Curvilinear friction coefficient

In the semidilute solution, the hydrodynamic interactions are shielded over the distance beyond the correlation length, just as the excluded volume is shielded. We can therefore approximate the dynamics of the test chain by a Rouse model, although the motion is constrained to the space within the tube. In the Rouse model, the chain as a whole receives the friction of N, where is the friction coefficient per bead. When the motion is limited to the curvilinear path of the primitive chain, the friction is the same. Because the test chain makes a Rouse motion within the tube, only the motion along the tube survives over time, leading to the translation of the primitive chain along its own contour. The one-dimensional diffusion coefficient for the motion of the primitive chain is called the curvilinear diffusion coefficient. It is therefore equal to Dq of the Rouse chain (Eq. 3.160) and given by... 

The mobility of the whole chain, free to move along the curvilinear axis of its tube is iV/iV jsmaller than that of one bead (the friction on the full necklace is the ft iction on one bead times the number of beads), leading to a curvilinear diffusion coefficient... 

The curvilinear diffusion constant of the chain in its tube is given by D= g7V5, where =(L/6)5q is the friction coefficient of the whole chain and 6=3.4 A is the contour length of one bp. The time it takes to disengage completely from a tube of length Na by this diffusion process is2 ... 

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