The role of topological constraints in the kinetics of collapse of macromolecules

It is shown that the kinetics of collapse of a polymer coil consisting of N segments after an abrupt decrease of temperature is a two-stage process if N >> Ne. The first stage takes a time ∼ N2 and leads to the peculiar state — crumpled, or fractal, globule. Any part of a chain of any scale is itself a globule in this state ; these parts are segregated from each other in space due to the non-phantomness of a chain. The chain fold in the crumpled globule is a fractal line with fractal dimension 3, equal to the space dimension. The second stage is a chain knotting ; it is realized by means of reptation-like mechanism of motion, takes a time ∼ N3 and is accompanied by an increase of globule density.