Liquid multicomponent systems thermodynamics

In developing the thermodynamic framework for ECES, we attempted to synthesize computer software that would correctly predict the vapor-liquid-solid equilibria over a wide range of conditions for multicomponent systems. To do this we needed a good basis which would make evident to the user the chemical and ionic equilibria present in aqueous systems. We chose as our cornerstone the law of mass action which simply stated says "The product of the activities of the reaction products, each raised to the power indicated by its numerical coefficient, divided by the product of the activities of the reactants, each raised to a corresponding power, is a constant at a given temperature. ... 

The objective of this review is to characterize the excimer formation and energy migration processes in aryl vinyl polymers sufficiently well that the excimer probe may be used quantitatively to study polymer structure. One such area of application in which some measure of success has already been achieved is in the analysis of the thermodynamics of multicomponent systems and the kinetics of phase separation. In the future, it is likely that the technique will also prove fruitful in the study of structural order in liquid crystalline polymers. 

Experimental studies were carried out to derive correlations for mass transfer coefficients, reaction kinetics, liquid holdup, and pressure drop for the packing MULTIPAK (35). Suitable correlations for ROMBOPAK 6M are taken from Refs. 90 and 196. The nonideal thermodynamic behavior of the investigated multicomponent system was described by the NRTL model for activity coefficients concerning nonidealities caused by the dimerisation (see Ref. 72). 

The thermodynamic equations for the Gibbs energy, enthalpy, entropy, and chemical potential of pure liquids and solids, and for liquid and solid solutions, are developed in this chapter. The methods used and the equations developed are identical for both pure liquids and solids, and for liquid and solid solutions therefore, no distinction between these two states of aggregation is made. The basic concepts are the same as those for gases, but somewhat different methods are used between no single or common equation of state that is applicable to most liquids and solids has so far been developed. The thermodynamic relations for both single-component and multicomponent systems are developed. 

In addition, several equations of state have been developed to predict the VLE behavior of a subcritical liquid mixture with a supercritical component. These theoretical models are of current research interest. In addition, several approaches have been formulated to extend the analysis to multicomponent systems utilizing concepts of continuous thermodynamics(9. 101. 

Here, we only present the simplest thermodynamic expressions used in the CALPHAD method for the major phase classes observed in multicomponent systems namely, disordered miscible and immiscible phases and ordered sublattice phases. The reader is referred to specialized textbooks for further discussion. The Gibbs energies for disordered two-component solid and liquid solution phases are most easily represented by the regular solution model (Eq. 2.10) or one of its variants ... 

First, we measured thermodynamic and mass transfer data of the multicomponent system olive 0U/CO2 (3,4). The phase equilibria was modulated by correlating the partition coefficients (Kj = y /x ) of each component present in the mixture as a function of the mole fraction of the FFA fraction in the liquid phase (3). Mass transfer studies were performed in a lab-scale countercurrent packed column. The experimental measured mass transfer coefficients were... 

For a pure supercritical fluid, the relationships between pressure, temperature and density are easily estimated (except very near the critical point) with reasonable precision from equations of state and conform quite closely to that given in Figure 1. The phase behavior of binary fluid systems is highly varied and much more complex than in single-component systems and has been well-described for selected binary systems (see, for example, reference 13 and references therein). A detailed discussion of the different types of binary fluid mixtures and the phase behavior of these systems can be found elsewhere (X2). Cubic ecjuations of state have been used successfully to describe the properties and phase behavior of multicomponent systems, particularly fot hydrocarbon mixtures (14.) The use of conventional ecjuations of state to describe properties of surfactant-supercritical fluid mixtures is not appropriate since they do not account for the formation of aggregates (the micellar pseudophase) or their solubilization in a supercritical fluid phase. A complete thermodynamic description of micelle and microemulsion formation in liquids remains a challenging problem, and no attempts have been made to extend these models to supercritical fluid phases. 

Vapor-Liquid Equilibria for the Ammonia, Hydrogen, Nitrogen, Argon, Methane System (Fig. 4). Because of the great importance of absorption processes in synthesis loop engineering (see Section 4.5.6), these binary and multicomponent systems have been experimentally and theoretically reinvestigated several times. The updates are based mainly on thermodynamic relationships in combination with equations of state. 

Thermodynamic effects of directional forces in liquid mixtures.— The theory applied to pure liquids in the last two sections can be generalized to liquid mixtures and can be used to discuss the effects of directional forces on the thermodynamic functions of mixing. Classical statistical mechanics leads to a complete expression for the free energy of a multicomponent system in terms of the intermolecular energies Ust for all pairs of components s and t. Each Ust can be expanded in the general manner (2.1), so that it is separated into a spherically symmetric part and various directional terms. 

Multicomponent Effects. Only limited experimental data are available for multicomponent diffusion in liquids. The binary correlations are sometimes employed for (he case of a solute diffilsing through a mixed solvent of uniform composition.3,33 It Is clanr that thermodynamic nonideslities In multicomponent systems can cause sigaiflcanl effects. The resder is referred to Cussler s book4 for a discussion of available experimental information on diffusion in multicomponent systems. 

Multicomponent reaction systems with poorly known interactions among the various components and imprecisely known kinetics Vapor-liquid or liquid-liquid thermodynamic equilibria for multicomponent systems... 

Rates of Diffusion. When the solid and liquid of a multicomponent system are in thermodynamic equilibrium, the composition of the solid wul usually differ from that of the liquid. When the system is submitted to further melting or crystallization, the composition of at least one of the phases will change in the vicinity of the contact surface. Diffusion tends to equalize the concentration differences occurring both in the solid and in the liquid phases and should, therefore, be promoted. 

Block-like and segmented polymers represent chemically bound "multicomponent" systems that, in our opinion, are able to mimic some of the non-bonded interactions occurring in blends of either compatible or not compatible pol3nners, and to describe phenomena connected with phase segregation and the onset of peculiar micromorpho-logical properties. Additionally, liquid crystal polymers, even though "monocomponent" from a macrochemical point of view in that constituted of only one polymeric material, in reality do behave, under certain selected thermodynamic conditions, as mechanical mixtures of at least two components. 

As will be evident from the examples cited below, the S-S theory for multicomponent systems has been successful in describing thermodynamics (e.g., phase equilibria, CED, solubility) and PVT behavior of polymer mixtures with gases, liquids, or solids. For binary systems, Eqs. (6.49) and (6.51) might be written as... 

Multicomponent systems that present polyamorphism have also been reported in computer simulation studies. For example, in Ref. [35], it is found that silica has a LLCP at very low temperature. Silica is also a tetrahedral liquid and it shares many of the thermodynamic properties observed in water. In Ref. [35], two silica models were considered. In both models, the interactions among O and Si atoms are isotropic, due to single point charges and short-range interacting sites located on each atom. Both models considered in Ref. [35] are characterized by a LLCP at very low temperature and coexistence between two liquids is observed in out of equilibrium simulations close to one of the spinodal lines (see Fig. 2b). The location of the LLCP was estimated to be below the glass transition in real silica and hence, unaccessible in experiments. We note that polyamorphism in the glass state is indeed observed in compression experiments on amorphous silica [14], and is qualitatively reproduced in computer simulations [89]. Other examples of multicomponent systems that show LLPT in simulations are presented in Refs [65,90]. In these cases, a substance that already shows polymorphism is mixed with a second component. 

This chapter deals with the use of differential scanning calorimetry (DSC) in the study of some of the properties of self-assembling thermodynamically stable, multicomponent systems that appear to the naked eye as homogeneous and mono-phasic. Typical examples are micellar and microemulsion systems [1]. Both of these liquids are charaeterized by the presence of a dispersed phase, whether in the form of aggregates or droplets (diameter 10 nm), a dispersing medium, and a large interphasal area that becomes increasingly important as the particle size decreases. 

Most of the multicomponent systems are non-ideal. From thermodynamic viewpoint, the transfer of mass species i at constant temperature and pressure from one phase to the other in a two-phase system is due to existing the difference of chemical potential 7t, x p between phases, in which /t,- p =p + T Fln where y, is the activity coefficient of component i is p at standard state. In other words, for a gas (vapor)-liquid system, the driving force of component i transferred from gas phase to the adjacent liquid phase along direction z is the... 

For a multicomponent system Eqs. (1.2) and (1.3) can be primary extended by a term describing the composition influence of the participated components xa,b,c,...-The thermodynamic activity of any component (e. g. A) is expressed by the chemical potential gA = ftA + T-T In Xa i corresponds to solid or liquid or vapor. The chemical potential can be understood in terms of the Gibbs free energy per mole of substance, and it demonstrates the decreasing influence of a pure element or a compound in a diluted system. If any pure component is diluted then the term R- T In Xa will always take values lower than zero (note, that only an ideal solution behavior is considered by the mole fraction Xa- Eor real cases the so-called activity... 

This data handbook provides a unique opportunity to locate a substantial amount of adsorption equilibrium data in one source. The book contains a summary of thermodynamic equations for adsorption of gases and liquids and their mixtures and their application to experimental data. The authors intention was to provide a reference for engineers and scientists interested in the application of adsorption to the separation of gas and liquid mixtures. Since single component isotherms cannot be calculated from first principles, the authors correctly argue that it is necessary to use experimental data. Hence the need for the data book. Once single component data are available it is possible to use models to predict equilibrium data for multicomponent systems. Data sources are fully referenced. 

---