2020 Statistical Mechanics for Polymers

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

Course description: This course treats statistical mechanics, which is the basis of any materials science. Statistical mechanics applies probability theory to study macroscopic thermodynamic behavior of systems from the viewpoint of microscopic individual atoms, molecules as their components. Since a polymer chain itself is a kind of molecular assembly, it is indispensable to have such a viewpoint to understand its properties. This course aims at the acquisition of fundamental knowledge of polymer physics with learning the basics of statistical mechanics.
Course aims: Through this course students can learn the basic of statistical mechanics, which is the basis of any materials science. Furthermore, they will understand how the acquired knowledge is utilized in polymer physics.

Student learning outcomes

Students learn the following abilities by this lecture.
1) They learn basic concepts of statistical mechanics such as microcanonical, canonical and grandcanonical ensembles, partition function.
2) Through exercise problems in each class, they learn such concepts with more practical problems.
3) They learn basic knowledge of statistical mechanical treatments of polymers.


microcanonical ensemble, canonical ensemble, grandcanonical ensemble, partition function, entropy, free energy, mean-field approximation, rubber elasticity

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. During the class, students are given exercise problems related to the lecture given that day to solve.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Mathematical preparation (basic of probability theory) Mathematical preparation such as probability theory will be reviewed as an introduction to statistical mechanics.
Class 2 Microcanonical ensemble The method of microcanonical ensemble will be reviewed together with the new concept of temperature based on the context of statistical mechanics.
Class 3 Internal energy and entropy Based on the method of microcanonical ensemble, the concepts of internal energy and entropy will be reviewed.
Class 4 Canonical ensemble and thermodynamic potentials The method of canonical ensemble will be reviewed together with the understanding of partition function and its relationship to thermodynamics quantities.
Class 5 Interacting systems Ising model and several approximation methods such as mean-field theory will be reviewed to treat interacting systems.
Class 6 Application to polymeric systems Statistical mechanics on a single polymer chain, rubber elasticity will be reviewed.
Class 7 Practice problems and interpretation for confirming the level of understanding Practice problems will be given to ensure accurate understanding of the above all lectures.

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.


Atkins' Physical Chemistry, Oxford University Press; 10th Revised (2014)

Reference books, course materials, etc.

To be announced

Assessment criteria and methods

By final exams. Exercise problems can be the source of evaluation if necessary.

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.P521 : Advanced Polymer Physics

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

There is no requirement to take this course, while students who have learned thermodynamics are welcome.

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