2003/09/30 by Hsiao-Ping Hsu, Peter Grassberger · 68 citations
Chemistry · Materials Science · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Lattice (music) #Material Dynamics and Properties #Monte Carlo method #Random walk #Scaling #Self-avoiding walk #Simple cubic lattice #Slab #Theoretical and Computational Physics #Transverse plane #cond-mat.soft
paper · pdf · doi:10.1063/1.1636454
published in The Journal of Chemical Physics 120(4), 2034-2041 (American Institute of Physics) · 8 pages, 14 figures included
openalex publication_date 2004/01/22 · arxiv created 2004/01/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Single three-dimensional polymers confined to a slab, i.e., to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by N-step walks on a simple cubic lattice confined to the region 1< or = z < or = D. The simulations cover both regions D<<RF and D>>RF (where RF approximately Nnu is the Flory radius, with nu approximately 0.587), as well as the cross-over region in between. Chain lengths are up to N=80 000, slab widths up to D=120. In order to test the analysis program and to check for finite size corrections, we actually studied three different models: (a) ordinary random walks (mimicking Theta polymers); (b) self-avoiding walks; and (c) Domb-Joyce walks with the self-repulsion tuned to the point where finite size corrections for free (unrestricted) chains are minimal. For the simulations we employ the pruned-enriched-Rosenbluth method with Markovian anticipation. In addition to the partition sum (which gives us a direct estimate of the forces exerted onto the walls), we measure the density profiles of monomers and of end points transverse to the slab, and the radial extent of the chain parallel to the walls. All scaling laws and some of the universal amplitude ratios are compared to theoretical predictions.