An understandable approach to the temperature dependence of electric properties of polymer-filler composites using elementary quantum mechanics

Masaru Matsuo,Rong Zhang,Yuezhen Bin

doi:10.1515/cti-2020-0014

Abstract

Abstract In today’s society, with a high percentage of elderly people, floor heating to ensure constant temperature and heat jackets in winter play important roles in winter to them to live comfortable lives without compromising health – except tropical zones. Under floor heating maintains a comfortable temperature in a room without polluting the air and heat jackets allow for light clothing at comfortable temperatures. The two facilities are attributed to Joule heat generated by tunnel currents between adjacent short carbon fillers in flexible polymer matrixes under low voltage. The current between adjacent conductive fillers is due to electron transfer associated with elementary quantum mechanics. Most of undergraduate students investigating polymer physics will have learned about electron transfer in relation to the temperature dependence of the conductivity of conductive filler-insulator polymer composites as well as the phenomenon of Joule heat at high school. Despite their industrial importance, most students show little interest for investigating electric properties, since most of polymers are insulation materials. Polymer scientists have carried out qualitative analyses for tunneling current using well-known simplified equations derived from complicated mathematical process formulated by solid-state physicists. Hence this paper is focused on a teaching approach for temperature dependence on electric properties of the polymer-filler composites relating to tunnel current in terms of elementary quantum mechanics. The approach also attempts to bridge education and research by including reference to the application limit of the well-known theories to such complicated composite systems that fillers are dispersed uniformly in the polymer matrix.

Highlights

Most polymers are insulation materials that are easy to mold
When teaching the electric property of insulation polymer-conductive filler composites at the measured temperatures, the mechanism of electron transfer between adjacent fillers embedded in polymer matrix is important to understand tunnel current
To facilitate understanding the electron transfer, electron transmittance based on rectangular potential barrier was presented by using the one-dimensional Schrödinger wave function

Summary

Introduction

Most polymers are insulation materials that are easy to mold. Mixing conductive fillers into polymer matrix provides the temperature dependent conductive property by generation of Joule heat. Through complicated treatments represented in Supplementary material II, the wave functions, φI(x) (Region I), φII(x) (Region II) and φIII(x) (Region III) are described as Eqs.

Results

Conclusion