Critical concentration of the viscosimetry

For the determination of the intrinsic viscosity [q] of the particular polymer-solvent system, the specific viscosity /jsp can be evaluated from the relative viscosity r j. via Eq. (2.11). With the specific viscosity and known concentrations of the solutions, the evaluation can be directly started according to Eq. (4.9) in Determination of the intrinsic viscosity by viscosimetric measurements in the next chapter. With the determined intrinsic viscosity [q], the critical concentration of the viscosimetry can be evaluated according Eq. (7.7). 

Fig. 7.2. Critical concentration c as function of the mass average molar mass for poly(styrene) (PS) in toluene at 7=25 C and poly(acrylamide) (PAAm) in H20.The closed symbols show the critical concentration of the viscosimetry (Eq. 7.7), the open symbols...

A critical concentration determined in this way is also denoted as the critical concentration of light scattering, since the radius of gyration can be determined directly via light scattering experiments [74]. As shown in Fig. 7.2 for two different polymer-solvent systems, the critical concentration c s is roughly a factor of -10 smaller than the critical concentration of the viscosimetry c n] (Eq.7.7). 

However, for practical applications even an exact hydrodynamical, critical concentration is just a guideline, since superproportional changes of the flow behavior do not occur abruptly at the critical concentration. Due to the diffuse character of a real polymer coil in solution, a change in the flow behavior above c occurs gradually over a range of concentrations around c. For practical applications a determination of or c Ls is sufficient. The discussion about an exact determination of the hydrodynamic radius is therefore more of an academic nature. However, for a classification of the critical concentration of the viscosimetry or c ls> it is important to know about the possible range of critical concentrations. 

Fig. 5.1. Reduced viscosity /]red as a function of the concentration c for poly(acrylamide) (PAAm) of different molar masses in aqueous solution.The mass average molar masses Mw are given for each data set.The value of 1/10 of the critical concentration c i] of the viscosimetry (at which already 10% of the solution volume is filled with polymer coils) is shown to demonstrate that deviations from the linear relation between the reduced viscosity / red and the concentration c are caused by intermolecular interactions between the polymer coils. Data from [89]...

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