Polymers m Dilute and Semidilute Solutions

Callaghan and Pinder48,49 used the PGSE method in a detailed examination of the diffusion of linear polystyrene molecules dissolved in CC14. They applied standard dilute hydrodynamic theory to self-diffusion (as distinct from mutual diffusion) and identified the lowest-order concentration dependence of D with the coefficient kF, writing 

They obtained a scaling behavior D0(M) characteristic of inferior solvents (see Eq. 10) n = —0.51 0.02. Plots of D-1 vs. c were linear up to more than 60 kg of polymer per m3 of solution at low M (M 3 x 104) (see Fig. 6). The dependence of kF on M was explained by the hydrodynamic model of Pyun and Fixman so at lower M, and by that of Yamakawa 5 at the highest molecular weights. The Pyun-Fixman model, as elaborated by King et al.52), permits relating kF to D0 and thus to M  

The authors semiquantitatively described a semidilute concentration regime with limits 

In fact, their data for M 10s displayed scaling behavior of this sort, although even in their smallest polystyrenes a tangent of slope—1.75 could be drawn to plots of log D vs. log c. 

Further, reptation theory asserts26) that the molecular-weight dependence of the diffusion coefficient in an entangled gel should have the form 

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