A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation-Reference-Cited by-同舟云学术

A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation

Published:2024-03 Issue:2286 Volume:480 Page:
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Kodama Hiroki¹^ORCID,Morita Hiroshi²³^ORCID,Kotani Motoko¹³^ORCID

Affiliation:

1. Advanced Institute for Materials Research (AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai-shi, Miyagi 980-8577, Japan

2. Research Center for Computational Design of Advanced Functional Materials (CD-FMat), National Institute of Advanced Industrial Science and Technology (AIST), Central2-1, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan

3. Mathematics for Advanced Materials Open Innovation Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan

Abstract

In this study, a mathematical model based on graph theory is developed to analyse the deformed structures and mechanical properties of thermoplastic elastomers (TPEs) using ABA-type triblock copolymers. TPEs exhibit a network structure formed by bridge chains; deformation of this network structure causes stress. During the deformation of TPEs, domain breakage and coalescence occur, accompanied by topological changes in the chains, such as conformational transitions between the bridge and loop chains. By employing the mathematical concepts of harmonic realization of graphs in the physical space and the tension tensor to quantify the stress in the bridge-chain network structure, an effective method for analysing topologicalchanges in microstructures caused by elongation is proposed. As an application of this method, optimal geometric structures of block copolymers with desired functionalities can be determined.

Funder

Core Research for Evolutional Science and Technology

Japan Science and Technology Agency

Publisher

The Royal Society

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2023.0389

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