Equilibrium melting temperature using Thomson-Gibbs equation

Thermal analysis data on lamellar crystals of polyethylene over a wide range of thicknesses are plotted in Fig. 2.90. The Gibbs-Thomson equation is a good mathematical description of the observed straight line and can be used to calculate the equilibrium melting temperature by setting C = (t ° = 414.2 K). Also, the ratio of the surface free energy to the heat of fusion can be obtained from the equation. 

Despite the shortcomings that have been described, efforts have been made to explain isomorphism and isodimorphism based on the theories that have been outlined. Equilibrium theories as embodied in Eqs. (5.33) and (5.35) will require equilibrium melting temperatures, or approaches thereto. Observed melting temperatures can be used with nonequiUbrium theories. Unfortunately, for cases where it has been established that co-units enter the lattice, the proposed equilibrium theories have been tested with directly observed melting temperatures. In some instances, attempts to account for the small crystallite thicknesses have been made by invoking the Gibbs-Thomson equation.(16) However, there are other factors that cause the observed melting temperatures to be reduced from the required equilibrium ones. 

In this study the universal empirical values of U = 1500 cal/mol and = Tg-SOK was used for the kinetic analysis of P(3HB-co-3HH) samples. In addition, the value of 194 °C, determined by the Gibbs-Thomson equation has been used for the equilibrium melting temperature T, of P(3HB-co-3HH) copolyesters with different compositions in consideration of the same crystal structure of copolyesters. 

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