# Stretching Some Polymer

1. Sep 2, 2014

### CottonHill

The question tells me that some experiments have shown that the force needed to stretch a polymer molecule by an amount (Δl) is given approximately by:

F= (kBT/P)*((1/4)*(Lo2/(L-Δl)2-(1/4)+(Δl/L))

Yea, I know, nasty looking. Anywho:

F = Force
T = Temp.
kB = Boltzmann's Constant
P = Persistence Length
Lo = Contour Length
Δl = Amount of Stretch of Polymer Molecule

After giving all of that lovely info, the question says to show that if Δl is small relative to Lo, it approximates Hooke's Law. Then it asks to find the effective spring constant of the molecule.

So far I have taken that equation and said if Δl approaches zero and L0 approaches ∞ then we get down to:

F=(kB*T)/P

I can explain that Hooke's Law says that a force (F) equals a constant relating to energy of a spring (k) times the distance (x).....
And that relates to the above equation by having a force (F) equals a constant relating to energy of stretching (kB) times a a distance (P). Ignoring T.

Is my logic correct and how would I find the spring constant of this molecule? Thanks in advance.

2. Sep 3, 2014

### BvU

Don't understand F is a constant. Does that mean F is non-zero even when Δl is zero ? You say
This is true, but it's not the same as taking the limit ${\Delta {\rm l}\over {\rm L}}\, \rightarrow 0$

(Note you don't want L $\rightarrow \infty$)

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