The Huggins Equation

Huggins (1942) derived Eq. (4.6) to characterize vs ct. The frictional coefficient (k) was included to account for the sizes, shapes and cohesional properties of long-chain, neutral molecules  

This exaggeration makes possible the characterization of polysaccharides by coordinate orientation (Walter, 1991). For routine purposes, accuracy to more than the squared term is seldom required. 

---

Equation (6.20) is known as the Huggins equation. From it, we can see that the limiting case as c tends to zero is that the term (p - PoVho c tends to a... 

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. 

Next, we use the following relationship, which we sometimes call the Huggins equation [1 ] ... 

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] ... 

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

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%. 

Fig. 1.2 Viscosity data on some fractions of PMBzI, plotted according to the Huggins equation. (From ref. [39])...

Equation (4.9) is a logarithmic equivalent of the Huggins equation that obscures the exaggerated effect of the exponent and yields a wider linear range ... 

The Kraemer equation is another logarithmic equivalent of the Huggins equation ... 

Rudin et al. (1973) compared correlations with one, two and three terms of Eq. (16.5) and found that a two-term equation provided very accurate values of [77]. With a two-term equation (i.e. the Huggins equation) slightly different values of [77] were found, but for most purposes the accuracy of these [77] values was sufficient. 

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 ... 

The quantity (In rjjc) is called the inherent viscosity. It too can be expressed as a power law in c in a similar fashion to the Huggins equation. In addition, In rjKl can be... 

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 Huggins equation has been used much more extensively and in Figure 1-6 intrinsic viscosity determination of mesquite seed gum, a galactose-mannose polymer, based on the equation is illustrated (Yoo et al., 1994). 

Figure 1-4 Intrinsic Viscosity Determination of Mesquite Seed Gum, a Galactose-Mannose Polymer, Based on the Huggins equation.

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

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 ... 

In contrast to neutral polymer solutions, where reduced viscosity, 17sp/c, plotted against weight concentration (usually g/dL) shows a straight line (expressed by the Huggins equation) [32], the typical viscosity behavior of a polyelectrolyte solution is shown in Figure 4. This polyelectrolyte was made by quatemization of poly(styrene-co l-vinylpyridine) with n-butyl bromide [16]. The solvents used were a nitromethane/dioxane mixture. Figure 4... 

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 ... 

This chapter reports the syntheses and viscosity behavior in aqueous salt solution of two recently prepared polyampholytes. These polymers, derived from cationic-anionic vinyl monomer pairs, exhibit viscosity behavior in salt solution that is contrary to that of normal polyelectrolytes. The intrinsic viscosity is found to increase with increasing salt concentration for one of the samples and remain virtually unchanged for the other. Also, a modified form of the EinsteinSimha equation is observed to correlate especially well with the experimental data, where, in some cases, the Huggins equation apparently is not appropriate. In the context of these findings, some previous results with regard to the behavior of a polyvinylimidazolium sulfobetaine are discussed. 

Preliminary viscosity studies in KC1 solution have been conducted for poly(MPTMA AMPS) and poly(MPDMA AMPS). The results are reported in Table I. The results shown came from treating the data in two ways using the Huggins equation (Equation 1) and plotting... 

Capillary Viscometry. The viscosity data are plotted in Figure 1 as the reduced viscosity r re as a function of concentration. The curve shows two linear plots that intersect at a polymer concentration, c, of0.075 g dL If the Huggins equation (5)... 

The Kfauion betwwn the ipedlie viscoeity of dilute MlutiaB end that of a concentre ted lolution is shown by the Huggins equation. 

Graphically, two equations may be used to determine [ ] The Huggins equation is... 

---