Jeon Geunwoong, Fagnoni Justin, Wan Hao, Santore Maria M, Grason Gregory M
Department of Physics, University of Massachusetts, Amherst, MA 01003, USA.
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003, USA.
Soft Matter. 2024 Jul 24;20(29):5754-5768. doi: 10.1039/d4sm00439f.
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 fluid-planar 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 prolate to 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 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.
受近期关于在流体双层相中集成有二维固体域的两相脂质囊泡研究的启发，我们研究了具有单个平面圆形内含物的封闭囊泡的形状平衡。虽然二维固体弹性倾向于消除高斯曲率，但拓扑结构要求封闭囊泡保持平均非零高斯曲率，从而导致一种形状受挫的基本机制，这种机制会随着内含物尺寸的增加而增强。我们通过解析和计算研究了流体 - 平面复合囊泡的赫尔弗里希模型的弹性基态，它是平面分数和约化体积的函数。值得注意的是，我们表明仅加入百分之几的平面内含物就会使囊泡的基态形状从主要为长形显著转变为扁形，而且，会使最佳表面积与体积比远离球形。我们表明，对于足够小的平面内含物，弹性基态会打破对称性，呈现出各种复杂的不对称扁形、长形和三轴形状，而当内含物尺寸超过约8%时，复合囊泡会采用轴对称扁形。这些预测为流体 - 固体复合囊泡的新兴形状和力学响应提供了有用的启示。
