Theoretical Outline - The Zimm Model

In the equation of motion (13), the friction force with the solvent 

We can take the Rouse term l/ ke 02rm/0m2 (ke = 3kBT//2) entropic spring constant) into consideration formally, if we define the element Tnm of the Oseen tensor as Tnm = E/ . The equation of motion (13) thus becomes 

Equation (72) is a coupled non-linear differential equation which is difficult to handle. We therefore consider a number of approximations. 

For small deviations from equilibrium, we average r — rm 1 by the statistical segment distribution. For a Gaussian chain which is realized under 

The long-range coupling via the flow field which only decreases with 1/r leads to a qualitatively different behavior from that of the Rouse model. Equation (75) is approximately solved by transformation to Rouse normal coordinates. Its solution [6,91] leads to the spectrum of relaxation rates 

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