Force-Induced Formation of Twisted Chiral Ribbons

Balchunas, Andrew; Jia, Leroy L.; Zakhary, Mark; Robaszewski, Joanna; Gibaud, Thomas; Dogic, Zvonimir; Pelcovits, Robert A.

doi:10.1103/physrevlett.125.018002

Cited by 9 publications

(12 citation statements)

References 41 publications

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“…Fitting of the edge profiles of other saddles of various orders yields similar results. We note that the magnitude of the chiral modulus is comparable to previous estimates [28,41], while κ is nearly an order of magnitude greater than the value for single component membranes. Also, recall that the Gauss-Bonnet theorem shows that the Gaussian curvature energy is effectively an edge energy, despite the fact that it is written as an integral over the entire surface in Eq.…”

Section: Saddle-shaped Membranes Are Enneper-like Minimal Surfacessupporting

confidence: 76%

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Controlling the shape and topology of two-component colloidal membranes

Khanra,

Jia,

Mitchell

et al. 2022

Preprint

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Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micron length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well-approximated by Enneper's minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing positive Gaussian modulus, which in turn is controlled by the fraction of short rods. Further coalescence of saddleshaped surfaces leads to diverse topologically distinct structures, including catenoids, tri-noids, four-noids, and higher order structures. At long time scales, we observe the formation of a systemspanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a novel pathway towards control of thin elastic sheets' shape and topology -a pathway driven by the emergent elasticity induced by compositional heterogeneity. RESULTS Assembly of colloidal membranesColloidal membranes are one-rod-length thick fluid monolayers composed of aligned rods that self-assemble

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Section: Saddle-shaped Membranes Are Enneper-like Minimal Surfacessupporting

confidence: 76%

“…The conformation of a colloidal membrane is described by an energy that accounts for a resistance to bending [26,40], a fixed area, a free edge with an edge tension, a resistance to edge bending, and a preference for a twist due to the chiral constituents [28,41]:…”

Section: Saddle-shaped Membranes Are Enneper-like Minimal Surfacesmentioning

confidence: 99%

Controlling the shape and topology of two-component colloidal membranes

Khanra,

Jia,

Mitchell

et al. 2022

Preprint

Self Cite

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“…We will see that some of these shapes are allowed when there is an external force. The scope of this paper is limited to axisymmetric shapes, although some non-axisymmetric shapes such as helicoids can be treated by similar methods 26 .…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric membranes with edges under external force: buckling, minimal surfaces, and tethers

Jia,

Pei,

Pelcovits

et al. 2021

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We use theory and numerical computation to determine the shape of an axisymmetric fluid membrane with a resistance to bending and constant area. The membrane connects two rings in the classic geometry that produces a catenoidal shape in a soap film. In our problem, we find infinitely many branches of solutions for the shape and external force as functions of the separation of the rings, analogous to the infinite family of eigenmodes for the Euler buckling of a slender rod. Special attention is paid to the catenoid, which emerges as the shape of maximal allowable separation when the area is less than a critical area equal to the planar area enclosed by the two rings. A perturbation theory argument directly relates the tension of catenoidal membranes to the stability of catenoidal soap films in this regime. When the membrane area is larger than the critical area, we find additional cylindrical tether solutions to the shape equations at large ring separation, and that arbitrarily large ring separations are possible. These results apply for the case of vanishing Gaussian curvature modulus; when the Gaussian curvature modulus is nonzero and the area is below the critical area, the force and the membrane tension diverge as the ring separation approaches its maximum value. We also examine the stability of our shapes and analytically show that catenoidal membranes have markedly different stability properties than their soap film counterparts.

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“…Here we focus on colloidal membranes with curved surfaces. While flat circular discs are the most stable structures, a disc can be transformed into a twisted ribbon (helicoid) by lowering temperature [5] or by applying stretching force [7]. Lowering temperature is known to increase molecular chirality which in turn lowers the effective line tension at the membrane edges.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref [7], it was shown that a disk shaped colloidal membrane can transform into a twisted ribbon under external stretching force. Here the contribution of the chiral nematic field, spread over the ribbon shaped membrane, was approximated to the energy of the open edges of the ribbon, assuming an uniform orientation of the rods in the bulk of the ribbon.…”

Section: Introductionmentioning

confidence: 99%

Chiral molecules on curved colloidal membranes

Akram¹,

Behera²,

Sharma³

et al. 2020

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Colloidal membranes, self assembled monolayers of aligned rod like molecules, offer a template for designing membranes with definite shapes and curvature, and possibly new functionalities in the future. Often the constituent rods, due to their molecular chirality, are tilted with respect to the membrane normal. Spatial patterns of this tilt on curved membranes result from a competition among depletion forces, nematic interaction, molecular chirality and boundary effects. We present a covariant theory for the tilt pattern on minimal surfaces, like helicoids and catenoids, which have been generated in the laboratory only recently. We predict several non-uniform tilt patterns, some of which are consistent with experimental observations and some, which are yet to be discovered.

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Force-Induced Formation of Twisted Chiral Ribbons

Cited by 9 publications

References 41 publications

Controlling the shape and topology of two-component colloidal membranes

Controlling the shape and topology of two-component colloidal membranes

Axisymmetric membranes with edges under external force: buckling, minimal surfaces, and tethers

Chiral molecules on curved colloidal membranes

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