Crystallization adjacent reentry model

Fig. 11-4. Possible conformations of poly inerchains al the surfaces of chain-folded single crystals, (a) Adjacent reentry model with smooth, regular chain folds, (b) adjacent reentry model with rough fold surface, and (c) random reentry (switchboard) model.

From all these data analyses, we can definitely say that the D and H chain stems are distributed statistically randomly in the crystalline lamellae of the D/H cocrystallized blend. This conclusion is quite important in relation with the chain-folding problem, a controversial research theme that had been discussed for a long time (30). The random distribution of the D and H chain stems naturally supports the idea that the D and H chains reenter randomly into and out of the crystalline lamellae as shown in Fig. 5.7. The regular adjacent reentry model is impossible to apply at all as for as the melt-crystallized sample is concerned. 

Figure 2.7 Folded-chain models for single crystals, (a) Regular adjacent reentry (b) nonregular random reentry.

In Sect. 3 a set of experimental data on cyclic molecules is described supporting the basic discussions of Sects. I and 2. Central are the cycloalkanes that ultimately serve as a model for adjacent reentry, sharply folded polyethylene crystals. Chain-folded polyethylene was shown in the early 1960 s to thicken in the crystalline state by straightening as many as 100 to 1000 folds when brought to elevated pressure and temperature. This surprising observation found its explanation in the fast reptation possible in the condis-crystal state. 

FIGURE 11.5 Schematics of possible chain morphology in a single polymer crystal (a) regular folding with adjacent reentry of chains, (b) switchboard model with random reentry of chains. 

Physical Properties. All polyethylene above 0.86 g/cm density is semicrystalline. The basic crystalline structure for most commercial LLDPE is chain-folded lamellae (Fig. 7). The body of the crystal consists of polymer backbone segments, and the surfaces are a collection of chain folds, loose cilia, and tie chains (chains incorporated into more than one crystal). When crystallized isothermally, it has been foimd that 95% of the lamellae in a given sample are within 5% of the same thickness (10). There is some debate over the mechanism of chain folding and of the subsequent fold loops. The most likely model includes adjacent reentry, loose adjacent reentry, and nonadjacent reentry. Short-chain branch length... 

The Folded-Chain Model This led to the folded-chain model, illustrated in Figure 6.10 (41). Ideally the molecules fold back and forth with hairpin turns. W ile adjacent reentry has been generally confirmed by small-angle neutron scattering and infrared studies for single crystals, the present understanding of bulk crystallized polymers indicates a much more complex situation (see below). 

The result was a type of block copolymer with alternating epoxy and double-bonded segments. NMR analyses showed that for the two samples studied the chain-folded portion was about 2.4 and 3 mers thick, whereas the stems were 15.2 and 40.8 mers thick, respectively. Since the number of mer units to complete the tightest fold in this polymer has been calculated to be about three (51), the NMR study strongly favors a tight adjacent reentry fold model for single crystals. 

Recent quantitative calculations of the absolute scattering intensities expected from various crystallite models for single crystals by Keller (121) and Yoon and Flory (125-127) (Figure 6.34) on polyethylene suggested that the model for adjacent reentry does not correlate with experiment. Rather, Yoon and Flory put forward a model requiring a stem dilution by a factor of 2-3. The calculated scattering functions are shown in Figure 6.34 this leads to the... 

Melt-Crystallized Polymers Upon crystallization from the melt, an entirely different result emerges. Experiments by Sadler and Keller (120-122) showed that nearly random stem reentry was most likely that is, some type of switchboard model was correct. Quantitative calculations by Yoon and Flory (125-127) and by Dettenmaier et al. (128,129) on melt-crystallized polyethylene (130) and isotactic polypropylene (131) also showed that adjacent reentry should occur only infrequently on cooling from the melt. 

On the other hand, Hoffman (76) showed that the density of the amorphous phase is better accounted for by having at least about 2/3 adjacent reentries, which he calls the variable cluster model. An illustration of how a chain can crystallize with a few folds in one lamella, then move on through an amorphous region to another lamella, where it folds a few more times and so on, is illustrated in Figure 6.36 (124). Thus a regime III crystallization according to the variable cluster model will substantially retain its melt value of Rg. 

Figure 7. Adjacent reentry and regular sharp fold model (a) and random reentry fold model (switchboard model) (b) at the surface of HDPE single crystal.

---