Mark-Houwink-Sakurada equation exponents

Ito et al. [65] investigated the MW dependence of the limiting viscosity for a series of regular polymacromonomers from PEO macromonomers, 26 (m=l) and demonstrated that the universal SEC calibration holds for these polymers. The exponent, a, in the Mark-Houwink-Sakurada equation defined by... 

Table 5. Polymer-solvent systems characterized by a rdatively large exponent v in the Mark-Houwink-Sakurada equation...

Introducing the v values evaluated by assuming v =(a+l)/3 from the exponent a in the Mark-Houwink-Sakurada equations, [j7]=KM [9], into eq 7, we have the calculated results denoted by the solid lines in Figure 4. As shown in the figure 7 °u appears to be expressed as a universal function of C[ 7 ] and its experimental dependence appears to agree with the calculated line in 0. 5M NaCl solutions, whereas 7 is not expressed as a universal function and its dependences are lower than the calculated lines in O.OIM NaCl solutions. 

An interesting extension of the GPC viscometry technique is that it is possible to measure the exponent a in the Mark-Houwink-Sakurada equation. Since both ln[i/] and InM are known, a plot of ln[ /] versus InM has a slope equal to a. This plot can either be constructed from a mixture of monodisperse polymer samples or from a broad molecular weight distribution polymer sample. 

Much of the above discussion indicates that, to study excluded volume effects, an accurate determination of unperturbed dimensions is required. For this, a common procedure is to extrapolate intrinsic viscosity of known molecular weight samples to zero molecular weight. Several extrapolations have been used, notably the Stockmayer-Fixman plot. Dondos and Benoit have now introduced a modified version of this, which appears to be linear over a wider range of molecular weights. It introduces a parameter D, which is shown to be linearly related to the exponent of the Mark-Houwink-Sakurada equation. 

The [f] values of the polymers obtained using fBuOK were very low in the range from 0.040 to 0.046 dL g The sec-malls dependence of [r for the polymer is shown in Figure 7.15. On the basis of these results, the exponent a of the Mark-Houwink-Sakurada equations of the polymers obtained using r-BuOK were determined to be 0.25-0.27. Our experimental a values... 

The exponent a" in the Mark-Houwink-Sakurada (MHS) equation [ ] = K(Mv) for various polymer conformations. 

In Pulling-up-sphere Method , we also showed that the value of the exponent a of the Mark-Houwink-Sakurada relation (equation (12-25)) is indicative of the shape of polymers in the solution. The a value estimated from log[ ] vs. log Mn plots in... 

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