Dilute Solutions of Hookean Dumbbells

1 Dilute Solutions of Hookean Dumbbells at Constant Temperature 

This model consists of two identical beads with bead friction coefficient C joined by a Hookean spring with spring constant H. 

For this model, there is but one connector vector, called Q (the vector from bead 1 to bead 2 ) and only one term in the summations in Eq. (13.4). There is only one element in the Rouse matrix (see Eq. (2.12)), namely An =2, and = iH(Q Q). For this system we postulate as a solution of Eq. (13.4) a normalized Gaussian distribution of the form  

Here B is the standard Finger strain tensor used in continuum mechamcs, and Yfo] = 8 — B IS a relative finite strain tensor, defined in DPL, Eq. D.3-4. We note in passing that it follows from Eq. (13.5) that the quantity HfkT) QQ P, dQ is equal to oi and thus satisfies Eq. (13.6). 

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