Temperature-dependent Interaction Parameters Research Articles

Asymmetry in Polymer-Solvent Interactions Yields Complex Thermoresponsive Behavior.

We introduce a lattice framework that incorporates elements of Flory-Huggins solution theory and the q-state Potts model to study the phase behavior of polymer solutions and single-chain conformational characteristics. Without empirically introducing temperature-dependent interaction parameters, standard Flory-Huggins theory describes systems that are either homogeneous across temperatures or exhibit upper critical solution temperatures. The proposed Flory-Huggins-Potts framework extends these capabilities by predicting lower critical solution temperatures, miscibility loops, and hourglass-shaped spinodal curves. We particularly show that including orientation-dependent interactions, specifically between monomer segments and solvent particles, is alone sufficient to observe such phase behavior. Signatures of emergent phase behavior are found in single-chain Monte Carlo simulations, which display heating- and cooling-induced coil-globule transitions linked to energy fluctuations. The framework also capably describes a range of experimental systems. Importantly, and by contrast to many prior theoretical approaches, the framework does not employ any temperature- or composition-dependent parameters. This work provides new insights regarding the microscopic physics that underpin complex thermoresponsive behavior in polymers.

A comprehensive thermodynamic modeling of the solubility of sugar alcohols in ionic liquids

Environmental regulations have recently drawn attention from fossil sources to green materials, among which sugar alcohols (SA) have particular importance due to their vast use in the nutrition, pharmaceutical, and chemical industries. Their properties and equilibrium conditions, including the extraction and solubility behavior utilizing novel solvents such as ionic liquids (ILs), are essential for developing further processes and their optimization. On account of this, the present study aims to develop a comprehensive thermodynamic approach based on simple and accurate tools such as activity coefficient models (ACMs) and equations of state (EoSs), which have not been hitherto addressed. To this end, eleven calculation schemes based on these two approaches were applied to the largest databank investigated thus far (13 SAs, 21 ILs, and 653 data points), and the performance of the models was analyzed. NRTL, free-volume Flory-Huggins (FVFH), and Redlich-Kister (RK) ACMs with different schemes, as well as athermal and ideal solution models, were evaluated and compared against well-known cubic EoSs such as Peng-Robinson (PR) and Valderrama-Patel-Teja (VPT). Benefitting from three adjustable parameters and a simple form, the three-parameter RK model yielded the best results with a 0.82 % (2.77 K) deviation in the entire databank. Moreover, employing temperature-dependent interaction parameters with FVFH ACM (3.55 K, 1.05 %), PR EoS (3.60 K, 1.07 %), and VPT EoS (3.66 K, 1.08 %) improved the accuracy of the calculations remarkably. The results of this contribution prove that thermodynamic models based on NRTL, FVFH, and RK ACMs are the best options for calculating solid–liquid conditions equilibrium of SA-IL systems with a simple and precise calculation procedure, and can therefore be employed for the simulation and optimization tools. This study investigates the most extensive SA-IL databank, a large number of models from different routes, and the nature of SA-IL pairs employing the obtained parameters.

Solubility modeling of hydrogen sulfide in aqueous sodium salt solutions

Accurate solubility prediction of hydrogen sulfide in aqueous electrolyte solutions is critical for gas exploitation and geological storage. However, there is a lack of electrolyte Equation of State model that can accurately calculate the solubilities of hydrogen sulfide in aqueous electrolyte solutions over wide ranges of temperature, pressure, and salt molality. This work presents a modeling study on the solubilities of hydrogen sulfide in pure water and several aqueous sodium salt solutions. The thermodynamic framework used in this work is an electrolyte version of Cubic-Plus-Association Equation of State. The model’s temperature-dependent ion-gas binary interaction parameters are obtained by regressing the experimental solubilities in the aqueous electrolyte solutions. The modeling results show that the electrolyte Cubic-Plus-Association Equation of State can satisfactorily correlate the solubilities of hydrogen sulfide in aqueous electrolyte solutions over wide ranges of temperature, pressure, and salt molality. For the typical water–sodium chloride–hydrogen sulfide system, the model can satisfactorily correlate the gas solubilities with the mean relative deviation being 6.2%, with the temperature up to 593.95 K, pressure up to 32.30 MPa, and salt molality up to 6.0 mol⋅kg−1 water. Moreover, the salting-out effects and model adaptability are analyzed and discussed.

Mixing properties of liquid Al-Au alloys

The thermodynamic and structural properties of liquid Al-Au alloy have been studied in frame-work of R-K polynomial using temperature-dependent energy interaction parameters at different temperatures. Thermodynamic properties, excess free energy of mixing and activity, and in structural properties, concentration fluctuation in long wave-length limit have been computed at temperatures 1338 K, 1500 K and 1600 K. The properties, such as surface tension and surface concentration of the system have been computed at above mentioned temperatures using Butler model. The system shows transformation from segregating to ordering in nature with increase in concentration of Au.

High Temperature Stability of K-Pb Liquid Alloy

The study explores the thermo-physical properties of complex binary liquid potassium-lead alloy at temperature 848 K as a function of concentration by considering complex using different model equations. The Quasi Chemical approximation and the R-K equation are used to investigate features such as free energy, heat of mixing, chemical activity, and concentration fluctuation in the long wave limit at temperature of 848 K. However, at 900 K and 1000 K, these are exclusively examined using the R-K equation. The temperature dependent exponential interaction parameters proposed by Kaptay are taken into account in the RK equation. The study goes on to look at the alloy's viscosity and surface tension using the Budai-Benko-Kaptay model and the Kaptay's improved derivation of Butler equation. The mixing nature of the system is investigated in depth, with a focus on the interaction energy parameters between the alloy's surrounding atoms. The work investigates the fact that the liquid alloy has a moderately interacting as well as ordering character throughout a whole concentration range, and the computed theoretical thermodynamic facts are in reasonable agreement with the corresponding experimental data at 848 K. At greater temperatures, the alloy's tendency goes from ordering to segregating. The alloy's viscosity and surface tension decrease as the temperature rises.

Exponential Temperature-Dependent Parameters for Thermodynamic and Structural Properties of Al-Ti Melt

Thermodynamic and structural properties of Al-Ti melt have been estimated in the framework of Redlich-Kister (R-K) polynomial using linear temperature-dependent (T-dependent) interaction parameters above melting temperatures. These calculations show the existence of the artificial inverted miscibility gaps (artifacts) at temperatures 2000 K, 2500 K, and 2700 K. Therefore, interaction parameters are assumed to vary exponentially with temperature and have been optimised for excess free energy of mixing. The artifacts do not appear in the calculation of these properties of the concerned alloy when these optimized parameters are used. BIBECHANA 19 (2022) 75-82

Liquid-liquid equilibrium of systems encountered in glycerol transesterification with dimethyl carbonate

Glycerol carbonate is a value-added glycerol derivative, which can be obtained by transesterification with dimethyl carbonate. Phase splitting and merging exist in the transesterification due to the low solubilities of glycerol with dimethyl carbonate. The isobaric liquid-liquid equilibrium data for two ternary systems (glycerol – dimethyl carbonate – glycerol carbonate/methanol) and one quaternary system (glycerol – dimethyl carbonate – glycerol carbonate – methanol) involved in the glycerol transesterification were measured at reaction relevant temperatures (333.2, 353.2, 373.2, and 393.2 K) and 1.5 MPa. The equilibrium data were correlated using the NRTL model to calculate activity coefficients, with temperature-dependent interaction parameters, which were estimated through data regression and validated by checking the consistency of the Gibbs free energy. The NRTL model with the regressed parameters could reproduce the phase equilibrium trends of all the studied systems.

A long-range order in a thermally driven system with temperature-dependent interactions.

Aggregation of macro-molecules under an external force is far from being understood. An important driving situation is achieved by temperature difference. Inter-particle interactions in metallic nanoparticles with ligand capping are reported to be sensitive to temperature and the zeta potential of the particles being reduced in the cold region. Such particles form aggregates in the cold region of the system in the presence of temperature difference. Here we study the aggregation of particles in the presence of temperature difference with temperature-dependent interaction parameters using Brownian dynamics simulation. The particle interaction and particle diffusion are considered to be sensitive to the local temperature. We identify a long-range structural order in the cold region of the system using the Avrami equation for crystal growth kinetics. Our observations might be useful in designing ordered structures with macro-molecules under non-equilibrium steady-state conditions.

Random Forest Predictor for Diblock Copolymer Phase Behavior.

Physics-based models are the primary approach for modeling the phase behavior of block copolymers. However, the successful use of self-consistent field theory (SCFT) for designing new materials relies on the correct chemistry- and temperature-dependent Flory-Huggins interaction parameter χAB that quantifies the incompatibility between the two blocks A and B as well as accurate estimation of the ratio of Kuhn lengths (bA/bB) and block densities. This work uses machine learning to model the phase behavior of AB diblock copolymers by using the chemical identities of blocks directly, obviating the need for measurement of χAB and bA/bB. The random forest approach employed predicts the phase behavior with almost 90% accuracy after training on a data set of 4768 data points, almost twice the accuracy obtained using SCFT employing χAB from group contribution theory. The machine-learning model is notably sensitive toward the uncertainty in measuring molecular parameters; however, its accuracy still remains at least 60% even for highly uncertain experimental measurements. Accuracy is substantially reduced when extrapolating to chemistries outside the training set. This work demonstrates that a random forest phase predictor performs remarkably well in many scenarios, providing an opportunity to predict self-assembly without measurement of molecular parameters.

Sub-3-Nanometer Domain Spacings of Ultrahigh-χ Multiblock Copolymers with Pendant Ionic Groups.

We investigated the temperature-dependent phase behavior and interaction parameter of polyethylene-based multiblock copolymers with pendant ionic groups. These step-growth polymers contain short polyester blocks with a single Li+SO3- group strictly alternating with polyethylene blocks of x-carbons (PESxLi, x = 12, 18, 23). At room temperature, these polymers exhibit layered morphologies with semicrystalline polyethylene blocks. Upon heating above the melting point (∼130 °C), PES18Li shows two order-to-order transitions involving Ia3̅d gyroid and hexagonal morphologies. For PES12Li, an order-to-disorder transition accompanies the melting of the polyethylene blocks. Notably, a Flory-Huggins interaction parameter was determined from the disordered morphologies of PES12Li using mean-field theory: χ(T) = 77.4/T + 2.95 (T in Kelvin) and χ(25 °C) ≈ 3.21. This ultrahigh χ indicates that the polar ionic and nonpolar polyethylene segments are highly incompatible and affords well-ordered morphologies even when the combined length of the alternating blocks is just 18-29 backbone atoms. This combination of ultrahigh χ and short multiblocks produces sub-3-nm domain spacings that facilitate the control of block copolymer self-assembly for various fields of study, including nanopatterning.

Crystal Engineering of Binary Organic Eutectics: Significant Improvement in the Physicochemical Properties of Polycyclic Aromatic Hydrocarbons via the Computational and Mechanochemical Discovery of Composite Materials

Derivatives of polycyclic aromatic hydrocarbons (PAHs) are widely used in optoelectronic materials. However, the poor solubility of unfunctionalized PAHs represents a challenge for the continued application of these compounds in emerging technologies. For organic compounds bearing one or more functional groups capable of engaging in directional hydrogen or halogen-bonding interactions, the crystal engineering toolkit currently offers many routes for optimizing the solid-state properties of these compounds. Such efforts typically lead to the discovery of periodic crystal forms that display strong adhesive intermolecular forces between the molecular fragments. By contrast, the crystal engineering of organic eutectic composites is relatively unexplored and poorly understood. Here, we report the mechanosynthesis and experimental characterization of the properties of three eutectic composites of pyrene (PYR) and anthracene (ANTH) that were discovered using the coformer bisphenol A (BPA) or phenothiazine (PTZ). The resulting eutectic composites (PYR-BPA, PYR-PTZ, and ANTH-PTZ) display significant melting point depressions ranging from 19 to 51 °C relative to the melting point of the PAH. The equilibrium solubilities of the composite materials were also observed to be 2–5 times greater than that of the PAH. The crystal engineering of eutectic solid forms is currently hampered by the lack of reliable empirical or theoretical tools for predicting their formation. A weighted Monte Carlo simulation was used to estimate the mixing energies and binding modes of a limited set of molecular pairs, leading to temperature-dependent interaction parameters that show promise in the selection of coformers with a high likelihood of forming eutectic composites. Complementary dispersion-corrected density functional theory (DFT-D) calculations on a set of PYR and ANTH composite models reveal that organic eutectic composites are not driven to form on the basis of favorable thermodynamics as evidenced by an average interaction energy of 2.60 kJ mol–1 across the series. Synthon incompatibility and molecular shape mismatch appear to be important factors to consider in targeting eutectic solid forms. This work paves the way for the systematic crystal engineering of organic eutectic solid forms with tunable physicochemical properties using a synergistic computational modeling and mechanosynthesis approach.

Study of excess free energy of mixing and heat of mixing of liquid ternary Al–Li–Zn alloy by assessing the thermodynamic properties of sub-binary alloys

The exponential temperature-dependent interaction parameters of the Redlich-Kister (R–K) polynomial for the binary sub-systems of the liquid Al–Li–Zn ternary alloy were optimized using available literature data. The ternary interaction terms of the Redlich-Kister-Maggianu (R–K–M) polynomial were then optimized in order to determine the excess Gibbs free energy of mixing (GMxs) and the enthalpy of mixing (HM) of the system. These functions for the liquid ternary alloys were also computed at temperatures of 973 K, 1273 K and 1573 K. The calculated inverted miscibility gap that appeared in GMxs while using the linear temperature-dependent interaction parameters was suppressed in this work by the assumption of the interaction parameters to be exponential temperature dependent. The enthalpy of mixing of the alloy so calculated was found to be in good agreement with the available experimental data.

Study of artifacts in thermodynamic and structural properties of Li–Mg alloy in liquid state using linear and exponential models

Temperature-dependent interaction parameters of Redlich-Kister (R–K) polynomials for Li–Mg alloy in liquid phase have been optimized using experimental data in the framework of linear and exponential models. These parameters have then been used to compute the thermodynamic properties (excess Gibbs free energy of mixing, enthalpy of mixing and activity) and structural property (concentration fluctuations in the long-wavelength limit) of the alloy at temperatures 1000 K, 1300 K, 1600 K, 1900 K, and 2200 K. The negative values of excess Gibbs free energy of mixing computed using linear T-dependent parameters increases with the rise in the temperature of the system beyond 1000 K while the same physical quantity computed using the exponential T-dependent interaction parameters decreases with the rise in temperatures and does not show any unusual trends up to 2200 K. Similar behavior has been found in the case of other thermodynamic and structural functions. The unusual behavior that appears in the thermodynamic and structural functions computed using linear T-dependent parameters can be eliminated if these functions are computed using exponential T-dependent parameters.

High Temperature Assessment of K-Tl Binary Liquid Alloy

Theoretical study of thermodynamic properties of binary liquid Potassium-Thallium alloy at temperatures 798 K, 1000 K, 1200 K and 1400 K have been analyzed as a function of concentration by considering temperature dependent exponential interaction parameters in the framework of R-K polynomials. The viscosity and surface tension of the alloy have been studied by BBK model and improved derivation of Butler equation respectively. The study provides the information of moderately interacting as well as segregating nature at the low concentration of Thallium and ordering nature at high concentration of Thallium and the viscosity and surface tension of the alloy decrease with increase in temperature.

Surface Properties of Al–Fe–Si Liquid Alloy Using Thermodynamic Database

Temperature-dependent interaction parameters for excess free energies of mixing of sub-binary systems of Al-Fe-Si ternary liquid alloys were optimised using the experiment data in the frame of Redlich-Kister (R-K) polynomials. These optimised parameters were then used to compute the partial excess free energy of sub-binary and ternary liquid alloys. The surface tension and surface concentration of sub-binary and the ternary liquid alloys were computed using Butler equation. The temperature dependent coefficients of R-K polynomials for excess surface tensions of the sub-binary systems were optimised which were then used to estimate the surface tension of ternary alloy using Chou, Kohler and Toop modelling equations at temperatures 1773, 1873, 1973 and 2073 K. The surface tension of the ternary alloy obtained using aforementioned models were found to be in good agreement from Fe and Al corners but some deviations were observed from Si corner.

Temperature dependence of interaction parameters for Al–Li liquid alloy

ABSTRACT In the studies related to thermodynamic and structural functions of liquid alloys at high temperatures using linear temperature-dependent interaction parameters, in some cases, artificial miscibility gaps or artefacts are noticed. These artificial miscibility gaps in these functions at higher temperatures are usually asymmetric with respect to the concentration. The presence of the artificial miscibility gaps in the properties of the alloys at higher temperatures makes them less reliable and such data cannot be accepted at all. In the present work, we have computed thermodynamic and structural properties of liquid Al–Li alloy at temperatures 800, 1300 and 2000 K in the framework of Redlich–Kister (R-K) polynomials assuming interaction parameters to be linear temperature dependent and some artefacts were observed in these functions at around 2000 K. We have then obtained the optimised set of exponential temperature-dependent interaction parameters and computed the properties of the alloy again from the same polynomials where no miscibility gap was noticed at higher temperatures.

Temperature dependence of interaction parameters of Cu–Si liquid alloy

The thermodynamic and structural properties of Cu–Si liquid alloys were computed at different temperatures assuming that the interaction parameters were linearly and exponentially dependent on the temperature in the framework of R–K polynomials. Both these assumptions were found appropriate in explaining the mixing properties of the alloy near the melting temperature. However, the assumption of the linear temperature dependence of interaction parameters could not explain the properties of the alloy when the temperature was elevated. The exponential temperature dependence of the interaction parameters was found successful in explaining the thermodynamic and structural properties of the alloys over a large temperature range.

Artifacts in Al–Mn liquid alloy

The presence of artifacts in thermodynamic and structural properties of the Al–Mn liquid alloy at higher temperatures has been investigated assuming the interaction parameters present in the modeling equations to be linearly and exponentially temperature dependent. When the concept of linear temperature dependence of interaction parameters is employed to explain the thermo-structural properties of the Al–Mn liquid alloy some asymmetric artifacts appear in these properties at higher temperatures. However, these artifacts are successfully eliminated from the thermo-structural properties of the Al–Mn liquid alloy when the interaction parameters present in the modeling equations are considered to be exponentially temperature dependent.

Mutual and Thermal Diffusivities as well as Fluid-Phase Equilibria of Mixtures of 1-Hexanol and Carbon Dioxide.

This work contributes to an improved understanding of the fluid-phase behavior and diffusion processes in mixtures of 1-hexanol and carbon dioxide (CO2) at temperatures around the upper critical end point (UCEP) of the system. Raman spectroscopy and dynamic light scattering were used to determine the composition at saturation conditions as well as Fick and thermal diffusivities. An acceleration of the Fick diffusive process up to CO2 mole fractions of about 0.2 was found, followed by a strong slowing-down approaching vapor-liquid-liquid equilibrium or critical conditions. The acceleration of the Fick diffusive process vanished at temperatures much higher than the UCEP. Experimental Fick diffusivity data were compared with predictions from equilibrium molecular dynamics simulations and excess Gibbs energy calculations using interaction parameters from the literature. Both theoretical methods were not able to predict that the thermodynamic factor is equal to zero at the spinodal composition, stressing the need for new methodologies under such conditions. Thus, new sets of temperature-dependent interaction parameters were developed for the nonrandom two-liquid model, which improve the prediction of the Fick diffusion coefficient considerably. The link between the Fick diffusion coefficient and the nonrandomness of the liquid phases is also discussed.

Identification of UNIQUAC binary interaction parameters in liquid-liquid equilibrium

An algorithm is presented for the estimation of the UNIQUAC interaction parameters for liquid-liquid equilibrium of ternary systems. The algorithm is based on two optimization levels. In the inner level the algorithm performs the minimization of an objective function based on the isoactivity conditions. The outer level aims to minimize the error between calculated and experimental compositions. The Common Tangent Plane condition is checked at the end to guarantee a thermodynamically consistent representation of the phase behavior of ternary liquid systems.The algorithm is challenged with a historical Type 1 ternary liquid-liquid equilibrium system from the seminal study of Anderson and Prausnitz in which the authors showed the limitations of the original UNIQUAC model and justified its amendment in the modified UNIQUAC model. The present algorithm makes available single temperature and temperature-dependent interaction parameters enabling accurate and thermodynamically correct description of the experimental data with the original UNIQUAC model, therefore without the need of any model modification. This outcome does not change when the interaction parameters from the binary partially miscible constituent pair are first regressed and kept constant during the estimation of the remaining parameters on ternary equilibrium data. This investigation confirms that a model cannot be judged if the correctness of the model parameters has not been proved first.