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Controlling the shape and topology of two-component colloidal membranes. Proc Natl Acad Sci U S A 2022; 119:e2204453119. [PMID: 35914159 PMCID: PMC9371715 DOI: 10.1073/pnas.2204453119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
Abstract
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 micrometer-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 the positive Gaussian modulus, which in turn, is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including shapes similar to catenoids, trinoids, four-noids, and higher-order structures. At long timescales, we observe the formation of a system-spanning, 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 pathway toward control of thin elastic sheets' shape and topology-a pathway driven by the emergent elasticity induced by compositional heterogeneity.
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Kuhnhold A, Göth N, Helmer N. Colloidal membranes of chiral rod-like particles. SOFT MATTER 2022; 18:905-921. [PMID: 35014647 DOI: 10.1039/d1sm01303c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We study colloidal (or smectic) membranes composed of chiral rod-like particles through Monte Carlo simulations. These objects are formed due to the presence of Asakura-Oosawa spheres acting as depletants and creating an effective attraction between the rods. The membranes' shape and structure can be influenced by several parameters, e.g. the number of spheres and rods, their length and their interaction. In order to compare simulation results to an elastic theory, we follow two ansatzes, approximating the free elastic energy in different ways. Both of them lead to reasonable results and capture the behaviour of the colloidal membrane system. One approximation, however, is not suited for achiral rods, where twisting occurs due to surface energy rather than elastic energy. We extract the inverse cholesteric pitch and twist penetration depth for chiral rods with this approximation. The other one is used to introduce a complementary method to estimate elastic constants from the shape of colloidal membranes. Besides, we describe the transition from homogeneously twisted membranes to membranes composed of substructures that occur when the chiral interaction exceeds a length-dependent threshold. We believe that our detailed study and discussion of different aspects of this model system are valuable from a fundamental research viewpoint and suitable for material design suggestions.
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Affiliation(s)
- Anja Kuhnhold
- Institute of Physics, University of Freiburg, 79104 Freiburg (Breisgau), Germany.
| | - Nils Göth
- Institute of Physics, University of Freiburg, 79104 Freiburg (Breisgau), Germany.
| | - Nadja Helmer
- Institute of Physics, University of Freiburg, 79104 Freiburg (Breisgau), Germany.
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Bacchin P, Leng J, Salmon JB. Microfluidic Evaporation, Pervaporation, and Osmosis: From Passive Pumping to Solute Concentration. Chem Rev 2021; 122:6938-6985. [PMID: 34882390 DOI: 10.1021/acs.chemrev.1c00459] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Evaporation, pervaporation, and forward osmosis are processes leading to a mass transfer of solvent across an interface: gas/liquid for evaporation and solid/liquid (membrane) for pervaporation and osmosis. This Review provides comprehensive insight into the use of these processes at the microfluidic scales for applications ranging from passive pumping to the screening of phase diagrams and micromaterials engineering. Indeed, for a fixed interface relative to the microfluidic chip, these processes passively induce flows driven only by gradients of chemical potential. As a consequence, these passive-transport phenomena lead to an accumulation of solutes that cannot cross the interface and thus concentrate solutions in the microfluidic chip up to high concentration regimes, possibly up to solidification. The purpose of this Review is to provide a unified description of these processes and associated microfluidic applications to highlight the differences and similarities between these three passive-transport phenomena.
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Affiliation(s)
- Patrice Bacchin
- Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, 31000 Toulouse, France
| | - Jacques Leng
- CNRS, Solvay, LOF, UMR 5258, Université de Bordeaux, 33600 Pessac, France
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Ding L, Pelcovits RA, Powers TR. Deformation and orientational order of chiral membranes with free edges. SOFT MATTER 2021; 17:6580-6588. [PMID: 34160539 DOI: 10.1039/d1sm00629k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to simulate these systems and determine the phase diagram for the liquid crystalline order of the rods and the membrane shape. We generalize the Lebwohl-Lasher model for a nematic with a chiral coupling to a curved surface with edge tension and a resistance to bending, and include an energy cost for tilting of the rods relative to the local membrane normal. The membrane is represented by a triangular mesh of hard beads joined by bonds, where each bead is decorated by a director. The beads can move, the bonds can reconnect and the directors can rotate at each Monte Carlo step. When the cost of tilt is small, the membrane tends to be flat, with the rods only twisting near the edge for low chiral coupling, and remaining parallel to the normal in the interior of the membrane. At high chiral coupling, the rods twist everywhere, forming a cholesteric state. When the cost of tilt is large, the emergence of the cholesteric state at high values of the chiral coupling is accompanied by the bending of the membrane into a saddle shape. Increasing the edge tension tends to flatten the membrane. These results illustrate the geometric frustration arising from the inability of a surface normal to have twist.
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Affiliation(s)
- Lijie Ding
- Department of Physics, Brown University, Providence, RI 02912, USA.
| | - Robert A Pelcovits
- Department of Physics, Brown University, Providence, RI 02912, USA. and Brown Theoretical Physics Center, Brown University, Providence, RI 02912, USA
| | - Thomas R Powers
- Department of Physics, Brown University, Providence, RI 02912, USA. and Brown Theoretical Physics Center, Brown University, Providence, RI 02912, USA and School of Engineering, Brown University, Providence, RI 02912, USA and Center for Fluid Mechanics, Brown University, Providence, RI 02912, USA
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Akram SA, Behera A, Sharma P, Sain A. Chiral molecules on curved colloidal membranes. SOFT MATTER 2020; 16:10310-10319. [PMID: 33237118 DOI: 10.1039/d0sm01276a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
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 interactions, 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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Affiliation(s)
- Sk Ashif Akram
- Department Of Physics, Indian Institute Of Technology Bombay, Powai-400076, Mumbai, India.
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Ding L, Pelcovits RA, Powers TR. Shapes of fluid membranes with chiral edges. Phys Rev E 2020; 102:032608. [PMID: 33075976 DOI: 10.1103/physreve.102.032608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2020] [Accepted: 08/25/2020] [Indexed: 06/11/2023]
Abstract
We carry out Monte Carlo simulations of a colloidal fluid membrane with a free edge and composed of chiral rodlike viruses. The membrane is modeled by a triangular mesh of beads connected by bonds in which the bonds and beads are free to move at each Monte Carlo step. Since the constituent viruses are experimentally observed to twist only near the membrane edge, we use an effective energy that favors a particular sign of the geodesic torsion of the edge. The effective energy also includes the membrane bending stiffness, edge bending stiffness, and edge tension. We find three classes of membrane shapes resulting from the competition of the various terms in the free energy: branched shapes, chiral disks, and vesicles. Increasing the edge bending stiffness smooths the membrane edge, leading to correlations among the membrane normals at different points along the edge. The normalized power spectrum for edge displacements shows a peak with increasing preferred geodesic torsion. We also consider membrane shapes under an external force by fixing the distance between two ends of the membrane and finding the shape for increasing values of the distance between the two ends. As the distance increases, the membrane twists into a ribbon, with the force eventually reaching a plateau.
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Affiliation(s)
- Lijie Ding
- Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
| | - Robert A Pelcovits
- Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
- Brown Theoretical Physics Center and Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
| | - Thomas R Powers
- Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
- Center for Fluid Mechanics and Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
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Balchunas A, Jia LL, Zakhary MJ, Robaszewski J, Gibaud T, Dogic Z, Pelcovits RA, Powers TR. Force-Induced Formation of Twisted Chiral Ribbons. PHYSICAL REVIEW LETTERS 2020; 125:018002. [PMID: 32678628 DOI: 10.1103/physrevlett.125.018002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2019] [Revised: 03/06/2020] [Accepted: 05/12/2020] [Indexed: 06/11/2023]
Abstract
We demonstrate that an achiral stretching force transforms disk-shaped colloidal membranes composed of chiral rods into twisted ribbons with handedness opposite the preferred twist of the rods. Using an experimental technique that enforces torque-free boundary conditions we simultaneously measure the force-extension curve and the ribbon shape. An effective theory that accounts for the membrane bending energy and uses geometric properties of the edge to model the internal liquid crystalline degrees of freedom explains both the measured force-extension curve and the force-induced twisted shape.
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Affiliation(s)
- Andrew Balchunas
- The Martin Fisher School of Physics, Brandeis University, 415 South Street, Waltham, Massachusetts 02454, USA
| | - Leroy L Jia
- Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA
| | - Mark J Zakhary
- The Martin Fisher School of Physics, Brandeis University, 415 South Street, Waltham, Massachusetts 02454, USA
| | - Joanna Robaszewski
- The Martin Fisher School of Physics, Brandeis University, 415 South Street, Waltham, Massachusetts 02454, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Thomas Gibaud
- Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - Zvonimir Dogic
- The Martin Fisher School of Physics, Brandeis University, 415 South Street, Waltham, Massachusetts 02454, USA
- Department of Physics, University of California at Santa Barbara, Santa Barbara, California 93106, USA
| | - Robert A Pelcovits
- Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
| | - Thomas R Powers
- Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
- School of Engineering, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA
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Siavashpouri M, Sharma P, Fung J, Hagan MF, Dogic Z. Structure, dynamics and phase behavior of short rod inclusions dissolved in a colloidal membrane. SOFT MATTER 2019; 15:7033-7042. [PMID: 31435626 DOI: 10.1039/c9sm01064e] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Inclusions dissolved in an anisotropic quasi-2D membrane acquire new types of interactions that can drive assembly of complex structures and patterns. We study colloidal membranes composed of a binary mixture of long and short rods, such that the length ratio of the long to short rods is approximately two. At very low volume fractions, short rods dissolve in the membrane of long rods by strongly anchoring to the membrane polymer interface. At higher fractions, the dissolved short rods phase separate from the background membrane, creating a composite structure comprised of bilayer droplets enriched in short rods that coexist with the background monolayer membrane. These results demonstrate that colloidal membranes serve as a versatile platform for assembly of soft materials, while simultaneously providing new insight into universal membrane-mediated interactions.
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Affiliation(s)
- Mahsa Siavashpouri
- Department of Physics, Brandeis University, Waltham, MA 02454, USA and Biologics Drug Product Development, Sanofi, Framingham, MA 01701, USA
| | - Prerna Sharma
- Department of Physics, Brandeis University, Waltham, MA 02454, USA and Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Jerome Fung
- Department of Physics, Brandeis University, Waltham, MA 02454, USA and Department of Physics and Astronomy, Ithaca College, Ithaca, NY 14850, USA
| | - Michael F Hagan
- Department of Physics, Brandeis University, Waltham, MA 02454, USA
| | - Zvonimir Dogic
- Department of Physics, Brandeis University, Waltham, MA 02454, USA and Department of Physics, University of California, Santa Barbara, CA 93106, USA.
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