Branching of Lamellae

In the initial stage of the crystallization, the formation of a skeleton of dominant lamellae of equal widths separated by the melt is clearly visible as shown in Fig. 12a. The onset of branching is also visible in Fig. 12a. As the crystal grows, the hedrite becomes more asymmetrical with respect to the central dominant lamellae because it is tilted with respect to the surface (c.f., Fig. 12b-d). The dynamics of this space filling can clearly be observed in Fig. 12c,d. The subsidiary lamellae originating from the edge of the skeleton eventually develop a dominant character. 

The appearance and disappearance of some of the induced nuclei suggest that they are formed at the surface as a result of a trapped polymer chain in the parent lamellae. In addition when a polymer crystallizes very quickly, stresses 

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FIGURE 4.7 Sphenilite crystals (a) appearance between crossed polarizing Hlters (b) branching of lamellae (c) orientation of chains in lamellae. 

Maltese cross (Blanshard, 1979). The crystallinity of starch is caused essentially by amylopectin pol)Tner interactions (Banks and Greenwood, 1975 Biliaderis, 1998 Donald, 2004 Hizukuri, 1996). An illustration of currently accepted starch granule structure is given in Fig. 5.5. It is believed that the outer branches of amylopectin molecules interact to arrange themselves into "crystallites" forming crystalline lamellae within the granule (Fig. 5.5 Tester et al., 2004). A small number of amylose polymers may also interact with amylopectin crystallites. This hypothetical structure has been derived based on the cluster model of amylopectin (Hizukuri, 1986 Robin et ah, 1974 Fig. 5.1). 

Much effort has been devoted to investigating the detailed architectures and the construction of spherulites. Early investigations of the crystallization of polymers through optical microscopy (OM) [7,8] posited that polymer spherulites consisted of radiating fibrous crystals with dense branches to fill space. Later, when electron microscopy (EM) became available, spherulites were shown to be comprised of layer-like crystallites [9,10], which were named lamellae. The lamellae are separated by disordered materials. In the center of the spherulites, the lamellae are stacked almost in parallel [5,6,11-15]. Away from the center, the stacked lamellae splay apart and branch, forming a sheaf-like structure [11,13-15]. It was also found that the thicknesses of lamellae are different [5,6,11,12]. The thicker ones are believed to be dominant lamellae while the thinner ones are subsidiary lamellae. 

Fig. 20 a A schematic illustrating the branching of a founding lamella and b a plot of the reciprocal of induction time for subsidiary lamellae as a function of crystallization temperature [64]... 

Fig. 21 In-situ phase images of a BA-C10 film showing the lamellar branching at different temperatures a and b no branching at 80 °C c and d branching largely at the tips of lamellae when the temperature is quenched to 35 °C [64]. The time interval between a and b was about 106 min...

Early flow-visualization studies revealed the various mechanisms for creation and destruction of lamellae and dispersions during flow through porous media. Starting with these studies, rapid progress has recently been made in mathematically describing pore-level mechanisms. These descriptions form the basis for two divergent, but complementary branches of research, both of which are needed for soundly engineered field use. 

Foam (5) is a collection of gas bubbles with sizes ranging from microscopic to infinite for a continuous gas path. These bubbles are dispersed in a connected liquid phase and separated either by lamellae, thin liquid films, or by liquid slugs. The average bubble density, related to foam texture, most strongly influences gas mobility. Bubbles can be created or divided in pore necks by capillary snap-off, and they can also divide upon entering pore branchings (5). Moreover, the bubbles can coalesce due to instability of lamellae or change size because of diffusion, evaporation, or condensation (5,8). Often, only a fraction of foam flows as some gas flow is blocked by stationary lamellae (4). 

Within a BPE with a distribution of branches, there will be a distribution of lamella thickness. This will result in a broad melting range. BPE with a bimodal distribution of branches will have a bimodal distribution of lamella thickness and a corresponding melting temperature range. When two polyethylenes are blended, assuming they are miscible, they will cocrystallize only where they have common MSL. Some molecular segments in each BPE will crystallize independently of... 

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