Packing Polydisperse Colloids into Crystals: When Charge-Dispersity Matters.

Monte Carlo simulations, fully constrained by experimental parameters, are found to agree well with a measured phase diagram of aqueous dispersions of nanoparticles with a moderate size polydispersity over a broad range of salt concentrations, c_{s}, and volume fractions, ϕ. Upon increasing ϕ, the colloids freeze first into coexisting compact solids then into a body centered cubic phase (bcc) before they melt into a glass forming liquid. The surprising stability of the bcc solid at high ϕ and c_{s} is explained by the interaction (charge) polydispersity and vibrational entropy.

Jellium and cell model for titratable colloids with continuous size distribution.

A good understanding and determination of colloidal interactions is paramount to comprehend and model the thermodynamic and structural properties of colloidal suspensions. In concentrated aqueous suspensions of colloids with a titratable surface charge, this determination is, however, complicated by the density dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addition, colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper, we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., [J. Chem. Phys. 128, 154906 (2008)] are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various commercially available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calculated. The importance of size and charge polydispersity as well as the validity of these two models is discussed in light of the results.

Mesocrystalline calcium silicate hydrate: A bioinspired route toward elastic concrete materials.

Calcium silicate hydrate (C-S-H) is the binder in concrete, the most used synthetic material in the world. The main weakness of concrete is the lack of elasticity and poor flexural strength considerably limiting its potential, making reinforcing steel constructions necessary. Although the properties of C-S-H could be significantly improved in organic hybrids, the full potential of this approach could not be reached because of the random C-S-H nanoplatelet structure. Taking inspiration from a sea urchin spine with highly ordered nanoparticles in the biomineral mesocrystal, we report a bioinspired route toward a C-S-H mesocrystal with highly aligned C-S-H nanoplatelets interspaced with a polymeric binder. A material with a bending strength similar to nacre is obtained, outperforming all C-S-H-based materials known to date. This strategy could greatly benefit future construction processes because fracture toughness and elasticity of brittle cementitious materials can be largely enhanced on the nanoscale.

Effective pair potential between charged nanoparticles at high volume fractions.

Simulations of charged colloidal dispersions are technically challenging. One possible workaround consists in reducing the system to the colloids only, whose interactions are described through an effective pair potential, wf. Still, the determination of wf is difficult mainly because it depends on the colloidal density, ϕ. Here we propose to calculate wf from simulations of a pair of colloids placed in a cubic box with periodic boundary conditions. The variation in ϕ is mimicked by an appropriate change in the concentration of counterions neutralized by an homogeneous background charge. The method is tested at the level of the primitive model. A good description of the structure of the colloidal dispersion is obtained in the low and high coupling regimes, even at high ϕ (≈30%). Furthermore, the method can easily be used in popular molecular simulation program packages and extended to non-spherical objects.

Elastic Response of Cementitious Gels to Polycation Addition.

The high compressive strength of cementitious materials stems from the creation of a percolated network of calcium silicate hydrate (C-S-H) nanoparticles glued together by strong Ca2+-Ca2+ correlation forces. Although strong, the ion correlation force is short range and yields poor elastic properties (elastic limit and resilience). Here, the use of polycations to partially replace Ca2+ counterions and enhance the resilience of cementitious materials is reported. Adsorption isotherms, electrophoretic mobility, as well as small angle X-ray scattering and dynamic rheometry measurements, are performed on C-S-H gels, used as nonreactive models of cementitious systems, in the presence of different linear and branched polycations for various electrostatic coupling, that is, surface charge densities (pH) and Ca2+ concentrations. The critical strain of the C-S-H gels was found to be improved by up to 1 order of magnitude as a result of bridging forces. At high electrostatic coupling (real cement conditions), only branched polycations are found to improve the deformation at the elastic limit. The results were corroborated by Monte Carlo simulations.

Structure and Yielding of Colloidal Silica Gels Varying the Range of Interparticle Interactions.

The relationship between interaction range, structure, fluid-gel transition, and viscoelastic properties of silica dispersions at intermediate volume fraction, Φv ≈ 0.1 and in alkaline conditions, pH = 9 was investigated. For this purpose, rheological, physicochemical, and structural (synchrotron-SAXS) analyses were combined. The range of interaction and the aggregation state of the dispersions were tuned by adding either divalent counterions (Ca(2+)) or polycounterions (PDDA). With increasing calcium chloride concentration, a progressive aggregation was observed which precludes a fluid-gel transition at above 75 mM of calcium chloride. In this case, the aggregation mechanism is driven by short-range ion-ion correlations. Upon addition of PDDA, a fluid-gel transition, at a much lower concentration, followed by a reentrant gel-fluid transition was observed. The gel formation with PDDA was induced by charge neutralization and longer range polymer bridging interactions. The refluidification at high PDDA concentrations was explained by the overcompensation of the charge of the silica particles and by the steric repulsions induced by the polycation chains. Rheological measurements on the so-obtained gels reveal broad yielding transition with two steps when the size of the silica particle clusters exceeds ≈0.5 µm.

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations.

We report small-angle x-ray scattering experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity, 14%; size, 8 nm). Over a range of volume fractions, the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB_{2}, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and it suggests routes for designing self-assembling colloidal crystals from the bottom up.

Interaction grand potential between calcium-silicate-hydrate nanoparticles at the molecular level.

Calcium-silicate-hydrate (or C-S-H), an inosilicate, is the major binding phase in cement pastes and concretes and a porous hydrated material made up of a percolated and dense network of crystalline nanoparticles of a mean apparent spherical diameter of ∼5 nm that are each stacks of multiple C-S-H layers. Interaction forces between these nanoparticles are at the origin of C-S-H chemical, physical, and mechanical properties at the meso- and macroscales. These particle interactions and the resulting properties may be affected significantly by nanoparticle density and environmental conditions such as the temperature, relative humidity, or concentration of chemical species in the bulk solution. In this study, we combined grand canonical Monte Carlo simulations and an extension of the mean force integration method to derive the pair potentials. This approach enables realistic simulation of the physical environment surrounding the C-S-H particles. We thus constructed the pair potentials for C-S-H nanoparticles of defined chemical stoichiometry at 10% relative humidity (RH), varying the relative crystallographic orientations at a constant particle density of ρpart ∼ 2.21 mmol L(-1). We found that cohesion between nanoparticles is affected strongly by both the aspect ratio and the crystallographic misorientation of interacting particles. This method and the findings underscore the importance of accounting for relative dimensions and orientation among C-S-H nanoparticles in descriptions of physical and simulated multiparticle aggregates or mesoscale systems.

Aggregation of Calcium Silicate Hydrate Nanoplatelets.

We study the aggregation of calcium silicate hydrate nanoplatelets on a surface by means of Monte Carlo and molecular dynamics simulations at thermodynamic equilibrium. Calcium silicate hydrate (C-S-H) is the main component formed in cement and is responsible for the strength of the material. The hydrate is formed in early cement paste and grows to form platelets on the nanoscale, which aggregate either on dissolving cement particles or on auxiliary particles. The general result is that the experimentally observed variations in these dynamic processes generically called growth can be rationalized from interaction free energies, that is, from pure thermodynamic arguments. We further show that the surface charge density of the particles determines the aggregate structures formed by C-S-H and thus their growth modes.

Long-ranged and soft interactions between charged colloidal particles induced by multivalent coions.

Forces between charged particles in aqueous solutions containing multivalent coions and monovalent counterions are studied by the colloidal probe technique. Here, the multivalent ions have the same charge as the particles, which must be contrasted to the frequently studied case where multivalent ions have the opposite sign as the substrate. In the present case, the forces remain repulsive and are dominated by the interactions of the double layers. The valence of the multivalent coion is found to have a profound influence on the shape of the force curve. While for monovalent coions the force profile is exponential down to separations of a few nanometers, the interaction is much softer and longer-ranged in the presence of multivalent coions. The force profiles in the presence of multivalent coions and in the mixtures of monovalent and multivalent coions can be accurately described by Poisson-Boltzmann theory. These results are accurate for different surfaces and even in the case of highly charged particles. This behavior can be explained by the fact that the force profile follows the near-field limit to much larger distances for multivalent coions than for monovalent ones. This limit corresponds to the conditions with no salt, where the coions are expelled between the two surfaces.

Stability of negatively charged platelets in calcium-rich anionic copolymer solutions.

Controlling the stability of anisotropic particles is key to the development of advanced materials. Here, we report an investigation, by means of mesoscale molecular dynamics simulations, of the stability and structural change of calcium-rich dispersions containing negatively charged nanoplatelets, neutralized by calcium counterions, in the presence of either comb copolymers composed of anionic backbones with attached neutral side chains or anionic-neutral linear block copolymers. In agreement with experimental observations, small stacks of platelets (tactoids) are formed, which are greatly stabilized in the presence of copolymers. In the absence of polymers, tactoids will grow and aggregate strongly due to large attractive Ca(2+)-Ca(2+) correlation forces. Unlike comb copolymers which only adsorb on the external surfaces, block copolymers are found to intercalate between the platelets. The present results show that the stabilization is the result of a free energy barrier induced by the excluded volume of hydrophilic chains, while the intercalation is due to bridging forces. More generally, the results shed new light on the recent finding of the first hybrid cementitious mesocrystal.

Identification of binding peptides on calcium silicate hydrate: a novel view on cement additives.

Phage display experiments on industrially important calcium silicate hydrates (C-S-H), the main hydration product of ordinary Portland cement, suggest fundamentally different specific binding motifs compared to hitherto existing commercial cement additives. According to that, a strong and specific adsorbing additive on C-S-H should have three features which are a negative charge, H-bond formers (especially amide functions) and a hydrophobic part.

Monte Carlo simulations of parallel charged platelets as an approach to tactoid formation in clay.

The free energy of interaction between parallel charged platelets with divalent counterions has been calculated using Monte Carlo simulations to investigate the electrostatic effects on aggregation. The platelets are primarily intended to represent clay particles. With divalent counterions, the free energy for two platelets or two tactoids (clusters of parallel platelets) shows a minimum at a short separation due to the attraction caused by ion-ion correlations. In a salt-free system, the free energy of interaction has a long-range repulsive tail beyond the minimum. The repulsion increases for tactoids with larger aggregation numbers, whereas the depth of the free-energy minimum is gradually reduced. For large enough aggregation numbers, the repulsion is dominating and the minimum is no longer a global free-energy minimum. This is an effect of the depletion of counterions free in solution (outside tactoids) as counterions and platelets aggregate into tactoids and the resulting redistribution of counterions in the system changes the effective interactions between platelets and tactoids. The difference in tactoid-tactoid interactions as a function of aggregation number can be removed by adding enough salt to mask the depletion. Adding salt also reduces the repulsive tail of the free energy of interaction and enhances the minimum. No dependence on the aggregation number suggests that an isodesmic model with a monotonically decaying distribution of aggregation numbers can be used to describe a clay system. This may help to explain the experimental observations of low average numbers of platelets in tactoids, although factors not included in the simulation model may also play an important role.

On the origin of the halo stabilization.

Monte Carlo simulations show that charge-regulation alone can cause highly charged zirconium nanoparticles to adsorb to a similarly charged or neutral silica particle and thereby stabilizing the latter. This mechanism, referred to as halo stabilization, is quite general and applicable in a range of systems provided that pH, van der Waals forces, and dissociation constants of the charge-regulating particles are properly chosen. In our modeling we see an overall attraction at low volume fractions of nanoparticles, while at higher a repulsive barrier is created, stabilizing the microparticles and protecting them from aggregation. The charge-regulation mechanism also turns the silica surface from positively charged, without nanoparticles, to negatively charged in the presence of nanoparticles.

Coarse-graining intermolecular interactions in dispersions of highly charged colloids.

Effective pair potentials between charged colloids, obtained from Monte Carlo simulations of two single colloids in a closed cell at the primitive model level, are shown to reproduce accurately the structure of aqueous salt-free colloidal dispersions, as determined from full primitive model simulations by Linse et al. (Linse, P.; Lobaskin, V. Electrostatic Attraction and Phase Separation in Solutions of Like-Charged Colloidal Particles. Phys. Rev. Lett.1999, 83, 4208). Excellent agreement is obtained even when ion-ion correlations are important and is in principle not limited to spherical particles, providing a potential route to coarse-grained colloidal interactions in more complex systems.

Liquid Crystal Phases in Suspensions of Charged Plate-Like Particles.

Anisotropic interactions in colloidal suspensions have recently emerged as a route for the design of new soft materials. Nonisotropic particles can form nematic, smectic, hexatic, and columnar liquid crystals. Although the formation of these phases is well rationalized when excluded volume is solely at play, the role of electrostatic interactions still remains unclear and even less so when particles present a charge heterogeneity, for example, clays. Here, we use Monte Carlo simulations of concentrated suspensions of charged disk-like particles to reveal the role of Coulomb interactions and charge anisotropy underlying liquid crystal formation and structures. We observe a vast zoo of exotic structures, going from hexatic to columnar phases, which are shown to be controlled by the charge anisotropy. The particle volume fraction at which these phases start to form is found to decrease with increasing Coulomb interactions and charge anisotropy, which suggests a route to tune the structure of aqueous liquid crystals.

Calcium mediated polyelectrolyte adsorption on like-charged surfaces.

Monte Carlo simulations within the primitive model of calcium-mediated adsorption of linear and comb polyelectrolytes onto like-charged surfaces are described, focusing on the effect of calcium and polyion concentrations as well as on the ion pairing between polymers and calcium ions. We use a combination of Monte Carlo simulations and experimental data from titration and calcium binding to quantify the ion pairing. The polymer adsorption is shown to occur as a result of surface overcharging by Ca(2+) and ion pairing between charged monomers and Ca(2+). In agreement with experimental observations, the simulations predict that the polymer adsorption isotherm goes through a maximum as the calcium or the polymer concentration is increased. The non-Langmuir isotherms are rationalized in terms of charge-charge correlations.

Adsorption of monovalent and divalent cations on planar water-silica interfaces studied by optical reflectivity and Monte Carlo simulations.

Adsorption on planar silica substrates of various monovalent and divalent cations from aqueous solution is studied by optical reflectivity. The adsorbed amount is extracted by means of a thin slab model. The experimental data are compared with grand canonical Monte Carlo titration simulations at the primitive model level. The surface excess of charge due to adsorbed cations is found to increase with pH and salt concentration as a result of the progressive dissociation of silanol groups. The simulations predict, in agreement with experiments, that the surface excess of charge from divalent ions is much larger than from monovalent ions. Ion-ion correlations explain quantitatively the enhancement of surface ionization by multivalent cations. On the other hand, the combination of experimental and simulation results strongly suggests the existence of a second ionizable site in the acidic region. Variation of the distance of closest approach between the ions and surface sites captures ion specificity of water-silica interfaces in an approximate fashion.

Ettringite surface chemistry: Interplay of electrostatic and ion specificity.

This paper presents a detailed experimental study combined with Monte Carlo (MC) simulations within the primitive model of the physical chemistry at the ettringite-water interface over a wide range of pH and bulk conditions for which ettringite exists thanks to its solubility in aqueous solutions. Ettringite, which is an important phase in hydrated cement-based systems, bears a permanent and positive structural charge. In contrast with previous studies, electrokinetic measurements together with the careful chemical analysis of the equilibrium solutions of the dispersions have brought strong support to designate sulfate as being the ion determining the potential. Simulations showed that electrostatics, through ion-ion correlations, are not strong enough to explain the charge reversal of ettringite immersed in sulfate salt solutions. However, an excellent agreement between simulated and experimental data was obtained including a short-range nonelectrostatic adsorption potential for the sulfate ion. This result strongly suggests the existence of a chemical specificity of sulfate ions for an ettringite surface.

Acid-base properties of 2:1 clays. I. Modeling the role of electrostatics.

We present a theoretical investigation of the titratable charge of clays with various structural charge (sigma(b)): pyrophyllite (sigma(b) = 0 e x nm(-2)), montmorillonite (sigma(b) = -0.7 e x nm(-2)) and illite (sigma(b) = -1.2 e x nm(-2)). The calculations were carried out using a Monte Carlo method in the Grand Canonical ensemble and in the framework of the primitive model. The clay particle was modeled as a perfect hexagonal platelet, with an "ideal" crystal structure. The only fitting parameters used are the intrinsic equilibrium constants (pK(0)) for the protonation/deprotonation reactions of the broken-bond sites on the lateral faces of the clay particles, silanol, =SiO(-) + H(+) --> =SiOH, and aluminol, =AlO(-1/2) + H(+) --> =AlOH(+1/2). Simulations are found to give a satisfactory description of the acid-base titration of montmorillonite without any additional fitting parameter. In particular, combining the electrostatics from the crystal substitutions with ionization constants, the simulations satisfactorily catch the shift in the titration curve of montmorillonite according to the ionic strength. Change in the ionic strength modulates the screening of the electrostatic interactions which results in this shift. Accordingly, the PZNPC is found to shift toward alkaline pH upon increasing the permanent basal charge. Unlike previous mean field model results, a significant decrease in PZNPC values is predicted in response to stack formation. Finally, the mean field approach is shown to be inappropriate to study the acid-base properties of clays.