Static Properties of Polymer Melts in Two Dimensions

Abstract

Self-avoiding polymers in strictly two-dimensional ($d=2$) melts are investigated by means of molecular dynamics simulation of a standard bead-spring model with chain lengths ranging up to N=2048. % The chains adopt compact configurations of typical size $R(N)\sim N^{\hat{I}}½$ with $\hat{I}½=1/d$. % The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents $\hat{I}{˜}_0=3/8$, $\hat{I}{˜}_1=1/2$ and $\hat{I}{˜}_2=3/4$ predicted by Duplantier. % Due to the segregation of the chains the ratio of end-to-end distance $\Rend(N)$ and gyration radius $\Rgyr(N)$ becomes $\Rend^2(N)/\Rgyr^2(N) \approx 5.3 < 6$ for $N\gg 100$ and the chains are more spherical than Gaussian phantom chains. % The second Legendre polynomial $P_2(s)$ of the bond vectors decays as $P_2(s)\sim 1/s^{1+\hat{I}½\hat{I}{˜}_2}$ measuring thus the return probability of the chain after $s$ steps. % The irregular chain contours are shown to be characterized by a perimeter length $L(N) \sim R(N)^{\dc}$ of fractal line dimension $\dc = d-Θ_2 =5/4$. % % In agreement with the generalized Porod scattering of compact objects with fractal contour the Kratky representation of the intramolecular structure factor $F(q)$ reveals a strong non-monotonous behavior with $q^{d}F(q)\sim 1/(qR(N){)}^{\hat{I}{˜}_2}$ in the intermediate regime of the wave vector $q$. This may allow to confirm the predicted contour fractality in a real experiment.

14 figures, accepted at J.Chem.Phys.