2020 Polymer Physics III (Rheology)

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Academic unit or major
Undergraduate major in Chemical Science and Engineering
Tokita Masatoshi 
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Course description and aims

This course focuses on rheology of linear amorphous polymers. Topics include elasticity of a polymer chain, unentangled polymer dynamics, and entangled polymer dynamics.
Rheology is the science of the deformations and flowing of objects in gas, liquid, and solid states and mesophases between them. Rheology of polymers is vital in the field of polymer processing.

Student learning outcomes

At the end of this course, students will be able to
1) Explain viscoelasticity of polymers phenomenologically and in molecular theory (polymer structures).
2) Explain rubber elasticity in molecular theory (polymer structures) and thermodynamics.
3) Have an understanding of time-temperature superposition principle, and based on this, produce and explain master curves.


viscoelasticity, rubber elasticity, reptation, Rouse model, time-temperature superposition principle, master curve

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Each class is devoted to letting students reach the required learning from fundamentals. To allow students to get a good understanding of the course contents and practical applications, problems related to the contents of this course are provided.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Liquid and Solid; Stress and Strain; Viscosity, Elasticity, and Viscoelasticity Calculate the modulus and viscosity from the stress and strain on uniaxial elongation or simple shear deformation.
Class 2 Phenomenology on Viscoelasticity Explain phenomenological theory on stress relaxation and creep using mechanical models. Calculate the storage and loss moduli on applying oscillating strain to a viscoelastic model.
Class 3 Phenomenology on Viscoelasticity (2) Derive the relationships between relaxation modulus and viscosity and complex modulus from the Boltzmann's superposition principle.
Class 4 Molecular Approach to Polymer Viscoelasticity Calculate the tension of rubber and the modulus of a polymer chain. Calculate the cross-linking density from the rubber modulus.
Class 5 Molecular Approach to Polymer Viscoelasticity (2) Explain the frequency dependence of complex modulus in the glass transition and terminal flow regions based on the Rouse model. Explain the rubber plateau and molecular weight dependence of viscosity for entangled polymer melts based on the reptation model.
Class 6 Time-Temperature Superposition Principle Understand the phenomenological theory on the time-temperature superposition principle. Explain the temperature dependence of relaxation time based on the free-volume theory to deviate the Williams-Landel-Ferry equation.
Class 7 Relaxation Processes; Measurement Techniques Estimate characteristic times from master curves to understand relaxation processes in polymer melts quantitatively. Explain the measurement techniques of polymer viscoelasticity.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


The Society of Polymer Science, Japan, ed., Kiso Kobunshi Kagaku (Introduction to Polymer Science) 2nd ed., 2020, Tokyo: Tokyo Kagaku Dojin, ISBN :978-4-8079-0962-9 (Japanese)

Reference books, course materials, etc.

M. Rubinstein and R. H. Colby, Polymer Physics, Oxford University Press, 2003. ISBN 0-19-852059-X

Assessment criteria and methods

Learning achievement is evaluated by the final examination and the score of quiz given in class.

Related courses

  • CAP.P201 : Polymer Science
  • CAP.P221 : Polymer Physics I (Polymer Solutions)
  • CAP.P222 : Polymer Physics II (Solid Structures)
  • CAP.P322 : Polymer Physics IV (Physical Properties)
  • CAP.P353 : Exercises in Basic of Polymer Science I
  • CAP.P354 : Exercises in Basic of Polymer Science II
  • CAP.P361 : Polymer Chemistry Laboratory I
  • CAP.P354 : Exercises in Basic of Polymer Science II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Physical Chemistry (Thermodynamics),Polymer Science, Polymer Physics I, Polymer Physics II or have equivalent knowledge.

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