Entropy driven self-assembly of nonamphiphilic colloidal membranes

A Two-Step Intermolecular Interaction Of Molecular Macroions With Multivalent Counterions

Macroion-counterion interaction is essential for regulating the solution behaviors of hydrophilic macroions, as simple models for polyelectrolytes. Here, we explore the interaction between uranyl peroxide molecular cluster Li68K12(OH)20[UO2(O2)OH]60 (U60) and multivalent counterions. Different from interaction with monovalent counterions that shows a simple one-step process, isothermal titration calorimetry, combined with light/X-ray scattering measurements and electron microscopy, confirm a two-step process for their interaction with multivalent counterions: an ion-pairing between U60 and the counterion with partial breakage of hydration shells followed by strong U60-U60 attraction, leading to the formation of large nanosheets with severe breakage and reconstruction of hydration shells. The detailed studies on macroion-counterion interaction can be nicely correlated to the microscopic (self-assembly) and macroscopic (gelation or phase separation) phase transitions in the dilute U60 aqueous solutions induced by multivalent counterions.

Two-Step Chirality Transfer to Twisted Assemblies: Synergistic Interplay of Chiral and Aggregation Interactions

Chirality plays a pivotal role in both the origin of life and the self-assembly of materials. However, the governing principles behind chirality transfer in hierarchical self-assembly across multiple length scales remain elusive. Here, we propose a concise and versatile simulation strategy using the patchy particle chain model to investigate the self-assembly of rods interacting through chiral and aggregation interactions. We reveal that chiral interaction possessing an entropic nature, amplifies the fluctuations and twists in the alignment of rods, while aggregation interaction serves as a foundational platform for aggregation and assembly. When both interactions exhibit moderate absolute and relative values, their synergistic interplay facilitates the chirality transfer from rods to assemblies, resulting in the formation of chiral mesoscale ordered structures. Furthermore, we observe a two-step chirality transfer process by monitoring the formation kinetics of the twisted assemblies. This work not only provides a comprehensive insight into chirality transfer mechanisms, but also introduces a versatile mesoscale simulation framework for exploring the role of chirality in hierarchical self-assembly.

The Secret Ballet Inside Multivesicular Bodies

Lipid bilayers possess the capacity for self-assembly due to the amphipathic nature of lipid molecules, which have both hydrophobic and hydrophilic regions. When confined, lipid bilayers exhibit astonishing versatility in their forms, adopting diverse shapes that are challenging to observe through experimental means. Exploiting this adaptability, lipid structures motivate the development of bio-inspired mechanomaterials and integrated nanobio-interfaces that could seamlessly merge with biological entities, ultimately bridging the gap between synthetic and biological systems. In this work, we demonstrate how, in numerical simulations of multivesicular bodies, a fascinating evolution unfolds from an initial semblance of order toward states of higher entropy over time. We observe dynamic rearrangements in confined vesicles that reveal unexpected limit shapes of distinct geometric patterns. We identify five structures as the basic building blocks that systematically repeat under various conditions of size and composition. Moreover, we observe more complex and less frequent shapes that emerge in confined spaces. Our results provide insights into the dynamics of multivesicular systems, offering a richer understanding of how confined lipid bodies spontaneously self-organize.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Thermodynamically controlled multiphase separation of heterogeneous liquid crystal colloids

Phase separation is a universal physical transition process whereby a homogeneous mixture splits into two distinct compartments that are driven by the component activity, elasticity, or compositions. In the current work, we develop a series of heterogeneous colloidal suspensions that exhibit both liquid-liquid phase separation of semiflexible binary polymers and liquid crystal phase separation of rigid, rod-like nanocellulose particles. The phase behavior of the multicomponent mixture is controlled by the trade-off between thermodynamics and kinetics during the two transition processes, displaying cholesteric self-assembly of nanocellulose within or across the compartmented aqueous phases. Upon thermodynamic control, two-, three-, and four-phase coexistence behaviors with rich liquid crystal stackings are realized. Among which, each relevant multiphase separation kinetics shows fundamentally different paths governed by nucleation and growth of polymer droplets and nanocellulose tactoids. Furthermore, a coupled multiphase transition can be realized by tuning the composition and the equilibrium temperature, which results in thermotropic behavior of polymers within a lyotropic liquid crystal matrix. Finally, upon drying, the multicomponent mixture undergoes a hierarchical self-assembly of nanocellulose and polymers into stratified cholesteric films, exhibiting compartmentalized polymer distribution and anisotropic microporous structure.

Elastic response of colloidal smectic liquid crystals: Insights from microscopic theory

Elongated colloidal rods at sufficient packing conditions are known to form stable lamellar or smectic phases. Using a simplified volume-exclusion model, we propose a generic equation of state for hard-rod smectics that is robust against simulation results and is independent of the rod aspect ratio. We then extend our theory by exploring the elastic properties of a hard-rod smectic, including the layer compressibility (B) and bending modulus (K_{1}). By introducing weak backbone flexibility we are able to compare our predictions with experimental results on smectics of filamentous virus rods (fd) and find quantitative agreement between the smectic layer spacing, the out-of-plane fluctuation strength, as well as the smectic penetration length λ=sqrt[K_{1}/B]. We demonstrate that the layer bending modulus is dominated by director splay and depends sensitively on lamellar out-of-plane fluctuations that we account for on the single-rod level. We find that the ratio between the smectic penetration length and the lamellar spacing is about two orders of magnitude smaller than typical values reported for thermotropic smectics. We attribute this to the fact that colloidal smectics are considerably softer in terms of layer compression than their thermotropic counterparts while the cost of layer bending is of comparable magnitude.

The thermodynamic origins of chiral twist in monolayer assemblies of rod-like colloids

The propagation of chirality across scales is a common but poorly understood phenomenon in soft matter. Here, using computer simulations, we study twisted monolayer assemblies formed by both chiral and achiral rod-like particles in the presence of non-adsorbing polymer and characterise the thermodynamic driving forces responsible for the twisting. We observe assemblies with both like and inverted chirality relative to the rods and show that the preferred twist is already determined during the initial stage of the self-assembly. Depending on the geometry of the constituent rods, the chiral twist is regulated by either the entropy gain of the polymer, or of the rods, or both. This can include important contributions from changes in both the surface area and volume of the monolayer and from rod fluctuations perpendicular to the monolayer. These findings can deepen our understanding of why chirality propagates and of how to control it.

Effect of combined roundness and polydispersity on the phase behavior of hard-rectangle fluids

We introduce a model for a fluid of polydisperse rounded hard rectangles where the length and width of the rectangular core are fixed, while the roundness is taken into account by the convex envelope of a disk displaced along the perimeter of the core. The diameter of the disk has a continuous polydispersity described by a Schulz distribution function. We implemented the scaled particle theory for this model with the aim of studying: (i) the effect of roundness on the phase behavior of the one-component hard-rectangle fluid and (ii) how polydispersity affects phase transitions between isotropic, nematic, and tetratic phases. We found that roundness greatly affects the tetratic phase, whose region of stability in the phase diagram strongly decreases as the roundness parameter is increased. Also, the interval of aspect ratios where the tetratic-nematic and isotropic-nematic phase transitions are of first order considerably reduces with roundness, both transitions becoming weaker. Polydispersity induces strong fractionation between the coexisting phases, with the nematic phase enriched in particles of lower roundness. Finally, for high enough polydispersity and certain mean aspect ratios, the isotropic-to-nematic transition can change from second (for the one-component fluid) to first order. We also found a packing-fraction inversion phenomenon for large polydispersities: the coexisting isotropic phase has a higher packing fraction than the nematic.

Entropic control of nanoparticle self-assembly through confinement

Entropy can be the sole driving force for the construction and regulation of ordered structures of soft matter systems. Specifically, under confinement, the entropic penalty could induce enhanced entropic effects which potentially generate visually ordered structures. Therefore, spatial confinement or a crowding environment offers an important approach to control entropy effects in these systems. Here, we review how spatial confinement-mediated entropic effects accurately and even dynamically control the self-assembly of nanoscale objects into ordered structures, focusing on our efforts towards computer simulations and theoretical analysis. First, we introduce the basic principle of entropic ordering through confinement. We then introduce the applications of this concept to various systems containing nanoparticles, including polymer nanocomposites, biological macromolecular systems and macromolecular colloids. Finally, the future directions and challenges for tailoring nanoparticle organization through spatial confinement-mediated entropic effects are detailed. We expect that this review could stimulate further efforts in the fundamental research on the relationship between confinement and entropy and in the applications of this concept for designer nanomaterials.

Controlling the shape and topology of two-component colloidal membranes

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.

Colloidal membranes of chiral rod-like particles

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.

Multiphase Coexistences in Rod-Polymer Mixtures

Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod-polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer-rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod-polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. ( J. Chem. Phys. 107, 1997 1551).

Thin smectic liquid crystalline fibrils of chiral rodlike particles

Inspired by recent experimental work on virus-polymer mixtures, we study the properties of thin smectic fibrils composed of chiral rodlike particles using Monte Carlo simulations. Due to the interplay between surface energy, elastic deformation energy, and entropic effects, the fibril's layers relax into a twisted state. We focus our study on the layers' twist direction and map our results to the antiferromagnetic Ising model. In this view, the chiral interaction mimics an external field that drives the layers to have the same sense of twist. Besides, we determine the free energy difference and barrier height between an alternating and a nonalternating sequence of twisted layers composed of achiral rods and find that an alternating sequence is slightly preferred. We also see that the fibrils contract on increasing the chiral interaction strength and think that further studies on self-assembled functional materials can use our results.

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

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.

Tuning the photonic properties of graphene oxide suspensions with nanostructured additives

Photonic materials that can selectively reflect light across the visible spectrum are valuable for applications in optical devices, sensors, and decoration. Although two-dimensional (2D) colloids that stack into layers with spacing of hundreds of nanometers are able to selectively diffract light, controlling their separation in solution has proven challenging. In this work, we investigate the role of additives to control the photonic properties of hybrid colloidal suspensions of graphene oxide (GO). We discovered that low concentrations of colloidal additives like cellulose nanocrystals (CNCs) and clay nanoparticles (hectorite) added to GO suspensions lead to dramatic color changes. These hybrid colloidal suspensions demonstrate tunable structural colors and temperature-sensitive properties that likely originate from the entropically driven ejection of guests between the sheets, and from the interactions between colloidal electrical double layers and additional counterions. On the other hand, blending polymeric or molecular additives with GO suspensions either deteriorates or does not impact the photonic properties. These results are helpful to understand the interaction between GO suspensions and additives over different length scales, and open a path to advancing photonic materials based on hybrid colloidal suspensions.

Chiral molecules on curved colloidal membranes

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.

Tunable assembly of hybrid colloids induced by regioselective depletion

Assembling colloidal particles using site-selective directional interactions into predetermined colloidal superlattices with desired properties is broadly sought after, but challenging to achieve. Herein, we exploit regioselective depletion interactions to engineer the directional bonding and assembly of non-spherical colloidal hybrid microparticles. We report that the crystallization of a binary colloidal mixture can be regulated by tuning the depletion conditions. Subsequently, we fabricate triblock biphasic colloids with controlled aspect ratios to achieve regioselective bonding. Without any surface treatment, these biphasic colloids assemble into various colloidal superstructures and superlattices featuring optimized pole-to-pole or centre-to-centre interactions. Additionally, we observe polymorphic crystallization, quantify the abundancy of each form using algorithms we developed and investigate the crystallization process in real time. We demonstrate selective control of attractive interactions between specific regions on an anisotropic colloid with no need of site-specific surface functionalization, leading to a general method for achieving colloidal structures with yet unforeseen arrangements and properties.

Shapes of fluid membranes with chiral edges

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.

Role of Entropy in Colloidal Self-Assembly

Entropy plays a key role in the self-assembly of colloidal particles. Specifically, in the case of hard particles, which do not interact or overlap with each other during the process of self-assembly, the free energy is minimized due to an increase in the entropy of the system. Understanding the contribution of entropy and engineering it is increasingly becoming central to modern colloidal self-assembly research, because the entropy serves as a guide to design a wide variety of self-assembled structures for many technological and biomedical applications. In this work, we highlight the importance of entropy in different theoretical and experimental self-assembly studies. We discuss the role of shape entropy and depletion interactions in colloidal self-assembly. We also highlight the effect of entropy in the formation of open and closed crystalline structures, as well as describe recent advances in engineering entropy to achieve targeted self-assembled structures.

When does entropy promote local organization?

Crowded soft-matter and biological systems organize locally into preferred motifs. Locally-organized motifs in soft systems can, paradoxically, arise from a drive to maximize overall system entropy. Entropy-driven local order has been directly confirmed in model, synthetic colloidal systems, however similar patterns of organization occur in crowded biological systems ranging from the contents of a cell to collections of cells. In biological settings, and in soft matter more broadly, it is unclear whether entropy generically promotes or inhibits local organization. Resolving this is difficult because entropic effects are intrinsically collective, complicating efforts to isolate them. Here, we employ minimal models that artificially restrict system entropy to show that entropy drives systems toward local organization, even when the model system entropy is below reasonable physical bounds. By establishing this bound, our results suggest that entropy generically promotes local organization in crowded soft and biological systems of rigid objects.

Depletion Effect-mediated Association of Carbon Nanotube-Polymer Composites and Their Application as Inexpensive Electrode Support Materials

The association between carbon nanotubes (CNTs) and polymers to afford functional composites has been attributed to enthalpic interactions, neglecting the entropic depletion effect, in which bound solvents are released during the association process. Here, we show that association between multiwalled CNTs and common polymers is governed by the depletion effect, generating a corresponding entropic free energy up to ca. 13 kJ mol^-1 at room temperature, while the enthalpic contribution is insignificant or even negative. Notably, association between the polymers and the CNTs takes place preferentially at the highly stacked CNT junctions, leading to mechanical reinforcement without impacting conductivity. Consequently, high-performance composite membranes were fabricated from inexpensive multiwalled CNTs and polyacrylonitrile (PAN) and were used as electrode supports for platinum (Pt) nanoparticles, affording specific currents 6-7-fold higher than that of Pt foil in the hydrogen evolution reaction and displaying outstanding stability.

Force-Induced Formation of Twisted Chiral Ribbons

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.

All twist and no bend makes raft edges splay: Spontaneous curvature of domain edges in colloidal membranes

Using theory and experiments, we study the interface between two immiscible domains in a colloidal membrane composed of rigid rods of different lengths. Geometric considerations of rigid rod packing imply that a domain of sufficiently short rods in a background membrane of long rods is more susceptible to twist than the inverse structure, a long-rod domain in a short-rod membrane. The midplane tilt at the interdomain edge forces splay, which, in turn, manifests as spontaneous edge curvature with energetics controlled by the length asymmetry of constituent rods. A thermodynamic model of such tilt-curvature coupling at interdomain edges explains a number of experimental observations, including annularly shaped long-rod domains, and a nonmonotonic dependence of edge twist on domain radius. Our work shows how coupling between orientational and compositional degrees of freedom in two-dimensional fluids gives rise to complex shapes of fluid domains, analogous to shape transitions in 3D fluid vesicles.

From Equilibrium Liquid Crystal Formation and Kinetic Arrest to Photonic Bandgap Films Using Suspensions of Cellulose Nanocrystals

The lyotropic cholesteric liquid crystal phase developed by suspensions of cellulose nanocrystals (CNCs) has come increasingly into focus from numerous directions over the last few years. In part, this is because CNC suspensions are sustainably produced aqueous suspensions of a fully bio-derived nanomaterial with attractive properties. Equally important is the interesting and useful behavior exhibited by solid CNC films, created by drying a cholesteric-forming suspension. However, the pathway along which these films are realized, starting from a CNC suspension that may have low enough concentration to be fully isotropic, is more complex than often appreciated, leading to reproducibility problems and confusion. Addressing a broad audience of physicists, chemists, materials scientists and engineers, this Review focuses primarily on the physics and physical chemistry of CNC suspensions and the process of drying them. The ambition is to explain rather than to repeat, hence we spend more time than usual on the meanings and relevance of the key colloid and liquid crystal science concepts that must be mastered in order to understand the behavior of CNC suspensions, and we present some interesting analyses, arguments and data for the first time. We go through the development of cholesteric nuclei (tactoids) from the isotropic phase and their potential impact on the final dry films; the spontaneous CNC fractionation that takes place in the phase coexistence window; the kinetic arrest that sets in when the CNC mass fraction reaches ∼10 wt.%, preserving the cholesteric helical order until the film has dried; the ’coffee-ring effect’ active prior to kinetic arrest, often ruining the uniformity in the produced films; and the compression of the helix during the final water evaporation, giving rise to visible structural color in the films.

Structure, dynamics and phase behavior of short rod inclusions dissolved in a colloidal membrane

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.

Equation of state of colloidal membranes

In the presence of a non-adsorbing polymer, monodisperse rod-like colloids assemble into one-rod-length thick liquid-like monolayers, called colloidal membranes. The density of the rods within a colloidal membrane is determined by a balance between the osmotic pressure exerted by the enveloping polymer suspension and the repulsion between the colloidal rods. We developed a microfluidic device for continuously observing an isolated membrane while dynamically controlling the osmotic pressure of the polymer suspension. Using this technology we measured the membrane rod density over a range of osmotic pressures than is wider that what is accessible in equilibrium samples. With increasing density we observed a first-order phase transition, in which the in-plane membrane order transforms from a 2D fluid into a 2D solid. In the limit of low osmotic pressures, we measured the rate at which individual rods evaporate from the membrane. The developed microfluidic technique could have wide applicability for in situ investigation of various soft materials and how their properties depend on the solvent composition.

Conformational switching of chiral colloidal rafts regulates raft-raft attractions and repulsions

Membrane-mediated particle interactions depend both on the properties of the particles themselves and the membrane environment in which they are suspended. Experiments have shown that chiral rod-like inclusions dissolved in a colloidal membrane of opposite handedness assemble into colloidal rafts, which are finite-sized reconfigurable droplets consisting of a large but precisely defined number of rods. We systematically tune the chirality of the background membrane and find that, in the achiral limit, colloidal rafts acquire complex structural properties and interactions. In particular, rafts can switch between 2 chiral states of opposite handedness, which alters the nature of the membrane-mediated raft-raft interactions. Rafts with the same chirality have long-ranged repulsions, while those with opposite chirality acquire attractions with a well-defined minimum. Both attractive and repulsive interactions are qualitatively explained by a continuum model that accounts for the coupling between the membrane thickness and the local tilt of the constituent rods. These switchable interactions enable assembly of colloidal rafts into intricate higher-order architectures, including stable tetrameric clusters and "ionic crystallites" of counter-twisting domains organized on a binary square lattice. Furthermore, the properties of individual rafts, such as their sizes, are controlled by their complexation with other rafts. The emergence of these complex behaviors can be rationalized purely in terms of generic couplings between compositional and orientational order of fluids of rod-like elements. Thus, the uncovered principles might have relevance for conventional lipid bilayers, in which the assembly of higher-order structures is also mediated by complex membrane-mediated interactions.

Phase-dependent shear-induced order of nanorods in isotropic and nematic wormlike micelle solutions

Small angle X-ray scattering with in situ shear was employed to study the assembly and ordering of dispersions of gold nanorods within wormlike micelle solutions formed by the surfactant cetylpyridinium chloride (CPyCl) and counter-ion sodium salicylate (NaSal). Above a threshold CPyCl concentration but below the isotropic-to-nematic transition of the micelles, the nanorods self-assembled under quiescent conditions into isotropically oriented domains with hexagonal order. Under steady shear at rates between 0.5 and 7.5 s-1, the nanorod assemblies acquired macroscopic orientational order in which the hexagonal planes were coincident with the flow-vorticity plane. The nanorods could be re-dispersed by strong shear but re-assembled following cessation of the shear. In the nematic phase of the micelles at higher surfactant concentration, the nanorods did not acquire hexagonal order but instead formed smectic-like layers in the gradient-vorticity plane under shear. Finally, at still higher surfactant concentration, where the micelles form a hexagonal phase, the nanorods showed no translational ordering but did acquire nematic-like order under shear due to alignment in the flow. Depletion forces mediated by the wormlike micelles are identified as the driving mechanism for this sequence of nanorod ordering behaviors, suggesting a novel mechanism for controlled, reconfigurable assembly of nanoparticles in solution.

Directing Liquid Crystalline Self-Organization of Rodlike Particles through Tunable Attractive Single Tips

Dispersions of rodlike colloidal particles exhibit a plethora of liquid crystalline states, including nematic, smectic A, smectic B, and columnar phases. This phase behavior can be explained by presuming the predominance of hard-core volume exclusion between the particles. We show here how the self-organization of rodlike colloids can be controlled by introducing a weak and highly localized directional attractive interaction between one of the ends of the particles. This has been performed by functionalizing the tips of filamentous viruses by means of regioselectively grafting fluorescent dyes onto them, resulting in a hydrophobic patch whose attraction can be tuned by varying the number of bound dye molecules. We show, in agreement with our computer simulations, that increasing the single tip attraction stabilizes the smectic phase at the expense of the nematic phase, leaving all other liquid crystalline phases invariant. For a sufficiently strong tip attraction, the nematic state may be suppressed completely to get a direct isotropic liquid-to-smectic phase transition. Our findings provide insights into the rational design of building blocks for functional structures formed at low densities.

Nanoparticle Ligand Exchange and Its Effects at the Nanoparticle-Cell Membrane Interface

The nanoparticle (nano)-cell membrane interface is one of the most important interactions determining the fate of nanoparticles (NPs), which can stimulate a series of biological events, allowing theranostic and other biomedical applications. So far, there remains a lack of knowledge about the mechanisms governing the nanoparticle-cell membrane interface, especially the impact of ligand exchange, in which molecules on the nanosurface become replaced with components of the cell membrane, resulting in unique interfacial phenomena. Herein, we describe a family of gold nanoparticles (AuNPs) of the same core size (∼13 nm core), modified with 12 different kinds of surface ligands, and the effects of their exchangeable ligands on both nanoparticle-supported lipid bilayers (SLBs) and nanoparticle-natural cell membrane interfaces. The ligands are categorized according to their molecular weight, charge, and bonding modes (physisorption or chemisorption). Importantly, we found that, depending on the adsorption affinity and size of ligand molecules, physisorbed ligands on the surface of NPs can be exchanged with lipid molecules. At a ligand exchange-dominated interface, the AuNPs typically aggregated into an ordered monolayer in the lipid bilayers, subsequently affecting cell membrane integrity, NP uptake efficiency, and the NP endocytosis pathways. These findings advance our understanding of the underlying mechanisms of the biological effects of nanoparticles from a new point of view and will aid in the design of novel, safe, and effective nanomaterials for biomedicine.

Self assembly of cyclic polygon shaped fluid colloidal membranes through pinning

2D fluid monolayer membranes of rod-like viruses spontaneously form in a mixture of rods and polymers through depletion attraction. The rods are uniformly oriented within the bulk and twist in a zone around the membrane edge. Surprisingly, we find that cyclic polygonal shaped colloidal membranes form when polymers are added to a mixture of long and short-thick rods with the long and short-thick rods forming the faceted core and lobes of the polygon, respectively. We demonstrate that the origin of this anisotropic shape lies in the phenomenon of spreading of one liquid over another in the presence of disorder. As a membrane of short-thick rods spreads over another of longer rods, the edge bound rods untwist to become part of the newly formed two-rod interface. However, a small fraction of rods fail to untwist as the two rod interface forms and act as mobile pinning centers. Capillary flow of short-thick rods drives all the pinning centers to a single location in the composite membrane which now acts like a junction. This pinning junction inhibits complete engulfing of one membrane by the other. Repeated sequential events like this then lead to formation of multiple junctions and the overall cyclic polygon topology. We find that pinning junctions are weakly cross-linked in nature instead of being topological defects. We outline the necessary and sufficient constraints on the nature of rods to obtain stable out of equilibrium cyclic polygon membranes. Our results show a unique counter-intuitive scenario where defects lead to self-assembly of ordered structures.

Elementary Edge and Screw Dislocations Visualized at the Lattice Periodicity Level in the Smectic Phase of Colloidal Rods

Topological defects such as dislocations play a major role in science, from condensed matter and geophysics to cosmology. These line defects present in periodically ordered structures mediate phase transitions and determine many distinctive features of materials, from crystal growth to mechanical properties. However, despite theoretical predictions, the detailed structure of dislocations remains largely elusive. By using a model system of tip-labeled rod-shaped particles enabling improved resolution and contrast by optical microscopy, in situ visualization and quantitative characterization of elementary dislocations has been performed at the lattice periodicity level in a colloidal smectic phase. Thanks to the micrometer layer spacing, the displacement field around an edge dislocation has been experimentally established and compared with the profile predicted by elastic theory. The local morphology of screw dislocations has also been evidenced, with the determination of the core size as well as the chiral handedness of the defect. Self-diffusion experiments performed at the individual particle level reveal for the first time nematiclike or "melted" ordering of the defect core.

Direct Liquid to Crystal Transition in a Quasi-Two-Dimensional Colloidal Membrane

Using synchrotron-based small-angle X-ray scattering, we study rigid fd viruses assembled into isolated monolayers from mixtures with a nonabsorbing polymer, which acts as an osmotic agent. As the polymer concentration increases, we observe a direct liquid to crystal transition, without an intermediate hexatic phase, in contrast with many other similar systems, such as concentrated DNA phases or packings of surfactant micelles. We tentatively attribute this effect to the difference in stiffness. The liquid phase can be well described by a hard-disk fluid, while we model the crystalline one as a hexagonal harmonic lattice and we evaluate its elastic constants.

Dynamic modulation of inter-particle correlation during colloidal assembly in a confined medium: revealed by real time SAXS

Using real time small-angle X-ray scattering, we ellucidate a hitherto unobserved non-monotonic evolution of inter-particle correlation while colloidal particles assemble across pore boundary in a confined medium under influence of solvent evaporation. Time variation of local volume fraction of the particles passes through distinct modulation prior to reaching equilibrium. It has been demonstrated that the amplitude of oscillation depends strongly on size of the assembling particles. We comprehend such non-linear temporal evolution of particle correlation through density functional theory and molecular dynamics simulation.

From dynamic self-assembly to networked chemical systems

Although dynamic self-assembly, DySA, is a relatively new area of research, the past decade has brought numerous demonstrations of how various types of components - on scales from (macro)molecular to macroscopic - can be arranged into ordered structures thriving in non-equilibrium, steady states. At the same time, none of these dynamic assemblies has so far proven practically relevant, prompting questions about the field's prospects and ultimate objectives. The main thesis of this Review is that formation of dynamic assemblies cannot be an end in itself - instead, we should think more ambitiously of using such assemblies as control elements (reconfigurable catalysts, nanomachines, etc.) of larger, networked systems directing sequences of chemical reactions or assembly tasks. Such networked systems would be inspired by biology but intended to operate in environments and conditions incompatible with living matter (e.g., in organic solvents, elevated temperatures, etc.). To realize this vision, we need to start considering not only the interactions mediating dynamic self-assembly of individual components, but also how components of different types could coexist and communicate within larger, multicomponent ensembles. Along these lines, the review starts with the discussion of the conceptual foundations of self-assembly in equilibrium and non-equilibrium regimes. It discusses key examples of interactions and phenomena that can provide the basis for various DySA modalities (e.g., those driven by light, magnetic fields, flows, etc.). It then focuses on the recent examples where organization of components in steady states is coupled to other processes taking place in the system (catalysis, formation of dynamic supramolecular materials, control of chirality, etc.). With these examples of functional DySA, we then look forward and consider conditions that must be fulfilled to allow components of multiple types to coexist, function, and communicate with one another within the networked DySA systems of the future. As the closing examples show, such systems are already appearing heralding new opportunities - and, to be sure, new challenges - for DySA research.

Elastocapillary Driven Assembly of Particles at Free-Standing Smectic-A Films

Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetting conditions of particles at the smectic film, are reported. This work paves the way to exploiting LC interfaces as a means to direct spontaneously formed, reconfigurable, and optically active materials.

Spontaneous membrane formation and self-encapsulation of active rods in an inhomogeneous motility field

We study the collective dynamics of self-propelled rods in an inhomogeneous motility field. At the interface between two regions of constant but different motility, a smectic rod layer is spontaneously created through aligning interactions between the active rods, reminiscent of an artificial, semipermeable membrane. This "active membrane" engulfes rods which are locally trapped in low-motility regions and thereby further enhances the trapping efficiency by self-organization, an effect which we call "self-encapsulation." Our results are gained by computer simulations of self-propelled rod models confined on a two-dimensional planar or spherical surface with a stepwise constant motility field, but the phenomenon should be observable in any geometry with sufficiently large spatial inhomogeneity. We also discuss possibilities to verify our predictions of active-membrane formation in experiments of self-propelled colloidal rods and vibrated granular matter.

Relevance of packing to colloidal self-assembly

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures composed of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals at any finite pressure are imperfect versions of the ideal packing shape.

Controlled Self-Assembly of Photofunctional Supramolecular Nanotubes

Designing supramolecular nanotubes (SNTs) with distinct dimensions and properties is highly desirable, yet challenging, since structural control strategies are lacking. Furthermore, relatively complex building blocks are often employed in SNT self-assembly. Here, we demonstrate that symmetric bolaamphiphiles having a hydrophobic core comprised of two perylene diimide moieties connected via a bipyridine linker and bearing polyethylene glycol (PEG) side chains can self-assemble into diverse molecular nanotubes. The structure of the nanotubes can be controlled by assembly conditions (solvent composition and temperature) and a PEG chain length. The resulting nanotubes differ both in diameter and cross section geometry, having widths of 3 nm (triangular-like cross-section), 4 nm (rectangular), and 5 nm (hexagonal). Molecular dynamics simulations provide insights into the stability of the tubular superstructures and their initial stages of self-assembly, revealing a key role of oligomerization via side-by-side aromatic interactions between bis-aromatic cores. Probing electronic and photonic properties of the nanotubes revealed extended electron delocalization and photoinduced charge separation that proceeds via symmetry breaking, a photofunction distinctly different from that of the fibers assembled from the same molecules. A high degree of structural control and insights into SNT self-assembly advance design approaches toward functional organic nanomaterials.

Interfacially active polydopamine for nanoparticle stabilized nanocapsules in a one-pot assembly strategy toward efficient drug delivery

Polydopamine (PDA) nanoparticle stabilized nanocapsules possess great potential for drug delivery via the non-endocytotic pathway.

Bundle formation of supramolecular fibers of amphiphilic diarylethene by depletion force

Supramolecular nanofibers composed of the closed-ring isomer of a diarylethene formed bundles in a methylcellulose aqueous solution and showed a photoinduced shrinking of more than 100 μm under visible light irradiation.

Filamentous phages as building blocks for reconfigurable and hierarchical self-assembly

Filamentous bacteriophages such as fd-like viruses are monodisperse rod-like colloids that have well defined properties of diameter, length, rigidity, charge and chirality. Engineering these viruses leads to a library of colloidal rods, which can be used as building blocks for reconfigurable and hierarchical self-assembly. Their condensation in an aqueous solution with additive polymers, which act as depletants to induce attraction between the rods, leads to a myriad of fluid-like micronic structures ranging from isotropic/nematic droplets, colloid membranes, achiral membrane seeds, twisted ribbons, π-wall, pores, colloidal skyrmions, Möbius anchors, scallop membranes to membrane rafts. These structures, and the way that they shape-shift, not only shed light on the role of entropy, chiral frustration and topology in soft matter, but also mimic many structures encountered in different fields of science. On the one hand, filamentous phages being an experimental realization of colloidal hard rods, their condensation mediated by depletion interactions constitutes a blueprint for the self-assembly of rod-like particles and provides a fundamental foundation for bio- or material-oriented applications. On the other hand, the chiral properties of the viruses restrict the generalities of some results but vastly broaden the self-assembly possibilities.

Thermoreversible Self-Assembly of Perfluorinated Core-Coronas Cellulose-Nanoparticles in Dry State

Self-assembly of nanoparticles (NPs) forming unique structures has been investigated extensively over the past few years. However, many self-assembled structures by NPs are irreversible, because they are generally constructed using their suspensions. It is still challenging for NPs to reversibly self-assemble in dry state, let alone of polymeric NPs with general sizes of hundreds of nm. Herein, this study reports a new reversible self-assembly phenomenon of NPs in dry state, forming thermoreversible strip-like supermolecular structures. These novel NPs of around 150 nm are perfluorinated surface-undecenoated cellulose nanoparticles (FSU-CNPs) with a core-coronas structure. The thermoreversible self-assembled structure is formed after drying in the air at the interface between FSU-CNP films and Teflon substrates. Remarkably, the formation and dissociation of this assembled structure are accompanied by a reversible conversion of the surface hydrophobicity, film transparency, and anisotropic properties. These findings show novel feasibility of reversible self-assembly of NPs in dry state, and thereby expand our knowledge of self-assembly phenomenon.

Curvature instability of chiral colloidal membranes on crystallization

Buckling and wrinkling instabilities are failure modes of elastic sheets that are avoided in the traditional material design. Recently, a new paradigm has appeared where these instabilities are instead being utilized for high-performance applications. Multiple approaches such as heterogeneous gelation, capillary stresses, and confinement have been used to shape thin macroscopic elastic sheets. However, it remains a challenge to shape two-dimensional self-assembled monolayers at colloidal or molecular length scales. Here, we show the existence of a curvature instability that arises during the crystallization of finite-sized monolayer membranes of chiral colloidal rods. While the bulk of the membrane crystallizes, its edge remains fluid like and exhibits chiral ordering. The resulting internal stresses cause the flat membrane to buckle macroscopically and wrinkle locally. Our results demonstrate an alternate pathway based on intrinsic stresses instead of the usual external ones to assemble non-Euclidean sheets at the colloidal length scale.

Buckling and wrinkling are instabilities which involve thin elastic sheets and are well-investigated phenomena at the macroscale. Here Saikia et al. investigate curvature instabilities at the colloidal lengthscale in quasi-2D monolayers of rod-like viruses across the fluid-crystal phase transition.

How roughness affects the depletion mechanism

We develop a simple model, in the spirit of the Asakura-Oosawa theory, able to describe the effects of surface roughness on the depletion potential. The resulting explicit expressions are easily computed, without free parameters, for a wide range of physically interesting conditions. Comparison with recent numerical simulations [M. Kamp et al., Langmuir, 2016, 32, 1233] shows an encouraging agreement and allows predicting the onset of colloidal aggregation in dilute suspensions of rough particles. Furthermore, the model proves to be suitable to investigate the role of the geometry of the roughness.

Molecular engineering of chiral colloidal liquid crystals using DNA origami

Establishing precise control over the shape and the interactions of the microscopic building blocks is essential for design of macroscopic soft materials with novel structural, optical and mechanical properties. Here, we demonstrate robust assembly of DNA origami filaments into cholesteric liquid crystals, one-dimensional supramolecular twisted ribbons and two-dimensional colloidal membranes. The exquisite control afforded by the DNA origami technology establishes a quantitative relationship between the microscopic filament structure and the macroscopic cholesteric pitch. Furthermore, it also enables robust assembly of one-dimensional twisted ribbons, which behave as effective supramolecular polymers whose structure and elastic properties can be precisely tuned by controlling the geometry of the elemental building blocks. Our results demonstrate the potential synergy between DNA origami technology and colloidal science, in which the former allows for rapid and robust synthesis of complex particles, and the latter can be used to assemble such particles into bulk materials.