ON THE NUMBER OF INTERSECTIONS OF SELF-REPELLING POLYMER-CHAINS

We give a detailed analysis of the intersection properties of polymers . Using the renormalization group we provide a full crossover function for the dependence of the number of intersections in a single polymer on chain length and excluded volume strength. We compare our results with Monte-Carlo data and with exact calculations for a random walk, f inding good agreement in ail respects. Restricting to the vicinity of the eight ternary fixed points we also calculate the number of interse ctions between two chains placed at a fixed distance. including tile t wo halves of a block-copolymer. The analysis of these systems confirms the interpretation of the different contributions to the number of in tersections in a single chain. Due to the highly nontrivial character of the correlations in a polymer chain the correction exponents in bot h cases however are different. None of the results can be extracted fr om any Flory-type estimate.