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On the Scaling Behavior of the Force/Extension Relation of a Chain
Author(s) -
Kosmas Marios K.
Publication year - 2010
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201000037
Subject(s) - scaling , exponent , chain (unit) , extension (predicate logic) , statistical physics , mathematics , power law , random walk , scaling law , mathematical analysis , physics , geometry , quantum mechanics , statistics , computer science , programming language , philosophy , linguistics
Applying an extending force F along the end‐to‐end vector r of a chain enlarges the initial size ρ i ∼ | r i | leading to a final state with ρ f larger than ρ i . Assuming a power law dependence of the size ρ ∼ N ν of the chain on its length N , at the two different states with different exponents ν i and ν f , a scaling relationship is derived between the measure of the extending force F and the extension ρ of the chain. The exponent γ of the force/extension relation, ρ ∼ F γ , depends on both exponents ν i and ν f of the initial and the final states. A relation between γ and the exponents ν i and ν f is derived which permits the explanation of previous results and predicts some more. The scaling behavior is checked with the exactly soluble model of a random walk under a force.