Crystallization kinetics of colloidal spheres under stationary shear flow

Shearing-induced formation of Au nanowires

Shearing-induced nucleation is known in our daily lives, yet rarely discussed in nano-synthesis. Here, we demonstrate an unambiguous shearing-induced growth of Au nanowires. While in static solution Au would predominately deposit on pre-synthesized triangular nanoplates to form nano-bowls, the introduction of stirring or shaking gives rise to nanowires, where an initial nucleation could be inferred. Under specific growth conditions, CTAB is responsible for stabilizing the growth materials and the resulting oversaturation promotes shearing-induced nucleation. At the same time, all Au surfaces are passivated by ligands, so that the growth materials are diverted to relatively fresher sites. We propose that the different degrees of "focused growth" in active surface growth could be represented by watersheds of different slopes, so that the subtle differences between neighbouring sites would set course to opposite pathways, with some sites becoming ever more active and others ever more inhibited. The shearing-induced nuclei, with their initially ligand-deficient surface and higher accessibility to growth materials, win the dynamic inter-particle competition against other sites, explaining the dramatic diversion of growth materials from the seeds to the nanowires.

Motility-induced shear thickening in dense colloidal suspensions

Phase transitions and collective dynamics of active colloidal suspensions are fascinating topics in soft matter physics, particularly for out-of-equilibrium systems, which can lead to rich rheological behaviours in the presence of steady shear flow. Here the role of self-propulsion in the rheological response of a dense colloidal suspension is investigated by using particle-resolved Brownian dynamics simulations. First, the combined effect of activity and shear in the solid on the disordering transition of the suspension is analyzed. While both self-propulsion and shear destroy order and melt the system if critical values are exceeded, self-propulsion largely lowers the stress barrier needed to be overcome during the transition. We further explore the rheological response of the active sheared system once a steady state is reached. While passive suspensions show a solid-like behaviour, turning on particle motility fluidises the system. At low self-propulsion, the active suspension behaves in the steady state as a shear-thinning fluid. Increasing the self-propulsion changes the behaviour of the liquid from shear-thinning to shear-thickening. We attribute this to clustering in the sheared suspensions induced by motility. This new phenomenon of motility-induced shear thickening (MIST) can be used to tailor the rheological response of colloidal suspensions.

Universal Nucleation Behavior of Sheared Systems

Using molecular simulations and a modified classical nucleation theory, we study the nucleation, under flow, of a variety of liquids: different water models, Lennard-Jones, and hard sphere colloids. Our approach enables us to analyze a wide range of shear rates inaccessible to brute-force simulations. Our results reveal that the variation of the nucleation rate with shear is universal. A simplified version of the theory successfully captures the nonmonotonic temperature dependence of the nucleation behavior, which is shown to originate from the violation of the Stokes-Einstein relation.

Homogeneous nucleation of sheared liquids: advances and insights from simulations and theory

One of the most ubiquitous and technologically important phenomena in nature is the nucleation of homogeneous flowing systems. The microscopic effects of shear on a nucleating system are still imperfectly understood, although in recent years a consistent picture has emerged. The opposing effects of shear can be split into two major contributions for simple atomic and molecular liquids: increase of the energetic cost of nucleation, and enhancement of the kinetics. In this perspective, we describe the latest computational and theoretical techniques which have been developed over the past two decades. We collate and unify the overarching influences of shear, temperature, and supersaturation on the process of homogeneous nucleation. Experimental techniques and capabilities are discussed, against the backdrop of results from simulations and theory. Although we primarily focus on simple systems, we also touch upon the sheared nucleation of more complex systems, including glasses and polymer melts. We speculate on the promising directions and possible advances that could come to fruition in the future.

Classical nucleation theory for the crystallization kinetics in sheared liquids

While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate can be rationalized within the CNT framework by an additional elastic work proportional to the droplet volume. We extract the local stress and strain inside solid droplets, which yield size-dependent values for the shear modulus that are about half of the bulk value. Finally, we show that for a complete description one also has to take into account the change of interfacial work between the strained droplet and the sheared liquid. From scaling reasons, we expect this extra contribution to dominate the work formation of small nuclei but become negligible compared to the elastic work for droplets composed of a few hundreds of particles.

High-Throughput Acoustofluidic Self-Assembly of Colloidal Crystals

Colloidal crystals are encountered in a variety of energy-harvesting applications, where they serve as waveguides or filters for electromagnetic and electro-optic energy. Techniques such as electric or magnetic assembly are used to assemble colloidal crystals, but are limited by crystal size, yield, and throughput. This article demonstrates the continuous, high-throughput assembly of two-dimensional (2D)-colloidal crystals in an acoustofluidic flow cell. The device is fabricated using off-the-shelf components and does not require a clean-room access. An experimental state diagram shows how the fluid flow rate and voltage applied to the piezoelectric element in our device can tune the crystal microstructure. Highly ordered colloidal crystals are continuously assembled in less than a minute with a throughput yield of several hundred particles per minute using this device. The acoustically assembled ordered 2D crystals are immobilized using a UV-curable resin and extracted as ordered polymer-particle fibers, demonstrating the ability of using acoustic fields to assemble ordered structures embedded in bulk materials. Particle tracking is used to construct the cross-channel particle distribution to understand the effect of acoustic compression on colloidal crystal assembly. Microparticle image velocimetry data is compared to a theoretical transport model to quantify the effect fluid flow and acoustic trapping has on the colloidal crystal ensemble.

Effects of shear flow on phase nucleation and crystallization

Classical nucleation theory offers a good framework for understanding the common features of new phase formation processes in metastable homogeneous media at rest. However, nucleation processes in liquids are ubiquitously affected by hydrodynamic flow, and there is no satisfactory understanding of whether shear promotes or slows down the nucleation process. We developed a classical nucleation theory for sheared systems starting from the molecular level of the Becker-Doering master kinetic equation and we analytically derived a closed-form expression for the nucleation rate. The theory accounts for the effect of flow-mediated transport of molecules to the nucleus of the new phase, as well as for the mechanical deformation imparted to the nucleus by the flow field. The competition between flow-induced molecular transport, which accelerates nucleation, and flow-induced nucleus straining, which lowers the nucleation rate by increasing the nucleation energy barrier, gives rise to a marked nonmonotonic dependence of the nucleation rate on the shear rate. The theory predicts an optimal shear rate at which the nucleation rate is one order of magnitude larger than in the absence of flow.

Shear melting at the crystal-liquid interface: Erosion and the asymmetric suppression of interface fluctuations

The influence of an applied shear on the planar crystal-melt interface is modeled by a nonlinear stochastic partial differential equation of the interface fluctuations. A feature of this theory is the asymmetric destruction of interface fluctuations due to advection of the crystal protrusions on the liquid side of the interface only. We show that this model is able to qualitatively reproduce the nonequilibrium coexistence line found in simulations. The impact of shear on spherical clusters is also addressed.

The role of shear in crystallization kinetics: From suppression to enhancement

In many technical applications crystallization proceeds in the presence of stresses and flows, hence the importance to understand the crystallization mechanism in simple situations. We employ molecular dynamics simulations to study the crystallization kinetics of a nearly hard sphere liquid that is weakly sheared. We demonstrate that shear flow both enhances and suppresses the crystallization kinetics of hard spheres. The effect of shear depends on the quiescent mechanism: suppression in the activated regime and enhancement in the diffusion-limited regime for small strain rates. At higher strain rates crystallization again becomes an activated process even at densities close to the glass transition.

Shear-induced criticality near a liquid-solid transition of colloidal suspensions

We investigate colloidal suspensions under shear flow through numerical experiments. By measuring the time-correlation function of a bond-orientational order parameter, we find a divergent time scale near a transition point from a disordered fluid phase to an ordered fluid phase, where the order is characterized by a nonzero value of the bond-orientational order parameter. We also present a phase diagram in the (ρ,γ(ex)) plane, where ρ is the density of the colloidal particles and γ(ex) is the shear rate of the solvent. The transition line in the phase diagram terminates at the equilibrium transition point, while a critical region near the transition line vanishes continuously as γ(ex)→0.

Boundary-driven colloidal crystallization in simple shear flow

Using confocal microscopy, we directly observe that simple shear flow induces transient crystallization of colloids by wall-normal propagation of crystallization fronts from each shearing surface. The initial rate of the front propagation was 1.75±0.07 colloidal layers per unit of applied strain. The rate slowed to 0.29±0.04 colloidal layers per unit of applied strain as the two fronts approached each other at the midplane. The retardation of the front propagation is caused by self-concentration of shear strain in the growing bands of the lower-viscosity crystal, an effect that leads to a progressive reduction of the shear rate in the remaining amorphous material. These findings differ significantly from previous hypotheses for flow-induced colloidal crystallization by homogeneous mechanisms.

Crystal nucleation and cluster-growth kinetics in a model glass under shear

Crystal nucleation and growth processes induced by an externally applied shear strain in a model metallic glass are studied by means of nonequilibrium molecular dynamics simulations, in a range of temperatures. We observe that the nucleation-growth process takes place after a transient, induction regime. The critical cluster size and the lag-time associated with this induction period are determined from a mean first-passage time analysis. The laws that describe the cluster-growth process are studied as a function of temperature and strain rate. A theoretical model for crystallization kinetics that includes the time dependence for nucleation and cluster growth is developed within the framework of the Kolmogorov-Johnson-Mehl-Avrami scenario and is compared with the molecular dynamics data. Scalings for the cluster-growth laws and for the crystallization kinetics are also proposed and tested. The observed nucleation rates are found to display a nonmonotonic strain rate dependency.

Direct investigation of anisotropic suspension structure in pressure-driven flow

Evidence is presented to show the microstructural anisotropy responsible for normal stress in sheared suspensions. Particle velocimetry is combined with three-dimensional particle locations obtained via confocal microscopy at rest. A range of volume fractions phi and local shear rates gamma are investigated in a weakly Brownian pressure-driven suspension. At high gamma, the pairwise distribution shows a strong probability along the axis of compression similar to observations from Stokesian dynamics simulation at phi=0.32. At the channel center where gamma-->0, the concentrated suspension at phi=0.56 behaves as a confined isotropic fluid.

Shear ordering in polymer photonic crystals

Optical scattering spectra are recorded in situ on flowing colloidal polymeric nanocomposites which are sheared into photonic crystals at 150 degrees C using a high-pressure quartz-cell multipass rheometer. Broadband spectroscopy of the resonant Bragg scattering peak allows the direct observation of crystal formation and melting of monodisperse core-shell particles. A range of flow conditions of this solventless, highly viscous melt reveals four distinct regimes of crystal growth and decay which match a simple rheological model. Extraction of crystal thickness, order and lattice spacing are validated by one-dimensional electromagnetic simulations.

Supersaturated dispersions of rodlike viruses with added attraction

The kinetics of isotropic-nematic (I-N) and nematic-isotropic (N-I) phase transitions in dispersions of rodlike fd viruses are studied. Concentration quenches were applied using pressure jumps in combination with polarization microscopy, birefringence, and turbidity measurements. The full biphasic region could be accessed, resulting in the construction of an experimental analog of the bifurcation diagram. The N-I spinodal points for dispersions of rods with varying concentrations of depletion agent (dextran) were obtained from orientation quenches using cessation of shear flow in combination with small-angle light scattering. We found that the location of the N-I spinodal point is independent of the attraction, which was confirmed by theory. Surprisingly, the experiments showed that also the absolute induction time, the critical nucleus, and the growth rate are insensitive of the attraction if the concentration is scaled to the distance to the phase boundaries.

Melting and crystallization of colloidal hard-sphere suspensions under shear

Shear-induced melting and crystallization were investigated by confocal microscopy in concentrated colloidal suspensions of hard-sphere-like particles. Both silica and polymethylmethacrylate suspensions were sheared with a constant rate in either a countertranslating parallel plate shear cell or a counterrotating cone-plate shear cell. These instruments make it possible to track particles undergoing shear for extended periods of time in a plane of zero velocity. Although on large scales, the flow profile deviated from linearity, the crystal flowed in an aligned sliding layer structure at low shear rates. Higher shear rates caused the crystal to shear melt, but, contrary to expectations, the transition was not sudden. Instead, although the overall order decreased with shear rate, this was due to an increase in the nucleation of localized domains that temporarily lost and regained their ordered structure. Even at shear rates that were considered to have melted the crystal as a whole, ordered regions kept showing up at times, giving rise to very large fluctuations in 2D bond-orientational order parameters. Low shear rates induced initially disordered suspensions to crystallize. This time, the order parameter increased gradually in time without large fluctuations, indicating that shear-induced crystallization of hard spheres does not proceed via a nucleation and growth mechanism. We conclude that the dynamics of melting and crystallization under shear differ dramatically from their counterparts in quiescent suspensions.

Shear effects on crystal nucleation in colloidal suspensions

Extensive two-dimensional Langevin dynamics simulations are used to determine the effect of steady shear flows on the crystal nucleation kinetics of charge stabilized colloids and colloids whose pair potential possess an attractive shallow well of a few k_{B}T 's (attractive colloids). Results show that in both types of systems small amounts of shear speeds up the crystallization process and enhances the quality of the growing crystal significantly. Moderate shear rates, on the other hand, destroy the ordering in the system. The very high shear rate regime where a reentering transition to the ordered state could exist is not considered in this work. In addition to the crystal nucleation phenomena, the analysis of the transport properties and the characterization of the steady state regime under shear are performed.

A new parallel plate shear cell for in situ real-space measurements of complex fluids under shear flow

We developed and tested a parallel plate shear cell that can be mounted on top of an inverted microscope to perform confocal real-space measurements on complex fluids under shear. To follow structural changes in time, a plane of zero velocity is created by letting the plates move in opposite directions. The location of this plane is varied by changing the relative velocities of the plates. The gap width is variable between 20 and 200 microm with parallelism better than 1 microm. Such a small gap width enables us to examine the total sample thickness using high numerical aperture objective lenses. The achieved shear rates cover the range of 0.02-10(3) s(-1). This shear cell can apply an oscillatory shear with adjustable amplitude and frequency. The maximum travel of each plate equals 1 cm, so that strains up to 500 can be applied. For most complex fluids, an oscillatory shear with such a large amplitude can be regarded as a continuous shear. We measured the flow profile of a suspension of silica colloids in this shear cell. It was linear except for a small deviation caused by sedimentation. To demonstrate the excellent performance and capabilities of this new setup we examined shear induced crystallization and melting of concentrated suspensions of 1 microm diameter silica colloids.

Tunable colloids: control of colloidal phase transitions with tunable interactions

Systems of spherical colloidal particles mimic the thermodynamics of atomic crystals. Control of interparticle interactions in colloids, which has recently begun to be extensively exploited, gives rise to rich phase behaviours as well as crystal structures with nanoscale and micron-scale lattice spacings. This provides model systems in which to study fundamental problems in condensed matter physics, such as the dynamics of crystal nucleation and melting, and the nature of the glass transition, at experimentally accessible lengthscales and timescales. Tunable control of these interactions provides reversible control. This will enable quantitative studies of phase transition kinetics as well as the creation of advanced materials with switchability of function and properties.

Nematic-isotropic spinodal decomposition kinetics of rodlike viruses

We investigate spinodal decomposition kinetics of an initially nematic dispersion of rodlike viruses. Quench experiments are performed from a flow-stabilized homogeneous nematic state at a high shear rate into the two-phase isotropic-nematic coexistence region at a zero shear rate. We present experimental evidence that spinodal decomposition is driven by orientational diffusion, in accordance with a very recent theory.