Self-assembly of Janus particles under shear

Aggregation of amphiphilic nanocubes in equilibrium and under shear

We investigate the self-assembly of amphiphilic nanocubes into finite-sized aggregates in equilibrium and under shear, using molecular dynamics (MD) simulations and kinetic Monte Carlo (KMC) calculations. These patchy nanoparticles combine both interaction and shape anisotropy, making them valuable models for studying folded proteins and DNA-functionalized nanoparticles. The nanocubes can self-assemble into various finite-sized aggregates ranging from rods to self-avoiding random walks, depending on the number and placement of the hydrophobic faces. Our study focuses on suspensions containing multi- and one-patch cubes, with their ratio systematically varied. When the binding energy is comparable to the thermal energy, the aggregates consist of only few cubes that spontaneously associate/dissociate. However, highly stable aggregates emerge when the binding energy exceeds the thermal energy. Generally, the mean aggregation number of the self-assembled clusters increases with the number of hydrophobic faces and decreases with increasing fraction of one-patch cubes. In sheared suspensions, the more frequent collisions between nanocube clusters lead to faster aggregation dynamics but also to smaller terminal steady-state mean cluster sizes. The results from the MD and KMC simulations are in excellent agreement for all investigated two-patch cases, whereas the three-patch cubes form systematically smaller clusters in the MD simulations compared to the KMC calculations due to finite-size effects and slow aggregation kinetics. By analyzing the rate kernels, we are able to identify the primary mechanisms responsible for (shear-induced) cluster growth and breakup. This understanding allows us to tune nanoparticle and process parameters to achieve desired cluster sizes and shapes.

Evaporation-driven assembly of colloidal nanoparticles into clusters: A dissipative particle dynamics study

In this work we consider a simulation strategy for assembling Janus nanoparticles in oil-in-water emulsion droplets by evaporation based on the dissipative particle dynamics method. Our simple method reproduces all the observed cluster configurations that have been explored experimentally. In addition, the kinetic process of cluster formation is systematically investigated. We observe a structural transition from spherical packings to minimal second-moment configurations via visual inspection and a simple angle parameter. We reveal that the critical volume at which the transition occurs is a cubic function of the number of particles, N. Our approach also allows us to anticipate higher-order clusters, overcoming the limitations of the standard methods in the literature. Similarly to small N values, we find that for each N in the range of 16-39, all final clusters have a unique configuration.

Self-Assembly of Amphiphilic Cubes in Suspension

We study the self-assembly of amphiphilic cubic colloids using molecular dynamics as well as rejection-free kinetic Monte Carlo simulations. We vary both the number and location of the solvophobic faces (patches) on the cubes at several colloid volume fractions and determine the resulting size and shape distributions of the self-assembled aggregates. When the binding energy is comparable to the thermal energy of the system, aggregates typically consist of only few spontaneously associating/dissociating colloids. Increasing the binding energy (or lowering the temperature) leads to the emergence of highly stable aggregates, e.g., small dimers in pure suspensions of one-patch cubes or large (system-spanning) aggregates in suspensions of multipatch colloids. In mixtures of one- and multipatch cubes, the average aggregation number increases with increasing number of solvophobic faces on the multipatch cubes as well with increasing fraction of multipatch cubes. The resulting aggregate shapes range from elongated rods over fractal objects to compact spheres, depending on the number and arrangement of solvophobic patches on the cubic colloids. Our findings establish the complex self-assembly pathways for a class of building blocks that combine both interaction and shape anisotropy, with the potential of forming hierarchically ordered superstructures.

Janus Droplet Formation via Thermally Induced Phase Separation: A Numerical Model with Diffusion and Convection

Microscale Janus particles have versatile potential applications in many physical and biomedical fields, such as microsensor, micromotor, and drug delivery. Here, we present a phase-field approach of multicomponent and multiphase to investigate the Janus droplet formation via thermally induced phase separation. The crucial kinetics for the formation of Janus droplets consisting of two polymer species and a solvent component via an interplay of both diffusion and convection is considered in the Cahn-Hilliard-Navier-Stokes equation. The simulation results of the phase-field model show that unequal interfacial tensions between the two polymer species and the solvent result in asymmetric phase separation in the formation process of Janus droplets. This asymmetric phase separation plays a vital role in the establishment of the so-called core-shell structure that has been observed in previous experiments. By varying the droplet size, the surface tension, and the molecular interaction between the polymer species, several novel droplet morphologies are predicted in the development process of Janus droplets. Moreover, we stress that the hydrodynamics should be reckoned as a non-negligible mechanism that not only accelerates the Janus droplet evolution but also has great impacts on the coarsening and coalescence of the Janus droplets.

Free-Energy Landscape and Isomerization Rates of Au4 Clusters at Finite Temperatures

In metallic nanoparticles, the geometry of atomic positions controls the particle's electronic band structure, polarizability, and catalytic properties. Analyzing the structural properties is a complex problem; the structure of an assembled cluster changes from moment to moment due to thermal fluctuations. Conventional structural analyses based on spectroscopy or diffraction cannot determine the instantaneous structure exactly and can merely provide an averaged structure. Molecular simulations offer an opportunity to examine the assembly and evolution of metallic clusters, as the preferred assemblies and conformations can easily be visualized and explored. Here, we utilize the adaptive biasing force algorithm applied to first-principles molecular dynamics to demonstrate the exploration of a relatively simple system, which permits a comprehensive study of the small metal cluster Au₄ in both neutral and charged configurations. Our simulation work offers a quantitative understanding of these clusters' dynamic structure, which is significant for single-site catalytic reactions on metal clusters and provides a starting point for a detailed quantitative understanding of more complex pure metal and alloy clusters' dynamic properties.

Computer simulations of self-assembly of anisotropic colloids

Computer simulations have played a significant role in understanding the physics of colloidal self-assembly, interpreting experimental observations, and predicting novel mesoscopic and crystalline structures. Recent advances in computer simulations of colloidal self-assembly driven by anisotropic or orientation-dependent inter-particle interactions are highlighted in this review. These interactions are broadly classified into two classes: entropic and enthalpic interactions. They mainly arise due to shape anisotropy, surface heterogeneity, compositional heterogeneity, external field, interfaces, and confinements. Key challenges and opportunities in the field are discussed.

Interaction of Active Janus Colloids with Tracers

Understanding the motion of artificial active swimmers in complex surroundings, such as a dense bath of passive particulate matter, is essential for their successful utilization as cargo (drug) carriers and sensors or for medical imaging, under microscopic domains. In this study, we experimentally investigated the motion of active SiO₂-Pt Janus particles (JPs) in a two-dimensional bath of smaller silica tracers dispersed with varying areal densities. Our observations indicate that when an active JP undergoes a collision with an isolated tracer, their interaction can have a significant impact on the swimmer's motion. However, the overall impact of tracers on the active JPs' motion (translation and rotation) depends on the frequency of collisions and also on the nature of the collision, which is marked by the time-duration for which the particles maintain contact during the collisions. Further, in the high-density tracer bath, our experiments reveal that the motion of the active JP results in a novel organizational behavior of the tracers on the trailing Pt (depletion of tracers) and the leading SiO₂ (accumulation of tracers) side. In laboratory frame the emergence and the subsequent vanishing of the depletion zone are discussed in detail.

Diffusion and sedimentation in colloidal suspensions using multiparticle collision dynamics with a discrete particle model

We study self-diffusion and sedimentation in colloidal suspensions of nearly hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to experimental data and Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne-Prager-Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.

Enhanced thermal conductivity of nanofluids by introducing Janus particles

The addition of nanoparticles to a base fluid (i.e., nanofluids) is an effective strategy to achieve a higher thermal conductivity of a fluid. In a common nanofluid, the suspended nanoparticles are mostly symmetrical spheres. In the present paper, we propose to add Janus nanoparticles into a fluid (termed as Janus nanofluids), to further enhance the thermal conductivity of nanofluids. By using molecular dynamics simulations, it is found that the thermal conductivity can be distinctly improved by introducing Janus particles into the nanofluids in contrast with common nanofluids. Based on the calculation results of the molecular radial distribution function around the nanoparticle, and the diffusion coefficient of the base fluid and the Janus nanoparticle, the enhancement in the thermal conductivity of Janus nanofluids is attributed to the enhanced Brownian motion of Janus nanoparticles, which increases the probability of inter-molecular collisions and leads to enhanced energy transfer in nanofluids. The Janus nanofluids proposed in this work provide insights for the design of nanofluids with high thermal conductivity.

Janus Particles at Fluid Interfaces: Stability and Interfacial Rheology

The use of the Janus motif in colloidal particles, i.e., anisotropic surface properties on opposite faces, has gained significant attention in the bottom-up assembly of novel functional structures, design of active nanomotors, biological sensing and imaging, and polymer blend compatibilization. This review is focused on the behavior of Janus particles in interfacial systems, such as particle-stabilized (i.e., Pickering) emulsions and foams, where stabilization is achieved through the binding of particles to fluid interfaces. In many such applications, the interface could be subjected to deformations, producing compression and shear stresses. Besides the physicochemical properties of the particle, their behavior under flow will also impact the performance of the resulting system. This review article provides a synopsis of interfacial stability and rheology in particle-laden interfaces to highlight the role of the Janus motif, and how particle anisotropy affects interfacial mechanics.

Stability of amphiphilic Janus dimers in shear flow: a molecular dynamics study

Amphiphilic Janus particles in a flow are thought to experience a torque due to the asymmetry in slip at their surfaces. This effect has the potential to destabilise self-assembled Janus structures in flows due to the forces and torques applied to individual Janus nanoparticles. In this work, we investigate the stability of amphiphilic Janus dimers and homogeneous hydrophobic dimers in shear flow using molecular dynamics, and study possible break-up mechanisms. In particular, we consider the influence of the activation enthalpy and entropy on the thermal break-up rate of these dimers. Janus dimers are less stable than hydrophobic dimers, and increasing the applied shear rate has a greater effect on break-up for Janus dimers. Two mechanisms leading to increased break-up in shear flow are studied, namely the rotational speed of the dimers and the orientation of individual spheres in the dimers, and we propose a descriptive equation for calculation of the break-up rate. Overall, the results indicate that the stability of dimers in shear flow depends on the slip length at the spheres' surfaces, and that the slip length difference on Janus dimers could contribute to destabilisation.

Dynamic Interfacial Trapping of Janus Nanorod Aggregates

Taking advantage of both shape and chemical anisotropy on the same nanoparticle offers rich self-assembly possibilities for nanotechnology. Through dissipative particle dynamics calculations, in the present work, the directed assembly of Janus nanorod aggregates and their capability to assemble into metastable novel structures at an interfacial level have been assessed. Symmetric Janus rods become kinetically trapped and exhibit either parallel or antiparallel alignment with respect to their long axis (different compositions). This depends on several factors that have been mapped herein and that can be precisely tuned: Flory-Huggins interaction parameter χ between polymer phases; concentration; shear rate; and even aggregate shape. Ultimately, two different aggregate structures result from rod tumbling that are not observed under quiescent conditions: monolayer-like aggregates exhibiting trapped rods with antiparallel configuration; and stacked nanorod arrays similar to superlattice sheets. These different structures can be controlled by the likelihood with which tumbling Janus rods encounter other aggregate portions showing parallel alignment. Hence, the present study offers fundamental insight into relevant parameters that govern the directed assembly of Janus nanoparticles at an interfacial level. Novel applications may potentially derive from the resulting aggregate structures, such as peculiar displays and sensors.

Self-assembly of magnetic colloids with radially shifted dipoles

Anisotropic potentials in Janus colloids provide additional freedom to control particle aggregation into structures of different sizes and morphologies. In this work, we perform Brownian dynamics simulations of a dilute suspension of magnetic spherical Janus colloids with their magnetic dipole moments shifted radially towards the surface of the particle in order to gain valuable microstructural insight. Properties such as the mean cluster size, orientational ordering, and nucleation and growth are examined dynamically. Differences in the structure of clusters and in the aggregation process are observed depending on the dipolar shift (s)-the ratio between the displacement of the dipole and the particle radius-and the dipolar coupling constant (λ)-the ratio between the magnetic dipole-dipole and Brownian forces. Using these two dimensionless quantities, a structural "phase" diagram is constructed. Each phase corresponds to unique nucleation and growth behavior and orientational ordering of dipoles inside clusters. At small λ, the particles aggregate and disaggregate resulting in short-lived clusters at small s, while at high s the particles aggregate in permanent triplets (long-lived clusters). At high λ, the critical nuclei formed during the nucleation process are triplets and quadruplets with unique orientational ordering. These small clusters then serve as building blocks to form larger structures, such as single-chain, loop-like, island-like, worm-like, and antiparallel-double-chain clusters. This study shows that dipolar shifts in colloids can serve as a control parameter in applications where unique size, morphology, and aggregation kinetics of clusters are required.

Structure and dynamics of amphiphilic Janus spheres and spherocylinders under shear

We study the structure formation and flow properties of colloidal dispersions comprised of Janus spheres, Janus spherocylinders, and their mixtures, using hybrid molecular dynamics simulations that take into account hydrodynamic interactions. We systematically vary the Janus balance and the shape anisotropy of the particles, and explore a range of colloid volume fractions in the liquid regime of the phase diagram. At rest, Janus spheres with small hydrophobic patches form spherical micelles for all investigated colloid concentrations. In contrast, Janus spheres with an entirely hydrophobic hemisphere aggregate to larger worm-like micelles and network-like structures. Janus spherocylinders exhibit a similar self-assembly behavior. At small and intermediate shear, we observe deformation and rearrangement of the micelles, accompanied by a Newtonian-like rheology with slightly higher shear viscosity compared to homoparticle dispersions at the same concentration. As the shear rate is increased further, the micelles eventually break up into small dimers and free particles, causing a distinct shear-thinning of the dispersions. The network-like structures exhibit a similar flow behavior at high shear rates, but for weak shear we find an almost threefold increase of the shear viscosity and a distinct shear-thinning behavior due to the fracturing of the intertwined networks. In general, we identify a strong correlation between the size of the aggregates and the rheology of the dispersions, allowing for the determination of dynamic properties solely based on structural information.

Colloidal fibers and rings by cooperative assembly

Janus colloids with one attractive patch on an otherwise repulsive particle surface serve as model systems to explore structure formation of particles with chemically heterogeneous surfaces such as proteins. While there are numerous computer studies, there are few experimental realizations due to a lack of means to produce such colloids with a well-controlled variable Janus balance. Here, we report a simple scalable method to precisely vary the Janus balance over a wide range and selectively functionalize one patch with DNA. We observe, via experiment and simulation, the dynamic formation of diverse superstructures: colloidal micelles, chains, or bilayers, depending on the Janus balance. Flexible dimer chains form through cooperative polymerization while trimer chains form by a two-stage process, first by cooperative polymerization into disordered aggregates followed by condensation into more ordered stiff trimer chains. Introducing substrate binding through depletion catalyzes dimer chains to form nonequilibrium rings that otherwise do not form.

Molecular dynamics simulations of Janus nanoparticles in a fluid flow

We study the forces and torques on individual Janus nanoparticles in a fluid flow using molecular dynamics simulations. In particular, we consider amphiphilic Janus nanospheres that have different slip boundary conditions on each hemisphere, and calculate the forces and torques experienced by them as a function of their orientation with respect to the flow direction. Furthermore, we examine nanoparticles that are deformed slightly from a spherical shape, and have no-slip boundary conditions. We compare the simulation results to the predictions of previously introduced theoretical approaches, which compute the forces and torques on particles with variable slip lengths or aspherical deformations that are much smaller than the particle radius. We found that there is good qualitative agreement between the forces and torques computed from our simulations and the theoretical predictions, and the forces quantitatively agree when the assumptions made in the theoretical descriptions are satisfied.

Plastic Crystal-to-Crystal Transition of Janus Particles under Shear

Colloidal Janus spheres in the bulk typically spontaneously assemble into plastic crystalline phases, while particle orientations exhibit glasslike dynamics without long-range order. Through Brownian dynamics simulations, we demonstrate that shear can trigger a phase transition from an isotropic crystal with orientational disorder to an orientationally ordered crystal with lamellae along the shear direction. This nonequilibrium transition is accompanied with the orientational ordering following a nucleation and growth mechanism. By performing a phenomenological extension of free energy analysis, we reveal that the nucleation originates from the orientation fluctuations induced by shear. The growth of the orientationally crystalline cluster is examined to be disklike, captured by developing a lattice model with memoryless state functions. These findings bring new insights into the mechanisms for the ordering transition of anisotropic particles at nonequilibrium states.

Shear-Induced Alignment of Janus Particle Lamellar Structures

Control over the alignment of colloidal structures plays a crucial role in advanced reconfigurable materials. In this work, we study the alignment of Janus particle lamellar structures under shear flow via Brownian dynamics simulations. Lamellar alignment (orientation relative to flow direction) is measured as a function of the Péclet number (Pe)-the ratio of the viscous shear to the Brownian forces-the particle volume fraction, and the strength of the anisotropic interaction potential made dimensionless with thermal energy. Under conditions where lamellar structures are formed, three orientation regimes are observed: (1) random orientation for very small Pe, (2) parallel orientation-lamellae with their normals parallel to the direction of the velocity gradient-for intermediate values of Pe, and (3) perpendicular orientation-lamellae with their normals parallel to the vorticity direction-for large Pe. To understand the alignment mechanism, we carry out a scaling analysis of competing torques between a pair of particles in the lamellar structure. Our results suggest that the change of parallel to perpendicular orientation is independent of the particle volume fraction and is caused by the hydrodynamic and Brownian torques on the particles overcoming the torques resulting from the interparticle interactions. This initial study of shear-induced alignment on lamellar structures formed by Janus colloidal particles also opens the door for future applications where a reversible actuator for structure orientation is required.

Molecular Dynamics Simulation of Trimer Self-Assembly Under Shear

The self-assembly of patchy trimer particles consisting of one attractive site and two repulsive sites is investigated with nonequilibrium molecular dynamics simulations in the presence of a velocity gradient, as would be produced by the application of a shear stress on the system. As shear is increased, globular-shaped micellar clusters increase in size and become more elongated. The globular clusters are also more stable at higher temperatures in the presence of shear than at equilibrium. These results help to increase our understanding of the effect of shear on self-assembly for a variety of applications.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).

Self-assembly of colloidal micelles in microfluidic channels

The self-assembly of amphiphilic Janus colloids in microfluidic channels is studied using hybrid molecular dynamics simulations with fully resolved hydrodynamic interactions incorporated through the multi-particle collision dynamics algorithm. The simulations are conducted at a density and temperature where the Janus particles spontaneously self-assemble into spherical micelles to minimize the interface between the solvophobic caps and the surrounding solvent. In confined systems, this contact area can also be reduced by aggregation at the channel walls. Indeed, a sizable fraction of free particles and small clusters with three and four members are found at the walls when the microfluidic channel is made up of a comparably solvophobic material as the Janus colloids. When the applied Poiseuille flow is sufficiently strong, the colloidal micelles break up into smaller fragments and isolated particles. However, at intermediate flow rates the shear-induced dissociation and reorganization of aggregates lead to a net growth of the micelles with a sizable amount of particles in icosahedral clusters with 13 particles. Furthermore, the parabolic velocity profile of the flow causes a highly non-uniform cluster size distribution between the channel walls, where the aggregation number decreases close to the walls.

Numerical study of cluster formation in binary charged colloids

Cluster formation of oppositely charged colloidal particles is studied numerically. A simple Brownian dynamics method with a screened-Coulomb (Yukawa) potential is employed for numerical simulations. An equilibrium phase which consists of clusters and unassociated particles is obtained. It is shown that the equilibrium association number of clusters and their shapes are determined by charge numbers and charge ratio of the binary particles. The phase diagram of cluster formation for various charge numbers and their ratios is obtained. A simple relation between the association number and the charge ratio is found. It is demonstrated that in the case of high charge ratio the cluster takes a multilayer structure which is highly symmetric. It is also pointed out that the cluster-particle interaction changes dynamically in the cluster formation process, which is involved in the selection of final cluster structure.

Shearing Janus Nanoparticles Confined in Two-Dimensional Space: Reshaped Cluster Configurations and Defined Assembling Kinetics

The self-assembly of anisotropic nanoparticles (ANPs) possesses a wide array of potential applications in various fields, ranging from nanotechnology to material science. Despite intense research of the thermodynamic self-assembly of ANPs, elucidating their nonequilibrium behaviors under confinement still remains an urgent issue. Here, by performing simulation and theoretical justification, we present for the first time a study of the shear-induced behaviors of Janus spheres (the most elementary ANPs) confined in two-dimensional space. Our results demonstrate that the collective effects of shear and bonding structures can give rise to reshaped cluster configurations, featured by the chiral transition of clusters. Scaling analysis and numerical modeling are performed to quantitatively capture the assembling kinetics of dispersed Janus spheres, thereby suggesting an exotic way to bridge the gap between anisotropic and isotropic particles. The findings highlight confinement and shearing engineering as a versatile strategy to tailor the superstructures formed by ANPs toward unique properties.

Rich Janus colloid phase behavior under steady shear

We study the assembly of single-patch colloidal Janus particles under steady shear flow via Brownian dynamics simulations. In the absence of flow, by varying the Janus patch size and the range and strength of the anisotropic interaction potential, Janus colloids form different aggregates such as micelles, wormlike clusters, vesicles and lamellae. Under shear flow we observe rearrangement, deformation, and break-up of aggregates. At small and intermediate Péclet (Pe) numbers-the ratio between shear and Brownian forces-the competition between rearrangement, deformation, and break-up favors the growth of micelles and vesicles increasing mean cluster size, which is consistent with a previous numerical study of Janus particles under shear. This initial shear-induced growth causes micelles and vesicles to reach a maximum cluster size at Pe ≈ 1 and Pe ≈ 10, respectively. After this growth micelles dissociate continuously to reach a dilute colloidal "gas phase" at Pe ≈ 10 while vesicles dissociate into micelles with high aspect ratio at Pe ≈ 10 and finally break-up into a gas phase at Pe ≈ 30. Wormlike clusters initially break-up into micelles with high aspect ratio at Pe ≈ 0.1, and proceed to finally reach a gas phase at Pe ≈ 10. Lamellae initially break into smaller lamellae that align with the flow in the velocity-velocity-gradient plane and finally break-up into a gas phase at Pe ≈ 100. The different cluster sizes and morphologies observed as functions of interaction range, Janus patch size, interaction strength, and shear rate, open new actuation routes for reconfigurable materials and applications.

Self-assembly of Janus nanoparticles with a hydrophobic hemisphere in nanotubes

We performed molecular simulations to investigate the morphologies and phase diagrams of self-assembled diblock Janus nanoparticles (JNPs) confined in nanotubes. A JNP is a unique anisotropic nanoparticle, which typically has more than two distinct surfaces, each with different properties. We derived qualitative phase diagrams of axial pressure versus the ratio of the diameter of the nanoparticle and the nanotube. Three distinct types of nanotube walls were considered: hydrophobic, hydrophilic, and hydroneutral. We observed diverse morphologies in JNP solutions, many of which have not been observed in bulk solutions. We also compared the self-assembled structures of diblock and triblock patchy particles. Under weak confinement, significant differences were observed between the different JNP designs. The orientation ordering and self-assembly behaviours of the JNPs can be qualitatively predicted based on the chemical nature of the nanotube wall and the JNP design.

Exploration of selective decoration of Janus silica particles within polymeric patterned pore arrays

Amphiphilic Janus particles were put into use as stabilizer in assisting the “breath figure” patterning process, demonstrating stronger interfacial activity comparing to the isotropic particles.