AUTHOR=Ma Panpan , Chan Ho-Kei 

TITLE=Densest-Packed Columnar Structures of Hard Spheres: An Investigation of the Structural Dependence of Electrical Conductivity

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.778001

DOI=10.3389/fphy.2021.778001

ISSN=2296-424X

ABSTRACT=<p>Identical hard spheres in cylindrical confinement exhibit a rich variety of densest-packed columnar structures. Such structures, which generally vary with the corresponding cylinder-to-sphere diameter ratio <italic>D</italic>, serve as structural models for a variety of experimental systems at the micro- or nano-scale. In this research, the electrical conductivity as a function of <italic>D</italic> has been studied for four different types of such columnar structures. It was found that, for increasing <italic>D</italic>, the electrical conductivity of each type of structures decreases monotonously, as a result of the system’s resistive components becoming more densely packed along the long axis of the cylindrical space. However, there exists a discontinuous rise in the system’s electrical conductivity at <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:msqrt><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msqrt><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math></inline-formula> (discontinuous zigzag-to-single-helix transition) and <italic>D</italic> = 2 (discontinuous double-helix-to-double-helix transition), respectively, as a result of the establishment of additional conducting paths upon an abrupt increase in the number of inter-particle contacts. This is not the case for the continuous single-helix-to-double-helix transition at <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>4</mml:mn><mml:msqrt><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msqrt><mml:mo>/</mml:mo><mml:mn>7</mml:mn></mml:math></inline-formula>. The results, which tell us how the system’s electrical conductivity can be tuned through a variation of <italic>D</italic>, could serve as a guide for the development of quasi-one-dimensional materials with a structurally tunable electrical conductivity.</p>