Polymer-diluent mixtures equilibrium

In this chapter we have found that for melting and phase equilibrium theory the same basic principles that are applicable to low molecular weight species also apply to polymers. In fact, a rather good measure of success is achieved. The only special treatment afforded to polymers is the formulation of the free energy of mixing of polymer and diluent. This also follows basic principles.(l) It is important to recognize that no new basic laws have had to be developed to understand the melting behavior of polymer-diluent mixtures. 

The first two terms on the right-hand side of Eq. (7.18) are identical to those obtained for the non-cross-linked polymer-diluent mixture at the same composition. The remaining terms represent the contribution of the elastic free energy of the mixed phase. For an open system, the composition of the mixed phase V2 is determined from Eq. (7.13), which specifies the swelling equilibrium.(34) Therefore V2 is an equilibrium quantity and should be so designated. It can be identihed with the reciprocal of the equilibrium swelling ratio at T = T. For a closed system, where... 

The melting-crystallization cycle of an oriented network that is conducted under equilibrium conditions results in a reversible contractile system when the force is held fixed. Alternatively, large changes in the tension are observed when the length is held constant. These two complementary observations are inherent properties of all types of macromolecular systems. The above analysis has been limited to apure one-component homopolymer of uniform cross-section. However, it can be extended, in a straightforward manner to include inhomogeneous fibers, copolymers, and polymer-diluent mixtures.(4)... 

This portion of the chapter can be summarized by noting that there is a substantial body of evidence demonstrating that formal phase-equilibrium thermodynamics can be successfully applied to the fusion of homopolymers, copolymers, and polymer-diluent mixtures. This conclusion has many far-reaching consequences. It has also been found that the same principles of phase equilibrium can be applied to the analysis of the influence of hydrostratic pressure and various types of deformation on the process of fusion [11], However, equilibrium conditions are rarely obtained in crystalline polymer systems. Usually, one is dealing with a metastable state, in which the crystallization is not complete and the crystallite sizes are restricted. Consequently, the actual molecular stmcture and related morphology that is involved determines properties. Information that leads to an understanding of the structure in the crystalline state comes from studying the kinetics and mechanism of crystallization. This is the subject matter of the next section. 

Based on a lattice model, Flory (10) treated the general case of N homopolymer molecules, each having exactly x repeating units, admixed with n molecules of a low molecular weight species. The composition of the mixture is characterized by the volume fraction of polymer v. Since in general the diluent will be structurally different from the polymer repeating unit it is assumed to be excluded from the crystal lattice. The objective of the calculation is to calculate the free energy of fusion under equilibrium conditions. 

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