Entropy driven self-assembly of nonamphiphilic colloidal membranes

Abstract

We demonstrate that homogeneous monodisperse rods in the presence of attractive interactions assemble into equilibrium 2D fluid-like membranes composed of a one-rod length thick monolayer of aligned rods. Unique features of our system allow us to simultaneously investigate properties of these membranes at both continuum and molecular lengthscales. Analysis of thermal fluctuations at continuum lengthscales yields the membranes' lateral compressibility and bending rigidity and demonstrates that the properties of colloidal membranes are comparable to those of traditional lipid bilayers. Fluctuations at molecular lengthscales, in which single rods protrude from the membrane surface, are directly measured by comparing the positions of individual fluorescently labeled rods within a membrane to that of the membrane's continuum conformation. As two membranes approach each other in suspension, protrusion fluctuations are suppressed leading to effective repulsive interactions. Motivated by these observations, we propose an entropic mechanism that explains the stability of colloidal membranes and offers a general design principle for the self-assembly of 2D nanostructured materials from rod-like molecules.colloids | liquid crystals | nanorods | depletion interaction I n hard-body fluids, interactions between individual particles are described by a steep repulsive potential that imposes an infinite energetic penalty for any overlapping particles. It follows that any accessible state of a hard particle fluid has no internal energy and that minimizing the free energy of such a system is equivalent to maximizing its entropy. Hard particles have served as essential model systems for our understanding of the liquid and solid state, demonstrating the existence of nematic and smectic phases in hard rods (1, 2) and a 3D crystalline phase in hard spheres (3). These results exemplify the counterintuitive yet well established notion that entropy alone can drive the self-assembly of ordered structures. In this paper, we extend these ideas of entropic self-assembly to a equilibrium structure, a colloidal membrane. We demonstrate that in the presence of attractive (depletion) interactions mediated by nonadsorbing polymer, monodisperse rod-like colloids (filamentous viruses) spontaneously assemble into 2D membranes. In contrast to the previous examples of entropic self-assembly, in which the constituent molecules assemble into 3D structures, the self-assembly of homogeneous rods into colloidal membranes is self-limited to two dimensions, similar to what is observed for the assembly of amphiphilic lipids into ubiquitous biological membranes (4). However, unlike amphiphilic molecules that have a heterogeneous molecular structure, all the molecules involved in assembly of colloidal membranes are homogeneous, suggesting that geometry as well as chemical heterogeneity can be used to design pathways for self-assembly of various molecular species (5).In what follows, we utilize two unique features of our model experimental virus/polymer system t...

Imprintable membranes from incomplete chiral coalescence

“…We assume that membranes and p-walls formed by filamentous fd viruses are type-II smectic materials, based on the analogy with superconductors 40,41 . In other words, the coherence length x, the length scale of the relaxation of the smectic order, is much smaller than the twist penetration depth l t , confirmed by the agreement of previous theories based on the Frank free energy of monolayers with experiments 13,39,48 . Moreover, we assume a linear p-wall, so that the fields in equation (2) depend only on x.…”

“…Adding nonadsorbing polymer induces effective attractive interactions between otherwise electrostatically repulsive rods through the well-studied depletion mechanism 23 . Under specific conditions, the depleting agent condenses homogeneous rod-like viruses into colloidal membranes, one rod-length-thick chiral smectic-A (Sm-A*) monolayers of aligned rods whose continuum properties are identical to those of conventional lipid bilayers 13,14 . A feature that critically affects the coalescence pathways is the membrane's edge, consisting of a twisted layer of rods that penetrate a small distance into the membrane interior (Fig.…”

“…Here we study the coalescence pathways of two-dimensional (2D) colloidal membranes composed of liquid monolayers of aligned rod-like viruses 13 . We present coalescence dynamics markedly different from that observed between either simple liquid droplets or complex lipid vesicles.…”

Confined chromonics and viral membranes

“…A beautiful series of experiments carried out by the Dogic group at Brandeis [7,8] demonstrated that filamentous viruses like fd-Y21M with half-length l f d = 430 nm or M13K07 with half-length l M13 = 560 nm form robust micron-scale monolayer membranes, depicted schematically in Fig. 3, when dispersed in water with a surfactant like dextran with a radius of a ≈ 25 nm, much less that the viral lengths.…”

“…This article, based on my plenary lecture at ILCC 2016 will review recent work done at the University of Pennsylvania on two separate topics: chromonic liquid crystals in confined geometries [1][2][3][4], carried out mostly in Arjun Yodh's lab by Joonwoo Park and Zoey Davidson with some theoretical assistance from me and my student Louis Kang, and a theory, which is mostly the work of Louis Kang [5,6], for multi-micron-sized two-dimensional membranes composed of filamentous viruses stabilized by depletants studied in exquisite detail by Zvonimir Dogic and collaborators [7,8].…”