Quasi-binary system approach

In practice, it is often feasible to reduce the multicomponent crystal in respect of its transport behavior to a quasi-binary system. Let us assume that the diffusion coefficients are DA>DB>DC, Dd, etc. The quasi-binary approach considers C, D, etc. as practically immobile, which means that A and B are interdiffusing in the im-... 

According to the McCabe-Thiele method, the system for separation is considered on a quasi-binary basis. In this approach, it must be possible to neglect the influence of the solvent, which is acceptable if the phase boundary lines (solubilities) do not change much with concentration during separation. In this case, the number of theoretical stages, the minimal reflux (ratio), the minimum number of theoretical stages, and their mutual dependence can be determined. 

At any conversion, p, of functional groups, a mixture of the distribution of Eni.n species with the modifier (M) constitutes a multicomponent system. A simplified description may be made by using an average species, E n, as representative of the whole population, with a size (mass) varying continuously with conversion. The simplified approach regards the system as a quasi-binary mixture of E n and M, for any conversion level. 

To approach AG of quasi-binary polymer solutions in an empirical way it is usual to invoke the Koningsveld-Staverman formalism [5], which chooses the familiar Flory-Huggins (FH) atheimal solution as the reference system and expresses AG as... 

The phase relations for quasi-binary solutions outlined in Section 1 are general and exact under the basic assumptions made. However, the computational work with them becomes exponentially difficult as the number of components increases. In fact, it is virtually impossible to solve the phase equilibrium equations for solutions of actual synthetic polymers, which contain an almost infinite number of components. We thus need a novel approach to analyze phase equilibrium data on such systems. The discipline called continuous thermodynamics has emerged to meet this requirement. It deals with mixtures of molecules whose physical properties such boiling point, molecular weight, and so forth vary continuously, and is the correct method for treating solutions of a truly polydisperse polymer (see Section 1.1 of this chapter for its definition). 

It would be desirable to apply analytical expressions for the activity coefficient, which are not only able to describe the concentration dependence, but also the temperature dependence correctly. Presently, there is no approach completely fulfilling this task. But the newer approaches, as for example, the Wilson [13], NRTL (nonrandom two liquid theory) [14], and UNIQUAC (universal quasi-chemical theory) equation [15] allow for an improved description of the real behavior of multicomponent systems from the information of the binary systems. These approaches are based on the concept of local composition, introduced by Wilson [13]. This concept assumes that the local composition is different from the overall composition because of the interacting forces. For this approach, different boundary cases can be distinguished ... 

Transformations between types of fluid phase behavior is closely related to the so-called Tamily concept, originally introduced by Schneider [8,9]. A transformation of type-II throu type-IV to type-III fluid phase behavior is known to occur, for example, for the series of binary systems CO2 + alkane with increasing carbon number of the alkane. The system CO2 + dodecane shows type-II [10], the system CO2 + tridecane belong to type-IV [11] and the system CO2 + tetradecane shows type-III fluid phase behavior [22]. A summary of all binary CEP data for the systems CO2 + alkane can be found in Miller and Luks [12]. A quasi-binary investigation of the system CO2 + alkane by de Loos et al. [13] indicated the occurrence of one TCP and one DCEP. Stamoulis [14] estimated the TCP at N p = 12.33 and Ttcp = 317.5 K, and the DCEP at Ndcep = 13.55 and Tdcep 296.0 K. Note, that in this theoretical (quasi-binary) approach the carbon number of the alkane does not necessarily have to take integer values, but can be considered as a continuous variable. 

Since we have only one non-stoichiometric solid phase, we will approach the study of this system by quasi-chemistiy of structure elements. However, this approach presents some difficulties. Indeed, hydrated salts are relatively conplex solids with at least three principal components the anion (itself often complex), the cation, and water. If salt admits several limiting hydrates, water molecules are not all equivalent. All these complexities require a simplification of the representation of solid. With this intention, we consider hydrated solids as pseudo-binary (see section 2.4.1) of which one of the components is the water concerned with dehydration and the other component is the skeleton of anhydrous salt or incorporates possible n molecules of water not implicated in the equilibrium under study. We will disregard specific defects related to the skeleton and thus take into account the following structure elements ... 

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