Fold Period and Crystal Growth Rate

We ve mentioned that the thickness, f, of the secondary nucleus must be bigger than /V if it is to be stable to further growth say by an amount (5/, therefore using Equation 10-36 we can write (Equation 10-40)  

The theory of Lauritzen and Hoffman, perhaps still the most commonly used model for the analysis of polymer crystallization data, then seeks to evaluate c5Z (usually of the order of 40 angstroms) by considering the rates at which stems and folds are successively laid down. We will not go into the details of this derivation, but the expressions that have been derived for the growth rate have the following form at low undercoolings (Equation 10-41)  

FIGURE 10-32 The rate of crystallization versus temperature for a 6000 g/mol poly(ethylene oxide) [redrawn from the data of Kovacs et al., J. Polym. SciPolym. Syrnp. EcL, 59,31 (1977)]. 

The experiments of Kovacs et al. also demonstrate beautifully that although the extended chain crystal is the thermodynamically most stable form, when the undercooling is sufficient, kinetics favors folded chain lamellae. As we have seen, long chain polymers only crystallize at finite rates at high undercoolings, so only form folded chain structures. 

to summarize, the theory predicts that the fold period (thickness) of the crystals increases with decreasing undercooling (i.e., higher temperature), while the rate of primary crystallization increases with decreasing temperature, at least at low undercoolings (more on this in a bit). 

---