Colloidal Model System Research Articles

Coupled dynamics in binary mixtures of model colloidal Yukawa systems.

The dynamical behavior of binary mixtures consisting of highly charged colloidal particles is studied by means of Brownian dynamics simulations. We investigate differently sized, but identically charged particles with nearly identical interactions between all species in highly dilute suspensions. Different short-time self-diffusion coefficients induce, mediated by electrostatic interactions, a coupling of both self and collective dynamics of differently sized particles: the long-time self-diffusion coefficients of a larger species are increased by the presence of a more mobile, smaller species and vice versa. Similar coupling effects are observed in collective dynamics where both time constant and functional form of intermediate scattering functions' initial decay are influenced by the presence of a differently sized species. We provide a systematic analysis of coupling effects in dependence on the ratio of sizes, number densities, and the strength of electrostatic interactions.

Simulating Crystallization in a Colloidal System Using State Predictive Information Bottleneck Based Enhanced Sampling.

We investigate crystal nucleation in supersaturated colloid suspensions using enhanced molecular dynamics simulations augmented with machine learning techniques. The simulations reveal that crystallization in the model colloidal system studied here, with particles interacting through a repulsive screened Coulomb Yukawa potential, proceeds from vapor to dense liquid droplet to crystalline phases across multiple high barriers. Employing a one-dimensional reaction coordinate derived from the State Predictive Information Bottleneck framework, our simulations capture back-and-forth phase transitions across multiple barriers effectively in biased metadynamics simulations. We obtain relative free energy differences between different phases and also quantify the roles of different molecular level features in driving the phase changes.

Memory effects in colloidal motion under confinement and driving

The transport of individual particles in inhomogeneous environments is complex and exhibits non-Markovian responses. The latter may be quantified by a memory function within the framework of the linear generalised Langevin equation (GLE). Here, we exemplify the implications of steady driving on the memory function of a colloidal model system for Brownian motion in a corrugated potential landscape, specifically, for one-dimensional motion in a sinusoidal potential. To this end, we consider the overdamped limit of the GLE, which is facilitated by separating the memory function into a singular (Markovian) and a regular (non-Markovian) part. Relying on exact solutions for the investigated model, we show that the random force entering the GLE must display a bias far from equilibrium, which corroborates a recent general prediction. Based on data for the mean-square displacement (MSD) obtained from Brownian dynamics simulations, we estimate the memory function for different driving strengths and show that already moderate driving accelerates the decay of the memory function by several orders of magnitude in time. We find that the memory may persist on much longer timescales than expected from the convergence of the MSD to its long-time asymptote. Furthermore, the functional form of the memory function changes from a monotonic decay to a non-monotonic, damped oscillatory behaviour, which can be understood from a competition of confined motion and depinning. Our analysis of the simulation data further reveals a pronounced non-Gaussianity, which questions the Gaussian approximation of the random force entering the GLE.

Exploring Colloidal Phase Transitions of Imogolite Nanotubes by Evaporation Induced Self‐Assembly in Levitation

AbstractEvaporation‐induced self‐assembly (EISA) is a versatile method for generating organized superstructures from colloidal particles, offering diverse design possibilities through the manipulation of colloid size, shape, substrate nature, and environmental conditions. While some work highlighted the potential of EISA to investigate phase transitions of inorganic liquid crystals, the influence of sample environment to determine their phase diagrams is often overlooked. In this work, the self‐assembly of lyotropic liquid crystals is compared by EISA on substrates, and by acoustic levitation (absence of substrate). The focus is on imogolite nanotubes, a model colloidal system of 1D charged objects, due to their tunable morphology and rich liquid‐crystalline phase behavior. It demonstrates the feasibility to obtain phase transitions in levitating droplets and on soft hydrophobic substrates, whereas self‐assembly is limited on rigid hydrophilic supports. Moreover, the aspect ratio of the nanotubes proves to be a pivotal factor, influencing both transitions and the resulting materials shape and surface. Besides material shaping, acoustic levitation emerges as a promising method for studying phase transitions by EISA, toward the rapid establishment of phase diagrams from diluted to highly concentrated states using a limited volume of sample.

Novel Microscopic Approach to Particle Size Evaluation in Colloidal Systems

Colloidal systems are peculiar mixtures formed by the uniform dispersion of sub-micro sized particles of one substance through another substance. In this framework, a particular colloidal system, known as sol, is a colloid in which the dispersed particles are solid, and the dispersing medium is fluid. Sols have extensive applications in industries ranging from material science to food to pharmaceuticals and cosmetics. The size and size distribution of colloidal particles within these systems play a pivotal role in determining their stability, rheological properties, and overall functionality (which in turn directly influence material quality, performance, and shelf life). As a result, this study is aimed at devising a new method to analyze the dimensions of the colloidal particles (dispersed phase) of a colloidal system (sol), like bitumen, by (i) a cheap and common technique, optical microscopy, and (ii) the more complex confocal laser scanning microscopy. To do so, a validation by comparison with a standard technique—in this case, atomic force microscopy is presented. Both optical and confocal microscopies turned out to be suitable, valid, and effective for particle size determination. Both techniques effectively revealed, upon bitumen aging, a shift of the size distribution to slightly larger sizes. Large particles, whose abundance did not increase significantly, appeared to be more inert than small ones. A huge advantage of optical microscopy is its popularity and cost-effectiveness as it is commonly featured in laboratories independently of the research topic. On the other hand, confocal microscopy can observe more particles, thus providing better statistics. It also appears to be more efficient for particles smaller than 1 µm2. These microscopy techniques were used to evaluate the dimensions of the asphaltenes present in a complex colloidal system; bitumen; the model colloidal system for this study, which was examined before and after an aging process which is expected to change the size distribution.

Effective patchiness from critical points of a coarse-grained protein model with explicit shape and charge anisotropy.

Colloidal model systems are successful in rationalizing emergent phenomena like aggregation, rheology and phase behaviour of protein solutions. Colloidal theory in conjunction with isotropic interaction models is often employed to estimate the stability of such solutions. In particular, a universal criterion for the reduced second virial coefficient at the critical point is frequently invoked which is based on the behavior of short-range attractive fluids (Noro-Frenkel rule, ). However, if anisotropic models for the protein-protein interaction are considered, e.g. the Kern-Frenkel (KF) patchy particle model, the value of the criterion is shifted to lower values and explicitly depends on the number of patches. If an explicit shape anisotropy is considered, as e.g. in a coarse-grained protein model, the normalization of becomes ambiguous to some extent, as no unique exclusion volume can be defined anymore. Here, we investigate a low-resolution, coarse-grained model for the globular protein bovine serum albumin (BSA) and study effects of charge-anisotropy on the phase diagram (determined by simulations) at the isoelectric point. We present methods of assigning an "effective patchiness" to our protein model by comparing its critical properties to the KF model. We find that doubling the native charges increases the critical temperature Tc by ≈14% and that our BSA model can be compared to a 3 to 5 patch KF model. Finally, we argue that applying existing criteria from colloidal theory should be done with care, due to multiple, physically plausible ways of how to assign effective diameters to shape-anisotropic models.

Application of the symmetric Poisson-Boltzmann theory to a model colloidal mixture.

A symmetric Poisson-Boltzmann theory is used to analyse the structure of a primitive model colloidal system which contains either 4 or 6 components. The approach symmetrizes the pair distribution function gij(r) between two asymmetric charged species with respect to an interchange of the indices. Good agreement is found with molecular dynamics simulation structural properties when the exclusion volume term is modelled by the Percus-Yevick uncharged hard sphere radial distribution function.

Nonadditivity in interactions between three membrane-wrapped colloidal spheres

Many cell functions require a concerted effort from multiple membrane proteins, for example, for signaling, cell division, and endocytosis. One contribution to their successful self-organization stems from the membrane deformations that these proteins induce. While the pairwise interaction potential of two membrane-deforming spheres has recently been measured, membrane-deformation-induced interactions have been predicted to be nonadditive, and hence their collective behavior cannot be deduced from this measurement. We here employ a colloidal model system consisting of adhesive spheres and giant unilamellar vesicles to test these predictions by measuring the interaction potential of the simplest case of three membrane-deforming, spherical particles. We quantify their interactions and arrangements and, for the first time, experimentally confirm and quantify the nonadditive nature of membrane-deformation-induced interactions. We furthermore conclude that there exist two favorable configurations on the membrane: (1) a linear and (2) a triangular arrangement of the three spheres. Using Monte Carlo simulations, we corroborate the experimentally observed energy minima and identify a lowering of the membrane deformation as the cause for the observed configurations. The high symmetry of the preferred arrangements for three particles suggests that arrangements of many membrane-deforming objects might follow simple rules.

Topological phases in nanoparticle monolayers: can crystalline, hexatic, and isotropic-fluid phases coexist in the same monolayer?

Topological phases are stable configurations of matter in 2-dimensions (2D) formed via spontaneous symmetry breaking. These play a crucial role in determining the system properties. Though a number of fundamental studies on topological phase transitions and topological defect dynamics have been conducted with model colloidal systems (typically microns in size), the same is lacking on nanoparticle monolayers (NPMLs, typically made of ligand-coated sub-ten nanometer particles). Here, we show that in an evaporation-driven self-assembly process, the three topological phases, namely crystalline, hexatic, and isotropic-fluid phases, can coexist within the same NPML. We associate this coexistence with the local variation in particle size, which can be described by a unique frequency parameter (p25), quantifying the fraction of NPs that has size deviation greater than or equal to 25% of the mean size (where the deviation,ζ is defined as ζ = ((|Size-mean|)/mean)). The p25-values for the three phases are distinctly different: crystalline arrangement occurs when p25 < ∼0.02, while a hexatic phase exists for 0.02 ≤ p25 ≤ 0.1. For p25 ≥ 0.1, the isotropic-fluid phase occurs. Following KTHNY-theory, we further numerically extrapolate the occurrence of each phase to the accumulated excess planar strain in the NPML due to the presence of various topological defects in the structures.

Fluid-solid transitions in photonic crystals of soft, thermoresponsive microgels.

Microgels are often discussed as well-suited model system for soft colloids. In contrast to rigid spheres, the microgel volume and, coupled to this, the volume fraction in dispersion can be manipulated by external stimuli. This behavior is particularly interesting at high packings where phase transitions can be induced by external triggers such as temperature in the case of thermoresponsive microgels. A challenge, however, is the determination of the real volume occupied by these deformable, soft objects and consequently, to determine the boundaries of the phase transitions. Here we propose core-shell microgels with a rigid silica core and a crosslinked, thermoresponsive poly-N-isopropylacrylamide (PNIPAM) shell with a carefully chosen shell-to-core size ratio as ideal model colloids to study fluid-solid transitions that are inducible by millikelvin changes in temperature. Specifically, we identify the temperature ranges where crystallization and melting occur using absorbance spectroscopy in a range of concentrations. Slow annealing from the fluid to the crystalline state leads to photonic crystals with Bragg peaks in the visible wavelength range and very narrow linewidths. Small-angle X-ray scattering is then used to confirm the structure of the fluid phase as well as the long-range order, crystal structure and microgel volume fraction in the solid phase. Thanks to the scattering contrasts and volume ratio of the cores with respect to the shells, the scattering data do allow for form factor analysis revealing osmotic deswelling at volume fractions approaching and also exceeding the hard sphere packing limit.

Structural characterization of systems with competing interactions confined in narrow spherical shells.

Systems with short-range attraction and long-range repulsion can form ordered microphases in bulk and under confinement. In fact, confinement has been proven to be a good strategy to induce the formation of novel ordered microphases that might be appealing to the development of functional nanomaterials. Using Grand Canonical Monte Carlo (GCMC) simulations, we study a model colloidal system with competing interactions under confinement in narrow spherical shells at thermodynamic conditions under which the hexagonal phase is stable in bulk. We observe the formation of three parent ordered structures formed by toroidal clusters and two spherical clusters (Type I), toroidal clusters and one spherical cluster (Type II), and toroidal clusters alone (Type III), depending on the radius of the confining shell, that can often coexist with other related structures derived from these parent ones by a simple transformation, in which the system is divided into two hemispheres that are rotated with respect to each other by a given angle. We propose a general method to characterize and predict the structures obtained under confinement in spherical shells in systems able to self-assemble into a hexagonal phase in bulk. We also show that deforming the spherical shells into ellipsoidal ones affects the structure of the system in such a way that helical structures are favoured by prolate ellipsoids and toroidal structures by oblate ellipsoids.

Continuous structural deformation of graphene oxide liquid crystal colloids under shear for hydrogel films

In the processing of two-dimensional (2D) liquid crystal (LC), the microstructure of 2D LC colloids is continuously deformed by shearing, which ultimately determines their physical properties. However, it is experimentally difficult to investigate and visualize how the microstructure continuously changes during processing involving shear stress. Thus, controlling the microstructure of 2D LCs using shear forces remains a more difficult problem.Herein, we report the in-situ analysis of structural deformation for 2D colloids liquid crystals focused on the reorientation of the liquid crystal (LC) under oscillatory shear. Graphene oxide (GO) was employed as a model system for 2D LC colloids, and polymers were added to control the 2D colloidal interactions. We found that the GO structure deforms in two steps: The first step is the transition to multi-domains of GO LC and the second transition brings the macroscopic alignment of GO. We additionally found that the added polymer causes the earlier disappearance of multiple GO LC domains and provides a better macroscopic alignment at the same shear condition. The study will be of great interest in the 2D colloidal process accompanying yielding behavior, providing an effective strategy to control the domain orientation and the resulting properties.

Direct imaging of contacts and forces in colloidal gels.

Colloidal dispersions are prized as model systems to understand the basic properties of materials and are central to a wide range of industries from cosmetics to foods to agrichemicals. Among the key developments in using colloids to address challenges in condensed matter is to resolve the particle coordinates in 3D, allowing a level of analysis usually only possible in computer simulations. However, in amorphous materials, relating mechanical properties to microscopic structure remains problematic. This makes it rather hard to understand, for example, mechanical failure. Here, we address this challenge by studying the contacts and the forces between particles as well as their positions. To do so, we use a colloidal model system (an emulsion) in which the interparticle forces and local stress can be linked to the microscopic structure. We demonstrate the potential of our method to reveal insights into the failure mechanisms of soft amorphous solids by determining local stress in a colloidal gel. In particular, we identify "force chains" of load-bearing droplets and local stress anisotropy and investigate their connection with locally rigid packings of the droplets.

How Softness Matters in Soft Nanogels and Nanogel Assemblies.

Softness plays a key role in determining the macroscopic properties of colloidal systems, from synthetic nanogels to biological macromolecules, from viruses to star polymers. However, we are missing a way to quantify what the term "softness" means in nanoscience. Having quantitative parameters is fundamental to compare different systems and understand what the consequences of softness on the macroscopic properties are. Here, we propose different quantities that can be measured using scattering methods and microscopy experiments. On the basis of these quantities, we review the recent literature on micro- and nanogels, i.e. cross-linked polymer networks swollen in water, a widely used model system for soft colloids. Applying our criteria, we address the question what makes a nanomaterial soft? We discuss and introduce general criteria to quantify the different definitions of softness for an individual compressible colloid. This is done in terms of the energetic cost associated with the deformation and the capability of the colloid to isotropically deswell. Then, concentrated solutions of soft colloids are considered. New definitions of softness and new parameters, which depend on the particle-to-particle interactions, are introduced in terms of faceting and interpenetration. The influence of the different synthetic routes on the softness of nanogels is discussed. Concentrated solutions of nanogels are considered and we review the recent results in the literature concerning the phase behavior and flow properties of nanogels both in three and two dimensions, in the light of the different parameters we defined. The aim of this review is to look at the results on micro- and nanogels in a more quantitative way that allow us to explain the reported properties in terms of differences in colloidal softness. Furthermore, this review can give researchers dealing with soft colloids quantitative methods to define unambiguously which softness matters in their compound.

Sustained order-disorder transitions in a model colloidal system driven by rhythmic crosslinking.

Biological systems have the unique ability to self-organize and generate autonomous motion and work. Motivated by this, we investigate a 2D model colloidal network that can repeatedly transition between disordered states of low connectivity and ordered states of high connectivity via rhythmic binding and unbinding of biomimetic crosslinkers. We use Langevin dynamics to investigate the time-dependent changes in structure and collective properties of this system as a function of colloidal packing fractions and crosslinker oscillation periods and characterize the degree of order in the system by using network connectivity, bond length distributions, and collective motion. Our simulations suggest that we can achieve distinct states of this colloidal system with pronounced differences in microstructural order and large residence times in the ordered state when crosslinker kinetics and lifetimes depend directly on the oscillation period and this oscillation period is much larger than the colloidal diffusion time. Our results will provide insights into the rational design of smart active materials that can independently cycle between ordered and disordered states with desired material properties on a programmed schedule.

Ordering and Dynamics of Interacting Colloidal Particles under Soft Confinement

Confinement can induce substantial changes in the physical properties of macromolecules in suspension. Soft confinement is a particular class of restriction where the boundaries that constraint the particles in a region of the space are not well-defined. This scenario leads to a broader structural and dynamical behavior than observed in systems enclosed between rigid walls. In this contribution, we study the ordering and diffusive properties of a two-dimensional colloidal model system subjected to a one-dimensional parabolic trap. Increasing the trap strength makes it possible to go through weak to strong confinement, allowing a dimensional transition from two- to one-dimension. The non-monotonic response of the static and dynamical properties to the gradual dimensionality change affects the system phase behavior. We find that the particle dynamics are connected to the structural transitions induced by the parabolic trap. In particular, at low and intermediate confinement regimes, complex structural and dynamical scenarios arise, where the softness of the external potential induces melting and freezing, resulting in faster and slower particle diffusion, respectively. Besides, at strong confinements, colloids move basically along one direction, and the whole system behaves structurally and dynamically similar to a one-dimensional colloidal system.

Shape-Tunable Janus Micromotors via Surfactant-Induced Dewetting.

The ability to tune shapes of micromotors is challenging yet crucial for creating intelligent and functional micromachines with shape-dependent dynamics. Here, we demonstrate a facile strategy to synthesize Janus micromotors in large quantity whose shapes can be precisely tuned by a surfactant-induced dewetting strategy. The Janus micromotor is composed of a TiO2 microparticle partially encapsulated within a polysiloxane microsphere. A range of particle shapes, from approximately spherical to snowman, is achieved, and the shape-tunable dynamics of the micromotors are quantified. Our strategy is versatile and can be applicable to other photoactive materials, such as ZnO and Fe2O3 nanoparticles, demonstrating a general approach to synthesize Janus micromotors with controllable shapes. Such shape-tunable micromotors provide colloidal model systems for fundamental research on active matter, as well as building blocks for the fabrication of micromachines.

Phenomenological model of viscoelasticity for systems undergoing sol–gel transition

A material undergoing sol–gel transition evolves from the pre-gel (sol) state to the post-gel state through the critical gel state. It is well-known that critical gels exhibit power-law rheology. The faster decay of the relaxation modulus in the pre-gel state can be empirically described by modifying this power-law decay with a stretched exponential factor. A phenomenological analytical expression for the relaxation modulus in the post-gel state is proposed by invoking the symmetry associated with the evolution of the relaxation time on either side of the critical gel state and by accounting for natural constraints. This expression, which depends on the extent of cross-linking, can be suitably transformed to obtain analytical expressions for the dynamic moduli and the continuous relaxation time spectrum. Thus, the proposed model facilitates a comprehensive description of viscoelastic evolution from the pre-gel to the post-gel states. It is validated by carrying out experiments on a model colloidal gel-forming system and by considering other diverse gel-forming systems studied in the literature. After calibrating the parameters of the phenomenological model, it is found to be in excellent agreement with experimental data. Such a well-calibrated phenomenological model can be used to determine any linear viscoelastic response over a wide range of frequencies and extents of cross-linking encompassing the entire sol–gel transition.

Synthesis of Rough Colloidal SU-8 Rods and Bananas via Nanoprecipitation

Surface roughness plays an important role in determining the mechanical properties, wettability, and self-assembly in colloidal systems. In this work, we develop a simple and fast method to produce rough colloidal SU-8 rods, bananas, and spheres, via the nanoprecipitation of SU-8 in water. During this process, SU-8 nanospheres are absorbed onto the surface of the colloidal SU-8 particles and then cross-linked using UV-light. The size of the spherical asperities and the asperity density are controlled by the concentration of SU-8 used during the nanoprecipitation reaction. Fluorescent labeling of the rough SU-8 colloidal particles allows for their confocal imaging, which demonstrates their stability at high packing fractions. With these newly developed rough particles, we provide a colloidal model system that allows for studies addressing the impact of surface roughness on materials composed of anisotropic particles.

Freezing of a soft-core fluid in a one-dimensional potential: appearance of a locked smectic phase

ABSTRACT We investigate the phase behaviour of a two-dimensional colloidal model system of ultra-soft particles on a substrate which varies periodically along one spatial direction. Our calculations are based on mean-field density functional theory for a system of particles interacting via an ultra-soft potential, that is, the generalised exponential model with index four (GEM-4). For suitable substrate periodicities (with commensurability parameter p = 2), we find a succession of phase transitions from a modulated liquid to a locked smectic and then to a locked floating solid phase. The appearance of a locked smectic phase is consistent with earlier theoretical predictions and experiments for freezing of more repulsive systems on structured surfaces (with p = 2). However, the present ultra-soft system does not display re-entrant melting. We here investigate the details of the density distributions of the different phases, thereby supplementing earlier work on GEM-4 systems with p = 1 [Phys. Rev. E 101, 012609 (2020)]. Interestingly, the observed succession of phase transitions can be triggered through different paths along which physical control parameters are changed.