Core Thermodynamic Relationships

Chapter 3 starts with the laws, derives the Gibbs equations, and from them, develops the fundamental differential thermodynamic relationships. In some ways, this chapter can be thought of as the core of the book, since the extensions and applications in all the chapters that follow begin with these relationships. Examples are included in this chapter to demonstrate the usefulness and nature of these relationships. 

The second important characteristic of the micellar solution that relates to solubilization is the micelle size. Poor aqueous soluble compounds are solubilized either within the hydrocarbon core of the micelle or, very commonly, within the head group layer at the surface of the micelle or in the palisade portion of the micelle. Predictions of the micelle size have relied on the use of empirical relationships employed within a thermodynamic model, for instance the law of mass action where micellization is in equilibrium with the associated and unassociated (monomer) surfactant molecules (Attwood and Florence, 1983). 

In summary, the predictions of analytic PRISM theory [67] for the phase behavior of asymmetric thread polymer Uends display a ly rich dependence on the single chain structural asymn try variables, the interchain attractive potential asymmetries, the ratio of attractive and repulsi interaction potential length scales, a/d, and the thermodynamic state variaUes t) and < ). Moreover, these dependences are intimately coupled, which mathematically arises within the compressible PRISM theory from cross terms between the repulsive (athermal) and attractive potential contributions to the k = 0 direct correlations in the spinodal condition of Eq. (6.6). The nonuniversality and nonadditivity of the consequences of molecular structural and interaction potential asymmetries on phase stability can be viewed as a virtue in the sense that a great variety of phase behaviors are possible by rational chemical structure modification. Finally, the relationship between the analytic thread model predictions and numerical PRISM calculations for more realistic nonzero hard core diameter models remains to be fully established, but preliminary results suggest the thread model predictions are qualitatively reliable for thermal demixing [72,85]. 

The equilibrium swelling with Z-j of both shell and core may be calculated thermodynamically utilizing the following relationship ... 

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