Mark-Houwink relations

Suspension- and emulsion-polymerized PVDF exhibit dissimilar behavior in solutions. The suspension resin type is readily soluble in many solvents even in good solvents, solutions of the emulsion resin type contain fractions of microgel, which contain more head-to-head chain defects than the soluble fraction of the resin (116). Concentrated solutions (15 wt %) and melt rheology of various PVDF types also display different behavior (132). The Mark-Houwink relation (rj = KM°-) for PVDF in A/-methylpyrrohdinone (NMP) containing 0.1 molar LiBr at 85°C, for the suspension (115) and emulsion... 

In all the other solvents used, the intrinsic viscosities are smaller (possibly as a result of charge screening by electrolytes) cuid follow a single Mark-Houwink relation. This equation is found to be ... 

The intrinsic viscosity appears to depend on the molar mass according to the Mark-Houwink relation ... 

The Mark-Houwink relation for polypropylene in o-dichlorobenzene at 130°C was calibrated as follows. A series of sharp fractions of the polymer was obtained by fractionation, and the molecular weight of each fraction was determined by membrane osmometry in toluene at 90"C. The samples were then dissolved in o-dichlorobenzene at I30°C and their intrinsic viscosities ([ ]) were measured. The resulting data fitted an expression of the form... 

Mark-Houwink Relations. The Mark-Houwink relationships obtained for pullulans and dextrans in 0.2 M NaNOa are as follows ... 

If a concentration-selective detector, such as a DRI, is connected on-line with the viscosity detector, the ratio of the two signals yields the intrinsic viscosity distribution of the polymer sample. In polymer characterization, the intrinsic viscosity can be a property just as important as the molecular-weight distribution. Furthermore, polymer intrinsic viscosity follows the Mark-Houwink relation to the molecular weight, M, where K and a are Mark-Houwink viscosity constants ... 

Anger, H., and Berth, G. 1986. Gel permeation chromatography and the Mark-Houwink relations for pectins with different degrees of esterification. Carbohydr. Polym., 6 (3) 193-202. 

Mark-Houwink relation for polymers, from which it can be determined that the polymer chains arc characterized [36] by a random coil geometry in these solvents. This clearly demonstrates that the single polymer chain is flexible, and the torsional degree of freedom must be the main cause for this flexibility. 

Solution characteristics of the polymer have been studied particularly in dimethylformamide that was made 0.1 V in anhydrous lithium bromide to suppress an apparent polyelectrolyte effect occasionally observed [16]. In this system the Mark-Houwink relation for the intrinsic viscosity at 90°C was found to be... 

If no standards of the polymer to be investigated are available, one has to apply universal calibration [34]. This is based on the fact that polymer chains with the same hydrodynamic volume, of which the product [> ]>MM is a good measure, elute at the same time. What is needed then, is a suitable relation between MM and [ij] for both the investigated polymer and the polymer of which standards are available. The Mark-Houwink relation. Equation (11.2), is veiy often used to find the required relations [26,29], in which case [ij] - MM = KM K... 

Higher order moments can be defined, but they are less useful because they cannot be determined as accurately. Other measures of molecular weight include the peak value, Mp, which corresponds to the maximum in the distribution, and Af , determined from the intrinsic viscosity, [rj, using the Mark-Houwink relation (Chapter 3 herein) ... 

The fraction of the sample which gives nin=L6 dL/g has a molecular weight (as estimated from the Mark-Houwink relations ) in the range from about 15,000 (rigid chain limit) to about 60,000 (flexible chain limit). Based on these estimates of the molecular weight, the concentration (lO mole/liter) used for the solution spectroscopic studies is dilute i.e. involving negligible interchain interaction. 

Complementary structural information can be obtained by the Mark-Houwink relation between viscosity and molecular weight (Eq. 4). 

If the Mark-Houwink coefficients for the polymer-solvent system are known, then the IVD measured by SEC-viscornetry can be converted into the molecular weight distribution using the Mark-Houwink relation. This should give greater precision in the measurement of molecular weight distribution than SEC-vi scorn etry with universal calibration, because the IVD measurement is much less sensitive to experimental conditions than a calibration curve. 

There is no need to restrict the definitions to integer-order averages. Indeed the intrinsic viscosity of a polymer is related to the degree of polymerization through the Mark-Houwink relation [9]... 

Atkinson and Dietz [41], using 12 fractions of i-PP and a set of polystyrene standard samples, obtained the universal calibration for polypropylene in ODCB at 135°C. The Mark-Houwink relation and the unperturbed dimensions were determined for polypropylene. The previous studies were compared and the following points made ... 

For their characterization, alginates must first be purified and isolated under their sodium form. NMR spectroscopy ( H and C) is the most powerful technique to characterize the chemical composition and the microstructure of alginates [46 9]. Purified alginates, isolated under the sodium salt form, were also characterized by steric exclusion chromatography (SEC)with three detectors on line. For commercial products, molecular weights may range between 32 000 and 400 000. A further means of characterization is their intrinsic viscosity using the Mark-Houwink relation ... 

---