On the Scaling Behavior of the Force/Extension Relation of a Chain

✍ Scribed by Marios K. Kosmas

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 143 KB
• Volume: 19
• Category: Article
• ISSN: 1022-1344
• DOI: 10.1002/mats.201000037

✦ Synopsis

Abstract

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.

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