How Can the Molar Mass of a Polymer Be Determined by Viscosity Measurements?

The molar mass of a polymer can be determined by viscosity measurements by comparing the flow times of polymer solutions to a pure solvent, this method allows us to find what is known as the viscosity average molecular weight.

Understanding Viscosity and Polymer Molecular Weight

Viscosity, in simple terms, is a measure of a fluid's resistance to flow. When we dissolve a polymer in a solvent, the viscosity of the resulting solution increases compared to the pure solvent. This increase is directly related to the size and shape of the polymer molecules. Larger polymer molecules cause more resistance to flow, thus increasing the solution's viscosity. This relationship is the basis of viscosity-based molecular weight determination.

The Viscometer: A Key Tool

A viscometer is used to measure the flow times of liquids. According to the reference, the viscosity is measured by comparing the flow times of two liquids of equal volumes using the same viscometer. In this method, we compare the time it takes for a specific volume of a polymer solution to flow through a narrow tube to the time it takes for the same volume of a pure solvent to flow through the same tube under the same conditions. This comparative measurement provides the necessary information to calculate the polymer's molar mass.

How the Process Works:

1. Solution Preparation: A series of polymer solutions with known concentrations are prepared in a suitable solvent.

2. Flow Time Measurement: Using a viscometer, the flow times of the polymer solutions and the pure solvent are accurately measured.

3. Relative Viscosity Calculation: The relative viscosity (η_rel) is calculated by dividing the flow time of the solution (t) by the flow time of the pure solvent (t₀):

   • η_rel = t / t₀

4. Specific Viscosity Calculation: The specific viscosity (η_sp) is calculated by subtracting 1 from the relative viscosity:

   • η_sp = η_rel - 1

5. Reduced Viscosity Calculation: The reduced viscosity (η_red) is calculated by dividing the specific viscosity by the concentration of the solution (c):

   • η_red = η_sp / c

6. Intrinsic Viscosity Determination: By plotting the reduced viscosity against the polymer concentration, and extrapolating to zero concentration, we can obtain the intrinsic viscosity [η].

7. Molecular Weight Calculation: The intrinsic viscosity is then related to the polymer's viscosity-average molecular weight (M_v) using the Mark-Houwink equation:

   • [η] = K * M_v^a

     where K and a are constants specific to the polymer-solvent system and temperature.

The Viscosity Average Molecular Weight

The molecular weight of the polymer determined through viscosity measurements is called the viscosity average molecular weight. It is an average that is weighted by the size of the polymer chains. Specifically, it places higher emphasis on the larger chains in the sample.

Key Points:

• The technique involves comparative measurements of flow times.
• The viscometer is used to compare the flow times of polymer solutions and the solvent, which is a critical aspect of the technique.
• The viscosity average molecular weight is derived from the relationship between solution viscosity and polymer size.
• The Mark-Houwink equation relates the intrinsic viscosity to the viscosity average molecular weight.