Fast Diffusion of Long Guest Rods in a Lamellar Phase of Short Host Particles

Rheology and Microstructural Behavior of Semidilute Suspensions of Semiflexible Rods across Five Decades of Shear Rate

Rod-like particles are efficient rheology modifiers and are commonly found in a variety of biological and industrially relevant suspensions, from biofilaments to worm-like surfactant micelles. These suspensions display strong shear-thinning behavior, and ongoing efforts aim to understand the microstructural changes of these fluids: how they depend upon the properties of the suspended particles and how these changes manifest in the resulting rheology. With suspensions of fd bacteriophage as a model monodisperse rod system, we use capillary microrheometry and flow birefringence to determine rheological behavior across nearly six decades of shear rate up to 6 × 105 s-1, at various semidilute concentrations. A single, and surprisingly large, primary fitting parameter accounting for the characteristic distance of hydrodynamic interactions is consistent with viscosity data up to very high shear rates. These results may prompt other work to understand the mechanics of these interactions.

Self-diffusion in isotropic and liquid crystalline phases of fd virus colloidal rods: a combined single particle tracking and differential dynamic microscopy study

In this article, we investigate the dynamics of self-organised suspensions formed by rod-like fd virus colloids. Two methods have been employed for analysing fluorescence microscopy movies: single particle tracking (SPT) in direct space and differential dynamic microscopy (DDM) in reciprocal space. We perform a quantitative analysis on this anisotropic system with complex diffusion across different self-assembled states, ranging from dilute and semi-dilute liquids to nematic and smectic organisations. By leveraging the complementary strengths of SPT and DDM, we provide new insights in the dynamics of viral colloidal rods, such as long time diffusion coefficients in the smectic phase. We further discuss the advantages and limitations of both methods for studying the intricate dynamics of anisotropic colloidal systems.

Monodisperse nanosheet mesophases

Self-assemblies of anisotropic colloidal particles into colloidal liquid crystals and well-defined superlattices are of great interest for hierarchical nanofabrications that are applicable for various functional materials. Inorganic nanosheets obtained by exfoliation of layered crystals have been highlighted as the intriguing colloidal units; however, the size polydispersity of the nanosheets has been preventing precise design of the assembled structures and their functions. Here, we demonstrate that the anionic titanate nanosheets with monodisperse size reversibly form very unusual superstructured mesophases through finely tunable weak attractive interactions between the nanosheets. Transmission electron microscopy, polarizing optical microscopy, small-angle x-ray scattering, and confocal laser scanning microscopy clarified the reversible formation of the mesophases (columnar nanofibers, columnar nematic liquid crystals, and columnar nanofiber bundles) as controlled by counter cations, nanosheet concentration, solvent, and temperature.

Preferential ordering of incommensurate-length guest particles in a smectic host

Using density functional theory, we study the preferential ordering of rod-like guest particles immersed in a smectic host fluid. Within a model of perfectly aligned rods and assuming that the guest particles do not perturb the smectic host fluid, simple excluded-volume arguments explain that guest particles that are comparable in length to the host particles order in phase with the smectic host density layering, whereas guest particles that are considerably shorter or longer order in antiphase. The corresponding free-energy minima are separated by energetic barriers on the order of the thermal energy kBT, suggesting that guest particles undergo hopping-type diffusion between adjacent smectic layers. Upon introducing a slight orientational mismatch between the guest particles and the perfectly aligned smectic host, an additional, smaller free-energy barrier emerges for a range of intermediate guest-to-host length ratios, which splits the free-energy minimum into two. Guest particles in this range occupy positions intermediate between in-phase ordering and in-antiphase ordering. Finally, we use Kramers' theory to identify slow, fast, and intermediate diffusive regimes for the guest particles as a function of their length. Our model is in qualitative agreement with experiment and simulation and provides an alternative, complementary explanation in terms of a free-energy landscape for the intermediate diffusive regime, which was previously hypothesized to result from temporary caging effects [M. Chiappini, E. Grelet, and M. Dijkstra, Phys. Rev. Lett. 124, 087801 (2020)]. We argue that our simple model of aligned rods captures the salient features of incommensurate-length guest particles in a smectic host if a slight orientational mismatch is introduced.

Insight into the Viscoelasticity of Self-Assembling Smectic Liquid Crystals of Colloidal Rods from Active Microrheology Simulations

The rheology of colloidal suspensions is of utmost importance in a wide variety of interdisciplinary applications in formulation technology, determining equally interesting questions in fundamental science. This is especially intriguing when colloids exhibit a degree of long-range positional or orientational ordering, as in liquid crystals (LCs) of elongated particles. Along with standard methods, microrheology (MR) has emerged in recent years as a tool to assess the mechanical properties of materials at the microscopic level. In particular, by active MR one can infer the viscoelastic response of a soft material from the dynamics of a tracer particle being dragged through it by external forces. Although considerable efforts have been made to study the diffusion of guest particles in LCs, little is known about the combined effect of tracer size and directionality of the dragging force on the system's viscoelastic response. By dynamic Monte Carlo simulations, we apply active MR to investigate the viscoelasticity of self-assembling smectic (Sm) LCs consisting of rodlike particles. In particular, we track the motion of a spherical tracer whose size is varied within a range of values matching the system's characteristic length scales and being dragged by constant forces that are parallel, perpendicular, or at 45° to the nematic director. Our results reveal a uniform value of the effective friction coefficient as probed by the tracer at small and large forces, whereas a nonlinear, force-thinning regime is observed at intermediate forces. However, at relatively weak forces the effective friction is strongly determined by correlations between the tracer size and the structure of the host fluid. Moreover, we also show that external forces forming an angle with the nematic director provide additional details that cannot be simply inferred from the mere analysis of parallel and perpendicular forces. Our results highlight the fundamental interplay between tracer size and force direction in assessing the MR of Sm LC fluids.

Unconventionally fast transport through sliding dynamics of rodlike particles in macromolecular networks

Transport of rodlike particles in confinement environments of macromolecular networks plays crucial roles in many important biological processes and technological applications. The relevant understanding has been limited to thin rods with diameter much smaller than network mesh size, although the opposite case, of which the dynamical behaviors and underlying physical mechanisms remain unclear, is ubiquitous. Here, we solve this issue by combining experiments, simulations and theory. We find a nonmonotonic dependence of translational diffusion on rod length, characterized by length commensuration-governed unconventionally fast dynamics which is in striking contrast to the monotonic dependence for thin rods. Our results clarify that such a fast diffusion of thick rods with length of integral multiple of mesh size follows sliding dynamics and demonstrate it to be anomalous yet Brownian. Moreover, good agreement between theoretical analysis and simulations corroborates that the sliding dynamics is an intermediate regime between hopping and Brownian dynamics, and provides a mechanistic interpretation based on the rod-length dependent entropic free energy barrier. The findings yield a principle, that is, length commensuration, for optimal design of rodlike particles with highly efficient transport in confined environments of macromolecular networks, and might enrich the physics of the diffusion dynamics in heterogeneous media.

M13-Phage-Based Star-Shaped Particles with Internal Flexibility

We report on the construction and the dynamics of monodisperse star-shaped particles, mimicking, at the mesoscale, star polymers. Such multiarm star-like particles result from the self-assembly of gold nanoparticles, forming the core, with tip-linked filamentous viruses (M13 bacteriophages) acting as spines in a sea urchin-like structure. By combining fluorescence and dark-field microscopy with dynamic light scattering, we investigate the diffusion of these hybrid spiny particles. We reveal the internal dynamics of the star particles by probing their central metallic core, which exhibits a hindered motion that can be described as a Brownian particle trapped in a harmonic potential. We therefore show that the filamentous viruses and specifically their tip proteins behave as entropic springs, extending the relevance of the study of such hybrid mesoscopic analogues of star polymers to phage biotechnology.

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.

When bigger is faster: A self-Van Hove analysis of the enhanced self-diffusion of non-commensurate guest particles in smectics

We investigate the anomalous dynamics in smectic phases of short host rods where, counter-intuitively, long guest rod-shaped particles diffuse faster than the short host ones due to their precise size mismatch. In addition to the previously reported mean-square displacement, we analyze the time evolution of the self-Van Hove functions G(r, t), as this probability density function uncovers intrinsic heterogeneous dynamics. Through this analysis, we show that the dynamics of the host particles parallel to the director becomes non-Gaussian and therefore heterogeneous after the nematic-to-smectic-A phase transition, even though it exhibits a nearly diffusive behavior according to its mean-squared displacement. In contrast, the non-commensurate guest particles display Gaussian dynamics of the parallel motion, up to the transition to the smectic-B phase. Thus, we show that the self-Van Hove function is a very sensitive probe to account for the instantaneous and heterogeneous dynamics of our system and should be more widely considered as a quantitative and complementary approach of the classical mean-squared displacement characterization in diffusion processes.

Self-diffusion of nonspherical particles fundamentally conflicts with effective sphere models

Modeling diffusion of nonspherical particles presents an unsolved and considerable challenge, despite its importance for the understanding of crowding effects in biology, food technology and formulation science. A common approach in experiment and simulation is to map nonspherical objects on effective spheres to subsequently use the established predictions for spheres to approximate phenomena for nonspherical particles. Using numerical evaluation of the hydrodynamic mobility tensor, we show that this so-called effective sphere model fundamentally fails to represent the self-diffusion in solutions of ellipsoids as well as rod-like assemblies of spherical beads. The effective sphere model drastically overestimates the slowing down of self-diffusion down to volume fractions below 0.01. Furthermore, even the linear term relevant at lower volume fraction is inaccurate, linked to a fundamental misconception of effective sphere models. To overcome the severe problems related with the use of effective sphere models, we suggest a protocol to predict the short-time self-diffusion of rod-like systems, based on simulations with hydrodynamic interactions that become feasible even for more complex molecules as the essential observable shows a negligible system-size effect.

Application of Bacteriophages in Nanotechnology

Bacteriophages (phages for short) are viruses, which have bacteria as hosts. The single phage body virion, is a colloidal particle, often possessing a dipole moment. As such, phages were used as perfectly monodisperse systems to study various physicochemical phenomena (e.g., transport or sedimentation in complex fluids), or in the material science (e.g., as scaffolds). Nevertheless, phages also execute the life cycle to multiply and produce progeny virions. Upon completion of the life cycle of phages, the host cells are usually destroyed. Natural abilities to bind to and kill bacteria were a starting point for utilizing phages in phage therapies (i.e., medical treatments that use phages to fight bacterial infections) and for bacteria detection. Numerous applications of phages became possible thanks to phage display-a method connecting the phenotype and genotype, which allows for selecting specific peptides or proteins with affinity to a given target. Here, we review the application of bacteriophages in nanoscience, emphasizing bio-related applications, material science, soft matter research, and physical chemistry.

Speeding up Dynamics by Tuning the Noncommensurate Size of Rodlike Particles in a Smectic Phase

Using simulations, we study the diffusion of rodlike guest particles in a smectic environment of rodlike host particles. We find that the dynamics of guest rods across smectic layers changes from a fast nematiclike diffusion to a slow hopping-type dynamics via an intermediate switching regime by varying the length of the guest rods with respect to the smectic layer spacing. We determine the optimal rod length that yields the fastest and the slowest diffusion in a lamellar environment. We show that this behavior can be rationalized by a complex 1D effective periodic potential exhibiting two energy barriers, resulting in a varying preferred mean position of the guest particle in the smectic layer. The interplay of these two barriers controls the dynamics of the guest particles yielding a slow, an intermediate, and a fast diffusion regime depending on the particle length.

Anisotropic dynamics and kinetic arrest of dense colloidal ellipsoids in the presence of an external field studied by differential dynamic microscopy

Anisotropic dynamics on the colloidal length scale is ubiquitous in nature. Of particular interest is the dynamics of systems approaching a kinetically arrested state. The failure of classical techniques for investigating the dynamics of highly turbid suspensions has contributed toward the limited experimental information available up until now. Exploiting the recent developments in the technique of differential dynamic microscopy (DDM), we report the first experimental study of the anisotropic collective dynamics of colloidal ellipsoids with a magnetic hematite core over a wide concentration range approaching kinetic arrest. In addition, we have investigated the effect of an external magnetic field on the resulting anisotropic collective diffusion. We combine DDM with small-angle x-ray scattering and rheological measurements to locate the glass transition and to relate the collective short- and long-time diffusion coefficients to the structural correlations and the evolution of the zero shear viscosity as the system approaches an arrested state.

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.

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.

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.