     Next: Viscosity of a dilute Up: The Rouse chain Previous: Correlation of the end-to-end

# Monomer motion

In this section we study the mean square displacements  of the individual monomers. Using Eq. (6.24) and the fact that different modes are not correlated, we get  (6.43)

Introducing Eq. (6.38) we get  (6.44)

where we have used Eqs. (6.30) and (6.31) to calculate the first term, and Eqs. (6.39) and (6.40 ) for the second term.

There are two different limits to Eq. (6.44). First, when tis very large, i.e. , the first term will dominate, yielding (6.45)

This is consistent with the fact that the polymer as a whole diffuses with diffusion constant DG.

Secondly, suppose . Then the sum in Eq. (6.44) will dominate. Averaging over all monomers, and replacing the sum over kby an integral we get = = = (6.46)

Performing the final integral we get (6.47)

So, at short times the mean square displacement of a typical monomer goes like the square root of t.     Next: Viscosity of a dilute Up: The Rouse chain Previous: Correlation of the end-to-end
W.J. Briels