Perimeter Length and Form Factor of Two-Dimensional Polymer Melts

2009/05/07 by H. Meyer, Meyer, H., T. Kreer +11
Physics and Astronomy · #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft

paper · pdf · doi:10.48550/arxiv.0905.1002

4 pages, 4 figures, accepted for PRE Rapid Communications

arxiv created 2009/05/07 · arxiv updated 2009/12/01

Abstract

Self-avoiding polymers in two-dimensional (d=2) melts are known to adopt compact configurations of typical size R(N) ∼ 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) ∼ R(N)^\dpm of fractal dimension \dpm = d-Θ₂ =5/4 with Θ₂=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 arc-lengths s down to a few monomers. The Kratky representation of the intramolecular form factor F(q) reveals a strong non-monotonous behavior with q²F(q) ∼ 1/(qN^1/d)^Θ₂ in the intermediate regime of the wavevector q. Measuring the scattering of labeled subchains %(s F(q) ∼ L(s)) the form factor may allow to test our predictions in real experiments.

Related

• Conformational properties of strictly two-dimensional equilibrium polymers
• Strictly two-dimensional self-avoiding walks: Thermodynamic properties revisited
• Mapping onto ideal chains overestimates self-entanglements in polymer melts
• Ring polymers in two-dimensional melts double-fold around randomly branching "primitive shapes"
• Effect of Dispersity on Dynamic Properties of Polymer Melts: Insights from Coarse-Grained Molecular Dynamics Simulations