TRANSLATIONAL DIFFUSION CONSTANT OF POLYMER CHAINS

The formal theory of the translational diffusion constant is reexamined in order to display in isolation the contributions from (a) the equilibrium average derived by Kirkwood, and (b) corrections due to distortion of the equilibrium segment distribution. The corrections are found to be small in good or poor solvents. The equilibrium contribution requires a calculation of (1/rij)eq for all pairs of segments i and j in the chain, and this calculation has been carried through on the basis of a boson operator formalism recently introduced. It is first shown that the boson formalism in lowest order gives a Gaussian distribution of rih with a variance dependent on i and j and on the magnitude of the excluded volume. A calculation of the frictional expansion factor as shows that it increases much less rapidly with increasing goodness of solvent than other measures of chain dimension. However, the tentative conclusion is expressed that this behavior of as is due to the sensitivity of (1/rij)eq to non-Gaussian statistics, in comparison with (rij)2. Methods for dealing with this sensitivity are outlined. © 1968, American Chemical Society. All rights reserved.