Figure 7.

Bond-vector orientation correlation function, c(z) (eq 25), as a function of the number of entanglements z = /L_e along the chain. Lines of equal color are for the same chain stiffness (see legend), full colors are for the longest rings (N = 640), while lines in fainter colors are for chains of shorter contour lengths (see arrow’s direction). The long-dashed lines correspond to the exponential decay typical of linear polymers with local stiffness, namely, , where the values for ⟨ cos θ⟩^ring are reported in Table 1. The short-dashed line is the analytical function for an exactly double-folded polymer filament of contour length = 2L_e (see the text for details).