Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate
© 2017 Elsevier B.V. We analytically study acoustic modes of a close-packed hexagonal lattice of spheres adhered to a substrate, propagating along a high-symmetry direction. The model, accounting for both normal and shear coupling between the spheres and between the spheres and the substrate, yields...
| Main Authors: | , , , , , , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2021
|
| Online Access: | https://hdl.handle.net/1721.1/133450 |
| _version_ | 1811075495129776128 |
|---|---|
| author | Vega-Flick, A Duncan, RA Wallen, SP Boechler, N Stelling, C Retsch, M Alvarado-Gil, JJ Nelson, KA Maznev, AA |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Vega-Flick, A Duncan, RA Wallen, SP Boechler, N Stelling, C Retsch, M Alvarado-Gil, JJ Nelson, KA Maznev, AA |
| author_sort | Vega-Flick, A |
| collection | MIT |
| description | © 2017 Elsevier B.V. We analytically study acoustic modes of a close-packed hexagonal lattice of spheres adhered to a substrate, propagating along a high-symmetry direction. The model, accounting for both normal and shear coupling between the spheres and between the spheres and the substrate, yields three contact-based vibrational modes involving both translational and rotational motion of the spheres. In addition to contact-based modes, we also study the effect of sphere–substrate and sphere–sphere contacts on spheroidal vibrational modes of the spheres using a perturbative approach. The sphere–substrate interaction results in a frequency upshift for the modes having a non-zero displacement at the contact point with the substrate as well as mode-splitting for some of the degenerate modes of the free sphere. Sphere–sphere interactions result in dispersion of spheroidal modes. Analytical dispersion relations for both contact-based and spheroidal modes are presented and compared with results obtained for a square lattice. |
| first_indexed | 2024-09-23T10:07:01Z |
| format | Article |
| id | mit-1721.1/133450 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:07:01Z |
| publishDate | 2021 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1334502023-02-23T15:03:15Z Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate Vega-Flick, A Duncan, RA Wallen, SP Boechler, N Stelling, C Retsch, M Alvarado-Gil, JJ Nelson, KA Maznev, AA Massachusetts Institute of Technology. Department of Chemistry © 2017 Elsevier B.V. We analytically study acoustic modes of a close-packed hexagonal lattice of spheres adhered to a substrate, propagating along a high-symmetry direction. The model, accounting for both normal and shear coupling between the spheres and between the spheres and the substrate, yields three contact-based vibrational modes involving both translational and rotational motion of the spheres. In addition to contact-based modes, we also study the effect of sphere–substrate and sphere–sphere contacts on spheroidal vibrational modes of the spheres using a perturbative approach. The sphere–substrate interaction results in a frequency upshift for the modes having a non-zero displacement at the contact point with the substrate as well as mode-splitting for some of the degenerate modes of the free sphere. Sphere–sphere interactions result in dispersion of spheroidal modes. Analytical dispersion relations for both contact-based and spheroidal modes are presented and compared with results obtained for a square lattice. 2021-10-27T19:52:55Z 2021-10-27T19:52:55Z 2018 2019-09-26T15:23:39Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133450 en 10.1016/j.wavemoti.2017.10.010 Wave Motion Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Vega-Flick, A Duncan, RA Wallen, SP Boechler, N Stelling, C Retsch, M Alvarado-Gil, JJ Nelson, KA Maznev, AA Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate |
| title | Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate |
| title_full | Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate |
| title_fullStr | Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate |
| title_full_unstemmed | Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate |
| title_short | Contact-based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate |
| title_sort | contact based and spheroidal vibrational modes of a hexagonal monolayer of microspheres on a substrate |
| url | https://hdl.handle.net/1721.1/133450 |
| work_keys_str_mv | AT vegaflicka contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT duncanra contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT wallensp contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT boechlern contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT stellingc contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT retschm contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT alvaradogiljj contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT nelsonka contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate AT maznevaa contactbasedandspheroidalvibrationalmodesofahexagonalmonolayerofmicrospheresonasubstrate |