Monday, September 17, 2012

Failure of the spherical cow approximation

Physicists think cows are spherical. But are they?
There is a very nice Perspective in Science Spare the (Elastic) Rod by Phil Nelson. He discusses recent experiments on DNA which show the limitations/breakdown of the much loved [at least by physicists] elastic model rod model for a polymer. This beautifully simple model has only a single parameter, the persistence length, on which length scale it is assumed that the polymer is inflexible. The models shows that the elasticity (on long length scales) of the polymer is due to entropic effects. For DNA the persistence length is estimated to be about one hundred base pairs.

This model is so simple that it can be taught in an undergraduate statistical mechanics class. The mathematics is analogous to a paramagnetic in a magnetic field. Slightly different versions go by names such as Freely Jointed Chain and Worm Like Chain.
A nice review is by Cocco, Marko, and Monasson and contains the helpful figure below.

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