Polymers and Statistical Mechanics

• TANAKA Fumihiko

  Dept. of Polymer Chemistry, Graduate School of Engineering, Kyoto University

Bibliographic Information

Other Title

• 数学と高分子　　高分子と統計力学―ループ・レプリカ・カスケード―
• コウブンシ ト トウケイ リキガク ループ レプリカ カスケード
• ループ・レプリカ・カスケード

Abstract

This paper sketches the history of interplay between polymer science and mathematics by focusing on three unique mathematical methods utilized in statistical-mechanical studies of polymers, and presents the perspectives for the future. First, we consider the conformational entropy of polymeric loops as the origin of the singularity in Appell's function, and see how the latter characterizes the nature of the phase transitions in the polymer systems. We next review the replica theory of random systems developed in the study of cross-linking of polymer chains and rubber elasticity, including its application to spin glasses, to see how theoretical ideas in polymer science gave impacts on other fields of materials research. Finally, we review the cascade theory of polycondensation reaction leading to gelation, with potential extension to multiple condensation.

Journal

• Kobunshi

  Kobunshi 57 (2), 76-80, 2008

  The Society of Polymer Science, Japan

Keywords

• Loop Entropy
• Bose-Einstein Condensation
• Replica Method
• Spin Glass
• Residual Entropy
• Gelation
• Cascade Process
• Tree Statistics

Details

• CRID: 1390282679057369216
• NII Article ID: 10021118898
• NII Book ID: AN00084926
• DOI: 10.1295/kobunshi.57.76
• COI: 1:CAS:528:DC%2BD1cXjtlanurk%3D
• ISSN: 21859825
• ISSN: 04541138
• NDL BIB ID: 9368604
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9368604
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed