Self-assembly in binary mixtures of dipolar colloids: Molecular dynamics simulations

Spatially Confined Assembly and Immobilization of Hierarchical Nanoparticle Architectures inside Microdroplets in Magnetic Fields

Magnetic field-directed colloidal interactions offer facile tools for assembly of structures that range from linear chains to multidimensional hierarchical architectures. While the field-driven assembly of colloidal particles has commonly been investigated in unbounded media, a knowledge gap remains concerning such assembly in confined microenvironments. Here, we investigate how confinement of ferromagnetic nanoparticles in microspheres directs their magnetic assembly into hierarchical architectures. Microdroplets from polydimethylsiloxane (PDMS) liquid precursor containing dispersed iron oxide magnetic nanoparticles (MNPs) were placed in a static magnetic field leading to the formation of organized assemblies inside the host droplets. By changing the MNP concentrations, we revealed a sequence of microstructures inside the droplets, ranging from linear chains at a low MNP loading, transitioning to a combination of chains and networked bundles, to solely 3D bundles at high MNP loading. These experimental results were analyzed with the aid of COMSOL simulations where we calculated the potential energy to identify the preferred assembly conformations. The chains at high MNP loading minimized their energy by aggregating laterally to form bundles with their MNP dipoles being out-of-registry. We cured these PDMS droplets to immobilize the assemblies by forming soft microbeads. These microbeads constitute an "interaction toolbox" with different magnetic macroscale responses, which are governed by the structuring of the MNPs and their magnetic polarizability. We show that thanks to their ability to rotate by field-induced torque under a rotating field, these microbeads can be employed in applications such as optical modulators and microrollers.

Porous Self-Assemblies Mediated by Dumbbell Particles as Cross-Linking Agents

Self-assembly of colloidal particles is emerging as a promising approach for producing novel materials. These colloidal particles can be synthesized with protrusions (lobes) on their surfaces that allow the formation of porous structures with a wide range of applications. Using Langevin dynamics simulations, we studied self-assembly in the binary mixtures of lobed colloidal particles with variations in their lobe sizes to investigate the feasibility of using dumbbell particles (with two lobes) as cross-linkers to increase the porosity in self-assembled morphologies. Each binary system was formed by mixing the dumbbell particles with one of the following types of particles: trigonal planar (three lobes), tetrahedral (four lobes), trigonal bipyramidal (five lobes), and octahedral (six lobes). We observed that the lobe size on each particle can be tuned to favor the formation of random aggregates and spherical aggregates when the lobes are larger and well-ordered crystalline structures when the lobes are smaller. We also observed that these polydisperse systems form self-assembled structures characterized by porosities higher than those of the structures formed by the monodisperse systems. These results indicate that the lobe size is an important design feature that can be optimized to achieve desired structures with distinct morphologies and porosities, and the dumbbell particles are effective cross-linking agents to enhance the porosity in self-assembled structures.

Bottom-Up Construction of the Interaction between Janus Particles

While the interaction between two uniformly charged spheres─viz colloids─is well-known, the interaction between nonuniformly charged spheres such as Janus particles is not. Specifically, the Derjaguin approximation relates the potential energy between two spherical particles with the interaction energy Vpl per unit area between two planar surfaces. The formalism has been extended to obtain a quadrature expression for the screened electrostatic interaction between Janus colloids with variable relative orientations. The interaction is decomposed into three zones in the parametric space, distinguished by their azimuthal symmetry. Different specific situations are examined to estimate the contributions of these zones to the total energy. The effective potential Vpl is renormalized such that the resulting potential energy is identical with the actual one for the most preferable relative orientations between the Janus particles. The potential energy as a function of the separation distance and the mutual orientation of a pair of particles compares favorably between the analytical (but approximate) form and the rigorous point-wise computational model used earlier. Coarse-grained models of Janus particles can thus implement this potential model efficiently without loss of generality.

Non-equilibrium relaxation and aging in the dynamics of a dipolar fluid quenched towards the glass transition

The recently developed non-equilibrium self-consistent generalized Langevin equation theory of the dynamics of liquids of non-spherically interacting particles [2016J. Phys. Chem. B1207975] is applied to the description of the irreversible relaxation of a thermally and mechanically quenched dipolar fluid. Specifically, we consider a dipolar hard-sphere liquid quenched (att_w= 0) from full equilibrium conditions towards different ergodic-non-ergodic transitions. Qualitatively different scenarios are predicted by the theory for the time evolution of the system after the quench (t_w> 0), that depend on both the kind of transition approached and the specific features of the protocol of preparation. Each of these scenarios is characterized by the kinetics displayed by a set of structural correlations, and also by the development of two characteristic times describing the relaxation of the translational and rotational dynamics, allowing us to highlight the crossover from equilibration to aging in the system and leading to the prediction of different underlying mechanisms and relaxation laws for the dynamics at each of the glass transitions explored.

Field-Driven Reversible Alignment and Gelation of Magneto-Responsive Soft Anisotropic Microbeads

Magnetic fields offer untethered control over the assembly, dynamics, and reconfiguration of colloidal particles. However, synthesizing "soft" colloidal particles with switchable magnetic dipole moment remains a challenge, primarily due to strong coupling of the dipoles of the adjacent nanoparticles. In this article, we present a way to overcome this fundamental challenge based on a strategy to synthesize soft microbeads with tunable residual dipole moment. The microbeads are composed of a polydimethylsiloxane (PDMS) matrix with internally embedded magnetic nanoparticles (MNPs). The distribution and orientation of the MNPs within the PDMS bead matrix is controlled by an external magnetic field during the synthesis process, thus allowing for the preparation of anisotropic PDMS microbeads with internal magnetically aligned nanoparticle chains. We study and present the differences in magnetic interactions between microbeads containing magnetically aligned MNPs and microbeads with randomly distributed MNPs. The interparticle interactions in a suspension of microbeads with embedded aligned MNP chains result in the spontaneous formation of percolated networks due to residual magnetization. We proved the tunability of the structure by applying magnetization, demagnetization, and remagnetization cycles that evoke formation, breakup, and reformation of 2D percolated networks. The mechanical response of the microbead suspension was quantified by oscillatory rheology and correlated to the propensity for network formation by the magnetic microbeads. We also experimentally correlated the 2D alignment of the microbeads to the direction of earth's magnetic field. Overall, the results prove that the soft magnetic microbeads enable a rich variety of structures and can serve as an experimental toolbox for modeling interactions in dipolar systems leading to various percolated networks, novel magneto-rheological materials, and smart gels.

Enhanced Porosity in Self-Assembled Morphologies Mediated by Charged Lobes on Patchy Particles

Colloidal patchy particles are particles with anisotropic "patches" decorating their surfaces. Several properties of these patches including their size, number, location, and interactions provide control over self-assembly of patchy particles into structures with desired properties. We report on simulation studies of particles where patches take the form of lobes. Based on the number and locations of lobes, these particles have different shapes (trigonal planar, square planar, tetrahedral, trigonal bipyramidal, and octahedral). We investigated the effect of incorporating charges on the lobes in achieving porous self-assembled morphologies across a range of temperatures. We observed that an increase in the charge on the lobe resulted in lobed particles assembling over a wider range of temperatures. We also observed that the lobed particles with charges self-assembled into structures with enhanced porosity in comparison to lobed particles without charges.

Spherical harmonic projections of the static structure factor of the dipolar hard sphere model: Theory vs simulations

We investigate the static correlations of a dipolar fluid in terms of the irreducible coefficients of the spherical harmonic expansion of the static structure factor. To this end, we develop a theoretical framework based on a soft-core version of Wertheim's solution of the mean spherical approximation (MSA), which renders the analytical determination of such coefficients possible. The accuracy of this approximation is tested by a comparison against the results obtained with the assistance of extensive molecular dynamics simulations at different regimes of concentration and temperature. Crucial aspects for the comparison of the results provided by the two methods are carefully discussed, concerning the different reference frames used in theory and simulations to describe rotations and orientations, and leading to important differences in the behavior of correlation functions with the same combination of spherical harmonic indices. We find a remarkable agreement between the two approaches in the fluid regime, thus providing a first stringent comparison of the irreducible coefficients of the spherical harmonic expansion of the dipolar fluid's static structure factor, provided by the MSA theory and molecular dynamics simulations.

Self-assembly of Pseudo-Dipolar Nanoparticles at Low Densities and Strong Coupling

Nanocolloids having directional interactions are highly relevant for designing new self-assembled materials easy to control. In this article we report stochastic dynamics simulations of finite-size pseudo-dipolar colloids immersed in an implicit dielectric solvent using a realistic continuous description of the quasi-hard Coulombic interaction. We investigate structural and dynamical properties near the low-temperature and highly-diluted limits. This system self-assembles in a rich variety of string-like configurations, depicting three clearly distinguishable regimes with decreasing temperature: fluid, composed by isolated colloids; string-fluid, a gas of short string-like clusters; and string-gel, a percolated network. By structural characterization using radial distribution functions and cluster properties, we calculate the state diagram, verifying the presence of string-fluid regime. Regarding the string-gel regime, we show that the antiparallel alignment of the network chains arises as a novel self-assembly mechanism when the characteristic interaction energy exceeds the thermal energy in two orders of magnitude, u_d/k_BT ≈ 100. This is associated to relevant structural modifications in the network connectivity and porosity. Furthermore, our results give insights about the dynamically-arrested nature of the string-gel regime, where we show that the slow relaxation takes place in minuscule energy steps that reflect local rearrangements of the network.

Arrested dynamics of the dipolar hard sphere model

We report the combined results of molecular dynamics simulations and theoretical calculations concerning various dynamical arrest transitions in a model system representing a dipolar fluid, namely, N (soft core) rigid spheres interacting through a truncated dipole-dipole potential. By exploring different regimes of concentration and temperature, we find three distinct scenarios for the slowing down of the dynamics of the translational and orientational degrees of freedom: at low (η = 0.2) and intermediate (η = 0.4) volume fractions, both dynamics are strongly coupled and become simultaneously arrested upon cooling. At high concentrations (η≥ 0.6), the translational dynamics shows the features of an ordinary glass transition, either by compressing or cooling down the system, but with the orientations remaining ergodic, thus indicating the existence of partially arrested states. In this density regime, but at lower temperatures, the relaxation of the orientational dynamics also freezes. The physical scenario provided by the simulations is discussed and compared against results obtained with the self-consistent generalized Langevin equation theory, and both provide a consistent description of the dynamical arrest transitions in the system. Our results are summarized in an arrested states diagram which qualitatively organizes the simulation data and provides a generic picture of the glass transitions of a dipolar fluid.

Speeding up the study of diluted dipolar systems

We study the regimes of a diluted dipolar system through Monte Carlo numerical simulations in the NVT ensemble. To accelerate the dynamics, several approximations and speed-up algorithms are proposed and tested. In particular, it turns out that "cluster move Monte Carlo" algorithm speeds-up to two decades faster than the traditional Monte Carlo, depending on temperature and density. We find simple-fluid, chain-fluid, ring-fluid, gel, and antiparallel columnar regimes, which are studied and characterized through positional, orientational, and thermodynamical observables.

Key characteristics and modelling of bigels systems: A review

Bigels are interesting semisolid formulations with better properties for different applications such as cosmetics and pharmaceutical systems. Due to the mixing of two phases of different nature (polar and apolar), bigels possess some interesting features like ability to deliver hydrophilic and hydrophobic drugs, better spreadability and water washability, improved permeability of drugs, enhanced hydration of stratum corneum and ability to manipulate the drug release rate. The main objective of this review article is to provide a thorough insight into the important characteristics of bigels together with the discussion on modelling of bigel systems to relate their properties with individual constituents and different parameters. Moreover, some important applications of bigels are also discussed by considering some examples from the literature.

In-situ Observation of Hierarchical Self-Assembly Driven by Bicontinuous Gelation in Mixed Nanodisc Dispersions

The search for new functional soft materials with precise and reconfigurable structures at the nano and meso-scale is a major challenge as well as objective of the current science. Patchy colloids of different shapes and functionalities are considered important new building blocks of a bottom-up approach towards rational design of new soft materials largely governed by anisotropic interactions. Herein, we investigate the self-assembly, growth of hierarchical microstructures and aging dynamics of 2D nano-platelets of two different aspect ratios (Laponite ~25 and Montmorillonite ~250) which form gels with different porosity that is achieved by tuning their mixing ratios. Qualitative in situ real-space studies are carried out, including fluorescent confocal microscopy imaging of the bicontinuous gelation process or final states, which provides dynamic visualization of the self-organization. The bicontinuous gels exhibit a foam-like morphology having pores of a few micrometers in size that can be tuned by varying the mixing ratio of nanoplatelets. It is shown that this new class of clay gels has unique and tunable physical properties that will find potential applications in the development of low cost lithium ion batteries, nanocomposites and nuclear waste management.

Phase behavior of a binary fluid mixture of quadrupolar molecules

We propose a model molecule to investigate microscopic properties of a binary mixture with a closed-loop coexistence region. The molecule is comprised of a Lennard-Jones particle and a uniaxial quadrupole. Gibbs ensemble Monte Carlo simulations demonstrate that the high-density binary fluid of the molecules with the quadrupoles of the same magnitude but of the opposite signs can show closed-loop immiscibility. We find that an increase in the magnitude of the quadrupoles causes a shrinkage of the coexistence region. Molecular dynamics simulations also reveal that aggregates with two types of molecules arranged alternatively are formed in the stable one-phase region both above and below the coexistence region. String structures are dominant below the lower critical solution temperature, while branched aggregates are observed above the upper critical solution temperature. We conclude that the anisotropic interaction between the quadrupoles of the opposite signs plays a crucial role in controlling these properties of the phase behavior.

Changing the magnetic properties of microstructure by directing the self-assembly of superparamagnetic nanoparticles

Magnetic nanoparticles (MNPs) in a liquid dispersion can be organized through controlled self-assembly by applying an external magnetic field that regulates inter-particle interactions. Thus, micro- and nanostructures of desired morphology and superlattice geometry that show emergent magnetic properties can be fabricated. We describe how superferromagnetism, which is a specific type of emergence, can be produced. Here, superparamagnetic nanoparticles that show no individual residual magnetization are organized into structures with substantial residual magnetization that behave as miniature permanent magnets. We investigate the emergence of superferromagnetism in an idealized system consisting of two MNPs, by considering the influence that interparticle magnetostatic interactions have on the dynamics of the magnetic moments. We use this model to illustrate the design principles for self-assembly in terms of the choice of material and MNP particle size. We simulate the dynamics of the interacting magnetic moments by applying the stochastic Landau-Lifshitz-Gilbert equation to verify our principles. The findings enable a method to pattern material magnetization with submicron resolution, a useful feature that has potential applications for magnetic recording and microfluidic particle traps. The analysis also yields useful empirical generalizations that could facilitate other theoretical developments.

Bigels formed via spinodal decomposition of unfolded protein

Bigels (or double network gels) are an emerging class of tuneable soft materials characterized by two discrete but interpenetrating gel networks in which both networks contribute to the physical and mechanical properties of the material. We describe, for the first time, the formation of a bigel network from two different proteins. By careful control of solution conditions, kinetics and specific protein chemistry the inter-species interactions in the two protein system are weak compared with the intra-protein attraction, which leads to bigel formation. The resulting protein bigel has an elastic modulus four times greater than the combined elastic moduli of the parent gels, has an elastic response over several deformation cycles and is both thermo- and chemo-responsive. These gels have the potential to be used as biomimetics in tissue culture, in drug delivery or for biomedical applications such as wound healing.

Tunable assembly of colloidal crystal alloys using magnetic nanoparticle fluids

We demonstrate a magnetic technique for assembling bidisperse and tridisperse colloidal particle fluids into a variety of complex structures with dimensionality ranging from 0-D (rings) to 1-D (chains) to 2-D (tiles). Compared with prior work on bidisperse particles that are commensurate in size, here we explore the assembly of different sized particles, and we show that due to packing constraints, new particle structures can be realized experimentally. Extending these experiments to a tridisperse system, we demonstrate that at low concentrations the smallest particle does not change the underlying crystal structures of the bidisperse system; however, it can assist in the formation of crystallite structures that were not stable in a bidisperse system. Additionally, we discovered that the smallest particle mimics the role of the ferrofluid, by shifting the locations in phase space where the bidisperse crystal structures can be experimentally obtained. Finally, we demonstrate that 3-particle crystal structures can be tuned by varying the strength of the external field, which is not possible in a 2-particle system.