Chapter 6 - Dynamics of single chains

Question 1

How is the Einstein relation defined?

Answer 1

D = kT/ç,

ç = friction coefficient.

Question 2

How is the Stokes-Einstein relation defined?

Answer 2

D = kT/(6πetaR)

Question 3

What is Stokes law?

Answer 3

Stokes law says that the friction coefficient of a sphere moving in a Newtonian liquid is

ç = 6πetaR

Question 4

What is the Rouse model?

Answer 4

In the Rouse model, each polymer has N beads connected by springs of root-mean-square size b, each bead having a friction coefficient ç. The total friction coefficient is

ç_R = Nç,

and the diffusion coefficient is

D_r = kT/Nç.

Question 5

What is the Rouse time?

Answer 5

The time it takes for a polymer to travel over a distance of the order of its size R.

tau_R = ç/kT * NR^2.

Question 6

What modes are active for time scales shorter than the Rouse time in the Rouse model?

Answer 6

Viscoelastic modes.

Question 7

What motion is seen on time scales longer than the Rouse time in the Rouse model?

Answer 7

Only diffusive motion.