2002/05/06 by Oded Farago, Yacov Kantor, Mehran Kardar · 86 citations
Engineering · Mathematics · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #Composite material #Force Microscopy Techniques and Applications #Knot (papermaking) #Materials science #Mathematics #Monomer #Monte Carlo method #Physics #Polymer #Sports Dynamics and Biomechanics #Statistical physics #Statistics #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1209/epl/i2002-00317-0
published in Europhysics Letters (EPL) 60(1), 53-59 (Institute of Physics) · 5 pages, 3 figures
arxiv created 2002/05/06 · openalex publication_date 2002/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We compare Monte Carlo simulations of knotted and unknotted polymers whose ends are connected to two parallel walls. The force f exerted on the polymer is measured as a function of the separation R between the walls. For unknotted polymers of several monomer numbers N , the product fN ν is a simple function of R / N ν , where ν ≃ 0.59. By contrast, knotted polymers exhibit strong finite-size effects which can be interpreted in terms of a new length scale related to the size of the knot. Based on this interpretation, we conclude that the number of monomers forming the knot scales as N t , with t = 0.4 ± 0.1.