Summary of thermodynamics

Since SANS has a limited -range, in practice 5(0) and are determined by fitting data to Eq. (4.93), as shown in Fig. 4.13. 

The astute reader will recognize that the scattering function for polymer blends [Eq. (4.86)] is defined in a subtly different manner than for polymer solutions [Eq. (3.126)]. In both cases, the scattering function is normalized by the number of monomers in the system. In Section 3.5, monomers occupy volume fraction (j) of the total volume, while in the blend the combined volume fraction of monomers of type A and B is unity. The scattering function of Section 3.5 is related to that of the present section as S(q)l4 . To facilitate comparison, we rewrite Eq. (4.88)  

In this chapter, the thermodynamics of binary mixtures was discussed in the framework of a lattice model. For simplicity, polymers were divided into monomers that fit onto this lattice and the free energy of mixing was written per lattice site (AFniix). Rescaling the monomers to more conventional definitions (such as either the chemical monomer of Chapter 1 or the Kuhn monomer of Chapter 2) is trivial because the volume of an A chain V/y — Nf Vn and the volume of a B chain vr = ApVn 

For this reason, the binodal is often referred to as the cloud point. 

The free energy of mixing has two parts entropic and energetic. The entropic part per unit volume,------------------------------------------------ 

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Units of Energy 209. The First Law of Thermodynamics 210, Entropy Production Flow Systems 214. Application of (he Second Law 216. Summary of Thermodynamic Equations 223. 

Summary of Thermodynamic Relations (Basis Unit mass of Fluid)... 

Fig. 21 Schematic summary of thermodynamic phase behaviour for neat, composition-ally symmetric PI-fc-PS-fc-PDMS (ISD) and PS-fc-PI-fc-PDMS (SID) terpolymers. Heating PI-fc-PS-fc-PDMS or decreasing molecular weight causes transition from three-domain lamellae to hexagonally packed two-domain cylindrical morphologies, followed by disordering. PS-fc-PI-fc-PDMS disorders directly from three-domain lamellar state. From [88], Copyright 2002 American Chemical Society...

The science of thermodynamics deals with energy and its changes. For a useful summary of thermodynamics see P. Atkins, Four Laws that Drive the Universe, Oxford University Press, Oxford, 2007. 

Several of the reference texts and review articles on kinetics give discussions of entropies of activation in terms of structure and mechanism, and it is sufficient here only to refer briefly to a few of them. Values of AS (or its equivalent, frequency factors) for unimolecular gas reactions have been considered in some detail (Benson, 1960b Frost and Pearson, 1961c Gowenlock, 1960). Summaries of thermodynamic data for solution reactions may be found in several sources (Frost and Pearson, 1961d Moelwyn-Hughes, 1947 Pearson, 1952). 

Table 5.2 Summary of thermodynamic relationships among modifications of 5-XII (From Yu et al. 2000, with permission.)...

TABLE 11. Summary of thermodynamic results for hydrogen-bonded complexes of phenols with various bases at 25 °C in different solvents... 

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