Question

Which one of the following permits the direct determination of intrinsic viscosity of a polymer solution for known molecular weight of the polymer?

• A. Flory-Huggins equation
• B. Newton's law of viscosity
• C. Williams-Landel-Ferry equation
• D. Mark-Houwink equation

Hint:

The {Mark-Houwink equation} is a cornerstone of polymer solution characterization, helping to relate intrinsic viscosity to molecular weight. Knowing the molecular weight allows you to directly calculate the intrinsic viscosity using this equation.

Answer 1

The Correct Option is D

Intrinsic viscosity is a key property that helps determine how a polymer solution behaves in terms of its viscosity relative to its molecular weight. There are several equations that describe different aspects of polymer solution behavior. Let’s explore the options given.
- Flory-Huggins equation is used to describe the thermodynamic properties of polymer solutions, particularly focusing on the interaction between the polymer and solvent. It is useful for understanding enthalpy and entropy changes in the solution, but it does not directly provide the intrinsic viscosity.
- Newton's law of viscosity is a fundamental equation used to describe the relationship between shear stress and shear rate in a fluid. While important for describing fluid dynamics, it does not address the determination of intrinsic viscosity in polymer solutions.
- Williams-Landel-Ferry equation is a model used for understanding the temperature dependence of polymer solution behavior, particularly in the context of viscosity and viscoelastic properties. While useful in some polymer studies, it does not directly relate to intrinsic viscosity for a given molecular weight.
- Mark-Houwink equation is the most direct equation for determining the intrinsic viscosity of a polymer solution from its molecular weight. The equation is given by: \[ [\eta] = K M^a \] where \( [\eta] \) is the intrinsic viscosity, \( M \) is the molecular weight of the polymer, and \( K \) and \( a \) are constants that depend on the polymer-solvent system. This equation allows for the direct calculation of intrinsic viscosity given the molecular weight of the polymer, making it the correct choice for this question.
Thus, the correct answer is (D) Mark-Houwink equation.