Viscosity-molecular weight relations

The Mark-Houwink molecular weight-viscosity relation for LPEI in methanol at 25 °C has been determined. ... 

For higher molecular weight polydimethyl siloxanes (Af > 2500), the number-average molecular weight is related to the bulk viscosity by the foUowiag formula, where the viscosity units are mm /s(=cSt). 

Equation (21) describes the relationship between viscosity and molecular weight. Since molecular weight is related to the size of the polymer chain. Generally, for proteins using the following equation ... 

If two different polymers in the same solvent have the same intrinsic viscosity, then their molecular weights are related as... 

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. 

The dielectric constant and loss tangent are the substrate variables. The loss tangent is apparently related to variables such as the molecular weight, viscosity, and conductivity of the material to be dried. Some examples will serve to illustrate the difficulty in predicting the rate at which a material will be heated. 

Viscosity-Average Moiecuiar Weight. The viscosity of dilute polymer solutions may be related to the molecular weight of the polymer by the appropriate calibration (see Viscometry). The polymer is usually separated into narrow molecular weight distribution fractions, which are characterized by absolute molecular weight methods. The molecular weight is related to the intrinsic viscosity [ j] by the Mark-Houwink relationship (eq. 6). 

Where is the radius of a sphere of equivalent hydrodynamic properties, is the radius of gyration of the pol3aner, a is the empirical factor related to a function of molecular weight, p is related to effective moment of unit length, and is the monomer unit molecular weight. Viscosity measurements on proteins in 6M guanidinium chloride have related with M in the following manner... 

For molecules of one type (a g. linear) of a given polymer, intrinsic viscosity and molecular weight are related by the Mark-Houwink equation... 

Equation (8.21) describes the relationship between viscosity and molecular weight. Since molecular weight is related to the size of the polymer chain, Eq. (8.21) also describes the relationship between [q] and N (the number of links in a polymer chain) or [q] and (R ) (the mean-square end-to-end distance). This has stimulated a great deal, interest over the last 40 years as to how they are related. More specifically, what are the meaning of K and a ... 

The molecular weight can be also estimated for petroleum fractions whose boiling point is not known precisely starting with a relation using the viscosities at 100 and 210°F ... 

Viscosity additives are aliphatic polymers of high molecular weight whose main chain is flexible. It is known that in a poor solvent, interactions between the elements making up the polymer chain are stronger than interactions between the solvent and the chain (Quivoron, 1978), to the point that the polymer chain adopts a ball of yarn configuration. The macromolecules in this configuration occupy a small volume. The viscosity of a solution being related to the volume occupied by the solute, the effect of polymers on the viscosity in a poor solvent will be small. 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

Experiments based on the Poiseuille equation make intrinsic viscosity an easily measured parameter to characterize a polymer. In the next section we consider how this property can be related to the molecular weight of a polymer. 

Molecular Weight. The molecular weight of polypropylene is typically determined by viscosity measurements. The intrinsic viscosity [Tj] of the polymer in solution is related to the molecular weight, Af, by the Matk-Houwink equation ... 

Of the three worldwide manufacturers of poly(ethylene oxide) resins. Union Carbide Corp. offers the broadest range of products. The primary quaUty control measure for these resins is the concentrated aqueous solution viscosity, which is related to molecular weight. Specifications for Polyox are summarized in Table 4. Additional product specifications frequendy include moisture content, particle size distribution, and residual catalyst by-product level. 

The limiting low shear or 2ero-shear viscosity T q of the molten polymer can be related to its weight-average molecular weight, by the same... 

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