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.
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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
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|
|Class 1||scaling law of ideal chains||The scaling laws of ideal chains are reviewed to understand the behavior of chains under several constraint conditions.|
|Class 2||scaling law of real chains||Understand the scaling laws of real chains and the blob model.|
|Class 3||mean field theory||Mean-field theory by Floy-Huggins is reviewed.|
|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.|
|Class 8||Practice problems and remarks for confirming the level of understanding||Solve practice problems by accurately understanding all of the above lectures.|
Pierre-Gilles de Gennes "Scaling Concepts in Polymer Physics", Cornell University Press (1979)
To be announced
By final exams. Exercise problems can be the source of evaluation if necessary.
There is no requirement to take this course.
Contact by e-mail in advance to make an appointment