Dynamic Monte Carlo simulations of anisotropic colloids

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.     

Interaction between amphiphiles and water molecules in concentrated bilayer aqueous colloids

Interaction between amphiphiles and water molecules in micelle or bilayer structure has been investigated using aqueous colloids of various amphiphiles through the rheological data and the spin-lattice relaxation timeT ₁ of the proton of water molecule.T ₁ of the water proton has been measured by the inversion recovery method and determined as a single exponential relaxation process.The chemical shift of the water proton is almost independent of the amphiphilic concentration; however, it shifts toward a higher magnetic field with increasing temperature in a way similar to that in pure water and in the amphiphilic aqueous systems. These facts mean that there is no significant difference in the magnetic field environment of the water protons in these systems.The water molecule is not necessarily bound in the fully developed micelle or bilayer (rod-like or lamella) structure which induces the high viscosity or high rigidity of the colloidal system. On the other hand, the water molecule is bound in the micelle colloids of amphoteric amphiphiles or amphiphiles whose molecular assembly creates a relatively strong electrostatic field. The activation entropy of the bound water is negative and this suggests that water molecules assume some ordered structure in the bound state.     

Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).     

Charge reversal in real colloids: Experiments, theory and simulations

In the last years, the inclusion of ionic short-range correlations in the study of colloidal stability has led to significant disagreements with the predictions obtained from classical treatments. An example of these discrepancies is the occurrence of charge reversal of charged particles. In order to shed light on this issue, the charge reversal of latex particles in the presence of asymmetric electrolytes has been investigated through Monte Carlo (MC) simulations. In particular, experimental results concerning electrophoretic mobility reversals and the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) predictions have been compared with simulations in which two alternative methods for evaluating energies have been applied. A realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, the existence of a reversal in the electrophoretic mobility due to ion size correlations and without requiring specific counterion adsorption is probed. Moreover, the simulations appears as a useful tool for explaining those results in which the HNC/MSA does not reproduce the experimental trends.     

Aggregation kinetics of polymer colloids in reaction limited regime: experiments and simulations

The kinetics of reaction-limited cluster aggregation of fluorinated polymer colloids in a broad range of particle volume fractions has been investigated experimentally by measuring independently the Fuchs stability ratio W and the time evolution of both the average radius of gyration and the average hydrodynamic radius of the aggregates mass distribution. The W value is determined from the aggregation rate at the very initial stage of the aggregation, where the presence of triplets is negligible. The time evolutions of and are then simulated using the cluster mass distribution calculated from the population balance equations with various aggregation kernels proposed in the literature. It is found that, when the measured W value is used, the only kernels that can correctly simulate the experimental results are the product kernel and the one derived by Odriozola et al. (Europhys. Lett. 53 (2001) 797), with some proper tuning of the exponent in the kernel. For the particle volume fraction phi<1%, the obtained value for the exponent is 0.4 and independent of phi, while it tends to decrease for larger phi values, most likely indicating a significant effect of multi-body interactions on the aggregation kinetics.     

Trends in computational simulations of electrochemical processes under hydrodynamic flow in microchannels

Computational modeling and theoretical simulations have recently become important tools for the development, characterization, and validation of microfluidic devices. The recent proliferation of commercial user-friendly software has allowed researchers in the microfluidics community, who might not be familiar with computer programming or fluid mechanics, to acquire important information on microsystems used for sensors, velocimetry, detection for microchannel separations, and microfluidic fuel cells. We discuss the most popular computational technique for modeling these systems—the finite element method—and how it can be applied to model electrochemical processes coupled with hydrodynamic flow in microchannels. Furthermore, some of the limitations and challenges of these computational models are also discussed.     

Krylov subspace methods for computing hydrodynamic interactions in Brownian dynamics simulations

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a Brownian dynamics simulation. However, the calculation of correlated Brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing Brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the Brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N(2)) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the "block" version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10 000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale Brownian dynamics simulations with hydrodynamic interactions.     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

Phase behavior of colloids and proteins in aqueous suspensions: Theory and computer simulations

The fluid phase behavior of colloidal suspensions with short-range attractive interactions is studied by means of Monte Carlo computer simulations and two theoretical approximations, namely, the discrete perturbation theory and the so-called self-consistent Ornstein-Zernike approximation. The suspensions are modeled as hard-core attractive Yukawa (HCAY) and Asakura-Oosawa (AO) fluids. A detailed comparison of the liquid-vapor phase diagrams obtained through different routes is presented. We confirm Noro-Frenkel's extended law of scaling according to which the properties of a short-ranged fluid at a given temperature and density are independent of the detailed form of the interaction, but just depend on the value of the second virial coefficient. By mapping the HCAY and AO fluids onto an equivalent square-well fluid of appropriate range at the critical point we show that the critical temperature as a function of the effective range is independent of the interaction potential, i.e., all curves fall in a master curve. Our findings are corroborated with recent experimental data for lysozyme proteins.     

A new model system for diffusion NMR studies of concentrated monodisperse and bidisperse colloids

A method to prepare monodisperse and simultaneously NMR-visible and fluorescent colloidal particles is described, and a systematic approach to obtain spectrally resolved diffusion coefficient for every component in a monodisperse colloidal suspension is presented. We also prepared bidisperse colloidal suspensions, where each colloid component has a distinct NMR spectral signature, and obtained the diffusion coefficients of both colloid species simultaneously in concentrated colloidal suspensions, with volume fractions between 20 and 50%. The colloidal model system developed in this work enables the study of colloidal phase behavior in binary mixtures for different number and size ratios.     

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic interaction

The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N(1/3)Wi(2/3) at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N(-1/2)kappa(-3)(l(B)|sigmaq|)(3/2), where kappa is the inverse screening length, l(B) is the Bjerrum length, sigma is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.     

Rigorous calculations of linearized Poisson-Boltzmann interaction between dissimilar spherical colloids and osmotic pressure in concentrated dispersions

We present computational results on the static properties of concentrated dispersions of bidisperse colloids. The long-range electrostatic interactions between dissimilar spherical colloids are determined using the singularity method, which provides rigorous solutions to the linearized electrostatic field. The NVT Monte Carlo simulation is applied to the bulk suspension to obtain the radial distribution function for the concentrated system. The increasing trend of osmotic pressure with increasing total particle concentration is reduced as the concentration ratio between large and small particles is increased. The increase of electrostatic interaction between similarly charged particles caused by the Debye screening effect provides an increase in the osmotic pressure. From the estimation of total structure factor, we observe the strong correlations developed between dissimilar spheres, and the small spheres are expected to tend to fit into the spaces between the larger ones. As the particle concentration increases at a given ionic strength, the magnitude of the first peak in structure factors increases and also moves to higher wavenumber values.     

Interpretation of conservative forces from Stokesian dynamic simulations of interfacial and confined colloids

This paper presents Stokesian dynamics simulations of experiments involving one or two charged colloids near either a single charged wall or confined between parallel charged walls. Equilibrium particle-particle and particle-wall interactions are interpreted from dynamic particle trajectories in simulations involving (1) a single particle levitated above a wall, (2) two particles below a wall, and (3) two particles confined between two parallel walls. By specifying only repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek (DLVO) potentials and including multibody hydrodynamics, we successfully recover expected potentials in some cases, while anomalous attraction is observed in other cases. Attraction inferred in the latter simulations displays quantitative agreement with literature measurements when particle dynamics are interpreted using reported analyses. Because anomalous attraction is reproduced in simulations using only electrostatic repulsive DLVO potentials, our results reveal the one-dimensional analyses to be invalid for configurations that are inherently multidimensional via multibody hydrodynamics. Parameters related to experimental sampling of particle dynamics are also found to be critical for obtaining accurate potentials. We explain the anomalous attraction in each experiment using effective potentials, which can be employed in an a priori fashion to assist the confident design of future experiments involving interfacial and confined colloids. Ultimately, our findings reveal the importance of dimensionality and multibody hydrodynamics for understanding nonequilibrium dynamics of colloids near surfaces.     

Isotropic-nematic spinodals of rigid long thin rodlike colloids by event-driven Brownian dynamics simulations

The isotropic-nematic spinodals of solutions of rigid spherocylindrical colloids with various shape anisotropies L/D in a wide range from 10 to 60 are investigated by means of Brownian dynamics simulations. To make these simulations feasible, we developed a new event-driven algorithm that takes the excluded volume interactions between particles into account as instantaneous collisions, but neglects the hydrodynamic interactions. This algorithm is applied to dense systems of highly elongated rods and proves to be efficient. The calculated isotropic-nematic spinodals lie between the previously established binodals in the phase diagram and extrapolate for infinitely long rods to Onsager's [Ann. N. Y. Acad. Sci. 51, 627 (1949)] theoretical predictions. Moreover, we investigate the shear induced shifts of the spinodals, qualitatively confirming the theoretical prediction of the critical shear rate at which the two spinodals merge and the isotropic-nematic phase transition ceases to exist.     

Photoisomerization dynamics of 3,3'-diethyloxadicarbocyanine iodide in ionic liquids: breakdown of hydrodynamic Kramers model

Photoisomerization dynamics of 3,3'-diethyloxadicarbocyanine iodide (DODCI) has been examined in a series of 1-alkyl-3-methylimidazolium (alkyl = methyl, ethyl, propyl, butyl, and hexyl) bis(trifluoromethylsulfonyl)imides by measuring its fluorescence lifetimes and quantum yields. This study has essentially been undertaken to find out whether the process of photoisomerization of DODCI in ionic liquids is different compared to that observed in conventional solvents such as alcohols. Activation energy of the reaction has been attained with the aid of isoviscosity plots and was found to be 22 ± 3 kJ mol(-1), which is a factor of two higher compared to that obtained in alcohols. The significantly higher activation energy obtained in bis(trifluoromethylsulfonyl)imides compared to alcohols is probably due to the highly ordered nature of the ionic liquids, which hinders the twisting process. Kramers theory has been applied to understand the reduced isomerization rate constants in terms of solvent friction. As in case of alcohols, the isomerization data could not be explained by the Kramers model. However, a power law relation, which is a phenomenological functional form, could mimic the observed trend.     

Re-entrant kinetic arrest and elasticity of concentrated suspensions of spherical and nonspherical repulsive and attractive colloids

We have designed and studied a new experimental colloidal system to probe how the weak shape anisotropy of uniaxial particles and variable repulsive (Coulombic) and attractive (van der Waals) forces influence slow dynamics, shear elasticity, and kinetic vitrification in dense suspensions. The introduction of shape anisotropy dramatically delays kinetic vitrification and reduces the shear elastic modulus of colloidal diatomics relative to their chemically identical spherical analogs. Tuning the interparticle interaction from repulsive, to nearly hard, to attractive by increasing suspension ionic strength reveals a nonmonotonic re-entrant dynamical phase behavior (glass-fluid-gel) and a rich variation of the shear modulus. The experimental results are quantitatively confronted with recent predictions of ideal mode coupling and activated barrier hopping theories of kinetic arrest and elasticity, and good agreement is generally found with a couple of exceptions. The systems created may have interesting materials science applications such as flowable ultrahigh volume fraction suspensions, or responsive fluids that can be reversibly switched between a flowing liquid and a solid nonequilibrium state based on in situ modification of suspension ionic strength.     

Calculation of flocculation and coalescence rates for concentrated dispersions using emulsion stability simulations

A simple procedure for the quantification of flocculation (k(f)) and coalescence (k(c)) rates from emulsion stability simulations (ESS) of concentrated systems is presented. It is based on a simple analytical equation, which results from the sum of well-known formulas for the separate processes of flocculation and coalescence. The expression contains k(f) and k(c) as fitting parameters and is found to reproduce the behavior predicted by ESS spanning a wide range of volume fractions (1 < phi < 30%) and surfactant concentrations (1.2 x10(-5) < C < 1.2 x 10(-4) M). This procedure allows interpretation of ESS data in terms of the referred kinetic rates. Furthermore, it could also provide an additional mean for the direct comparison of the simulation data with experimental results.     

Aggregation kinetics and gel formation in modestly concentrated suspensions of oppositely charged model ceramic colloids: a numerical study

Aggregation kinetics and gel formation in aqueous suspensions that undergo heteroaggregation are studied by means of Brownian dynamics simulations. The simulated system, described in a previous paper [M. A. Piechowiak, A. Videcoq, F. Rossignol, C. Pagnoux, C. Carrion, M. Cerbelaud, R. Ferrando, Langmuir, 2010, 26(15), 12540-12547.], is constituted of two kinds of synthesized, almost equally sized colloids: silica particles that are negatively charged and alumina-coated silica particles that are positively charged. The interactions between colloids are modeled by the DLVO potential. Several compositions are analyzed, from silica-rich to alumina-rich cases. The particle volume fraction φ is varied in the range 6-12%. The study of the aggregation kinetics allows us to clarify the effect of those variations on the clustering process. Gelation is analyzed by detection of spanning clusters in each x-, y-, z-direction of the cubic simulation box. Percolating networks start to be observed from φ = 7%, a low value of the volume fraction close to the solid volume fraction experimentally measured in sediments of those suspensions.     

Microstructure of concentrated solutions in the water-lithium nitrate-calcium nitrate ternary system from molecular dynamics simulations

By classical molecular dynamics, a series of solutions in the ternary water-lithium nitrate-calcium nitrate system is simulated. The radial distribution functions for different atom pairs are calculated, the coordination numbers are estimated, and the pattern of change of their first solvation shell composition with a change in the component ratio in the model system is examined. The first sphere of water molecule in the solutions with different concentration is considered in detail. Eight main structural types of the nearest-neighbor water molecule surrounding and their major features are identified, the probabilities of the occurrence of these structures in the ternary system are estimated.     

3D simulations of hydrodynamic drag forces on two porous spheres moving along their centerline

This paper numerically evaluates the hydrodynamic drag force exerted on two highly porous spheres moving steadily along their centerline through a quiescent Newtonian fluid over a Reynolds number ranging from 0.1 to 40. At creeping-flow limit, the drag forces exerted on both spheres were approximately identical. At higher Reynolds numbers the drag force on the leading sphere (sphere #1) was higher than the following sphere (sphere #2), revealing the shading effects produced by sphere #1 on sphere #2. At dimensionless diameter beta<2 (beta=d(f)/2k(0.5), d(f) and k are sphere diameter and interior permeability, respectively), the spheres can be regarded as "no-spheres" limit. At increasing beta for both spheres, the drag force on sphere #2 was increased because of the more difficult advective flow through its interior, and at the same time the drag was reduced owing to the stronger wake flow produced by the denser sphere #1. The competition between these two effects leads to complicated dependence of drag force on sphere #2 on beta value. These effects were minimal when beta became low.