Polyethylene lamellar thickness

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... 

The estimated value of the free energy of the fold surface (q3 = oy) is 90 mJ/m for polyethylene, whereas that of the lateral surface (ai = a/) is 15 mJ/m. Therefore we expect the lamellar thickness to be 6 times larger than the lateral dimension, specifically, a cylinder shape, instead of a disklike shape. This is in stark contrast to the facts described in Section II. The thermodynamic estimate of lamellar thickness is about two orders of magnitude larger than the observed values for polyethylene and other polymers. In view of this discrepancy, we are led to the conclusion that lamellae are not in equilibrium. 

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... 

Fig. 10. Schematic structure models of the bulk-crystallized polyethylene samples. 1, II, and 111 indicate the crystalline, interfacial, and interzonal regions, respectively. Models A, B, C, D, and E express the molecular crystal, unpeeled crystal, disheveled unpeeled crystal, and lamellar crystals for medium and large molecular weight samples, respectively66), f and x designate the lamellar thickness and the extended molecular chain length, respectively...

Nevertheless, it has subsequently been suggested that, for polyethylene, there could be a phase inversion at small lamellar thickness which could make the hexagonal the precursor of orthorhombic crystallization from the melt even at atmospheric pressure [4]. The basis of this proposal will now be outlined and the conclusion reached that it is inapplicable, in part because the effective fold surface energy during growth of hexagonal lamellae is not sufficiently low. 

The (3 relaxation in polyethylene, which is most prominent in the low-crystallinity LDPE, is associated with the amorphous regions and almost certainly corresponds to what would be a glass transition in an amorphous polymer a diiference in its position in mechanical and dielectric spectra is therefore not surprising. The a relaxation, as discussed in section 7.6.3, is associated with helical jumps in the crystalline regions and, provided that the lamellar thickness is reasonably uniform, might be expected to correspond to a fairly well-defined relaxation time and to a narrow peak in the relaxation spectrum. The dielectric peak is indeed quite narrow, because the rotation of the dipoles in the crystalline regions is the major contribu-... 

In the following figures, further experiments are linked to the annealing and recrystallization of a number of additional polymers. In Fig. 6.81 the increase of lamellar thickness is illustrated on the example of solution-grown polyethylene. The crystals were collected in dried mats. The graph on the right side allows a comparison with data on melt-crystallized and annealed polyethylene (see also Sect. 5.2). Sufficiently mobile and flexible molecules, such as polyethylene, can thicken by chain... 

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