Viscosity, dilute solution Huggins equation

The relation between the specific viscosity (tjsp) of a dilute solution and that of a concentrated solution is shown by the Huggins equation,... 

We have seen (Chap. 16) that the Huggins equation for the viscosity of a dilute solution has this form it can be expressed in the following way ... 

Numerous empirical equations have been proposed to express the vis cosities as a function of concentrations for the determination of intrinsic viscosity. These equations have been tabulated in several textbooks (see, for example, Philippoff, 1942), but many of them have only limited applications and are already obsolete. Here we will only mention three commonly used ones. For dilute solutions the well-known Huggins equation (1942) can be written as... 

The relative viscosities of polymer solutions are measured at different concentrations and a plot of the reduced viscosity versus concentration is made, in order to extrapolate to zero concentration. The concentration dependence of the viscosity of polymer solutions, in the dilute regime, may be expressed by several linear equations. For practical extrapolation to zero concentration, the most commonly employed are the Huggins equation ... 

In practice, dilute solution viscosity is measured at multiple concentrations and two different forms of Eq. (1.97) are used to extrapolate to zero concentration. One form is the Huggins equation-----------------------------------... 

Viscosities of dilute polymer solutions increase as the polymer concentration is increased (21). Several correlations between these two variables have been suggested. A widely used relationship is the Huggins equation which relates the viscosity to concentration in a quadratic functionality as follows ... 

From the Eq. (4) it follows, that the e q)onent aq, earlier assumed purely empirical characteristic, has a clear structural interpretation. One from the calculated methods of Df determination uses the known Huggins equation, which gives the dependence of reduced viscosity qred on concentration c for diluted polymer solutions [8] ... 

Also known as limiting viscosity number. See also dilute-solution viscosity, Huggins equation, and viscosity-average molecular weight. 

See also Huggins equation and dilute-solution viscosity. Huggins constant, k, and Kraemer s, k, are related by k — k" = 0.5. Thus, since k is often between 0.6 and 0.8, k" will often lie between 0.1 and 0.3. Kamide K, Dobashi T (2000) Physical chemistry of polymer solutions. Elsevier, New York. Huggins ML (1958) Physical chemistry of high polymers. John Wiley and Sons Inc., New York. 

Preliminary viscosity results obtained by using a variable shear Ubbelohde dilution viscometer showed that neither of the three polyampholytes were shear dependent in their dilute solution viscosity behaviorr and all viscosity measurements were subsequently carried out using an ordinary Ubbelohde dilution viscometer. The results were first treated by the well known Huggins equation (Equation 1) (16) ... 

It is known that for dilute polymer solutions and according to the Flory-Huggins equation, the reduced viscosity is a linear function of polymer concentration as follows ... 

Therefore the critical concentration is proportional to the reciprocal intrinsic viscosity. The factor of 2.5 assumes that the polymer coils behave like hard spheres in solution. Viscosimetric measurements for the determination of the intrinsic viscosity have to be performed in dilute solutions at concentrations clearly below c for an exact linear extrapolation according to the Huggins equation (Eq. 4.9). This condition is fulfilled for example in Fig. 4.2, where it is shown that the data points for the viscosimetric determination are below the critical concentration calculated from Eq. (7.7). 

A plot of q,p/C verses C is shown in Figure 5.2. Such plots are normally linear for dilute solutions. On extrapolating the curve to zero concentration, we get an intercept on the Y-axis. The value ofq /C at this dilution gives us the intrinsic viscosity of a solution, depicted by Iq). We also call it thehnuting viscosity number. The Huggins constant k in the equation (3) is obtained from the slope of the curve. The quantity r /C is sometimes called the reduced viscosity. 

Intrinsic viscosity (rj) is the viscosity of an infinitely diluted polymer solution. It is a measure of the hydrodynamic volume occupied by a macromolecule, which is closely related to the size and conformation of the chain, but is independent of concentration of macromolecule. In dilute solutions, by definition, the polymer chains are separated and there is negligible interaction between them. Therefore, the (rj) of polymer in solution depends only on the dimension and the molecular weight of polymer chain. Experimentally determined values of the relative and specific polymer viscosities were used to calculate it, according to Huggins [53] and Kraemer [64] equations given by... 

Viscosity measurements on dilute polymer pseudo-solutions can be used to determine the molecular weight of the dissolved polymer. If polymer concentrations are restricted to levels that give a solution viscosity no more that 1.5 times the solvent viscosity, then the viscosity versus concentration plot determined by measurements on a group of polymer pseudo-solutions can be used with the Huggins (15a.), Krammerer(15b.), Schulz-Blaschka(15c), or Martin (15d.) equations to determine the limiting viscosity number of the polymer, [ ]. 

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