Phase transformations in binary colloidal monolayers

Internal-stress-induced solid-solid transition involving orientational domains of anisotropic particles

Colloidal particles with anisotropic interaction, such as Janus particles, are important model systems for anisotropic atoms and molecules. Janus particles in a single crystal can rotate collectively and form polycrystalline orientational domains as the temperature increases, while the lattice structure in the translational degree of freedom is preserved. Such an unusual solid-solid transition preserves the long-range translational order but loses the orientational order, and its mechanism is unclear. We find that the transition is induced by internal strains and the orientation-position coupling plays an essential role in the transition. We explain the mechanism using the anisotropic elasticity theory and derive the transition condition and the directions of the domain boundaries by analyzing the strain energy and the stress. The results of the molecular dynamics simulation are consistent with the theoretical analysis. Such a transition mechanism can exist in other anisotropic particle systems.

Shape- and Material-Dependent Self-Propulsion of Photocatalytic Active Colloids, Interfacial Effects, and Dynamic Interparticle Interactions

Active colloids powered by self-generated, local chemical concentration gradients exhibit dynamics that are a function of the particles' morphology and material properties. These characteristics also govern how the active colloids interact with surfaces, including other particles and nearby walls. Thus, by targeted design, the dynamic behavior, on average, can be engineered, despite a lack of "external" control such as an applied magnetic field. This allows for the development of new applications and the investigation of novel effects that arise when self-propelled active colloids have complex shapes and material composition. Here, we explore some of our recent work on this topic including the dynamics and interactions of photoactivated, self-propelled colloids with such multifaceted properties. We also delve into some special cases, such as a new variety of active particle-particle interaction that we recently developed, in which direct contact between the active colloids is forbidden, and the direction of propulsion for pairs of particles is correlated. The unifying theme of the work highlighted herein is the relationship between the physical, chemical, and material properties of active colloids and their motive behavior, the understanding of which opens up a wide range of new possibilities as we move toward the ultimate goal of realizing functional, man-made micro- and nanomachinery.

Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites

Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.

Melting and solid-solid transitions of two-dimensional crystals composed of Janus spheres

Colloidal model systems have been extensively used in the studies of various phase transitions, but melting and solid-solid transitions have rarely been explored in monolayer colloidal crystals with anisotropic attractions. Patchy colloidal particles have served as important model systems of atoms and molecules with anisotropic interactions. In this work, we study the melting and solid-solid transitions of two-dimensional crystals composed of Janus colloidal spheres using Langevin dynamics simulation. We discovered a first-order solid-solid transition from a single crystal with uniform stripes to a novel crystal with polycrystalline domains of stripes. The centers of masses of the particles maintain the morphology of a single crystal with long-range translational and bond-orientational orders, but particle orientations form polycrystalline domains of stripes. The stripe domains form by a strain-induced nucleation process via the collective rotation of particles. In addition to this solid-solid transition, the melting transition at a higher temperature follows a two-step Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario, similar to most isotropic particle systems.

Tunable interactions between particles in conically rotating electric fields

Tunable interactions between colloidal particles in external conically rotating electric fields are calculated, while the (vertical) axis of the field rotation is normal to the (horizontal) particle motion plane. The comparison of different approaches, including the methods of noninteracting, self-consistent dipoles, and the boundary element method, indicates that the last method is the most suitable for tunable interaction analysis. Thorough analysis, performed for interactions in pairs and clusters of colloidal particles, indicate that two- and three-body interactions make the main contributions in the interaction energy, while the effect of high-order terms is negligible. The tunable interactions are determined by the dielectric properties of the particles and solvent and can be changed in a wide range, providing a rich variety for the experimental "design" of different interactions, including repulsion, attraction, combination of short-range repulsion with long-range attraction, barrier-type interactions with short-range attraction and long-range repulsion, and double-scale repulsive (core-shoulder) interactions. These conclusions can be generalized for magnetically induced tunable interactions. The results indicate that tunable interactions can be widely applied in self-assembly and particle-resolved studies of generic phenomena in fluids and crystals, and, therefore, are of broad interest in the fields of chemical physics, physical chemistry, materials science, and soft matter.

Binary colloidal crystals (BCCs): Interactions, fabrication, and applications

The organization of matter into hierarchical structures is a fundamental characteristic of functional materials and living organisms. Binary colloidal crystal (BCC) systems present a diversified range of nanotopographic structures where large and small colloidal particles simultaneously self-assemble into either 2D monolayer or 3D hierarchical crystal lattices. More importantly, understanding how BCCs form opens up the possibility to fabricate more complex systems such as ternary or quaternary colloidal crystals. Monolayer BCCs can also offer the possibility to achieve surface micro- and nano-topographies with heterogeneous chemistries, which can be challenging to achieve with other traditional fabrication tools. A number of fabrication methods have been reported that enable generation of BCC structures offering high accuracy in growth with controllable stoichiometries; however, it is still a challenge to make uniform BCC structures over large surface areas. Therefore, fully understand the mechanism of binary colloidal self-assembly is crucial and new/combinational methods are needed. In this review, we summarize the recent advances in BCC fabrication using particles made of different materials, shapes, and dispersion medium. Depending on the potential application, the degree of order and efficiency of crystal formation has to be determined in order to induce variability in the intended lattice structures. The mechanisms involved in the formation of highly ordered lattice structures from binary colloidal suspensions and applications are discussed. The generation of BCCs can be controlled by manipulation of their extensive phase behavior, which facilitates a wide range potential applications in the fields of both material and biointerfacial sciences including photonics, biosensors, chromatography, antifouling surfaces, biomedical devices, and cell culture tools.

Tunable hydrodynamics: a field-frequency phase diagram of a non-equilibrium order-to-disorder transition

We present experiments on a model system consisting of dielectric (silicone oil) drops in a "leaky dielectric" (castor oil) carrier fluid that exhibits dynamic non-equilibrium phases as a function of the amplitude and frequency of an external AC electric field. At high frequencies, the dielectric drops are pinned to a periodic lattice by dielectrophoretic forces induced by a patterned bottom electrode. Beginning with this state of imposed order, we examine the processes that take this system from order to disorder, with decreasing frequency corresponding to an increase in the range of the hydrodynamic forces. We find two kinds of disorder, shape- and translational disorder, that occur in frequency-amplitude space. We also find regimes where drop breakup is dominant, and where order/disorder of large drops can be probed without significant drop breakup. With decreasing frequency (i.e., increasing hydrodynamic coupling between drops) and on timescales from seconds to minutes, the drops exhibit motion that resembles Brownian motion of particles in a crystal, with an effective temperature that increases with the strength of the electrohydrodynamic driving force. In this limit, the system behaves like a thermal system and the lattice is seen to melt at an effective Lindemann parameter of L_eff ∼ 0.08. This non-equilibrium thermodynamics, probed on timescales from seconds to minutes, likely arises from the pseudo-random velocity fields in the carrier fluid, as evidenced by the fractional, t^3/2, super-diffusive tracer dynamics at shorter timescales.

Contrasting the dynamics of elastic and non-elastic deformations across an experimental colloidal Martensitic transition

We present a framework to segregate the roles of elastic and non-elastic deformations in the examination of real-space experiments of solid-solid Martensitic transitions. The Martensitic transformation of a body-centred-tetragonal (BCT) to a body-centred-orthorhombic (BCO) crystal structure has been studied in a model system of micron-scale ionic microgel colloids (P. S. Mohanty, P. Bagheri, S. Nöjd, A. Yethiraj and P. Schurtenberger, Phys. Rev. X, 2015, 5, 011030). Non-affine fluctuations, i.e., displacement fluctuations that do not arise from purely elastic (affine) deformations, are detected in particle configurations acquired from the experiment. Tracking these fluctuations serves as a highly sensitive tool in signaling the onset of the Martensitic transition and precisely locating particle rearrangements occurring at length scales of a few particle diameters. Particle rearrangements associated with non-affine displacement modes become increasingly favorable during the transformation process. The nature of the displacement fluctuation modes that govern the transformation are shown to be different from those predominant in an equilibrium crystal. We show that BCO crystallites formed through shear may, remarkably, co-exist with those resulting from local rearrangements within the same sample.

Diffusive and martensitic nucleation kinetics in solid-solid transitions of colloidal crystals

Solid–solid transitions between crystals follow diffusive nucleation, or various diffusionless transitions, but these kinetics are difficult to predict and observe. Here we observed the rich kinetics of transitions from square lattices to triangular lattices in tunable colloidal thin films with single-particle dynamics by video microscopy. Applying a small pressure gradient in defect-free regions or near dislocations markedly transform the diffusive nucleation with an intermediate-stage liquid into a martensitic generation and oscillation of dislocation pairs followed by a diffusive nucleus growth. This transformation is neither purely diffusive nor purely martensitic as conventionally assumed but a combination thereof, and thus presents new challenges to both theory and the empirical criterion of martensitic transformations. We studied how pressure, density, grain boundary, triple junction and interface coherency affect the nucleus growth, shape and kinetic pathways. These novel microscopic kinetics cast new light on control solid–solid transitions and microstructural evolutions in polycrystals.

Solid-solid transitions between different crystalline structures have broad implications in earth science, steel and ceramic materials. Peng et al. show a transformation pathway that starts off as being martensitic then switches to diffusive at the single particle level in a colloidal system under pressure.

Assembly of hard spheres in a cylinder: a computational and experimental study

Hard spheres are an important benchmark of our understanding of natural and synthetic systems. In this work, colloidal experiments and Monte Carlo simulations examine the equilibrium and out-of-equilibrium assembly of hard spheres of diameter σ within cylinders of diameter σ≤D≤ 2.82σ. Although phase transitions formally do not exist in such systems, marked structural crossovers can nonetheless be observed. Over this range of D, we find in simulations that structural crossovers echo the structural changes in the sequence of densest packings. We also observe that the out-of-equilibrium self-assembly depends on the compression rate. Slow compression approximates equilibrium results, while fast compression can skip intermediate structures. Crossovers for which no continuous line-slip exists are found to be dynamically unfavorable, which is the main source of this difference. Results from colloidal sedimentation experiments at low diffusion rate are found to be consistent with the results of fast compressions, as long as appropriate boundary conditions are used.

Phase diagram and aggregation dynamics of a monolayer of paramagnetic colloids

We have developed a tunable colloidal system and a corresponding theoretical model for studying the phase behavior of particles assembling under the influence of long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and a rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle θ of the rotating magnetic field. For a purely in-plane field, θ=90^{∘}, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles 50^{∘}≲θ≲55^{∘}, the two-body interaction gives a short-range attractive and long-range repulsive interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We further characterize the anomalous regime by measuring the time-dependent cluster size distribution.

Crystallization kinetics of binary colloidal monolayers

Experiments and simulations are used to study the kinetics of crystal growth in a mixture of magnetic and nonmagnetic particles suspended in ferrofluid. The growth process is quantified using both a bond order parameter and a mean domain size parameter. The largest single crystals obtained in experiments consist of approximately 1000 particles and form if the area fraction is held between 65-70% and the field strength is kept in the range of 8.5-10.5 Oe. Simulations indicate that much larger single crystals containing as many as 5000 particles can be obtained under impurity-free conditions within a few hours. If our simulations are modified to include impurity concentrations as small as 1-2%, then the results agree quantitatively with the experiments. These findings provide an important step toward developing strategies for growing single crystals that are large enough to enable follow-on investigations across many subdisciplines in condensed matter physics.

Interpolation method for pair correlations in classical crystals

Effects of anharmonicity on the pair correlation function of classical crystals are studied. The recently proposed shortest-graph approach using the Gaussian representation of the individual correlation peaks (the peak width is determined by the length of the shortest graph connecting a given pair of particles) is further improved, to account for anharmonic corrections due to finite temperatures and hard-sphere-like interactions. Two major effects are identified, leading to a modification of the correlation peaks at large or short distances: (i) the peaks at large distances, well described by Gaussians, should be calculated from the finite-temperature phonon spectra; (ii) at short distances, the correlation peaks deviate significantly from the Gaussian form due to the lattice discreteness. We propose the analytical interpolation method, based on the shortest-graph approach, which includes both effects. By employing the molecular dynamics simulations, the accuracy of the method is verified for three- and two-dimensional crystals with the Yukawa, inverse-power-law, and pseudo-hard-sphere pair interactions. The capabilities of the method are demonstrated by calculating the phase diagram of a three-dimensional Yukawa system.

Nonclassical Nucleation in a Solid-Solid Transition of Confined Hard Spheres

A solid-solid phase transition of colloidal hard spheres confined between two planar hard walls is studied using a combination of molecular dynamics and Monte Carlo simulation. The transition from a solid consisting of five crystalline layers with square symmetry (5□) to a solid consisting of four layers with triangular symmetry (4△) is shown to occur through a nonclassical nucleation mechanism that involves the initial formation of a precritical liquid cluster, within which the cluster of the stable 4△ phase grows. Free-energy calculations show that the transition occurs in one step, crossing a single free-energy barrier, and that the critical nucleus consists of a small 4△ solid cluster wetted by a metastable liquid. In addition, the liquid cluster and the solid cluster are shown to grow at the planar hard walls. We also find that the critical nucleus size increases with supersaturation, which is at odds with classical nucleation theory. The △-solid-like cluster is shown to contain both face-centered-cubic and hexagonal-close-packed ordered particles.