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Need help: Relation between polymer end-to-end distance and mechanical properties

Ashfaq Adnan's picture


I found in polymer books and some literatures that mechanical properties of polymer improve with the increase of their radius of gyration or end-to-end distance for a fixed molecular weight. I, however, could not find any experimental evidence or any physical explanation. 

It will be a great help to me if anyone refer me some literatures that explains the connection between these two parameters.


Ashfaq Adnan


Hi, Ashfaq.

I think that the paper by Frey and coworkers may be the one you would like
to read for experiments which shows the relationship between end-to-end distance
and the persistent length, related to bending rigidity, of microtubules.

Pampaloni, F., et al., PNAS, 103, p10248

You may also find the similar paper by Frey group for experiments showing the
end-to-end distance distributions of DNA chain.

Andrew Norris's picture

Hi Ashfraq,

The stiffness of a macromolecule increases with end-to-end separation in most (all?) inextensible chain models.  This is common in rubber elasticity and also in DNA.    Inextensible chain models describe entropic elasticity, where e.g. the chain entropy decreases as the chain is lengthened.   

A good starting point might be the recent paper by Ogden et al. "On worm-like chain models within the three-dimensional continuum mechanics framework " Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2006, Vol. 462,  pp. 749-768.    They use the worm-like chain (WLC) model, and compare with some experimental data, I think.    A nice overview (of the WLC model is given by Marko and Siggia: "Stretching DNA " Macromolecules; 1995; 28(26) pp 8759 - 8770.   This is a "dense" paper but well worth the effort if you want to understand the WLC. 


Ashfaq Adnan's picture

Hello Drs Norris and Eom,

I am looking forward to reading these articles. Recently, I simulated deformation and failure of adhesive joints with varying nanoscale thickness using MD. I found from my simulation that the end-to-end distance of polymer chains with identical Mw as well as joint strength/stiffness tends to increase as thickness reduces. I failed to find any explanation between <R> and strengths/stiffness.

Thansk again for the reference.


-Ashfaq Adnan 


Ashfaq Adnan

Phd Student, Schoold of Aeronautics and Astronautics

Purdue University, West Lafayette, Indiana 47907

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