Upon aging, a collapsed long chain evolves from a crumpled state to a self-entangled globule which can be thought of as a large knot. Swelling of an equilibrium globule in good solvent is a two-step process: (i) fast swelling into an arrested stretched structure with conserved entanglement topology followed by (ii) slow disentanglement. Using computer simulation, we found both mass-mass (m-m) and entanglement-entanglement (e-e) power law correlations inside the swollen globule. The m-m correlations are characterized by a set of two exponents in agreement with a Flory-type argument. The e-e correlations are also characterized by two exponents, both of them larger (by $\sim 0.3$) than the related m-m exponents. We interpret this difference as evidence of distance-dependent repulsion $E=-0.3\ln (\rho )k_{B}T$ between entanglements sliding along the polymer chain.

• Received 27 February 2003

DOI:https://doi.org/10.1103/PhysRevLett.90.225504