Lamellae growth rate

The model described in Sect. 3.5.1 is a very crude representation of a true three-dimensional lamella, and over the years modifications have been applied in order to make it more realistic. The major assumptions, however, are still inherent in all of them, that is, the deposition of complete stems is controlled by rate constants which obey Eq. (3.83). No other reaction paths are allowed and the growth rate is then given by nucleation and spreading formulae. We do not give the details of the calculations which are very similar, but more complicated, than those already given. Rather, we try to provide an overview of the work which has been done. Most of this has been mentioned already elsewhere in this review. 

The average thickness may easily be measured as the average stem length in the bulk part of the lamella, and the growth rate is the mean distance moved by the growth front during a number of Monte Carlo time-steps, nt, divided by nt. 

Finally, we were led to the last stage of research where we treated the crystallization from the melt in multiple chain systems [22-24]. In most cases, we considered relatively short chains made of 100 beads they were designed to be mobile and slightly stiff to accelerate crystallization. We could then observe the steady-state growth of chain-folded lamellae, and we discussed the growth rate vs. crystallization temperature. We also examined the molecular trajectories at the growth front. In addition, we also studied the spontaneous formation of fiber structures from an oriented amorphous state [25]. In this chapter of the book, we review our researches, which have been performed over the last seven years. We want to emphasize the potential power of the molecular simulation in the studies of polymer crystallization. 

Though the overall crystallinity showed a monotonic increase until around 330 K with lowering temperature, the detailed growth rate of each lamella... 

Fig. 26 Growth of each lamella, the number of atoms in the lamella, vs. time, a at 330 K and b at 350 K. Please notice that the lamellae show quite different growth rates especially at higher temperatures...

At high crystallisation temperatures, the high molar mass polymer crystallised alone. Data for the fold surface free energy obtained from linear growth rate data supported the view that the nature of the fold surface of the dominant lamellae was related only to the molar mass of the crystallising component and was not affected by the composition of the melt. 

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