Frictional Properties of Polymers in Solution

The polymer is then treated as a string of beads where the frictional force on each bead is described by Stokes law. However, this results in a relationship between [77] and molecular weight, M, of the form [77] AF+Jl, where A is a small fraction. Experimentally, we have seen that [77] AP, where a usually has values between 0.5 and 0.8. Obviously, the assumption that the polymer beads do not perturb the solvent is not a good one. 

Going to the other extreme, it can be assumed that the polymer perturbs the medium so much that near the center of the coil the solvent molecules actually move with the same velocity as the beads. This means that the polymer coil can be treated as if it were a sphere that is, in effect, impenetrable to the solvent molecules that happen to lie outside its domain. Of course, this cannot be quite right, because (among other things) 

The nice thing about the assumption of an equivalent hydrodynamic sphere is that it allows you to do two things first, use the Einstein relationship for the viscosity of a dilute solution of solid particles, given previously in Equation 12-43. Then we can use the definition of a volume fraction, j (Equation 12-51)  

X yt I V V. CviS-. /, i / (A -ii We now make the assumption that the volume occupied by a polymer coil is equal to that of a sphere whose diameter is defined by the root mean square end-to-end distance,  

FIGURE 12-32 Schematic diagram of the equivalent hydrodynamic sphere. 

---

Another of the major figures in polymer science to collaborate with Flory at Cornell was Arthur M. Bueche (1920-1981). He received his Ph.D. in Physical Chemistry with Debye on the conformational and frictional properties of polymers in solution. He became an expert on light scattering from polymer solutions. 

---