Crystalline lamellae, defined

Gupta et al. investigated Rigidex 9 in parallel with the studies of low density polyethylene already reviewed. X-ray observations were interpreted as showing a structure after annealing of crystalline lamellae at about 45° to the stretch direction. The lamellae are poorly defined in cold-drawn specimens, which showed also some orientation of noncrystalline material. 

Because of chain inextensibility, the shear rate of any slip system is not dependent on the normal-stress component in the chain direction (Parks and Ahzi 1990). This renders the crystalline lamellae rigid in the chain direction. To cope with this problem operationally, and to prevent global locking-up of deformation, a special modification is introduced to truncate the stress tensor in the chain direction c. Thus, we denote by S° this modification of the deviatoric Cauchy stress tensor S in the crystalline lamella to have a zero normal component in the chain direction, i.e., by requiring that 5 c,c = 0, where c,- and c,- are components of the c vector (Lee et al. 1993a). The resolved shear stress in the slip system a can then be expressed as r = where R is the symmetrical traceless Schmid tensor of stress resolution associated with the slip system a. The components of the symmetrical part of the Schmid tensor / , can be defined as = Ksfw" + fs ), where if and nj are the unit-vector components of the slip direction and the slip-plane normal of the given slip system a, respectively. 

We note that representing the rubbery behavior of the amorphous component between crystalline lamellae by the formaUsm of rubber elasticity is done primarily for operational expediency because it successfully represents the macroscopic mechanical response. Clearly, caution is required in the literal interpretation of the behavior of this well-defined material on the molecular level by consideration of it as a rubber. 

In the case of crystalline polymers such as high density polyethylene (FiDPE), the effect of orientation on the morphology has been extensively studied [32,48]. The isotropic sample consists of crystalline lamellae (thickness 100-400 A) embedded in an amorphous matrix. Each lamella is composed of a mosaic of crystalline blocks of lateral dimension 100-200 A with boundaries defined by dislocations. The lamellae are randomly oriented and generally arrange themselves end to end in ribbon-like structures which grow out from nucleating centers to form... 

For semicrystalline polymers, melting temperature (Tu) is correlated to the thickness of crystalline lamellae. If all other variables are held constant, thinner lamellae will melt at lower temperatures than thicker ones. Thus, the melting temperature Tu, defined as the maximum temperature within a melting regime M, can be used to approximate the lamellar thickness. Within the first DSC run curves of polypropylenes prepared by 9a, typically several melting transitions. Mi, M2, and M3, with maxima 7mi, Tm2, and Tu, can be seen (Figure 9.13). 

Semicrystalline materials are often considered as composite materials at a nanoscale and then the use of micromechanical models to predict the macroscopic properties is quite natm al. But semicrystalline materials camiot be put so easily in one of the three classical previous modeled families defined for composites and polycrystalline materials because the crystalline microstructure is complex and organized at several scales. Therefore, the first question is At which scale do we have to consider this composite material At a microscale, that is the scale of the crystalline microstructure (spherulites, shish-kebabs) Or at the nanoscale of the crystalline lamellae ... 

The thickness of the amorphous regions is probably defined by the minimum distance, two independently growing nuclei can have to each other. This value is obviously not influenced by the temperature. Above 235 °C, la seems to increase at expense of the crystalline regions. The sample is in a partially molten state, which leads to the existence of amorphous islands. It could be shown that these islands are filled with smaller lamellae, when the temperature is decreased so far that they can become thermodynamically stable. 

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