Construction of a General Theory of Entanglement based on Topology.

Research Project

Project/Area Number	60470104
Research Category	Grant-in-Aid for General Scientific Research (B)
Allocation Type	Single-year Grants
Research Field	高分子物性
Research Institution	The Research Institute for Material Science and Engineering, Faculty of Engineering, Fukui University
Principal Investigator	FURUSHIMA Teruo (1986) assistant professor, The Research Institute for Materia Science and Enginerring, Fukui University, 工学部附属繊維・機能性材料研究施設, 助教授 (60016376) 岩田一良 (1985) 福井大学, 工学部, 教授
Co-Investigator(Kenkyū-buntansha)	MIZUNO Kazuko Research assistant, The Research Institute for Material Science and Engineering,, 工学部附属繊維・機能性材料研究施設, 教務員 (10126641) IWATA Kazuyoshi professor, The Research Institute for Material Science and Engineering, Fukui Un, 工学部附属繊維・機能性材料研究施設, 教授 (00020230)
Project Period (FY)	1985 – 1986
Project Status	Completed (Fiscal Year 1986)
Budget Amount *help	¥5,000,000 (Direct Cost: ¥5,000,000) Fiscal Year 1986: ¥600,000 (Direct Cost: ¥600,000) Fiscal Year 1985: ¥4,400,000 (Direct Cost: ¥4,400,000)
Keywords	Topological Theory of Entanglement / Topological Second Virial Coefficient of Ring Polymers Topological Interaction Parameter / 高分子の位相幾何学的パラメータ / 高分子の平坦領域の剛性率 / からみ合いの位相幾何学 / 高分子の慣性半径 / 中性子小角散乱 / 網目高分子 / 弾性自由エネルギー / 剛性率
Research Abstract	(1) It is shown that the abnormal second virial coefficient A_2^<<theta>> of ring polystylene found by Roovers and Toporowsky comes from the topologica repulsive force. A_2^<<Theta>> of ring polymers in the <theta> -state is named "topological second virial coefficient A_2^<<theta>>". Using their experimental data of A_2^<<theta>>, topological interaction parameter <gamma>^^- is determined. (2) Our previous topological theory of entanglement is improved and a ne model, "localized Gauss integral model", which is applied to concentrated an highly entangled polymer systems, is proposed and theoretical expression o plateau modulus G_n is derived. Using literature vaules of G_n, <gamma>^^- of various polymers are determined and their A_2^<<theta>> is predicted numerically. It is important that <gamma>^^- determined from G_n for pol ystylene is almost agree with that determined from A_2^<<theta>> . An unexpected result is found that A_2^<<theta>> is numerically equal to G_n/cRT, where c is the weight concentration of polymer molecules, R is the gas constant and T is the measurement temperature of G_n It is further shown that the present model is essentially identical with th repatation model. (3) In summary, it is show in these wroks that A_2^<<theta>> and G_n, which seem to be quite different physical quantities, are essentially identical in th topological theory, and we believe that, combining the present works to ou previous work on the topological rubber elasticity theory, we have constructe the fundamental framework of unified topological theory of entanglement.