Static properties of polymer melts in two dimensions

• Published in: The Journal of chemical physics 2010-05, Vol.132 (18), p.184904-184904-12
• Main Authors: Meyer, H., Wittmer, J. P., Kreer, T., Johner, A., Baschnagel, J.
• Format: Article
• Language: English
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.3429350

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 ) ∼ N ν with ν = 1 / d . The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents Θ 0 = 3 / 8 , Θ 1 = 1 / 2 , and Θ 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 ) ≈ 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 ) ∼ 1 / s 1 + ν Θ 2 , 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 ) ∼ R ( N ) d p of fractal line dimension d p = 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 nonmonotonous behavior with q d F ( q ) ∼ 1 / ( q R ( N ) ) Θ 2 in the intermediate regime of the wave vector q . This may allow to confirm the predicted contour fractality in a real experiment.