Dilute Solutions of Rouse Chains

2 Dilute Solutions of Rouse Chains at Constant Temperature 

This model consists of identical beads each with friction coefiicient C joined together linearly by Hookean springs each with spring constant H. For this model the solution to Eq. (13.4) is  

Here the Aj = cJlH are the time constants for the Af,-bead Rouse model, with the Cj being the eigenvalues of the Kramers matrix Ctj = which is the 

That is, the are the elements of an (N - 1) x - 1) orthogonal matrix that diagonalizes the Kramers and Rouse matrices. For the complete derivation of the above results, see DPL Sect. 15.3. 

Other solutions for the singlet configuration-space distribution function are those for the steady-state, homogeneous potential flow of elastic dumbbells with any kind of spring (DPL, Eq. (13.2-14)), and the first few terms in a perturbation solution for steady-state, homogeneous flow of FENE dumbbells (DPL, Eq. (13.2-15)). 

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