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# Intrinsic viscosity determination – dilute solution viscometry

Intrinsic viscosity determination is used in the field of polymer chemistry, a chemistry subdiscipline which deals with the synthesis of polymers as well as the analysis of a polymer’s structure and properties. The intrinsic viscosity is used to classify polymers and helps to identify the applications that specific polymers can be used for.

Polymers are macromolecules which are composed of small repeating units called “monomers” (Figure 1).

Depending on the type of monomer, the size and molecular structure of the polymer molecule, polymers show unique properties. Many different techniques for polymer characterization are available. One of those is “dilute solution viscometry” by which parameters such as the intrinsic viscosity can be determined.

## Determination of the intrinsic viscosity

### Dilute solution viscometry

Dilute solution viscometry is a well-known analytical technique in polymer chemistry for characterizing polymers in solution. The technique is based on the fact that dissolving a polymer in a solvent increases the viscosity of the final polymer solution. The increase of viscosity depends on the temperature, the type of polymer and solvent, the concentration of the polymer, and the molar mass of the polymer. Generally, it can be said that the higher the molar mass of a polymer, the higher the viscosity of the polymer solution will be.[1]

The viscosity of the pure solvent and the viscosity of the polymer solution (polymer dissolved in solvent) are set in relation to each other, which leads to a relative viscosity value. From this basic parameter various polymer parameters can be calculated as shown in Figure 2[1].

The flow behavior of the polymer solution is highly dependent on the molecular structure of the polymer as well as on interactions of the molecules with each other in solution. As the molecular interactions decrease with decreasing concentrations, viscosity measurements are carried out with very dilute solutions. A solution free of any interactions between the polymer molecules could only be reached in the state of the “ideal dilute solution”.[4] In this “ideal dilute solution” the concentration approaches zero meaning that the polymer molecules are isolated from each other and only interact with the solvent molecules. However, this state can never be reached in reality and therefore small polymer interactions have to be considered.[4] Both the calculation of the reduced and the inherent viscosity require the concentration value and therefore the intrinsic viscosity is an important parameter as it is an extrapolation to a theoretical zero concentration.

Various types of glass capillary viscometers, especially Ubbelohde-type glass capillary viscometers, are used for the determination of the intrinsic viscosity and other polymer parameters. Falling-ball- and rolling-ball viscometers are suitable alternatives. The rolling-ball viscometer in particular offers several advantages in comparison to Ubbelohde viscometers . It has a smaller footprint and energy consumption as well as lower solvent and sample consumption. Furthermore, the system is closed and can be automated which makes handling much safer, efficient, and convenient for the users.

Independent of the instrument used, the determination of the intrinsic viscosity can be done in two ways as described in the following paragraphs.

### Single-concentration measurements

Multi-concentration measurements are very time-consuming as first the sample preparation for various polymer solutions has to be done followed by viscosity determination of the various polymer solutions.[4] Therefore, it is possible to determine the intrinsic viscosity from one single polymer solution as well, especially when the intrinsic viscosity is only determined approximately. Most of the equations used are simplifications of the equations used for multi-concentration measurements and derive from the relative and specific viscosity (Figure 3).[6]

### Multi-concentration measurements

In multi-concentration measurements polymer solutions with different concentrations are prepared.Depending on the regression afterwards, the specific, reduced, or inherent viscosity is determined from these solutions.[2] The determined viscosity is then plotted against the concentration of the investigated polymer solutions.[1] The intersection with the y-axis gives the intrinsic viscosity. To guarantee an exact analysis the relative viscosities of the investigated polymer solutions should lie between 1.2 and 2.5.[4] Various regression models can be used, depending on the type of polymer investigated.[2][4] Some exemplary regressions are listed in Figure 4.

Before use, it has to be tested which equation is applicable for a certain polymer-solvent combination. As an example an extrapolation of the reduced viscosity to zero concentration using the Huggins equation (Figure 4, [1]) is shown in Figure 5.

## Intrinsic viscosity calculation

The intrinsic viscosity represents the most relevant variable for describing the viscous behavior of a polymer solution. This is due to the fact that intrinsic viscosity gives the true viscosity-enhancing properties of a polymer independent of its concentration in solution.[2] It is used in various industries to describe the storage stability and quality of a product. One example in which the intrinsic viscosity is used is the plastics industry. However, intrinsic viscosity is also a relevant testing parameter in the pharmaceutical industry. As such it is listed in several monographs of the EU Pharmacopoeia and US Pharmacopeia.

Viscosity measurements for calculating the intrinsic viscosity should always be done at a shear rate approaching 0. At high shear rates the viscosity becomes shear-dependent as the polymer solutions start to show non-Newtonian behavior which is not the case at low shear rates (zero-shear viscosity).[4] To determine the intrinsic viscosity at a shear rate approaching zero, polymer solutions can be measured at various shear rates. The viscosity values obtained are then extrapolated. The intersection with the y-axis gives the zero-shear intrinsic viscosity (Figure 6).

## Intrinsic viscosity and molar mass

The intrinsic viscosity of a polymer in a certain solvent can be correlated with the molar mass via the Mark-Houwink equation.[3]

$$[\eta] = KM^{a}$$

$[\eta]$ = intrinsic viscosity
K,a = Mark-Houwink constants
Figure 7: Mark-Houwink equation

K and a are constants for a given polymer-solvent combination at a certain temperature. If they are not known from literature, they have to be determined experimentally by plotting the logarithm of the intrinsic viscosity as a function of the logarithmic molar mass (Figure 8). The intersection with the y-axis of a linear fit of data gives the constant log K, the slope of the curve gives the constant a (△x/△y).[4]

Examples of K and a for some polymer-solvent combinations are given in Table 1.

Polymer/Solvent Temperature K x10^5 [dL/g] a
Polypropylene/Cyclohexane 25 °C 3.97 0.820
Cellulose Acetate/Water 25 °C 20.9 0.600
Hyaluronic Acid/0.2 M NaCl 25 °C 22.8 0.816
Polystyrene/Toluene 20 °C 11.2 0.722
Natural rubber/THF 25 °C 10.9 0.790

Table 1: K and a for selected polymer-solvent combinations[1][5]

## Conclusion

The intrinsic viscosity is one of the most frequently determined parameters used to characterize polymers. It is used in a wide range of applications, from quality control in plastic processing and plastic recycling to quaility control of ingredients for the production of medicine in the pharmaceutical industry. Among other analytical techniques “dilute solution viscometry” is widely used in polymer chemistry as it is cheap, easily accessible, but also precise. Therefore, it is present in many laboratories around the world and several ISO and ASTM standards are available for testing a large variety of polymers.

## References

1. Tieke, B. (2005). Makromolekulare Chemie. 2nd ed. Weinheim: WILEY_VCH Verlag GmbH & Co. KGaA
2. Nicholson, J. (2017). The chemistry of polymers. 5th ed. Croydon: CPI Group.
3. Chanda, M. (2006). Plastics Technology Handbook. 4th ed. Boca Raton: CRC Press
4. Kulicke, W., Clasen C. (2004) Viscosimetry of Polymers and Polyelectrolytes. Berlin:Springer-Verlag.
5. www.ampolymer.com/Mark-Houwink.html (accessed 20.03.2018)
6. Lovell, P. (1989). Dilute Solution Viscometry. Comprehensive Polymer Science and Supplements. Vol.1. p173–197.