Phase partitioning, thermodynamics

We now turn to processing situations in which heat effects are of primary importance examples include chemical reactors and separators that exploit phase partitioning. Thermodynamic analysis of these situations invoke the stuff equations in particular, steady-state heat effects are computed from (12.3.5). To obtain the partial molar enthalpies that appear in (12.3.5), we need enthalpies as functions of composition so in 12.4.1 we show how enthalpy-concentration diagrams can be constructed from volumetric equations of state applied to binary mixtures in phase equilibrium. Then we apply the energy balance (12.3.5) to multicomponent flash separators ( 12.4.2), binary absorbers ( 12.4.3), and chemical reactors ( 12.4.4). 

All of the first-generation vapors from VOC SOA will certainly undergo further gas-phase oxidation, which will in turn influence the phase partitioning thermodynamics of the OA mixture, i.e., gas-phase aging of SOA. 

We begin, however, our discussion of air/liquid phase partitioning by reiterating some general thermodynamic considerations that we will need throughout this chapter. 

There is a general belief that peptides are not thermodynamically stable [99], but the formation of an internal bond in a peptide chain actually corresponds to a process that is not far from equilibrium (Kpep 0.1 M-1) and enzymatic peptide synthesis can yield peptides in satisfactory yield provided that the product is removed from the solution by precipitation or other systems of phase partition [100,101]. 

So far we have considered chemical equihbrirun in solution only. The thermodynamic constraints can be applied to reactions among all phases, including gas partitioning between vapor and liquid phases, and reactions between sohd and dissolved phases. A thermodynamically related tool for determining the quantitative constraints among phases in an equihbrium system is the Gibbs phase rule. 

A significant amount of work has demonstrated the feasibility and the interest of reversed micelles for the separation of proteins and for the enhancement or inhibition of specific reactions. The number of micellar systems presently available and studied in the presence of proteins is still limited. An effort should be made to increase the number of surfactants used as well as the set of proteins assayed and to characterize the molecular mechanism of solubilization and the microstructure of the laden organic phases in various systems, since they determine the efficiency and selectivity of the separation and are essential to understand the phenomena of bio-activity loss or preservation. As the features of extraction depend on many parameters, particular attention should be paid to controlling all of them in each phase. Simplified thermodynamic models begin to be developed for the representation of partition of simple ions and proteins between aqueous and micellar phases. Relevant experiments and more complete data sets on distribution of salts, cosurfactants, should promote further developments in modelling in relation with current investigations on electrolytes, polymers and proteins. This work could be connected with distribution studies achieved in related areas as microemulsions for oil recovery or supercritical extraction (74). In addition, the contribution of physico-chemical experiments should be taken into account to evaluate the size and structure of the micelles. 

The one-step procedures can be utilized for the separations of the sample components with similar dimensions but different adsorption characteristics in the given system gel-eluent. The non-adsorbed part of the sample is separated according to the steric exclusion mechanism, while the elution of the adsorbed part of the sample is retarded [26]. Another combined procedure utilizes the thermodynamic partition of the sample as the auxiliary separation mechanism the gel is either swollen by a solvent immiscible with eluent [27] or a mixed eluent is used, one component of which is preferentially sorbed within the gel matrix [28]. In both cases, the composition of the stagnant phase within the gel differs significantly from the composition of the mobile phase and thermodynamic partition takes place. The extent of the partition is controlled by the porous structure of the gel so that steric exclusion remains the principal separation mechanism. 

The thermodynamics of semi-volatile phase partitioning for atmospheric OA mixtures has been extensively treated in the literature [17, 18, 39, 40] and will only briefly be reviewed here. We express the effective saturation concentration (C ) of an organic compound by converting its saturation vapor pressure into mass concentration units and multiplying by the appropriate activity coefficient for the organic mixture (this is the inverse of the partitioning coefficient used in some formulations = 1/C ). The general effect of a solution is to lower the... 

Equations (11) and (12) show that devolatilization is strongly affected by the thermodynamic equilibria of the VOCs between different phases. High values of the polymer partides/aqueous-phase partition coefficient imply that the concentration in the aqueous phase will be low and hence it will be difficult to remove the VOC from the particles. Similarly, a low value of the Henry s law constant means that the concentration of VOCs in the gas phase is low and hence, devolatilization will be difficult. Figure 18.7 shows the kinetics of devolatilization of vinyl acetate, acetaldehyde, and n-butanol in a VAc/BA/AA latex, and that of BA in a BA/S/AA latex by stripping in laboratory-scale equipment, under equilibrium conditions. It can be seen that the devolatilization of BA was slow due to the high affinity (high feS,) of BA to the polymer particles. The removal of n-butanol was also very slow because of its high solubility in the aqueous phase and low vapor pressure (a low value of the Henry s law constant). 

In Section 3.3, we illustrated the thermodynamic relations that govern the conditions of equilibrium distribution of a species between two or more immiscible phases under thermodynamic equilibrium. In Section 4.1, we focus on the value of the separation factor or other separation indices for two or more species present in a variety of two-phase separation systems under thermodynamic equilibrium in a closed vessel. The closed vessels of Figure 1.1.2 are appropriate for such equilibrium separation calculations. There is no bulk or diffusive flow into or out of the system in the closed vessel. The processes achieving such separations are called equilibrium separation processes. Separations based on such phenomena in an open vessel with bulk flow in and out are studied in Chapters 6, 7 and 8. No chemical reactions are considered here however, partitioning between a bulk fluid phase and an individual molecule/macromolecule or collection of molecules for noncovalent solute binding has been touched upon here. The effects of chemical reactions are treated in Chapter 5. Partitioning of one species between two phases is an important aspect ever present in this section. 

It is obvious to the user at this juncture that the subject of environmental chemical fate models enjoys many individual mass transfer processes. Besides this, the flux equations used for the various individual processes are often based on different concentrations such as Ca, Cw, Cs, and so on. Since concentration is a state variable in all EC models, the transport coefficients and concentrations must be compatible. Several concentrations are used because the easily measured ones are the logical mass-action rate drivers for these first-order kinetic mechanisms. Unfortunately, the result is a diverse set of flux equations containing various mechanism-oriented rate parameters and three or more media concentrations. Complications arise because the individual process parameters are based on a specific concentration or concentration difference. As argued in Chapter 3, the fiigacity approach is much simpler. Conversions to an alternative but equivalent media chemical concentration are performed using the appropriate thermodynamic equilibrium statement or equivalent phase partition coefficients. The process was demonstrated above in obtaining the overall deposition velocity Equation 4.9. In this regard, the key purpose of Table 4.2 is to provide the user with the appropriate transport rate constant compatible with the concentration chosen to express the flux. Eor each interface, there are two choices of concentration... 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

Current use of statistical thermodynamics implies that the adsorption system can be effectively separated into the gas phase and the adsorbed phase, which means that the partition function of motions normal to the surface can be represented with sufficient accuracy by that of oscillators confined to the surface. This becomes less valid, the shorter is the mean adsorption time of adatoms, i.e. the higher is the desorption temperature. Thus, near the end of the desorption experiment, especially with high heating rates, another treatment of equilibria should be used, dealing with the whole system as a single phase, the adsorbent being a boundary. This is the approach of the gas-surface virial expansion of adsorption isotherms (51, 53) or of some more general treatment of this kind. 

---