The Critical Concentration from Absolute Polymer Coil Radii

The critical concentration is reached for a volume fraction 0 of the polymer of one. In this case, Eq. (4.3) yields 

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). 

4 The Critical Concentration from Absolute Polymer Coil Radii 

If the absolute diameter or radius of a polymer coil is known, a direct calculation of a critical concentration is possible without viscosimetric data. Common methods for the determination of absolute coil dimensions are the different light scattering methods. The critical concentration calculated from these dimensions is therefore often denoted as the critical concentration of light scattering, c ls since the radius R (see Chap. 8) can be determined directly from static light scattering. 

The critical concentration is then directly calculated from the molar mass and the radius of the polymer coil  

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The critical concentration c of a polymer-solvent system was calculated in The critical concentration from absolute polymer coil radii in Chap. 7 for polymer coils with an absolute radius. For a real polymer coil the question arises, at which concentration the polymer coils touch each other and which absolute radius should be used to calculate the critical concentration. 

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