Fd-virus Suspensions Research Articles

On the stability and finite-size effects of a columnar phase in single-component systems of hard-rod-like particles

ABSTRACTColloidal rod-like particles self-assemble into a variety of liquid crystal phases. In contrast to the formation of the nematic and smectic phases for which it is well understood that it can be driven by entropy, the stabilisation mechanism of a prolate columnar phase (), observed for example in fd-virus suspensions, is still unclear. Here, we investigate whether or not a phase can exist in a purely entropy-driven single-component system. We perform computer simulations of hard particles with different shapes: spherocylinders, top-shaped rods, cuboidal particles, and crooked rods. We show that the phases observed in previous simulation studies are mere artefacts due to either finite-size effects or simulation boxes that are incommensurate with the stable thermodynamic phase. In particular, we observe that the characteristic layering of the stable smectic or crystal phase disappears when the dimension of the simulation box along the direction of the layers is too small. Such a system-size effect depends both on particle shape and the competing phases, and appears to be more pronounced for less anisotropic particles.

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.

The Connection between Biaxial Orientation and Shear Thinning for Quasi-Ideal Rods.

The complete orientational ordering tensor of quasi-ideal colloidal rods is obtained as a function of shear rate by performing rheo-SANS (rheology with small angle neutron scattering) measurements on isotropic fd-virus suspensions in the two relevant scattering planes, the flow-gradient (1-2) and the flow-vorticity (1-3) plane. Microscopic ordering can be identified as the origin of the observed shear thinning. A qualitative description of the rheological response by Smoluchowski, as well as Doi–Edwards–Kuzuu theory is possible, as we obtain a master curve for different concentrations, scaling the shear rate with the apparent collective rotational diffusion coefficient. However, the observation suggests that the interdependence of ordering and shear thinning at small shear rates is stronger than predicted. The extracted zero-shear viscosity matches the concentration dependence of the self-diffusion of rods in semi-dilute solutions, while the director tilts close towards the flow direction already at very low shear rates. In contrast, we observe a smaller dependence on the shear rate in the overall ordering at high shear rates, as well as an ever-increasing biaxiality.

Tuning chirality in the self-assembly of rod-like viruses by chemical surface modifications

Filamentous viruses of similar molecular and subunitary structure can form either a liquid crystalline nematic phase or a chiral nematic – also called cholesteric – phase, which is an elegant example of how self-organization of nanorods, with otherwise similar properties, can be affected by only subtle differences of surface properties and of the arrangement of the constituent subunits. In this work, we studied the influence of viral surface properties on the self-assembly of rod-like fd virus suspensions into the chiral nematic phase. For this purpose, the filamentous fd virus has been subjected to various chemical modifications on its capsid proteins: several organic molecules of different sizes and structures, including two popular fluorescent dyes (fluorescein and rhodamine), were coupled to the surface amino groups of the virus. The resulting chemically modified viruses still form a cholesteric phase in an aqueous suspension, but with a lower helicity compared to suspensions made of wild-type fd viruses. The degree of unwinding of the helical periodicity (or cholesteric pitch) depends on the structure of the labeled molecules. In addition, the chemically modified viruses exhibit a well-defined first order phase transition between the isotropic liquid and the liquid-crystalline state. Besides these modifications targeting the amino groups, the surface carboxyl groups were coupled with amino compounds so that the surface charge of fd viruses was reversed from negative to positive. The resulting particles can only form a nematic phase without any macroscopic helicity. These results suggest that inter-particle interactions, together with the intrinsic chirality of the virus, play an important role in the origin of the helical twist in the cholesteric phase.

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.

Electric-field-induced polarization of the layer of condensed ions on cylindrical colloids

In concentrated suspensions of charged colloids, interactions between colloids can be induced by an external electric field through the polarization of charge distributions (within the diffusive double layer and the layer of condensed ions) and/or electro-osmotic flow. In case of rod-like colloids, these field-induced inter-colloidal interactions have recently been shown to lead to anomalous orientation perpendicular to the external field, and to phase/state transitions and dynamical states, depending on the field amplitude and frequency of the external field. As a first step towards a (semi-) quantitative understanding of these phenomena, we present a linear-response analysis of the frequency-dependent polarization of the layer of condensed ions on a single, long and thin cylindrical colloid. The in-phase and out-phase response functions for the charge distribution and the electric potential are calculated for arbitrary orientation of the cylindrical colloid. The frequency-dependent degree of alignment, which is proportional to the electric-field-induced birefringence, is calculated as well, and compared to experiments on dilute fd virus suspensions.

Electric-field induced transitions in suspensions of charged colloidal rods

We explore transitions in suspensions of fd virus at a low ionic strength, induced by external electric fields at frequencies where double layers are polarized. On the basis of the different optical morphologies, phase/state diagrams are constructed in the field-amplitude versus frequency plane and the field-amplitude versus concentration plane. Due to interactions between polarized double layers, for low frequencies, various phases and dynamical states are found: a nematic phase, a striped phase and a dynamical state where nematic domains melt and reform. At relatively high frequencies of a few kHz, a uniform homeotropic phase is induced. The various phases and states are characterized by means of polarization microscopy, birefringence, dynamic light scattering and video-correlation spectroscopy. An expression is derived for the attenuation of the electric field due to electrode polarization, which is tested experimentally. This theory is used to correct phase/state diagrams for electrode polarization.

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.

Rotational dynamics of colloidal spheres probed with fluorescence recovery after photobleaching.

We report a polarized fluorescence recovery after photobleaching (pFRAP) method to measure the rotational dynamics of fluorescent colloids over a wide dynamic range. The method is based on the polarization anisotropy in the fluorescence intensity, generated by bleaching of fluorescently labeled particles with an intense pulse of linearly polarized laser light. The rotational mobilities of the fluorescent particles can be extracted from the relaxation kinetics of the postbleach fluorescence polarization anisotropy. Our pFRAP setup has access to correlation times over a range of time scales from tens of microseconds to tens of seconds, and is highly sensitive, so very low concentrations of labeled particles can be probed. We present a detailed description of the theoretical background of pFRAP. The performance of the equipment is demonstrated for fluorescent colloidal silica spheres, dispersed in pure solvents as well as in fd-virus suspensions.

Shear-banding and microstructure of colloids in shear flow.

We shall discuss the following phenomena found in various colloidal systems in shear flow. We recently observed shear-banding in suspensions of fd-virus in a cylindrical shear cell. Small angle light scattering experiments revealed that the shear-banding transition is preceded by a relatively fast process (minutes) of nematic-to-paranematic phase separation during which inhomogeneities on the micrometer length scale are formed. After the formation of these inhomogeneities, a slow (hours) appearence of shear-bands is observed, which have a height of a few mm. In the stationary state it is found, by means of polarization microscopy, that inhomogeneities exist within the bands. Small angle, time resolved light scattering experiments on near-critical microstructural order in a mixture of colloidal spheres and free polymer under stationary shear flow are discussed. The unexpected distortion of microstructure in directions perpendicular to the flow direction is quantitatively explained by extending an already existing theory, to include shear-induced short-ranged microstructural distortion. In colloidal systems consisting of "hairy colloids", where a spherical core is decorated with relatively long polymers, shear-induced polymer brush deformation might be important for its structural and rheological behavior. Preliminary neutron scattering and rheology experiments are performed to study polymer brush deformation in (semi-) dilute suspensions.

Electro-optic effects of aqueous fd-virus suspensions at very low ionic strength

The orientation in external electric fields of rod-like fd-virus particles (length l=895 nm, diameter d=9 nm) in aqueous suspensions is examined by the electric birefringence method. In aqueous suspensions the negatively charged fd-particles are surrounded by a diffuse Debye cloud of counterions, which is characterized by the Debye-Huckel parameter κ. A special experimental set-up is used to vary the ionic strength of the suspension, i.e. the Debye-Huckel parameter, and therefore the electrostatic interparticle interaction. The birefringence signal Δn is measured as a function of the strength and frequency of the applied electric field in suspensions of very low ionic strength (10 -6 M-10 -4 M). At low field strengths Kerr-behaviour is found. From the dependence of the electric anisotropy Δα el on the Debye-Huckel parameter κ it is concluded that the orientation of the fd-particles is correlated to an induced dipole due to a deformation of the diffuse Debye cloud. Saturation electric birefringence values are far from that theoretically expected. This can be interpreted as a destruction of the diffuse Debye cloud at high electric fields. At low field strengths the frequency dispersion below 1 kHz of Δn of the electrostatically interacting fd-virus suspensions shows anomalous behaviour. This negative electro-optic effect is an evidence for the orientation of the particle's long symmetry axis perpendicular to the applied electric field. The dispersion has a positive maximum at about 2 kHz. This maximum could be explained by different frequency dependencies of the electric polarizabilities parallel and perpendicular to the long symmetry axis of the fd-rods

Dynamic light scattering from semidilute suspensions of fd virus

Dynamic light scattering from semidilute suspensions of fd virus

Dynamic light-scattering study of suspensions of fd virus. Application of a theory of light-scattering spectrum of weakly bending filaments

Dynamic light-scattering study of suspensions of fd virus. Application of a theory of light-scattering spectrum of weakly bending filaments