Question

The force-extension (f and x) behavior of the freely-jointed chain worked out in lecture takes a different form from that of the worm-like chain model applied by Rief el at (1997) to stetching of spectrin with the AFM. Their equation (given in the caption of their Fig. 3.) employed a "persistence" length p in: f(x)=(kT/p)[0.25(1-x/L) 2-0.25 + xL] whereas the freely jointed chain has a form given in lecture in terms of the link-length a: XL=coth(fa/kT) – (kT/fa) 1. Calculate the low force (fa/kt <<I) or small extension (x/L«<1) limits for both equations and deduce the simple numerical relationship between p and a for this limit. 2. Calculate the high force (fa/kT>>1), large extension (x/L ~ 1) limits and rearrange your expressions into the generic form: (fp/kT)" = 2 – 2 (x/L) what is the exponent n for the two models? And which model would you say is stiffer (more force required for a given x) in this limit as x approaches to L? So does one have to work against more or less entropy in pulling on a freely jointed chain?

Answer 1

I Ansi 2 . | 0 41 | |--(-) 0.5 + where! for n folk1 we have i 44 卷) - 幸生在 + | bo (ie: [-(-)- ) + ) - 「雪 - 對 | ih) 雞器 He a = 2