Free Energy Change Of Mixing Research Articles

Thermodynamic modelling of miscibility in (InAs) x (GaAs)1−x solid solutions

Current methods used to model the solution thermodynamics of III–V compound semiconductors involve the use of the valence force field as the molecular model and the regular solution model (with the temperature independent interaction parameter and underlying assumption of random mixing) as the engineering model. In this study, excess free energy models (with three or less adjustable parameters) are investigated to predict the solid–solid miscibility of (InAs) x (GaAs)1− x . The models investigated include the Porter/one-constant Margules (OCM) model, the two-constant Margules (TCM) model and the non-random two liquid (NRTL) model. These models are fit to excess free energy values derived from free energy change of mixing (variation with composition) data available from molecular simulations at different temperatures. The parameters in all the models have been found to be temperature dependent. The coexistence compositions are best predicted by the NRTL model, indicating the need to consider non-random mixing effects present in these solid solutions. The TCM model predicts better equilibrium composition data as compared to the OCM model.

Numerical Analysis on Si Deoxidation of Molten Fe, Ni, Fe-Ni, Fe-Cr, Fe-Cr-Ni, Ni-Cu and Ni-Co Alloys by Quadratic Formalism

Numerical analysis on Si deoxidation of molten Fe, Ni, Fe-Ni, Fe-Cr, Fe-Cr-Ni, Ni-Cu and Ni-Co alloys have been carried out. The excess Gibbs free energy change of mixing has described with Redlich-Kister type polynomial using the relation derived from Darken's quadratic formalism. Excellent agreement between present work and experimental results was found for equilibrium Si and O contents in molten Fe, Ni, Fe-Ni, Fe-Cr, Fe-Cr-Ni, Ni-Cu and Ni-Co alloys. Si deoxidation equilibrium of not only one component metal but also alloys can be analyzed numerically using the formula determined in the present work. Also, interaction parameters of Redlich-Kister type polynomial can be easily converted into interaction coefficients with Taylor's series, which are widely used in steelmaking processes.

Phase behavior of ternary blends containing dimethylpolycarbonate, tetramethylpolycarbonate and poly[styrene‐co‐(methyl methacrylate)] copolymers (or polystyrene)

AbstractThe miscibility and phase behavior of ternary blends containing dimethylpolycarbonate (DMPC), tetramethylpolycarbonate (TMPC) and poly[styrene‐co‐(methyl methacrylate)] copolymer (SMMA) have been explored. Ternary blends containing polystyrene (PS) instead of SMMA were also examined. Blends of DMPC with SMMA copolymers (or PS) did not form miscible blends regardless of methyl methacrylate (MMA) content in copolymers. However, DMPC blends with SMMA (or PS) blends become miscible by adding TMPC. The miscible region of ternary blends is compared with the previously determined miscibility region of binary blends having the same chemical components and compositions. The region where the ternary blends are miscible is much narrower than that of binary blends. Based on lattice fluid theory, the observed phase behavior of ternary blends was analyzed. Even though the term representing the Gibbs free energy change of mixing for certain ternary blends had a negative value, blends were immiscible. It was revealed that a negative value of the Gibbs free energy change of mixing was not a sufficient condition for miscible ternary blends because of the asymmetry in the binary interactions involved in ternary blends. Copyright © 2004 Society of Chemical Industry

A combined statistical mechanics and molecular dynamics approach for the evaluation of the miscibility of polymers in good, poor and non-solvents

A newly proposed method based on combining statistical mechanics and molecular dynamics techniques was developed to evaluate the miscibility of polymers in various solvents. The focus in this article is the miscibility of poly(ethylene imine), PEI, in different solvents for its crucial significance in all its industrial applications. The statistical mechanics techniques were used to derive an expression for the deformational entropy of the polymeric chains suitable enough for evaluation during a molecular dynamics run. Molecular dynamics methods were then used to evaluate the enthalpy of mixing, entropy of mixing, the loss in entropy due to the deformation of the polymeric chains and the total free energy change of mixing. The enthalpy of mixing of PEI with water was shown to have a higher negative value than that of PEI with ethanol. This was attributed to the strong attractive interactions between PEI and water molecules due to the formation of strong hydrogen bonding between the molecules. PEI and n-dodecane had, however, a positive value for the enthalpy of mixing, thus indicating repulsive interactions between the polymer and the solvent. Evaluation of the loss in entropy due to the deformation of the polymer chain showed that in both cases, the coiling of the chains in case of a non-solvent or the swelling of the chain in case of a good solvent, the entropy loss will be of a positive value thus lowering the overall entropy change. Nevertheless, the loss will be more pronounced in case of the former than the latter. Overall evaluation of the free energy change has accurately predicted a strong miscibility for PEI with water, a moderate miscibility for PEI with ethanol and immiscibility for PEI in n-dodecane and thus affirming the validity of the developed approach in evaluating the miscibility behavior of PEI in various solvents. An account of the solubility parameters and the polymer–solvent interaction parameter ( χ) was also discussed.

Polymerization-induced phase separation in silica sol-gel systems containing formamide

Silica gels with well-defined pores both in micrometer and nanometer ranges were obtained by acid-catalyzed hydrolysis and polymerization of tetramethoxysilane in the presence of formamide. The micrometer-range structures of these gels are studied in terms of the phase diagram of the quasi two-component system, namely solvent-rich and silica-rich end compositions. The resulting interconnected structures and aggregates of particles are related to the occurrence of spinodal phase separation. The composition region that gave interconnected structures for the present system was much more limited and their characteristic sizes were much smaller than those for the previously reported systems containing an organic polymer. These results could be explained qualitatively by the effect of the degree of polymerization on the Flory-Huggins' type free energy change of mixing.

Studies on Aqueous Solutions of Guanidinium Salts. VIII. Free Energy of Mixing of Guanidinium Bromide and Tetrabutylammonium Bromide in Aqueous Solution at 25 °C

Abstract Osmotic and activity coefficients have been determined by the isopiestic comparison method on the water–guanidinium bromide–tetrabutylammonium bromide system at 25 °C. The values of the excess free energy change of mixing and the interaction parameter g0 on Friedman’s formalism were large and negative in magnitude. These results have been discussed in terms of the mixed ion pairing and structural change of water.