Gibbs Energy of Mixing Function: Topological Analysis in Azeotropic Systems

ESAT 2014. 27th European Symposium on Applied Thermodynamics, Eindhoven University of Technology, July 6-9, 2014.

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer`s equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer`s model (combining a long-range term, based on the Debye-Huckel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid-liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems. (c) 2008 Elsevier B.V. All rights reserved.

Vapor-liquid equilibria using the Gibbs energy and the common tangent plane criterion

Phase thermodynamics is often perceived as a difficult subject that many students never become fully comfortable with. The Gibbsian geometrical framework can help students to gain a better understanding of phase equilibria. An exercise to interpret the vapor-liquid equilibrium of a binary azeotropic mixture, using the equilibrium condition based on the common tangent plane criterion (the Gibbs stability test), is presented in this paper. From a T-composition phase diagram for the mixture, the temperature is set at different values: above, intermediate to, and below the boiling temperatures of the pure components, to intersect different regions of the system. Students prepare an Excel spreadsheet where the Gibbs energy of mixing of the vapor and liquid mixtures are calculated and represented over the whole range of compositions and then, apply the Gibbs stability test to ascertain the aggregation state of the system and to calculate the VL phase equilibrium compositions. Finally, Matlab is used to generate the 3D Gibbs energy of mixing surfaces for both phases over the whole range of temperatures which facilitates the geometrical interpretation of the vapor-liquid equilibrium.

Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.

Pitfalls in the Evaluation of the Thermodynamic Consistency of Experimental VLE Data Sets

The thermodynamic consistency of almost 90 VLE data series, including isothermal and isobaric conditions for systems of both total and partial miscibility in the liquid phase, has been examined by means of the area and point-to-point tests. In addition, the Gibbs energy of mixing function calculated from these experimental data has been inspected, with some rather surprising results: certain data sets exhibiting high dispersion or leading to Gibbs energy of mixing curves inconsistent with the total or partial miscibility of the liquid phase, surprisingly, pass the tests. Several possible inconsistencies in the tests themselves or in their application are discussed. Related to this is a very interesting and ambitious initiative that arose within the NIST organization: the development of an algorithm to assess the quality of experimental VLE data. The present paper questions the applicability of two of the five tests that are combined in the algorithm. It further shows that the deviation of the experimental VLE data from the correlation obtained by a given model, the basis of some point-to-point tests, should not be used to evaluate the quality of these data.

Graphical User Interface (GUI) for the representation of GM surfaces (using the NRTL model) and curves, including tie-lines and Hessian matrix

A single and very easy to use Graphical User Interface (GUI- MATLAB) based on the topological information contained in the Gibbs energy of mixing function has been developed as a friendly tool to check the coherence of NRTL parameters obtained in a correlation data procedure. Thus, the analysis of the GM/RT surface, the GM/RT for the binaries and the GM/RT in planes containing the tie lines should be necessary to validate the obtained parameters for the different models for correlating phase equlibrium data.

Miscibility studies in poly(methyl vinyl ether)/hydroxypropylcellulose binary system in aqueous solutions and solid state

The phase separation behaviour in aqueous mixtures of poly(methyl vinyl ether) and hydroxypropylcellulose has been studied by cloud points method and viscometric measurements. The miscibility of these blends in solid state has been assessed by infrared spectroscopy; methanol vapours sorption experiments and scanning electron microscopy. The values of Gibbs energy of mixing of the polymers and their blends with methanol as well as between each other were calculated. It was found that in solid state the polymers can interact with methanol very well but the polymer-polymer interactions are unfavourable. Although in aqueous solutions the polymers exhibit some intermolecular interactions their solid blends are not completely miscible. (C) 2005 Elsevier Ltd. All rights reserved.

Modelling liquid–liquid equilibria for island type ternary systems

Closed miscibility gaps in ternary liquid mixtures, at constant temperature and pressure, are obtained if phase separations occur only in the ternary region, whilst all binary mixtures involved in the system are completely miscible. This type of behaviour, although not very frequent, has been observed for a certain number of systems. Nevertheless, we have found no information about the applicability of the common activity coefficient models, as NRTL and UNIQUAC, for these types of ternary systems. Moreover, any of the island type systems published in the most common liquid–liquid equilibrium data collections, are correlated with any model. In this paper, the applicability of the NRTL equation to model the LLE of island type systems is assessed using topological concepts related to the Gibbs stability test. A first attempt to correlate experimental LLE data for two island type ternary systems is also presented.

Pitfalls on computing liquid-liquid phase equilibria using the k-value method

Poster presented in the 11th Mediterranean Congress of Chemical Engineering, Barcelona, October 21-24, 2008.

The Gibbs free energy of formation of a glass alloy

A simple expression for the Gibbs free energy of formation of a pure component or a eutectic alloy glass, relative to the stable crystalline phase (or phases) at the same temperature is deduced by use of thermodynamic arguments. The expression obtained is supposed to apply to both monocomponent and multicomponent liquid alloys that might become glasses from the supercooled liquid state, irrespective of the critical cooling rate needed to avoid crystallization.

Heats of mixing using an isothermal titration calorimeter: Associated thermal effects

[EN] The correct determination of the energy generated or absorbed in the sample cell of an Isothermal Titration Calorimeter (ITC) requires a thorough analysis of the calorimetric signal. This means the identification and quantification of any thermal effect inherent to the working method. In this work, it is carried out a review on several thermal effects, studied by us in previous work, and which appear when an ITC is used for measuring the heats of mixing of liquids in a continuous mode. These effects are due to: (i) the difference between the temperature of the injected liquid and the temperature of the mixture during the mixing process, (ii) the increase of the liquid volume located in the mixing cell and (iii) the stirring velocity. Besides, methods for the identification and quantification of the mentioned effects are suggested.

Effect of mixing sequence on the workability and performance of asphalt mixtures

In Sweden, during recent years, a new type of mixing protocol has been applied, in which the order of mixing is changed from the conventional method. Improved workability and diminished mixing and compaction energy needs have been important drivers for this. Considering that it is the mastic phase, which is modified by changing the mixing order, it provides an interesting case study for explaining the mechanisms of workability in connection with the mastic phase. To do so, an analytical viscosity framework was combined with a mixture morphology framework to upscale to the mixing level and tribology principles to explain the interaction between the mastic and the aggregates. From the mastic viscosity protocol, it was found that the mixing order significantly affects the resulting mastic viscosity. To analyse the effect of this on the workability and resulting mixture performance, X-ray computed tomography was used to analyse mixtures produced by the two different mixing sequences. Mechanical testing was utilised to determine the long-term mechanical performance. In this part of the study, mastic viscosity as a function of particle concentration and distribution was directly coupled to improved mixture workability and enhanced long-term performance.

The force, power, and energy of the 100 meter sprint

At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen [Am. J. Phys. 77, 224-228 (2009)] studied Bolt's performance and predicted that Bolt could have run about one-tenth of a second faster, which was confirmed in Berlin. In this paper we extend the analysis of Eriksen to model Bolt's velocity time dependence for the Beijing 2008 and Berlin 2009 records. We deduce the maximum force, the maximum power, and the total mechanical energy produced by Bolt in both races. Surprisingly, we conclude that all of these values were smaller in 2009 than in 2008.

Resummation of infrared divergences in the free energy of spin-two fields

We derive a closed form expression for the sum of all the infrared divergent contributions to the free energy of a gas of gravitons. An important ingredient of our calculation is the use of a gauge fixing procedure such that the graviton propagator becomes both traceless and transverse. This has been shown to be possible, in a previous work, using a general gauge fixing procedure, in the context of the lowest order expansion of the Einstein-Hilbert action, describing noninteracting spin-two fields. In order to encompass the problems involving thermal loops, such as the resummation of the free energy, in the present work, we have extended this procedure to the situations when the interactions are taken into account.

Energy of the first excited state of (43)Ar

Results of proton-proton-gamma coincidence measurements using the (36)S+(9)Be reaction revealed a gamma ray of 201.27 +/- 0.16 keV that most probably corresponds to the transition between the predicted 7/2(-) first excited state to the 5/2(-) ground state of (43)Ar.