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

• Published in: Frontiers in physics 2021-11, Vol.9
• Main Authors: Ma, Panpan, Chan, Ho-Kei
• Format: Article
• Language: English
• Subjects: conductivity; helix; packing; resistor network; sphere; structure
• ISSN: 2296-424X; 2296-424X
• DOI: 10.3389/fphy.2021.778001

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 D , 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 D has been studied for four different types of such columnar structures. It was found that, for increasing D , 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 D = 1 + 3 / 2 (discontinuous zigzag-to-single-helix transition) and D = 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 D = 1 + 4 3 / 7 . The results, which tell us how the system’s electrical conductivity can be tuned through a variation of D , could serve as a guide for the development of quasi-one-dimensional materials with a structurally tunable electrical conductivity.