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arXiv · 0905.1002

Perimeter Length and Form Factor of Two-Dimensional Polymer Melts

H. Meyer·T. Kreer·M. Aichele·A. Cavallo·A. Johner·J. Baschnagel·J. P. Wittmer
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Abstract

Self-avoiding polymers in two-dimensional ($d=2$) melts are known to adopt compact configurations of typical size $R(N) \sim N^{1/d}$ 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 $L(N) \sim R(N)^{\dpm}$ of fractal dimension $\dpm = d-Θ_2 =5/4$ with $Θ_2=3/4$ being a well-known contact exponent. Due to the self-similar structure of the chains, compactness and perimeter fractality repeat for subchains of all 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 $q^2F(q) \sim 1/(qN^{1/d})^{Θ_2}$ in the intermediate regime of the wavevector $q$. Measuring the scattering of labeled subchains %($s F(q) \sim L(s)$) the form factor may allow to test our predictions in real experiments.

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H. Meyer, T. Kreer, M. Aichele, A. Cavallo, A. Johner, J. Baschnagel, J. P. Wittmer. 2009-05-07. Perimeter Length and Form Factor of Two-Dimensional Polymer Melts. https://arxiv.org/abs/0905.1002

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