The structure factor of dense two-dimensional polymer solutions

Abstract

According to the generalized Porod law the intramolecular structure factor F ( q ) of compact objects with surface dimension d s scales as F ( q ) / N ≈ 1 / ( R ( N ) q ) 2 d − d s in the intermediate range of the wave vector q with d being the dimension of the embedding space, N the mass of the objects and R ( N ) ∼ N 1 / d their typical size. By means of molecular-dynamics simulations of a bead-spring model with chain lengths up to N = 2048 it is shown that dense self-avoiding polymers in strictly two dimensions ( d = 2 ) adopt compact configurations of surface dimension d s = 5 / 4 . In agreement with the generalized Porod law the Kratky representation of F ( q ) thus reveals a nonmonotonous behavior with q 2 F ( q ) ∼ 1 / ( N 1 / 2 q ) 3 / 4 . Using a similar data analysis we argue briefly that melts of non-concatenated rings in three dimensions become marginally compact with d s = d = 3 , i.e. q 2 F ( q ) ∼ N 0 / q , for asymptotically long chains.