Huggins equation, viscosity measurements dilute polymer solutions

Intrinsic viscosity (rj) is the viscosity of an infinitely diluted polymer solution. It is a measure of the hydrodynamic volume occupied by a macromolecule, which is closely related to the size and conformation of the chain, but is independent of concentration of macromolecule. In dilute solutions, by definition, the polymer chains are separated and there is negligible interaction between them. Therefore, the (rj) of polymer in solution depends only on the dimension and the molecular weight of polymer chain. Experimentally determined values of the relative and specific polymer viscosities were used to calculate it, according to Huggins [53] and Kraemer [64] equations given by... 

The relative viscosities of polymer solutions are measured at different concentrations and a plot of the reduced viscosity versus concentration is made, in order to extrapolate to zero concentration. The concentration dependence of the viscosity of polymer solutions, in the dilute regime, may be expressed by several linear equations. For practical extrapolation to zero concentration, the most commonly employed are the Huggins equation ... 

Viscosity measurements on dilute polymer pseudo-solutions can be used to determine the molecular weight of the dissolved polymer. If polymer concentrations are restricted to levels that give a solution viscosity no more that 1.5 times the solvent viscosity, then the viscosity versus concentration plot determined by measurements on a group of polymer pseudo-solutions can be used with the Huggins (15a.), Krammerer(15b.), Schulz-Blaschka(15c), or Martin (15d.) equations to determine the limiting viscosity number of the polymer, [ ]. 

Therefore the critical concentration is proportional to the reciprocal intrinsic viscosity. The factor of 2.5 assumes that the polymer coils behave like hard spheres in solution. Viscosimetric measurements for the determination of the intrinsic viscosity have to be performed in dilute solutions at concentrations clearly below c for an exact linear extrapolation according to the Huggins equation (Eq. 4.9). This condition is fulfilled for example in Fig. 4.2, where it is shown that the data points for the viscosimetric determination are below the critical concentration calculated from Eq. (7.7). 

---