The aggregate or pseudo-affine deformation scheme

The last assumption is the pseudo-affine assumption it should be seen immediately that this makes the model somewhat unphysical. It is therefore sometimes called the needles in plasticine model, in which each unit corresponds to a needle and the plasticine corresponds to the surrounding polymer. In spite of this unreality, the model often predicts well the orientation distribution of the crystallites for a drawn semicrystalline polymer. 

The distribution of orientations of the unique axes of the units for this scheme is given simply by equation (11.1) with 6 instead of 6, i.e. 

When (P2(cos 6)) is calculated from equation (11.8) it is found to depend on X as shown in fig. 11.3. The variation of Pn cos,6)) with X is quite similar except that it is slightly concave upwards below Xva2 and (P4(cos0)) has a somewhat lower value than (P2(cos0)) for a given X, as shown in fig. 11.3. Unlike the curves for the affine rubber deformation scheme, which are different for different values of n, these curves have no free parameters, so that they are the same for all polymers. The shapes contrast strongly with those for the rubber model, being concave to the abscissa, whereas the latter are convex. The curves for the affine rubber 

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