The crystallization of proteins or colloids is often hindered by the appearance of aggregates of low fractal dimension called gels. Here we study the effect of electrostatics upon crystal and gel formation using an analytic model of hard spheres bearing point charges and short range attractive interactions. We find that the chief electrostatic free energy cost of forming assemblies comes from the entropic loss of counterions that render assemblies charge-neutral. Because there exists more accessible volume for these counterions around an open gel than a dense crystal, there exists an electrostatic entropic driving force favoring the gel over the crystal. This driving force increases with increasing sphere charge, but can be counteracted by increasing counterion concentration. We show that these effects cannot be fully captured by pairwise-additive macroion interactions of the kind often used in simulations, and we show where on the phase diagram to go in order to suppress gel formation.
Tuning the chain-end functionality of a short-chain cationic homopolymer, owing to the nature of the initiator used in the ATRP polymerisation step, can be used to mediate the formation of a gel of this poly(electrolyte) in water. While a neutral end group gives a solution of low viscosity, a highly homogeneous gel is obtained with a phosphonate anionic moiety, as characterized by rheometry and diffusion NMR. This novel type of supramolecular control over poly(electrolytic) gel formation could find potential use in a variety of applications in the field of electroactive materials.
We study colloidal gels formed by competing electrostatic repulsion and short-range attraction by means of extensive numerical simulations under external shear. We show that, upon varying the repulsion strength, the gel structure and its viscoelastic properties can be largely tuned. In particular, the gel fractal dimension can be either increased or decreased with respect to mechanical equilibrium conditions. Unexpectedly, gels with stronger repulsion, despite being mechanically stiffer, are found to be less viscous with respect to purely attractive ones. We provide a microscopic explanation o…
A comprehensive theory encompassing the kinetics of sol-to-gel transition is yet to be formulated due to break-down of the mean-field Smoluchowski Equation. Using high temporal-resolution Monte Carlo simulation of irreversible aggregation systems, we show that this transition has three distinct regimes with kinetic exponent z ranging between 1 and 2, corresponding to aggregation of sol clusters proceeding to the ideal gel point (IGP); z ranging between 2 and 5.7 for gelation of sol clusters beyond IGP; and z ranging between 2 and 3.5 for a hitherto unidentified regime involving aggregation of …
The possibility for proteins to aggregate in different superstructures, i.e. large-scale polymorphism, has been widely observed, but an understanding of the physico-chemical mechanisms behind it is still out of reach. Here we present a theoretical model for the description of a generic aggregate formed from an ensemble of charged proteins. The model predicts the formation of multi-fractal structures with the geometry of the growth determined by the electrostatic interactions between single proteins. The model predictions are successfully verified in comparison with experimental curves for aggr…
Neutral grains made of the same dielectric material can attain considerable charges due to collisions and generate long-range interactions. We perform molecular dynamic simulations in three dimensions for a dilute, freely-cooling granular gas of viscoelastic particles that exchange charges during collisions. As compared to the case of clustering of viscoelastic particles solely due to dissipation, we find that the electrostatic interactions due to collisional charging alter the characteristic size, morphology and growth rate of the clusters. The average cluster size grows with time as a power …
Electrostatic interactions provide a convenient way to modulate interactions between nanoparticles, colloids, and biomolecules because they can be adjusted by the solution pH or salt concentration. While the presence of salt provides an easy method to control the net interparticle interaction, the nonlinearities arising from electrostatic screening make it difficult to quantify the strength of the interaction. In particular, when charged particles assemble into clusters or aggregates, nonlinear effects render the interactions strongly non-pairwise. Here we report Brownian dynamics simulations …
We report molecular dynamics simulations of a gel-forming mixture of ellipsoidal patchy particles with different functionality. We show that in this model, which disfavors the formation of bond-loops, elapsed time during irreversible aggregation -- leading to the formation of an extended network -- can be formally correlated with equilibrium temperature in reversible aggregation. We also show that it is possible to develop a parameter-free description of the self-assembly kinetics, bringing reversible and irreversible aggregation of loopless branched systems to the same level of understanding …
Using molecular dynamics simulations, the kinetics of bundle formation for stiff polyelectrolytes such as actin is studied in the solution of multivalent salt. The dominant kinetic mode of aggregation is found to be the case of one end of one rod meeting others at right angle due to electrostatic interactions. The kinetic pathway to bundle formation involves a hierarchical structure of small clusters forming initially and then feeding into larger clusters, which is reminiscent of the flocculation dynamics of colloids. For the first few cluster sizes, the Smoluchowski formula for the time evolu…
Industrial as well as natural aggregation of fine particles is believed to be associated with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we analyze conditions necessary to hold aggregates together with electrostatic forces. We find that aggregates of particles charged with the same sign can be held together due to dielectric polarization, we evaluate the effect of aggregate size, and we briefly summarize consequences for practical aggregation.
The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas -- a model representative of the above physical processes -- have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases tha…
We report the formation of stable nanoparticle-polymer clusters obtained by electrostatic complexation. The nanoparticles placed under scrutiny are nanoceria (CeO2) coated by short poly(acrylic acid) moieties, whereas the polymers are cationic-neutral block copolymers. The cluster formation was monitored using different formulation pathways, including direct mixing, dialysis, dilution and quenching. In the first process, the hybrids were obtained by mixing stock solutions of polymers and nanoparticles. Dialysis and dilution were based on controlled desalting kinetics according to methods devel…
Polymer chains adsorbed onto oppositely charged spherical 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 kinetically stable aggregates can form which display several unexpected and interesting peculiarities and some intriguing biotechnological implications. The attractive interaction contribution between two oppositely particles arises from the correlated adsorption of polyions at the oppositely charged particle surface…
Impact of Initial Charge Distributions on the Kinetics of Charged Particle Coagulation
Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins（奥希金斯大学工程科学研究所）；Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile（智利大学物理与数学科学学院物理系）
Hypotheses: To correctly predict the aggregation number and size of wormlike micelles from ionic surfactants, the molecular-thermodynamic theory has to calculate the free energy per molecule in the micelle with accuracy better than 0.01 kT, which is a serious challenge. The problem could be solved if the effects of mutual confinement of micelle counterion atmospheres, as well as the effects of counterion binding, surface curvature and ionic interactions in the electric double layer (EDL), are accurately described. Theory: The electric field is calculated using an appropriate cell model, which …
In this article, we demonstrate a method for inducing reversible crystal-to-crystal transitions in binary mixtures of soft colloidal particles. Through a controlled decrease of salinity and increasingly dominating electrostatic interactions, a single sample is shown to reversibly organize into entropic crystals, electrostatic attraction-dominated crystals or aggregated gels, which we quantify using microscopy and image analysis. We furthermore analyze crystalline structures with bond order analysis to discern between two crystal phases. We observe the different phases using a sample holder geo…
Molecular dynamics (MD) simulation has been employed to study the nonequilibrium structure formation of two types of particles in a colloidal suspension, driven by type-dependent forces. We examined the time evolution of structure formation as well as the structural properties of the resulting aggregation by studying the radial distribution function (RDF). The resulting aggregation is well described by a binary colloidal gelation. We compared the structural properties to those for one type of particles. From the MD results, it is evident that there are significant differences between the RDF's…
The impact of nanomaterials on lung fluids or on the plasma membrane of living cells has prompted researchers to examine the interactions between nanoparticles and lipid vesicles. Recent studies have shown that nanoparticle-lipid interaction leads to a broad range of structures including supported lipid bilayers (SLB), particles adsorbed at the surface or internalized inside vesicles, and mixed aggregates. Today, there is a need to have simple protocols that can readily assess the nature of structures obtained from particles and vesicles. Here we apply the method of continuous variation for me…
The aggregation of clay particles in aqueous solution is a ubiquitous everyday process of broad environmental and technological importance. However, it is poorly understood at the all-important atomistic level since it depends on a complex and dynamic interplay of solvent-mediated electrostatic, hydrogen-bonding, and dispersion interactions. With this in mind we have performed an extensive set of classical molecular dynamics simulations (included enhanced sampling simulations) on the interactions between model kaolinite nanoparticles in pure and salty water. Our simulations reveal highly aniso…
Electrostatic interactions play an important role in numerous self-assembly phenomena, including colloidal aggregation. Although colloids typically have a dielectric constant that differs from the surrounding solvent, the effective interactions that arise from inhomogeneous polarization charge distributions are generally neglected in theoretical and computational studies. We introduce an efficient technique to resolve polarization charges in dynamical dielectric geometries, and demonstrate that dielectric effects \emph{qualitatively} alter the predicted self-assembled structures, with surprisi…
