Molecular size, determining from viscosity

In practice, molecular sizes have usually been determined from viscosities on the basis of formulae which are semiempirical (i.e., based partly on theory and partly on experiment). A particularly useful relationship was suggested by Herman F. Mark and R. Houwink ... 

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 molar mass from the viscosity of dilute macromolecular solutions. Since this experiment can be rapidly performed with simple equipment, it is, in practice, the most important molar mass 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. 

A very wide distribution of molecular weights or hydrodynamic coil sizes are usually found within each EOR polymer solution. Because of this polydispersity, the molecular weights or hydrodynamic sizes determined by viscosity measurements are only averages. No information on macromolecular polydispersity is obtained from viscosity measurements. However, characterization of polydispersity is important because EOR polymers which have molecular weight or coil size distributions containing a large proportion of smaller... 

Diffusion and sedimentation measurements on dilute solutions of flexible chain molecules could be used to determine the molecular extension or the expansion factor a. However, the same information may be obtained with greater precision and with far less labor from viscosity measurements alone. For anisometric particles such as are common among proteins, on the other hand, sedimentation velocity measurements used in conjunction with the intrinsic viscosity may yield important information on the effective particle size and shape. ... 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

Earlier (Sect. 18.3.6) we have shown that the diffusion coefficient of liquid penetrants appears to be determined by the viscosity of the solvent (at room temperature) as a measure of molecular size. This conclusion is confirmed by experiments of Ueberreiter (1965) on plasticizers where s and 8 were measured simultaneously and D could be calculated from Eq. (18.63). 

The polystyrene sizes were not the sizes commonly assumed for polystyrenes based on extended chains, but instead were determined from the viscosities (measured by Arro Labs, Joliet, Illinois) as described in Reference 8. Other types of standards and methods of calibration have been used for the GPC of residua samples (3, 9), including the Benoit universal calibration (10). However, these all relate the molecular weight to elution time, and for this work a molecular-size-elution-time relationship was needed. The polystyrene and n-alkane sizes were used to construct a In size vs. elution time calibration that was fit to a fourth-order polynomial to give a smooth curve. 

The average LDL size and density are found to vary between individuals (Adams and Schumaker, 1969 Fisher ft o/., 1975 Krauss and Burke, 1982), and these studies suggest that the variation is due to both genetic and dietary factors. Figure 2 shows hydrodynamic data taken from three studies of subfractionated LDLs and IDLs isolated from different individuals, as summarized by Schumaker (1973). Subfractionation of LDLs by density has yielded particles differing substantially in molecular weights, as determined from their flotation coefficients. To compare values measured under different solvent conditions in these three studies, the flotation coefficients for the particles shown in Fig. 2 have all been corrected for solvent density and viscosity to the values they would exhibit in a KBr solvent with a density of 1.20 g/ml, and the viscosity of KBr at 25°C (Schumaker, 1973). A quantitative molecular model for LDLs consistent with these data will be developed next. 

Tomato PG I and PG II are similar in many respects. Both enzymes are endo-PG s although PG II is more effective in reducing the viscosity of pectate (30). Their pH optima are near 4.5, and both enzymes exhibit broad peaks of activity extending from pH 1.5 to 5.5 when hydrolyzing short-chained substrates (30). They are basic glycoproteins with pH s of 8.6 and 9.4 for PG I and PG II, respectively (12). Antibodies raised against PG II react also with PG I (32). The same polypeptide is obtained when PG I and PG II are denatured in SDS solutions (12., 36). However, the enzymes differ markedly in molecular size and stability to heat. The molecular weights, as determined by gel filtrations are 100,000 and... 

In conclusion, polymer hydrodynamic size estimations from intrinsic viscosity measurements can be in error because shear rate and/or concentration conditions are too high. If intrinsic viscosities are correctly measured, then a viscous average molecular weigh can be determined from the Mark-Houwink equation provided that... 

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