Crystallization temperature lamellar thickness

Figure 4.7. Schematic diagram of the free enthalpy as a function of temperature. For the metastable lamellar crystals, their lamellar thickness, /, is indicated. Compare to Figure 4.3.

The effect of different types of comonomers on varies. VDC—MA copolymers mote closely obey Flory s melting-point depression theory than do copolymers with VC or AN. Studies have shown that, for the copolymers of VDC with MA, Flory s theory needs modification to include both lamella thickness and surface free energy (69). The VDC—VC and VDC—AN copolymers typically have severe composition drift, therefore most of the comonomer units do not belong to crystallizing chains. Hence, they neither enter the crystal as defects nor cause lamellar thickness to decrease, so the depression of the melting temperature is less than expected. 

In the classical Lauritzen-Hoffman theory for the mechanism of polymer crystal growth [106], it is assumed that the observed lamellar thickness corresponds to those crystallites that happen to have the largest growth velocity. However, this picture is hard to reconcile with the experimental observation that the thickness of polyethylene single crystals can be modulated by varying the temperature at which they are grown [117,118]. In fact, simulations by Doye et al. [119,120] suggest that the observed lamellar thickness does... 

Thus, the initial lamellar thickness is inversely proportional to supercooling. Combining Eqs. (1.31) and (1.32), the dependence of lamellar thickness on the crystallization temperature Tc is given by... 

This imphes that for a given lamellar thickness, the melting temperature and the crystallization temperature should be the same. In practice, this is not observed. 

Since A i is proportional to the supercooling, the LH theory predicts that as the crystallization temperature is lowered to a value when Eq. (1.95) is satisfied, the lamellar thickness would diverge. This is referred to as the 8L catastrophe. By taking reasonable experimental values for the various parameters and assuming t / = 1 (no barriers for attachment of each stem), the necessary supercooling for the appearance of this catastrophe is 55 K for polyethylene. This is not observed experimentally. To fix this discrepancy, vf/ is taken to be zero so that... 

The rate of cooling from above the melting temperature has significant effects on lamellar thickness and perfection as well as on physical properties. " There is a progressive increase in lamellar thickness and measured density with slower rates of cooling from 380°C. Quenched specimens, in our work, have a specific gravity of 2.136 g/cm compared to 2.180 0.003 for specimens cooled at die very slow rate of 0.02 deg/min. Annealing a quenched sample for 5 hours at 312°C causes die density to increase to 2.158 g/cm. For perspective, the density of totally noncrystalline PTFE is estimated to be 2.00 and the perfect-crystal density is 2.301 g/cm by X-ray diffraction. 

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