Mark-Houwink-Sakurada exponent

Experimentally, as the solvent quality approaches the theta condition, the exponent ai approaches the Mark-Houwink-Sakurada exponent, a, which, in turn, approaches the limiting value 0.5. The applicability of Eqs. (1.100) and (1.101) was found to extend to concentrations in excess of the entanglement concentration. 

Discriminating branched and star polymers from linear ones can always be achieved by measuring the properties in dilute solution. In fact, molecules having the same molar mass but different macromolecular architectures exhibit different transport and light scattering properties. More specifically, a branched macromolecule is more compact than a linear molecule having the same molar mass, and therefore it will display less friction and will diffuse more easily in the solvent. Viscometry can be used to detect branched structures, since the Mark-Houwink-Sakurada exponent (Eq. 2.23) for branched and star-shaped polymers is lower tiian that for the corresponding linear chain. Unfortunately, in order to measure the difference, one must have a sample made exclusively... 

Table 3.11 Values of the Mark-Houwink-Sakurada exponent a...

In Section 3.3.3, we learned that the Mark-Houwink-Sakurada exponent greater than 1 indicates a stiffness in the chain conformation. Here, we consider the intrinsic viscosity of the rodlike molecule. However, calculation of the excess stress is tedious. We look at the result only. To the linear order of k, the excess stress Acr is given as... 

VM, viscometry under moderate solvent conditions (Mark-Houwink-Sakurada exponent larger than 0.5 but smaller than 0.6 ... 

Table 11. Exponents and constants of the Kuhn-Mark-Houwink-Sakurada relationship [r ]=KMa for PDADMAC in 1 mol L 1 NaCl ([r ] in cm3 g, M in g-rnol )...

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...

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

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. 

Table 2 Mark-Houwink-Sakurada (MHS) exponents for different solvent/polymer systems at 25° C.

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. 

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... 

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... 

Several authors have published the method for determining molar masses of DADMAC polymers, primarily in connection with practical applications [1]. In Table 11 intrinsic viscosity-molar mass relations of PDADMAC are summarized in the form of the Mark-Kuhn-Houwink-Sakurada (MKHS) relationship. The relatively high exponent of the relationships is attributed to the greater chain stiffness in comparison with vinyl backbones. One has to look quite skeptically at the values from reference [59] given its deviation from the remainder of the published data. 

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