2021 Advanced Polymer Physics

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Academic unit or major
Graduate major in Chemical Science and Engineering
Nakajima Ken 
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Course description and aims

This course offers an opportunity to revisit polymer physics, especially static and dynamic behaviors of polymers using scaling concepts developed by P. G. de Gennes. The scaling concept is the methodology to extract simple yet universal properties of polymer chains with abstracting any chemical details of them, by which one can reconsider several subjects in polymer physics. This course aims at the acquisition of introductory knowledge of scaling concepts.
Through this course students can master the scaling concepts, which now became a kind of common sense among polymer physicists.

Student learning outcomes

Students will be able to do the following by taking this course.
1) list the physical properties of polymers using scaling laws, beginning with the concept of dimensional analysis.
2) explain the so-called blob model for single strands, polymer blends, and crosslinked polymers.
3) explain how the blob model is derived from a description of entanglement with nature and its relationship with critical phenomena.


dimensional analysis, scaling law, ideal chains, real chains, segregation, gels, dynamic scaling, reptation

Competencies that will be developed

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

Class flow

The detailed contents of the classes will be shown using blackboards and slides on a projector. Free discussion among students will be also inserted during the class.

Course schedule/Required learning

  Course schedule Required learning
Class 1 dimension analysis and scaling law Understand the basic concept of dimension analysis and scaling laws.
Class 2 scaling law of ideal chains The scaling laws of ideal chains are reviewed to understand the behavior of chains under several constraint conditions.
Class 3 scaling law of real chains Understand the scaling laws of real chains and the blob model.
Class 4 scaling law of athermal solvents The importance of overlap threshold is introduced by the scaling laws of athermal solvents.
Class 5 segregation problems Segregations of Polymer-polymer and polymer-solvent systems are reviewed.
Class 6 scaling law of gels The scaling laws of gels are reviewed to understand a percolation model.
Class 7 dynamic scaling and relaxation time, reptation of a single chain The understanding of dynamic scaling is introduced to consider the meaning of relaxation times. Through a reptation model for a single chain long-time relaxation is studied.

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.


Pierre-Gilles de Gennes "Scaling Concepts in Polymer Physics", Cornell University Press (1979)

Reference books, course materials, etc.

To be announced

Assessment criteria and methods

By Assignment

Related courses

  • CAP.P201 : Polymer Science
  • CAP.P221 : Polymer Physics I (Polymer Solutions)
  • CAP.P222 : Polymer Physics II (Solid Structures)
  • CAP.P321 : Polymer Physics III (Rheology)
  • CAP.P322 : Polymer Physics IV (Physical Properties)
  • CAP.P202 : Statistical Mechanics for The Polymers

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

There is no requirement to take this course.

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