Scaling relation for translational diffusion coefficient

In the second interpretation, Eq. (10.27), the driving force dc/dx is identical to a gradient of chemical potential hence, the equation for D involves the activity coefficient y of the polymer. The equation fits into the analysis of an interacting multicomponent system. Of course, it must be remembered that osmotic pressure and chemical potential are closely related, as discussed in Chapter 9. 

Scaling relations for quantities that are time independent, for example, the osmotic pressure 7t, the mean-square end-to-end distance (R ), and the screen length are known as static scaling relations. Those for time-dependent quantities, such as the translational diffusion coefficient, are called dynamic scaling relations. 

The Rouse model considers the polymer chain as a succession of beads, ri. r , r +i, separated by springs along the vectors ai. a (see Chapter 8). If all the internal forces add up to zero, the equation is reduced to 

In scaling relations, we can put the diffusion coefficient in the form (Adler and Freed, 1979) 

In a 0 solvent where the excluded volume effect vanishes, Eq. (10.28) reduces to Zimm s extension of the Rouse treatment  

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