Truly polydisperse solution

We denote AG per unit volume of solution by AG. Thermodynamics tells us that AG of a quasi-binary solution is a function of T, p, and 4>i. For a given polymer species it also may depend on the distribution of relative chain length in the polymer mij re. Thus, when the pressure effect is not considered, the basic variables for AG of quasi-binaiy solutions are T, , and /(P) as the basic variables. For a paucidisperse polymer, q is finite and /(P) is represented by q delta functions with different strength, while for a truly poly-disperse polymer, q is infinitely large and /(P) becomes a continuous function of P. Thus, AG for quasi-binary solutions of a truly polydisperse polymer is a functional with respect to /(P), and requites sophisticated mathematics for its treatment. 

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). 

The size-selective precipitation (SPP) was predominantly developed by Pileni [50c]. One example (SPP) is monodisperse silver particles (2.3 nm, 0= 15%), which are precipitated from a polydisperse silver colloid solution in hexane by the addition of pyridine in three iterative steps. Recently, Schmid [52a] has reported the two-dimensional crystallization of truly monodisperse AU55 clusters. Chromatographic separation methods have thus far proven unsuccessful because the colloid decomposed after the colloidal protecting shell had been stripped off [42a]. The size-selective ultracentrifuge separation of Pt colloids has been developed by Colfen [52b]. Although this elegant separation method gives truly monodisperse metal... 

The binodal curve is the boundary between thermodynamically stable and metastable solutions. The term binodal is used in truly binary systems while in actual polydisperse systems the correct denomination is cloud-point curve (CPC). Thus the experimental determination of this boundary always leads to a CPC. 

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