Intrinsic viscosity shape factor

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. ... 

The hydrodynamic shape factor and axial ratio are related (see Eigure 4.18), but are not generally used interchangeably in the literature. The axial ratio is used almost exclusively to characterize the shape of biological particles, so this is what we will utilize here. As the ellipsoidal particle becomes less and less spherical, the viscosity deviates further and further from the Einstein equation (see Eigure 4.19). Note that in the limit of a = b, both the prolate and oblate ellipsoid give an intrinsic viscosity of 2.5, as predicted for spheres by the Einstein equation. 

The viscosity starts to increase above the CMC and it is well established that the viscosity of a colloidal solution can give information on size and shape of the particles. From studies of the viscosity as a function of micellar concentration, the intrinsic viscosity may be obtained by extrapolation. The intrinsic viscosity depends on a shape factor, and the micelle specific volume and viscosity studies are therefore used to determine micelle shape and hydration. In many cases, these factors appear to be quite constant over a wide concentration range above the CMC. In other cases, such as hexadecyltrimethylammonium bromide (Fig. 2.9), dramatic increases in viscosity are observed at higher concentrations35). Studies of surfactants with low... 

The relation (1 10) leads to a number of interesting consequences. In a theta solvent, in which the shape of the chain is described by the random flight model, is proportional to M2, so that the intrinsic viscosity should be proportional to M /2. And this prediction has been applied and verified. In solvent media better than 0-solvents, the theory of Flory [11,46] predicts that the linear expansion factor a increases for any polymer - homologous series with chain length. Thus the exponent v in the empirical equation should be larger than 0.50. 

Figure 4.1. Theoretical values of the shape factor for ellipsoids. This is a plot of the shape factor, log v versus log of the axial ratio alb) for prolate and oblate ellipsoids. Note that intrinsic viscosity can be approximated by the shape factor for ellipsoids.

Here [i/] is the intrinsic viscosity and f sh > shape factor having the value of 2.5 for spheres is greater than 2.5 for ellipsoids. For compact globular proteins. 

Extraction Rates. The design of large-scale solvent extraction vessels must accommodate the rate at which equilibrium is attained between the free miscella flowing past the solid particles and the miscella absorbed within the solids. Attainment of equilibrium may be quite slow, particularly as the oil content of the solid material drops to low levels. Investigations show that the rate at which equilibrium is approached (in effect, the extraction rate) is influenced by many factors, including the intrinsic capacity for diffusion of solvent and oil, which is determined primarily by the viscosities of the two the size, the shape, and the internal structure of the solid particles and, at low oil levels in the solids, the rate at which the solvent dissolves nontriglyceride substances that are soluble but dissolve less readily than the triglycerides. 

In fact both the above factors are complex. The rotational motion of a molecule is a function of not only its own size and shape, but also depends upon the viscosity of the solution, as well as the temperature. The larger the molecule, the less will be its rotational mobility, the lesser will be the loss of polarization. Thus macromolecules show substantial polarization owing to their greatly decreased mobility. The higher the viscosity, the lower the rotational motion, the lower will be the extent of loss of polarization (in fact at very high viscosity, the polarization observed may be very near that of the intrinsic polarization since the molecule will elicit veiy low rotational motion). The higher the temperature, the more will be the rotational motion, the more will be the loss of polarization. 

Depolarization is a manifestation of the intrinsic properties of the macromolecule. It is the result of Brownian motion and it involves the translation of molecules and their rotational movements. Since Brownian motion is affected by temperature, solvent viscosity, and the size and shape of the molecule, these factors also affect the value of p. The angle 0 between the original direction of the molecules in a... 

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