to the destruction of the solvation shells surrounding the transition metal ions in solution. Thus, the ratios of kinetic and thermodynamic quantities indicated that a significant contribution to the process of adsorption of Cu(II) ions by a modified zeolite was made by processes associated with the chemical interaction of adsorbate molecules and functional nitrogen and sulphur containing groups of thiosemicarbazide.

The Gibbs-Helmholtz equation and the enthalpy–entropy compensation (EEC) phenomenon in the formation of micelles in an aqueous solution of surfactants and the cloud point effect

Here, the hidden thermodynamic processes in the micellization of an aqueous surfactant solution are analyzed analytically. Based on the hidden processes, an equation for the self-association process was obtained, which represents the Gibbs-Helmholtz equation. For the existence of the enthalpy–entropy compensation (EEC) effect, the temperature dependence of the Gibbs free energy of micellization is necessary. In order to compare the EEC parameters of the clouding point effect with the EEC parameters of micellization, it is necessary to observe the clouding process in the direction of the surfactant transfer from the aqueous solution to the crystalline phase (opposite to what is usual in the literature). EEC parameter b (enthalpy change when entropy changes have the zero value) in the micellization process always has a negative value. In contrast, in the clouding point effect process, it can have both positive and negative values.

Thermodynamic study of choline chloride-based deep eutectic solvents with dimethyl sulfoxide and isopropanol

The thermodynamic properties of four binary mixtures of deep eutectic solvent (DES), i.e., ChCl/Gly (choline chloride + glycerol at a molar ratio of 1:2) and ChCl/EG (choline chloride + ethylene glycol at a molar ratio of 1:2) with two common co-solvents, i.e., dimethyl sulfoxide (DMSO) and isopropanol (IPA), were studied. Density and viscosity were determined at temperatures from 288.15 to 323.15 K, while measuring the enthalpy of mixing was performed at 308.15 and 318.15 K. The volumetric properties (i.e., excess molar volume and excess partial molar volume) and excess viscosities (i.e., viscosity deviation and logarithmic excess viscosity) were further calculated to investigate the effects of temperature, types of co-solvent and DES, and their contents on the non-ideal behavior of these systems, where the influence of treating the DES as a mixture of two components or a pseudo-component was discussed. The results of volumetric properties indicate that the combined influence of packing effects and H-bonding interactions between the DES and co-solvents led to the contraction of mixture volume, and the results of excess viscosities show H-bonding interactions play an important role in their variations. The results of enthalpy of mixing show that the mixing of DES with IPA is endothermic, while the mixing of DES with DMSO is exothermic. Furthermore, the nonrandom two-liquid (NRTL) model and Gibbs-Helmholtz equation were combined to represent the experimental results of the enthalpy of mixing, and the total average relative deviation (ARD) of all studied systems is 5.43%.

Measurement of the solubility and density of the saturated solution of 3-aminophenol in different pure solvents from 283.1 to 323.1 K: Correlative to pure predictive thermodynamic modeling and molecular dynamic simulation

The solubility of 3-aminophenol was measured in water, isopropanol, ethyl acetate, chloroform, and tert-butyl methyl ether (MTBE) from 283.1 to 323.1 K at atmospheric pressure. In addition, the density of pure solvents and the saturated 3-aminophenol solutions was measured. The experimental solubility data were correlated and predicted using four types of thermodynamic models, including correlative (Wilson, NRTL, and UNIQUAC), semi-predictive (NRTL-SAC, and UNIQAUC-SAC), predictive group contribution methods (UNIFAC, and UNIFAC-DMD), and pure predictive COSMO-SAC model. The NRTL-SAC and UNIQUAC-SAC as semi-predictive models were used to obtain 3-aminophenol conceptual segment numbers, and then, using the NRTL-SAC model, the solubility of 3-aminophenol was predicted in 58 FDA approved solvents in the pharmaceutical industry. The predictive models including UNIFAC and UNIFAC-DMD were also used to predict the 3-aminophenol solubility and compared with the experimental data. The results of the COSMO-SAC model have a large deviation from experimental data. In addition, the experimental solubility data were correlated using the PR equation of state with relative success. The segment-based models such as NRTL-SAC and UNIQUAC-SAC are suggested in the fast solvent screening procedure. Finally, the standard dissolution enthalpy (ΔdisH), the standard dissolution entropy (ΔdisS), and the standard dissolution Gibbs energy (ΔdisG) of 3-aminophenol in the selected solvents were calculated by the Van’t Hoff model and the Gibbs-Helmholtz equation. These values imply that the solubility of 3-aminophenol is an entropy-driven non-spontaneous endothermic process in all chosen single solvents. Using the molecular dynamic (MD) simulation the solvation free energy of 3-aminophenol was calculated. The order of the absolute value of free energy of solvation is as ethyl acetate > isopropanol > MTBE > water > chloroform which is consistent with the order of solubility data.

Native and Non-Native aggregation pathways of antibodies anticipated by cold-accelerated studies

Assessment of cold stability is essential for manufacture and commercialization of biotherapeutics. Storage stability is often estimated by measuring accelerated rates at elevated temperature and using mathematical models (as the Arrhenius equation). Although, this strategy often leads to an underestimation of protein aggregation during storage. In this work, we measured the aggregation rates of two antibodies in a broad temperature range (from 60 °C to −25 °C), using an isochoric cooling method to prevent freezing of the formulations below 0 °C. Both antibodies evidenced increasing aggregation rates when approaching extreme temperatures, because of hot and cold denaturation. This behavior was modelled using Arrhenius and Gibbs-Helmholtz equations, which enabled to deconvolute the contribution of unfolding from the protein association kinetics. This approach made possible to model the aggregation rates at refrigeration temperature (5 °C) in a relatively short timeframe (1–2 weeks) and using standard characterization techniques (SEC-HPLC and DLS).

Holonomic and Non-Holonomic Geometric Models Associated to the Gibbs–Helmholtz Equation

By replacing the internal energy with the free energy, as coordinates in a “space of observables”, we slightly modify (the known three) non-holonomic geometrizations from Udriste’s et al. work. The coefficients of the curvature tensor field, of the Ricci tensor field, and of the scalar curvature function still remain rational functions. In addition, we define and study a new holonomic Riemannian geometric model associated, in a canonical way, to the Gibbs–Helmholtz equation from Classical Thermodynamics. Using a specific coordinate system, we define a parameterized hypersurface in R4 as the “graph” of the entropy function. The main geometric invariants of this hypersurface are determined and some of their properties are derived. Using this geometrization, we characterize the equivalence between the Gibbs–Helmholtz entropy and the Boltzmann–Gibbs–Shannon, Tsallis, and Kaniadakis entropies, respectively, by means of three stochastic integral equations. We prove that some specific (infinite) families of normal probability distributions are solutions for these equations. This particular case offers a glimpse of the more general “equivalence problem” between classical entropy and statistical entropy.

Estimation of cold denaturation temperature and its utilization in predicting protein stability as an aid in functionalizing pea protein isolate through cold denaturation

Plant-based proteins are commonly used to generate new textures in food by inducing changes in their molecular structures with the application of heat, shear, pressure, and other methods of protein denaturation. One structural transformation that is relatively less understood is cold denaturation, which mainly occurs due to a weakening of hydrophobic forces at low temperatures. In this work, the Gibbs-Helmholtz equation is used to produce stability curves and estimate the temperature of cold denaturation for pea protein. The equation is solved with data obtained from differential scanning calorimetry conducted as a function of the solution pH and salt concentration. It is found that at pH 3, the temperature of cold denaturation is 3.85 °C. The protein functionality is then tested through zeta potential, surface hydrophobicity, solubility, and the emulsion activity/stability index at these low temperatures and compared to results from room temperature. It is found that surface hydrophobicity increases, the magnitude of the zeta potential increases, solubility decreases, and the emulsion activity/stability increases at low temperatures.

Performance of a high capacity polyamine: Measurement and modeling of the solubility of carbon dioxide in aqueous solutions of 1, 4-bis (3-amino-propyl) piperazine and its heat of absorption

This study focused on measuring the carbon dioxide (CO2) uptake capacity of an amine, 1, 4-Bis (3-aminopropyl) piperazine. The solubility of CO2 was measured at 313.15 K and 333.15 K for three amine concentrations (10, 20, and 30 wt%) of importance in industry and different CO2 partial pressures up to 2.4 MPa. CO2 loadings (mol of CO2/mol amine) were measured using the pressure decay method. At all concentrations, 1,4-Bis(3-aminopropyl) piperazine showed a higher CO2 loading compared to two benchmark amines namely, ethanolamine (MEA) and Piperazine (PZ). The proposed amine had also a higher capacity for CO2 than all other polyamines found in the literature, except, 3, 3 ’-Iminobis (N, N-dimethyl-propylamine) which has two tertiary and one secondary amino group. The experimental measurements were modeled comprehensively with the electrolyte–Non-Random Two Liquid (NRTL) model and the Redlich-Kwong (RK) equation of state (EOS) for the gas phase. The binary NRTL and molecule–ion pair parameters were regressed and reported. The overall percentage of the average absolute deviation (%AAD) between the experimental and estimated values for the temperature, pressure, and mole fractions were 0.12%, 0.07%, and 0.32%, respectively. Finally, the heats of absorption of CO2 in 1, 4-Bis (3-aminopropyl) piperazine were calculated using the Gibbs-Helmholtz equation based on the obtained experimental solubility data. The modeling results for MEA, DEA, and MDEA between the elec-NRTL and the soft-SAFT models were compared. The estimation of the heat of absorptions for the amines was almost the same.

Thermodynamic Behavior of (2-Propanol + 1,8-Cineole) Mixtures: Isothermal Vapor-Liquid Equilibria, Densities, Enthalpies of Mixing, and Modeling.

Vapor pressures and other thermodynamic properties of liquids, such as density and enthalpy of mixtures, are the key parameters in chemical engineering for designing new process units, and are also essential for understanding the physical chemistry, macroscopic and molecular behavior of fluid systems. In this work, vapor pressures between 278.15 and 323.15 K, densities and enthalpies of mixtures between 288.15 and 318.15 K for the binary mixture (2-propanol + 1,8-cineole) have been measured. From the vapor pressure data, activity coefficients and excess Gibbs energies were calculated via the Barker's method and the Wilson equation. Excess molar volumes and excess molar enthalpies were also obtained from the density and calorimetric measurements. Thermodynamic consistency test between excess molar Gibbs energies and excess molar enthalpies has been carried out using the Gibbs-Helmholtz equation. Robinson-Mathias, and Peng-Robinson-Stryjek-Vera together with volume translation of Peneloux equations of state (EoS) are considered, as well as the statistical associating fluid theory that offers a molecular vision quite suitable for systems having highly non-spherical or associated molecules. Of these three models, the first two fit the experimental vapor pressure results quite adequately; in contrast, only the last one approaches the volumetric behavior of the system. A brief comparison of the thermodynamic excess molar functions for binary mixtures of short-chain alcohol + 1,8-cineole (cyclic ether), or +di-n-propylether (lineal ether) is also included.

Impact of host-guest complexation between norfloxacin and -cyclodextrin on fluorescence quenching: Steady-state and time resolved fluorescence study

The behaviour of host-guest interaction of the drug i.e. Norfloxacin (NFX) with β-Cyclodextrin (β-CD) has been investigated by the fluorescence quenching method in acidic and neutral pH using copper as a quencher at various temperatures. The stoichiometry of the host-guest complication has been estimated using the Benesi−Hildebrand relationship. The incorporation of NFX inside the cavity of β-CD is revealed by fluorescence anisotropy and fluorescence lifetime measurements. The effect of temperature on the Stern-Volmer quenching constant (KSV) and binding constant (K) has been analyzed, and the type of quenching was confirmed from the fluorescence lifetime measurement. Using van’t-Hoff equation and Gibbs-Helmholtz equation, thermodynamic parameters like change of enthalpy (ΔH), entropy (ΔS) and free energy (ΔG) have been determined. The negative value of ΔH and the positive value of ΔS validate the hydrophobic interaction between drug and quencher, and the negative value of ΔG suggests that the complex is spontaneous in nature.

Molecular Dynamic Modeling of Magnesium in the Scheme of the Embedded Atom Model

Potentials of the embedded atom model (EAM) for solid and liquid magnesium are proposed. Properties of magnesium are studied by means of molecular dynamics (MD) at binodals of up to 1500 K, and under conditions of static and shock compression. The main characteristics of bcc and liquid magnesium (structure, density, energy, compressibility, speed of sound, and coefficients of self-diffusion) are calculated. The static compression isotherm at 298 K up to a pressure of 108 GPa and the Hugoniot adiabat up to a pressure of 80 GPa are calculated with allowance for electron contributions. Values of the excess energy of the surfaces of magnesium nanoclusters with 13 to 2869 particles are found, and the Gibbs–Helmholtz equation for the relationship between surface tension and surface energy is estimated.

Исследование гигроскопических параметров желатина из отходов переработки рыбы

We studied the hygroscopic properties of gelatin from waste-products after processing of common fresh-water fish species form the Astrakhan region (skin, scales, bones, fins, and cartilage) as an object of drying. The analysis of the thermodynamics of internal mass transfer was carried out during the interaction of the substance of the specified product with water. The objects of study were concentrates obtained by convective-radiation drying of gelatin granules, previously foamed to a constant expansion ratio and cooled to the gelatinization temperature. The studies were carried out experimentally and analytically using the tensometric method by Van Bamelen. For the thermodynamic analysis of hygroscopic characteristics, classical Gibbs–Helmholtz equation was used. On the basis of empirical data, sorption isotherms were obtained – functional dependences of the level of water activity Aw on the equilibrium moisture content and temperature of the product. The isotherms of the concentrates of the studied gelatin are S-shaped, typical for colloidal capillary-porous bodies, which is due to the foam structure of the product. The curves can be conventionally subdivided into three zones, corresponding to the moisture of monomolecular and polymolecular adsorption, structural, microcapillary, and microcapillary moisture. Based on the analysis of sorption isotherms for the product under study, the hygroscopic moisture content of gelatin was determined for its various temperatures: Wg1 = 0.280 kg/kg for T = 283 K and Wg2 = 0.301 kg/kg for T = 303 K. The specified moisture content is a threshold for the range of hygroscopic states and is important from the point of view of rationalization and modeling heat and mass transfer during material dehydration. As a result of calculations using sorption isotherms and the Gibbs–Helmholtz equation, the dependences of free, bound, and internal energy as well as the total specific thermal energy of water evaporation on moisture content and temperature of the product under study were derived. It has been established that the nature of these dependences for the studied samples of gelatin concentrates is generally consistent with the published data for a number of materials of a biopolymer nature. These dependencies can be used in the development of dehydration processes and in the design of drying equipment for the production of gelatin concentrates from fish waste.

CALORIMETRIC STUDY OF PHASE TRANSITION OF Cu8GeSe6 AND COMPARISON WITH OTHER ARGYRODITE FAMILY COMPOUNDS

This work is a continuation of our work on the thermodynamic study of synthetic analogues of the mineral argyrodite. In this work, a calorimetric study of the phase transition of the Cu8GeSe6 compound was carried out using the differential scanning calorimetry (DSC) method. Based on the data of DSC curves of samples of the studied compound with different masses, the temperature and enthalpy of the phase transition from the low-temperature orthorhombic modification to the high-temperature cubic modification were established. Using the Gibbs-Helmholtz equation, the entropy of the phase transition was also calculated and the comparative analysis of the obtained thermodynamic values of the studied compound with other argyrodite phases was carried out.

Gibbs–Helmholtz graph neural network: capturing the temperature dependency of activity coefficients at infinite dilution

A hybrid model that combines the Gibbs–Helmholtz equation with Graph Neural Networks for predicting limiting activity coefficients.

Molecular Dynamics Model of Liquid Tin in the Scheme of the Embedded Atom Model

Results from calculating the properties of liquid tin using the EAM (Embedded Atom Model) interparticle potential are analyzed, and the surface properties of tin are calculated according to molecular dynamics (MD). Calculations based on the EAM generally agree better with experiments for the properties of liquid tin than ones based on the MEAM. The accuracy of the Gibbs–Helmholtz equation for the relationship between surface tension and surface energy is evaluated.

Measurements and correlation of activity coefficients at infinite dilution for organic solutes in 1-heptyl-3-methylimidazolium chloride

This work is a continuation of our studies on the determination of activity coefficients at infinite dilution (γi∞) for organic solutes (i) in ionic liquids (ILs) and their use in separation processes. The values of γi∞ for 31 organic solutes including alkanes, cycloalkanes, 1,4-dioxane, aromatic hydrocarbons, cyclohexene, chloromethanes, acetonitrile, acetone, tetrahydrofuran, ethyl acetate and alcohols in the IL 1-heptyl-3-methylimidazolium chloride ([C7MIm]Cl) at six temperatures in range of (313.15–363.15) K were determined by gas-liquid chromatography (GLC). The density of [C7MIm]Cl as a function of temperature at pressure p= 101.33 kPa was measured and the values of gas-liquid partition coefficients (KL) were obtained. The linear relationship between lnγi∞ and 1/T was fitted by the Gibbs-Helmholtz equation. The molar excess thermodynamic functions including the infinite dilution partial molar excess Gibbs free energies (G¯iE,∞), partial molar excess enthalpies (H¯iE,∞) and entropies (TrefS¯iE,∞) at Tref = 298.15 K were calculated. In addition, the solubility parameters (δi) of [C7MIm]Cl were obtained from the regular solution theory combined with Flory “combinatorial” equation. The interaction between the solute and the IL was quantified based on the linear free energy relationship (LFER) model. The infinite dilution selectivity coefficients (Sij∞) of n-hexane (i)/benzene (j) and cyclohexane (i)/benzene (j) were calculated at T = 323.15 K from γi∞ and compared to literature values for [Cl]-based ILs for the same separation problems.

Post-combustion capture of CO2 using novel aqueous Triethylenetetramine and 2-Dimethylaminoethanol amine blend: Equilibrium CO2 loading-empirical model and optimization, CO2 desorption, absorption heat, and 13C NMR analysis

The equilibrium CO2 loading was estimated by absorption of CO2 gas in the bubble column reactor for novel aqueous amine blend of triethylenetetramine (TETA) and 2-dimethylaminoethanol (DMAE). The absorption study was performed at a temperature of 298.15 to 333.15 K, mole fraction of TETA from 0.05 to 0.2, solution concentration varied from 1 to 3 mol/L, and CO2 partial pressure ranging from 10.13 to 25.33 kPa. The maximum experimental equilibrium CO2 loading was 0.92 mol CO2/mol amine at 315.65 K temperature, 17.73 kPa CO2 partial pressure, 0.13 mol fraction of TETA, and 1 mol/L solution concentration. The absorption results were validated by an empirical model with an average absolute relative deviation of 5.631 %. The desorption study was performed at a constant temperature and pressure of 393.15 K and 17.73 kPa, respectively. The cyclic loading capacity of this blend at 3 mol/L concentration showed 55.03 % higher results than that of 30 wt% (5 mol/L) monoethanolamine (MEA). The Gibbs-Helmholtz equation calculated the heat of CO2 absorption, and for this amine blend, it was found to be −67.135 KJ/mol. 13C nuclear magnetic resonance (NMR) spectroscopy was adopted to identify the chemical species in CO2-loaded and unloaded amine blends. Response surface methodology software optimized the final response. It predicted optimal equilibrium CO2 loading of 0.926207 mol CO2/mol amine at 304.36 K temperature, 0.14 mol fraction of TETA, 17.24 kPa partial pressure of CO2, and 1 mol/L solution concentration.

Effects of hydroxyethyl group on monoethanolamine (MEA) derivatives for biomethane from biogas upgrading

Upgrading of biogas to produce biomethane is an essential way to increase the calorific value of biogas by separating CH4 and CO2 to satisfy the global renewable energy demand. In this study, the efficiency of carbon dioxide (CO2) trapping in aqueous monoethanolamine (MEA), diglycolamine (DGA), diethanolamine (DEA), and triethanolamine (TEA) solution during biogas upgrading for biomethane was determined. Effects of hydroxyethyl groups on MEA derivatives were investigated in terms of biogas upgrading and regeneration, CO2 desorption heat, initial CO2 absorption rate and CO2/CH4 selectivity. The duration of upgraded biogas meeting certain European Union (EU) application standards for methane purity during upgrading was reduced by 70, 78 and 200 mins for DGA, DEA and TEA respectively compared to MEA due to the partial substitution of H-bonds by hydroxyethyl groups, and the absorption rate was also reduced, whereas TEA was not suitable for biogas upgrading as it was inefficient for biogas upgrading effect and absorption rate. The calculated results from the Gibbs-Helmholtz equation showed that MEA had the largest CO2 desorption heat (82.47 kJ/mol CO2) and the other MEA derivatives had lower desorption heat than MEA, indicating that MEA consumes more energy in the desorption process. As for the equilibrium partial pressure, all amine solutions absorbed less than 0.4% of the total volume of CH4 and had a high CO2/CH4 selectivity.

ENTHALPY AS A MEASURE OF THE ORGANIZATIONS’ POTENTIAL

Energy is a universal category and have a relevant meaning for each type of system. For organizations energy is a resource used in the energy exchange process with the external environment. Energy exchange, dissipation, interaction with the external environment by the form of "external part of the structure" of the organization and temperature as an indicator of the effectiveness of this interaction in the context not only economically but also with uncertainty - all this is the result of the second thermodynamics law universality. The development of entropy management concept and the idea of considering organizations as an analogue of a thermodynamic system, which is characterized by energy exchange processes within the system and with the external environment, grounds to the necessity to expand the set of indicators of the organization’ state in this context. The functions of states include enthalpy, that reflects the amount of energy available for transformation into heat according to accepted understanding. Enthalpy in the context of organizations reflects the "available resource" of the system for energy exchange with the external environment and maintaining the structure of the system. The purpose of this study is to substantiate and analyze the enthalpy equation for organizations. This approach is approved by the development of the idea to apply the thermodynamics laws to the management of organizations. In the framework of this study, the equation of enthalpy change based on the Gibbs-Helmholtz equation is proposed. This equation unifies the increase of free energy, entropy and uncertainty (information entropy). Enthalpy in this approach assesses the energy potential of the organization. Formulas for calculating the relevant indicators of changes in the realized energy potential and dissipation are proposed, that, in fact, make it is possible to evaluate the quality of management as the quality of entrepreneurial energy.