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Updated: Jun 23, 2026

Interactive Molecular Model Assembly with 3D Printing
Published on: August 13, 2020
Universal scaling, entanglements, and knots of model chain molecules
Katerina Foteinopoulou1, Nikos Ch Karayiannis, Manuel Laso
1Institute for Optoelectronics and Microsystems, Universidad Politécnica de Madrid, José Gutiérrez Abascal 2, 28006 Madrid, Spain.
Abstract:
By identifying the maximally random jammed state of freely jointed chains of tangent hard spheres we are able to determine the distinct scaling regimes characterizing the dependence of chain dimensions and topology on volume fraction. Calculated distributions of (i) the contour length of the primitive paths and (ii) the number of entanglements per chain agree remarkably well with recent theoretical predictions in all scaling regimes. Furthermore, our simulations reveal a hitherto unsuspected connection between purely intramolecular (knots) and intermolecular (entanglements) topological constraints.
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