Densest helical structures of hard spheres in narrow confinement: An analytic derivation
The emergence of helicity from the densest possible packings of equal-sized hard spheres in narrow cylindrical confinement can be understood in terms of a density maximization of repeating microconfigurations. At any cylinder-to-sphere diameter ratio D∈(1+3/2,2), a sphere can only be in contact with...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2019-12-01
|
| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.5131318 |
| _version_ | 1819138374873645056 |
|---|---|
| author | Ho-Kei Chan Yuqian Wang Hongyu Han |
| author_facet | Ho-Kei Chan Yuqian Wang Hongyu Han |
| author_sort | Ho-Kei Chan |
| collection | DOAJ |
| description | The emergence of helicity from the densest possible packings of equal-sized hard spheres in narrow cylindrical confinement can be understood in terms of a density maximization of repeating microconfigurations. At any cylinder-to-sphere diameter ratio D∈(1+3/2,2), a sphere can only be in contact with its nearest and second nearest neighbors along the vertical z-axis, and the densest possible helical structures are results of a minimized vertical separation between the first sphere and the third sphere for every consecutive triplet of spheres. By considering a density maximization of all microscopic triplets of mutually touching spheres, we show, by both analytical and numerical means, that the single helix at D∈(1+3/2,1+43/7) corresponds to a repetition of the same triplet configuration and that the double helix at D∈(1+43/7,2) corresponds to an alternation between two triplet configurations. The resulting analytic expressions for the positions of spheres in these helical structures could serve as a theoretical basis for developing novel chiral materials. |
| first_indexed | 2024-12-22T11:05:46Z |
| format | Article |
| id | doaj.art-b88ee0aa1acc484a93cbcae3d2efcd65 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-22T11:05:46Z |
| publishDate | 2019-12-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-b88ee0aa1acc484a93cbcae3d2efcd652022-12-21T18:28:20ZengAIP Publishing LLCAIP Advances2158-32262019-12-01912125118125118-810.1063/1.5131318Densest helical structures of hard spheres in narrow confinement: An analytic derivationHo-Kei Chan0Yuqian Wang1Hongyu Han2School of Science, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, People’s Republic of ChinaSchool of Science, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, People’s Republic of ChinaSchool of Science, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, People’s Republic of ChinaThe emergence of helicity from the densest possible packings of equal-sized hard spheres in narrow cylindrical confinement can be understood in terms of a density maximization of repeating microconfigurations. At any cylinder-to-sphere diameter ratio D∈(1+3/2,2), a sphere can only be in contact with its nearest and second nearest neighbors along the vertical z-axis, and the densest possible helical structures are results of a minimized vertical separation between the first sphere and the third sphere for every consecutive triplet of spheres. By considering a density maximization of all microscopic triplets of mutually touching spheres, we show, by both analytical and numerical means, that the single helix at D∈(1+3/2,1+43/7) corresponds to a repetition of the same triplet configuration and that the double helix at D∈(1+43/7,2) corresponds to an alternation between two triplet configurations. The resulting analytic expressions for the positions of spheres in these helical structures could serve as a theoretical basis for developing novel chiral materials.http://dx.doi.org/10.1063/1.5131318 |
| spellingShingle | Ho-Kei Chan Yuqian Wang Hongyu Han Densest helical structures of hard spheres in narrow confinement: An analytic derivation AIP Advances |
| title | Densest helical structures of hard spheres in narrow confinement: An analytic derivation |
| title_full | Densest helical structures of hard spheres in narrow confinement: An analytic derivation |
| title_fullStr | Densest helical structures of hard spheres in narrow confinement: An analytic derivation |
| title_full_unstemmed | Densest helical structures of hard spheres in narrow confinement: An analytic derivation |
| title_short | Densest helical structures of hard spheres in narrow confinement: An analytic derivation |
| title_sort | densest helical structures of hard spheres in narrow confinement an analytic derivation |
| url | http://dx.doi.org/10.1063/1.5131318 |
| work_keys_str_mv | AT hokeichan densesthelicalstructuresofhardspheresinnarrowconfinementananalyticderivation AT yuqianwang densesthelicalstructuresofhardspheresinnarrowconfinementananalyticderivation AT hongyuhan densesthelicalstructuresofhardspheresinnarrowconfinementananalyticderivation |