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

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.