Melting of network-diluent mixtures

The intensity of the electron beam used to examine thin crystalline polymer films by electron microscopy is usually of sufficient intensity to induce cross-linking. It is not surprising, therefore, after initial examination in the crystalline state, that thin films of poly(amides) and polyethylene display ordered structures when subsequently examined in the molten state by this technique. These observations are to be expected. They cannot be construed as evidence that, in general, the liquid state in polymers is an ordered one.(33) The partially ordered liquid represents an interesting, unique situation that results from the nature of the chain arrangement at the time of network formation. 

The free energy change AG for the formation of the mixed phase from its pure components, the pure solvent and the pure isotropic amorphous network, consists of two parts. One is the free energy of mixing AGm and the other is the elastic free energy AGei that results from the expansion of the network structure because of swelling (4,34) 

From the Rory-Huggins theory (34,35) of polymer solutions 

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 

A comparison of Eq. (7.18) with Eq. (3.2) indicates that the melting point depression should be greater for a network than for just a collection of polymer chains of the same constitution at the same concentration. This is due to the contribution from the elastic free energy to Eq. (7.18). However, since the values of p usually encountered are of the order of 0.01 to 0.02 or less, this effect is quite small. It manifests itself only when V2 of the mixed phase becomes less than 0.5. 

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