Lamellar crystallization force

Figure 9.22. Scanning force microscopy images of polyethylene films formed on a model planar chromium polymerization catalyst. The small white stripes are lamellar crystals. These form the well-known spherulite superstructure upon crystallization from the...

The barrier factor, i.e. the expression before the bracket, decreases exponentially with increasing stem length l and the driving force factor (the term in brackets) increases with l (see Fig. 6). The product G has a maximum at an l value which is considered as the kinetically determined lamellar crystal thickness in polydisperse polymers. G becomes positive at the minimum stable fold length /mjn ... 

It is known that in a solid state polymerization occurs along the certain axis of the monomer crystal and extended chain crystals are formed [146]. In the polymerization from liquid phase, on the other hand, lamellar crystals are formed. This indicates that back-biting reaction proceeds not at random but in a specific manner, forced by the nature of crystals. The model of growth of lamellar crystals of polyoxymethylene is known [147]. According to this model, the subsequent layers are formed on the surface of the crystal by growth of folded chain as shown schematically below ... 

The low inter-lamellar attractive forces in molybdenum disulphide consist only of weak Van der Waals forces. In addition the separation distance between the sulphur layers of adjacent lamellae is 3.49A, and is larger than the 3.1 A thickness of an individual lamella. Cleavage or shear of molybdenum disulphide crystals between adjacent lamellae is therefore inherently likely to be easy. 

Faint contrast in the error signal is a good indication for an optimized feedback loop. At the same time the dimension and the habit and possible defects of the crystal, including the fold domain boundaries, are very well visualized. For several polymers including PE [49] and poly(4-methyl-l-pentene) [50], the friction forces measured on the surface of the lamellar crystals obtained from solution are anisotropic (Fig. 3.20 bottom right). This anisotropy is related to the direction of the folds on the crystal surface. 

Fig. 10.28 Height image of torsional tapping atomic force microscopy on a sheared PE film with the shear direction from down-right to up-left (Mullin and Hobbs 2011). The circle indicates the wedge-shaped profile at the growth front of lamellar crystals (Courtesy of Jamie Hobbs)...

Platelet- or needle-shaped particles, often inorganic crystals, can associate via van der Waals forces to form a framework interpenetrated by liquid. The possibility that large, folded-chain lamellar crystals could fulfil a similar role and form a colloidal framework has not been reported, but the formation of other types of network involving folded-chain crystals has been studied (see subsection on... 

Solution-grown single lamellar crystals of, eg, PEO (147), POM (148), PE (149,150), syndiotactic PP, poly(dimethyl silane) (151), poly(4-methyl-pentene) (152), and poly[(i )-3-hydroxybutyrate] (153) deposited onto solid substrates have been studied by SFM. The habit and thickness of the lamellae in flat-on projection are directly accessible and in addition to these data, which have previously been typically provided by TEM in conjunction with shadow evaporation techniques (4), more subtle details of domain boundaries and fold direction orientation have been revealed. In Figure 14, the habit of a collapsed PE lamellae is depicted, as well as the anisotropic lateral force recorded in the different fold sectors (154). 

Fig. 14. Contact mode SFM height image of single lamellar crystal of PE deposited on mica (left) and friction image of the same PE lamella (right fnction forces increase from dark to bright contrast). Reprinted in part with permission from Ref. 154. Copyright (1999) American Chemical Society.

In the present multiscale approach, SAXS data analysis reveals that already at low deformations (lower than e(start)) the lamellar crystals oriented with their normal parallel to the tensile force, in order to alleviate compressive transversal stress, undergo buckling instability, with consequent formation of undulated chevron-like super-structures (Fig. 11.12b ). However, at deformations close to e(end) up to the breaking the effect of lamellar stacking and parallel orientation of the lamellar normal to the stretching direction on the SAXS intensity becomes buried by the large diffuse scattering localized on the equator due to cavitation (Fig. 11.12c"). 

Figure 9. Friction force image (left, z-scale dark 0.0 V - bright 0.5 V) and adhesion force image (right, z-scale bright 1 nN - dark 60 nN) on PE lamellar crystal obtained in water. The contrast in the adhesion images is defined on the basis of the convention that attractive forces are negative.

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