Effective kinetic phase diagrams

The composition of a solid solution that is growing at conditions well away from equilibrium is not prescribed by equilibrium thermodynamics, but is determined kinetically. It depends both on the surface kinetics and on the transport of mass and heat to and away from the solidification front. In previous work, we have formulated a model for the kinetic or nonequilibrium segregation taking place at the solidification front enabling the construction of kinetic phase diagrams, which gives the growth composition of a solid solution as a function of the liquid composition and undercooling at the surface. In the present work, we extend this model to include both mass and heat transport, giving rise to effective kinetic phase diagrams. An overview of the tendencies in the calculated effective kinetic phase diagrams is given by scanning a large part of the parameter space, covering different types of materials, including metals, semiconductors, and molecular systems. We find striking and characteric differences in the relative contribution of the various processes to the effective segregation. For molecular mixtures, interfacial undercooling and heat transport limitation can be expected to be much more important than for metal and semiconductor mixtures where mass transport limitation is dominant.     

Supercritical phase equilibria involving solids

The solubility of solids in supercritical solvents is reviewed in a phenomenological discussion of binary and ternary systems containing one highly volatile component. Solubility and selectivity are greatly determined by the course of the binary critical curves, the ternary critical end-point curves, and the locations of the triple points of the solids. The mean-field lattice-gas model is used to review some important molecular parameters.     

Quantum topology phase diagrams for molecules,clusters, and solids

The need to make more quantitative use of the total electronic charge density distribution is demonstrated in this short perspective. This is framed in the perspective of the ground breaking early work of Bader and coworkers, along with mathematicians who captured the essential nature of a molecule in a suitably compact form in real space. We see that this simple form is the Poincaré–Hopf relation for molecules and clusters and the Euler–Hopf relation in solids. Thom's theory of elementary catastrophes combined with the Poincaré–Hopf relation provides the inspiration for the new quantum topology. An alternative use of the Poincaré–Hopf relation, molecular recognition, is discussed. Quantum topology is then used to create a topology phase diagram for both molecules and solids. The author adds their perspectives of the huge potential of the quantum topology approach by demonstrating the ease with which new theoretical ideas can be generated. © 2013 Wiley Periodicals, Inc.     

Solution thermochemistry of diethyldithiocarbamato-iron(III)

The enthalpy change (303 K) for the standard state solid phase complexation reaction

is derived using conventional solution calorimetric techniques (ΔH°_R=?82.7±2.0 kJ mol^?1. Knowlege of ΔH°_R is a necessary pre-requisite for the future derivation of the FeS thermochemical bond energy.     

Thermodynamics and phase equilibrium studies of silver halide-cobalt(II) halide systems

Phase diagrams for the systems AgCl-CoCl₂ and AgBr-CoBr₂ were determined by differential scanning calorimetry. The systems are of the eutectic type. Eutectic points are at 271±2 K, 19.5 mol% CoCl₂ and 653±2 K, 17.0 mol% CoBr₂, respectively. The solid solubility does not exceed 2 and 4 mol% in the systems AgCl-CoCl₂ and AgBr-CoBr₂, respectively. Thermodynamic activities of components in molten mixtures and molar free enthalpies of mixing were determined for both systems on the basis of liquidus curves. Deviations from ideality were not found to be considerable.     

Modified Pechini synthesis of Na3Ce(PO4)2 and thermochemistry of its phase transition

Effect of the synthesis conditions of Pechini technique on crystallinity and purity of Na₃Ce(PO₄)₂ compound was investigated. Nano-sized cerium-sodium phosphate obtained when EDTA was used as an additional chelating agent for Ln³⁺. The total enthalpy change of Na₃Ce(PO₄)₂ phase transition was determined as 14.2±0.7 kJ mol⁻¹ for sample synthesized by conventional solid-solid reaction. The phase transition process was confirmed to occur at 1060°C or in temperature range 920–1060°C depending on thermal treatment of powders.     

Evaluation of the protonation thermochemistry obtained by the extended kinetic method

An evaluation of the results obtained by the extended kinetic method for a series of representative bases is presented here. Analysis of the original experimental data is conducted using the orthogonal distance regression (ODR) statistical treatment. A comparison with the proton affinities and protonation entropies obtained from variable temperature equilibrium constant measurements demonstrate deviations, which may be ascribed to random and systematic errors. Considerable random errors are associated with the extended kinetic method if the number of reference bases and the range of effective temperatures are too low. It is also confirmed that large systematic errors on proton affinities and protonation entropies are obtained when large protonation entropy is associated with the considered system. It is, however, encouraging to note that the gas phase basicities obtained by the extended kinetic method are generally comparable to that obtained by other methods within a few kJ/mol.     

Thermodynamics of water intrusion in nanoporous hydrophobic solids

We report a joint experimental and molecular simulation study of water intrusion in silicalite-1 and ferrerite zeolites. The main conclusion of this study is that water condensation takes place through a genuine first-order phase transition, provided that the interconnected pores structure is 3-dimensional. In the extreme confinement situation (ferrierite zeolite), condensation takes place through a continuous transition, which is explained by a shift of both the first-order transition line and the critical point with increasing confinement. The present findings are at odds with the common belief that conventional phase transitions cannot take place in microporous solids such as zeolites. The most important features of the intrusion/extrusion process can be understood in terms of equilibrium thermodynamics considerations. We believe that these findings are very general for hydrophobic solids, i.e. for both nonwetting as well as wetting water-solid interface systems.     

A thermochemistry and kinetic study on the thermal decomposition of ethoxyquinoline and ethoxyisoquinoline

Quantum chemical calculations were used to study the production of ethylene and keto/enol tautomers from ethoxyquinoline (2‐EQ) and ethoxyisoquinoline (1‐EisoQ and 3‐EisoQ) in the gas phase and ethanol at the MP2/6‐311++G(2d,2p)//BMK/6‐31+G(d,p) level. The obtained data indicate that the elimination of ethylene from 1‐EisoQ and 2‐EQ is slightly more favorable than from 3‐EisoQ. Formation of quinolone and isoquinolone (2‐EQO, 1‐EisoQO, and 3‐EisoQO) is kinetically favored compared to their enols. Decomposition of 2‐EQ and 1‐EisoQ to ethylene and keto forms is thermodynamically and kinetically preferable more stable than the corresponding enols. However, the hydroxy form of 3‐EisoQ is more stable than its keto tautomer in the gas phase and ethanol. The enol tautomers cost less energy when formed from their keto forms rather than from the parent ethoxyquinolone and ethoxyisoquinoline.     

Poly(ethylene oxide)/poly(methyl methacrylate) (semi-)interpenetrating polymer networks: Synthesis and phase diagrams

Interpenetrating polymer networks (IPNs) of poly(ethylene oxide) (PEO) and poly(methyl methacrylate) (PMMA) were prepared by simultaneous network formation. The PEO network was produced by acid-catlayzed self-condensation of α,ω-bis(triethoxysilane)-terminated PEO in the presence of small amounts of water. The PMMA network was formed by free radical polymerization of MAA in the presence of divinylbenzene as crosslinker. The reaction conditions were adjusted to obtain similar crosslinking kinetics for both reactions. An attempt was made to construct a phase diagram of the IPNs by measuring the composition of the IPNs at the moment of the appearance of the phase separation, as indicated by the onset of turbidity. This composition could be determined because the siloxane crosslinks of the PEO network could be hydrolyzed in aqueous NaOH with the formation of linear, soluble PEO chains. The phase diagram was compared with phase diagrams of blends of linear polymers and of semi-IPNs (crosslinked PMMA and linear PEO), obtained under similar conditions, i.e. polymerization of MMA in the presence of varying amounts of PEO. It was observed that the form of the phase diagrams of the linear polymers is similar to that of the IPNs, but is quite different from that of the semi-IPNs. Thus, homogeneous transparent materials containing up to 60% of PEO could be prepared in the blends and the IPNs, but in the semi-IPNs, phase separation occurred with PEO contents as low as 10%.     

Calculated phase diagrams for the electrochemical oxidation and reduction of water over Pt(111)

Ab initio density functional theory is used to calculate the electrochemical phase diagram for the oxidation and reduction of water over the Pt(111) surface. Three different schemes proposed in the literature are used to calculate the potential-dependent free energy of hydrogen, water, hydroxyl, and oxygen species adsorbed to the surface. Despite the different foundations for the models and their different complexity, they can be directly related to one another through a systematic Taylor series expansion of the Nernst equation. The simplest model, which includes the potential only as a shift in the chemical potential of the electrons, accounts very well for the thermochemical features determining the phase-diagram.     

Semiempirical dynamic phase diagrams of nanocrystalline products during copper (II) acetylacetonate vapour decomposition

Nanoparticle production by Cu(acac)₂ vapour decomposition was studied. The composition of the produced particles varied from Cu to Cu₂O depending on experimental conditions. In order to explain the crystalline phase behaviour, a kinetic model to build a semiempirical dynamic phase diagram of the products was proposed. Prevailing role of copper dimers in the processes of copper and copper (I) oxide particle growth was demonstrated. The composition of products was determined by reactions on the surface of growing particles and depended on the ratio of gaseous species. The calculated dynamic phase diagrams were in excellent agreement with the experimental results.     

Solubility limits and phase diagrams for fatty acids in anionic (SLES) and zwitterionic (CAPB) micellar surfactant solutions

The limiting solubility of fatty acids in micellar solutions of the anionic surfactant sodium laurylethersulfate (SLES) and the zwitterionic surfactant cocamidopropyl betaine (CAPB) is experimentally determined. Saturated straight-chain fatty acids with n=10, 12, 14, 16, and 18 carbon atoms were investigated at working temperatures of 25, 30, 35, and 40°C. The rise of the fatty acid molar fraction in the micelles is accompanied by an increase in the equilibrium concentration of acid monomers in the aqueous phase. Theoretically, the solubility limit is explained with the precipitation of fatty acid crystallites when the monomer concentration reaches the solubility limit of the acid in pure water. In agreement with theory, the experiment shows that the solubility limit is proportional to the surfactant concentration. For ideal mixtures, the plot of the log of solubility limit vs. the chainlength, n, must be a straight line, which is fulfilled for n=14, 16, and 18. For the fatty acids of shorter chains, n=10 and 12, a deviation from linearity is observed, which is interpreted as non-ideal mixing due to a mismatch between the chainlengths of the surfactant and acid. The data analysis yields the solubilization energy and the interaction parameter for the fatty acid molecules in surfactant micelles. By using the determined parameter values, phase diagrams of the investigated mixed solutions are constructed. The four inter-domain boundary lines intersect in a quadruple point, whose coordinates have been determined. The results can be applied for the interpretation and prediction of the solubility, and phase behavior of medium- and long-chain fatty acids and other amphiphiles that are solubilizable in micellar surfactant solutions, as well as for determining the critical micellization concentration (CMC) of the respective mixed solution.     

Thermodynamics of redox reactions involving nicotinamide adenine dinucleotide

Literature data on the thermodynamics of redox nicotinamide adenine dinucleotide (NAD) dependent reactions have been analyzed. It has been established that for the redox reaction of NAD

where all substances except H₂ are in the aqueous buffer with the ionization enthalpy equal to zero, the most reliable thermodynamic parameters should be considered as: ΔH(298.15 K; pH 7)=?27.4±1.7 kJ mole^?1; ΔG (298.15K; pH 7)=±17.8 kJ mole^?1. From the above thermodynamic parameters of the reaction ΔH, ΔG and ΔS for reactions of NAD with natural substrates, synthetic mediators and some inorganic compounds have been calculated.     

On the enumeration of phase diagrams

The topological isomorphism of polyhedra with trivalent vertices and solid-liquid diagrams of three-component systems allows the problem of constructing the complete set of the topological types of diagrams with a given set of characteristics to be reduced to the problem of the generation of marked cubic graphs, which are the Schlegel projections of polyhedra. The problem of the enumeration of possible topological types of melting diagrams containing M binary and N ternary stoichiometric congruently melting compounds is considered. Relations between the topological characteristics of such diagrams are given. The total number of topologically different types of melting diagrams with one binary and one ternary congruently melting compounds was found to be 64.     

Calculation of Ln-Ba (Ln = Gd,Pr, Nd,and Sm) phase diagrams

A thermodynamic model of liquid was suggested and Ln-Ba (Ln = Gd, Pr, Nd, and Sm) phase diagrams were calculated on the basis of generalization of literature data on thermodynamic properties and phase equilibria in lanthanide-barium metallic systems. The interaction parameter of Gd_{1 ? x} Ba _x regular melt was estimated on the assumption of a proportionality between the particle-particle interaction energies of liquid lanthanide and liquid barium, on the one hand, and the lanthanide radius, on the other.     

Computational study of the thermochemistry of organophosphorus(III) compounds

The enthalpies of formation of organophosphorus(III) compounds have been calculated at the G3X, G3X(MP2), and B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d,p) levels of theory using the atomization energy procedure and the method of isodesmic reactions. The Delta f H298 degree values for 50 relatively large molecules with up to 10 non-hydrogen atoms, such as P(CH3)3, P(C2H5)3, P(OCH3)3, n-C4H9OPCl2, [(CH3)2N]2PCl, (C2H5)2NPCl2, and [(CH3)2N]2PCN, have been calculated directly from the G3X atomization energies. A good agreement between the known experimental values and G3X results for 14 compounds provides support to our predictions for remaining species whose experimental enthalpies of formation are unknown or known with relatively large uncertainties. On the basis of our calculations and sometimes conflicting experimental data a set of internally consistent enthalpies of formation has been recommended for organophosphorus(III) compounds. Our computational results call into question the experimental enthalpies of formation of P(C2H5)3 and P(n-C4H9)3. From comparison with most reliable experimental data, the accuracy of the theoretical enthalpies of formation is estimated as ranging from 5 to 10 kJ/mol. The recommended Delta f H298 degree values were used to derive the group additivity values (GAVs) for 45 groups involving the phosphorus(III) atom. These GAVs significantly extend the applicability of Benson's group additivity method and may be used to estimate the enthalpies of formation of larger organophosphorus(III) compounds, where high level quantum chemical calculations are impracticable.     

Theoretical and experimental investigation of the thermochemistry of CrO2(OH)2(g)

In this paper, we report the results of equilibrium pressure measurements designed to identify the volatile species in the Cr-O-H system and to resolve some of the discrepancies in existing experimental data. In addition, ab initio calculations were performed to lend confidence to a theoretical approach for predicting the thermochemistry of chromium-containing compounds. Equilibrium pressure data for CrO2(OH)2 were measured by the transpiration technique for the reaction 0.5Cr2O3(s) + 0.75O2(g) + H2O(g) = CrO2(OH)2(g) over a temperature range of 573 to 1173 K at 1 bar total pressure. Inductively coupled plasma atomic emission spectroscopy (ICP-AES) was used to analyze the condensate in order to quantify the concentration of Cr-containing volatile species. The resulting experimentally measured thermodynamic functions are compared to those computed using B3LYP density functional theory and the coupled-cluster singles and doubles method with a perturbative correction for connected triple substitutions [CCSD(T)].