2010/04/23 by H. Meyer, J. P. Wittmer, T. Kreer +2 · 60 citations
Materials Science · Mathematics · Physics and Astronomy · #Chain (unit) #Combinatorics #Condensed matter physics #Dimension (graph theory) #Form factor (electronics) #Fractal #Fractal dimension #Geometry #Gyration #Legendre polynomials #Material Dynamics and Properties #Mathematical analysis #Mathematics #NMR spectroscopy and applications #Optics #Physics #Polymer #Quantum mechanics #RADIUS #Radius of gyration #Scattering #Structure factor #Theoretical and Computational Physics #Unit vector #cond-mat.soft
paper · pdf · doi:10.1063/1.3429350
published in The Journal of Chemical Physics 132(18) (American Institute of Physics) · 14 figures, accepted at J.Chem.Phys.
arxiv created 2010/04/23 · openalex publication_date 2010/05/13 · arxiv updated 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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)∼Nν with ν=1/d. The precise measurement of various distributions of internal chain distances allows a direct test of the contact exponents Θ0=3/8, Θ1=1/2, and Θ2=3/4 predicted by Duplantier. Due to the segregation of the chains the ratio of end-to-end distance Re(N) and gyration radius Rg(N) becomes Re2(N)/Rg2(N)≈5.3<6 for N⪢100 and the chains are more spherical than Gaussian phantom chains. The second Legendre polynomial P2(s) of the bond vectors decays as P2(s)∼1/s1+νΘ2, 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)dp of fractal line dimension dp=d−Θ2=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 qdF(q)∼1/(qR(N))Θ2 in the intermediate regime of the wave vector q. This may allow to confirm the predicted contour fractality in a real experiment.