Viscosity-Molar Mass Relationship

A comparison of the expressions giving the molar mass dependence of the intrinsic viscosity shows that the relationships can be generalized for all macromolecular types in the form of the modified Staudinger equation [77] = KM (see also Table 9-7). Both K and a, are usually unknown. For each polymer homologous series, therefore, the modified Staudinger equation must be empirically determined. To do this, the molar masses and intrinsic 

Only measured values for ellipsoidal, compact proteins at a, = 0.1 deviate from this relationship. 

Since it is only valid to compare like averages with each other in a calibration of this kind, the question arises as to what kind of molar mass average is obtained from Equation (9-151). According to Equation (9-125), the intrinsic viscosity of a polymolecular substance is a mass average. Equation (9-151) can thus be written as 

9 Determination of Molar Mass and Molar Mass Distributions 

Finally, log [rj] is plotted against log Mr,), and Kand Ur, are again evaluated. This procedure is continued until K and Ur, cease to change on further iteration. 

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Cellulose and its derivatives have o values of about 2, i.e., thermodynamically they are about as flexible as poly(isobutylene). Thus, cellulose chains are not extraordinarily stiff, although they are often assumed to be so on the basis of their high exponents in the intrinsic viscosity-molar mass relationship (see Section 9.9.7). These high exponents are interpreted as arising from the particular (high) draining properties of the cellulose molecule. 

Table 9-7. Theoretical Exponents arj of the Viscosity-Molar Mass Relationship [Equation (9-/5/)]...

Fig. 8.17. Intrinsic viscosity-molar mass relationship for PI in diisobutylene (DIB) at 20 °C and in cyclohexane at 30 °C. Data collected in Flory s book [105]...

The value of the exponent of NaCMC dissolved In 0.1 M NaCI shows that the shape of the molecule is probably similar to that of the nonionic cellulose ethers in water. In contrast, the increase in this exponent, in going to 0.01 A/f and 0.001/W NaCI, Indicates transition from coil to rodlike form. In reality, thermodynamic data indicate that cellulose chains may not be as stiff as they are assumed to be, on the basis of their high exponents in the intrinsic viscosity-molar mass relationship [20]. 

This method is cmnbersome more often used is the temperature dependence of the intrinsic viscosity/molar mass relationship... 

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