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March 06, 2025 | UR Gate

Determination of Molecular Weight of a Polymer


Determination of Molecular Weight (M.wt.) of Polymer by Viscosity Measurement

1. Theoretical Principle

There are several methods to determine the molecular weight of a polymer, one of which is the viscosity measurement method. This method was introduced in 1930 by Staudinger and is fundamentally based on the direct relationship between the solution viscosity and the polymer molecular size. The simplicity of measurement and application has made this method one of the most widely used techniques for determining the molecular weight of polymers.

Before explaining the procedure, it is essential to define some viscosity-related terms:

1.1 Relative viscosity

It is expressed as:

Where:
  • η = viscosity coefficient of the solution (or absolute viscosity of the solution).
  • ηo = viscosity coefficient of the solvent (or absolute viscosity of the solvent).
  • t = time taken for the solution to pass through the capillary tube in the viscometer.
  • to = time taken for the solvent to pass through the capillary tube under the same conditions.

1.2 Specific Viscosity

It is expressed by the equation:
Where:
  • ηsp = Specific viscosity.
  • ηrel = Relative viscosity.

1.3 Reduced Viscosity

Also known as the viscosity number, it is expressed by the equation:


  • Where C is the concentration, expressed in grams per 100 cm³ of the solution. Since the viscosity of the solution is directly proportional to the concentration, when diluted to infinity, we obtain what is called the intrinsic viscosity.


1.4 Intrinsic Viscosity

It is mathematically expressed by the following relationship:


  • Where [η] is the intrinsic viscosity.

From the Mark-Houwink relationship, the molecular weight of the polymer can be determined using the following equation:

Where:

  • Mv = Viscosity-average molecular weight of the polymer (M.wt.).
  • K = A constant that depends on the polymer, the solvent used, and the temperature.
  • a = A constant that depends on the steric configuration of the polymer molecule.


2. The Experimental Procedure

Required Tools:
The setup consists of a water bath to maintain a constant temperature, a stopwatch, and a modified Ostwald viscometer. There are various types of viscometers, as shown in Figure (1).



2.1 Procedure:

  1. Place the cleaned and dried viscometer vertically inside the water bath.
  2. Add approximately 25 cm³ of the solvent into the wide arm of the viscometer.
  3. Allow the device to sit for about five minutes to stabilize the solvent temperature to match the water bath temperature.
  4. Using a rubber tube, draw the solvent up to a level above the upper mark on the capillary tube.
  5. Release the solvent and measure the time it takes to pass between the upper and lower marks on the capillary tube. Repeat this measurement several times to obtain t0.
  6. Empty the viscometer and add a small amount of the polymer solution (approximately 5% w/v).
  7. After allowing it to sit for about five minutes, measure the time it takes for the solution to pass through the capillary tube. Repeat this measurement several times to obtain t1.
  8. Dilute the solution inside the viscometer by adding approximately 5 cm³ of solvent, mix well, and allow the temperature to stabilize.
  9. Measure the time for the diluted solution to pass through the capillary tube, denoted as t2.
  10. Repeat the dilution and measurement process 5-6 times, recording the times for each dilution.
  11. After completing the measurements, empty the viscometer and wash it with the solvent.
  12. Organize the results as shown in the following table:
  • Plot the relationship between ηsp/C and concentration C, then determine the intrinsic viscosity [η] at the point where the line intersects the ηsp/C axis, as shown in Figure (2).
  • Calculate the molecular weight using the Mark-Houwink equation.


3. Results and Discussion

3.1 What is the purpose of the experiment?

The purpose of the experiment is to determine the molecular weight of a polymer using viscosity measurements. This method relies on the relationship between the viscosity of the solution and the polymer's structure and molecular size. This is achieved by:
  • Measuring the time it takes for the solution to pass through the viscometer.
  • Calculating the relative, specific, and reduced viscosities.
  • Using the Mark-Houwink equation to calculate the polymer's molecular weight based on the intrinsic viscosity.

3.2 What is the structural formula of the chosen polymer, and what is its name?

The polymer used in the experiment was not specified. However, as an example of polymers commonly used in viscosity measurements, polystyrene (Polystyrene) can be chosen, and its structural formula is:


If you have the specific polymer used in the experiment, please provide its name for the exact structural formula.


3.3 What are the other methods available for measuring the viscosity of solutions?

In addition to the Ostwald viscometer used in the experiment, other methods for measuring viscosity include:
  1. Rotational Viscometer: Measures the resistance of a liquid to rotation around a specific axis.
  2. Falling Ball Viscometer: Measures the time it takes for a spherical object to fall through the liquid.
  3. Capillary Viscometer: Similar to the Ostwald method but designed for more precise measurements.
  4. Vibrational Viscometer: Measures changes in the vibration frequency of an object immersed in the liquid.
  5. Digital Viscometer: Uses electronic sensors to measure the liquid's resistance to flow.

3.4 What factors affect the viscosity of a polymer?

Several factors influence the viscosity of a polymer solution, including:
  1. Molecular Weight of the Polymer: Viscosity increases with molecular weight because larger molecules experience greater resistance to flow.
  2. Concentration: As the polymer concentration increases, viscosity increases due to greater entanglement of polymer chains.
  3. Temperature: Increasing temperature reduces viscosity because molecules move more freely, and intermolecular forces decrease.
  4. Type of Solvent: Viscosity varies with the solvent type, as the interaction forces between the polymer and solvent affect the size of the polymer molecules in the solution.
  5. Steric Configuration (Conformation): The spatial arrangement of polymer chains affects viscosity, with more entangled or coiled chains leading to higher viscosity.
  6. Presence of Impurities or Additives: Impurities or additives, such as fillers, can increase or decrease viscosity by altering the interactions between molecules.

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