Intrinsic Zero-shear viscosity, related

In earlier studies on solutions of synthetic polymers (Ferry, 1980), the zero-shear viscosity was found to be related to the molecular weight of the polymers. Plots of log r] versus log M often resulted in two straight lines with the lower M section having a slope of about one and the upper M section having a slope of about 3.4. Because the apparent viscosity also increases with concentration of a specific polymer, the roles of both molecular size and concentration of polymer need to be understood. In polymer dispersions of moderate concentration, the viscosity is controlled primarily by the extent to which the polymer chains interpenetrate that is characterized by the coil overlap parameter c[r] (Graessley, 1980). Determination of intrinsic viscosity [r]] and its relation to molecular weight were discussed in Chapter 1. The product c[jj] is dimensionless and indicates the volume occupied by the polymer molecule in the solution. 

The intrinsic viscosity can be related to the overlap concentration, c, by assuming that each coil in the dilute solution contributes to the zero-shear viscosity as would a hard sphere of radius equal to the radius of gyration of the coil. This rough approximation is reasonable as a scaling law because of the effects of hydrodynamic interactions which suppress the flow of the solvent through the coil, as we shall see in Section 3.6.1.2. The Einstein formula for the contribution of suspended spheres to the viscosity is... 

In contrast, a recent study from this laboratory ( 3) concludes that native xanthan molecules are better viewed as stiff but wormlike chains. This conclusion follows from measurements of zero-shear intrinsic viscosity for a homologous series of xanthans of different molecular weight for native xanthan the exponent z in the relation [n ] = KM is only 0.96 rather than 1.8 as expected for rigid rods. It is the goal of this paper to explore whether a wormlike model is consistent with other experimental data, especially the dependence of intrinsic viscosity on shear stress (non-Newtonian behavior). 

Intrinsic viscosities (17) were determined using a Ubbelhode type capillary viscometer and extrapolating to zero shear I4J. Molecular weights for DNA samples were derived from sedimentation constant and intrinsic obesity measurements according to the relations given by Eigner and Doty [5]. 

With appropriate calibration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to zero concentration yield the intrinsic storage and loss moduli [Gr] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instrument provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 Hz. High frequency (20 to 500 K Hz) viscoelastic properties can be measured with another instrument, the high frequency torsional rod apparatus (HFTRA) (294). 

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