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.     

Stability boundaries, percolation threshold, and two-phase coexistence for polydisperse fluids of adhesive colloidal particles

We study the polydisperse Baxter model of sticky hard spheres (SHS) in the modified mean spherical approximation (mMSA). This closure is known to be the zero-order approximation C0 of the Percus-Yevick closure in a density expansion. The simplicity of the closure allows a full analytical study of the model. In particular we study stability boundaries, the percolation threshold, and the gas-liquid coexistence curves. Various possible subcases of the model are treated in details. Although the detailed behavior depends upon the particularly chosen case, we find that, in general, polydispersity inhibits instabilities, increases the extent of the nonpercolating phase, and diminishes the size of the gas-liquid coexistence region. We also consider the first-order improvement of the mMSA (C0) closure (C1) and compare the percolation and gas-liquid boundaries for the one-component system with recent Monte Carlo simulations. Our results provide a qualitative understanding of the effect of polydispersity on SHS models and are expected to shed new light on the applicability of SHS models for colloidal mixtures.     

Layer-by-layer growth of attractive binary colloidal particles

We investigate the two-dimensional (2D) colloidal structures formed by oppositely charged polystyrene monolayers grown layer-by-layer, where the electrostatic forces are recruited to assist in the packing of the layers. Our results show a transition through several 2D-superlattices to more close-packed structures with increasing ionic strength. The observed geometrical packing constraints of the 2D-superlattice structures agree well with the estimated Debye screening length of the electric double layer. By tuning interaction forces between charged colloids, electrostatic interactions could enhance the template-directed self-assembly process to achieve more complex and diverse structures.     

Viscoelasticity of mono- and polydisperse inverse ferrofluids

We report on measurements of a magnetorheological model fluid created by dispersing nonmagnetic microparticles of polystyrene in a commercial ferrofluid. The linear viscoelastic properties as a function of magnetic field strength, particle size, and particle size distribution are studied by oscillatory measurements. We compare the results with a magnetostatic theory proposed by De Gans et al. [Phys. Rev. E 60, 4518 (1999)] for the case of gap spanning chains of particles. We observe these chain structures via a long distance microscope. For monodisperse particles we find good agreement of the measured storage modulus with theory, even for an extended range, where the linear magnetization law is no longer strictly valid. Moreover we compare for the first time results for mono- and polydisperse particles. For the latter, we observe an enhanced storage modulus in the linear regime of the magnetization.     

Structure formation and fractionation in systems of polydisperse attractive rods

Fractionation effects and the formation of structured domains are investigated in polydisperse systems of attractive spherocylinders with the help of Monte Carlo simulations. For sufficiently high attractive interaction strength and pressure, the large rods in the system aggregate and form a highly ordered hexatic monolayer that coexists with an isotropic fluid of smaller rods. Fractionation diminishes with decreasing interaction strength but is still observed for hard rod systems, in which the large rods form a nematic droplet rather than a monolayer. Results for polydisperse systems are accompanied by phase diagrams for monodisperse systems of attractive spherocylinders. Here, the phase behavior is shown as a function of rod length and pressure.     

Direct imaging of repulsive and attractive colloidal glasses

Coherent anti-Stokes Raman scattering microscopy is performed on glassy systems of poly(methylmethacrylate) colloidal particles in density- and refractive-index-matched solvents. Samples are prepared with varying amounts of linear polystyrene, which induces a depletion driven attraction between the nearly hard-sphere particles. Images collected over several hours confirm the existence of a reentrant glass transition. The images also reveal that the dynamics of repulsive and attractive glasses are qualitatively different. Colloidal particles in repulsive glasses exhibit cage rattling and escape, while those in attractive glasses are nearly static while caged but exhibit large displacements upon (infrequent) cage escape.     

Structural and dynamical analysis of monodisperse and polydisperse colloidal systems

We present a semigrand ensemble Monte Carlo and Brownian dynamics simulation study of structural and dynamical properties of polydisperse soft spheres interacting via purely repulsive power-law potentials with a varying degree of "softness." Comparisons focus on crystal and amorphous phases at their coexistence points. It is shown through detailed structural analysis that as potential interactions soften, the "quality of crystallinity" of both monodisperse and polydisperse systems deteriorates. In general, polydisperse crystalline phases are characterized by a more ordered structure than the corresponding monodisperse ones (i.e., for the same potential softness). This counter-intuitive feature originates partly from the fact that particles of different sizes may be accommodated more flexibly in a crystal structure and from the reality that coexistence (osmotic) pressure is substantially higher for polydisperse systems. These trends diminish for softer potentials. Potential softness eventually produces substitutionally disordered crystals. However, substitutional order is apparent for the hard-spherelike interactions. Diffusionwise, crystals appear quite robust with a slight difference in the vibrational amplitudes of small and large particles. This difference, again, diminishes with potential softness. Overcrowding in amorphous polydisperse suspensions causes "delayed" diffusion at intermediate times.     

Anomalous columnar order of charged colloidal platelets

Monte Carlo computer simulations are carried out for a model system of like-charged colloidal platelets in the isothermal-isobaric ensemble (NpT). The aim is to elucidate the role of electrostatic interactions on the structure of synthetic clay systems at high particle densities. Short-range repulsions between particles are described by a suitable hard-core model representing a discotic particle. This potential is supplemented with an electrostatic potential based on a Yukawa model for the screened Coulombic potential between infinitely thin disklike macro-ions. The particle aspect-ratio and electrostatic parameters were chosen to mimic an aqueous dispersion of thin, like-charged, rigid colloidal platelets at finite salt concentration. An examination of the fluid phase diagram reveals a marked shift in the isotropic-nematic transition compared to the hard cut-sphere reference system. Several statistical functions, such as the pair correlation function for the center-of-mass coordinates and structure factor, are obtained to characterize the structural organization of the platelets phases. At low salinity and high osmotic pressure we observe anomalous hexagonal columnar structures characterized by interpenetrating columns with a typical intercolumnar distance corresponding to about half of that of a regular columnar phase. Increasing the ionic strength leads to the formation of glassy, disordered structures consisting of compact clusters of platelets stacked into finite-sized columns. These so-called "nematic columnar" structures have been recently observed in systems of charge-stabilized gibbsite platelets. Our findings are corroborated by an analysis of the static structure factor from a simple density functional theory.     

Numerical methods for inverse problems in electrooptics of polydisperse colloids

In this paper we propose a new method for the determination of the distribution of electrical and geometrical particle parameters based on electrooptical experimental data. The electrooptical method leads to the solution of inverse ill-posed problems. The main equations for the determination of the distribution of particles on these parameters are presented. To find out the distribution functions from the electrooptical experimental data one has to solve the first-kind Fredholm integral equation corresponding to the problem under study. The proposed method of its solution is based on the penalty functions method. The results of modelling that let us compare the various numerical methods are presented.     

Time-resolved and steady state spectroscopy of polydisperse colloidal silver nanoparticle samples

A signal due to coherently excited vibrational motion has been observed in polydisperse silver nanoparticle samples. The particles were synthesized via a wet chemistry seed mediated method, which yields different particle shapes, including spheres, rods, and irregular triangular-shaped particles. The measured vibrational periods were compared to the results from continuum mechanics calculations. This analysis shows that the observed signal arises from the triangular-shaped particles, rather than the rods or spheres. The period of vibration increases as the dimensions of the triangular-shaped particles increase; specifically, we find that the period is given by 2h/c(l), where h is the bisector of the triangle and c(l) is the longitudinal speed of sound in silver.     

Microrheology of wormlike micellar fluids from the diffusion of colloidal probes

The microrheology of cationic micellar solutions has been investigated as a function of added organic salts using quasielastic light scattering (QELS). Two organic salts, sodium p-toluene sulfonate and sodium salicylate, were used to induce microstructural changes in cetyl trimethylammonium bromide (CTAB) micelles. The mean-squared displacement (MSD) of polystyrene probe particles embedded in CTAB micellar solutions was monitored by QELS in the single-scattering regime. Through the use of the generalized Stokes-Einstein relationship, the frequency-dependent complex shear moduli of each fluid were estimated from the Laplace transform of the corresponding MSD. The salt-induced transition from nearly spherical to elongated wormlike micelles and consequent changes in fluid response from viscous to viscoelastic are clearly captured by microrheology.     

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.     

Structure of polymer fluids in colloidal dispersions

We have calculated some structural properties of a fluid of hard sphere polymer chains about a variable sized central hard sphere with the Monte Carlo method in the canonical ensemble. We have additionally calculated these structural properties with an integral equation based on density functional theory. The integral equation theory gives good agreement with the simulations at all but the highest densities.     

De-mixing of polydisperse fluids: experimental test of a universal relation

Colloids, emulsions, polymer blends, and other important complex fluids, are polydisperse, i.e. there are variations among their constituent particles. Polydispersity is usually regarded as an ubiquitous, uncontrollable nuisance causing experimental inconsistencies. We have varied the polydispersity of a complex fluid, whilst keeping all other parameters constant, and report the first measurements of some universal physics. At coexistence (e.g. between liquid and vapour), fractionation occurs—each phase receives a different mix of the various ingredients, e.g. with the liquid disproportionately abundant with larger particles. Theory predicts, at low polydispersity, that this de-mixing becomes universal, irrespective of the material, with chemical differences between the phases proportional to polydispersity to the power two. We have studied colloid–polymer suspensions at two-phase coexistence and, using light scattering, measured the exponent as 2.16±0.44.     

Anomalous temperature dependence of interfacial tension in water-hydrocarbon mixtures

An experimental study of the interfacial tension (IFT) as a function of temperature for three water-hydrocarbon mixtures is reported. The interfacial tension rises with increasing temperature for all mixtures studied, which contradicts the Antonov rule.     

Predicting interfacial tension between water and nonpolar fluids from a Cahn-type theory

We propose an accurate method to predict interfacial tension between water and nonpolar fluids by using Cahn gradient theory. The only necessary elements are (i) a water contact energy function and (ii) an equation of state (EoS) for the nonpolar fluid, chosen here as the Peng-Robinson EoS. The contact energy, a function of the fluid (adsorbate) surface density, is related to interfacial tension (IFT) by means of the Gibbs adsorption equation. Examining a large number of IFT data, we observe that the water contact energy is a universal function of adsorbate's surface density when proper scaling variables are used: it depends neither on adsorbate nor on temperature. A corresponding-states principle appears to govern the interfacial behavior between water and any nonpolar compound that is sparingly soluble in water. A predictive method (without any adjustable parameter) is therefore available for estimating IFT between water and any nonpolar fluid, whether the fluid is in supercritical or in subcritical states. The method performs well when the adsorbate is sparingly soluble in water, but slightly overestimates IFTs when the adsorbate's solubility in water is significant (e.g., CO2 and H2S). A similar behavior should also hold for interfaces involving a solid substrate.     

The non-random distribution of free volume in fluids: polydisperse polymer systems

A new equation-of-state model is presented that accounts for the non-random distribution of free volume in multicomponent fluid mixtures. The classical quasi-chemical approach is used in connection with the Lattice Fluid (LF) model. The model is extended via continuous thermodynamics to polydisperse polymer systems. The algorithm for the application of the model to phase equilibrium calculations is also presented. The model is applied to both solvent—polydisperse polymer and to polydisperse polymer—polydisperse polymer systems. Besides phase equilibrium calculations, the distributions of the polymeric species in principal and conjugate phases are obtained. The comparison with available experimental data is satisfactory.