Statics and Dynamics of Stretching Fluctuations

One of the objectives of the research described here, carried out in collaboration with Amit Chakrabarti of Kansas State University, is to understand the characteristic distances (static, or time-averaged properties) and characteristic times for the polymer fluctuations.

There are two length scales associated with the polymers: the side-to-side fluctuation distance which is proportional to the square root of the polymer length (the side-to-side excursions may be modeled as random walks), and the vertical fluctuation distance, which is proportional to the polymer length. For long chains, the vertical fluctuations thus occur over a much larger distance than do the side-to-side motions.

Similarly, there are two time scales associated with the chain - the time needed to flop from side to side, and the time needed to fluctuate vertically. If the polymers are shorter these relaxation times have different power-law dependences. However, if the polymers are longer than a critical length, they become entangled with one another and the relaxation becomes very slow, since the chains must slide along their own path to change shape appreciably. This makes the vertical and horizontal relaxation times the same, since the underlying relaxation process is associated with a slithering motion which doesn't depend on direction. The movie shows chains which each have about two entanglements along their length, so it is hard to see the confinement by entanglements visually, but quantitative analysis of these chains makes the entanglement effects clear.


Last modified: May 23, 1994

John Marko, marko@msc.cornell.edu