Anomalous potentials from inverse analyses of interfacial polydisperse attractive colloidal fluids

This paper investigates effects of using monodisperse inverse analyses to extract particle-particle and particle-surface potentials from simulated interfacial colloidal fluids of polydisperse attractive particles. Effects of polydispersity are investigated as functions of particle concentration and attractive well depth and range for van der Waals and depletion potentials. Forward Monte Carlo simulations are used to generate particle distribution functions for polydisperse interfacial colloidal fluids from which inverted potentials are obtained using an inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method. Attractive potentials are successfully recovered for monodisperse colloidal fluids, but polydispersity that is unaccounted for in inverse analyses produces (1) apparent softening of strong forces, (2) anomalous repulsive and attractive interactions, and (3) aphysical particle overlaps. This investigation provides insights into the role of polydispersity in altering the equilibrium structure and corresponding inverted potentials of attractive colloidal fluids near surfaces. These findings should assist the design and interpretation of optical microscopy experiments involving interfacial colloidal fluids similar to the simulated experiments reported here.     

Measurement and interpretation of particle-particle and particle-wall interactions in levitated colloidal ensembles

This paper reports measurements of particle-wall and particle-particle interactions in levitated colloidal ensembles using integrated total internal reflection microscopy (TIRM) and video microscopy (VM) techniques. In levitated colloidal ensembles with area fractions of phiA = 0.03-0.25, ensemble TIRM measured height distribution functions are used to interpret particle-wall interactions, and VM measured pair distribution functions are used to interpret particle-particle interactions using inverse Ornstein-Zernike (OZ) and three-dimensional inverse Monte Carlo (MC) analyses. An inconsistent finding is the observation of an anomalous long-range particle-particle attraction and recovery of the expected Derjaguin-Landau-Verwey-Overbeek (DLVO) particle-wall interactions for all concentrations examined. Because particle-wall and particle-particle potentials are expected to be consistent in several respects, the analytical and experimental methods employed in this investigation are examined for possible sources of error. Comparison of inverse OZ and three-dimensional inverse MC analyses are used to address uncertainties related to dimensionality, effects of particle concentration, and assumptions of the OZ theory and closure relations. The possible influence of charge heterogeneity and particle size polydispersity on measured distribution functions is discussed with regard to inconsistent particle-wall and particle-particle potentials. Ultimately, achieving a consistent understanding of particle-wall and particle-particle interactions in interfacial and confined colloidal systems is essential to numerous complex fluid and advanced material technologies.     

Self-diffusion in submonolayer colloidal fluids near a wall

Theoretical expressions are developed to describe self-diffusion in submonolayer colloidal fluids that require only equilibrium structural information as input. Submonolayer colloidal fluids are defined for the purpose of this work to occur when gravity confines colloids near a planar wall surface so that they behave thermodynamically as two dimensional fluids. Expressions for self-diffusion are generalized to consider different colloid and surface interaction potentials and interfacial concentrations from infinite dilution to near fluid-solid coexistence. The accuracy of these expressions is demonstrated by comparing self-diffusion coefficients predicted from Monte Carlo simulated equilibrium particle configurations with standard measures of self-diffusion evaluated from Stokesian Dynamics simulated particle trajectories. It is shown that diffusivities predicted for simulated equilibrium fluid structures via multibody hydrodynamic resistance tensors and particle distribution functions display excellent agreement with values computed from mean squared displacements and autocorrelation functions of simulated tracer particles. Results are obtained for short and long time self-diffusion both parallel and normal to underlying planar wall surfaces in fluids composed of particles having either repulsive electrostatic or attractive van der Waals interactions. The demonstrated accuracy of these expressions for self-diffusion should allow their direct application to experiments involving submonolayer colloidal fluids having a range of interaction potentials and interfacial concentrations.     

Interfacial colloidal sedimentation equilibrium. I. Intensity based confocal microscopy

This paper reports confocal microscopy measurements of inhomogeneous colloidal sedimentation equilibrium profiles near planar wall surfaces for conditions when colloid dimensions are comparable to the characteristic gravitational length scale. The intensity based confocal method developed in this work enables real-space measurements of one-dimensional density profiles of Brownian colloids without identifying many single colloid centers in large imaging volumes. Measured sedimentation equilibrium profiles for single-phase interfacial fluids and for coexisting inhomogeneous fluid and solid phases are in agreement with a perturbation theory and Monte Carlo simulations within the local density approximation. Monte Carlo simulated colloid scale density profiles display some minor differences with confocal images in terms of microstructural transitions involving the onset of interfacial crystallization and the precise elevation of the fluid-solid interface. These discrepancies are attributed to polydispersity unaccounted for in the analyses, sensitivity of the perturbation theory to the effective hard sphere size, and the influence of ensemble, system size, and box shape in Monte Carlo simulations involving anisotropic/inhomogeneous solids. Successful demonstration of intensity based confocal microscopy provides a basis for future measurements of three-dimensional colloidal interactions, dynamics, and structure near surfaces.     

Gas-liquid phase separation in oppositely charged colloids: stability and interfacial tension

We study the phase behavior and the interfacial tension of the screened Coulomb (Yukawa) restricted primitive model (YRPM) of oppositely charged hard spheres with diameter sigma using Monte Carlo simulations. We determine the gas-liquid and gas-solid phase transitions using free energy calculations and grand-canonical Monte Carlo simulations for varying inverse Debye screening length kappa. We find that the gas-liquid phase separation is stable for kappasigma相似文献   

Interfacial colloidal crystallization via tunable hydrogel depletants

We demonstrate an approach using temperature-dependent hydrogel depletants to thermoreversibly tune colloidal attraction and interfacial colloidal crystallization. Total internal reflection and video microscopy are used to measure temperature-dependent depletion potentials between approximately 2 microm silica colloids and surfaces as mediated by approximately 0.2 microm poly-N-isopropylacrylamide (PNIPAM) hydrogel particles. Measured depletion potentials are modeled using the Asakura-Oosawa theory while treating PNIPAM depletants as swellable hard spheres. Monte Carlo simulations using the measured potentials predict reversible, quasi-2D crystallization and melting at approximately 27 degrees C in quantitative agreement with video microscopy images of measured microstructures (i.e., radial distribution functions) over the temperature range of interest (20-29 degrees C). Additional measurements of short-time self-diffusivities display excellent agreement with predicted diffusivities by considering multibody hydrodynamic interactions and using a swellable hard sphere model for the PNIPAM solution viscosity. Our findings demonstrate the ability to quantitatively measure, model, and manipulate kT-scale depletion attraction and phase behavior as a means of formally engineering interfacial colloidal crystallization.     

Concentrated diffusing colloidal probes of Ca2+-dependent cadherin interactions

We report video microscopy measurements and inverse simulation analyses of specific Ca(2+)-dependent interactions between N-cadherin fragments attached to supported lipid bilayer-coated silica colloids in quasi-2D concentrated configurations. Our results include characterization of the bilayer formation and fluidity and the attachment of active extracellular cadherin fragments on bilayers. Direct measurements of interaction potentials show nonspecific macromolecular repulsion between cadherin fragments in the absence of Ca(2+) and irreversible bilayer fusion via cadherin-mediated attraction at >100 μM Ca(2+). Analysis of Ca(2+)-dependent N-cadherin bond formation in quasi-2D concentrated configurations using inverse Monte Carlo and Brownian Dynamics simulations show measurable attraction starting at 0.1 μM Ca(2+), a concentration significantly below previously reported values.     

Effect of Polydispersity and Charge Heterogeneity on the Depletion Interaction in Colloidal Systems

The effect of polydispersity in the macromolecule size and surface potential on the depletion attraction and structural repulsion between two charged spherical particles in a solution of nonadsorbing charged spherical macromolecules was investigated using a modified form of the force-balance model of J. Y. Walz and A. Sharma [J. Colloid Interface Sci. 168, 495 (1994)]. The distribution of sizes and potentials was described by a log-normal distribution with values of the coefficient of variation (CV) as large as 60%. Comparisons with the case of purely monodisperse macromolecules were made under the condition of either constant macromolecule number density, rho(infinity), or constant volume fraction, φ. For purely hard spheres, polydispersity increases the depletion attraction at constant rho(infinity) but decreases the interaction at constant φ. A simple scaling analysis is used to show that these trends are true for any arbitrary distribution of macromolecule size. Surface charge is found to amplify the effect of polydispersity at constant φ but actually negates the effect at constant rho(infinity). The repulsive structural contribution, arising from the interaction between the macromolecules themselves, is significantly decreased by polydispersity except for the case of charged macromolecules at constant rho(infinity), where the effect is relatively small. Finally, polydispersity in the macromolecule surface potential (no polydispersity in size) has only a minor effect on both the depletion attraction and structural repulsion, even for CV values as large as 60%. Copyright 2000 Academic Press.     

Pair interaction potentials of colloids by extrapolation of confocal microscopy measurements of collective suspension structure

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, U(r). We use Monte Carlo simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) particles dispersed in the solvent dioctyl phthalate to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.     

How do interactions control droplet size during nanoprecipitation?

Nanoprecipitation provides colloidal dispersions through successive recombination events between nanometric objects. In the present article, we explain why the nanoprecipitation pathways induced through solvent-shifting – the Ouzo effect –, are fascinating study-cases. Indeed, they allow to address the question of how the interactions between the colloidal particles control the dynamics of the process, thus the particle size distribution. Experimental monitoring of the precipitation dynamics demonstrates that the colloidal dispersion polydispersity decreases over time as the droplets coalesce. Monte Carlo simulations within the Smoluchowski framework agree quantitatively with these observations, and show how the interactions between the particles naturally force the system to become nearly monodisperse. The mechanistic understanding gained from the solvent-shifting experiments is also relevant to other nanoprecipitation processes.     

Liquid-gas coexistence and critical point shifts in size-disperse fluids

Specialized Monte Carlo simulations and the moment free energy (MFE) method are employed to study liquid-gas phase equilibria in size-disperse fluids. The investigation is made subject to the constraint of fixed polydispersity, i.e., the form of the "parent" density distribution rho(0)(sigma) of the particle diameters sigma, is prescribed. This is the experimentally realistic scenario for, e.g., colloidal dispersions. The simulations are used to obtain the cloud and shadow curve properties of a Lennard-Jones fluid having diameters distributed according to a Schulz form with a large (delta approximately 40%) degree of polydispersity. Good qualitative accord is found with the results from a MFE method study of a corresponding van der Waals model that incorporates size dispersity both in the hard core reference and the attractive parts of the free energy. The results show that polydispersity engenders considerable broadening of the coexistence region between the cloud curves. The principal effect of fractionation in this region is a common overall scaling of the particle sizes and typical interparticle distances, and we discuss why this effect is rather specific to systems with Schulz diameter distributions. Next, by studying a family of such systems with distributions of various widths, we estimate the dependence of the critical point parameters on delta. In contrast to a previous theoretical prediction, size dispersity is found to raise the critical temperature above its monodisperse value. Unusually for a polydisperse system, the critical point is found to lie at or very close to the extremum of the coexistence region in all cases. We outline an argument showing that such behavior will occur whenever polydispersity affects only the range, rather than the strength of the interparticle interactions.     

Polydisperse hard spheres at a hard wall

The structural properties of polydisperse hard spheres in the presence of a hard wall are investigated via Monte Carlo simulation and density functional theory (DFT). Attention is focused on the local density distribution rho(sigma,z), measuring the number density of particles of diameter sigma at a distance z from the wall. Estimates of rho(sigma,z) are obtained for bulk volume fractions eta(b)=0.2 and eta(b)=0.4, and for two choices of the bulk parent distribution: a top-hat form, which we study for degrees of polydispersity delta=11.5% and delta=40.4%, and a truncated Schulz form having delta=40.7%. Excellent overall agreement is found between the DFT and simulation results, particularly at eta(b)=0.2. A detailed analysis of rho(sigma,z) confirms the presence of oscillatory size segregation effects, as observed in a previous DFT study [I. Pagonabarraga, M. E. Cates, and G. J. Ackland, Phys. Rev. Lett. 84, 911 (2000)]. For large delta, the character of these oscillation is observed to depend strongly on the shape of the parent distribution. In the vicinity of the wall, attractive sigma-dependent depletion interactions are found to greatly enhance the density of the largest particles. The local degree of polydispersity delta(z) is suppressed in this region, while further from the wall it exhibits oscillations.     

Predicting atomic dopant solvation in helium clusters: the MgHe(n) case

We present a quantum Monte Carlo study of the solvation and spectroscopic properties of the Mg-doped helium clusters MgHe(n) with n=2-50. Three high-level [MP4, CCSD(T), and CCSDT] MgHe interaction potentials have been used to study the sensitivity of the dopant location on the shape of the pair interaction. Despite the similar MgHe well depth, the pair distribution functions obtained in the diffusion Monte Carlo simulations markedly differ for the three pair potentials, therefore indicating different solubility properties for Mg in He(n). Moreover, we found interesting size effects for the behavior of the Mg impurity. As a sensitive probe of the solvation properties, the Mg excitation spectra have been simulated for various cluster sizes and compared with the available experimental results. The interaction between the excited 1P Mg atom and the He moiety has been approximated using the diatomics-in-molecules method and the two excited 1pi and 1sigma MgHe potentials. The shape of the simulated MgHe50 spectra shows a substantial dependency on the location of the Mg impurity, and hence on the MgHe pair interaction employed. To unravel the dependency of the solvation behavior on the shape of the computed potentials, exact density-functional theory has been adapted to the case of doped He(n) and various energy distributions have been computed. The results indicate the shape of the repulsive part of the MgHe potential as an important cause of the different behaviors.     

Size fractionation in a phase-separated colloidal fluid

Phase separation of a polydisperse colloidal dispersion implies size fractionation. An application of this effect is given by size-selective purification procedures associated with the colloidal synthesis of so-called monodisperse nanoparticles. We used electron microscopy to determine detailed particle size distributions of coexisting colloidal fluid phases containing highly polydisperse iron oxide nanoparticles with a log-normal distribution (sigma = 0.54 for the total system). Analysis of N approximately 10000 particles per phase yields the first five statistical moments of the distributions. Within experimental error, the interdependence of the statistical moments is in quantitative agreement with the "universal law of fractionation" proposed by Evans, Fairhurst, and Poon [Phys. Rev. Lett. 1998, 81, 1326], even though the theory was derived in the limit of slight polydispersity.     

Structure of polydisperse inverse ferrofluids: theory and computer simulation

By using theoretical analysis and molecular dynamics simulations, we investigate the structure of colloidal crystals formed by nonmagnetic microparticles (or magnetic holes) suspended in ferrofluids (called inverse ferrofluids), by taking into account the effect of polydispersity in size of the nonmagnetic microparticles. Such polydispersity often exists in real situations. We obtain an analytical expression for the interaction energy of monodisperse, bidisperse, and polydisperse inverse ferrofluids. Body-centered tetragonal (bct) lattices are shown to possess the lowest energy when compared with other sorts of lattices and thus serve as the ground state of the systems. Also, the effect of microparticle size distributions (namely, polydispersity in size) plays an important role in the formation of various kinds of structural configurations. Thus, it seems possible to fabricate colloidal crystals by choosing appropriate polydispersity in size.     

Interfacial colloidal sedimentation equilibrium. II. Closure-based density functional theory

In Part I [R. E. Beckham and M. A. Bevan, J. Chem. Phys. 127, 164708 (2007)], results were presented for the sedimentation equilibrium of concentrated colloidal dispersions using confocal scanning laser microscopy experiments, Monte Carlo (MC) simulations, and a local density approximation perturbation theory. In this paper, we extended the modeling effort on those systems to include nonlocal density functional theory (DFT), which is capable of predicting the microstructure of the sediment at length scales comparable to the colloidal particle dimension. Specifically, we use a closure-based DFT formulation to predict interfacial colloidal sedimentation equilibrium density profiles. The colloid-colloid and colloid-surface interactions were modeled with DLVO screened electrostatic potentials using parameters taken directly from the experimental work. The DFT profiles were compared to the experimental and MC results from Part I. Good agreement was found for relatively dilute interfacial colloidal fluids, but agreement was less satisfactory as interfacial layering became more pronounced for conditions approaching the onset of interfacial crystallization. We also applied DFT in an inverse sense using the measured colloid density profile to extract the underlying colloid-surface potential; this can be thought of as a microscopic analog to the well-known procedure of using the macroscopic (coarse-grained) density profile to extract the osmotic equation of state. For the dilute interfacial fluid, the inverse DFT calculations reproduced the true colloid-surface potential to within 0.5kT at all elevations.     

Reverse Monte Carlo modeling of the structure of colloidal aggregates

In this work we present results for the structure of aerogels coming from the diffusion-limited cluster aggregation simulation method. Pair distribution functions and structure factors, resulting from simulation, were considered as experimental input for reverse Monte Carlo modeling. The modeling yielded structural models with pair distribution functions and structure factors nearly identical to the results of the simulations. Particle configurations from both the simulations and reverse Monte Carlo modeling have been analyzed in terms of the distribution of the number of neighbors. It is suggested that the reverse Monte Carlo method, when applied to the structure factor, may be a suitable technique for the interpretation of experimental scattering data on colloidal aerogels.     

Effect of quenched size polydispersity on the fluid-solid transition in charged colloidal suspensions

We study the effect of quenched size polydispersity on the phase behavior of charged colloidal suspensions using free-energy calculations in Monte Carlo simulations. The colloids are assumed to interact with a hard-core repulsive Yukawa (screened-Coulomb) interaction with constant surface potential, so that the particles are polydisperse both in size and charge. In addition, we take the size distribution to be fixed in both the fluid and crystal phase (no size fractionation is allowed). We study the fluid-solid transition for various screening lengths and surface potentials, finding that upon increasing the size polydispersity the freezing transition shifts toward higher packing fractions and the density discontinuity between the two coexisting phases diminishes. Our results provide support for a terminal polydispersity above which the freezing transition disappears.     

Depletion interaction mediated by polydisperse rods

The interaction between a colloidal hard sphere of radius R and a wall or between two spheres in a dilute suspension of infinitely thin rods of length L is calculated numerically. The method allows the study of depletion potentials for any value of LR and, consequently, the influence of rod length polydispersity can be investigated. It was observed that both the depth and the range of the potential increase drastically if the relative standard deviation sigma of the length distribution is larger than 0.25, while the potential is virtually indistinguishable from that caused by monodisperse rods, if sigma < or similar to 0.1.     

In situ recording of particle network formation in liquids by ion conductivity measurements

The formation of fractal silica networks from a colloidal initial state was followed in situ by ion conductivity measurements. The underlying effect is a high interfacial lithium ion conductivity arising when silica particles are brought into contact with Li salt-containing liquid electrolytes. The experimental results were modeled using Monte Carlo simulations and tested using confocal fluorescence laser microscopy and ζ-potential measurements.