Apparent molecular weight, concentration dependence

To overcome the problem of non-ideality the work be carried out at the Q temperature because in nonideal solutions the apparent Molecular weight is a linear function of concentration at temperatures near Q and the slope depending primarily on the second virial coefficient. 

Fig. 6. Concentration dependences of a apparent molecular weights ", and b freezing-point depression 6 per unit concentration c in benzene of poly(a-phenylethyl isocyanide) of Mn = 34800. [Reproduced from Ref. (21), with permission of J. Wiley and Sons, Publ.]...

Under conditions of partly screened interactions in dilute solutions (high added salt concentration cs and low polymer concentration c), the solution osmotic pressure can be expressed via a virial expansion (Eq. 24). Then light scattering becomes a useful tool to obtain values of second virial coefficients characterizing interactions in solution. The second virial coefficient can be calculated from the slope of the dependence given by Eq. 25. The relation between the true and the apparent second virial coefficient is similar to the relation between the true and the apparent molecular weight (see the previous section for more details and the meaning of the symbols) ... 

The calculated dependence of the concentrations of the multimer and the unimers on the total concentration c shows a more or less accentuated kink (Figure 6-6). This kink is generally known as the critical micelle concentration (cmc). As can be seen for the concentration dependence of the apparent molecular weights, such critical micelle concentrations are also observed there. The position of this critical micelle concentration depends on the measurement method used. The cmc is not a well-defined physical quantity, and it is certainly not the concentration at which associates first appear (see also Figure 6-6). 

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