Excess Free Energy Research Articles

Thermodynamics-consistent graph neural networks.

We propose excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures. The GE-GNN architecture ensures thermodynamic consistency by predicting the molar excess Gibbs free energy and using thermodynamic relations to obtain activity coefficients. As these are differential, automatic differentiation is applied to learn the activity coefficients in an end-to-end manner. Since the architecture is based on fundamental thermodynamics, we do not require additional loss terms to learn thermodynamic consistency. As the output is a fundamental property, we neither impose thermodynamic modeling limitations and assumptions. We demonstrate high accuracy and thermodynamic consistency of the activity coefficient predictions.

Effect of water on the excess properties of eutectic solvents

Three eutectic solvents were created utilizing a heating and stirring process. The solvents consist of tetrabutylammonium bromide and levulinic acid, as well as tetrabutylammonium chloride with either levulinic acid or lactic acid. The characterization of the samples was conducted using 1H NMR and IR techniques. The density and viscosity of three different low eutectic solvent and water binary mixture systems were determined within the temperature range of 293.15 to 333.15 K. The volume properties (excess molar volume, coefficient of expansion, coefficient of excess expansion) of the binary mixtures with different amounts of water were thoroughly investigated across the complete range of mole fraction. The study also investigated the impact of viscosity parameters, such as viscosity deviation and Excess activation Gibbs free energy of viscous flow. Furthermore, an analysis was conducted on the interaction between the eutectic solvent and the solvent molecules in the binary mixture. This analysis revealed the presence of hydrogen bonds between the eutectic solvent and water molecules. Moreover, it was confirmed that the excess properties could be fitted with the Redlich-Kister equation with r2 ≥ 0.99,demonstrating high suitability for binary mixes consisting of low eutectic solvents and water.

Model based study of temperature dependent thermodynamic and surface properties of Al-Ti-Ni-Cr system in liquid state

Thermodynamic and surface properties of Al-Ti-Ni liquid alloy with adding Cr, Al-Ti-Ni-Cr, were studied at 2000 K, 2100 K, 2200 K, 2300 K, and 2400 K using different theoretical models. The self-consistent energy interaction parameters of constituent binary subsystems were taken from the literature for the purpose. The thermodynamic properties like excess Gibbs free energy of mixing and the activities of the components in the alloy were investigated using the General Solution Model (GSM). Surface tension of the liquid alloy and surface concentrations of components in it were calculated using Butler's model with the aid of determined thermodynamic functions. The mixing tendency of the Al-Ti-Ni-Cr liquid alloy was found to decrease with the addition of Cr atoms for all compositions at its melting temperature, 2000 K. The activity of Cr decreased while those of the remaining components increased with the temperature rise. The surface tension of both Al-Ti-Ni and Al-Ti-Ni-Cr liquid alloys decreased linearly at elevated temperatures.

Effectiveness of supercooled freezing in suppressing ice recrystallization during frozen storage

Ice recrystallization often occurs during frozen food storage, an undesirable occurrence that can cause further damage to food cells and tissues. One factor that triggers its occurrence is the initial structure of the ice crystals formed during the freezing phase. During frozen storage, small ice crystals may recrystallize due to their high surface-to-volume ratio and excess free energy. In this study, the ice recrystallization of supercooled frozen tofu was evaluated during a 12-week frozen storage period and compared with that of slowly and rapidly frozen tofu. The storage temperature was at − 10 ± 2 ℃. Slow freezing at − 10 ℃ static air has produced large crystals up to 0.6 mm before storage and tended not to grow further. Rapid freezing at − 80 ℃ static air with elongated ice crystals exhibits the highest recrystallization rate, especially on the surface of the sample, where the maximum ice crystals grew from 0.23 mm before storage to 0.45 mm after 12 weeks. Supercooled freezing has produced small and homogeneous ice crystals, the largest being 0.15 mm, but their spherical shape tends to have a low affinity for recrystallization, which has allowed the crystals to maintain their size and structure during the frozen storage.

Lipid Specificity of the Fusion of Bacterial Extracellular Vesicles with the Host Membrane.

Bacterial membrane vesicles (MVs) facilitate the long-distance delivery of virulence factors crucial for pathogenicity. The entry and trafficking mechanisms of virulence factors inside host cells are recently emerging; however, whether bacterial MVs can fuse and modulate the physicochemical properties of the host lipid membrane and membrane lipid parameter for fusion remains unknown. In this study, we reconstituted the interaction of bacterial MVs with host cell lipid membranes and quantitatively showed that bacterial MV interaction increases the fluidity, dipole potential, and compressibility of a biologically relevant multicomponent host membrane upon fusion. The presence of cylindrical lipids, such as phosphatidylcholine, and a moderate acyl chain length of C16 help the MV interaction. While significant binding of bacterial MVs to the raft-like lipid membranes with phase-separated regions of the membrane was observed, however, MVs prefer binding to the liquid-disordered regions of the membrane. Furthermore, the elevated levels of cholesterol tend to hinder the interaction of bacterial MVs, as evident from the favorable excess Gibbs free energy of mixing bacterial MVs with host lipid membranes. The findings provide new insights that might have implications for the regulation of host machinery by bacterial pathogens through manipulation of the host membrane properties.

The thermodynamic behavior of binary systems isoamyl acetate and alcohol through experimental measurements and modeling

The thermodynamic and transport properties are experimentally determined for three binary liquid mixtures consisting of isoamyl acetate and different alcohols at ambient pressure and in temperature range. From measured density, viscosity and refractive index are calculated excess molar volume, viscosity and refractive index deviations. Isentropic compressibility and excess molar Gibbs free energies of viscous flow are determined combining density with speed of sound and viscosity data. All mentioned derived properties are used to analyze the changes taking place in investigated binary systems causing deviations from the ideal mixture. Additionally, partial molar volumes and excess partial molar volumes, as well as thermal expansion coefficient, were calculated. The results are discussed in terms of chemical structure of used compounds and the influence of the alcohol present in the mixture on the mixture behavior. The study showed that higher influence has branching of the alcohol molecule and position of the –OH group rather than the length of the primary alcohol chain. Beside the experimental part, the modeling of the excess molar volume and viscosity was also performed, and the percentage deviations are used as the indicator of model performance in terms of model approach, predictive or correlative, and number of model parameters, one to three parameters optimized.

Thermodynamic, Structural and Surface Properties of Liquid Al-Sr Alloy at Different Temperatures

Thermodynamic functions like excess Gibbs free energy of mixing (∆GxsM) and activity (a) of liquid Al-Sr alloy were studied in the temperature range 1323-1623 K in the frame work of Redlich-Kister (R-K) polynomial. The compositional and temperature dependence of structural functions like concentration fluctuation in long wavelength limit (Scc(0)), Warren-Cowley short range order parameter (α) and ratio of mutual to intrinsic diffusion coefficients (Dm/Did) were computed and analysed using the same approach. The surface tension (σ) and surface segregation (xsi) tendencies of the atoms in the liquid mixture were computed and studied using Butler’s model. Present investigations revealed that association tendency among the atoms of metallic mixture gradually decreased with increase in temperature.

New analysis of the temperature-dependent threshold density for electron self-trapping in gaseous helium.

We present the results of a new analysis of the literature data on electron mobility μ in dense helium gas aimed at determining the existence of a threshold density for electron self-trapping in gaseous helium as a function of temperature. We have investigated the density dependence of μ and, when available, its dependence on the electric field. The experimental data are favorably rationalized by minimizing the excess free energy of the self-localized states within the optimum fluctuation model. It is shown that the formation of electron bubbles via the self-trapping phenomenon is determined by the delicate balance between the electron thermal energy, the density dependence of the electron energy at the bottom of the conduction band in the gas, and the work necessary to expand the bubble. We show that the self-trapping phenomenon is not limited to low temperatures but occurs at any temperatures for large enough densities.

Thermodynamic, structural, surface and transport properties of Au-Cu melt

Thermodynamic, structural, surface and transport properties of Au-Cu liquid alloy were calculated on the basis of different theoretical modeling equations. The thermodynamic properties, such as excess Gibbs free energy of mixing, enthapy of mixing and activity were estimated and compared with the available experimental and literature data on the basis of simple theory of mixing (STM). The best fit values of model parameters were estimated using the experimental values of excess Gibbs free energy of mixing and enthalpy of mixing of the system at 1550 K. Using the same model parameters and frame, the concentration fluctuation in long wave-length limit and Warren-Cowley short range order parameter were calculated and analysed to understand the local arrangement of atoms in the liquid mixture. The surface tension and extent of surface segregation of atoms in the initial melt were computed using Butler’s model. In transport properties, the ratio of mutual to intrinsic diffusion coefficients was calculated using STM and viscosity was calculated using Kaptay equation. The system showed complete ordering tendency at its melting temperature.

Physicochemical properties and CO2 absorption performance of poly(ethylene glycol) 300 + hydroxyethyl ethylenediamine mixed solution

Density (ρ) and viscosity (η) data of the polyethylene glycol 300 (PEG300) and hydroxyethyl ethylenediamine (AEEA) mixed solution were measured at P = 1005 hPa and T = (298.15–318.15) K. Following these data, Jouyban-Acree model exhibited superior correlation to density in the mixed system compared to nonlinear least square method, while the McAllister four-body equation yielded a better fitting for kinematic viscosity than other models. Utilizing ρ and η data, the Redlich-Kister equation was employed for the systematic computation and analysis of excess molar volume (VmE), excess activation Gibbs free energy (ΔG*E), partial molar volumes (V1¯ and V2¯), and viscosity deviation (Δη) in the PEG300 (1) + AEEA (2) mixed solution. These excess properties indicated the advantageous nature of intermolecular binding in the PEG300 (1) + AEEA (2) mixed solution, further substantiated on the basis of various spectroscopic characterizations. Finally, under conditions of CO2 flow rate at 150 mL/min, absorption experiments were conducted for 4 h in the PEG300 (1) + AEEA (2) mixed solution, pure AEEA, and pure PEG300, which indicated that the mixed solution exhibited the highest CO2 absorption capacity of 0.95 mol CO2/mol AEEA, demonstrating superior absorption performance compared to the two pure substances.

Theoretical exploration of thermodynamic characteristics in lead-free liquid alloys: Zn-Bi-In System

The calculations of Zn activities in the ternary liquid solder alloy Zn-Bi-In at 873 K were conducted through the application of the Molecular Interaction Volume Model (MIVM). The calculated values were compared to experimental data for three different cross-sectional examinations, namely for the bismuth-to-indium ratios (xBi: xIn) of 1:2, 1:1, and 2:1. Moreover, the integral excess free energy of these ternary liquid alloys was assessed using the same model parameters in order to test their validity. Then, the values were compared to the relevant experimental data reported in the literature that was already in existence. A satisfactory concordance has been observed between the theoretical predictions and the experimental findings.

Phase behavior of ionic fluid in charged confinement: An associating polymer density functional theory study

AbstractWith the rapid advancement of the new energy industry, porous electrode materials and complex electrolytes have gained widespread usage. Electrolytes exhibit distinctive phase behavior when subjected to the combined influence of confined space and electric fields. However, the measurement and prediction of such phase behavior encounter significant challenges. Consequently, numerous theoretical tools have been employed to establish models for phase equilibrium calculations. Nevertheless, current research in this field has notable limitations and fails to address the confinement of space or complex polymer electrolytes. Considering these shortcomings, an associating polymer density functional theory (PDFT) was developed by modifying excess free energy. This study examines the phase behavior of electrolytes with various chain lengths within diverse confined slits, revealing that the confinement effect and fluid tail chains can narrow the phase diagram. Additionally, a linear correlation between the electric field strength and the phase equilibrium offset has been identified, and a quantitative relationship is derived. The results of this investigation contribute to a deeper comprehension of complex fluid phase behavior and guide the design of electrochemical devices.

An excess free energy and chemical potential for hard homonuclear diatomics from integral equation approach

It has been shown that an improved prediction of the thermodynamic quantity for the hard homonuclear diatomics can be performed with an interpolation scheme that relates the thermodynamic property of the hard sphere to that of tangent hard spheres at the same density. Using the analytic expressions based on the solution of an integral equation an excess Helmholtz free energy per particle and chemical potential for hard homonuclear diatomic fluid have been computed. Calculations are carried out for hard homonuclear diatomics with reduced internuclear separations of 0.1 to 1 at reduced densities of 0.2 to 0.9. Our findings for the excess Helmholtz free energy from the Percus–Yevickand Martynov–Sarkisov approximations presents good agreement with available accurate data, having maximum deviations of 15% from it over the separation and density ranges of the calculations. The excess chemical potential from the Martynov–Sarkisov approximation shows better agreement with accurate available data than those from the Percus–Yevick approximation. For the excess chemical potential, a maximum deviation of 9.5% over the range of the calculations has been shown up for the Percus–Yevick approximation.

Kirkwood-Buff Analysis of Binary and Ternary Systems Consisting of Alcohols (Methanol, Ethanol, 1-Propanol, and 2-Propanol), Water, and n-Hexane to Understand the Formation of Surfactant-Free Microemulsions.

Surfactant-free microemulsion (SFME) represents a class of fluid mixtures that can form microheterogeneous structures without detergents, offering an environmentally benign alternative to traditional microemulsions. However, the formation mechanism is still elusive. This work applies the Kirkwood-Buff theory to mixtures of alcohols, water, and n-hexane to elucidate the SFME formation mechanism. To ensure robust calculation of the Kirkwood-Buff integrals (KBIs), we construct a data set of densities and excess free energies of binary and ternary systems. Multiple excess Gibbs free energy models are assessed against this data set to select the most suitable model reproducing the experimental results. In addition, we introduce statistical methods to determine the optimal polynomial order of the Redlich-Kister correlation for the excess volume data. We first validate our methodology in binary systems. Then, we extend the calculation method to ternary mixtures. The KBI calculation results reveal that the alcohol-hexane and water-hexane interactions do not significantly affect SFME formation. In contrast, the interplay among water-water, water-alcohol, and alcohol-alcohol interactions critically influences the ability of a liquid mixture to form SFME structures. SFME systems exhibit the facile formation of water aggregates enveloped by alcohols, whereas non-SFME systems demonstrate homogeneous alcohol/water droplets dispersed in an oil continuous medium.

Statistical theory of fluids confined in quenched disordered porous media.

We develop a theory to calculate structural correlations and thermodynamic properties of a fluid confined in a random porous solid medium (matrix). We used density functional formalism to derive an annealed averaged expression for the density profile and excess free energy of fluid arising due to random fields of a particular realization of the matrix. After performing the second average over the quenched-disordered variables, the excess free energy is organized to give one- and two-body potentials for fluid particles. The average over disorder reduces the system to an effective one-component system of fluid in which particles feel one-body (external) potential and interact via effective pair potential. The effective pair potential is a sum of the bare (the one in the pure fluid) and the matrix-induced potential. The resulting partition function involves only fluid variables. Equations are derived for fluid-fluid and fluid-matrix correlation functions and for free energy, pressure, and chemical potential of the fluid. The theory is applied to a model system of hard spheres and results for the effective pair potential, correlation functions, and thermodynamic properties are reported. The effective pair potential is found to be attractive at the contact and develops a repulsive peak before decaying to zero. Results for pair correlation function and structure factor are compared with simulation results for several fluid densities at two matrix densities. In all the cases, a very good agreement has been found.

Surface miscibility of Gemini surfactants and DOPE in binary mixed monolayers

AbstractSurface pressure (π)–molecular area (A) isotherms were gathered to characterize the packing of binary mixed Langmuir monolayers of 1,2‐dioleoyl‐sn‐glycero‐3‐phosphoethanolamine (DOPE) and one of two Gemini surfactants (GS), N,N‐bis(dimethyloctadecyl)‐1,7‐nonanediammonium dibromide (18‐7‐18) or 1,9‐bis(octadecyl)‐1,1,9,9‐tetramethyl‐5‐amino‐1,9‐nonanediammonium dibromide (18‐7NH‐18) of varying molar fractions. Information about miscibility behavior was derived from the π–A curves by examining the excess free energy of mixing (ΔGexc) that was calculated through the surface area additivity rule. Surface compressibility modulus (Cs−1) was also used to characterize intermolecular interactions. Mutual interactions between GS and DOPE were analyzed in terms of excess Gibbs energy of mixing and the value of this parameter depended strongly on the composition of the mixed film. GS and DOPE are generally miscible as DOPE reduces intermolecular repulsion between highly charged GS molecules leading to the formation of more densely packed mixed monolayers. However, GS and DOPE are immiscible in equimolar mixtures due to tail group packing mismatch between saturated and unsaturated alkyl chains. The prevalence of attractive synergistic interactions in the monolayers studied differs from a previous finding of antagonistic mixing behavior in GS/DOPE micelles. These results contribute to the understanding of GS‐lipid interactions and packing that are critical to the in vitro and in vivo stability of liposomes composed of these molecules used for non‐viral gene therapy applications.

Temperature dependence investigations of molecular interactions and excess thermodynamic parameters of binary mixtures of ionic liquids and water using Flory's statistical theory

AbstractFlory's Statistical Theory (FST) has been applied to investigate excess thermodynamical parameters viz., excess enthalpy, excess entropy, and excess Gibbs free energy for eight binary mixtures of ionic liquids and water at different concentration and temperatures. The concentration and temperature dependent variations of excess enthalpy suggest that ionic liquid mixtures exhibit an endothermic nature and the presence of weak dispersive forces among their constituents. The positive excess Gibbs free energy of mixing points out that the pure components do not mix thoroughly for the systems under study. Overall, these binary systems are thermodynamically unfavorable suggesting that the mixing of ionic liquids and water is not energetically favored or spontaneous. Experimental molar volumes are compared with those calculated using FST and these values show excellent agreement. It affirms the validity of FST's application to these systems. Additionally, some partial properties have also been determined to explore the solute‐solvent interactions. The Redlich‐Kister (R‐K) polynomial model has been applied to excess thermodynamical parameters The high R2 values and low standard deviation values confirm the validity of fitting the RK polynomial model to the functions obtained using FST of liquids for these systems within the given temperature range.

Enhancement of the Rate of Surface Reactions by the Elastocapillary Effect.

We examined the effect of deformability of a solid substrate on the kinetics of a surface reaction that occurs between chemical species present in it and a liquid dispensed on it. In particular, we have dispensed aqueous solutions of gold and silver salt as sessile drops or as a liquid pool on a cross-linked film of poly(dimethylsiloxane) (PDMS). The PDMS surface contains organosilane (SiH), which reduces the salt, producing metallic nanoparticles at the solid-liquid interface. These experiments reveal that, for a sufficiently soft solid, the reaction proceeds about three times faster in the drop mode than in the pool mode. The reaction conditions in both cases remain exactly identical except that, for the drop, the vertical component of the liquid surface tension deforms the solid substrate at the three-phase contact line. We have estimated the solid-liquid and solid-air interfacial energy, which along with the surface energy of the liquid gives an estimate of excess free energy. This energy is found to be different for the drop and pool modes. By considering that this excess free energy decreases the activation energy barrier for the reaction, we have shown that the reaction rate constant in the drop mode should indeed exceed that in the pool mode by about three times.

Electrochemical behavior and effective extraction of Er in fused LiCl-KCl eutectic

For the efficient electrolytic extraction of Er from spent nuclear fuel, a series of electrochemical methods was used to research the electrochemical behavior of Er(III) in the LiCl-KCl system on inert (Mo) electrode and on reactive (Ni) electrodes. On the inert Mo electrode, the reduction of Er(III) to Er(0) is a one-step with three-electron and quasi-reversible reaction process. Meanwhile, the apparent generation Gibbs free energy and activity coefficients of Er(III) on the inert electrode were determined. Thereafter, the electrochemical reduction of Er(III) on the Ni electrode was emphatically investigated. Er(III) is reduced at a corrected potential owing to the formation of Ni-Er alloys. In addition, thermodynamic parameters such as partial excess Gibbs free energy change of Er in Ni, activity and apparent generation Gibbs free energy of the Ni-Er alloys were determined by the electromotive force method. Finally, different Ni-Er alloys were produced using potentiostatic electrolysis on the Ni cathode by controlling different potentials. Moreover, electrolytic extraction was carried out on the Ni cathode at the potential of –2.0 V, and the separation efficiency of Er reaches 99.72%, which proves the practicability of separating Er from LiCl-KCl eutectic on the reactive Ni cathode.

Density, viscosity, excess properties, and intermolecular interaction of propylene glycol methyl ether + 1,2-propylenediamine binary system

In this work, the systematic measurements of physicochemical properties, viz., density (ρ) and viscosity (η) values of propylene glycol methyl ether (PGME) + 1,2-propylenediamine (1,2-PDA) binary system, including pure substances, over the entire mole fraction range at the temperatures of T/K = (298.15 to 318.15) under atmospheric pressure of P = 100.5 kPa. The fundamental data were used to calculate several excess properties, including excess molar volume (VmE), viscosity deviation (Δη), and excess activation Gibbs free energy (ΔG∗E). Meanwhile, the work further investigated the values of thermal expansion coefficient (αp), partial molar volume (V¯) and apparent molar volume (Vφ), thereby offering a comprehensive understanding on non-ideal behavior of the binary system. Furthermore, the variations in ρ values with various molar ratios and temperatures were evaluated through Jouyban-Acree model and nonlinear least squares method. Simultaneously, Grunberg-Nissan model, Eyring-Margules model, Heric model, and McAllister model, were used to fit the dependence of η values on the molar ratio. Arrhenius equation was employed to fit the temperature dependency of η values. In addition, Redlich-Kister (R-K) equation was utilized to fit the VmE, Δη, and ΔG∗E values of binary system. Based on spectral analyses of Raman, ultra-violet (UV), and 1H Nuclear Magnetic Resonance (NMR) and density functional theory (DFT) calculation, the intermolecular hydrogen bond (IHB) of PGME with 1,2-PDA was discussed in depth.