Interface geometry of binary mixtures on curved substrates

Fonda, Piermarco; Rinaldin, Melissa; Kraft, Daniela J.; Giomi, Luca

doi:10.1103/physreve.98.032801

Cited by 15 publications

(33 citation statements)

References 60 publications

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“…circles, whose total area is fixed solely by the values of x LO,LD . Furthermore, a single, non-maximal circle is the most stable interface 36 , consistent with Fig. 2a and the fact that we never observed more than two coexisting domains on spherical SLVs.…”

Section: Resultssupporting

confidence: 91%

Geometric pinning and antimixing in scaffolded lipid vesicles

et al. 2020

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Previous studies on the phase behaviour of multicomponent lipid bilayers found an intricate interplay between membrane geometry and its composition, but a fundamental understanding of curvature-induced effects remains elusive. Thanks to a combination of experiments on lipid vesicles supported by colloidal scaffolds and theoretical work, we demonstrate that the local geometry and global chemical composition of the bilayer determine both the spatial arrangement and the amount of mixing of the lipids. In the mixed phase, a strong geometrical anisotropy can give rise to an antimixed state, where the lipids are mixed, but their relative concentration varies across the membrane. After phase separation, the bilayer organizes in multiple lipid domains, whose location is pinned in specific regions, depending on the substrate curvature and the bending rigidity of the lipid domains. Our results provide critical insights into the phase separation of cellular membranes and, more generally, twodimensional fluids on curved substrates.

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Section: Resultssupporting

confidence: 91%

Geometric pinning and antimixing in scaffolded lipid vesicles

et al. 2020

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“…Not surprisingly, this equation is precisely the one obtained by the first functional variation of the Jülicher-Lipowsky sharp interface model [45], which we treated in detail in [58]. This latter result hints at a more general concept.…”

Section: Coupling Mechanisms Between Curvature and Order Parametersupporting

confidence: 64%

“…In Ref. [58], we have discussed this and other related phenomena in the framework of the sharp interface limit (i.e. with ξ = 0).…”

Section: The Effect Of Curvaturementioning

confidence: 99%

“…While on a flat plane constant κ g lines are circles (and geodesics are straight lines), on an arbitrary surface they can have significantly less trivial shapes. We explored this subject in much more detail in [58], and refer the interested reader there. Note that (14) does not constrain the topology of γ: in principle it could consist of many simple curves, provided they all have the same curvature.…”

Section: The Effect Of Curvaturementioning

confidence: 99%

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Thermodynamic equilibrium of binary mixtures on curved surfaces

et al. 2019

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We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on non-trivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical sub-diagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as "antimixed" states below the critical temperature. We corroborate our semi-analytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multi-component lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surface of arbitrary geometry.

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“…Ellis [16] studied the effect of self-propulsion and curvature on the degree of defect unbinding. On the other hand, curvature can induce spontaneous flow and flocking [22][23][24][25][26][27][28]. Sanchez and coworkers [22] experimentally studied selfpropelled microtubule bundles on curved surfaces and reported the spontaneous generation of a streaming flow.…”

Section: Introductionmentioning

confidence: 99%

Collective transport of polar active particles on the surface of a corrugated tube

Zhu

Liao

2019

New J. Phys.

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We study collective transport of polar active particles on the surface of a corrugated tube. Particles can be rectified on the surface of the asymmetric tube. The system shows different motion patterns which are determined by the competition between alignment strength and rotational diffusion. For a given alignment strength, there exist transitions from the circulating band state to the travelling state, and finally to the disordered state when continuously changing rotational diffusion. The circulating band is a purely curvature-driven effect with no equivalent in the planar model. The rectification is greatly improved in the travelling state and greatly suppressed in the circulating band state. There exist optimal parameters (modulation amplitude, alignment strength, rotational diffusion, and selfpropulsion speed) at which the rectified efficiency takes its maximal value. Remarkably, in the travelling state, we can observe current reversals by changing translational diffusion.

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Interface geometry of binary mixtures on curved substrates

Cited by 15 publications

References 60 publications

Geometric pinning and antimixing in scaffolded lipid vesicles

Geometric pinning and antimixing in scaffolded lipid vesicles

Thermodynamic equilibrium of binary mixtures on curved surfaces

Collective transport of polar active particles on the surface of a corrugated tube

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