Static properties of polymer melts in two dimensions
H Meyer and JP Wittmer and T Kreer and A Johner and J Baschnagel, JOURNAL OF CHEMICAL PHYSICS, 132, 184904 (2010).
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) similar to N(nu) with nu=1/d. The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents Theta(0)=3/8, Theta(1)=1/2, and Theta(2)=3/4 predicted by Duplantier. Due to the segregation of the chains the ratio of end-to-end distance R(e)(N) and gyration radius R(g)(N) becomes R(e)(2)(N)/R(g)(2)(N) approximate to 5.3 < 6 for N >> 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) similar to 1/s(2)(1+nu Theta), thus measuring the return probability of the chain after s steps. The irregular chain contours are shown to be characterized by a perimeter length L(N) similar to R(N)(d)(p) of fractal line dimension d(p)=d-Theta(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 nonmonotonous behavior with q(d)F(q) similar to 1/(qR(N))(Theta)(2) in the intermediate regime of the wave vector q. This may allow to confirm the predicted contour fractality in a real experiment.
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