Multiscale simulation of irreversible deposition in presence of double layer interactions

Sequential lattice Monte Carlo simulations, in which the transition probabilities are derived from the discrete form of the continuum-level mass conservation law, are used to predict the morphology of colloidal deposits. The simulations account for particle-surface (P-S) and particle-particle (P-P) electrostatic and van der Waals interactions. Simulation results for maximum coverage for monolayer deposition are in quantitative agreement with the hard-sphere RSA jamming limit. Moreover, as reported in earlier studies, monolayer simulations in the absence of P-S interactions qualitatively predict the monotonic increases in fractional coverage with increasing ionic strength, characterized by the Debye screening length (kappa a). Monolayer simulations with P-S interactions show that the dependence of fractional coverage on kappa a is strongly influenced by the ratio of particle to surface potentials (Psi(p)/Psi(s)). P-S and P-P forces achieve their respective maximum at different values of kappa a leading to a nonmonotonic trend in surface coverage as a function of kappa a. These results indicate that the incorporation of P-S interactions into colloidal deposition studies allows more accurate interpretation of the experimental data. In multilayer deposition simulations, balance between long-ranged weak interactions and short-ranged strong interactions between P-P and P-S, coupled with physical screening effects, resulted in widely varying coverages with height of the deposit, ionic strength, and Psi(p)/Psi(s). Moreover, fractal dimension of the deposit ranged from approximately 1 (kappa a < 1) to 1.7 (kappa a > 1). Qualitative kinetic analysis showed widely varying deposition rates in different layers depending on Psi(p)/Psi(s) and ionic strength. The multilayer system approached the monolayer system in the limit kappa a--> infinity and Psi(p)/Psi(s)--> infinity.     

Dressed ion theory of size-asymmetric electrolytes: effective ionic charges and the decay length of screened Coulomb potential and pair correlations

The effects of ionic size asymmetry on long-range electrostatic interactions in electrolyte solutions are investigated within the primitive model. Using the formalism of dressed ion theory we analyze correlation functions from Monte Carlo simulations and the hypernetted chain approximation for size asymmetric 1:1 electrolytes. We obtain decay lengths of the screened Coulomb potential, effective charges of ions, and effective permittivity of the solution. It is found that the variation of these quantities with the degree of size asymmetry depends in a quite intricate manner on the interplay between the electrostatic coupling and excluded volume effects. In most cases the magnitude of the effective charge of the small ion species is larger than that of the large species; the difference increases with increasing size asymmetry. The effective charges of both species are larger (in absolute value) than the bare ionic charge, except for high asymmetry where the effective charge of the large ions can become smaller than the bare charge.     

Polymorph selection in the crystallization of hard-core Yukawa system

Colloid-colloid interactions in charge-stabilized dispersions can to some extent be represented by the hard-core Yukawa model. The crystallization process and polymorph selection of hard-core Yukawa model are studied by means of smart Monte Carlo simulations in the region of face-centered-cubic (fcc) phase. The contact value of hard-core Yukawa potential and the volume fraction of the colloids are fixed, while the Debye screening length can be varied. In the early stage of the crystallization, the precursors with relatively ordered liquid structure have been observed. Although the crystal structure of thermodynamically stable phase is fcc, the system crystallizes into a mixture of fcc and hexagonal close-packed (hcp) structures under small Debye screening length since the colloidal particles act as effective hard spheres. In the intermediate range of Debye screening length, the system crystallizes into a mixture of fcc, hcp, and body-centered-cubic (bcc). The existence of metastable hcp and bcc structures can be interpreted as a manifestation of the Ostwald’s step rule. Until the Debye screening length is large enough, the crystal structure obtained is almost a complete fcc suggesting the system eventually reaches to a thermodynamically stable state.     

Using force-matching to reveal essential differences between density functionals in ab initio molecular dynamics simulations

The exchange-correlation (XC) functional and value of the electronic fictitious mass μ can be two major sources of systematic errors in ab initio Car-Parrinello Molecular Dynamics (CPMD) simulations, and have a significant impact on the structural and dynamic properties of condensed-phase systems. In this work, an attempt is made to identify the origin of differences in liquid water properties generated from CPMD simulations run with the BLYP and HCTH∕120 XC functionals and two different values of μ (representative of "small" and "large" limits) by analyzing the effective pairwise atom-atom interactions. The force-matching (FM) algorithm is used to map CPMD interactions into non-polarizable, empirical potentials defined by bonded interactions, pairwise short-ranged interactions in numerical form, and Coulombic interactions via atomic partial charges. The effective interaction models are derived for the BLYP XC functional with μ=340 a.u. and μ=1100 a.u. (BLYP-340 and BLYP-1100 simulations) and the HCTH∕120 XC functional with μ=340 a.u. (HCTH-340 simulation). The BLYP-340 simulation results in overstructured water with slow dynamics. In contrast, the BLYP-1100 and HCTH-340 simulations both produce radial distribution functions (indicative of structure) that are in reasonably good agreement with experiment. It is shown that the main difference between the BLYP-340 and HCTH-340 effective potentials arises in the short-ranged nonbonded interactions (in hydrogen bonding regions), while the difference between the BLYP-340 and BLYP-1100 interactions is mainly in the long-ranged electrostatic components. Collectively, these results demonstrate how the FM method can be used to further characterize various simulation ensembles (e.g., density-functional theory via CPMD). An analytical representation of each effective interaction water model, which is easy to implement, is presented.     

Electrostatic potential around charged finite rodlike macromolecules: nonlinear Poisson-Boltzmann theory

In this paper, we show that the far field electrostatic potential created by a highly charged finite size cylinder within the nonlinear Poisson-Boltzmann (PB) theory, is remarkably close to the potential created within the linearized PB approximation by the same object at a well-chosen fixed potential. Comparing the nonlinear electrostatic potential with its linear counterpart associated to a fixed potential boundary condition (called the effective surface potential), we deduce the effective charge of the highly charged cylinder. Values of the effective surface potential are provided as a function of the bare surface charge and Debye length of the ionic solution. This allows to compute the anisotropic electrostatic interaction energy of two distant finite rods.     

Density-functional theory and Monte Carlo simulation for the surface structure and correlation functions of freely jointed Lennard-Jones polymeric fluids

We present a nonlocal density-functional theory of polymeric fluids consisting of freely jointed Lennard-Jones chains with explicit consideration of the segment size, van der Waals attraction, and structural correlations due to chain connectivity. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the short-ranged repulsion and the first-order thermodynamic perturbation theory for chain connectivity. The contribution of the long-ranged attraction to the Helmholtz energy functional is taken into account using a quadratic density expansion with the direct correlation function obtained from the first-order mean-spherical approximation. The numerical performance of the density-functional theory is compared well with the simulation results from this work as well as those from the literature for the segment-level density profiles and correlation functions of Lennard-Jones chains in slit pores, near isolated nanoparticles, or in bulk.     

On the interactions of ions with the air/water interface

In the vicinity of a charged interface, the Poisson-Boltzmann approach considers that the ions obey Boltzmann distributions in a mean electrical field that satisfies the Poisson equation. However, the boundary between two dielectrics generates additional interactions between ions and the interface. The traditional models of ion hydration interactions, that assume that water is a homogeneous dielectric, predict that these interactions are repulsive for all kinds of ions, since all ions should prefer the medium with a larger dielectric constant, where they are better hydrated. In reality, the interactions between the ions and the neighboring water molecules can generate additional short-range ion-hydration interactions, which are either repulsive (for structure-making ions) or attractive (for structure-breaking ions). In the present paper, various models for the ion-hydration forces are examined and compared with the results of molecular dynamics simulations. At large ionic strengths, the latter results could be reproduced qualitatively only when short-ranged attractions between the structure-breaking ions and the interface were taken into account.     

Liquid—gas transition for hard spheres with attractive Yukawa tail interactions

We describe the liquid-gas transition in the hard sphere system with Yukawa tail interactions in the mean spherical approximation. The dependence of critical temperature and density on the range of the interaction is shown and the spinodal curve for a short-ranged potential and a long—ranged potential is presented. The compressibility, energy and virial pressures are presented for a long-ranged potential. Liquid phase pressures are calculated by integrating round the coexistence region, rather than through it.     

Double-layer in ionic liquids: paradigm change?

Applications of ionic liquids at electrified interfaces to energy-storage systems, electrowetting devices, or nanojunction gating media cannot proceed without a deep understanding of the structure and properties of the interfacial double layer. This article provides a detailed critique of the present work on this problem. It promotes the point of view that future considerations of ionic liquids should be based on the modern statistical mechanics of dense Coulomb systems, or density-functional theory, rather than classical electrochemical theories which hinge on a dilute-solution approximation. The article will, however, contain more questions than answers. To trigger the discussion, it starts with a simplified original result. A new analytical formula is derived to rationalize the potential dependence of double-layer capacitance at a planar metal-ionic liquid interface. The theory behind it has a mean-field character, based on the Poisson-Boltzmann lattice-gas model, with a modification to account for the finite volume occupied by ions. When the volume of liquid excluded by the ions is taken to be zero (that is, if ions are extremely sparsely packed in the liquid), the expression reduces to the nonlinear Gouy-Chapman law, the canonical result typically used to describe the potential dependence of capacitance in electrochemical double layers. If ionic volume exclusion takes more realistic values, the formula shows that capacitance-potential curves for an ionic liquid may differ dramatically from the Gouy-Chapman law. Capacitance has a maximum close to the potential of zero charge, rather than the familiar minimum. At large potenials, capacitance decreases with the square root of potential, rather than increases exponentially. The reported formula does not take into account the specific adsorption of ions, which, if present, can complicate the analysis of experimental data. Since electrochemists use to think about the capacitance data in terms of the classical Gouy-Chapman theory, which, as we know, should be good only for electrolytes of moderate concentration, the question of which result is "better" arises. Experimental data are sparse, but a quick look at them suggests that the new formula seems to be closer to reality. Opinions here could, however, split. Indeed, a comparison with Monte Carlo simulations has shown that incorporation of restricted-volume effects in the mean-field theory of electrolyte solutions may give results that are worse than the simple Gouy-Chapman theory. Generally, should the simple mean-field theory work for such highly concentrated ionic systems, where the so-called ion-correlation effects must be strong? It may not, as it does not incorporate a possibility of charge-density oscillations. Somehow, to answer this question definitely, one should do further work. This could be based on density-functional theory (and possibly not on what is referred to as local density approximation but rather "weighted density approximation"), field theory methods for the account of fluctuations in the calculation of partition function, heuristic integral equation theory extended to the nonlinear response, systematic force-field computer simulations, and, most importantly, experiments with independently determined potentials of zero charge, as discussed in the paper.     

Soft repulsive mixtures under gravity: brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

A binary mixture of particles interacting via long-ranged repulsive forces is studied in gravity by computer simulation and theory. The more repulsive A-particles create a depletion zone of less repulsive B-particles around them reminiscent to a bubble. Applying Archimedes' principle effectively to this bubble, an A-particle can be lifted in a fluid background of B-particles. This "depletion bubble" mechanism explains and predicts a brazil-nut effect where the heavier A-particles float on top of the lighter B-particles. It also implies an effective attraction of an A-particle towards a hard container bottom wall which leads to boundary layering of A-particles. Additionally, we have studied a periodic inversion of gravity causing perpetuous mutual penetration of the mixture in a slit geometry. In this nonequilibrium case of time-dependent gravity, the boundary layering persists. Our results are based on computer simulations and density functional theory of a two-dimensional binary mixture of colloidal repulsive dipoles. The predicted effects also occur for other long-ranged repulsive interactions and in three spatial dimensions. They are therefore verifiable in settling experiments on dipolar or charged colloidal mixtures as well as in charged granulates and dusty plasmas.     

Self-consistent Ornstein-Zernike approximation for the Yukawa fluid with improved direct correlation function

Thermodynamic consistency of the mean spherical approximation as well as the self-consistent Ornstein-Zernike approximation (SCOZA) with the virial route to thermodynamics is analyzed in terms of renormalized gamma-ordering. For continuum fluids, this suggests the addition of a short-ranged contribution to the usual SCOZA direct correlation function, and the shift of the adjustable parameter from the potential term to this new term. The range of this contribution is fixed by imposing consistency with the virial route at the critical point. Comparison of the results of our theory for the hard-core Yukawa potential with the simulation data show very good agreement for cases where the liquid-vapor transition is stable or not too far into the metastable region with respect to the solid state. In the latter case for extremely short-ranged interactions discrepancies arise.     

Probing the limits of the Derjaguin approximation with scanning force microscopy

We have measured the interaction force between a silicon nitride scanning force microscopy (SFM) probe and the basal plane of highly oriented pyrolitic graphite as a function of pH and ionic concentration in aqueous solutions. Forces in the range +/- 50 pN were reconstructed from measured signals using dynamical analysis of the cantilever. We modeled the force-separation data using a flat plate electric double-layer interaction and assumed the Derjaguin approximation to adapt the flat plate geometry for the SFM probe shape. Measured forces were well modeled by the theory at high ionic concentrations (10 and 100 mM), where Debye lengths were 3.0 and 0.96 nm, respectively. The theory failed to model forces at a lower ionic concentration (1 mM), where the Debye length was 9.6 nm. To investigate this, we calibrated the SFM probe geometry using blind reconstruction and obtained an apex radius of 7 nm. This value suggested that failure of the theory was due to an invalidation of the Derjaguin approximation at long Debye lengths, where the characteristic length scale for the interaction was larger than the size of the SFM probe. The errors were reduced by replacing the Derjaguin approximation with a surface element integration. The result experimentally demonstrates the limitations of the Derjaguin approximation for predicting interactions of nanoscale colloids.     

Numerical study supplemented with simplified model on electrophoresis of a hydrophobic colloid incorporating finite ion size effects and ion-solvent interactions

We consider a modified electrokinetic model to study the electrophoresis of a hydrophobic particle by considering the finite sized ions. The mathematical model adopted in this study incorporates the ion steric repulsion, ion-solvent interactions as well as Maxwell stress on the electrolyte. The dielectric permittivity and viscosity of the electrolyte is considered to vary with the local ionic volume fraction. Based on this modified model for the electrokinetics we have analyzed the electrophoresis in a single as well as mixture of electrolytes of monovalent and non-$z:z$ electrolytes. The dependence of viscosity on local ionic volume fraction modifies the hydrodynamic drag as well as diffusivity of ions, which are ignored in existing studies on electrophoresis. A simplified model for electrophoresis of a hydrophobic particle incorporating the ion steric repulsion and ion-solvent interactions is developed based on the first-order perturbation on applied electric field. This simplified model is established to be efficient for a Debye layer thinner than the particle size and a smaller range of slip length. This model can be implemented for any number of ionic species as well as non-$z:z$ electrolytes. It is established that the ion steric interactions and dielectric decrement creates a counterion saturation in the Debye layer leading to an enhanced mobility compared to the standard model. However, experimental data for non-dilute cases often under predicts the theoretically determined mobility. The present modified model fills this lacuna and demonstrate that the consideration of finite ion size modifies the medium viscosity and hence, ionic mobility, which in combination lowers the mobility value.     

Monte Carlo computer simulations and electron microscopy of colloidal cluster formation via emulsion droplet evaporation

We consider a theoretical model for a binary mixture of colloidal particles and spherical emulsion droplets. The hard sphere colloids interact via additional short-ranged attraction and long-ranged repulsion. The droplet-colloid interaction is an attractive well at the droplet surface, which induces the Pickering effect. The droplet-droplet interaction is a hard-core interaction. The droplets shrink in time, which models the evaporation of the dispersed (oil) phase, and we use Monte Carlo simulations for the dynamics. In the experiments, polystyrene particles were assembled using toluene droplets as templates. The arrangement of the particles on the surface of the droplets was analyzed with cryogenic field emission scanning electron microscopy. Before evaporation of the oil, the particle distribution on the droplet surface was found to be disordered in experiments, and the simulations reproduce this effect. After complete evaporation, ordered colloidal clusters are formed that are stable against thermal fluctuations. Both in the simulations and with field emission scanning electron microscopy, we find stable packings that range from doublets, triplets, and tetrahedra to complex polyhedra of colloids. The simulated cluster structures and size distribution agree well with the experimental results. We also simulate hierarchical assembly in a mixture of tetrahedral clusters and droplets, and find supercluster structures with morphologies that are more complex than those of clusters of single particles.     

Self-diffusion in solutions of a 20 base pair oligonucleotide: effects of concentration and ionic strength

The long-time self-diffusion coefficients of a 20 base pair duplex oligonucleotide are measured as functions of 20-mer and added NaCl salt concentrations. The self-diffusion coefficients decrease monotonically with increasing 20-mer concentrations for the high-added salt sample and display non-monotonically decreasing 20-mer concentration dependences at lower added salt concentrations. The non-monotonic behavior is attributed to the opposing effects of the tendency to increase the interactions between 20-mers as the concentration is increased and to a decrease in the extent of the Coulomb forces as counterions from the 20-mer increasingly screen them. Attempts to account for the effect of the Coulomb forces on the self-diffusion coefficients by using effective dimensions in the hard rod theory give good agreement with experiment at the highest salt concentration studied. For the lower salt concentrations there appear to be two scaling regimes--one at low polyion concentration in which the high salt scaling of the rod dimensions by adding the Debye screening to the length and diameter of the rod is appropriate and one at high polyion concentrations where the scaling of the dimensions is the addition of 1/2 the Debye screening length. Estimates of the "overlap" concentration C*=1/L(eff) indicate that the non-monotonic decrease occurs at concentrations lower than C*. Finally, the fluorescence correlation spectroscopy self-diffusion coefficients measured here are compared with the mutual diffusion coefficients measured by dynamic light scattering.     

Microphase separation in a mixture of ionic and nonionic liquids

We use a Flory-Huggins type approach and the random phase approximation (RPA) to describe a microphase separation in the mixture of ionic and nonionic liquids. The mixture is modeled as a "three-component" system including anions, cations, and neutral molecules. Each ion is considered to consist of a charged group surrounded by a neutral "bulky" shell. The shells of the anion and cation are assumed to have different affinities to the neutral molecules. We show that, if the difference of the Flory-Huggins parameters describing affinities of the anions and cations to the neutral molecules is higher than a certain value, the microphase separation can occur. The physical reason for the separation is a delicate balance between the short-range segregating interactions and the long-range Coulomb interactions.     

A molecular Debye-Hückel theory and its applications to electrolyte solutions

In this report, a molecular Debye-Hu?ckel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Hu?ckel theory which is related to the dressed ion theory in the static case. Due to the multi-pole structure of dielectric function of ionic fluids, the electric potential around a single ion has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Hu?ckel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to binary as well as multi-component primitive models of electrolyte solutions demonstrated the accuracy of our approach. More importantly, for electrolyte solution models with soft short-ranged interactions, it is shown that the traditional perturbation theory can be extended to ionic fluids successfully just as the perturbation theory has been successfully used for short-ranged systems.     

Localization in Spatially Disordered Systems: Screening and Band Structure Effects at the EMA Level

Abstract

An analysis is given of Anderson localization in a one-band tight-binding model with off-diagonal disorder characteristic of a quenched liquid-like structure. We extend a localization criterion due to Logan and Wolynes, based on a self-consistent determination of the most probable value of the imaginary part of the site self-energy, to include screening arising from many-body terms in the renormalized perturbation series. Liquid state methods are used to examine screening, as embodied in an effective energy and density dependent transfer matrix element, at the level of the effective medium approximation. It is shown that this effective transfer matrix element is screened in high energy regions and anti-screened in low energy regions, so that extended states tend to occur in the low energy low density of states regime. Theoretical predictions for the mobility edge trajectories are found to be in reasonable agreement with recent computer simulations. The effects of the short-ranged structure of the system are also examined.