WLC_model

# WLC_model - The Worm-like Chain Model For forces> k T/P...

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Unformatted text preview: The Worm-like Chain Model For forces > k T/P, the force-extension behavior of the chain can be obtained from the effective energy of a stretched WLC: r (s) z ˆ z E elastic k B T = 1 2 EI ∂ 2 r ( s ) ∂ s 2 2 ds- Fz L ∫ F At high forces, the extension of the WLC approaches its coutour length, L, and the tangent vectors fluctuate only slightly around the pulling axis, : ˆ z ˆ t The Worm-like Chain Model ˆ t ˆ t ⊥ t z t z = 1- t ⊥ 2 2245 1- t ⊥ 2 2 + ϑ ( t ⊥ 4 ) + .... k ≡ ∂ 2 r ( s ) ∂ s 2 = ∂ ˆ t ∂ s = ∂ ∂ s ( t z ˆ z + ˆ t ⊥ ) k = ∂ ∂ s (1- t ⊥ 2 2 ) ˆ z + t ⊥ k = - t ⊥ • ∂ t ⊥ ∂ s ˆ z + ∂ t ⊥ ∂ s Since t ⊥ • ∂ t ⊥ ∂ s = t ⊥ ∂ t ⊥ ∂ s , then k = ∂ t ⊥ ∂ s 2 1 + t ⊥ 2 ( 29 2245 ∂ t ⊥ ∂ s k 2 = ∂ t ⊥ ∂ s 2 Now: This is substitution 1. We can write the energy of the stretched molecule: The Worm-like Chain Model...
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WLC_model - The Worm-like Chain Model For forces> k T/P...

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