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- W2005307735 abstract "The degree of folding of a single three-dimensional (3D) polymer configuration is a general concept associated with the pattern of interpenetrations between chain loops. In the present context, this notion applies to the state of a rigid chain, regardless of the polymer being permanently or only temporarily entangled. Folding features represent an important aspect of macromolecular shape, one whose characterization must take into consideration both the 3D geometry and the bond connectivity of the polymer. In this work, we present a measure of folding complexity for planar objects. These systems include self-avoiding walks on planar lattices used for modeling 2D (adsorbed) polymers. In 3D chains, folding patterns are usually compared in terms of the number of bond-bond projected crossings, averaged over all rigid projections (the so-called mean overcrossing number). The characterization of molecular shape in 2D systems must be based on different notions since bond-bond crossings may not occur. Here, we generalize the concept of ``overcrossings'' as a descriptor of folding complexity in 2D structures. We show that the resulting molecular shape descriptor exhibits a power-law scaling with the number of monomers, both in regular conformers and in a continuum of random configurations. The method can be applied to study the adsorption of polymers with various topologies, as well as the complexity of random structures, such as those in crack patterns, soap froths, and other cellular decompositions of the plane." @default.
- W2005307735 created "2016-06-24" @default.
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- W2005307735 date "1999-04-01" @default.
- W2005307735 modified "2023-09-26" @default.
- W2005307735 title "Quantitative measure of folding in two-dimensional polymers" @default.
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- W2005307735 doi "https://doi.org/10.1103/physreve.59.4209" @default.
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