Intrinsic viscosity (IV) is a parameter commonly used for investigating interactions in formulations as well as characterising molecules in solution. IV is known as the increase in viscosity of a solution, as an infinitesimally small volume of solute is added to a solvent. Using the IV, it is possible to estimate the hydrodynamic radius. Below is a list of applications relevant to IV measurements:

- Determination of molecule size or weight
- Measuring interactions in protein solutions
- Stability of molecules in terms of aggregation or conformational change
- Studying polymerisation
- Studying degradation

Determining IV is seen as a more reliable method than light scattering for characterisation of molecules in solution. This is due to the scattering of light being highly disturbed by small particulate matter in solution, whereas, the relative change in viscosity as solute concentration is changing, is not.

In order to determine IV, the viscometer used requires exceptional repeatability, the Rheosense *m*-VROC® is unsurpassable, with a repeatability of 0.5% of the reading, as well as an accuracy of 2% of the reading, most other viscometry tools are not suitable for this purpose. In comparison to glass capillary viscometers where the operation is often laborious and time consuming, the *m*-VROC® does not require cleaning between each miscible sample and has a straight forward operation. With the *m*-VROC®’s small volume size and shear rate range of 0.5-1,400,000 s^{-1}, this is a perfect tool for determining IV.

In addition to this, the Rheosense VROC® initium One Plus is a high throughput instrument also capable of determining the intrinsic viscosity using either a 40 vial rack or a 96 well plate, testing either Newtonian or non-Newtonian samples. The initium can be left to measure samples automatically, allowing multiple concentrations to be measured quickly. In addition, having such a small sample requirement of 26 µL means that there can be a wider range of applications. Following testing, values such as hydrodynamic radius and IV can be calculated on the Rheosense Clariti™ software.

The value of IV correlates to the size and molecular weight of macromolecules. This can be empirically modelled using the Mark-Houwink-Sakurada relation:

In this relation, K and a are constant for a given solvent and macromolecule interaction, this will vary dependent on temperature and molecular weight range. The value of a can indicate the conformation of a molecule.

- a = 0, molecule is a compact sphere shape
- a = 0.5-0.8, consists of random coiled shapes
- a = 1.8, consists of rigid rod shapes

Intrinsic viscosity is a measurement of the contribution of a given solute to a dilute solution viscosity. IV can be calculated using the equation below:

Where η is the solution viscosity, η_{r} is the relative viscosity, η_{s} is the solvent viscosity and C is the concentration in mg/mL or mg/dL.

Intrinsic viscosity is equal to the equation below, when at zero concentration:

Multi-point method

The multi-point method is the most common for measuring IV, this is where the viscosity is measured at multiple concentrations. There are two expressions derived from a Taylor series expansion of relative and inherent viscosities, assuming that as the solutes concentration increases, as does the viscosity. The equations are shown below:

Where k_{H} and k_{K} are constants respectively.

These equations can be used to determine IV by extrapolating to establish the value at zero concentration. (See Fig.1 below)

**Figure 1. Determination of IV using a Huggins-Kraemer plot**

Single point method

In order to make intrinsic viscosity measurements faster and easier, it is possible to reduce the viscosity measurements to a singular concentration. Using a single solution and an expression known as the Solomon-Ciuta equation (see below), IV can be determined. In this equation, k_{H} and k_{K} are assumed as being constant, with k_{H} + k_{K} = 0.5

After obtaining the IV, combining this with the molecular weight, it is possible to estimate the hydrodynamic radius using the Einstein-Simha equation:

Where N_{A} is Avogadro’s number and M is the molecular weight.

For more information on intrinsic viscosity, visit the Rheosense website for application notes and blog posts.

Contact us if you’d like to book a demo, find out more information or organise sample testing with any of the Rheosense systems.