Lamellae chain-axis direction

It is known that elevating the crystallization temperature [42,49] or annealing above the crystallization temperature [50] of PE results in a thicker folded-chain lamella of up to —200 nm. In addition to the higher temperature, if high pressure is applied, crystals can grow as thick as several micrometers in the chain axis direction [2-4,51]. 

E and Ec are respectively the (temperature-dependent) Young s moduli of the sample as a whole and of the crystal lamellae in chain axis direction, x is the degree of sample crystallinity. 

Fig. 37 Three dimensional pictures of growing lamellae of Ciooo at 370 K 3 at 0.128 ns, b at 6.4 ns, c at 12.8 ns, and d at 19.2 ns. We again see the tapered growth fronts and their advances in the normal (the z-axis) direction together with the lamella thickening along the chain axis (the y-axis direction)...

Another shortcoming of the present model is that the MD cell size in the y-axis direction, the direction parallel to the crystalline chain axis, was rather small. There must be serious size effects along this direction, even if we adopt the periodic condition in this direction. Here again we need a much larger MD cell in order to reproduce the lamella thickness vs. temperature relation in crystallization from the melt. 

For a moderately crossllnked network, equation (13) predicts a declining stress with lamellae formation from the amorphous melt. A stress Increase can be achieved with this model only by reorientation of the chain axis to the directions perpendicular (or nearly so) to the stress direction. If then this model is suitable for lightly crystalline materials, its behavior is in good accord with the observations of Luch and Yeh (6) on stretched natural rubber networks. They reported simultaneous lamellae formation and declining network stress. 

Lamellae are thin, flat platelets on the order of 100-200 A (0.01-0.02 pm) thick and several microns in lateral dimensions, while polymer molecules are generally on the order of 1,000-10,000 A long. Since the polymer chain axis is perpendicular to the plane of the lamellae, as revealed by electron diffraction, the polymer molecules must therefore be folded back and forth within the crystal. This arrangement has been shown to be sterically possible. In polyethylene, for example, the molecules can fold in such a way that only about five chain carbon atoms are required for the fold, that is, for the chain to reverse its direction. Each molecule folds up and down in a regular fashion to establish a fold plane. As illustrated in Figure 1.14a, a single fold plane may contain many polymer chains. The height of the fold plane is known as the fold period. It corresponds to the thickness of the lamellae. 

Fig. 17.12. Lamella of ) form oriented with the chain axes directed normal to the fiber axis and therefore with the axis, the piling direction of bilayers of chains, parallel to the j-axis (fiber axis, cross-f) orientation)...

In an isotropic polycrystalline polymer whose microstructure consists of stacked lamellae arranged in the form of spherolites, the slip systems activated depend on the local orientation of the lamellae with respect to the applied stress and, as deformation proceeds, these orientations are modified. To calculate the evolution of the crystalline texture, one can consider the polymer to behave as a crystalline aggregate. Although the entropic contribution of chain orientation in the amorphous regions may also need to be considered, the major contribution to work hardening in tension is rotation of the slip planes toward the tensile axis, so that the resolved shear stress in the slip direction diminishes. This results in a fiber texture in the limit of large deformations, such that the crystallites are oriented with their c axis (the chain axis) parallel to the stretch direction. Despite the relative success of such models, they do not explicitly address the micro-mechanisms involved in the transformation of the spherulitic texture into a fiber texture. One possibility is that the... 

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