Crystal growth equilibrium melting temperatur

Large variations of the thermodynamic parameters, such as surface free energy of crystals and equilibrium melting temperature, and the overall crystallization kinetics (depending on the combined effect of primary nucleation and growth) are generally observed for mis-... 

Primary crystallization occurs when chain segments from a molten polymer that is below its equilibrium melting temperature deposit themselves on the growing face of a crystallite or a nucleus. Primary crystal growth takes place in the "a and b directions, relative to the unit cell, as shown schematically in Fig. 7.8. Inevitably, either the a or b direction of growth is thermodynamically favored and lamellae tend to grow faster in one direction than the other. The crystallite thickness, i.e., the c dimension of the crystallite, remains constant for a given crystallization temperature. Crystallite thickness is proportional to the crystallization temperature. 

The expression for Gi nicely shows its nonmonotonic dependence on the crystallization temperature. Close to the equilibrium melting temperature, the growth is nucleation-dominated and is given essentially by Gi, . For temperatures far below T , but closer to Tq, the Gi d term dominates and the growth rate precipitously decreases with supercooling. 

As a melt is cooled below its liquidus (the equilibrium melting temperature of the crystalline phases), the nucleation rate is initially small because AG /T is large. Further cooling reduces AG jT until it approximately equals Q/T. At this temperature, the maximum nucleation rate occurs. Further cooling increases Q/T relative to AG /T that is, diffusion becomes the limiting factor, and nucleation eventually stops. Because the maximum nucleation rate often occurs at a lower temperature than the temperature at which the crystal growth rate is maximum, numerous nuclei can form. 

The first term represents the diffusion of chains to the growth front while the second is related to the secondary nucleation barrier. Go represents a preexponential factor, U is the activation energy for chain mobility, R is the gas constant, Tc is the isothermal crystallization temperature and Ar=T — TV is the supercooling (T is the equilibrium melting temperature). Too is the temperature where viscous flow ceases (AT —30A) and/is a temperature correction factor defined as 2TV / (T -)- TV), while Kg is the nucleation constant (which is proportional to the energy barrier for secondary nucleation) given by ... 

Central to most crystallization is the idea of an equilibrium melting temperature, J, above which crystallization does not occur. The rate of crystal growth is therefore related to the extent to which supercooling (AT) occurs and is defined by... 

Fig. 6. A graph of the variation in growth rate with temperature for poly(hydroxybutjrrate), showing the tjrpically observed bell-shaped temperature dependence, with the crystallization rate reducing to zero well before the equilibrium melting temperature ( 198°C for this poljrmer) and, after passing through a maximum, again reducing to zero before the glass-transition temperature ( 0 = C). (Unpublished data of the author.)...

Solid layer crystallization is a process in which the growth of a crystal layer takes place perpendicular to a cooled surface into the bulk of a melt (sophase change is used as the basis for the separation of the feed mixture. Such a phase separation is possible due to different equilibrium concentrations of the solid and liquid phases of the mixture (see Chapter 3). The driving force for the crystal growth is the temperature difference between the equilibrium temperature of the melt (the bulk) in front of the soUd layer and the temperature of the cooled surface (see Figure 15.2). 

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