Fd-virus Particles Research Articles

Underlying mechanism of shear-banding in soft glasses of charged colloidal rods with orientational domains

Soft glasses of colloidal rods (fd-virus particles) with orientational domains were recently shown to exhibit inhomogeneous flow profiles [Dhont et al., Phys. Rev. Fluids 2, 043301 (2017)]: fracture and accompanied plug flow at small shear rates, which transits to gradient shear-banding on increasing the shear rate, while a uniform flow profile develops at sufficiently high shear rates. These flow profiles coexist with Taylor-vorticity bands. The texture of such glasses under flow conditions consists of domains with varying orientations. The observed gradient shear-banding was solely attributed to the strong shear thinning behavior of the material inside the domains (henceforth abbreviated as domain-interior), without considering the texture stress that is due to interactions between the glassy domains. Here, we present new experiments on the shear-banding transition to assess the role played by the texture stress in comparison to the domain-interior stress. For a large concentration, well into the glassy state, it is found that both texture stress and domain-interior stress contribute significantly to the gradient shear-banding transition in the shear-rate region where it occurs. On the other hand, for a small concentration close to the glass-transition concentration, the domains are shown to coalesce within the shear-rate range where gradient shear-banding is observed. As a result, the texture stress diminishes and the domain-interior stress increases upon coalescence, leading to a stress plateau. Thus, a subtle interplay exists between the stresses arising from the structural order on two widely separated length scales from interactions between domains and from the rod-rod interactions within the domain-interior for both concentrations.

Conformations and membrane-driven self-organization of rodlike fd virus particles on freestanding lipid membranes.

Membrane-mediated interactions and aggregation of colloidal particles adsorbed to responsive elastic membranes are challenging problems relevant for understanding the microscopic organization and dynamics of biological membranes. We experimentally study the behavior of rodlike semiflexible fd virus particles electrostatically adsorbed to freestanding cationic lipid membranes and find that their behavior can be controlled by tuning the membrane charge and ionic strength of the surrounding medium. Three distinct interaction regimes of rodlike virus particles with responsive elastic membranes can be observed. (i) A weakly charged freestanding cationic lipid bilayer in a low ionic strength medium represents a gentle quasi-2D substrate preserving the integrity, structure, and mechanical properties of the membrane-bound semiflexible fd virus, which under these conditions is characterized by a monomer length of 884 ± 4 nm and a persistence length of 2.5 ± 0.2 μm, in perfect agreement with its properties in bulk media. (ii) An increase in the membrane charge leads to the membrane-driven collapse of fd virus particles on freestanding lipid bilayers and lipid nanotubes into compact globules. (iii) When the membrane charge is low, and the mutual electrostatic repulsion of membrane-bound virus particles is screened to a considerable degree, membrane-driven self-organization of membrane-bound fd virus particles into long linear tip-to-tip aggregates showing dynamic self-assembly/disassembly and quasi-semiflexible behavior takes place. These observations are in perfect agreement with the results of recent theoretical and simulation studies predicting that membrane-mediated interactions can control the behavior of colloidal particles adsorbed on responsive elastic membranes.

Synchronized oscillations of dimers in biphasic charged fd-virus suspensions.

Micron-sized colloidal spheres that are dispersed in an isotropic-nematic biphasic host suspension of charged rods (fd-virus particles) are shown to spontaneously form dimers, which exhibit a synchronized oscillatory motion. Dimer formation is not observed in the monophase of isotropic and nematic suspensions. The synchronized oscillations of dimers are connected to the inhomogeneous state of the host suspension of charged rods (fdviruses) where nematic domains are in coexistence with isotropic regions. The synchronization of oscillations occurs in bulk states, in the absence of an external field. With a low field strength of an applied electric field, the synchronization is rather reduced, but it recovers again when the field is turned off. In this Rapid Communication, we report this observation as an example of the strange attractor, occurring in the mixture of PS (polystyrene) dimers in an isotropic-nematic coexistence biphasic fd-virus network. Furthermore, we highlight that the synchronization of PS-dimer oscillations is the result of a global bifurcation diagram, driven by a delicate balance between the short-attractive "twisted" interaction of PS dimers and long-ranged electrostatic repulsive interactions of charged fd rods. The interest is then in the local enhancement of "twist-nematic" elasticity in reorientation of the dimer oscillations. An analysis of image-time correlations is provided with the data movies and Fourier transforms of averaged orientations for the synchronized oscillations of dimers in the biphasic I-N coexistence concentration of charged fd-virus suspensions.

An electric-field induced dynamical state in dispersions of highly charged colloidal rods: comparison of experiment and theory.

Concentrated dispersions of highly charged rod-like colloids (fd-virus particles) in isotropic-nematic coexistence exhibit a dynamical state when subjected to low-frequency electric fields [Soft Matter, 2010, 6, 273]. This dynamical state consists of nematic domains which persistently melt and form on time scales typically of the order of seconds. The origin of the dynamical state has been attributed to a field-induced, cyclic dissociation and association of condensed ions [Soft Matter, 2014, 10, 1987, Soft Matter, 2015, 11, 2893]. The ionic strength increases on dissociation of condensed ions, rendering the nematic domains unstable, while the subsequent decrease of the ionic strength due to association of condensed ions leads to a recurrent stabilization of the nematic state. The role of dissociation/association of condensed ions in the phase/state behaviour of charged colloids in electric fields has not been addressed before. The electric field strength that is necessary to dissociate sufficient condensed ions to render a nematic domain unstable, depends critically on the ambient ionic strength of the dispersion without the external field, as well as the rod-concentration. The aim of this paper is to compare experimental results for the location of transition lines and the dynamics of melting and forming of nematic domains at various ionic strengths and rod-concentrations with the ion-dissociation/association model. Phase/state diagrams in the field-amplitude versus frequency plane at two different ambient ionic strengths and various rod-concentrations are presented, and compared to the theory. The time scale on which melting and forming of the nematic domains occurs diverges on approach of the transition line where the dynamical state appears. The corresponding critical exponents have been measured by means of image time-correlation spectroscopy [Eur. Phys. J. E, 2009, 30, 333], and are compared to the theoretical values predicted by the ion-dissociation/association model.

Direct calculation of distortion energies in colloidal liquid crystals from single-particle data

We report a method to calculate distortion energies of a colloidal liquid crystal from single-particle data via a triangulation of the particle positions followed by a linear interpolation of the particle orientations. Our method provides local information on the strength and type of distortions present in a liquid crystal. We validate our method by applying it to artificially generated data and show that the results are in good agreement with exact calculations of the distortion energy. We further illustrate our method by using it on laser scanning confocal microscopy images of the nematic phase of fd-virus particles in wedge-shaped microfluidics channels.

Charged Colloidal Rods Out of Equilibrium

This article is a comprehensive overview of the ongoing research of the author on charged colloidal rods out of equilibrium, under external electric fields and at high concentrations around the glass transition. The suspensions of fd-virus particles are used as a model system for charged colloidal rods, which exhibit several disorder-order (and liquid-crystalline) phase transitions. When a low AC electric field is applied to suspensions in isotropic-nematic coexistence concentration, with frequencies that are sufficiently low to polarize the electric double layer and the layer of condensed ions, various phases/states are induced: a chiral nematic, a dynamical state where nematic domains persistently melt and form, and a uniform homeotropic phase. A point in the field-amplitude versus frequency diagram, where various transitions lines meet, can be identified as a non-equilibrium critical point. Without an electric field, at high concentrations of charged fd-rods, various self-assembled orientation textures are found beyond the isotropic-nematic coexistence regions, and a glass transition is observed on approach and within the glass state that are probed. The presented system exhibits transient behaviors of repulsive glasses and slow dynamics out of equilibrium.

Effect of bending flexibility on the phase behavior and dynamics of rods.

We study by means of molecular and Brownian dynamics simulations the influence of bending flexibility on the phase behavior and dynamics of monodisperse hard filamentous particles with an aspect ratio of 8 and persistence lengths equal to 3 and 11 times the particle length. Although our particles are much shorter, the latter corresponds to the values for wild-type and mutant fd virus particles that have been subject of a recent experimental study, where the diffusion of these particles in the nematic and smectic-A phase was investigated by means of video fluorescence microscopy [E. Pouget, E. Grelet, and M. P. Lettinga, Phys. Rev. E 84, 041704 (2011)]. In agreement with theoretical predictions and simulations, we find that for the more flexible particles (shorter persistence length) the nematic (N) to smectic-A (Sm-A) phase transition shifts to larger values of the particle density. Interestingly, we find that for the more rigid particles (larger persistence length), the smectic layer-to-layer distance decreases monotonically with increasing density, whereas for the more flexible ones, it first increases, reaches a maximum and then decreases. For our more flexible particles, we find a smectic-B phase at sufficiently high densities. Moreover, in line with experimental observations and theoretical predictions, we find heterogeneous dynamics in the Sm-A phase, in which particles hop between the smectic layers. We compare the diffusion of our two types of particle at identical values of smectic order parameter, and find that flexibility does not change the diffusive behavior of particles along the director yet significantly slows down the diffusion perpendicular to it. In our simulations, the ratio of diffusion constants along and perpendicular to the director decreases just beyond the N-Sm-A phase transition for both our stiff and more flexible particles.

Interaction of Semiflexible Filamentous Virus Particles with Freestanding Lipid Membranes

Understanding of the mechanisms of interaction of macromolecules and colloidal particles with lipid membranes is far from complete, and the questions related to role of local perturbation of the membrane properties in these interactions are still largely unsolved. Previously, we have found [1] that interaction of DNA molecules with strongly charged freestanding cationic lipid bilayers [2] leads to an unexpected phenomenon of membrane-mediated coil-globule transition of membrane-absorbed DNA macromolecules. To elucidate the effect of the persistence length in these phenomena, we study the behavior of much stiffer semiflexible fd virus particles (persistence length ∼2.2 μm) electrostatically adsorbed on freestanding cationic lipid membranes. At low membrane charge densities, membrane-adsorbed fd virus particles behave as semiflexible filaments in 2D. On the other hand, we find that membrane-driven interactions at higher membrane charge densities are strong enough to induce the membrane-mediated coil-globule transition of the relatively stiff fd virus particles, which agrees with the recent theoretical predictions [3]. Further, for fd virus particles adsorbed at higher surface densities on weakly charged membranes we observe a new unexpected phenomenon of membrane-driven self-organization of the filamentous virus particles into long linear chain aggregates. [1] C. Herold, P. Schwille, and E. P. Petrov, Phys. Rev. Lett.104 (2010) 148102. [2] C. Herold, G. Chwastek, P. Schwille, and E. P. Petrov, Langmuir28 (2012) 5518. [3] A. G. Cherstvy and E. P. Petrov (2013) submitted.

An electric-field induced dynamical state in dispersions of charged colloidal rods

The response of concentrated dispersions of charged colloids to low-frequency electric fields is governed by field-induced inter-colloidal interactions resulting from the polarization of electric double layers and the layer of condensed ions, association and dissociation of condensed ions, as well as hydrodynamic interactions through field-induced electro-osmotic flow. The phases and states that can be formed by such field-induced interactions are an essentially unexplored field of research. Experiments on concentrated suspensions of rod-like colloids (fd-virus particles), within the isotropic-nematic phase coexistence region, showed that a number of phases/states are induced, depending on the field amplitude and frequency [Soft Matter, 2010, 6, 273]. In particular, a dynamical state is found where nematic domains form and melt on a time scale of the order of seconds. We discuss the microscopic origin of this dynamical state, which is attributed to the cyclic, electric-field induced dissociation and association of condensed ions. A semi-quantitative theory is presented for the dynamics of melting and formation of nematic domains, including a model for the field-induced dissociation/association of condensed ions. The resulting equation of motion for the orientational order parameter is solved numerically for parameters complying with the fd-virus system. A limit-cycle is found, with a cycling-time that diverges at the transition line in the field-amplitude versus frequency plane where the dynamical state first appears, in accord with experimental findings.

Translational and rotational diffusion of semiflexible DNA polymers and rod-like fd virus particles on weakly charged freestanding cationic lipid membranes

Translational and rotational diffusion of semiflexible DNA polymers and rod-like fd virus particles on weakly charged freestanding cationic lipid membranes

Fractional Hoppinglike Motion in Columnar Mesophases of Semiflexible Rodlike Particles

We report on single-particle dynamics of strongly interacting filamentous fd virus particles in the liquid-crystalline columnar state in aqueous solution. From fluorescence microscopy, we find that rare, discrete events take place, in which individual particles engage in sudden, jumplike motion along the main rod axis. The jump length distribution is bimodal and centered at half- and full-particle lengths. Our Brownian dynamics simulations of hard semiflexible particles mimic our experiments and indicate that full-length jumps must be due to collective dynamics in which particles move in stringlike fashion in and between neighboring columns, while half jumps arise as a result of particles moving into defects. We find that the finite domain structure of the columnar phase strongly influences the observed dynamics.

Glass Transition in Suspensions of Charged Rods: Structural Arrest and Texture Dynamics

We report on the observation of a glass transition in suspensions of very long and thin, highly charged colloidal rods (fd-virus particles). Structural particle arrest is found to occur at a low ionic strength due to caging of the charged rods in the potential setup by their neighbors through long-ranged electrostatic interactions. The relaxation time of density fluctuations as probed by dynamic light scattering is found to diverge within a small concentration range. The rod concentration where structural particle arrest occurs is well within the full chiral-nematic state, far beyond the two-phase isotropic-nematic coexistence region. The morphology of the suspensions thus consists of nematic domains with various orientations. We quantify the dynamics of the resulting texture with image-time correlation spectroscopy. Interestingly, the decay times of image correlation functions are found to diverge in a discontinuous fashion at the same concentration of charged rods where structural particle arrest is observed. At the glass-transition concentration, we thus find both structural arrest and freezing of the texture dynamics.

Thermophoresis of charged colloidal rods

The thermal diffusion behavior of dilute solutions of very long and thin, charged colloidal rods (fd-virus particles) is studied using a holographic grating technique. The Soret coefficient of the charged colloids is measured as a function of the Debye screening length, as well as the rod-concentration. The Soret coefficient of the fd-viruses increases monotonically with increasing Debye length, while there is a relatively weak dependence on the rod-concentration when the ionic strength is kept constant. An existing theory for thermal diffusion of charged spheres is extended to describe the thermal diffusion of long and thin charged rods, leading to an expression for the Soret coefficient in terms of the Debye length, the rod-core dimensions, and the surface charge density. The thermal diffusion coefficient of a charged colloidal rod is shown to be accurately represented, for arbitrary Debye lengths, by a superposition of spherical beads with the same diameter of the rod and the same surface charge density. The experimental Soret coefficients are compared with this and other theories, and are contrasted against the thermal diffusion behaviour of charged colloidal spheres.

Structural arrest and texture dynamics in suspensions of charged colloidal rods

There is an abundance of experiments and theories on the glass transition of colloidal systems consisting of spherical particles. Much less is known about possible glass transitions in suspensions of rod-like colloids. In this study we present observations of a glass transition in suspensions of very long and thin rod-like, highly charged colloids. We use as a model system fd-virus particles (a DNA strand covered with coat proteins) at low ionic strength, where thick electric double layers are present. Structural arrest as a result of particle-caging is observed by means of dynamic light scattering. The glass-transition concentration is found to be far above the isotropic–nematic coexistence region. The morphology of the system thus consists of nematic domains with different orientations. Below the glass-transition concentration the initial morphology with large shear-aligned domains breaks up into smaller domains, and equilibrates after typically 50–100 hours. We quantify the dynamics of the transitional and the equilibrated texture by means of image time-correlation. A sharp increase of relaxation times of image time-correlation functions is found at the glass-transition concentration. The texture dynamics thus freezes at the same concentration where structural arrest occurs. We also observe a flow instability, which sets in after very long waiting times (typically 200–300 hours), depending on the rod concentration, which affects the texture morphology.

Electrophoresis of fd-Virus Particles: Experiments and an Analysis of the Effect of Finite Rod Lengths

The electrophoretic mobility of rodlike fd viruses is measured and compared to theory, with the theoretical calculations performed according to Stigter (Stigter, D. Charged Colloidal Cylinder with a Gouy Double-Layer. J. Colloid Interface Sci. 1975, 53, 296-306. Stigter, D. Electrophoresis of Highly Charged Colloidal Cylinders in Univalent Salt- Solutions. 1. Mobility in Transverse Field. J. Phys. Chem. 1978, 82, 1417-1423. Stigter, D. Electrophoresis of Highly Charged Colloidal Cylinders in Univalent Salt Solutions. 2. Random Orientation in External Field and Application to Polyelectrolytes. J. Phys. Chem. 1978, 82, 1424-1429. Stigter, D. Theory of Conductance of Colloidal Electrolytes in Univalent Salt Solutions. J. Phys. Chem. 1979, 83, 1663-1670), who describes the electrophoretic mobility of infinite cylinders including relaxation effects. Using the dissociation constants of the ionizable groups on the surfaces of the fd viruses, we can calculate the mobility without any adjustable parameter (apart from the possible Stern layer thickness). In addition, the approximation in the theoretical description of Stigter (and others) of using a model of infinitely long cylinders, which consequently is independent of the aspect ratio, is examined by performing more elaborate numerical calculations for finite cylinders. It is shown that, although the electrophoretic mobility of cylindrical particles in the limit of low ionic strength depends on the aspect ratio much more than "end effects", at moderate and high ionic strengths the finite and infinite cylinder models differ only to a degree that can be attributed to end effects. Furthermore, the range of validity of the Stokes regime is systematically calculated.

Orientational Order of Carbon Nanotube Guests in a Nematic Host Suspension of Colloidal Viral Rods

In order to investigate the coupling between the degrees of alignment of elongated particles in binary nematic dispersions, surfactant stabilized single-wall carbon nanotubes (CNTs) have been added to nematic suspensions of colloidal rodlike viruses in aqueous solution. We have independently measured the orientational order parameter of both components of the guest-host system by means of polarized Raman spectroscopy and by optical birefringence, respectively. Our system allows us therefore to probe the regime where the guest particles (CNTs) are shorter and thinner than the fd virus host particles. We show that the degree of order of the CNTs is systematically smaller than that of the fd virus particles for the whole nematic range. These measurements are in good agreement with predictions of an Onsager-type second-viral theory, which explicitly includes the flexibility of the virus particles, and the polydispersity of the CNTs.

The effects of shape and flexibility on bio-engineered fd-virus suspensions

We present a theoretical model to describe binary mixtures of semi-flexible rods, applied here to fd-virus suspensions. We investigate the effects of rod stiffness on both monodisperse and binary systems, studying thick-thin and long-short mixtures. For monodisperse systems, we find that fd-virus particles have to be made extremely stiff to even approach the behavior of rigid rods. For thick-thin mixtures, we find increasingly rich phase behavior as the rods are either made more flexible or if their diameter ratio is increased. For long-short rod mixtures we find that the phase behavior is controlled by the relative stiffness of the rods, with increasing the stiffness of the long rods or decreasing that of the short rods resulting in richer phase behavior. We also calculate the state point dependent effective shape of the rods. The flexible rods studied here always behave as shorter, thicker rigid rods, but with an effective shape that varies widely throughout the phase diagrams, and plays a key role in determining phase behavior.

Phase Diagram and Effective Shape of Semiflexible Colloidal Rods and Biopolymers

We study suspensions of semiflexible colloidal rods and biopolymers using an Onsager-type second-virial functional for a segmented-chain model. For mixtures of thin and thick fd virus particles, we calculate full phase diagrams, finding quantitative agreement with experimental observations. We show that flexibility, which renders the rods effectively shorter and thicker depending on the state point, is crucial to understanding the topologies of the phase diagrams. We also calculate the stretching of wormlike micelles in a host fd virus suspension, finding agreement with experiments.

Image time-correlation, dynamic light scattering, and birefringence for the study of the response of anisometric colloids to external fields

In this paper, a detailed description of equipment is given, specially designed to characterize the response of non-spherical colloids to external fields. To characterize slow structural changes on a large length scale we developed an image correlation method, fast dynamics on the colloidal-particle level is probed by means of a vertically mounted, small angle dynamic light scattering setup, while the orientational order (induced by the external field) is measured with a birefringence setup with off-normal incidence. The performance of this in situ set of instruments is illustrated by experiments on concentrated dispersions of very long and thin, charged colloidal rods (fd-virus particles) in external electric fields. Here, the frequency of the field is sufficiently low to polarize electrical double layers, leading to additional inter-colloidal interactions which are found to give rise to phase/state transitions and dynamical states (K. Kang and J. K. G. Dhont, Soft Matter 6, 273, 2010).

Criticality in a non-equilibrium, driven system: Charged colloidal rods (fd-viruses) in electric fields

Experiments on suspensions of charged colloidal rods (fd-virus particles) in external electric fields are performed, which show that a non-equilibrium critical point can be identified. Several transition lines of field-induced phases and states meet at this point and it is shown that there is a length- and time-scale which diverge at the non-equilibrium critical point. The off-critical and critical behavior is characterized, with both power law and logarithmic divergencies. These experiments show that analogous features of the classical, critical divergence of correlation lengths and relaxation times in equilibrium systems are also exhibited by driven systems that are far out of equilibrium, related to phases/states that do not exist in the absence of the external field.