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The four-parameter model has been applied to study the thermodynamic properties like excess free energy of mixing, free energy of mixing, activity coefficients, activity, excess entropy of mixing, entropy of mixing, heat of mixing and microscopic function like concentration fluctuations in the long wavelength limit, SCC(0) of compound forming AlCu liquid alloys at 1373 K. The theoretical data have been compared with the experimental data available in the literature. There is an excellent agreement between the theoretical and experimental data. For the validation of experimental data, the available CALPHAD data have been used to compare the excess free energy of mixing, free energy of mixing, activity of AlCu liquid alloys at 1373 K. For the understanding of the atomic order of liquid alloy, the short-range order parameter has been computed for AlCu liquid alloys at 1373 K. The negative value of short-range order parameter indicates that AlCu liquid alloy at 1373 K is ordering in nature. Again the model parameters are temperature dependent.

The quasi-lattice theory based on the joint effect of size ratio and the energetic (or enthalpic) contribution as well as entropic effect has been applied to study the concentration dependence of the thermodynamic and structural properties of AgCu liquid alloys at 1423 K. The analytical expressions for the thermodynamic properties such as excess free energy of mixing, free energy of mixing, entropy of mixing, heat of mixing and the structural properties like the concentration fluctuations in the long wavelength limit and short range order parameter for a binary liquid alloy have been derived in the framework of quasi-lattice theory. The analytical expressions have been used to compute the various thermodynamic and structural properties of liquid AgCu alloys at 1423 K. The theoretical data of thermodynamic and structural properties have been compared with the available experimental data. The present theoretical investigation successfully explains the observed symmetries in the properties of mixing of liquid AgCu alloys at 1423 K.Further the energy parameter is found to be temperature dependent.

Bulk metallic glass has been a fascinating class of metallic systems with remarkable corrosion resistance, elastic modulus, and wear resistance, while evaluating the glass forming ability has been a very interesting aspect for decades. Machine learning techniques, viz., artificial neural networks and KNearest Regressor-based models have been developed in this work to predict the glass forming ability, given the composition of the bulk metallic glassy alloy. A new criterion of classification of atoms present in a bulk metallic glass is proposed. Feature importance analysis confirmed that the accuracy of the prediction depends mainly on change in enthalpy of mixing and change in entropy of mixing. However, among the artificial neural network models and KNearest Regressor models developed, the former showed a promising performance in prediction of the glass formation ability (critical thickness). It has been successfully demonstrated and validated with experimental critical thickness that the glass forming ability can be predicted using an artificial neural network given the elemental composition alone. A computational algorithm was also developed to classify the atoms as big/small in each given alloy. The outcome of this algorithm is used as input parameters to the ANN and other machine learning models used in this work.

Electrooxidation of components from different phase structures obtained by combined electrodeposition of lead and platinum on the surface of a graphite electrode (GE) was investigated. Electrodeposition of precipitate components on the GE surface was carried out in “in situ” mode. There was made an assumption about the composition of phase structures on the surface of the GE. Heat of mixing of components of binary alloy of lead-platinum is calculated by using the thermodynamic theory of alloys. The displacement of the equilibrium potential of lead during selective electrooxidation of it from the binary electrolytic precipitate of lead-platinum was estimated in the approximation of the theory of regular solutions. It has been shown that the equilibrium potential of lead in a platinum alloy depends on the composition of the intermetallic compound (IC). After electroconcentration on the surface of the GE there are phases: lead, platinum and IC PtPb. Selective electrooxidation of lead from IC PtPb is observed at a potential of –0.3 V. The possibility of determining platinum (II, IV) ions by the inversion voltammetry (IV) method on the peak of selective electrooxidation of lead from an intermetallic compound with platinum at a potential of –0.3 V.

The objective of the present investigations was to assess the use of thermodynamic phase diagrams and the Gibbs free energy of mixing, ΔGmix, for the screening of the polymeric carriers by determining the ideal drug-loading for an amorphous solid dispersion formulation and optimum processing temperature for the hot-melt extrusion of a non-glass-forming drug. Mefenamic acid (MFA) was used as a model non-glass-forming drug and four chemically distinct polymers with close values of the solubility parameters, viz. Kollidon® VA64, Soluplus®, Pluronic® F68, and Eudragit® EPO, were used as carriers. The thermodynamic phase diagrams were constructed using the melting point depression data, Flory-Huggins theory, and Gordan-Taylor equation. The Gibbs free energy of mixing was estimated using the values of the drug-polymer interaction parameter, χ, and Flory-Huggins theory. The rank order miscibility of MFA in the four polymeric carriers estimated based on the difference in the values of their solubility parameters, Δδ, did not correlate well with the thermodynamic phase diagrams and Gibbs free energy plots. The study highlights the limitation of using the solubility parameter method in screening the polymeric carriers for poorly glass-forming drugs and reiterates the applicability of thermodynamic phase diagrams and Gibbs free energy plots in determining the ideal drug-loading and optimum processing temperature for hot-melt extrusion.

Average effective interdiffusion coefficients of individual components and tracer diffusion coefficient of Ni were experimentally determined in FCC CoCrFeNi high entropy alloys. Average effective interdiffusion coefficients of individual elements in CoCrFeNi alloys were determined using the Dayananda-Sohn approach. Cr had the highest while Ni had the lowest magnitude of the average effective interdiffusion coefficient in the CoCrFeNi alloy. The tracer diffusion coefficient of Ni was determined without the application of radiotracers using the novel analytical method proposed by Belova et al. based on linear response theory coupled with the Boltzmann-Matano approach and Gaussian distribution function. Both average effective interdiffusion coefficients and tracer diffusion coefficients in CoCrFeNi were compared with the relevant high entropy alloys with varying entropy of mixing. The diffusion of individual elements in Al-containing high entropy alloys (e.g., Al-Co-Cr-Fe-Ni and Al-Co-Cr-Fe-Ni-Mn), with higher entropy of mixing, was higher than that in CoCrFeNi alloy, with relatively lower entropy of mixing. Therefore, diffusion cannot a priori consider to be sluggish in alloys with higher configurational entropy. Moreover, potential energy fluctuations determined in quinary and senary Al-containing high entropy alloys were higher than that in quaternary CoCrFeNi alloy. This also suggests that the diffusivity of a component may not be always lower in the alloys which possess higher fluctuations in potential energy or configurational entropy of mixing.

In the present study, swelling kinetics of cellulose pulp over a wide range of N-methyl-morpholine-N-oxide (NMMO) concentration and the temperature was investigated and a mathematical model was developed based on a corrected swelling ratio. The swelling ratio of cellulose pulp was measured using an offline mass-based method for the different swelling times. The swelling data thus generated was subsequently corrected by eliminating aqueous NMMO trapped in the porous structure of the pulp. It has been observed that the swelling kinetics data of cellulose in aqueous NMMO solution follow the second-order rate equation. A unified correlation is developed to express the dependence of rate constant and equilibrium swelling on NMMO concentration and temperature. Further heat of mixing is calculated from this correlation and it is seen that the swelling phenomena are endothermic in nature.

The Helmholtz free energy, energy, and entropy of mixing of N,N-dimethylformamide (DMF) and water are calculated in the entire composition range by means of Monte Carlo computer simulations and thermodynamic integration using all possible combinations of five DMF and three widely used water models. Our results reveal that the mixing of DMF and water is highly non-ideal. Thus, in their dilute solutions, both molecules induce structural ordering of the major component, as evidenced by the concomitant decrease in the entropy. Among the 15 model combinations considered, only 4 reproduce the well-known full miscibility of DMF and water, 3 of which strongly exaggerate the thermodynamic driving force of the miscibility. Thus, the combination of the CS2 model of DMF and the TIP4P/2005 water model reproduces the properties of the DMF-water mixtures far better than the other combinations tested. Our results also reveal that moving a fractional negative charge from the N atom to the O atom of the DMF molecule, leading to the increase in its dipole moment, improves the miscibility of the model with water. Starting from the CS2 model and optimizing the charge to be moved, we propose a new model of DMF that reproduces very accurately both the Helmholtz free energy of mixing of aqueous DMF solutions in the entire composition range (when used in combination with the TIP4P/2005 water model) and also the internal energy of neat DMF.

The cluster expansion formalism for alloys is used to construct surrogate models for three refractory high-entropy alloys (NbTiVZr, HfNbTaTiZr, and AlHfNbTaTiZr). These cluster expansion models are then used along with Monte Carlo methods and thermodynamic integration to calculate the configurational entropy of these refractory high-entropy alloys as a function of temperature. Many solid solution alloy design guidelines are based on the ideal entropy of mixing, which increases monotonically with $$N$$ N , the number of elements in the alloy. However, our results show that at low temperatures, the configurational entropy of these materials is largely independent of $$N$$ N , and the assumption described above only holds in the high-temperature limit. This suggests that alloy design guidelines based on the ideal entropy of mixing require further examination.

In the present work, using mixing Gibbs free energies and Chou’s general solution model (GSM), by considering the excess activation energies from the binary subsystems, the viscosities of the simple ternary Au–Ag–Cu, Al–Cu–Si, and Fe–Ni–Co and liquid alloys of binary subsystems have been evaluated via well known Chou model and physical models, such as Kaptay, Kozlov–Romanov–Petrov (KRP), and Schick et al. at temperatures 1373, 1375, and 1873 K. A comparison between the evaluated results and experimental values of the Au–Ag–Cu, Al–Cu–Si, and Fe–Ni–Co ternary alloys was carried out. In this study, the success of the application of the aforementioned geometric and physical models to the viscosity calculations of the alloys discussed and the viscosite data are presented to the literature. In order to determine the applicability success, the mean square deviation analysis was performed. According to the values in this table, Schick et al. and KRP models which are derived from the physical quantities among the models discussed provide best description of the viscosity for the Al–Cu–Si and Au–Ag–Cu alloys, respectively.

To validate the ‘sluggish diffusion’ in high-entropy alloys, interdiffusion coefficients of individual elements and tracer diffusion coefficient of Ni were experimentally determined in FCC Al0.25CoCrFeNi alloy. The tracer diffusion coefficient was determined without the application of radio-tracers using a novel analytical method proposed by Belova et al. based on linear response theory coupled with Boltzmann-Matano approach and Gaussian distribution function. Sluggish diffusion kinetics was not observed in alloys with higher configuration entropy in comparison to alloys with lower configuration entropy. Correspondingly, potential energy fluctuations in alloys with higher configuration entropy may not always result in anomalously slow diffusion kinetics. Diffusion is determined not to be necessarily sluggish in Al0.25CoCrFeNi high-entropy alloy by experimental measurement of chemical and tracer diffusion coefficients.

Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.

Structural α-relaxation dispersion in binary molecular glass forming mixtures with distinct mixing enthalpy ΔHmix was investigated using enthalpic and dielectric relaxation measurements across the entire composition range. This study focused on the dependence of the relaxation dispersion on the mixing thermodynamics by determining the non-exponential exponent β, and its composition dependence. The β values determined by the enthalpic and dielectric relaxations agree well. Remarkably, it is found that the systems with positive enthalpy of mixing (exothermic, ΔHmix >0) have positive deviations in the composition dependence of β from the linear averaging of the two β values of the pure components, while negative deviations are observed for the systems with negative enthalpy of mixing (endothermic, ΔHmix

Relative role of enthalpy and entropy in the stabilization of senary FCC Al-Co-Cr-Fe-Ni-Mn high entropy alloys was investigated via a high throughput combinatorial solid-to-solid diffusion couple approach. Many off-equiatomic compositions of FCC AlpCoqCrrFesNitMnu were generated by the diffusing Al and Ni in equiatomic Co20Cr20Fe20Ni20Mn20 alloy, i.e., the Al48Ni52 vs Co20Cr20Fe20Ni20Mn20 diffusion couple, annealed at 900°, 1000°, 1100°, and 1200 °C. Above 1000 °C, the solubility limit of Al in off-equiatomic AlpCoqCrrFesNitMnu alloy was determined to be higher than the solubility limit of Al in equiatomic AlxCoCrFeNiMn alloy. Compositions corresponding to the highest solubility limit of Al in off-equiatomic AlpCoqCrrFesNitMnu alloy exhibited a lower free energy of mixing, i.e., higher thermodynamic stability, than equiatomic AlxCoCrFeNiMn compositions, at 1100 °C and above. Therefore, the role of enthalpy was estimated to be significant in achieving higher thermodynamic stability in off-equiatomic alloys, since they always have lower entropy of mixing than their equiatomic counterparts. The magnitude of interdiffusion coefficients of individual elements in Al-Co-Cr-Fe-Ni-Mn alloys were compared to the interdiffusion coefficients in relevant quinary, quaternary, and ternary solvent-based alloys. Interdiffusion coefficients were not necessarily lower in FCC Al-Co-Cr-Fe-Ni-Mn alloys; therefore no sluggish diffusion was observed in FCC HEA, but diffusion of individual elements in BCC Al-Co-Cr-Fe-Ni-Mn alloy followed the sluggish diffusion hypothesis except for Ni. All compositions in the FCC Al-Co-Cr-Fe-Ni-Mn alloy were observed to comply with existing empirical single phase formation rules in high entropy alloys.

Partial and integral thermodynamic functions of the mixing and evaporation of nickel–calcium melts are calculated from the values of calcium vapor pressure at 900–1300°C (1173–1573 K), determined using the boiling points approach (isothermal version), and those of nickel, found via numerical integration of the Gibbs–Duhem equation. It is established that the formation of alloys containing up to 65.5 mol % calcium (the rest is nickel) is exothermic, while at higher Ca content the process is endothermic. The excess entropy of mixing is negative up to a Ca content of ∼64 mol %, testifying to a certain ordering in the melts due to the existence of associates. Using data on the pressure of a saturated vapor of calcium and nickel, the state diagram is supplemented by the fields of the coexistence of melts and vapor at atmospheric pressure and in vacuums of 1.33 and 0.7 kPa. The location of the boundaries of the fields of vapor–liquid equilibrium confirms the possibility of separation of the Ni–Ca melts by distillation in a vacuum.

We have computed interchange energy by estimating the best fit experimental and theoretical values at 800K using Flory’s model. Taking these values at 800K, interchange energy at different temperatures are calculated using optimization method and with the help of which free energy of mixing, heat of mixing and entropy of mixing are obtained. The partial excess free energy is calculated with the help of values of free energy of mixing which is used to find surface tension. Butler’s equation and Layered structure approach have been used to calculate surface tension of Zn-Cd alloy. Viscosity is obtained from Singh and Sommer’s formulation, Moelwyn-Hughes equation, and Kaptay equation.

The thermophysical properties of Ni–Al. Ni–Ti, and Al–Ti alloys, i.e., viscosity and surface tension, have been investigated using the evaluated thermodynamic properties, i.e., enthalpy of mixing $$ \Delta H_{\text{mix}} $$, Gibbs free energy of mixing $$ \Delta G_{\text{mix}} $$, and excess Gibbs free energy $$ \Delta G_{{}}^{\text{E}} $$, by the atom and molecular coexistence theory. Then, the third-degree Redlich–Kister (R–K) parameters for viscosity, surface tension, and excess Gibbs free energy at 1973 K were obtained. Based on this, the isothermal viscosity of Ni–Al–Ti ternary melts was simultaneously determined form the excess viscosity of the above-mentioned three binary systems by CALPHAD model and the similarity coefficients by Chou’s model, and the surface tension of the liquid ternary Ni–Al–Ti alloy systems was investigated with considering the excess surface tension of the three binary systems by Chou’s model as well as the excess Gibbs free energy of Ni–Al–Ti melts by Butler’s model for the multicomponent system at 1973 K. The results showed that the viscosity and surface tension of liquid Ni–Al–Ti alloy increase with the increase in Ti content at a fixed Al/Ni ratio, whereas decreases with increasing Al/Ni ratio at a given alloy composition at 1973 K.

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

Under continual disturbance such as vibration, tumbling, flow or aeration, granular or powder systems can display solid or fluid like behavior. Using a well-mixed system of same size (0.2 mm) non-cohesive glass beads and iron powder, we show that gentle aeration can completely segregate the components thereby reducing the entropy of mixing to create near total order from an initially chaotic mixture. We quantify the time dependence of the segregation process and identify two dynamic pathways that dominate depending on the intensity of the aeration. Such findings can facilitate the search for energy efficient methods to process granular systems in pharmaceutical, mining and waste recovery industries.

We propose an efficient way of increasing the entropy of mixing in high-entropy-alloy-type compounds, which can be achieved by multi-site alloying. As an example of this concept, we report the synthesis and observation of polycrystalline samples of new high-entropy-alloy-type metal chalcogenides (Ag,In,Pb,Bi)Te1-xSex (x = 0.0, 0.25, and 0.5) with a NaCl-type structure. The samples were synthesized using high pressure synthesis. Superconductivity with transition temperatures of 2.7, 2.5, and 2.0 K was observed with x = 0.0, 0.25, and 0.5, respectively. To investigate the multi-site alloying effect on the entropy of mixing (ΔSmix) for the examined samples, we calculated the total ΔSmix for two crystallographic sites. For the samples with x = 0.25 and 0.5, ΔSmix reaches 1.89R and 2.00R, respectively, which exceed the ΔSmix of 1.79R for a simple (single-site) high-entropy alloy containing six different elements.

The changes in extensive thermodynamic quantities, such as volume, energy, Helmholtz free energy and entropy, occurring upon mixing liquid methanol with supercritical CO2, are calculated using Monte Carlo simulations and thermodynamic integration for all eight combinations of four methanol and two CO2 potential models in the entire composition range at 313 K. The obtained results are also compared with experimental data whenever possible. The transition of the system from liquid to a supercritical state is found to occur at this temperature around a CO2 mole fraction value of 0.95 with all model combinations considered. This liquid to supercritical transition is always accompanied by positive Helmholtz free energy of mixing values and, consequently, by the non-miscibility of the two components. Furthermore, both this non-miscibility around the liquid to supercritical transition and also the miscibility of the two components below this transition, in the liquid regime, are found to be primarily of the energetic rather than entropic origin; the entropy of mixing turns out to be very close to zero, and around the liquid to supercritical transition even its qualitative behaviour is strongly model dependent. Finally, it is found that the methanol expansion coefficient is not sensitive to the details of the potential models, and it is always in excellent agreement with the experimental data. On the other hand, both the volume and the energy of mixing depend strongly on the molar volume of neat CO2 in the model being used, and in this respect the TraPPE model of CO2 [J. J. Potoff and J. I. Siepmann, AIChE J., 2001, 47, 1676] performs considerably better than that of Zhang and Duan [Z. Zhang and Z. Duan, J. Chem. Phys., 2005, 122, 214507].

We examine the role of water and urea in cellulose solubility in tetrabutylammonium hydroxide (TBAH). Molecular dynamics simulations were performed for several different solvent compositions with a fixed cellulose fraction. For each composition, two simulations were carried out with cellulose fixed in each of the crystalline and the dissolved states. From the enthalpy and the entropy of the two states, the difference in Gibbs free energy (ΔG) and hence the spontaneity is determined. A comparison with solubility experiments showed a strong correlation between the calculated ΔG and the experimental measurements. A breakdown of the enthalpic and entropic contributions reveals the roles of water and urea in solubility. At high water concentration, a drop in solubility is attributed to both increased enthalpy and decreased entropy of dissolution. Water displaces strong IL–cellulose interactions for weaker water–cellulose interactions, resulting in an overall enthalpy increase. This is accompanied by a strong decrease in entropy, which is primarily attributed to both water and the entropy of mixing. Adding urea to TBAH(aq) increases solubility by an addition to the mixing term and by reducing losses in solvent entropy upon dissolution. In the absence of urea, the flexible [TBA]+ ions lose substantial degrees of freedom when they interact with cellulose. When urea is present, it partially replaces [TBA]+ and to a lesser extent OH− near cellulose, losing less entropy because of its rigid structure. This suggests that one way to boost the dissolving power of an ionic liquid is to limit the number of degrees of freedom from the outset.

Model calculations of the whole set of thermodynamic properties of liquid alloys for the binary Cu–Eu and ternary Al–Cu–Eu systems have been performed. Authors used the ideal associated solution model (IAS model) for calculation of the entropies and excess Gibbs energies of mixing for these systems. The binaries were given as the Redlich-Kister polynomials. The thermodynamic properties for the ternary system are described using the Redlich-Kister-Muggianu formalism. A comparison of the surfaces of excess Gibbs energy and entropy of mixing for liquid Al–Cu–Eu alloys at 1350 K demonstrates that the ordering related to the formation of rather strong associates in the Al–Eu system significantly affects the concentration dependence of the excess Gibbs energy of mixing in the liquid phase at this temperature.

Micelle formation enthalpies (ΔmicH values) have been calorimetrically determined at 298 K for three sets of mixed zwitterionic/cationic gemini systems consisting of N-dodecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (ZW3-12) and a series of structurally related gemini surfactants, the N,N'-bis(dimethyldodecyl)-α,ω-alkanediammonium dibromide (12-s-12) systems. From the experimental and the estimated ideal micelle formation enthalpies, the excess enthalpies were obtained. The degrees of nonideality of the interaction in the mixed micelle (βm) from our previous work was used along with the excess enthalpy values to determine excess thermodynamic quantities of the surfactants in the mixed system according to Regular Solution Theory (RST) and Motomura's theory. The excess enthalpies for the ZW3-12/12-4-12 were positive in magnitude and rose sharply when small amounts of the zwittergent were distributed into the gemini micelles. The excess enthalpies for the ZW3-12/12-5-12 and the ZW3-12/12-6-12 systems were also >0 kJ mol−1, and as a function of zwittergent composition, were quite different to those of the ZW3-12/12-4-12 mixed micelles. These results indicate that the heat of mixed micelle formation is strongly dependent on electrostatic interactions and the structure of the surfactants involved, specifically, the length of the tether group for the 12-s-12 gemini surfactants. From the calorimetric data and the application of RST and Motomura's theory, we have obtained estimates of the excess Gibbs energy and entropy of mixing. An analysis of the three thermodynamic properties suggests that the relative contributions of enthalpic and entropic effects to nonideal behavior for mixed micelles involving gemini surfactants are strongly dependent on the gemini structure.