Phase separation and percolation of reversibly aggregating spheres with a square-well attraction potential

Breaking the size constraint for nano cages using annular patchy particles

Engineering structures like nanocages, shells, and containers, by self-assembly of colloids is a challenging problem. One of the main challenges is to define the shape of the individual subunits to control the radius of the closed shell structures. In this work, we have proposed a simple model for the subunit, which comprises a spheroidal or spherical hardcore decorated with an annular patch. The self-assembly of these building blocks leads to the formation of monodispersed spherical cages (close shells) or containers (curved clusters). For a spheroid with a given bonding range, the curvature of the shell is analytically related to only the patch angle of the building blocks and independent of the shape of the subunits. This model with only one control parameter can be used to engineer cages with the desired radius, which also have been verified using thermodynamic calculations. In the phase diagram of the system, 4 phases are identified which includes gas, closed shell, partially closed (containers) shell and percolated structures. When the diameters of the spherical cages formed are small, we observe an icosahedral symmetry similar to virus capsids. We also observed that the kinetics of the cage formation is very similar to the nucleation and growth kinetics of viruses and is the key factor in determining the yield of closed shells.

Brownian dynamics simulations of hard rods in external fields and with contact interactions

We propose a simulation method for Brownian dynamics of hard rods in one dimension for arbitrary continuous external force fields. It is an event-driven procedure based on the fragmentation and mergers of clusters formed by particles in contact. It allows one to treat particle interactions in addition to the hard-sphere exclusion as long as the corresponding interaction forces are continuous functions of the particle coordinates. We furthermore develop a treatment of sticky hard spheres as described by Baxter's contact interaction potential.

Phase diagram of two-patch colloids with competing anisotropic and isotropic interactions

Patchy particles are considered to be a good model for protein aggregation. We propose a novel method to generate different structures of glucose isomerase protein such as chains, crystals and bundles by utilising aggregation of two-patch colloidal particles in presence of competing isotropic and anisotropic potential. We calculate the equilibrium phase diagram of two-patch colloidal particles and demonstrates the coexistence of different phases like disordered clusters, chains, crystals and bundles depending on the relative strength of isotropic and anisotropic potential. We also show that the formation of network of bundles is metastable against the formation of thermodynamically favored finite sized bundles along with thermodynamically stable crystals. These bundles appear to be helical in structure similar to that observed in sickle cell hemoglobin. The simulation results show that the method can characterize phase behaviour of glucose isomerase protein, which provides a novel tool to unveil self-assembly mechanism of protein under different conditions.

Mobile obstacles accelerate and inhibit the bundle formation in two-patch colloidal particle

Aggregation of protein into bundles is responsible for many neurodegenerative diseases. In this work, we show how two-patch colloidal particles self-assemble into chains and a sudden transition to bundles takes place by tuning the patch size and solvent condition. We study the kinetics of formation of chains, bundles, and networklike structures using patchy Brownian cluster dynamics. We also analyze the ways to inhibit and accelerate the formation of these bundles. We show that in the presence of inert immobile obstacles, the kinetics of formation of bundles slows down. However, in the presence of mobile aggregating particles, which exhibit interspecies hard sphere repulsion and intraspecies attraction, the kinetics of bundle formation accelerates slightly. We also show that if we introduce mobile obstacles, which exhibit interspecies attraction and intraspecies hard sphere repulsion, the kinetics of formation of bundles is inhibited. This is similar to the inhibitory effect of peptide P4 on the formation of insulin fibers. We are providing a model of mobile obstacles undergoing directional interactions to inhibit the formation of bundles.

Gelation of food protein-protein mixtures

Gelation of proteins is one of the principal means to give desirable texture to food products. Gelation of individual proteins in aqueous solution has been investigated intensively in the past, but in most food products the system contains mixtures of different types of proteins. Therefore one needs to consider interaction between different proteins both before and during gelation. Most food proteins can be classified as globular proteins, but casein and gelatin are also important food proteins. In this review the focus is on gelation induced by heating or cooling, which is the most commonly used method. After briefly discussing general features of protein aggregation and gelation, the literature on gelation of mixtures of different types of globular proteins is reviewed as well as that of mixtures of globular proteins with gelatin or with casein. The effect on the gel stiffness and the microstructure of the gelled mixtures will be discussed in terms of different scenarios that can be envisaged: independent aggregation and gelation, co-aggregation and phase separation.

Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules

In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern–Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined three different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have also studied the bond angle distribution for this system, where for small patches only two angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.

Lattice animals in diffusion limited binary colloidal system

In a soft matter system, controlling the structure of the amorphous materials has been a key challenge. In this work, we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical gels. Irreversible aggregation of binary colloidal particles leads to the formation of a percolating cluster of one species or both species which are also called bigels. Before the formation of the percolating cluster, the system forms a self-similar structure defined by a fractal dimension. For a one component system when the volume fraction is very small, the clusters are far apart from each other and the system has a fractal dimension of 1.8. Contrary to this, we will show that for the binary system, we observe the presence of lattice animals which has a fractal dimension of 2 irrespective of the volume fraction. When the clusters start inter-penetrating, we observe a fractal dimension of 2.5, which is the same as in the case of the one component system. We were also able to predict the formation of bigels using a simple inequality relation. We have also shown that the growth of clusters follows the kinetic equations introduced by Smoluchowski for diffusion limited cluster aggregation. We will also show that the chemical distance of a cluster in the flocculation regime will follow the same scaling law as predicted for the lattice animals. Further, we will also show that irreversible binary aggregation comes under the universality class of the percolation theory.

Phase behaviour in complementary DNA-coated gold nanoparticles and fd-viruses mixtures: a numerical study

A new gel-forming colloidal system based on a binary mixture of fd-viruses and gold nanoparticles functionalized with complementary DNA single strands has been recently introduced. Upon quenching below the DNA melt temperature, such a system results in a highly porous gel state, that may be developed in a new functional material of tunable porosity. In order to shed light on the gelation mechanism, we introduce a model closely mimicking the experimental one and we explore via Monte Carlo simulations its equilibrium phase diagram. Specifically, we model the system as a binary mixture of hard rods and hard spheres mutually interacting via a short-range square-well attractive potential. In the experimental conditions, we find evidence of a phase separation occurring either via nucleation-and-growth or via spinodal decomposition. The spinodal decomposition leads to the formation of small clusters of bonded rods and spheres whose further diffusion and aggregation leads to the formation of a percolating network in the system. Our results are consistent with the hypothesis that the mixture of DNA-coated fd-viruses and gold nanoparticles undergoes a non-equilibrium gelation via an arrested spinodal decomposition mechanism.

Range effect on percolation threshold and structural properties for short-range attractive spheres

Percolation or aggregation in colloidal system is important in many fields of science and technology. Using molecular dynamics simulations, we study the percolation behavior for systems consisting of spheres interacting with short-range square-well (SRSW) which mimic colloidal particles, with different interaction ranges. We specifically focus on how the interaction range affects the percolation thresholds in the supercritical region. We find that the contact percolation boundaries are strongly dependent on the interaction ranges of SRSW, especially away from the liquid-liquid critical point. However, varying the interaction ranges of SRSW does not affect much the structure along percolation boundaries especially for low packing fractions. For instance, along the percolation boundary, distributions of coordination number show convergence, and distributions of cluster size are universal for different interaction ranges considered. In addition, either the bond percolation boundaries or isolines of average bond coordination number collapse to those for Baxter sticky model on phase diagram, which confirms the extended law of corresponding states.

Brownian cluster dynamics with short range patchy interactions: its application to polymers and step-growth polymerization

We present a novel simulation technique derived from Brownian cluster dynamics used so far to study the isotropic colloidal aggregation. It now implements the classical Kern-Frenkel potential to describe patchy interactions between particles. This technique gives access to static properties, dynamics and kinetics of the system, even far from the equilibrium. Particle thermal motions are modeled using billions of independent small random translations and rotations, constrained by the excluded volume and the connectivity. This algorithm, applied to a single polymer chain leads to correct static and dynamic properties, in the framework where hydrodynamic interactions are ignored. By varying patch angles, various local chain flexibilities can be obtained. We have used this new algorithm to model step-growth polymerization under various solvent qualities. The polymerization reaction is modeled by an irreversible aggregation between patches while an isotropic finite square-well potential is superimposed to mimic the solvent quality. In bad solvent conditions, a competition between a phase separation (due to the isotropic interaction) and polymerization (due to patches) occurs. Surprisingly, an arrested network with a very peculiar structure appears. It is made of strands and nodes. Strands gather few stretched chains that dip into entangled globular nodes. These nodes act as reticulation points between the strands. The system is kinetically driven and we observe a trapped arrested structure. That demonstrates one of the strengths of this new simulation technique. It can give valuable insights about mechanisms that could be involved in the formation of stranded gels.

A new measure of molecular attractions between nanoparticles near kT adhesion energy

The weak molecular attractions of nanoparticles are important because they drive self-assembly mechanisms, allow processing in dispersions e.g. of pigments, catalysts or device structures, influence disease through the attraction of viruses to cells and also cause potential toxic effects through nanoparticle interference with biomolecules and organs. The problem is to understand these small forces which pull nanoparticles into intimate contact; forces which are comparable with 3kT/2z the thermal impact force experienced by an average Brownian particle hitting a linear repulsive potential of range z. Here we describe a new method for measuring the atomic attractions of nanoparticles based on the observation of aggregates produced by these small forces. The method is based on the tracking of individual monosize nanoparticles whose diameter can be calculated from the Stokes-Einstein analysis of the tracks in aqueous suspensions. Then the doublet aggregates are distinguished because they move slower and are also very much brighter than the dispersed nanoparticles. By finding the ratio of doublets to singlets, the adhesive energy between the particles can be calculated from known statistical thermodynamic theory using assumptions about the shape of the interaction potential. In this way, very small adhesion energies of 2kT have been measured, smaller than those seen previously by atomic force microscopy (AFM) and scanning tunneling microscopy (STM).

Kinetic arrest in polyion-induced inhomogeneously charged colloidal particle aggregation

Polymer chains adsorbed onto oppositely charged colloidal particles can significantly modify the particle-particle interactions. For sufficient amounts of added polymers, the original electrostatic repulsion can even turn into an effective attraction and relatively large aggregates can form. The attractive interaction contribution between two particles arises from the correlated adsorption of polyions at the oppositely charged particle surfaces, resulting in a non-homogeneous surface charge distribution. Here, we investigate the aggregation kinetics of polyion-induced colloidal complexes through Monte Carlo simulation, in which the effect of charge anisotropy is taken into account by a DLVO-like inter-particle potential, as recently proposed by Velegol and Thwar (Langmuir 17, 7687 (2001)). The results reveal that the aggregation process slows down due to the progressive increase of the potential barrier height upon clustering. Within this framework, the experimentally observed cluster phases in polyelectrolyte-liposome solutions can be interpreted as a kinetic arrested state.

Temperature dependence of the colloidal agglomeration inhibition: computer simulation study

There exist experimental evidences that the structure and extension of colloidal aggregates in suspensions change dramatically with temperature. This results in an associated change in the suspension rheology. Experimental studies of the inhibitor applications to control the particle clustering have revealed some unexpected tendencies. Namely, the heating of colloidal suspensions has provoked either extension or reduction of the colloidal aggregates. To elucidate the origin of this behavior, we investigate the influence of temperature on the stabilizing effect of the inhibitor, applying an associative two-component fluid model. Our results of the canonical Monte Carlo simulations indicate that the anomalous effect of the temperature may not be necessarily explained by the temperature dependent changes in the inhibitor tail conformation, as has been suggested recently by Won et al. [Langmuir 21, 924 (2005)]. We show that the competition between colloid-colloid and colloid-inhibitor associations, which, in turn, depends on the temperature and the relative concentrations, may be one of the main reasons for the unexpected temperature dependence of inhibitor efficacy.

Self-diffusion of reversibly aggregating spheres

Reversible diffusion limited cluster aggregation of hard spheres with rigid bonds was simulated and the self-diffusion coefficient was determined for equilibrated systems. The effect of increasing attraction strength was determined for systems at different volume fractions and different interaction ranges. It was found that the slowing down of the diffusion coefficient due to crowding is decoupled from that due to cluster formation. The diffusion coefficient could be calculated from the cluster size distribution and became zero only at infinite attraction strength when permanent gels are formed. It is concluded that so-called attractive glasses are not formed at finite interaction strength.

Linking Phase Behavior and Reversible Colloidal Aggregation at Low Concentrations: Simulations and Stochastic Mean Field Theory

We have studied the link between the kinetics of clustering and the phase behavior of dilute colloids with short range attractions of moderate strength. This was done by means of computer simulations and a theoretical kinetic model originally developed to deal with reversible colloidal aggregation. Three different regions of the phase diagram were accessed. For weak attractions, a gas phase of small clusters in equilibrium forms in the system. For intermediate attractions, the system undergoes liquid-gas separation, which is signatured by the formation of a few large droplike aggregates, a gas phase of small clusters, and an overall kinetics where a few seeds succeed in explosively growing at long times, after a lag time. Finally, for very strong attractions, fractal unbreakable clusters form and grow following DLCA-like (diffusion limited cluster aggregation) kinetics; liquid-gas separation is prevented by the strength of the bonds, which do not allow restructuration. Good qualitative and quantitative agreement is found between the dynamic simulations and the kinetic model in all the three regions.