Shape equilibria of vesicles with rigid planar inclusions
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911839308218368 |
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| author | Jeon, Geunwoong Fagnoni, Justin Wan, Hao Santore, Maria M. Grason, Gregory M. |
| author_facet | Jeon, Geunwoong Fagnoni, Justin Wan, Hao Santore, Maria M. Grason, Gregory M. |
| contents | Motivated by recent studies of two-phase lipid vesicles possessing 2D solid domains integrated within a fluid bilayer phase, we study the shape equilibria of closed vesicles possessing a single planar, circular inclusion. While 2D solid elasticity tends to expel Gaussian curvature, topology requires closed vesicles to maintain an average, non-zero Gaussian curvature leading to an elementary mechanism of shape frustration that increases with inclusion size. We study elastic ground states of the Helfrich model of the planar-fluid composite vesicles, analytically and computationally, as a function of planar fraction and reduced volume. Notably, we show that incorporation of a planar inclusion of only a few percent dramatically shifts the ground state shapes of vesicles from predominantly {\it prolate} to {\it oblate}, and moreover, shifts the optimal surface to volume ratio far from spherical shapes. We show that for sufficiently small planar inclusions, the elastic ground states break symmetry via a complex variety of asymmetric oblate, prolate, and triaxial shapes, while inclusion sizes above about $8\%$ drive composite vesicles to adopt axisymmetric oblate shapes. These predictions cast useful light on the emergent shape and mechanical responses of fluid-solid composite vesicles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09355 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shape equilibria of vesicles with rigid planar inclusions Jeon, Geunwoong Fagnoni, Justin Wan, Hao Santore, Maria M. Grason, Gregory M. Soft Condensed Matter Materials Science Motivated by recent studies of two-phase lipid vesicles possessing 2D solid domains integrated within a fluid bilayer phase, we study the shape equilibria of closed vesicles possessing a single planar, circular inclusion. While 2D solid elasticity tends to expel Gaussian curvature, topology requires closed vesicles to maintain an average, non-zero Gaussian curvature leading to an elementary mechanism of shape frustration that increases with inclusion size. We study elastic ground states of the Helfrich model of the planar-fluid composite vesicles, analytically and computationally, as a function of planar fraction and reduced volume. Notably, we show that incorporation of a planar inclusion of only a few percent dramatically shifts the ground state shapes of vesicles from predominantly {\it prolate} to {\it oblate}, and moreover, shifts the optimal surface to volume ratio far from spherical shapes. We show that for sufficiently small planar inclusions, the elastic ground states break symmetry via a complex variety of asymmetric oblate, prolate, and triaxial shapes, while inclusion sizes above about $8\%$ drive composite vesicles to adopt axisymmetric oblate shapes. These predictions cast useful light on the emergent shape and mechanical responses of fluid-solid composite vesicles. |
| title | Shape equilibria of vesicles with rigid planar inclusions |
| topic | Soft Condensed Matter Materials Science |
| url | https://arxiv.org/abs/2404.09355 |