Rod-like Colloids Research Articles

Anisotropic thermophoresis.

Colloidal migration in a temperature gradient is referred to as thermophoresis. In contrast to particles with a spherical shape, we show that elongated colloids may have a thermophoretic response that varies with the colloid orientation. Remarkably, this can translate into a non-vanishing thermophoretic force in the direction perpendicular to the temperature gradient. Opposite to the friction force, the thermophoretic force of a rod oriented with the temperature gradient can be larger or smaller than when oriented perpendicular to it. The precise anisotropic thermophoretic behavior clearly depends on the colloidal rod aspect ratio, and also on its surface details, which provides an interesting tunability to the devices constructed based on this principle. By means of mesoscale hydrodynamic simulations, we characterize this effect for different types of rod-like colloids.

Binary mixtures of rod-like colloids under shear: microscopically-based equilibrium theory and order-parameter dynamics

This paper is concerned with the dynamics of a binary mixture of rod-like, repulsive colloidal particles driven out of equilibrium by means of a steady shear flow (Couette geometry). To this end we first derive, starting from a microscopic density functional in Parsons–Lee approximation, a mesoscopic free energy functional whose main variables are the orientational order parameter tensors. Based on this mesoscopic functional we then explore the stability of isotropic and nematic equilibrium phases in terms of composition and rod lengths. Second, by combining the equilibrium theory with the Doi–Hess approach for the order parameter dynamics under shear, we investigate the orientational dynamics of binary mixtures for a range of shear rates and coupling parameters. We find a variety of dynamical states, including synchronized oscillatory states of the two components, but also symmetry breaking behavior where the components display different in-plane oscillatory states.

Synthesis of Cone-Shaped Colloids from Rod-Like Silica Colloids with a Gradient in the Etching Rate.

We present the synthesis of monodisperse cone-shaped silica colloids and their fluorescent labeling. Rod-like silica colloids prepared by ammonia-catalyzed hydrolysis and condensation of tetraethyl orthosilicate in water droplets containing polyvinylpyrrolidone cross-linked by citrate ions in pentanol were found to transform into cone-shaped particles upon mild etching by NaOH in water. The diameter and length of the resulting particles were determined by those of the initial rod-like silica colloids. The mechanism responsible for the cone-shape involves silica etching taking place with a varying rate along the length of the particle. Our experiments thus also lead to new insights into the variation of the local particle structure and composition. These are found to vary gradually along the length of the rod, as a result of the way the rod grows out of a water droplet that keeps itself attached to the flat end of the bullet-shaped particles. Subtle differences in composition and structure could also be resolved by high-resolution stimulated emission depletion confocal microscopy on fluorescently labeled particles. The incorporation of a fluorescent dye chemically attached to an amine-based silane coupling agent resulted in a distribution of fluorophores mainly on the outside of the rod-shaped particles. In contrast, incorporation of the silane coupling agent alone resulted in a homogeneous distribution. Additionally, we show that etching rods, where a silane coupling agent alone was incorporated and subsequently coupled to a fluorescent dye, resulted in fluorescent silica cones, the orientation of which can be discerned using super-resolution confocal microscopy.

Realizing efficient upconversion and down-shifting dual-mode luminescence in lanthanide-doped NaGdF4 core–shell–shell nanoparticles through gadolinium sublattice-mediated energy migration

Monodisperse rod-like colloidal core–shell–shell NaGdF4:Yb/Tm@NaGdF4:Ce/Ln@NaYF4 (Ln = Tb, Eu, Dy and Sm) nanoparticles (25 nm in diameter and 37 nm in length) have been successfully synthesized through a facile wet chemical method. X-ray diffraction, transmission electron microscopy, upconversion and down-shifting photoluminescence were used to characterize the samples. The prepared nanoparticles exhibited both tunable upconversion and down-shifting emissions from Tb, Eu, Dy and Sm activators under 980 nm near-infrared and 254 nm ultraviolet excitation, respectively. The dual-model luminescence was achieved through gadolinium (Gd3+) sublattice-mediated energy migration: Yb3+ → Tm3+→n(Gd3+) → Ln3+ and Ce3+ → n(Gd3+)→Ln3+ energy-transfer process, respectively. The advances on these dual-mode luminescent nanoparticles offer exciting opportunities for developing multifunctional optical nanoprobes for biological applications.

Phase diagrams of charged colloidal rods: Can a uniaxial charge distribution break chiral symmetry?

We construct phase diagrams for charged rodlike colloids within the second-virial approximation as a function of rod concentration, salt concentration, and colloidal charge. Besides the expected isotropic-nematic transition, we also find parameter regimes with a coexistence between a nematic and a second, more highly aligned nematic phase including an isotropic-nematic-nematic triple point and a nematic-nematic critical point, which can all be explained in terms of the twisting effect. We compute the Frank elastic constants to see if the twist elastic constant can become negative, which would indicate the possibility of a cholesteric phase spontaneously forming. Although the twisting effect reduces the twist elastic constant, we find that it always remains positive. In addition, we find that for finite aspect-ratio rods the twist elastic constant is also always positive, such that there is no evidence of chiral symmetry breaking due to a uniaxial charge distribution.

Confinement Induced Plastic Crystal-to-Crystal Transitions in Rodlike Particles with Long-Ranged Repulsion.

Colloidal particles in geometrical confinement display a complex variety of packing structures different from their three-dimensional (3D) bulk counterpart. Here, we confined charged rodlike colloids with long-ranged repulsions to a thin wedge-shaped cell and show, by quantitative 3D confocal microscopy, that not only their positional but also their orientational order depends sensitively upon the slit width. Synchronized with transitions in lattice symmetry and number of layers confinement induces plastic crystal-to-crystal transitions. A model analysis suggests that this complex sequence of more or less rotationally ordered states originates from the subtle competition between the electrostatic repulsion of a rod with the wall and with its neighbors.

Equivalence of Brownian dynamics and dynamic Monte Carlo simulations in multicomponent colloidal suspensions.

We propose a simple but powerful theoretical framework to quantitatively compare Brownian dynamics (BD) and dynamic Monte Carlo (DMC) simulations of multicomponent colloidal suspensions. By extending our previous study focusing on monodisperse systems of rodlike colloids, here we generalize the formalism described there to multicomponent colloidal mixtures and validate it by investigating the dynamics in isotropic and liquid crystalline phases containing spherical and rodlike particles. In order to investigate the dynamics of multicomponent colloidal systems by DMC simulations, it is key to determine the elementary time step of each species and establish a unique timescale. This is crucial to consistently study the dynamics of colloidal particles with different geometry. By analyzing the mean-square displacement, the orientation autocorrelation functions, and the self part of the van Hove correlation functions, we show that DMC simulation is a very convenient and reliable technique to describe the stochastic dynamics of any multicomponent colloidal system. Our theoretical formalism can be easily extended to any colloidal system containing size and/or shape polydisperse particles.

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.

Elastocapillary interactions on nematic films

Rod-like colloids distort fluid interfaces and interact by capillarity. We explore this interaction at the free surface of aligned nematic liquid crystal films. Naive comparison of capillary and elastic energies suggests that particle assembly would be determined solely by surface tension. Here, we demonstrate that, under certain circumstances, the capillary and elastic effects are complementary and each plays an important role. Particles assemble end-to-end, as dictated by capillarity, and align along the easy axis of the director field, as dictated by elasticity. On curved fluid interfaces, however, curvature capillary energies can overcome the elastic orientations and drive particle migration along curvature gradients. Domains of dominant interaction and their transition are investigated.

Determination of the positions and orientations of concentrated rod-like colloids from 3D microscopy data

Confocal microscopy in combination with real-space particle tracking has proven to be a powerful tool in scientific fields such as soft matter physics, materials science and cell biology. However, 3D tracking of anisotropic particles in concentrated phases remains not as optimized compared to algorithms for spherical particles. To address this problem, we developed a new particle-fitting algorithm that can extract the positions and orientations of fluorescent rod-like particles from three dimensional confocal microscopy data stacks. The algorithm is tailored to work even when the fluorescent signals of the particles overlap considerably and a threshold method and subsequent clusters analysis alone do not suffice. We demonstrate that our algorithm correctly identifies all five coordinates of uniaxial particles in both a concentrated disordered phase and a liquid-crystalline smectic-B phase. Apart from confocal microscopy images, we also demonstrate that the algorithm can be used to identify nanorods in 3D electron tomography reconstructions. Lastly, we determined the accuracy of the algorithm using both simulated and experimental confocal microscopy data-stacks of diffusing silica rods in a dilute suspension. This novel particle-fitting algorithm allows for the study of structure and dynamics in both dilute and dense liquid-crystalline phases (such as nematic, smectic and crystalline phases) as well as the study of the glass transition of rod-like particles in three dimensions on the single particle level.

Electric-field induced microdynamics of charged rods

Electric-field induced phase/state transitions are observed in AC electric fields with small amplitudes and low frequencies in suspensions of charged fibrous viruses (fd), which are model systems for highly charged rod-like colloids. Texture- and particle-dynamics in these field-induced states, and on crossing transition lines, are explored by image time-correlation and dynamic light scattering, respectively. At relatively low frequencies, starting from a system within the isotropic-nematic coexistence region, a transition from a nematic to a chiral nematic is observed, as well as a dynamical state where nematic domains melt and reform. These transitions are preliminary due to field-induced dissociation/association of condensed ions. At higher frequencies a uniform state is formed that is stabilized by hydrodynamic interactions through field-induced electro-osmotic flow where the rods align along the field direction. There is a point in the field-amplitude versus frequency plane where various transition lines meet. This point can be identified as a “non-equilibrium critical point”, in the sense that a length scale and a time scale diverge on approach of that point. The microscopic dynamics exhibits discontinuities on crossing transition lines that were identified independently by means of image and signal correlation spectroscopy.

Rod Hydrodynamics and Length Distributions of Single-Wall Carbon Nanotubes Using Analytical Ultracentrifugation

Because of their repetitive chemical structure, extreme rigidity, and the separability of populations with varying aspect ratio, SWCNTs are excellent candidates for use as model rodlike colloids. In this contribution, the sedimentation velocities of length and density sorted single-wall carbon nanotubes (SWCNTs) are compared to predictions from rod hydrodynamic theories of increasing complexity over a range of aspect ratios from <50 to >400. Independently measuring all contributions to the sedimentation velocity besides the shape factor, excellent agreement is found between the experimental findings and theoretical predictions for numerically calculated hydrodynamic radius values and for multiterm analytical expansion approximations; values for the hydrodynamic radii in these cases are additionally found to be consistent with the apparent hydrated particle radius determined independently by buoyancy measurements. Lastly, we utilize this equivalency to calculate the apparent distribution of nanotube lengths in each population from their sedimentation coefficient distribution without adjustable parameters, achieving excellent agreement with distributions from atomic force microscopy. The method developed herein provides an alternative for the ensemble measurement of SWCNT length distributions and others rodlike particles.

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.

Mesoscale hydrodynamics simulations of particle suspensions under shear flow: From hard to ultrasoft colloids

We discuss the nonequilibrium properties of rodlike and ultrasoft, star-polymer like colloidal particles in shear flow. Conformational, dynamical, as well as rheological aspects are addressed for a broad range of concentrations. For concentrated solutions of rodlike colloids, we study the nonequilibrium properties of a phase separated system, where a disordered phase coexists with a nematic phase. For starlike polymers we consider systems of various functionality, starting from linear polymers. The individual rods, polymers, or stars exhibit an intriguing dynamical behavior, which determines their macroscopic rheological properties. Despite the diversity on the colloidal level, the various systems exhibit a qualitatively similar macroscopic behavior, e.g., shear thinning, yet with some quantitative differences.

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.

Preparation and Characterization of Multilayered Polymer Nanotube Dispersions

Despite considerable efforts to synthesize nanotubes using porous alumina or polycarbonate membrane templates, few studies have addressed the resulting nanotube dispersion. We prepared dispersions of multilayered polyethylenimine/maleic anhydride alternating copolymer (PEI/MAAC) nanotubes synthesized with porous alumina templates. After mechanical polishing to remove the residual polymer surface layer from templates and subsequent template dissolution, the multilayered PEI/MAAC nanotubes were easily dispersed in water at neutral pH by polyelectrolyte adsorption, producing nanotube dispersions that were stable for at least 3 months. We characterized the dispersions using phase-contrast optical microscopy, electro-optics, electrophoresis, and viscometry to help understand their colloidal properties in the dilute and semidilute regimes. The dispersions were resistant to salt-induced aggregation up to at least 1 mM NaCl and were optically anisotropic when subjected to an electric field or flow. Interestingly, the electrophoretic mobility of polystyrene sulfonate (PSS)-stabilized nanotubes increases with increasing ionic strength, because of the high surface charge and softness of the adsorbed polyelectrolyte. Furthermore, unlike many rod-like colloid systems, the polymer nanotube dispersion has low viscosity because of weak rotary Brownian motions and strong tendency to shear thinning. At the high shear rates achieved in capillary viscometry experiments, however, we observed a slight shear thickening, which can be attributed to transient hydrocluster formation.

Helicopter rotation and smectic-isotropic coexistence of strongly attractive rods

Hydrodynamic simulations of strongly attractive rodlike colloids are performed with and without shear flow. In the absence of flow, the isotropic-nematic coexistence becomes isotropic-smectic A, and the interfacial properties clearly vary with increasing attraction strength. In the presence of shear flow, a new collective rotation appears in which the director rotates in the vorticity-flow plane in a similar fashion to the movement of the rotor of a helicopter.

Cholesteric order in systems of helical Yukawa rods

We consider the interaction potential between two chiral rod-like colloids which consist of athin cylindrical backbone decorated with a helical charge distribution on the cylindersurface. For sufficiently slender helical rods a simple scaling expression is derived whichrelates the chiral ‘twisting’ potential to the microscopic properties of the particles, such asthe internal helical pitch, charge density and electrostatic screening parameter. To predictthe behaviour of the macroscopic cholesteric pitch of the fluid bulk phase we invoke asimple second-virial theory generalized to treat anisotropic states with weakly twisteddirector fields. It is shown that, while particles with weakly coiled helices always form acholesteric phase whose helical sense is commensurate with that of the internalhelix, more strongly coiled rods lead to the formation of a cholesteric state ofopposite sense. The correlation between the helical symmetry at the microscopic andmacroscopic scale is found to be very sensitive to the pitch of the Yukawa helix. Mixinghelical particles of sufficiently disparate length and internal pitch may give rise toa demixing of the uniform cholesteric phase into two fractions with a differentmacroscopic pitch. Our findings could be relevant to the interpretation of experimentalobservations in systems of cellulose and chitin microfibres, DNA and fd virus rods.

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.