Relationships for flexible coil polymers

Flory (1953) has derived the following theoretical relationship relating a to polymer molecular weight and temperature  

A random coil polymer in solution may be modelled as a string of beads which interacts frictionally with the solvent. The solvent molecules inside the immediate region of the 3-D polymer coil are associated to some extent with the polymer molecule. This is implied by the fact that the polymer coil cannot easily be separated from these associated solvent molecules by sedimentation in an ultracentrifuge (Vollmert, 1973). Consideration of the work required to rotate this model polymer/solvent coil leads to the relationship (Flory, 1953). 

Thus at the Flory temperature, where a is unity, then it is predicted that the intrinsic viscosity scales as the half-power of molecular weight. 

As the temperature becomes greater than the Flory temperature, then, from Equation 3.32, the quantity (a — a ) becomes positive and the approximation may also be made that a, which leads to the conclusion that where T 6f then 

A value of of 0.28 fim was estimated by Lynch and Macwilliams (1969) for an HPAM solution with M = 3 x 10 in a 3% NaCl solution. From the results of Smith (1970) using Millipore filters, the effective size of an HPAM molecule with M = 3 x 10 in 0.5% NaCl solution is between 0.3 and 1.0 //m. A more direct measure of molecular size was presented by Gogarty (1967) using Nuclepore filtration. Here, he showed that the effective size range of the HPAM molecule is 0.5-2 jam in distilled water and 0.4-1.5 jam for a 0.06% NaCl solution. 

---