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.

Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers.

We develop a theoretical model to describe structural effects on a specific system of charged colloidal polystyrene particles, upon the addition of non-adsorbing PEG polymers. This system has previously been investigated experimentally, by scattering methods, so we are able to quantitatively compare predicted structure factors with corresponding experimental data. Our aim is to construct a model that is coarse-grained enough to be computationally manageable, yet detailed enough to capture the important physics. To this end, we utilize classical polymer density functional theory, wherein all possible polymer configurations are accounted for, subject to a mean-field Boltzmann weight. We make efforts to counteract drawbacks with this mean-field approach, resulting in structural predictions that agree very well with computationally more demanding simulations. Electrostatic interactions are handled at the fully non-linear Poisson-Boltzmann level, and we demonstrate that a linearization leads to less accurate predictions. The particle charge is an experimentally unknown parameter. We define the surface charge such that the experimental and theoretical gel point at equal polymer concentration coincide. Assuming a fixed surface charge for a certain salt concentration, we find very good agreements between measured and predicted structure factors across a wide range of polymer concentrations. We also present predictions for other structural quantities, such as radial distribution functions, and cluster size distributions. Finally, we demonstrate that our model predicts the occurrence of equilibrium clusters at high polymer concentrations, but low particle volume fractions and salt levels.

Fused coarse-grained model of aromatic ionic liquids and their behaviour at electrodes.

A fused coarse-grained model of aromatic ionic liquids 1-alkyl-3-methylimidazoliums tetrafluoroborate ([CnMIM(+)][BF4(-)]) has been constructed. Structural and dynamical properties calculated from our model are compared with experimental data as well as with corresponding results from simulations of other suggested models. Specifically, we adopt a fused-sphere coarse-grained model for cations and anions. This model is utilized to study structure and differential capacitance in models of flat and porous carbon electrodes. We find that the capacitance varies with pore size, in a manner that is related to the packing of ions inside the pore. For very narrow pores, diffusion is slow and the establishment of thermodynamic equilibrium may exceed the practical limits for our molecular dynamics simulations.

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.

Classical density functional theory & simulations on a coarse-grained model of aromatic ionic liquids.

A new classical density functional approach is developed to accurately treat a coarse-grained model of room temperature aromatic ionic liquids. Our major innovation is the introduction of charge-charge correlations, which are treated in a simple phenomenological way. We test this theory on a generic coarse-grained model for aromatic RTILs with oligomeric forms for both cations and anions, approximating 1-alkyl-3-methyl imidazoliums and BF4⁻, respectively. We find that predictions by the new density functional theory for fluid structures at charged surfaces are very accurate, as compared with molecular dynamics simulations, across a range of surface charge densities and lengths of the alkyl chain. Predictions of interactions between charged surfaces are also presented.

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.

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.

Simulations of surface forces in polyelectrolyte solutions.

We have simulated interactions between charged surfaces in the presence of oppositely charged polyelectrolytes by coupling perturbations in the isotension ensemble to a free energy variance minimization scheme. For polymeric systems, this method completely outperforms configurationally biased versions of grand canonical simulations. Proper diffusive equilibrium between bulk and slit has been established for polyelectrolytes with up to 60 monomers per chain. A consequence of imposing diffusive equilibrium conditions, in contrast to previous more restricted models, is the possibility of surface charge inversion; ion-ion correlation and the cooperativity of monomer adsorption drive the formation of a polyion layer close to the surface, that overcompensates the nominal surface charge. This is observed even at modest surface charge densities, and leads to a build up of a long ranged electrostatic barrier. In addition, the onset of charge inversion requires very low bulk polymer densities. Due to screening effects, this leads to a higher and more long-ranged free energy barrier at low, compared to high, bulk densities. Oscillatory forces, reminiscent of those found in simple hard sphere systems, are resolved in the high concentration regime. As a consequence of a second surface charge inversion, the system "stratifies" to form a stable polyelectrolyte layer in the central part of the slit, stabilized by the adsorbed surface layers.

Simulating equilibrium surface forces in polymer solutions using a canonical grid method.

A new simulation method for nonuniform polymer solutions between planar surfaces at full chemical equilibrium is described. The technique uses a grid of points in a two-dimensional thermodynamic space, labeled by surface area and surface separations. Free energy differences between these points are determined via Bennett's optimized rates method in the canonical ensemble. Subsequently, loci of constant chemical potential are determined within the grid via simple numerical interpolation. In this way, a series of free energy versus separation curves are determined for a number of different chemical potentials. The method is applied to the case of hard sphere polymers between attractive surfaces, and its veracity is confirmed via comparisons with established alternative simulation techniques, namely, the grand canonical ensemble and isotension ensemble methods. The former method is shown to fail when the degree of polymerization is too large. An interesting interplay between repulsive steric interactions and attractive bridging forces occurs as the surface attraction and bulk monomer density are varied. This behavior is further explored using polymer density functional theory, which is shown to be in good agreement with the simulations. Our results are also discussed in light of recent self-consistent field calculations which correct the original deGennes results for infinitely long polymers. In particular, we look at the role of chain ends by investigating the behavior of ring polymers.

Simulations and density functional calculations of surface forces in the presence of semiflexible polymers.

We simulate interactions between adsorbing and nonadsorbing surfaces immersed in solutions containing monodisperse semiflexible chains. Apart from the nature of the surfaces, we investigate responses to changes of the intrinsic chain stiffness, the degree of polymerization, and the bulk concentration. Our simulations display a sufficient accuracy and precision to reveal free-energy barriers that are small on a typical scale of surface force simulations, but still of the same order as the expected van der Waals interactions. Two different approaches have been tested: grand canonical simulations, improved by configurational-biased techniques, and a perturbation method utilizing the isotension ensemble. We find the former to be preferable when the surfaces are nonadsorbing, whereas the isotension approach is superior for calculations of interactions between adsorbing surfaces, especially if the polymers are stiff. We also compare our simulation results with predictions from several versions of polymer density functional theory. We find that a crucial aspect of these theories, in quantitative terms, is that they recognize that end monomers exclude more volume to the surrounding than inner ones do. Those theories provide satisfactorily accurate predictions, particularly when the surfaces are nonadsorbing.

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.

Interaction and aggregation of charged platelets in electrolyte solutions: a coarse-graining approach.

A coarse-graining approach has been developed to replace the effect of explicit ions with an effective pair potential between charged sites in anisotropic colloidal particles by optimizing a potential of mean force against the results of simulations of two such colloidal particles with all ions in a cell model. More specifically, effective pair potentials were obtained for charged platelets in electrolyte solutions by simulating two rotating parallel platelets with ions at the primitive model level, enclosed in a cylindrical cell. One-component bulk simulations of many platelets interacting via the effective pair potentials are in excellent agreement with the corresponding bulk simulations with all mobile charges present. The bulk simulations were mainly used to study the effects of platelet size, flexibility, and surface charge density on platelet aggregation in an aqueous 2:1 electrolyte, but systems in a 1:1 electrolyte were also investigated.

Block polyelectrolytes and colloidal stability.

We simulate interactions between charged flat surfaces in the presence of block polymers, where the end blocks carry a charge opposite to the surfaces. Using a recently developed simulation technique, we allow full equilibrium, i.e. the chemical potential of the polyelectrolyte is retained as the separation is changed. In general, the block polyions will adsorb strongly enough to overcharge the surfaces. This results in a double layer repulsion at large separation, with a concomitant free energy barrier. At short separations, the surfaces are pulled together by bridging forces. We make some efforts to theoretically design the polymers to be efficient flocculants, i.e. minimize the free energy barrier and still allow for a long-ranged bridging attraction. Here, we also take into account the possibility of nonequilibrium circumstances, which may be relevant in practice. Our results suggest that short chains, with small charged end blocks and a (relatively speaking) long neutral mid block, are likely to promote rapid flocculation.

Interactions between charged surfaces immersed in a polyelectrolyte solution.

With grand canonical simulations invoking a configurationally weighted scheme, we have calculated interactions between charged surfaces immersed in a polyelectrolyte solution. In contrast to previous simulations of such systems, we have imposed full equilibrium conditions (i.e., we have included diffusive equilibrium with a bulk solution). This has a profound impact on the resulting interactions: even at modest surface charge densities, oppositely charged chains will, at sufficiently large separations, adsorb strongly enough to overcompensate for the nominal surface charge. This phenomenon, known as charge inversion, generates a double-layer repulsion and a free-energy barrier. Simpler canonical approaches, where the chains are assumed to neutralize the surfaces perfectly, will not capture this stabilizing barrier. The barrier height increases with the length of the polyions. Interestingly enough, the separation at which the repulsion becomes attractive is independent of chain length. The short chains here are unable to reach across from one surface to the other. We therefore conclude that the transition to an attractive regime is not provided by the formation of such "intersurface" bridges. With long chains and at large separations, charge inversion displays decaying oscillatory behavior (i.e., the apparent surface charge switches sign once again). This is due to polyion packing effects. We have also investigated responses to salt addition and changes in polyelectrolyte concentration. Our results are in qualitative and semiquantitative agreement with experimental findings, although it should be noted that our chains are comparatively short, and the experimental surface charge density is poorly established.

Surface forces mediated by charged polymers: effects of intrinsic chain stiffness.

The strength and range of surface forces in a system consisting of charged polymers with variable intramolecular stiffness confined between two charged planar surfaces have been investigated by Monte Carlo simulations. The negatively charged surfaces are neutralized by polymers carrying charges of opposite sign. Introducing the intermediate intrinsic stiffness of the chains gives rise to a weaker, but more long-ranged attraction between the surfaces. In the limit of infinitely stiff chains, this bridging attraction is lost, but it is replaced by a strong correlation attraction at short distances. Comparisons with predictions by a correlation-corrected polyelectrolyte Poisson-Boltzmann theory are made. The theory predicts surface attractions that are somewhat too weak, but all qualitative features are correctly reproduced. Given the crudeness of the model, the quantitative agreement is satisfactory.

Simulation of phase equilibria in lamellar surfactant systems.

The coexistence of two lamellar liquid crystalline phases has been investigated by means of Monte Carlo simulations. The surfaces of the negatively charged bilayers formed by the surfactant molecules are modeled as planar infinite walls with a uniform surface charge density. Water is treated as a dielectric continuum, and only electrostatic interactions are considered. The counterions are mono- and divalent point ions, and their ratio is allowed to vary. Monovalent counterions lead to a repulsive osmotic pressure at all separations, while an attractive region exists when the counterions are divalent. In the latter case, one would expect a phase separation to take place, although it is not observed experimentally due to the limited stability of the lamellar phase at high water content. In a system with mixed counterions, however, the osmotic pressure exhibits a van der Waals loop under such conditions that two phases can coexist. A phase diagram is constructed, and the agreement with experimental data is excellent.