ORDER AND LOCALIZATION IN RANDOMLY CROSS-LINKED POLYMER NETWORKS

We study, by molecular dynamics, the onset of order and localization i n randomly cross-linked polymer networks as the number n of cross link s is increased. We find a well-defined critical number of cross links n(c) above which the order parameter q = 1/N Sigma(i) [\exp ik . r(i)\ ](2) increases as q (n - n(c))(beta), with beta approximate to 0.5 for \k\ = 2 pi/L, where L is the length of the computational cell. At the same critical number of cross links, particles in the network become localized around their mean positions. We find that the distribution o f localization lengths P(xi) is a universal function when plotted in t erms of a suitable scaled variable.