Perimeter length and form factor in two-dimensional polymer melts
H Meyer and T Kreer and M Aichele and A Cavallo and A Johner and J Baschnagel and JP Wittmer, PHYSICAL REVIEW E, 79, 050802 (2009).
Self-avoiding polymers in two-dimensional (d=2) melts are known to adopt compact configurations of typical size R(N)similar to N(1/d), with N being the chain length. Using molecular-dynamics simulations we show that the irregular shapes of these chains are characterized by a perimeter length L(N)similar to R(N)(d)(p) of fractal dimension d(p)=d-Theta(2)=5/4, with Theta(2)=3/4 being a well-known contact exponent. Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all arclengths s down to a few monomers. The Kratky representation of the intramolecular form factor F(q) reveals a strong nonmonotonous behavior with q(2)F(q)similar to 1/(qN(1/d))(Theta)(2) in the intermediate regime of the wave vector q. Measuring the scattering of labeled subchains the form factor may allow to test our predictions in real experiments.
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