Chemical equilibrium in a heterogeneous fluid phase system: thermodynamic regularities and topology of phase diagrams

Singularities of the systems with simultaneous phase and chemical equilibria were examined. The thermodynamic regularities were revealed and topology of phase diagrams was presented for multicomponent heterogeneous systems including two or several equilibrium liquid phases (solution layering). The thermodynamic conditions for displacement of phase and chemical equilibrium are considered.     

The geometry of thermodynamic potentials

In this paper, the performance of a diagrammatic method based on geometric and algebraic considerations is illustrated. This method, based on the particular symmetry of a thermodynamic diagram, allows to obtain the most important thermodynamic expressions of a simple system. In fact, these thermodynamic expressions can be developed with the application of various geometric patterns to the proposed diagram. The particular symmetry of the thermodynamic diagram allows to develop a matrix formulation of the different geometric patterns. This matrix formalism requires that the thermodynamic parameters of the diagram be recast in a vectorial form.On sabbatical leave from November 1995 until October 1996. Address during this period: Centro de Quimica Fisica Molecular, Univerdade Técnica de Lisboa, IST, Av. Rovisco Pais, 1096 Lisboa-Codex, Portugal.     

Stochastic ensembles of thermodynamic potentials

The provision of uncertainty estimates along with measurement results or values computed thereof is metrologically mandatory. This is in particular true for observational data related to climate change, and thermodynamic properties of geophysical substances derived thereof, such as of air, seawater or ice. The recent International Thermodynamic Equation of Seawater 2010 (TEOS-10) provides such properties in a comprehensive and highly accurate way, derived from empirical thermodynamic potentials released by the International Association for the Properties of Water and Steam (IAPWS). Currently, there are no generally recognised algorithms available for a systematic and comprehensive estimation of uncertainties for arbitrary properties derived from those potentials at arbitrary input values, based on the experimental uncertainties of the laboratory data that were used originally for the correlations during the construction process. In particular, standard formulas for the uncertainty propagation which do not account for mutual uncertainty correlations between different coefficients tend to systematically and significantly overestimate the uncertainties of derived quantities, which may lead to practically useless results. In this paper, stochastic ensembles of thermodynamic potentials, derived from randomly modified input data, are considered statistically to provide analytical formulas for the computation of the covariance matrix of the related regression coefficients, from which in turn uncertainty estimates for any derived property can be computed a posteriori. For illustration purposes, simple analytical application examples of the general formalism are briefly discussed in greater detail.     

Phenomenological theory of phase diagrams with multicritical points

The breakup of multicritical points is studied in detail within the phenomenological theory of second-order phase transitions for a thermodynamic potential invariant with respect to the C _3v (3m) group of transformations. The general conditions of this breakup are obtained and possible types of derived diagrams are plotted from a parent phase diagram containing a multicritical point. Examples of experimental phase diagrams are given that qualitatively confirm the results from theoretical and computer simulations of phase equilibria.     

Calculation of phase equilibria and construction of phase diagrams by convex hull method

Recent findings for a new method developed to calculate phase equilibria are reviewed and analyzed. This method is based on the construction of the convex hulls for characteristic functions in heterogeneous systems. The theoretical basis of this method, as well as the possibilities and features of its practical application in scientific research and teaching chemical thermodynamics, is considered. Software packages developed at the Department of Chemistry of Moscow State University are briefly described.     

Rigorous nonlinear regression analysis of phase solubility diagrams to obtain complex stoichiometry and true thermodynamic drug-cyclodextrin complexation parameters

This work reports rigorous nonlinear regression procedures aimed at analyzing various types of phase solubility diagrams (PSDs) corresponding to the different soluble and insoluble complex stoichiometries, which are generally encountered in drug-cyclodextrin (CD) complexation studies. These are depicted in final equations that can be modeled to fit experimental data of measured drug solubility against CD concentration utilizing simple spreadsheet software available for all PCs (i.e., the Solver Add-in in Microsoft Excel). They cover all types of guest/host phase solubility diagrams (A-, B_S-and B_I-types) allowing accurate estimation of soluble and insoluble complex stoichiometries generally encountered in drug/CD complexes (1:1, 2:1, 1:2, 2:2, 2:3, 3:2), the corresponding thermodynamic complex formation constants (K₁₁, K₂₁, K₁₂, K₂₂, K₂₃, K₃₂) and solubility product constants (K_sp) of saturated complexes.     

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.     

Construction of solid-liquid phase diagrams in ternary systems by titration calorimetry

Titration calorimetry was used to construct the solid-liquid equilibrium line in ternary systems containing the solute and an aqueous mixed solvent by measuring the heat of dissolution of the solid solute during successive additions of the liquid solvent. The plot of cumulated heats versus the mole ratio, n_solvent/n_solute, yields two (almost) linear increases of different slopes. These two lines represent successively the enthalpy of dissolution then the enthalpy of dilution of the medium; their intersection gives the solubility and the enthalpy of dissolution of the solute. Phase diagrams have been established over the whole concentration range for o-anisaldehyde, 1,3,5-trimethoxybenzene and vanillin, in water + methanol, +ethanol, or +n-propanol at 303, 313 and 318 K.     

The topological characteristics of liquid-vapor phase diagrams

The existing forms of the rule of azeotropy are reviewed and a new form applicable to distillation (reactive distillation) diagrams and their fragments, which are simplicial complexes of arbitrary dimensions, is presented.     

Complete phase diagrams of mixtures of a nematic liquid crystal with n-alkanes

The full experimental phase diagrams of mixtures of the nematic liquid crystal 4.4'-azoxyanisole, (PAA), and n-tetracosane and of PAA and n-octadecane are given. Equilibria of a nematic phase with an isotropic phase, of two isotropic phases, and a reentrant isotropic phase could be observed directly. The experimental phase diagram is in qualitative agreement with the result derived from the Flory lattice model adopted for thermotropic systems.     

Revised phase diagrams based on racemic ibuprofen with thymol and l-menthol

Journal of Thermal Analysis and Calorimetry - The phase diagrams between thymol and racemic ibuprofen, on the one hand, and between l-menthol and this same ibuprofen, on the other hand, were...