Crystalline state fusion thermodynamics

Flory, P. J. (1949). Thermodynamics of crystallization in high polymers. IV. A theory of crystalline states and fusion in polymers, copolymers, and their mixtures with diluents. 

Flory and Garrett have analyzed the fusion of a particular collagen, rat tail tendon, in detail. (207) The appropriate thermodynamic quantities involved in fusion are given in Table 6.1. These quantities, characteristic of this naturally occurring polymer, are similar to those characteristic of synthetic polymers. Both the heat and entropy of fusion appear to be normal. The heat of fusion, on a weight basis, is similar to that of the synthetic poly(amides). Any enhanced stability endowed to the crystalline state of the polymer by virtue of hydrogen bond formation is not in evidence, unless this contribution is much smaller than beUeved. 

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. 

Thermodynamic approaches provide powerfiil tools to characterize the properties in identifying these metastable states to imderstand the effects of phase size, dimensionality, and composition on the materials properties. One well-known example is the density gradient column method to determine densities of semicrystalline polymers. Based on known equilibrium crystalhne and amorphous densities, the crystallinity of a semicrystalline sample can be calculated by using equations 4 and 5. However, it should be noted that the determination of these equilibrium density data is not trivial. Proper extrapolations are necessary to ensure the equilibrium nature of the results. Detailed issues discussed can be foimd in Reference 146. Another commonly used method is to measure the heat of crystallization or fusion by using dsc. By knowing the equilibrium heat of fusion, the crystallinity of a sample can be easily calculated. 

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