Treatment of Experimental Results Frictional Coefficients

Theory presented earlier in this chapter led to the expectation that the frictional coefficient /o for a polymer molecule at infinite dilution should be proportional to its linear dimension. This result, embodied in Eq. (18) where P is regarded as a universal parameter which is the analog of of the viscosity treatment, is reminiscent of Stokes law for spheres. Recasting this equation by analogy with the formulation of Eqs. (26) and (27) for the intrinsic viscosity, we obtain  

Equations (29), (30), and (10) might be applied to the elucidation of the frictional coefficient in a manner paralleling the procedure applied to the intrinsic viscosity. One should then determine/o (from sedimentation or from diffusion measurements extrapolated to infinite dilution) in a -solvent in order to find the value of Kf, and so forth. Instead of following this procedure, one may compare observed frictional coefficients with intrinsic viscosities, advantage being taken of the relationships already established for the viscosity. Eliminating from Eqs. (18) and (23) we obtain  

Thus the quantity on the left evaluated for a series of polymer fractions differing only in chain length should be independent of M. Results shown in Table XLII for fractions of poly-(methyl methacry-late) and of polyisobutylene covering unusually wide ranges confirm this prediction within experimental error. It is borne out also by less extensive results of sedimentation measurements on several other systems. Introduction of the values of v, p, and rjo enables 

Let us examine briefly some of the more important consequences of this treatment of the frictional coefficient of flexible chain molecules. It is evident from Eq. (29) and the previous discussion of the manner 

Experimental results are consistent with this relation, but inaccuracies in sedimentation constants preclude precise evaluation of the empirical exponent. Similarly, the diffusion constant at infinite dilution, given by 

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