Limits of the fractal dimension for irreversible kinetic aggregation of gold colloids

Viscoelastic properties of colloidal systems with attractive solid particles at low concentration: A review, new results and interpretations

This paper concerns the viscoelastic properties and the resulting structure of colloidal systems with short-range attractions in the regime where the volume fraction f is small. Unlike the high ϕ regime, which is well understood in terms of mode-coupling theory (MCT), the low ϕ regime is still the subject of a debate based on different concepts such as percolation, diffusion-limited colloidal aggregation (DLCA), jamming, or cluster mode-coupling approach. Prior to the analysis of three examples of attractive systems at low ϕ values, a summary of concepts relevant to understanding the formation and properties of such attractive particles is discussed in the present study. Afterwards, we re-analyze the behaviour at a low ϕ of i) suspensions of carbon black (CB) particles, ii) suspensions of poly(methyl methacrylate) (PMMA) hard spheres with a depletion attraction induced by the addition of polystyrene (PS), and iii) suspensions of amino acid organogelator molecules which form rod-like objects. The rheological properties of these systems have been studied in detail and their response has been interpreted as being due either to a solid network discussed in relation to the jamming state diagram or to a suspension formed by jamming of clusters. Our analysis shows that these three systems are in fact cluster fluids and that their solid-like response corresponds to a change in their viscoelastic response, the elastic component G' becoming greater than the viscous component G" at low frequencies. Due to the presence of weak interparticle interactions in the tens range from 1 to 15 kBT, a liquid-like state is reversibly achieved at high frequencies, as indicated by the crossover of G' and G" as a function of frequency for a given concentration. Moreover, all these attractive particle systems at low ϕ show for both moduli a master curve which characterizes these cluster fluids and allows for the classification of these attractive particle systems.

Plasmonic Ag Nanoparticles: Correlating Nanofabrication and Aggregation for SERS Detection of Thiabendazole Pesticide

The level of aggregation and aggregate morphology of metallic nanoparticles are factors that influence the SERS signal (surface-enhanced Raman scattering), affecting reproducibility and sensitivity. This study presents a systematic evaluation of the colloidal aggregation on the SERS signal by combining transmission electron microscopy and UV-vis extinction spectroscopy. It focuses on the effect of two methods of sample preparation ("external standard method-ESM" and "standard addition method-SAM") on the SERS signal using the fungicide thiabendazole (TBZ) in Ag colloid as a probe molecule. The TBZ critical concentration (concentration for which SERS reaches the maximum intensity) was 6.0 × 10-6 mol/L for ESM and 1.5 × 10-6 mol/L for SAM. Besides, TBZ exhibited a sigmoid-type isotherm for ESM, indicating formation of a TBZ first layer on Ag nanoparticles at lower concentrations (Ag aggregates more compact; size <500 nm) and TBZ multilayers at higher concentrations (Ag aggregates more branched; >2 μm). For SAM, the TBZ first layer formation was also observed at lower concentrations (Ag aggregates more branched; <2 μm). However, at higher concentrations, the Ag colloid degradation/precipitation was observed (Ag aggregates more compact; >2 μm). The Ag aggregation mechanisms align with reaction-limited colloidal aggregation at lower concentrations and diffusion-limited colloidal aggregation at higher concentrations. We believe these results contribute to the SERS research field despite all of the work already done over its 50-year history.

Fractal-Dependent Growth of Solidlike Condensates

The phenomenon of droplet growth occurs in various industrial and natural processes. Recently, the discovery of liquidlike condensates within cells has sparked an increasing interest in understanding their growth behaviors. These condensates exhibit varying material properties that are closely related to many cellular functions and diseases, particularly during the phase transition from liquidlike droplets to solidlike aggregates. However, how the liquid-to-solid phase transition affects the growth of condensates remains largely unknown. In this study, we investigate the growth of peptide-RNA condensates, which behave as either liquidlike droplets or solidlike aggregates depending on the RNA sequences. Dynamic light scattering experiments show that solidlike condensates grow surprisingly faster, with their hydrodynamic diameters increasing over time as d_{h}(t)∼t^{1/2}, contrasting with d_{h}(t)∼t^{1/3} for liquidlike droplets. By combining theoretical analysis and simulations, we demonstrate that this accelerated growth is caused by the noncoalescence aggregation of solidlike condensates and thus formation of percolated swollen structures with a decreased fractal dimension. Moreover, we demonstrate that the accelerated growth can be slowed down by introducing agents that can revert solidlike condensates back to their liquidlike states, such as urea or specific RNAs. Together, our work reveals a fractal-dependent growth mechanism of condensates, with useful insights for understanding the aging of condensates and modulating their aggregation behaviors in synthetic and biological systems.

New Insights into the Formation of Aggregates of Bidisperse Nano- and Microplastics in Water Based on the Analysis of In Situ Microscopy and Molecular Simulation

Microplastics (MPs) and nanoplastics (NPs) in water pose a global threat to human health and the environment. To develop efficient removal strategies, it is crucial to understand how these particles behave as they aggregate. However, our knowledge of the process of aggregate formation from primary particles of different sizes is limited. In this study, we analyzed the growth kinetics and structures of aggregates formed by polystyrene MPs in mono- and bidisperse systems using in situ microscopy and image analysis. Our findings show that the scaling behavior of aggregate growth remains unaffected by the primary particle size distribution, but it does delay the onset of rapid aggregation. We also performed a structural analysis that reveals the power law dependence of aggregate fractal dimension (df) in both mono- and bidisperse systems, with mean df consistent with diffusion-limited cluster aggregation (DLCA) aggregates. Our results also suggest that the df of aggregates is insensitive to the shape anisotropy. We simulated molecular forces driving aggregation of polystyrene NPs of different sizes under high ionic strength conditions. These conditions represent salt concentration in ocean water and wastewater, where the DLVO theory does not apply. Our simulation results show that the aggregation tendency of the NPs increases with the ionic strength. The increase in the aggregation is caused by the depletion of clusters of ions from the NPs surface.

Mechanistic Modeling of Amyloid Oligomer and Protofibril Formation in Bovine Insulin

Early phase of amyloid formation, where prefibrillar aggregates such as oligomers and protofibrils are often observed, is crucial for understanding pathogenesis. However, the detailed mechanisms of their formation have been difficult to elucidate because they tend to form transiently and heterogeneously. Here, we found that bovine insulin protofibril formation proceeds in a monodisperse manner, which allowed us to characterize the detailed early aggregation process by light scattering in combination with thioflavin T fluorescence and Fourier transform infrared spectroscopy. The protofibril formation was specific to bovine insulin, whereas no significant aggregation was observed in human insulin. The kinetic analysis combining static and dynamic light scattering data revealed that the protofibril formation process in bovine insulin can be divided into two steps based on fractal dimension. When modeling the experimental data based on Smoluchowski aggregation kinetics, an aggregation scheme consisting of initial fractal aggregation forming spherical oligomers and their subsequent end-to-end association forming protofibrils was clarified. Furthermore, the analysis of temperature and salt concentration dependencies showed that the end-to-end association is the rate-limiting step, involving dehydration. The established model for protofibril formation, wherein oligomers are incorporated as a precursor, provides insight into the molecular mechanism by which protein molecules assemble during the early stage of amyloid formation.

Growth of Floc Structure and Subsequence Compaction into Smaller Granules through Breakup and Rearrangement of Aluminum Flocs in a Constant Laminar Shear Flow

We have constructed an outer-cylinder-rotating Couette device for high-speed shear flow in laminar flow conditions and visualized the structure formation and subsequent rearrangement of PACl (flocculant made of aluminum hydroxide gel) and kaolinite flocs by visible light imaging. In a previous report, we analyzed the case of relatively low shear rate (G-value = 29 1/s) and confirmed that the flocculation process could be separated into two stages: a floc growth stage and a breakup/rearrangement stage. Once the large bulky flocs that reached the maximum size appeared, they rearranged and densified through structural fracture and rearrangement. In this report, this process was further investigated by conducting experiments under two different high shear rates (58 and 78 1/s) at which breakup and rearrangement became more pronounced, and three different aluminum kaolinite ratios (ALT ratios) that were over and under the optimum dosage (neutralization point by Zeta potential). Visualization results confirmed that, during the growth stage, the flocculation rate could be approximated by a scaling relationship between floc size and elapsed time, which depended on the ALT ratio. After reaching the maximum size, the floc rapidly became compact and dense following adsorption of the gel, incorporating fine fragments from erosion breakup. The over and under dosages created a lot of fragments of erosion breakup, but less so in the optimum dosage. In the optimum ALT ratio, fragments did not remain because they were incorporated into the flocs and densified, and the floc size was thought to be maintained. The floc circularity distribution peaked at around 0.6 and 1, suggesting that the flocs were spherical in shape due to erosion breakup.

Optimization of Mass and Light Transport in Nanoparticle-Based Titania Aerogels

Aerogels composed of preformed titania nanocrystals exhibit a large surface area, open porosity, and high crystallinity, making these materials appealing for applications in gas-phase photocatalysis. Recent studies on nanoparticle-based titania aerogels have mainly focused on optimizing their composition to improve photocatalytic performance. Little attention has been paid to modification at the microstructural level to control fundamental properties such as gas permeability and light transmittance, although these features are of fundamental importance, especially for photocatalysts of macroscopic size. In this study, we systematically control the porosity and transparency of titania gels and aerogels by adjusting the particle loading and nonsolvent fraction during the gelation step. Mass transport and light transport were assessed by gas permeability and light attenuation measurements, and the results were related to the microstructure determined by gas sorption analysis and scanning electron microscopy. Mass transport through the aerogel network was found to proceed primarily via Knudsen diffusion leading to relatively low permeabilities in the range of 10-5-10-6 m2/s, despite very high porosities of 96-99%. While permeability was found to depend mainly on particle loading, the optical properties are predominantly affected by the amount of nonsolvent during gelation, allowing independent tuning of mass and light transport.

Controlled Assembly of CdSe Nanoplatelet Thin Films and Nanowires

We assemble semiconductor CdSe nanoplatelets (NPs) at the air/liquid interface into 2D monolayers several micrometers wide, distinctly displaying nematic order. We show that this configuration is the most favorable energetically and that the edge-to-edge distance between neighboring NPs can be tuned by ligand exchange without disrupting film topology and nanoparticle orientation. We explore the rich assembly phase space by using depletion interactions to direct the formation of 1D nanowires from stacks of NPs. The improved control and understanding of the assembly of semiconductor NPs offers opportunities for the development of cheaper optoelectronic devices that rely on 1D or 2D charge delocalization throughout the assembled monolayers and nanowires.

Exploring non-equilibrium processes and spatio-temporal scaling laws in heated egg yolk using coherent X-rays

The soft-grainy microstructure of cooked egg yolk is the result of a series of out-of-equilibrium processes of its protein-lipid contents; however, it is unclear how egg yolk constituents contribute to these processes to create the desired microstructure. By employing X-ray photon correlation spectroscopy, we investigate the functional contribution of egg yolk constituents: proteins, low-density lipoproteins (LDLs), and yolk-granules to the development of grainy-gel microstructure and microscopic dynamics during cooking. We find that the viscosity of the heated egg yolk is solely determined by the degree of protein gelation, whereas the grainy-gel microstructure is controlled by the extent of LDL aggregation. Overall, protein denaturation-aggregation-gelation and LDL-aggregation follows Arrhenius-type time-temperature superposition (TTS), indicating an identical mechanism with a temperature-dependent reaction rate. However, above 75 °C TTS breaks down and temperature-independent gelation dynamics is observed, demonstrating that the temperature can no longer accelerate certain non-equilibrium processes above a threshold value.

In situ characterization of the agglutination of lectins via cross-linking of carbohydrates by time-resolved measurement of forward static light scattering

We present real-time observations of a structurally variable process for cross-linking agglutination between multivalent lectins and glycoclusters using a small-angle forward static light scattering (F-SLS) technique. In this study, a cross-linking agglutination reaction was carried out using a tetravalent Neu5Acα2,6LacNAc-glycocluster and Sambucus sieboldiana agglutinin (SSA). The scattering intensity of time-resolved F-SLS increased with formation of the Neu5Acα2,6LacNAc-glycocluster-SSA cross-linked complex. Using this approach, fine sequential cross-linking agglutination between glycoclusters and lectins was observed in real-time. The rate of increase in the intensity of time-resolved F-SLS increased with the concentration of sialo-glycoclusters and SSA. Structural analysis based on the fractal dimension using time-resolved F-SLS patterns revealed that the density of the aggregates changed with progression of the cross-linking reaction until equilibrium was reached. This is the first report to evaluate the cross-linking agglutination reaction between glycoclusters and lectins and analysis of the subsequent structure of the obtained aggregates using time-resolved measurements of F-SLS.

Pickering emulsions stabilized with differently charged particles

For addressing health issues and ecological concerns, the cosmetic and pharmaceutical industries are facing the challenge of designing emulsions without the use of surfactants. Emulsions stabilized by colloidal particles, known as Pickering emulsions, are promising in this matter. In this article, three different types of particles (neutral, anionic and cationic) are used alone or in binary mixtures as stabilizers of Pickering emulsions. The influence of the particles' charge on the emulsions' properties and the synergies between the different types of particles are studied. It is demonstrated that the kinetics of adsorption of the particles at the water/oil interface control the coverage and their organization at the droplet surface, rather than their interactions after adsorption. Binary mixtures of differently charged particles are a powerful way to control the droplet coverage and the particle loading in the emulsions. In particular, the combination of anionic and cationic particles led to smaller droplets and higher particle coverage of emulsion droplets.

Fractal dimension based geographical clustering of COVID-19 time series data

Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.

Effects of temperature and ionic strength on the microscopic structure and dynamics of egg white gels

We investigate the thermal gelation of egg white proteins at different temperatures with varying salt concentrations using x-ray photon correlation spectroscopy in the geometry of ultra-small angle x-ray scattering. Temperature-dependent structural investigation suggests a faster network formation with increasing temperature, and the gel adopts a more compact network, which is inconsistent with the conventional understanding of thermal aggregation. The resulting gel network shows a fractal dimension δ, ranging from 1.5 to 2.2. The values of δ display a non-monotonic behavior with increasing amount of salt. The corresponding dynamics in the q range of 0.002-0.1 nm^-1 is observable after major change of the gel structure. The extracted relaxation time exhibits a two-step power law growth in dynamics as a function of waiting time. In the first regime, the dynamics is associated with structural growth, whereas the second regime is associated with the aging of the gel, which is directly linked with its compactness, as quantified by the fractal dimension. The gel dynamics is characterized by a compressed exponential relaxation with a ballistic-type of motion. The addition of salt gradually makes the early stage dynamics faster. Both gelation kinetics and microscopic dynamics show that the activation energy barrier in the system systematically decreases with increasing salt concentration.

Ozonation/UV irradiation of dispersed Ag/AgI nanoparticles in water resources: stability and aggregation

Proliferation of nanoparticles (NPs) as aqueous pollutants is a matter of growing concern today. The aggregation kinetics of colloidal bare silver (Ag, 20.5 nm) and silver iodide (AgI, 15.3 nm) NPs were investigated during ozone/ultraviolet (O₃/UV) oxidation. Dynamic light scattering was applied to monitor the aggregation of NPs, and the z-average of treated samples was considered aggregate diameter. The effect of temperature, pH, and initial concentration of NPs was investigated on the aggregation rate constant and stability ratio. At a short oxidation period of approximately 1 min, the lower stability ratio was achieved for Ag NPs (< 50) than AgI NPs (> 100). Under acidic conditions, the negative surface charge of both NPs was neutralized that resulted in faster aggregation. In contrast, the impact of temperature and initial concentration of NPs on the aggregation rate was different for both NPs, which was due to the type of O₃/UV interaction with the surface of NPs and the thickness of the electrical double layer surrounding the NPs. The aggregation behavior of Ag NPs obeyed diffusion-limited regime, while an intermediate regime between diffusion- and reaction-limited was observed for AgI NP aggregation. The resulting aggregate morphologies showed that the clusters were ramified for Ag and compressed for AgI NPs. Applying the O₃/UV oxidation process for water treatment purposes leads to a significant reduction in aggregation time for inherently unstable Ag and stable AgI toxic NPs from several hours or days to several minutes.

Retention of graphene oxide and reduced graphene oxide in porous media: Diffusion-attachment, interception-attachment and straining

The aggregation, deposition and retention of graphene oxide (GO) and reduced graphene oxide (RGO) were investigated systematically to estimate their mobility in the environment. RGO aggregates faster than GO, resulting in weaker diffusive transfer and a lower deposition rate on oxide surfaces. In NaCl, the critical deposition concentration of RGO (CDC_RGO) is smaller than CDC_GO on the SiO₂ surface, indicating that RGO achieves favorable deposition at lower ionic strength. In CaCl₂, Ca²⁺ bridging causes close CDC_GO and CDC_RGO. The retention process was observed in the photolithographic SiO₂ and Al₂O₃ micromodels. GO and RGO particles approach collectors mainly via interception before attachment. The interactive forces have a limited effect on the particle retention. The larger RGO aggregates cause greater extent interception and straining, resulting in lower mobility than GO in porous media. The mobility of GO and RGO show different trends in quartz crystal microbalance with dissipation (QCM-D) and in micromodels because the interception and straining mechanisms exist in pore space. Micromodel observation confirms the processes of interception and straining. The combination of QCM-D and micromodel experiments provides the connection of diffusion-attachment, interception-attachment and straining, which comprehensively explains the higher mobility of GO than RGO in porous media.

Expanding the Range: AuCu Metal Aerogels from H2O and EtOH

Due to their self-supporting and nanoparticulate structure, metal aerogels have emerged as excellent electrocatalysts, especially in the light of the shift to renewable energy cycles. While a large number of synthesis parameters have already been studied in depth, only superficial attention has been paid to the solvent. In order to investigate the influence of this parameter with respect to the gelation time, crystallinity, morphology, or porosity of metal gels, AuxCuy aerogels were prepared in water and ethanol. It was shown that although gelation in water leads to highly porous gels (60 m2g−1), a CuO phase forms during this process. The undesired oxide could be selectively removed using a post-washing step with formic acid. In contrast, the solvent change to EtOH led to a halving of the gelation time and the suppression of Cu oxidation. Thus, pure Cu aerogels were synthesized in addition to various bimetallic Au3X (X = Ni, Fe, Co) gels. The faster gelation, caused by the lower permittivity of EtOH, led to the formation of thicker gel strands, which resulted in a lower porosity of the AuxCuy aerogels. The advantage given by the solvent choice simplifies the preparation of metal aerogels and provides deeper knowledge about their gelation.

Rheology Applied to Microgels: Brief (Revision of the) State of the Art

The ability of polymer microgels to rapidly respond to external stimuli is of great interest in sensors, lubricants, and biomedical applications, among others. In most of their uses, microgels are subjected to shear, deformation, and compression forces or a combination of them, leading to variations in their rheological properties. This review article mainly refers to the rheology of microgels, from the hard sphere versus soft particles' model. It clearly describes the scaling theories and fractal structure formation, in particular, the Shih et al. and Wu and Morbidelli models as a tool to determine the interactions among microgel particles and, thus, the viscoelastic properties. Additionally, the most recent advances on the characterization of microgels' single-particle interactions are also described. The review starts with the definition of microgels, and a brief introduction addresses the preparation and applications of microgels and hybrid microgels.

Mass fractal dimension from 2D-microscopy images via an aggregation model with variable compactness

Microscopy-image analysis provides precious information on size and structure of colloidal aggregates and agglomerates. The structure of colloids is often characterized using the mass fractal dimension d_f , which is different from the two-dimensional fractal dimension d_p that can be computed from microscopy-images. In this work we propose to use a recent morphological aggregation model to find a relationship between 2D image fractal dimension and 3D mass fractal dimension of aggregates and agglomerates. Our case study is represented by scanning transmission electron microscopy-images of boehmite colloidal suspensions. The behaviour of the computed d_f at different acid and base concentration shows a fair agreement with the results of Small Angle X-Ray Scattering and with the literature, enabling to use the d_f vs d_p relationship to study the impact of the composition of the colloidal suspension on the density of colloidal aggregates and agglomerates. This article is protected by copyright. All rights reserved.

Real-time imaging of metallic supraparticle assembly during nanoparticle synthesis

Observations of nanoparticle superlattice formation over minutes during colloidal nanoparticle synthesis elude description by conventional understanding of self-assembly, which theorizes superlattices require extended formation times to allow for diffusively driven annealing of packing defects. It remains unclear how nanoparticle position annealing occurs on such short time scales despite the rapid superlattice growth kinetics. Here we utilize liquid phase transmission electron microscopy to directly image the self-assembly of platinum nanoparticles into close packed supraparticles over tens of seconds during nanoparticle synthesis. Electron-beam induced reduction of an aqueous platinum precursor formed monodisperse 2-3 nm platinum nanoparticles that simultaneously self-assembled over tens of seconds into 3D supraparticles, some of which showed crystalline ordered domains. Experimentally varying the interparticle interactions (e.g., electrostatic, steric interactions) by changing precursor chemistry revealed that supraparticle formation was driven by weak attractive van der Waals forces balanced by short ranged repulsive steric interactions. Growth kinetic measurements and an interparticle interaction model demonstrated that nanoparticle surface diffusion rates on the supraparticles were orders of magnitude faster than nanoparticle attachment, enabling nanoparticles to find high coordination binding sites unimpeded by incoming particles. These results reconcile rapid self-assembly of supraparticles with the conventional self-assembly paradigm in which nanocrystal position annealing by surface diffusion occurs on a significantly shorter time scale than nanocrystal attachment.

Structural, mechanical, and vibrational properties of particulate physical gels

Our lives are surrounded by a rich assortment of disordered materials. In particular, glasses are well known as dense, amorphous materials, whereas gels exist in low-density, disordered states. Recent progress has provided a significant step forward in understanding the material properties of glasses, such as mechanical, vibrational, and transport properties. In contrast, our understanding of particulate physical gels is still highly limited. Here, using molecular dynamics simulations, we study a simple model of particulate physical gels, the Lennard-Jones (LJ) gels, and provide a comprehensive understanding of their structural, mechanical, and vibrational properties, all of which are markedly different from those of LJ glasses. First, the LJ gels show sparse, heterogeneous structures, and the length scale ξ_s of the structures grows as the density is lowered. Second, the LJ gels are extremely soft, with both shear G and bulk K moduli being orders of magnitude smaller than those of LJ glasses. Third, many low-frequency vibrational modes are excited, which form a characteristic plateau with the onset frequency ω_* in the vibrational density of states. Structural, mechanical, and vibrational properties, characterized by ξ_s, G, K, and ω_*, respectively, show power-law scaling behaviors with the density, which establishes a close relationship between them. Throughout this work, we also reveal that LJ gels are multiscale, solid-state materials: (i) homogeneous elastic bodies at long lengths, (ii) heterogeneous elastic bodies with fractal structures at intermediate lengths, and (iii) amorphous structural bodies at short lengths.

Protein microparticles visualize the contact network and rigidity onset in the gelation of model proteins

Protein aggregation into gel networks is of immense importance in diverse areas from food science to medical research; however, it remains a grand challenge as the underlying molecular interactions are complex, difficult to access experimentally, and to model computationally. Early stages of gelation often involve protein aggregation into protein clusters that later on aggregate into a gel network. Recently synthesized protein microparticles allow direct control of these early stages of aggregation, decoupling them from the subsequent gelation stages. Here, by following the gelation of protein microparticles directly at the particle scale, we elucidate in detail the emergence of a percolating structure and the onset of rigidity as measured by microrheology. We find that the largest particle cluster, correlation length, and degree of polymerization all diverge with power laws, while the particles bind irreversibly indicating a nonequilibrium percolation process, in agreement with recent results on weakly attractive colloids. Concomitantly, the elastic modulus increases in a power-law fashion as determined by microrheology. These results give a consistent microscopic picture of the emergence of rigidity in a nonequilibrium percolation process that likely underlies the gelation in many more systems such as proteins, and other strongly interacting structures originating from (bio)molecules.

Phase Transition of Catenated DNA Networks in Poly(ethylene glycol) Solutions

Conformational phase transitions of macromolecules are an important class of problems in fundamental polymer physics. While the conformational phase transitions of linear DNA have been extensively studied, this feature of topologically complex DNA remains unexplored. We report herein the polymer-and-salt-induced (Ψ) phase transition of 2D catenated DNA networks, called kinetoplasts, using single-molecule fluorescence microscopy. We observe that kinetoplasts can undergo a reversible transition from the flat phase to the collapsed phase in the presence of NaCl as a function of the crowding agent poly(ethylene glycol). The nature of this phase transition is tunable through varying ionic strengths. For linear DNA, the coexistence of coil and globule phases was attributed to a first order phase transition associated with a double well potential in the transition regime. Kinetoplasts, however, navigate from the flat to the collapsed phase by passing through an intermediate regime, characterized by the coexistence of a multipopulation with varying shapes and sizes. Conformations of individual molecules in the multipopulation are long-lived, which suggests a rugged energy landscape.

On the Cluster Formation of α-Synuclein Fibrils

The dense accumulation of α-Synuclein fibrils in neurons is considered to be strongly associated with Parkinson’s disease. These intracellular inclusions, called Lewy bodies, also contain significant amounts of lipids. To better understand such accumulations, it should be important to study α-Synuclein fibril formation under conditions where the fibrils lump together, mimicking what is observed in Lewy bodies. In the present study, we have therefore investigated the overall structural arrangements of α-synuclein fibrils, formed under mildly acidic conditions, pH = 5.5, in pure buffer or in the presence of various model membrane systems, by means of small-angle neutron scattering (SANS). At this pH, α-synuclein fibrils are colloidally unstable and aggregate further into dense clusters. SANS intensities show a power law dependence on the scattering vector, q, indicating that the clusters can be described as mass fractal aggregates. The experimentally observed fractal dimension was d = 2.6 ± 0.3. We further show that this fractal dimension can be reproduced using a simple model of rigid-rod clusters. The effect of dominatingly attractive fibril-fibril interactions is discussed within the context of fibril clustering in Lewy body formation.

Colloidal aggregation in anisotropic liquid crystal solvent

The mutual attraction between colloidal particles in an anisotropic fluid, such as the nematic liquid crystal phase, leads to the formation of hierarchical aggregate morphologies distinct from those that tend to form in isotropic fluids. Previously it was difficult to study this aggregation process for a large number of colloids due to the difficulty of achieving a well dispersed initial colloid distribution under good imaging conditions. In this paper, we report the use of a recently developed self-assembling colloidal system to investigate this process. Hollow, micron-scale colloids are formed in situ in the nematic phase and subsequently aggregate to produce fractal structures and colloidal gels, the structures of which are determined by colloid concentration and temperature quench depth through the isotropic to nematic phase transition point. This self-assembling colloidal system provides a unique method to study particle aggregation in liquid crystal over large length scales. We use fluorescence microscopy over a range of length scales to measure aggregate structure as a function of temperature quench depth, observe ageing mechanisms and explore the driving mechanisms in this unique system. Our analyses suggest that aggregate dynamics depend on a combination of Frank elasticity relaxation, spontaneous defect line annihilation and internal aggregate fracturing.

The macroscopic shape of assemblies formed from microparticles based on host-guest interaction dependent on the guest content

Biological macroscopic assemblies have inspired researchers to utilize molecular recognition to develop smart materials in these decades. Recently, macroscopic self-assemblies based on molecular recognition have been realized using millimeter-scale hydrogel pieces possessing molecular recognition moieties. During the study on macroscopic self-assembly based on molecular recognition, we noticed that the shape of assemblies might be dependent on the host-guest pair. In this study, we were thus motivated to study the macroscopic shape of assemblies formed through host-guest interaction. We modified crosslinked poly(sodium acrylate) microparticles, i.e., superabsorbent polymer (SAP) microparticles, with β-cyclodextrin (βCD) and adamantyl (Ad) residues (βCD(x)-SAP and Ad(y)-SAP microparticles, respectively, where x and y denote the mol% contents of βCD and Ad residues). Then, we studied the self-assembly behavior of βCD(x)-SAP and Ad(y)-SAP microparticles through the complexation of βCD with Ad residues. There was a threshold of the βCD content in βCD(x)-SAP microparticles for assembly formation between x = 22.3 and 26.7. On the other hand, the shape of assemblies was dependent on the Ad content, y; More elongated assemblies were formed at a higher y. This may be because, at a higher y, small clusters formed in an early stage can stick together even upon collisions at a single contact point to form elongated aggregates, whereas, at a smaller y, small clusters stick together only upon collisions at multiple contact points to give rather circular assemblies. On the basis of these observations, the shape of assembly formed from microparticles can be controlled by varying y.

An efficient approach to study membrane nano-inclusions: from the complex biological world to a simple representation

Membrane nano-inclusions (NIs) are of great interest in biophysics, materials science, nanotechnology, and medicine. We hypothesized that the NIs within a biological membrane bilayer interact via a simple and efficient interaction potential, inspired by previous experimental and theoretical work. This interaction implicitly treats the membrane lipids but takes into account its effect on the NIs micro-arrangement. Thus, the study of the NIs is simplified to a two-dimensional colloidal system with implicit solvent. We calculated the structural properties from Molecular Dynamics simulations (MD), and we developed a Scaling Theory to discuss their behavior. We determined the thermal properties through potential energy per NI and pressure, and we discussed their variation as a function of the NIs number density. We performed a detailed study of the NIs dynamics using two approaches, MD simulations, and Dynamics Theory. We identified two characteristic values of number density, namely a critical number density n c = 3.67 × 10-3 Å-2 corresponded to the apparition of chain-like structures along with the liquid dispersed structure and the gelation number density n g = 8.40 × 10-3 Å-2 corresponded to the jamming state. We showed that the aggregation structure of NIs is of fractal dimension d F < 2. Also, we identified three diffusion regimes of membrane NIs, namely, normal for n < n c, subdiffusive for n c ≤ n < n g, and blocked for n ≥ n g. Thus, this paper proposes a simple and effective approach for studying the physical properties of membrane NIs. In particular, our results identify scaling exponents related to the microstructure and dynamics of membrane NIs.

Mechanism of Permselectivity Enhancement in Polyelectrolyte-Dense Nanofiltration Membranes via Surfactant-Assembly Intercalation

Enhancing the water permeance while maintaining the solute rejection of a nanofiltration (NF) membrane can potentially result in significant cost-reduction for NF-a membrane process that excels in several unique environmental applications of growing interests. In this work, we demonstrate for the first time that intercalation of surfactant self-assemblies in the polyelectrolyte multilayer (PEM) can lead to significant performance enhancement of salt-rejecting dense NF membranes fabricated using layer-by-layer assembly of polyelectrolytes. Specifically, the intercalation of sodium dodecyl sulfate (SDS) bilayers in a PEM comprising poly(diallyldimethylammonium chloride) (PDADMAC) and poly (sodium 4-styrenesulfonate) (PSS) resulted in a decrease in PEM thickness, increase in pore size, and a smoother and more hydrophilic surface. The water permeance of the resulting PEM NF membrane increased by 100% without compromising the rejection of Na₂SO₄. Experiments with a quartz crystal microbalance also provide direct evidence that the intercalation of the surfactants substantially reduces the subsequent adsorption of the polyelectrolytes of a similar charge. Based on its mechanism of performance enhancement, surfactant intercalation may become a universally applicable and highly cost-effective approach for dramatically enhancing the performance of PEM NF membranes.

Reaction Rate Governs the Viscoelasticity and Nanostructure of Folded Protein Hydrogels

Hydrogels constructed from folded protein domains are of increasing interest as resilient and responsive biomaterials, but their optimization for applications requires time-consuming and costly molecular design. Here, we explore a complementary approach to control their properties by examining the influence of crosslinking rate on the structure and viscoelastic response of a model hydrogel constructed from photochemically crosslinked bovine serum albumin (BSA). Gelation is observed to follow a heterogeneous nucleation pathway in which BSA monomers crosslink into compact nuclei that grow into fractal percolated networks. Both the viscoelastic response probed by shear rheology and the nanostructure probed by small-angle X-ray scattering (SAXS) are shown to depend on the photochemical crosslinking reaction rate, with increased reaction rates corresponding to higher viscoelastic moduli, lower fractal dimension, and higher fractal cluster size. Reaction rate-dependent changes are shown to be consistent with a transition between diffusion- and rate-limited assembly, and the corresponding changes to viscoelastic response are proposed to arise from the presence of nonfractal depletion regions, as confirmed by SAXS. This controllable nanostructure and viscoelasticity constitute a potential route for the precise control of hydrogel properties, without the need for molecular modification.

Effects of Protein Unfolding on Aggregation and Gelation in Lysozyme Solutions

In this work, we investigate the role of folding/unfolding equilibrium in protein aggregation and formation of a gel network. Near the neutral pH and at a low buffer ionic strength, the formation of the gel network around unfolding conditions prevents investigations of protein aggregation. In this study, by deploying the fact that in lysozyme solutions the time of folding/unfolding is much shorter than the characteristic time of gelation, we have prevented gelation by rapidly heating the solution up to the unfolding temperature (~80 °C) for a short time (~30 min.) followed by fast cooling to the room temperature. Dynamic light scattering measurements show that if the gelation is prevented, nanosized irreversible aggregates (about 10–15 nm radius) form over a time scale of 10 days. These small aggregates persist and aggregate further into larger aggregates over several weeks. If gelation is not prevented, the nanosized aggregates become the building blocks for the gel network and define its mesh length scale. These results support our previously published conclusion on the nature of mesoscopic aggregates commonly observed in solutions of lysozyme, namely that aggregates do not form from lysozyme monomers in their native folded state. Only with the emergence of a small fraction of unfolded proteins molecules will the aggregates start to appear and grow.

Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction

The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is lacking. In particular, for intermediate particle density and attraction, the structure formation process remains unclear. Here, we show that the gelation of short-range attractive particles is governed by a nonequilibrium percolation process. We combine experiments on critical Casimir colloidal suspensions, numerical simulations, and analytical modeling with a master kinetic equation to show that cluster sizes and correlation lengths diverge with exponents  ~1.6 and 0.8, respectively, consistent with percolation theory, while detailed balance in the particle attachment and detachment processes is broken. Cluster masses exhibit power-law distributions with exponents  -3/2 and  -5/2 before and after percolation, as predicted by solutions to the master kinetic equation. These results revealing a nonequilibrium continuous phase transition unify the structural arrest and yielding into related frameworks.

Understanding Time-Dependent Surface-Enhanced Raman Scattering from Gold Nanosphere Aggregates Using Collision Theory

Aggregates or clusters of primary metal nanoparticles in solution are one of the most widely used platforms for surface-enhanced Raman scattering (SERS) measurements because these nanostructures induce strong electric fields or hot spots between nanoparticles and as a result, SERS signals. While SERS signals are observed to vary with time, the impact of cluster formation mechanisms on SERS activity has been less studied. Herein, variations in time-dependent SERS signals from gold nanosphere clusters and aggregates are considered both experimentally and theoretically. An excess of the Raman reporter molecule, 2-naphthalenethiol, is added to induce rapid monolayer formation on the nanoparticles. In this diffusion-limited regime, clusters form as loosely packed fractals and the ligands help control nanoparticle separation distances once clusters form. By systematically varying gold nanosphere concentration and diameter, the reaction kinetics and dynamics associated with cluster formation can be studied. Dynamic light scattering (DLS), localized surface plasmon resonance (LSPR) spectroscopy, and SERS reveal that aggregates form reproducibly in the diffusion-limited regime and follow a self-limiting cluster size model. The rate of cluster formation during this same reaction window is explained using interaction pair potential calculations and collision theory. Diffusion-limited reaction conditions are limited by sedimentation only if sedimentation velocities exceed diffusion velocities of the clusters or via plasmon damping through radiation or scattering losses. These radiative loses are only significant when the extinction magnitude near the excitation wavelength exceeds 1.5. By evaluating these responses as a function of both nanosphere radius and concentration, time-dependent SERS signals are revealed to follow collision theory and be predictable when both nanosphere concentration and size are considered.

Kinetically assembled binary nanoparticle networks

Embedding percolating networks of nanoparticles (NPs) within polymers is a promising approach for mechanically reinforcing polymers and for introducing novel electronic, transport, and catalytic properties into otherwise inert polymers. While such networks may be obtained through kinetic assembly of unary system of NPs, the ensuing structures exhibit limited morphologies. Here, we investigate the possibility of increasing the diversity of NP networks through kinetic assembly of multiple species of NPs. Using lattice Monte Carlo simulations we show that networks obtained from co-assembly of two NP species of different sizes exhibit significantly more diverse morphology than those assembled from a single species. In particular, we achieved considerable variations in the particle spatial distribution, proportions of intra- and interspecies contacts, fractal dimension, and pore sizes of the networks by simply modulating the stoichiometry of the two species and their intra and inter-species affinities. We classified these distinct morphologies into "integrated", "coated", "leaved", and "blocked" phases, and provide relevant phase diagrams for achieving them. Our findings are relevant to controlled and predictable assembly of particle networks for creating multifunctional composites with improved properties.

Computer simulations of colloidal gels: how hindered particle rotation affects structure and rheology

The effects of particle roughness and short-ranged non-central forces on colloidal gels are studied using computer simulations in which particles experience a sinusoidal variation in energy as they rotate. The number of minima n and energy scale K are the key parameters; for large K and n, particle rotation is strongly hindered, but for small K and n particle rotation is nearly free. A series of systems are simulated and characterized using fractal dimensions, structure factors, coordination number distributions, bond-angle distributions and linear rheology. When particles rotate easily, clusters restructure to favor dense packings. This leads to longer gelation times and gels with strand-like morphology. The elastic moduli of such gels scale as G'∝ω^0.5 at high shear frequencies ω. In contrast, hindered particle rotation inhibits restructuring and leads to rapid gelation and diffuse morphology. Such gels are stiffer, with G'∝ω^0.35. The viscous moduli G'' in the low-barrier and high-barrier regimes scale according to exponents 0.53 and 0.5, respectively. The crossover frequency between elastic and viscous behaviors generally increases with the barrier to rotation. These findings agree qualitatively with some recent experiments on heterogeneously-surface particles and with studies of DLCA-type gels and gels of smooth spheres.

Colloidal networks of fat crystals

The following paper traces the development of the study of colloidal networks of fat crystals. The work starts with traditional pre-fractal particle network models of fat crystal networks. Due to its central importance in the study of colloidal networks of fat crystals (and other colloidal aggregates), a short exposition of fractal geometry is provided. The development of fractal aggregation models as well as models that describe the rheology of networks of these fractal aggregates is introduced. Later sections of the paper show the application of these aggregation and mechanical models specifically to fats. Finally, recent work in elucidating the nanostructural elements of fat crystal networks and aggregates of these nanostructures is provided.

Interfacial aggregation of Janus rods in binary polymer blends and their effect on phase separation

Janus particles interfacially self-assemble into different structures when incorporated into multiphase systems. Dissipative particle dynamics simulations are employed herein to investigate the interplay between aggregation mechanisms and phase separation in polymer blends. Shorter rods with a standing configuration become increasingly "caged" or trapped in larger aggregates as weight fraction increases, which is reflected in the way that their diffusion is coupled to their aggregation rates. Janus rods of higher aspect ratios that are tilted at the interface aggregate side-by-side and are able to hinder phase separation kinetics. This is due to a combination of individual Janus rod conformations at the interface, their intrinsic aggregation mechanisms, aggregate fractal dimension, and aggregation rates, and can also be traced back to the scaling of the diffusion coefficient of aggregates with their size. Findings presented provide insight into the mechanisms governing two dimensionally growing colloidal aggregates at fluid interfaces, more specifically, those associated with Janus particles, and shed light on the potential of these systems in paving the way for designing new functional materials.

Self-Assembly of Fibrinogen in Aqueous, Thrombin-Free Solutions of Variable Ionic Strengths

Fibrinogen not only forms fibrin networks if assisted by thrombin but also exhibits self-assembly in dilute aqueous solutions in the absence of thrombin. It could be shown that self-assembly can be triggered in a controlled way by diluting the ionic strength set to a value of 0.14 M NaCl in the starting solutions. The present work unravels the mechanism of this self-assembly process by means of a combination of time-resolved multiangle static and dynamic light scattering and atomic force microscopy. Analysis was carried out as a function of the ionic strength adjusted by the drop in ionic strength and at variable salt compositions at a given final ionic strength. Composition was varied by changing the ratio of NaCl and phosphate buffer. The self-assembly induced by the drop of the ionic strength depends on the final value. The lower the final ionic strength gets, the faster is the self-assembly process. The variation of the salt composition at a given ionic strength has only a marginal effect, which depends on the ionic strength. The self-assembly obeys a step-growth process, where any intermediate cluster can coalesce with any other cluster. Interpretation of the data with a kinetic model based on the approach of von Smoluchowski follows a diffusion-limited cluster aggregation at ionic strength values lower than 30 mM. At an ionic strength of 30 mM, the model has to take into account a size dependence of the rate constant, and at 60 mM a transition is observed to a reaction-limited cluster aggregation.

Protein-Nanoparticle Interactions: What Are the Protein-Corona Thickness and Organization?

Protein adsorption on a surface is generally evaluated in terms of the evolution of the proteins' structures and functions. However, when the surface is that of a nanoparticle, the protein corona formed around it possesses a particular supramolecular structure that gives a "biological identity" to the new object. Little is known about the actual shape of the protein corona. Here, the protein corona formed by the adsorption of model proteins (myoglobin and hemoglobin) on silica nanoparticles was studied. Small-angle neutron scattering and oxygenation studies were combined to assess both the structural and functional impacts of the adsorption on proteins. Large differences in the oxygenation properties could be found while no significant global shape changes were seen after adsorption. Moreover, the structural study showed that the adsorbed proteins form an organized yet discontinuous monolayer around the nanoparticles.

Deposition of protein-coated multi-walled carbon nanotubes on oxide surfaces and the retention in a silicon micromodel

The aggregation, deposition and porous retention of bovine serum albumin treated multi-walled carbon nanotubes (BSA-MWCNTs) are investigated using dynamic light scattering (DLS), quartz crystal microbalance with dissipation (QCM-D) and 2-dimensional silicon micromodel, respectively. The aggregation of BSA-MWCNTs is consistent with Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The critical coagulation concentration (CCC) is 175 mM NaCl and 2.7 mM CaCl₂, suggesting that Ca²⁺ causes stronger aggregation. The BSA-MWCNT deposition on SiO₂ surface is unfavorable with critical deposition concentration (CDC) of 100 mM in NaCl and 0.9 mM in CaCl₂. The deposition on the Al₂O₃ surface is favorable. Deposition rate is dominated by electrostatic forces at low ionic strength (IS), but electrostatic interaction is eliminated when IS is above CDC. Therefore the deposition rate on SiO₂ or Al₂O₃ surface starts decreasing at the CDC point due to the reduced particle diffusion. In micromodel, the amount and position of attached BSA-MWCNTs in pore space can be observed by a microscope. The retention attachment efficiency increases at higher IS. The suspended BSA-MWCNTs approach to the collector through either diffusion or interception. The attached BSA-MWCNTs narrow the pore space and then clog the pore throats. The straining process happens on the clogged pore throats.

Controlling Superstructure-Property Relationships via Critical Casimir Assembly of Quantum Dots

The assembly of colloidal quantum dots (QDs) into dense superstructures holds great promise for the development of novel optoelectronic devices. Several assembly techniques have been explored; however, achieving direct and precise control over the interparticle potential that controls the assembly has proven to be challenging. Here, we exploit the application of critical Casimir forces to drive the growth of QDs into superstructures. We show that the exquisite temperature-dependence of the critical Casimir potential offers new opportunities to control the assembly process and morphology of the resulting QD superstructures. The direct assembly control allows us to elucidate the relation between structural, optical, and conductive properties of the critical Casimir-grown QD superstructures. We find that the choice of the temperature setting the interparticle potential plays a central role in maximizing charge percolation across QD thin-films. These results open up new directions for controlling the assembly of nanostructures and their optoelectronic properties.

In-Solution Microscopic Imaging of Fractal Aggregates of a Stressed Therapeutic Antibody

Aggregates of therapeutic proteins that can contaminate drug products during manufacture is a growing concern for the pharmaceutical industry because the aggregates are potentially immunogenic. Electron microscopy is a typical, indispensable method for imaging nanometer- to micrometer-sized structures. Nevertheless, it is not ideal because it must be performed with ex situ monitoring under high-vacuum conditions, where the samples could be altered by staining and drying. Here, we introduce a scanning electron-assisted dielectric microscopy (SE-ADM) technique for in-solution imaging of monoclonal immunoglobulin G (IgG) aggregates without staining and drying. Remarkably, SE-ADM allowed assessment of the size and morphology of the IgG aggregates in solution by completely excluding drying-induced artifacts. SE-ADM was also beneficial to study IgG aggregation caused by temporary acid exposure followed by neutralization, pH-shift stress. A box-counting analysis of the SE-ADM images provided fractal dimensions of the larger aggregates, which complemented the fractal dimensions of the smaller aggregates measured by light scattering. The scale-free or self-similarity nature of the fractal aggregates indicated that a common mechanism for antibody aggregation existed between the smaller and larger aggregates. Consequently, SE-ADM is a useful method for characterizing protein aggregates to bridge the gaps that occur among conventional analytical methods, such as those related to in situ/ ex situ techniques or size/morphology assessments.

Multi-scale approach for modeling stability, aggregation, and network formation of nanoparticles suspended in aqueous solutions

Suspensions of nanoparticles (NPs) in aqueous solutions hold promise in many research fields, including energy applications, water desalination, and nanomedicine. The ability to tune NP interactions, and thereby to modulate the NP self-assembly process, holds the key to rationally synthesize NP suspensions. However, traditional models obtained by coupling the DLVO (Derjaguin, Landau, Verwey, and Overbeek) theory of NP interactions, or suitable modifications of it, with the kinetic theory of colloidal aggregation are inadequate to precisely model NP self-assembly because they neglect hydration forces and discrete-size effects predominant at the nanoscale. By synergistically blending molecular dynamics and stochastic dynamics simulations with continuum theories, we develop a multi-scale (MS) model, which is able to accurately predict suspension stability, timescales for NP aggregation, and macroscopic properties (e.g., the thermal conductivity) of bare and surfactant-coated NP suspensions, in good agreement with the experimental data. Our results enable the formulation of design rules for engineering NP aqueous suspensions in a wide range of applications.

The different ways to chitosan/hyaluronic acid nanoparticles: templated vs direct complexation. Influence of particle preparation on morphology, cell uptake and silencing efficiency

This study is about linking preparative processes of nanoparticles with the morphology of the nanoparticles and with their efficiency in delivering payloads intracellularly. The nanoparticles are composed of hyaluronic acid (HA) and chitosan; the former can address a nanoparticle to cell surface receptors such as CD44, the second allows both for entrapment of nucleic acids and for an endosomolytic activity that facilitates their liberation in the cytoplasm. Here, we have systematically compared nanoparticles prepared either A) through a two-step process based on intermediate (template) particles produced via ionotropic gelation of chitosan with triphosphate (TPP), which are then incubated with HA, or B) through direct polyelectrolyte complexation of chitosan and HA. Here we demonstrate that HA is capable to quantitatively replace TPP in the template process and significant aggregation takes place during the TPP-HA exchange. The templated chitosan/HA nanoparticles therefore have a mildly larger size (measured by dynamic light scattering alone or by field flow fractionation coupled to static or dynamic light scattering), and above all a higher aspect ratio (R _g/R _H) and a lower fractal dimension. We then compared the kinetics of uptake and the (antiluciferase) siRNA delivery performance in murine RAW 264.7 macrophages and in human HCT-116 colorectal tumor cells. The preparative method (and therefore the internal particle morphology) had little effect on the uptake kinetics and no statistically relevant influence on silencing (templated particles often showing a lower silencing). Cell-specific factors, on the contrary, overwhelmingly determined the efficacy of the carriers, with, e.g., those containing low-MW chitosan performing better in macrophages and those with high-MW chitosan in HCT-116.

Assembly of colloidal particles in solution

Advances in both top-down and bottom-up syntheses of a wide variety of complex colloidal building blocks and also in methods of controlling their assembly in solution have led to new and interesting forms of highly controlled soft matter. In particular, top-down lithographic methods of producing monodisperse colloids now provide precise human-designed control over their sub-particle features, opening up a wide range of new possibilities for assembly structures that had been previously limited by the range of shapes available through bottom-up methods. Moreover, an increasing level of control over anisotropic interactions between these colloidal building blocks, which can be tailored through local geometries of sub-particle features as well as site-specific surface modifications, is giving rise to new demonstrations of massively parallel off-chip self-assembly of specific target structures with low defect rates. In particular, new experimental realizations of hierarchical self-assembly and control over the chiral purity of resulting assembly structures have been achieved. Increasingly, shape-dependent, shape-complementary, and roughness-controlled depletion attractions between non-spherical colloids are being used in novel ways to create assemblies that go far beyond early examples, such as fractal clusters formed by diffusion-limited and reaction-limited aggregation of spheres. As self-assembly methods have progressed, a wide variety of advanced directed assembly methods have also been developed; approaches based on microfluidic control and applying structured electromagnetic fields are particularly promising.

Cage dynamics leads to double relaxation of the intermediate scattering function in a binary colloidal system

A system of binary colloids where one fraction of particles is aggregating by forming irreversible bonds and the other fraction of particles only interacts as hard spheres, is simulated using Brownian cluster dynamics. These aggregating species always formed percolating clusters for the case of diffusing hard spheres while for the static case, formation of percolating clusters depended on the fraction of static hard spheres in the system. The dynamics of the hard spheres inside the percolating clusters was studied by restarting the simulation after the kinetics of aggregation was arrested. Two cases were studied, one where the percolated particles moved within the bonds or cage dynamics was allowed and another where the movement within the bonds was not allowed or the cages were static. The hard spheres showed anomalous diffusion in both cases. The mean square displacement showed that for the case of dynamic cages we always had diffusive hard spheres irrespective of the fraction of hard spheres for volume fractions below 0.49. Static cages, depending on the fraction of hard spheres, showed either diffusive or arrested behavior of hard spheres. The intermediate scattering function of only the hard sphere particles showed double relaxation similar to the colloidal glass system for low volume fraction, where the fraction of hard sphere particles was small. For higher fractions we observed only a single stretched exponential. We could differentiate between slow and fast particles for both static and dynamic cages. For the case of static cages the hard spheres were permanently stuck inside the cages while for the case of dynamic cages almost all the hard spheres were moving in and out of the cages.