The structure factor of dense two-dimensional polymer solutions

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 approximate to 1/(R(N)q)(2d-ds) 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) similar to 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) similar to 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) similar to N(0)/q, for asymptotically long chains. (C) 2010 Elsevier B.V. All rights reserved.