Huggins equation, viscosity measurements

The Huggins equation and Huggins constants can be used to determine values for the limiting viscosity number, [77]. For extrapolation procedmes related to [77] and kh, see (Ref. 4). Applications of the Huggins equation to measure [77] are given in Refs. (5,6). The latter gives an equation for... 

Assays. Nitrogen assays to determine 1-amidoethylene unit content were done by Kjeldahl method. Limiting viscosity numbers were determined from 4 or more viscosity measurements made on a Cannon-Fenske capillary viscometer at 30°C. Data was extrapolated to 0 g/dL polymer concentration using the Huggins equation(44) for nonionic polymers and the Fuoss equation(45) for polyelectrolytes. Equipment. Viscosities were measured using Cannon-Fenske capillary viscometers and a Brookfield LV Microvis, cone and plate viscometer with a CP-40, 0.8° cone. Capillary viscometers received 10 mL of a sample for testing while the cone and plate viscometer received 0.50 mL. 

In many applications a capiiiary viscometer is used to measure the viscosity of poiymer soiutions of differing concentrations, and then the data are piotted to obtain the intrinsic viscosity. Severai techniques have been used to determine intrinsic viscosity from soiution. One is the Huggins equation for intrinsic viscosity [1] ... 

Viscometry. Viscosities of aqueous polymer solutions were measured using a Cannon-Fenske 50 viscometer immersed in a 20°C water bath. The limiting viscosity number was determined from 5 viscosity measurements using the Huggins equation (9). The limiting viscosity number of aged poly( 1-amidoethylene) in 0.01 M aqueous Na2SC>4 was 2.45 dL/g. 

Viscosity Measurements. Viscosity measurements were made in filtered DMF and IN NaOH at 25 =t 0.05°C. The DMF was dried over molecular sieve. Flow times were measured in Cannon-Ubbelohde dilution viscometers, and intrinsic viscosities were obtained from the extrapolation of rjsp/c from the Huggins equation to zero concentration. When an apparent polyelectrolyte effect was found in DMF, the intrinsic viscosities were determined by adding CaCl2 to the DMF or by extrapolation from the higher concentration portion of the Huggins curve. Intrinsic viscosities are probably accurate to about 5%. 

The intrinsic viscosity [r ] is defined in the above equation as a limit at zero concentration. The rj/t o ratios which are actually measured are at finite concentrations, and there are a variety of ways to estimate [rj] from these data. The variation in solution viscosity (p) with increasing concentration can beexpres.sedasa power series in c. The equations usually used are the Huggins equation [8] ... 

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-----------------------------------... 

Figure 1.24 shows experimental determinations of the intrinsic viscosity. When both the Huggins and Kraemer equations provide the same intrinsic viscosity and Huggins coefficient, the higher-order terms in these equations can be safely ignored. On the other hand, if the Huggins and Kraemer plots are curved and do not give the same intercept, viscosity measurements need... 

The relationship between observed viscosity and intrinsic viscosity depends on the volume occupied by the polymer chains (dependent on the first power of their concentration) and the interactions between polymer chains (in the dilute and semi-dilute regions, dependent on the second power of their concentration). The resulting equation, eqn. (4.17), is known as the Huggins equation, with kii being the (dimensionless) Huggins coefficient, which measures chain-chain interaction ... 

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, [ ]. 

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) ... 

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). 

The viscosity number ought to be independent of polymer concentration. However, the Einstein equation is vahd only for noninteracting spheres this simation prevails as the concentration tends to zero. Consequently, we can extrapolate data to infinite dilution, and the result is known as the intrinsic viscosity or limiting viscosity number [t]]. In the past, this quantity was measured in units of deciliters per gram recent practice has been to use miUihters per gram. Data can generally be represented in terms of the Huggins equation. 

Enzyme Kinetics. The change in the number-average molecular weight of gelatin with time was determined as follows. Measurements of viscosity at known concentrations were extrapolated to infinite dilution to obtain the intrinsic viscosity r from Huggins and Kramer s equations,... 

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... 

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