Joule-Thomson coefficient in systems with multiple chemical equilibria

Multiple chemical equilibria under adiabatic conditionsH, P = const. are considered. It is shown that in this case the Joule-Thomson coefficient may also be expressed in terms of response equilibria, which were previously introduced in the study of equilibria achieved underT, P = const. Nevertheless, our approach reveals some noteworthy differences between the isothermic and adiabatic equilibria.     

ChipCheck--a program predicting total hybridization equilibria for DNA binding to small oligonucleotide microarrays

Presented here is the program ChipCheck that allows the computation of total hybridization equilibria for hybridization experiments involving small oligonucleotide arrays. The calculation requires the free energies of binding for all pairs of probes and targets as well as total strand concentrations and probe molecule numbers. ChipCheck has been tested computationally on microarrays with up to 100 spots and 42 target strands (4200 binding equilibria). It arrives at solutions through iterations employing the multidimensional Newton method. While currently running in simulation mode only, an extension of the approach to the exhaustive analysis of chip results is being outlined and may be implemented in the future. The output displays the extent of correct and cross hybridization both graphically and numerically. In principle, calculating total hybridization equilibria allows for eliminating noise from DNA chip results and thus an improvement in sensitivity and accuracy.     

Calculating binary and ternary multiphase equilibria: extensions of the integral area method

The area method was proposed in 1992 to calculate binary and ternary 2-phase equilibria. In its integral form, the method provides both the necessary and sufficient conditions required for the determination of the global minimum reduced Gibbs energy of mixing (Φ). The method has since been applied to the calculation of both pure component and ternary multiphase equilibria in a differential form. However, the extension of the original (2 point) integral area method to the direct calculation of both binary and ternary multiphase equilibria has not been completed. Direct 3 point and modified 2 point search methods have therefore been developed here and used to estimate the phase compositions of a representative binary vapour-liquid-liquid system. The 2 point area method principle has been extended and applied to the calculation of ternary multiphase equilibria using a net volume approach. However, this volume method was found to fail due to an underlying inconsistency in the bounding of the integrated Φ surface by the trial 3-phase region. A new method is proposed that overcomes this problem by minimising the area of intersection between a tangent plane and the Φ surface. This new method has successfully calculated the 3-phase compositions of two simple test systems from a variety of initial mixture starting points.     

On the Correct Use of the Dubinin-Astakhov Equation to Study the Mixed-Gas Adsorption Equilibria

This paper presents the possibilities of Integral Equation (IE) approach to study the mixed-gas adsorption equilibria. As a result, the generalizations of Dubinin-Astakhov equation for the case of mixed-gas adsorption are presented. These new equations are examined using a few adsorption systems recently published in literature.     

pH-metric titration technique for the study of metal-complexes in solution: A novel approach for the calculation of equilibrium constants

A new approach for the calculation of various parameters in metal-complex equilibria involving pH-titration curves is described. The calculations do not require a knowledge of the concentrations of either the mineral acid added to the system or of the titrant (alkali). Only the concentrations of the metal ions and the ligand are employed in obtaining the necessary relations. This simplifies the approach of Irving and Rossotti, and also the procedure described earlier by the present authors. It is further shown that for the complexation systems of monoprotonated ligands, the determination of protonation constant is not a prerequisite for obtaining the stepwise metal-ligand formation constants.     

The dynamics of micelle formation in bile salts I. Sodium cholate and sodium deoxycholate

It has been found that two bile salt solutions of NaC (trihydroxy cholanic salt ) and NaDC (dihydroxy cholanic salt have an excess ultrasonic absorption . This excess absorption fits a single relaxation in all cases . To explain this observed single relaxation the data are considered in terms of several existing models.Simple cation-anion reactions to form a monomer salt are ruled out on the grounds that our experimentations are carried out at concentrations far above the critical micelle concentrations (CMC). A second approach in which the excess absorption is attributed to micelle- counter ion reaction. The third existing model deals with an equilibria between the micelles and the monomers of the bile salts. Three different types of models emerge from this kind of equilibria. Only two (3a and 3b ) of them can be considered as a feasible possibility to explain part of the results.     

Phasepy: A Python based framework for fluid phase equilibria and interfacial properties computation

Phasepy is a Python based package for fluid phase equilibria and interfacial properties calculation from equation of state (EoS). Phasepy uses several tools (i.e., NumPy, SciPy, Pandas, Matplotlib) allowing use Phasepy under Jupyter Notebooks. Phasepy models phase equilibria with the traditional ϕ –γ and ϕ –ϕ approaches, where ϕ (fugacity coefficient) can be modeled as a perfect gas, virial gas or EoS fluid, whereas γ (activity coefficient) can be described by conventional models (NRTL, Wilson, Redlich-Kister expansion, and the group contribution modified-UNIFAC). Interfacial properties are based on the square gradient theory couple to ϕ –ϕ approach. The available EoSs are the cubic EoS family extended to mixtures through the quadratic, modified-Huron-Vidal, and Wong-Sandler mixing rules. Phasepy allows to analyze phase stability, compute phase equilibria, interfacial properties, and optimize their parameters for vapor–liquid, liquid–liquid, and vapor–liquid–liquid equilibria for multicomponent mixtures. Phasepy implementation, and robustness are illustrated for binary and ternary mixtures.     

Examining the effect of chain length polydispersity on the phase behavior of polymer solutions with the statistical associating fluid theory (Wertheim TPT1) using discrete and continuous distributions

Polymers are naturally polydisperse. Polydispersity may have a large effect on the phase behavior of polymer solutions, in particular, on the liquid-liquid phase equilibria. In this paper, we determine the cloud and shadow curves bounded by lower critical solution temperatures for a number of polymer+solvent systems where the polymer is polydisperse in terms of molecular weight (chain length). The moment method [P. Sollich, P. B. Warren, and M. E. Cates, Adv. Chem. Phys. 116, 265 (2001)] is applied with the SAFT approach to determine cloud and shadow curves with continuous Schulz-Flory distributions. It is seen that chain length polydispersity always enhances the extent of liquid-liquid phase equilibria. The predicted cloud curves obtained for continuous distributions are very similar to those obtained for simple ternary mixtures with the same polydispersity index, while the corresponding shadow curves can be very different depending on the composition of the parent distribution. The ternary phase behavior can be used to provide an understanding of the shape of the cloud and shadow curves. Regions of phase equilibria between three liquid phases are found for ternary systems when the chain length distribution is very asymmetrical; such regions are not observed for Schulz-Flory distributions even in the case of a large degree of polydispersity.     

Phase equilibria analysis of the binary N2-NH3 and H2-NH3 systems and prediction of ternary phase equilibria

The high-pressure phase equilibria of binary mixtures, hydrogen-ammonia and nitrogen-ammonia, have been analyzed. A combined Chemical Association + Redlich–Kwong Equation of State (A + RKEOS) approach is adopted to represent gas-phase non-idealities while the liquid phase non-idealities are modeled using the NRTL equations. The proposed approach gave better representation as compared to other modified Redlich–Kwong Equations of State. The new approach was satisfactorily used to predict the phase equilibria of the ternary system of hydrogen–nitrogen–ammonia.     

Calculation of chemical and phase equilibria via simulated annealing

We present a new class of techniques for the solution of the chemical and phase equilibria problem for reacting species in a closed system. The minimisation of the Gibbs free energy for all the species in the system is conducted using the technique of simulated annealing (SA). The SA objective function incorporates non‐ideal equations of state. This new approach is demonstrably able to solve multi‐species and multi‐phase LTCE problems in ideal‐gas solutions, ideal solutions and mixtures of ideal and non‐ideal solutions.     

Phase equilibria in polymer solutions

A theoretical study of phase equilibria in multicomponent polymer solutions is presented. The treatment is based on the virial expansion of the osmotic pressure. A program for the numerical determination of phase diagrams is worked out and applied to the polystyrene-cyclohexane system. The present approach is compared with the Flory-Huggins theory of polymer solutions, which is shown to represent a special class of approximations in the present treatment.     

Analysis of Equilibrium and Kinetics of Chromium-Fluoride Complexation from Spectroscopic Data via Chemometrics Methods

IntroductionStudies on reversible kinetic systems are consi-dered as a hotspot of chemical and biochemical kineticresearches[1,2]. Of late, some researches have been fo-cused on the simultaneous optimization of the obverseand reverse rate constants[3,4].H…     

Application of charged single isomer derivatives of cyclodextrins in capillary electrophoresis for chiral analysis

The review focuses on the role of ionic or ionisable single isomer derivatives (SIDs) of cyclodextrins on the separation of chiral analytes in capillary electrophoresis (CE), covering the period since the year 2000. The advantages of using pure compounds are discussed, as well as the ways to optimise the separations in the context of a rational approach to these techniques. Specific attention is paid to the modulation of the selector–analyte interaction. The advantage due to a detailed knowledge of equilibria occurring in solution during the CE run is underlined, particularly in the case of the presence of metal complexes, as occurs in chiral ligand exchange capillary electrophoresis (CLECE).     

Predicting vapor–liquid equilibria of fatty systems

In the present work, a group contribution method is proposed for the estimation of the vapor pressure of fatty compounds. For the major components involved in the vegetable oil industry, such as fatty acids, esters and alcohols, triacylglycerols (TAGs) and partial acylglycerols, the optimized parameters are reported. The method is shown to be accurate when it is used together with the UNIFAC model for estimating vapor–liquid equilibria (VLE) of binary and multicomponent fatty mixtures comprised in industrial processes such as stripping of hexane, deodorization and physical refining. The results achieved show that the group contribution approach is a valuable tool for the design of distillation and stripping units since it permits to take into account all the complexity of the mixtures involved. This is particularly important for the evaluation of the loss of distillative neutral oil that occurs during the processing of edible oils.The combination of the vapor pressure model suggested in the present work with the UNIFAC equation gives results similar to those already reported in the literature for fatty acid mixtures and oil–hexane mixtures. However, it is a better tool for predicting vapor–liquid equilibria of a large range of fatty systems, also involving unsaturated compounds, fatty esters and acylglycerols, not contemplated by other methodologies. The approach suggested in this work generates more realistic results concerning vapor–liquid equilibria of systems encountered in the edible oil industry.     

Artificial multiple criticality and phase equilibria: an investigation of the PC-SAFT approach

The perturbed-chain statistical associating fluid theory (PC-SAFT) is studied for a wide range of temperature, T, pressure, p, and (effective) chain length, m, to establish the generic phase diagram of polymers according to this theory. In addition to the expected gas-liquid coexistence, two additional phase separations are found, termed "gas-gas" equilibrium (at very low densities) and "liquid-liquid" equilibrium (at densities where the system is expected to be solid already). These phase separations imply that in one-component polymer systems three critical points occur, as well as equilibria of three fluid phases at triple points. However, Monte Carlo simulations of the corresponding system yield no trace of the gas-gas and liquid-liquid equilibria, and we conclude that the latter are just artefacts of the PC-SAFT approach. Using PC-SAFT to correlate data for polybutadiene melts, we suggest that discrepancies in modelling the polymer density at ambient temperature and high pressure can be related to the presumably artificial liquid-liquid phase separation at lower temperatures. Thus, particular care is needed in engineering applications of the PC-SAFT theory that aims at predicting properties of macromolecular materials.     

Predicting the tautomeric equilibrium of acetylacetone in solution. I. The right answer for the wrong reason?

This study investigates how the various components (method, basis set, and treatment of solvent effects) of a theoretical approach influence the relative energies between keto and enol forms of acetylacetone, which is an important model system to study the solvent effects on chemical equilibria from experiment and theory. The computations show that the most popular density functional theory (DFT) approaches, such as B3LYP overestimate the stability of the enol form with respect to the keto form by ～10 kJ mol^?1, whereas the very promising SCS‐MP2 approach is underestimating it. MP2 calculations indicate that in particular the basis set size is crucial. The Dunning Huzinaga double ζ basis (D95z(d,p)) used in previous studies overestimates the stability of the keto form considerably as does the popular split‐valence plus polarization (SVP) basis. Bulk properties of the solvent included by continuum approaches strongly stabilize the keto form, but they are not sufficient to reproduce the reversal in stabilities measured by low‐temperature nuclear magnetic resonance experiments in freonic solvents. Enthalpic and entropic effects further stabilize the keto form, however, the reversal is only obtained if also molecular effects are taken into account. Such molecular effects seem to influence only the energy difference between the keto and the enol forms. Trends arising due to variation in the dielectric constant of the solvent result from bulk properties of the solvent, i.e., are already nicely described by continuum approaches. As such this study delivers a deep insight into the abilities of various approaches to describe solvent effects on chemical equilibria. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Peptide conformational equilibria computed via a single-stage shifting protocol

We study the conformational equilibria of two peptides using a novel statistical mechanics approach designed for calculating free energy differences between highly dissimilar conformational states. Our results elucidate the contrasting roles of entropy in implicitly solvated leucine dipeptide and decaglycine. The method extends earlier work by Voter and overcomes the notorious "overlap" problem in free energy computations by constructing a mathematically equivalent calculation with high conformational similarity. The approach requires only equilibrium simulations of the two states of interest, without the need for sampling transition states. We discuss possible extensions and optimizations of the approach.