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.     

Inverse density-functional theory as an interpretive tool for measuring colloid-surface interactions in dense systems

Recent advances in optical microscopy, such as total internal reflection and confocal scanning laser techniques, now permit the direct three-dimensional tracking of large numbers of colloidal particles both near and far from interfaces. A novel application of this technology, currently being developed by one of the authors under the name of diffusing colloidal probe microscopy (DCPM), is to use colloidal particles as probes of the energetic characteristics of a surface. A major theoretical challenge in implementing DCPM is to obtain the potential energy of a single particle in the external field created by the surface, from the measured particle trajectories in a dense colloidal system. In this paper we develop an approach based on an inversion of density-functional theory (DFT), where we calculate the single-particle-surface potential from the experimentally measured equilibrium density profile in a nondilute colloidal fluid. The underlying DFT formulation is based on the recent work of Zhou and Ruckenstein [Zhou and Ruckenstein, J. Chem. Phys. 112, 8079 (2000)]. For model hard-sphere and Lennard-Jones systems, using Monte Carlo simulation to provide the "experimental" density profiles, we found that the inversion procedure reproduces the true particle-surface-potential energy to an accuracy within typical DCPM experimental limitations (approximately 0.1 kT) at low to moderate colloidal densities. The choice of DFT closures also significantly affects the accuracy.     

Closure-based density functional theory applied to interfacial colloidal fluids

The behavior of dense colloidal fluids near surfaces can now be probed in great detail with experimental techniques like confocal microscopy. In fact, we are approaching a point where quantitative comparisons of experiment with particle-level theory, such as classical density functional theory (DFT), are appropriate. In a forward sense, we may use a known surface potential to predict a particle density distribution function from DFT; in an inverse sense, we may use an experimentally measured particle density distribution function to predict the underlying surface potential from DFT. In this paper, we tested the ability of the closure-based DFT of Zhou and Ruckenstein (J. Chem. Phys. 2000, 112, 8079-8082) to perform forward and inverse calculations on potential models commonly employed for colloidal particles and surfaces. To reduce sources of uncertainty in this initial study, Monte Carlo simulation results played the role of experimental data. The combination of Rogers-Young and modified-Verlet closures consistently performed well across the different potential models. For a reasonable range of choices of the density, temperature, and potential parameters, the inversion procedure yielded particle-surface potentials to an accuracy on the order of 0.1kT.     

Hard sphere fluids at a soft repulsive wall: a comparative study using Monte Carlo and density functional methods

Hard-sphere fluids confined between parallel plates at a distance D apart are studied for a wide range of packing fractions including also the onset of crystallization, applying Monte Carlo simulation techniques and density functional theory. The walls repel the hard spheres (of diameter σ) with a Weeks-Chandler-Andersen (WCA) potential V(WCA)(z) = 4ε[(σ(w)/z)(12) - (σ(w)/z)(6) + 1/4], with range σ(w) = σ/2. We vary the strength ε over a wide range and the case of simple hard walls is also treated for comparison. By the variation of ε one can change both the surface excess packing fraction and the wall-fluid (γ(wf)) and wall-crystal (γ(wc)) surface free energies. Several different methods to extract γ(wf) and γ(wc) from Monte Carlo (MC) simulations are implemented, and their accuracy and efficiency is comparatively discussed. The density functional theory (DFT) using fundamental measure functionals is found to be quantitatively accurate over a wide range of packing fractions; small deviations between DFT and MC near the fluid to crystal transition need to be studied further. Our results on density profiles near soft walls could be useful to interpret corresponding experiments with suitable colloidal dispersions.     

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.     

Sedimentation equilibrium of colloidal suspensions in a planar pore based on density functional theory and the hard-core attractive Yukawa model

The sedimentation equilibrium of colloidal suspensions modeled by hard-core attractive Yukawa (HCAY) fluids in a planar pore is studied. The density profile of the HCAY fluid in a gravitational field and its distribution between the pore and uniform phases are investigated by a density functional theory (DFT) approach, which results from employing a recently proposed parameter-free version of the Lagrangian theorem-based density functional approximation (Zhou, S. Phys. Lett. A 2003, 319, 279) for hard-sphere fluids to the hard-core part of the HCAY fluid, and the second-order functional perturbation expansion approximation to the tail part as was done in a recent partitioned density functional approximation (Zhou, S. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2003, 68, 061201). The resultant DFT approach is, thus, the first adjustable parameter-free DFT for HCAY fluids. The validity of the present DFT for HCAY fluids of reduced range parameter z(red) = 1.8 under various external potentials is established in the first of the papers cited previously. The present DFT for HCAY fluids can predict the radial distribution function for the bulk HCAY fluid accurately in the colloidal limit (large value of z(red)), and in the hard-sphere limit, its prediction for the density profile of the hard-sphere fluid in a gravitational field is in very good agreement with the existing simulation data. The dependence of the density profile and distribution coefficient on the magnitude of the interparticle attraction, gravitational field, and degree of confinement is investigated in detail by the present DFT approach. Intuitive and qualitative analyses are also compared with the quantitative DFT calculational results.     

kT-scale colloidal interactions in high-frequency inhomogeneous AC electric fields. II. Concentrated ensembles

We report nonintrusive optical microscopy measurements of ensembles of polystyrene colloids in inhomogeneous AC electric fields as a function of field frequency and particle size. By using an inverse Monte Carlo (MC) simulation analysis of time-averaged particle microstructures, we sensitively measure induced dipole-dipole interactions on the kT energy scale. Measurements are reported for frequencies when the particle polarizability is greater and less than the medium, as well as the crossover between these conditions when dipole-dipole interactions vanish. By using measured single dipole-field interactions and associated parameters from Part I as input in the inverse analysis, the dipole-dipole interactions in this work are accurately modeled with no adjustable parameters for conditions away from the crossover frequency (i.e., |f(CM)| > 0). As dipolar interactions vanish at the crossover, a single frequency-dependent parameter is introduced to account for microstructures that appear to result from weak AC electro-osmotic flow induced interactions. By connecting quantitative measures of equilibrium microstructures and kT-scale dipole-field and dipole-dipole interactions, our findings provide a basis to understand colloidal assembly in inhomogeneous AC electric fields.     

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.     

Entropic wetting and the free isotropic-nematic interface of hard colloidal platelets

We study bulk and interfacial properties of a model suspension of hard colloidal platelets with continuous orientations and vanishing thickness using both density functional theory, based on either a second virial approach or fundamental measure theory (FMT), and Monte Carlo (MC) simulations. We calculate the bulk equation of state, bulk isotropic-nematic (IN) coexistence, and properties of the (planar) free IN interface and of adsorption at a planar hard wall, where we find complete wetting of the nematic phase at the isotropic-wall interface upon approaching bulk IN coexistence. We investigate in detail the asymptotic decay of correlations at large distances. In all cases, the results from FMT and MC agree quantitatively. Our findings are of direct relevance to understanding interfacial properties of dispersions of colloidal platelets.     

Monte Carlo versus molecular dynamics simulations in heterogeneous systems: an application to the n-pentane liquid-vapor interface

The Monte Carlo (MC) and molecular dynamics (MD) methodologies are now well established for computing equilibrium properties in homogeneous fluids. This is not yet the case for the direct simulation of two-phase systems, which exhibit nonuniformity of the density distribution across the interface. We have performed direct MC and MD simulations of the liquid-gas interface of n-pentane using a standard force-field model. We obtained density and pressure components profiles along the direction normal to the interface that can be very different, depending on the truncation and long range correction strategies. We discuss the influence on predicted properties of different potential truncation schemes implemented in both MC and MD simulations. We show that the MD and MC profiles can be made in agreement by using a Lennard-Jones potential truncated via a polynomial function that makes the first and second derivatives of the potential continuous at the cutoff distance. In this case however, the predicted thermodynamic properties (phase envelope, surface tension) deviate from experiments, because of the changes made in the potential. A further readjustment of the potential parameters is needed if one wants to use this method. We conclude that a straightforward use of bulk phase force fields in MD simulations may lead to some physical inconsistencies when computing interfacial properties.     

Role of polydispersity in anomalous interactions in electrostatically levitated colloidal systems

In this paper, we investigate the effects of using inverse analyses developed for monodisperse particles to extract particle-particle and particle-surface potentials from simulated interfacial colloidal configurations having finite-size polydispersity. Forward Monte Carlo simulations are used to generate three-dimensional equilibrium configurations of log normal-distributed polydisperse particles confined by gravity near an underlying surface. Particles remain levitated above the substrate and stabilized against aggregation by repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek pair potentials. An inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method are used to obtain interactions from simulated distribution functions as a function of polydispersity (sigma), relative range of repulsion (kappa a), and projected interfacial concentration (rho). Both inverse analyses successfully recover input potentials for all monodisperse cases, but fail for polydispersities often encountered in experiments. For different conditions (sigma, kappa a, and rho), our results indicate softened short-range repulsion, anomalous long-range attraction, and apparent particle overlaps, which are similar to commonly reported observations in optical microscopy measurements of quasi-two-dimensional interfacial colloidal ensembles. By demonstrating signatures of, and limitations due to, polydispersity when extracting pair potentials from measured distribution functions, our specific goal is to provide a basis to objectively interpret and resolve the effects of polydispersity in optical microscopy experiments.     

Structure and adsorption of a hard-core multi-Yukawa fluid confined in a slitlike pore: grand canonical Monte Carlo simulation and density functional study

Because of the increasing interest in studying the phenomenon exhibited by charge-stabilized colloidal suspensions in confining geometry, we present a density functional theory (DFT) for a hard-core multi-Yukawa fluid. The excess Helmholtz free-energy functional is constructed by using the modified fundamental measure theory and Rosenfeld's perturbative method, in which the bulk direct correlation function is obtained from the first-order mean spherical approximation. To validate the established theory, grand canonical ensemble Monte Carlo (GCMC) simulations are carried out to determine the density profiles and surface excesses of multi-Yukawa fluid in a slitlike pore. Comparisons of the theoretical results with the GCMC data suggest that the present DFT gives very accurate density profiles and surface excesses of multi-Yukawa fluid in the slitlike pore as well as the radial distribution functions of the bulk fluid. Both the DFT and the GCMC simulations predict the depletion of the multi-Yukawa fluid near a nonattractive wall, while the mean-field theory fails to describe this depletion in some cases. Because the simple form of the direct correlation function is used, the present DFT is computationally as efficient as the mean-field theory, but reproduces the simulation data much better than the mean-field theory.     

Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach

We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO(2) and poly(methyl methacrylate) CO(2) systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.     

Liquid-vapor density profiles from equilibrium limit of diffusion equation for interacting particles

Liquid-vapor density profiles are derived from the equilibrium limit of diffusion equation for interacting particles. These profiles are in good agreement with classical hyperbolic tangent relation. For simple Lennard-Jones fluids, predicted density distributions agree with computer simulation data, but have a slightly sharper transition zone. For alkali metals with Lennard-Jones-like potentials, the new equations predict a very good average distribution with quite satisfactory agreement with Monte Carlo simulation results. For liquid metals and water surfaces, accurate interfacial profile predictions also can be achieved by using effective two-body potential data instead of Lennard-Jones parameters.     

Density functional theory and quadratic complete basis set ab initio studies of the HNSi to HSiN isomerization and hydrogen insertion reactions with further isomerizations of the insertion products

Ab initio and density functional theory (DFT) computational studies were performed in order to determine the potential energy profiles for the inter-conversions of the small silicon–nitrogen built chemical systems: HSiN, HNSi, HSiNH₂, and HNSiH₂. Three hybrid DFT methods demonstrated high reliability in computing structures and potential energy profiles for these chemical transformations. The stability of some of these molecular systems and their interconversions was discussed and computational results were compared with experimental observations when available.     

Electron momentum density and band structure calculations of α- and β-GeTe

We have measured isotropic experimental Compton profile of α-GeTe by employing high energy (662 keV) γ-radiation from a ¹³⁷Cs isotope. To compare our experiment, we have also computed energy bands, density of states, electron momentum densities and Compton profiles of α- and β-phases of GeTe using the linear combination of atomic orbitals method. The electron momentum density is found to play a major role in understanding the topology of bands in the vicinity of the Fermi level. It is seen that the density functional theory (DFT) with generalised gradient approximation is relatively in better agreement with the experiment than the local density approximation and hybrid Hartree–Fock/DFT.     

Interfacial properties of compressible polymer solutions

A chemomechanical model for the interfacial concentration and density in compressible polymer solutions is formulated using variational principles. The nonlinear model with boundary conditions obtained from phase equilibrium calculations gives the coupled concentration and density profiles. The couplings between chemical and mechanical balances are identified and efficient ways to calculate the interfacial structure is identified. A specific model appropriate to high‐pressure processing of the polyolefins is developed using the modified Sanchez Lacombe equation of state. Bakker's formula for the interfacial tension is adapted to compressible polymer solutions. The structure and tension of a flat interface is characterized using the developed model and material properties of three molecular weight hydrogenated polybutadiene; the main variables of interest were the pressure, polymer molecular weight, and temperature. The relation between the pressure profile across the interface and the interfacial tension is characterized. Scaling power laws for interfacial tension and interfacial thickness as a function of pressure are obtained and contrasted with the corresponding laws observed and predicted for incompressible polymer solutions. It is found that the modified Sanchez Lacombe‐based power law prediction predictions for compressible solutions in terms of pressure quenches are similar to those from those obtained by the Flory‐Huggins incompressible model for temperature quenches. The present results provide the basis for the future study of the kinetics of pressure‐induced phase separation in compressible polymer solutions. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 640–654, 2009     

A combined experimental and theoretical quantum chemical studies on 4-morpholinecarboxaldehyde

Extensive spectroscopic investigations have been carried out by recording the Fourier transform infrared (FTIR) and FT-Raman spectra and carrying out the theoretical quantum chemical studies on 4-morpholinecarboxaldehyde (4MC). From the ab initio and DFT analysis using HF, B3LYP and B3PW91 methods with 6-31G(d,p) and 6-311G++(d,p) basis sets the energies, structural, thermodynamical and vibrational characteristics of the compound were determined. The energy difference between the chair equatorial and chair axial conformers of 4MC have been calculated by density functional theory (DFT) method. The optimised geometrical parameters, theoretical wavenumbers and thermodynamic properties of the molecule were compared with the experimental values. The effect of carbonyl group on the characteristic frequencies of the morpholine ring has been analysed. The mixing of the fundamental modes with the help of potential energy distribution (PED) through normal co-ordinate analysis has been discussed.     

The colloidal force of bead-spring chains in a good solvent

A recently developed density functional theory (DFT) for tethered bead-spring chains is used to investigate colloidal forces for the good solvent case. A planar surface of tethered chains is opposed to a bare, hard wall and the force exerted on the bare wall is calculated by way of the contact density. Previously, the case of large wall separation was investigated. The density profiles of the unperturbed chains, in that case, were found to be neither stepfunctions nor parabolas and were shown to accurately predict computer simulation results. In the present paper, the surface forces that result from the distortion of these density profiles at finite wall separation is studied. The resulting force function is analyzed for varying surface coverages, wall separations, and chain lengths. The results are found to be in near quantitative agreement with the scaling predictions of Alexander [S. Alexander, J. Phys. (Paris) 38, 983 (1977)] when the layer thickness is "correctly" defined. Finally, a hybrid Alexander-DFT theory is suggested for the analysis of experimental results.