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F(x) =((k B T)/(l p ))((1/4)(1-(x/L) -2 +(x/L)-(1/4)) This is an example of a wo

ID: 684859 • Letter: F

Question

F(x) =((kBT)/(lp))((1/4)(1-(x/L)-2 +(x/L)-(1/4)) This is an example of a worm-like-chain (WLC) model givenin the problem, where lp is persistance length and L isthe contour length and kB is Boltzmann's constant. Derive an expression of the work needed to stretch a WLC fromx1 to x2. F(x) =((kBT)/(lp))((1/4)(1-(x/L)-2 +(x/L)-(1/4)) This is an example of a worm-like-chain (WLC) model givenin the problem, where lp is persistance length and L isthe contour length and kB is Boltzmann's constant. Derive an expression of the work needed to stretch a WLC fromx1 to x2.

Explanation / Answer

F = (kB*T/lp) * [0.25(1 - x/L0)-2 - 0.25 + x/L0 ] Integrate with respect to x W = Integral F*dx = (kB*T/lp)*[0.25*L0*(1-x/L0)-1 -0.25x + x2/(2L0)] W = [ kB*T / (4*lp)] * [ L02/(L0 - x) - x +2x2/L0) Evaluate from x1 to x2 W = [ kB*T / (4*lp)] * [ L02/(L0 - x2)- L02/(L0 - x1) - x2 +x1 + 2x22/L0-2x12/L0)