Crystalline polymers equilibrium melting point

Generally, the crystalline melting point of a polymer corresponds to a change in state from a solid to a liquid and gives rise to an endothermic peak in the DSC curve [3,9], The equilibrium melting point may be defined as... 

Using Flory-Huggins theory it is possible to account for the equilibrium thermodynamic properties of polymer solutions, particularly the fact that polymer solutions show major deviations from ideal solution behavior, as for example, the vapor pressure of solvent above a polymer solution invariably is very much lower than predicted from Raoult s law. The theory also accounts for the phase separation and fractionation behavior of polymer solutions, melting point depressions in crystalline polymers, and swelling of polymer networks. However, the theory is only able to predict general trends and fails to achieve precise agreement with experimental data. 

When the melt of a crystalline polymer is cooled to a temperature between the glass-transition and the equilibrium melting point, the thermodynamic requirement for crystallization is fulfilled. 

The formation of miscible rubber blends slows the rate of crystallization (Runt and Martynowicz, 1985 Keith and Padden, 1964) when one of the components is crystallizable. This phenomenon accounts for data that show lower heats of fusion that correlate to the extent of phase homogeneity (Ghijsels, 1977) in elastomer blends. Additionally, the melting behavior of a polymer can be changed in a miscible blend. The stability of the liquid state by formation of a miscible blend reduces the relative thermal stability of the crystalline state and lowers the equilibrium melting point (Nishi and Wang, 1975 Rim and Runt, 1520). This depression in melting point is small for a miscible blend with only dispersive interactions between the components. 

Fig. 10.1 Illustration of (a) DSC curves corresponding to crystallization Tc and melting of polymers upon cooling and heating processes, respectively (b) ftee energy curves of amraphous and crystalline states of polymers, with the equilibrium melting point given by the crossover of two curves. The arrows indicate the phenomenon of supercooling...

Growing numbers of commercial materials are blends of two or more polymers in which at least one of the components is a crystalline polymer. The crystallization in miscible blends is restricted to temperatures between the blend glass transition temperature and the equilibrium melting point, T ,e, i.e., to the crystallization temperature, Tc < Tm e- The difference, Dc = T ,e - Tc, depends on the cooling rate and the nucleation process. There are three mechanisms of the crystallization nucleation (Utracki 1989) ... 

Polymer crystallization and melting are typically first-order phase transitions between the amorphous phase and the crystalline phase. When these two phases are in thermodynamic equilibrium, two phase transitions are thermodynamically reversible under a certain temperature. This temperature is referred to the equilibrium melting point of polymer crystallization. The free energy changes of amorphous phase and crystalline phase under various temperatures are depicted in Fig. 4.1, illustrating the definition of the equilibrium melting point 7. ... 

At the equilibrium melting point, the chemical potential of polymers in the amorphous phase is equal to that in the crystalline phase jf, thus... 

The equilibrium melting point (T ) of a crystalline polymer is the lowest temperature at which macroscopic equilibrium crystals completely melt (Prime and Wunderlich 1969 Prime et al. 1969). 

The heat of fusion of 100% crystalline polymer, or as it is sometimes called, the equilibrium heat of fusion (AHl), is the heat of fusion of the equilibrium polymeric crystals at the equilibrium melting point (the heat of fusion of 100% crystalline polymer depends somewhat on the melting temperature that is why AHf is given at T ). 

Taking the fully ordered extended chains as the ground state, and considering bulk polymers with infinitely long polymer chains, r -> oo, = 0, n = m2, one can get the free energy of the amorphous state from Equation 13.9, and let it to equal that of the ground crystalline state (zero). The equilibrium melting point of bulk polymers is approximately derived as... 

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