Molecular weight from solution viscosity

The viscosity of dilute polymer solutions is considerably higher than that of the pure solvent. The viscosity increase depends on the temperature, the nature of the solvent and polymer, the polymer concentration, and the sizes of the polymer molecules. This last dependence permits estimation of an average molecular weight from solution viscosity. The average molecular weight which is measured is the viscosity average A/v, which differs from those described so far in this text. Before viscosity increase data are used to calculate Afv of the solute it is necessary, however, to eliminate the effects of solvent viscosity and polymer concentration. The methods whereby this is achieved are described in this section. 

HDPE is not soluble in any known solvent at room temperature, although several solvents (ie, xylenes) have a swelling effect. However, certain binary solution mixtures including CS2 dissolve HDPE at as low as 30-40°C. Above 80°C HDPE dissolves in many aliphatic and aromatic hydrocarbons and their halogen-substituted derivatives. Solvents most frequently used include xylenes, tetralin, decalin, o-dichlorobenzene, 1,2,4-trichlorobenzene, and 1,2,4-trimethylbenzene. These solvents are employed for the determination of molecular weights from solution-viscosity data or by gpc. 

A relationship is shown to exist in viscometry experiments between particle size or molecular size and the viscosity of dispersions of inorganic colloids or the viscosity of macromolecular solutions. It is therefore possible to determine the molecular weight from the viscosity of dilute macromolecular solutions. Since this experiment can be rapidly performed with simple equipment, it is, in practice, the most important molecular-weight-determination method. However, the method is not an absolute one, since the viscosity depends on other molecular properties (for example, on the shape of the molecule), as well as on the molecular weight. 

Polymers obtained from PEL monomers of different optical purity were characterized as follows (1) for crystalline properties by differential scanning calorimetry (DSC) and wide-angle x-ray diffraction (2) for relative molecular weights by solution viscosity (3) for structure by IR and NMR spectroscopy and (4) for chiroptical properties in solution by optical rotatory dispersion (ORD) and circular dichroism (CO). Molecular weight and melting point data for both the racemic and optically-active PEL polymers are collected in Table I. 

The molecular weight of the polymer can be determined by either the absolute or relative method. Absolute methods, such as osmotic pressure and light scattering, are more accurate but are lengthy and complex. In practice, dilute solution viscosity is by far one of the most popular relative methods for characterizing the molecular size of the polymers. Molecular weight from intrinsic viscosity data can be determined as follows (9) ... 

The number-average molecular weight of most commercially available acetal resins is between 20,000 and 90,000. Weight-average molecular weight may be estimated from solution viscosities. 

The number average molecular weight is required. This is obtained directly from measurements of a colligative property, such as the osmotic pressure, of dilute polymer solutions (see Chap. VII). It is often more convenient to establish an empirical correlation between the osmotic molecular weight and the dilute solution viscosity, i.e., the so-called intrinsic viscosity, and then to estimate molecular weights from measurements of the latter quantity on the products of polymerization. 

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). 

Conformation in solution is indicated by the way in which the hydro-dynamic properties of the macromolecules change with change in molecular weight. From trends in the intrinsic viscosity, the sedimentation coefficient, or the diffusion constant with molecular weight we can learn something about the conformation of the molecule in solution (19,20). 

A rheological instrument such as a viscometer can be used to evaluate t and 7 and hence obtain a value for the shear viscosity, 17. Examples of Newtonian fluids are pure gases, mixtures of gases, pure liquids of low molecular weight, dilute solutions, and dilute emulsions. In some instances, a fluid may be Newtonian at a certain shear-rate range but deviate from Newton s law of viscosity under either very low or very high shear rates (2). 

We first consider below the commonly used nomenclature for solution viscosity and then describe in later sections the definition and significance of viscosity average molecular weight (Mv) and the method of its determination from solution viscosity. 

It will be shown in Chapter 13 that information gained from solution viscosity measurements under 0 conditions can also be used to predict the critical molecular weight Mcr. Mcr is... 

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