2016 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 required learning from fundamentals. To allow students to get good understanding ofnthe course contents and practical applications, problems related to the contents of this course are provided in Exersices on Physical Chemistry II.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Stress and Strain, Modulous and Viscosity, Linear viscoelasticity (I) Calculate the modulus and vicosity from the stress and strain on uniaxal elongation or simple shear deformation. Explain phenomenological theory on stress relaxation and creep using mechanical models.
Class 2 Linear viscoelasticity (II) Calculate the strage and loss moduli on applying oscillating strain to a viscoelastic model. Derive the relationships between relaxation modulus and vicosity and complex modulus from the Boltzmann's superposition principle.
Class 3 Rubber Elasticity Calculate the tention of rubber and the modulus of a polymer chain. Calculate the cross-linking density from the rubber modulus.
Class 4 Time-temperature superposition principle, Relaxation processes (I) Understand the phenomenological theory on time-temperature superposition principle. Explain temperature dependence of relaxation time based on the free-volume theory to deviate the Williams-Landel-Ferry equation.
Class 5 Unentangled polymer dynamics Explain frequency dependence of complex modulous in the glass transition and terminal fow regions based on the Rouse model.
Class 6 Entangled polymer dymaics Explain the rubber plateau and molecular weight dependence of viscosity for entangled polymer meolts based on the reptation model.
Class 7 Relaxation processes (II) Estimate characteristic times from master curves to understand relaxation processes in polymer melts quantitatively.
Class 8 Applications of viscoelasticity in polymer science / Review Understand applications of viscoelasticity in polymer science based on basic concepts.


The Society of Polymer Science, Japan, ed., Kiso Kobunshi Kagaku (Intoduction to Polymer Science), 2006, Tokyo: Tokyo Kagaku Dojin, ISBN :978-4-8079-0635-2 (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.P322 : Polymer Physics IV (Physical Properties)
  • ZUK.B301 : Exercise in Physical Chemistri II

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

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

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