Complexity of entanglements and degree of folding in branched polymers with excluded-volume interaction

Abstract

A methodology to characterize large-scale shape of macromolecular conformations is generalized and applied to a simple model of branched polymers. The standard global analysis of polymer configurations uses geometric shape descriptors, such as the mean radius of gyration. However, geometric descriptors alone do not depict well the intrincate folding features found in many macromolecules. For a more complete characterization, we employ here a new class of shape descriptors which convey the degree and complexity of the “entanglements” in a branched chain. Recently, the methodology has been applied to study statistical properties of linear polymer chains. In the present work, we extend the technique to branched polymers and analyze the configurational and long-chain behavior of their entanglement descriptors. A family of “stars” (polymers with a single branchpoint) with excluded volume interaction is studied, and the results are contrasted with those for linear chains. The relation between changes in geometric and shape descriptors within the polymer conformational space is presented. The complexity of entanglements for large chains and large stars are compared. The results suggest a similar scaling behavior of the entanglement descriptors for the two polymer architectures. © 1994 John Wiley & Sons, Inc.