Thursday, June 16, 2011

Contour Length of a Gaussian Bead-Spring Chain

Consider a Gaussian bead-spring chain with N springs of mean-squared length b*b. The distribution of the end-to-end vector is the standard Gaussian distribution:

With well known properties:

and,

However, note that,

which means that average spring length (N=1) is smaller b. Therefore the average contour length is not Nb.