Equation Mark-Houwink-Sakurada

The Mark-Houwink-Sakurada equation relates tire intrinsic viscosity to tire polymer weight ... 

Molecular weight calibration from a monomer to several million daltons can be carried out by a variety of techniques. Because narrow standards of p(methyl methacrylate) (pMMA) are available, these are often used. Narrow standards of p(styrene) (pSty) are also available and can be used. Using the Mark-Houwink-Sakurada equation and the parameters for pSty and pMMA, a system calibrated with pSty can give pMMA-equivalent values, and vice versa. 

Maleamic acid, cyclization of, 293 Maleic anhydride, 59 Maleimido azine, 307 Manganese diacetate catalysts, 71 Mark-Houwink-Sakurada equation, 57 Material safety data sheets (MSDSs), 246 Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS), 385, 388 McGrath, J. E., 327 MDI isomers, 210 MDIs. See Methylene diphenyl diisocyanates (MDIs)... 

To perform this analysis, we first prepare a dilute solution of polymer with an accurately known concentration. We then inject an aliquot of this solution into a viscometer that is maintained at a precisely controlled temperature, typically well above room temperature. We calculate the solution s viscosity from the time that it takes a given volume of the solution to flow through a capillary. Replicate measurements are made for several different concentrations, from which the viscosity at infinite dilution is obtained by extrapolation. We calculate the viscosity average molecular weight from the Mark-Houwink-Sakurada equation (Eq. 5.5). 

The specific viscosity )jsp of a dilute solution of spheres is directly related to their hydrodynamic volume VV Nl denotes Avogadro s number. Typically the intrinsic viscosity [tj] follows a scaling law, the so-called Mark-Houwink-Sakurada equation ... 

Many polymer properties can be expressed as power laws of the molar mass. Some examples for such scaling laws that have already been discussed are the scaling law of the diffusion coefficient (Equation (57)) and the Mark-Houwink-Sakurada equation for the intrinsic viscosity (Equation (36)). Under certain circumstances scaling laws can be employed advantageously for the determination of molar mass distributions, as shown by the following two examples. 

Not only good solubility but also solution behavior differs for hyperbranched polymers compared to linear polymers. For example, hyperbranched aromatic polyesters, described by Turner et al. [71,72], exhibit a very low a-value in the Mark-Houwink-Sakurada equation and low intrinsic viscosities. This is consist-... 

The viscosity average molecular weight is determined through the use of the Mark-Houwink-Sakurada equation [3] using solution viscosity ... 

Intrinsic viscosity is related to the relative viscosity via a logarithmic function and to the specific viscosity by a simple algebraic relationship. Both of these functions can be plotted on the same graph, and when the data are extrapolated to zero concentration they both should predict the same intrinsic viscosity. The specific viscosity function has a positive slope and the relative viscosity function has a negative slope, as shown in Fig. 3.7. The molecular weight of the polymer can be determined from the intrinsic viscosity, the intercept of either function, using the Mark-Houwink-Sakurada equation. 

Note 2 Kuhn and Sakurada have also made important contributions and their names are sometimes included, as, for example, in the Kuhn-Mark-Houwink-Sakurada equation. 

The relation between number molecular weight, Mn and intrinsic viscosity, [t ], for poly(penLachlorophenyI methacrylate) (PPCIPh) can be represented by the Mark - Houwink - Sakurada equation [44],... 

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...

We take the Mark-Houwink-Sakurada equation (Eq. 3-44) as given. We assume also that the same values of K and a will apply to all species in a polymer mixture dissolved in a given solvent. Consider a whole polymer to be made up of a series of I monodisperse macromolecules each with concentration (weight/volume) c, and molecular weight A/,. From the definition of [r ] in Eq. (3-37),... 

The conversion of a calibration curve for one polymer (say, polystyrene, as in Fig. 3-10) to that for another polymer can be accomplished directly if the Mark-Houwink-Sakurada equations are known for both species in the GPC solvent. From Eq, (3-43), one can write... 

Viscosity measurements alone cannot be directly used in the Mark-Houwink-Sakurada equation to relate absolute viscosity and polymer molecular weight, since additional unknowns, K and a must be determined. Therefore, viscometry does not yield absolute molecular weight values it rather gives only a relative measure of polymer s molecular weight. Viscosity measurements based on the principle of mechanical shearing are also employed, most commonly with concentrated polymer solutions or undiluted polymer these methods, however, are more applicable to flow properties of polymers, not molecular weight determinations. 

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