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. 

Due to dieir compact, branched structure and to die resulting lack of chain entanglement, dendritic polymers exhibit much lower melt and solution viscosity dian their lineal" counterparts. Low a-values in die Mark-Houwink-Sakurada intrinsic viscosity-molar mass equation have been reported for hyperbranched polyesters.198 199 Dendrimers do not obey diis equation, a maximum being observed in die corresponding log-log viscosity-molar mass curves.200 The lack of chain entanglements, which are responsible for most of the polymer mechanical properties, also explains why hyperbranched polymers cannot be used as diermoplastics for structural applications. Aldiough some crystalline or liquid... 

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)... 

Kasaai M.R. 2007. Calculation of Mark-Houwink-Sakurada (MHS) equation viscometric constants for chitosan in any solvent-temperature system using experimental reported viscometric constants data. Carbohydrate Polymers 68, 477-488. 

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 ... 

Using the Mark-Houwink-Sakurada relation [rj] — KMa [7] one finds... 

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. 

Mark-Houwink-Sakurada relationship, 1 309, 310t 20 439-440 Markov chain, 26 1006, 1018, 1024, 1025 HSTA algorithm and, 26 1030-1031 Markov chain Monte Carlo (MCMC) sampling method, 26 1017-1018 Markovnikov addition, in silicone network preparation, 22 563... 

Poly(Na acrylate30-co-acrylamide7o) Mark-Houwink-Sakurada correlations, 1 310t... 

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-... 

Kuhn-Mark-Houwink-Sakurada (KMHS) Equation.163... 

Staudinger realized that for macromolecules [77] depends characteristically on the molar mass which can be expressed by the Kuhn-Mark-Houwink-Sakurada (KMHS) relationship... 

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. 

The Mark-Houwink-Sakurada constants for PMMA resin are o = 0.73 and K = 1. X 10 Table 3.3 contains solvent viscosity versus concentration data. Find the intrinsic viscosity using both the specific and relative viscosities and the viscosity average molecular weight. 

Next, a plot is made for the terms and n(ri )/c as a function of c as was shown in Fig. 3.7. Extrapolation of the functions to a concentration of zero provides the intrinsic viscosity of 0.565 dl/g, as shown in Eig. 3.8. Using Mark-Houwink-Sakurada Eq. 3.22, the viscosity average molecular weight is calculated at 221,000 kg/kg-mole. 

While it can be expected that a number of physical properties of hyperbranched and dendritic macromolecules will be similar, it should not be assumed that all properties found for dendrimers will apply to hyperbranched macromolecules. This difference has clearly been observed in a number of different areas. As would be expected for a material intermediate between dendrimers and linear polymers, the reactivity of the chain ends is lower for hyperbranched macromolecules than for dendrimers [125]. Dendritic macromolecules would therefore possess a clear advantage in processes, which require maximum chain end reactivity such as novel catalysts. A dramatic difference is also observed when the intrinsic viscosity behavior of hyperbranched macromolecules is compared with regular dendrimers. While dendrimers are found to be the only materials that do not obey the Mark-Houwink-Sakurada relationship, hyperbranched macromolecules are found to follow this relationship, albeit with extremely low a values when compared to linear and branched polymers [126]. 

L.Dq/u.Rq dimensionless number Mark-Houwink-Sakurada constant Axial diffusion coefficient... 

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

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 thermodynamic quality of a solvent for a polymer can be also estimated from Kuhn-Mark-Houwink-Sakurada viscosity law (often called Mark-Houwink equation) ... 

An appropriate formalism for Mark-Houwink-Sakurada (M-H-S) equations for copolymers and higher multispecies polymers has been developed, with specific equations for copolymers and terpolymers created by addition across single double bonds in the respective monomers. These relate intrinsic viscosity to both polymer MW and composition. Experimentally determined intrinsic viscosities were obtained for poly(styrene-acrylonitrile) in three solvents, DMF, THF, and MEK, and for poly(styrene-maleic anhydride-methyl methacrylate) in MEK as a function of MW and composition, where SEC/LALLS was used for MW characterization. Results demonstrate both the validity of the generalized equations for these systems and the limitations of the specific (numerical) expressions in particular solvents. 

---