Perimeter Length and Form Factor of Two-Dimensional Polymer Melts

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 $\hat{I}{˜}_2=3/4$ 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 $q^{2}F(q)\sim 1/(q{N}^{1/d}{)}^{\hat{I}{˜}_2}$ in the intermediate regime of the wavevector $q$. Measuring the scattering of labeled subchains %($sF(q)\sim L(s)$) the form factor may allow to test our predictions in real experiments.

4 pages, 4 figures, accepted for PRE Rapid Communications