How is the Molecular Weight of a Polymer Determined by the Viscosity Method?

The molecular weight of a polymer is determined by the viscosity method by measuring the viscosity of a polymer solution and relating it to the polymer's molecular weight through established empirical relationships. The molecular weight obtained is specifically called the viscosity-average molecular weight.

Here's a more detailed breakdown:

Understanding Viscosity and Molecular Weight

• Viscosity: Viscosity is a measure of a fluid's resistance to flow. Polymer solutions are generally more viscous than the pure solvent due to the presence of the large polymer molecules, which hinder the flow.

• Molecular Weight and Viscosity: Larger polymer molecules cause greater entanglement and increased resistance to flow, leading to higher solution viscosity. Therefore, there's a relationship between the polymer's molecular weight and the solution's viscosity.

The Viscosity Method: A Step-by-Step Approach

1. Preparation of Polymer Solutions: Several solutions of the polymer are prepared at different concentrations using a suitable solvent. It is crucial that the polymer is completely dissolved in the solvent.

2. Viscosity Measurement: A viscometer (e.g., Ubbelohde viscometer, Ostwald viscometer) is used to measure the flow time of the polymer solutions and the pure solvent. The viscometer is typically placed in a temperature-controlled bath to maintain a constant temperature throughout the experiment.

3. Calculation of Relative Viscosity (η_rel): The relative viscosity is the ratio of the viscosity of the polymer solution (η) to the viscosity of the pure solvent (η₀):

   η_rel = η / η₀ ≈ t / t₀

   where t is the flow time of the polymer solution and t₀ is the flow time of the pure solvent. Because the density of diluted solutions is similar to the density of the solvent, the ratio of viscosities is often estimated from the ratio of flow times.

4. Calculation of Specific Viscosity (η_sp): The specific viscosity represents the increase in viscosity due to the presence of the polymer:

   η_sp = η_rel - 1

5. Calculation of Reduced Viscosity (η_red) and Inherent Viscosity (η_inh):

   • Reduced Viscosity (η_red): Also known as viscosity number, it is calculated by dividing the specific viscosity by the concentration (c) of the polymer solution:

     η_red = η_sp / c

   • Inherent Viscosity (η_inh): Calculated by dividing the natural logarithm of the relative viscosity by the concentration:

     η_inh = (ln η_rel) / c

6. Determination of Intrinsic Viscosity ([η]): The intrinsic viscosity, also known as the limiting viscosity number, is determined by extrapolating the reduced viscosity and/or inherent viscosity to zero concentration. This is typically done by plotting η_red and η_inh versus concentration and finding the y-intercept of the resulting line(s). Ideally, both lines should extrapolate to the same point, which is the intrinsic viscosity.

7. Mark-Houwink Equation: The intrinsic viscosity is related to the viscosity-average molecular weight (M_v) by the Mark-Houwink equation:

   [η] = K * M_v^a

   where:

   • [η] is the intrinsic viscosity
   • M_v is the viscosity-average molecular weight
   • K and a are Mark-Houwink constants, which are specific to the polymer-solvent system and temperature. These constants must be determined experimentally using polymers of known molecular weights.

8. Calculation of Molecular Weight: Once the intrinsic viscosity ([η]) and the Mark-Houwink constants (K and a) are known, the viscosity-average molecular weight (M_v) can be calculated using the Mark-Houwink equation.

Significance of Viscosity-Average Molecular Weight

The viscosity method provides a relatively simple and inexpensive way to estimate the molecular weight of a polymer. However, it's important to remember that the viscosity-average molecular weight (M_v) is an average value and depends on the specific polymer-solvent system and temperature used in the experiment. It is most sensitive to higher molecular weight fractions of the polymer.