Rod-like Colloids Research Articles

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.

Synthesis of Monodisperse, Rodlike Silica Colloids with Tunable Aspect Ratio

Although the experimental study of spherical colloids has been extensive, similar studies on rodlike particles are rare because suitable model systems are scarcely available. To fulfill this need, we present the synthesis of monodisperse rodlike silica colloids with tunable dimensions. Rods were produced with diameters of 200 nm and greater and lengths up to 10 μm, resulting in aspect ratios from 1 to ∼25. The growth mechanism of these rods involves emulsion droplets inside which silica condensation takes place. Due to an anisotropic supply of reactants, the nucleus grows to one side only, resulting in rod formation. In concentrated dispersions, these rods self-assemble in liquid crystal phases, which can be studied quantitatively on the single particle level in three-dimensional real-space using confocal microscopy. Isotropic, paranematic, and smectic phases were observed for this system.

Relaxation dynamics in the columnar liquid crystal phase of hard platelets

We perform Monte Carlo simulations to analyze the equilibrium dynamics and the long-time structural relaxation decay of columnar liquid crystals of disk-like colloidal particles. In the wake of recent studies on the columnar mesophase of hard calamitic (rod-like) colloids, we now focus on the diffusion of their discotic counterparts, here modeled as oblate hard spherocylinders. These systems exhibit a non-Gaussian column-to-column diffusion due to the combined action of transient cages and periodic free-energy barriers. We find that at fixed packing fraction the barrier height increases with decreasing particle thickness, resulting into a more heterogeneous and non-Gaussian dynamics for thinner platelets, and reducing the inter-column diffusion coefficient. Moreover, we observe the characteristic two-step relaxation decay of the structure in the plane perpendicular to the column axis. By contrast, the in-column dynamics is similar to the typical single-file diffusion of one-dimensional dense fluids, with a relatively fast decay of the correlation functions.

Interplay between a hydrodynamic instability and a phase transition: the Faraday instability in dispersions of rodlike colloids

Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited surface waves displays discontinuous and hysteretic features. This subcritical behaviour is attributed to the shear-thinning properties of our colloidal suspensions thanks to a phenomenological model based on rheological data under large amplitude oscillatory shear. Birefringence measurements provide direct evidence that Faraday waves induce local nematic ordering of the rodlike colloids. While local alignment simply follows the surface oscillations for dilute, isotropic suspensions, permanent nematic patches are generated by surface waves in samples close to the isotropic-to-nematic transition and above the transition large domains align in the flow direction. This strong coupling between the fluid microstructure and a hydrodynamic instability is confirmed by numerical computations based on the microstructural response of rodlike viruses in shear flow.

Depletion Interactions Effected by Different Variants of fd Virus

The depletion interaction between a probe sphere and a flat wall induced by fd virus is investigated by means of total internal reflection microscopy (TIRM). The viruses serve as a model system for monodisperse, rod-like colloids. We find that the experimental potentials are well described by the first-order density approximation up to an fd content of several overlap concentrations. This is in accordance with higher order density theory as confirmed by numerical calculations. Since the first-order analytical description still holds for all measurements, this exemplifies that higher order terms of the theory are unimportant for our system. Comparing the potentials induced by wild-type fd to those induced by a more rigid fd variant, it can be shown that the influence of the virus stiffness is beyond our experimental resolution and plays only a negligible role for the measured depletion potentials.

Confinement-Controlled Self Assembly of Colloids with Simultaneous Isotropic and Anisotropic Cross-Section

The phase behavior of building blocks with mushroom cap-shaped particle morphology is explored under 2D and quasi-2D confinement conditions. Fast confocal microscopy imaging of the particles sedimented in a wedge cell reveals a range of mono- and bilayer structures partially directed by the isotropic and anisotropic profiles of the particle geometry. The sequence of phases tracked with increasing confinement height includes those reported in spheres, in addition to the more complex rotator and orientation-dependent phases observed for a class of short rod-like colloids. In the later case, the major particle axis reorients with respect to the substrate. Closest packing considerations provide rationale for the observed 1Delta (hexagonal)-1Buckled-1Sides (rotator)-2square (square)-2Delta (hexagonal)-2Sides (rotator) structural transitions with height.

Charge Reversal of the Rodlike Colloidal fd Virus through Surface Chemical Modification

There is increasing interest in the use of viruses as model systems for fundamental research and as templates for nanomaterials. In this work, the rodlike fd virus was subjected to chemical modifications targeting different solvent-exposed functional groups in order to tune its surface properties, especially reversing the surface charge from negative to positive. The carboxyl groups of fd were coupled with different kinds of organic amines by carbodiimide chemistry, resulting in modified viruses that are positively charged over a wide range of pH. Care was taken to minimize intervirus cross linking, which often occurs because of such modifications. The surface amino groups were also grafted with poly(ethylene glycol) (PEG) end-functionalized with an active succinimidyl ester in order to introduce a steric stabilization effect. By combining charge reversal with PEG grafting, a reversible attraction between positively and negatively charged PEG-grafted fd viruses could be realized, which was tuned by the ionic strength of the solution. In addition, a charge-reversed fd virus forms only a pure nematic phase in contrast to the cholesteric phase of the wild type. These modified viruses might be used as model systems in soft condensed matter physics, for example, in the study of polyelectrolyte complexes or lyotropic liquid-crystalline phase behavior.

Effect of Particle Shape on Colloid Retention and Release in Saturated Porous Media

Colloidal particles of environmental concern often have nonspherical shapes. However, theories and models such as the classical filtration theory have been developed based on the behavior of spherical particles. This study examined the effect of particle shape on colloid retention (e.g., attachment and straining) and release in saturated porous media. Two- and three-step transport experiments were conducted in water-saturated glass bead columns using colloids dispersed in deionized water and an electrolyte solution. The particles used in the experiments were carboxylate-modified latex colloids of spherical (500 nm diam.) and rod (aspect ratio, 7.0) shapes. The rod-like particles were prepared by stretching the spherical particles. Analysis of the colloid breakthrough curves indicates that particle shape affected transport behavior, but retention did not increase with increasing aspect ratio. Retention of the spherical particles occurred mainly in the secondary energy minimum, whereas retention of rod-like particles occurred in primary and secondary energy minima. There was less straining of rod-like particles compared with spherical ones, indicating that the minor axis was the critical dimension controlling the process. Release of spherical particles on elution was instantaneous, whereas release of rod-like particles was rate limited, giving rise to long tails, implying an orientation effect for rod-like colloids. The results suggest that the differences in electrostatic properties and shape contributed to the observed different retention and release behaviors of the two colloids.

Reversible Gelation of Rod-Like Viruses Grafted with Thermoresponsive Polymers

The synthesis and selected macroscopic properties of a new model system consisting of poly(N-isopropylacrylamide) (PNIPAM)-coated rod-like fd virus particles are presented. The sticky rod-like colloids can be used to study effect of particle shape on gelation transition, the structure and viscoelasticity of isotropic and nematic gels, and to make both open isotropic as well as ordered nematic particle networks. This model system of rod-like colloids, for which the strength of attraction between the particles is tunable, is obtained by chemically grafting highly monodisperse rod-like fd virus particles with thermoresponsive polymers, e.g. PNIPAM. At room temperature, suspensions of the resulting hybrid PNIPAM-fd are fluid sols which are in isotropic or liquid crystalline phases, depending on the particle concentration and ionic strength. During heating/cooling, the suspensions change reversibly between sol and gel state near a critical temperature of approximately 32 degrees C, close to the lower critical solution temperature of free PNIPAM. The so-called nematic gel, which exhibits a cholesteric feature, can therefore be easily obtained. The gelation behavior of PNIPAM-fd system and the structure of the nematic gel have been characterized by rheology, optical microscopy and small-angle X-ray scattering.

Mesoscale hydrodynamics simulations of attractive rod-like colloids in shear flow

Suspensions of rod-like colloids show in equilibrium an isotropic–nematic coexistenceregion, which depends on the strength of an attractive interaction between the rods. Westudy the behavior of this system in shear flow for various interaction strengths. A hybridsimulation approach is employed, which consists of a mesoscale particle-basedhydrodynamics technique (multi-particle collision dynamics) for the solvent and moleculardynamics simulations for the colloidal rods. The shear flow induces alignment in theinitially isotropic phase, which generated an additional free volume around each rod andcauses the densification of the isotropic phase at the expense of an erosion ofthe initially nematic phase. Furthermore, the nematic phase exhibits a collectiverotational motion. The associated rotational time decreases linearly in with increasing shear rate , and increases with increasing attraction strength between the rods. The densitydifference between these two regions at different shear rates allows us to determine thebinodal line of the phase diagram. For large applied shear rates, the difference between thephases disappears in favor of a homogeneous flow-aligned state.

Suspensions of rod-like colloids and a depleting agent under confinement

We present a computer simulation study of suspensions of rod-like colloids and a depletantin confinement to a slit-pore. Mixtures of hard spherocylinders and ideal spheres werestudied by means of Monte Carlo simulations in the grand canonical ensemble. By use offinite size scaling analysis we determined the critical behaviour. In order to overcome largebarriers in the free energy we applied the successive umbrella sampling method(Virnau and Müller 2004 J. Chem. Phys. 120 10925). We find that, under confinement,the critical point of gas–liquid demixing shifts to higher concentrations of rodsand smaller concentrations of spheres due to the formation of an orientationallyordered surface film. If the separation between the walls becomes very small, thecritical point is shifted back to smaller concentrations of rods because the surfacefilm breaks up. In particular, we present a method for determining the wettingbehaviour from an analysis of the distribution of particle concentration. For large wallseparations we find wetting near the critical point consistent with the Cahn argument.

Gradient and vorticity banding

Banded structures of macroscopic dimensions can be induced by simple shear flow in many different types of soft matter systems. Depending on whether these bands extend along the or direction, the transition is referred to as gradient banding or vorticity banding, respectively. The main features of can be understood on the basis of a relatively simple constitutive equation. This minimal model for will be discussed in some detail, and its predictions are shown to explain many of the experimentally observed features. The minimal model assumes a decrease of the shear stress of the homogeneously sheared system with increasing shear rate within a certain shear-rate interval. The possible microscopic origin of the severe shear-thinning behaviour that is necessary for the resulting nonmonotonic flow curves is discussed for a few particular systems. Deviations between experimental observations and predictions by the minimal model are due to obvious simplifications within the scope of the minimal model. The most serious simplifications are the neglect of concentration dependence of the shear stress (or on other degrees of freedom) and of the elastic contributions to the stress, normal stresses, and the possibility of shear-induced phase transitions. The consequences of coupling of stress and concentration will be analyzed in some detail. In contrast to predictions of the minimal model, when coupling to concentration is important, a flow instability can occur that does not require strong shear thinning. Gradient is sometimes also observed in glassy- and gel-like systems, as well as in shear-thickening systems. Possible mechanisms that could be at the origin of gradient-band formation in such systems are discussed. Gradient can also occur in strongly entangled polymeric systems. Banding in these systems is discussed on the basis of computer simulations. Vorticity is less well understood and less extensively investigated experimentally as compared to banding. Possible scenarios that are at the origin of will be discussed. Among other systems, the observed vorticity-banding transition in rod-like colloids is discussed in some detail. It is argued, on the basis of experimental observations for these colloidal systems, that the vorticity-banding instability for such colloidal suspensions is probably related to an elastic instability, reminiscent of the Weissenberg effect in polymeric systems. This mechanism might explain in discontinuously shear-thickening systems and could be at work in other vorticity-banding systems as well. This overview does not include time-dependent phenomena like oscillations and chaotic behaviour.

Isotropic–isotropic phase separation in mixtures of rods and spheres: Some aspects of Monte Carlo simulation in the grand canonical ensemble

In this article we consider mixtures of non-adsorbing polymers and rod-like colloids in the isotropic phase, which upon the addition of polymers show an effective attraction via depletion forces. Above a certain concentration, the depletant causes phase separation of the mixture. We performed Monte Carlo simulations to estimate the phase boundaries of isotropic–isotropic coexistence. To determine the phase boundaries we simulated in the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120 (2004) 10925]. The location of the critical point was estimated by a finite size scaling analysis. In order to equilibrate the system efficiently, we used a cluster move in which rods and spheres were exchanged.

Depletion induced isotropic-isotropic phase separation in suspensions of rod-like colloids

When non-adsorbing polymers are added to an isotropic suspension of rod-like colloids, the colloids effectively attract each other via depletion forces. We performed Monte Carlo simulations to study the phase diagram of such rod-polymer mixture. The colloidal rods were modeled as hard spherocylinders; the polymers were described as spheres of the same diameter as the rods. The polymers may overlap with no energy cost, while the overlap of polymers and rods is forbidden. Large amounts of depletant cause phase separation of the mixture. We estimated the phase boundaries of isotropic-isotropic coexistence both in the bulk and in confinement. To determine the phase boundaries we applied the grand canonical ensemble using successive umbrella sampling [J. Chem. Phys. 120, 10925 (2004)], and we performed a finite size scaling analysis to estimate the location of the critical point. The results are compared with predictions of the free volume theory developed by Lekkerkerker and Stroobants [Nuovo Cimento D 16, 949 (1994)]. We also give estimates for the interfacial tension between the coexisting isotropic phases and analyze its power-law behavior on the approach of the critical point.

Use of Parsons-Lee and Onsager theories to predict nematic and demixing behavior in binary mixtures of hard rods and hard spheres

Parsons-Lee and Onsager theories are formulated for the isotropic-nematic transition in a binary mixture of hard rods and hard spheres. Results for the phase coexistence and for the equation of state in both phases for mixtures with different relative sizes and composition are presented. The two theories explain correctly the general behavior observed in experiments and computer simulations for these fluids. In particular, the theory accounts for the destabilization of the nematic phase when spherical or globular macromolecules are added to a system of rodlike colloids, and the entrance of the system into a demixed regime at high volume fractions of the spherical particles. Upon demixing a nematic state rich in rods coexists in equilibrium with an isotropic state much more diluted in the rodlike component. Onsager theory fails on quantitative grounds for aspect ratios of the rodlike molecules smaller than 100, and in the cases where the molar fractions of spheres becomes close to unity. On the contrary, the Parsons-Lee approximation remains accurate down to aspect ratios as small as 5. The spinodal analysis indicates that the isotropic-isotropic and nematic-nematic coexistences become feasible for sufficiently large spheres and long rods, respectively. The latter type of coexistence interferes partially with the isotropic-nematic coexistence regime of interest to the present work. Overall, the study serves to rationalize and control key aspects of the behavior of these binary nematogenic colloidal systems, which can be tuned with an appropriate choice of the relative size and molar fractions of the particles.

The renormalized jellium model for spherical and cylindrical colloids

Starting from a mean-field description for a dispersion of highly charged spherical or (parallel) rodlike colloids, we introduce the simplification of a homogeneous background to include the contribution of other polyions to the static field created by a tagged polyion. The charge of this background is self-consistently renormalized to coincide with the polyion effective charge, the latter quantity thereby exhibiting a nontrivial density dependence, which directly enters into the equation of state through a simple analytical expression. The good agreement observed between the pressures calculated using the renormalized jellium and Monte Carlo simulations confirms the relevance of the renormalized jellium model for theoretical and experimental purposes and provides an alternative to the Poisson-Boltzmann cell model since it is free of some of the intrinsic limitations of this approach.

Dynamics of ultrasonically induced birefringence of in rod-like colloidal solutions

This review summarized our experimental studies of ultrasonically induced birefringence on aqueous solution of rigid rod-like colloids and rod-like micelles from the view point of dynamics of particle orientation. For rigid rod-like colloids in dilute concentration, the orientational relaxation time was described in terms of the Debye–Einstein equation. This indicated that the ultrasonically induced birefringence could be one of useful tools for determining the size of particles of anisotropic shape. For rod-like micelles, the birefringence showed anomalous damping oscillation when the rod-like micelle was in an entangling state. The mechanism of damping oscillation was discussed using the results of the rheological measurements.

Transport of Rodlike Colloids through Packed Beds

The effect of colloid shape on filtration rates in porous media was examined by constructing particles with different aspect ratios and measuring their retention in packed beds. Spherical polystyrene latex microspheres (1.0-microm diameter) were heated, stretched to the desired aspect ratio (2:1 and 3:1, with a 1:1 control), and quickly cooled. These particles were injected into minicolumns containing glass beads (40-microm diameter) in solutions at two different ionic strengths (IS = 1 and 100 mM). The measured retentions increased with aspect ratio in both IS solutions. The zeta-potentialsfor all three aspect ratios were indistinguishable, and no charge nonuniformity was measured for any of the samples. Thus, the data supportthat changes in retention resulted from the different aspect ratios rather than from different surface chemistries. Interpretation of the retention data in terms of a collision efficiency (alpha) showed an increase with aspect ratio in both IS solutions, and for 1 mM the alpha increased from 0.011 (1:1) to 0.095 (2:1) to 0.26 (3:1). These results demonstrate for the first time the direct impact of particle shape on retention in porous media. Our findings have important implications for the transport of particles with high aspect ratios, such as rod-shaped bacteria, and for the modeling of such transport.

Anomalous field-induced particle orientation in dilute mixtures of charged rod-like and spherical colloids

Charged colloids in aqueous suspension often reconfigure counter-intuitively in the presence of an external electric field1,2,3,4,5,6,7. Despite decades of substantial theoretical effort, a clear understanding of such electrokinetic phenomena is only available for the electric polarization and migration of diluted spheres in low fields8. The interpretation of the electric response of charged rod-like particles is far less advanced. Here we report that diluted rod-like particles suspended in a sea of smaller spherical particles having similar charge align perpendicular to the external electric field. This ‘anomalous’ orientation, which contradicts the notion that charged rods in dilute suspensions always align parallel to external electric fields9, seems to be universal in dilute mixtures of charged rod-like and spherical colloids. The dependence of the perpendicular orientation on frequency and particle charge, size and concentration indicates the presence of field-induced asymmetric crowding of spherical particles around each rod, which gives rise to asymmetric electro-osmotic flows that induce a negative torque.

Simulation of complex fluids by multi-particle-collision dynamics

The particle-based mesoscale simulation technique called Multi-Particle-Collision Dynamics (MPCD) (also denoted as Stochastic Rotation Dynamics (SDR)) is introduced. The algorithm is outlined and applications to complex fluids are described. Results for the dynamics of a Gaussian polymer and a rodlike colloid are discussed. Moreover, the density dependence of the diffusion coefficient of a colloidal fluid is presented. Our investigations show that the MPCD algorithm accounts for hydrodynamic interactions.