Depletion potential in the infinite dilution limit

The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the rational function approximation method for the structural properties of hard-sphere mixtures [S. B. Yuste, A. Santos, and M. Lopez de Haro, J. Chem. Phys. 108, 3683 (1998)]. The cases of equal solute particles and of one big particle and a hard planar wall in a background monodisperse hard-sphere fluid are explicitly analyzed. An improvement over the performance of the Percus-Yevick theory and good agreement with available simulation results are found.     

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.     

Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions

The Polymer Reference Interaction Site Model (PRISM) theory is employed to investigate structure, effective forces, and thermodynamics in dense polymer-particle mixtures in the one and two particle limit. The influence of particle size, degree of polymerization, and polymer reduced density is established. In the athermal limit, the surface excess is negative implying an entropic dewetting interface. Polymer induced depletion interactions are quantified via the particle-particle pair correlation function and potential of mean force. A transition from (nearly) monotonic decaying, attractive depletion interactions to much stronger repulsive-attractive oscillatory depletion forces occurs at roughly the semidilute-concentrated solution boundary. Under melt conditions, the depletion force is extremely large and attractive at contact, but is proceeded by a high repulsive barrier. For particle diameters larger than roughly five monomer diameters, division of the force by the particle radius results in a nearly universal collapse of the depletion force for all interparticle separations. Molecular dynamics simulations have been employed to determine the depletion force for nanoparticles of a diameter five times the monomer size over a wide range of polymer densities spanning the semidilute, concentrated, and melt regimes. PRISM calculations based on the spatially nonlocal hypernetted chain closure for particle-particle direct correlations capture all the rich features found in the simulations, with quantitative errors for the amplitude of the depletion forces at the level of a factor of 2 or less. The consequences of monomer-particle attractions are briefly explored. Modification of the polymer-particle pair correlations is relatively small, but much larger effects are found for the surface excess including an energetic driven transition to a wetting polymer-particle interface. The particle-particle potential of mean force exhibits multiple qualitatively different behaviors (contact aggregation, steric stabilization, local bridging attraction) depending on the strength and spatial range of the polymer-particle attraction.     

Thermodynamically consistent closure approximation for hard spheres systems

We present a new closure relation that is an extension of the Percus-Yevick approximation. In the proposed closure, we introduce an additional term and a mixing coefficient that can be determined by imposing a condition of thermodynamic self-consistency. Moreover, the mixing coefficient is calculated analytically within a linear approximation. In the case of a monodisperse system of hard spheres, we compare the results of our model to well-established thermodynamic expressions and also to the structural properties of fairly known closure approximations. In the second case, and using an equivalent scheme, the new closure relation is extended to the depletion potential between two large hard spheres immersed in a liquid of small hard spheres. In both cases, the results of our model are in good agreement with numerical simulations performed at intermediate concentrations.     

Effective interactions in colloid-semipermeable membrane systems

We investigate effective interactions between a colloidal particle, immersed in a binary mixture of smaller spheres, and a semipermeable membrane. The colloid is modeled as a big hard sphere, and the membrane is represented as an infinitely thin surface, which is fully permeable to one of the smaller spheres and impermeable to the other one. Within the framework of the density functional theory, we evaluate depletion potentials and we consider two different approximate theories: the simple Asakura-Oosawa approximation and the accurate White-Bear version of the fundamental measure theory. The effective potentials are compared with the corresponding potentials for the hard, nonpermeable wall. Using statistical-mechanical sum rules, we argue that the contact value of the depletion potential between a colloid and a semipermeable membrane is smaller in magnitude than the potential between a colloid and a hard wall. A heuristic argument is provided that the colloid-semipermeable membrane effective interactions are generally weaker than these near a hard nonpermeable wall. These predictions are confirmed by explicit calculations, and the effect is more pronounced for smaller osmotic pressures. The depletion potential for a colloidal particle inside a semipermeable vesicle is stronger than the potential for the colloidal particle located outside of a vesicle. We find that the asymptotic decay of the depletion potential for the semipermeable membrane is similar to that for the nonpermeable wall and reflects the asymptotics of the total correlation function of the corresponding binary mixture of smaller spheres. Our results demonstrate that the ability of the membrane to change its shape as well as specific interactions constitute an important factor in determining the effective interactions between the semipermeable membrane and the colloidal macroparticle.     

Depletion potentials in colloidal mixtures of hard spheres and rods

The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.     

Relaxation scenarios in a mixture of large and small spheres: dependence on the size disparity

We present a computational investigation on the slow dynamics of a mixture of large and small soft spheres. By varying the size disparity at a moderate fixed composition different relaxation scenarios are observed for the small particles. For small disparity density-density correlators exhibit moderate stretching. Only small quantitative differences are observed between dynamic features for large and small particles. On the contrary, large disparity induces a clear time scale separation between the large and small particles. Density-density correlators for the small particles become extremely stretched and display logarithmic relaxation by properly tuning the temperature or the wave vector. Self-correlators decay much faster than density-density correlators. For very large size disparity, a complete separation between self- and collective dynamics is observed for the small particles. Self-correlators decay to zero at temperatures where density-density correlations are frozen. The dynamic picture obtained by varying the size disparity resembles features associated with mode coupling transition lines of the types B and A at, respectively, small and very large size disparities. Both lines might merge, at some intermediate disparity, at a higher-order point, to which logarithmic relaxation would be associated. This picture resembles predictions of a recent mode coupling theory for fluids confined in matrices with interconnected voids [V. Krakoviack, Phys. Rev. Lett. 94, 065703 (2005)].     

Synthesis and characterization of surface modified SBA-15 silica materials and their application in chromatography

Hexagonally ordered SBA-15 mesoporous silica spheres with large uniform pore diameters are obtained using the triblock copolymer, Pluronic P123, as template with a cosurfactant cetyltrimethylammonium bromide (CTAB) and the cosolvent ethanol in acidic media. A series of surface modified SBA-15 silica materials is prepared in the present work using mono- and trifunctional alkyl chains of various lengths which improves the hydrothermal and mechanical stability. Several techniques, such as element analysis, nitrogen sorption analysis, small angle X-ray diffraction, scanning electron microscopy (SEM), FTIR, solid-state (29)Si and (13)C NMR spectroscopy are employed to characterize the SBA-15 materials before and after surface modification with the organic components. Nitrogen sorption analysis is performed to calculate specific surface area, pore volume and pore size distribution. By surface modification with organic groups, the mesoporous SBA-15 silica spheres are potential materials for stationary phases in HPLC separation of small aromatic molecules and biomolecules. The HPLC performance of the present SBA-15 samples is therefore tested by means of a suitable test mixture.     

Diffusion of spheres in crowded suspensions of rods

Translational tracer diffusion of spherical macromolecules in crowded suspensions of rodlike colloids is investigated. Experiments are done using several kinds of spherical tracers in fd-virus suspensions. A wide range of size ratios L/2a of the length L of the rods and the diameter 2a of the tracer sphere is covered by combining several experimental methods: fluorescence correlation spectroscopy for small tracer spheres, dynamic light scattering for intermediate sized spheres, and video microscopy for large spheres. Fluorescence correlation spectroscopy is shown to measure long-time diffusion only for relatively small tracer spheres. Scaling of diffusion coefficients with a/xi, predicted for static networks, is not found for our dynamical network of rods (with xi the mesh size of the network). Self-diffusion of tracer spheres in the dynamical network of freely suspended rods is thus fundamentally different as compared to cross-linked networks. A theory is developed for the rod-concentration dependence of the translational diffusion coefficient at low rod concentrations for freely suspended rods. The proposed theory is based on a variational solution of the appropriate Smoluchowski equation without hydrodynamic interactions. The theory can, in principle, be further developed to describe diffusion through dynamical networks at higher rod concentrations with the inclusion of hydrodynamic interactions. Quantitative agreement with the experiments is found for large tracer spheres, and qualitative agreement for smaller spheres. This is probably due to the increasing importance of hydrodynamic interactions as compared to direct interactions as the size of the tracer sphere decreases.     

LaAlO3 hollow spheres: synthesis and luminescence properties

Nearly monodisperse LaAlO(3) hollow spheres are synthesized by a novel precursor thermal decomposition method. Spherical colloids of capsulelike precursors with uniform diameters of 273 ± 35 nm have been synthesized by a solvothermal method. These spherical colloids could convert to LaAlO(3) hollow spheres with diameters of 166 ± 26 nm by a thermal decomposition process. The thermal transformation process from the precursors to LaAlO(3) was characterized by thermogravimetric analysis (TGA), X-ray diffraction (XRD), and the Fourier transform infrared spectroscopy (FT-IR). By the doping of various lanthanide ions (Sm(3+), Eu(3+), and Tb(3+)), the emission luminescence of lanthanide-doped LaAlO(3) hollow microspheres can be tuned from red to green. In particular, these luminescent LaAlO(3) hollow spheres can be well dispersed in polar solvents such as the ethanol and water, which broadens the range of potential applications of these hollow spheres. The UV-vis absorption spectra show energy absorption at 211, 223, and 313 nm corresponding to the host lattice absorption and charge-transfer transitions. The results are in good agreement with the peaks observed in the excitation spectra.     

Haloing, flocculation, and bridging in colloid-nanoparticle suspensions

Integral equation theory with a hybrid closure approximation is employed to study the equilibrium structure of highly size asymmetric mixtures of spherical colloids and nanoparticles. Nonequilibrium contact aggregation and bridging gel formation is also qualitatively discussed. The effect of size asymmetry, nanoparticle volume fraction and charge, and the spatial range, strength, and functional form of colloid-nanoparticle and colloid-colloid attractions in determining the potential-of-mean force (PMF) between the large spheres is systematically explored. For hard, neutral particles with weak colloid-nanoparticle attraction qualitatively distinct forms of the PMF are predicted: (i) a contact depletion attraction, (ii) a repulsive form associated with thermodynamically stable "nanoparticle haloing," and (iii) repulsive at contact but with a strong and tight bridging minimum. As the interfacial cohesion strengthens and becomes shorter range the PMF acquires a deep and tight bridging minimum. At sufficiently high nanoparticle volume fractions, a repulsive barrier then emerges which can provide kinetic stabilization. The charging of nanoparticles can greatly reduce the volume fractions where significant changes of the PMF occur. For direct and interfacial van der Waals attractions, the large qualitative consequences of changing the absolute magnitude of nanoparticle and colloid diameters at fixed size asymmetry ratio are also studied. The theoretical results are compared with recent experimental and simulation studies. Calculations of the real and Fourier space mixture structure at nonzero colloid volume fractions reveal complex spatial reorganization of the nanoparticles due to many body correlations.     

用积分方程方法决定胶粒之间的空耗势

Binary components Ornstein-Zernike integral equation with the concentration of large particle component being set to zero was employed to study the depletion potential behavior between two large neutral colloid particles （modeled as hard spheres）immersed in a sea of small neutral solvent particles. The prediction for the depletion potential behavior compared well with simulation data and experimental data available in the literature. It is found that the Hansen-Verlet one phase criterion,based on the effective one component system with the present depletion potential,for the freezing transition is completely not suitable for the real binary components system. It is disclosed that the unsuitability is due to the volume term of the solid phase and liquid phase which can not be treated selfconsistently in the Hansen-Verlet one phase criterion.     

Multiphase coexistence in polydisperse colloidal mixtures

The authors study the phase behavior of mixtures of monodisperse colloidal spheres with a depletion agent which can have arbitrary shape and can possess a polydisperse size or shape distribution. In the low concentration limit considered here, the authors can employ the free-volume theory and take the geometry of particles of the depletion agent into account within the framework of fundamental measure theory. The authors apply their approach to study the phase diagram of a mixture of (monodisperse) colloidal spheres and two polydisperse polymer components. By fine tuning the distribution of the polymer, it is possible to construct a complex phase diagram which exhibits two stable critical points.     

Monodisperse magnetizable composite silica spheres with tunable dipolar interactions

We demonstrate that magnetic particles of maghemite (gamma-Fe(2)O(3)) and cobalt ferrite (CoFe(2)O(4)) can be irreversibly attached to colloidal silica that is grafted with 3-mercaptopropyl(trimethoxy)silane (followed by the controlled growth of a silica layer) to obtain stable dispersions of monodisperse colloidal silica spheres that contain a dense shell of ferrite particles at an adjustable distance from the sphere surface. Magnetization of the ferrite shell induces a large dipole moment, and adjusting the thickness of the outer silica layer enables one to tune the contact attraction. This novel type of magnetizable silica colloid exhibits structure formation in a homogeneous field that varies from isotropic distributions to elongated dipolar chains.     

An exact formula for the contact value of the density profile of a system of charged hard spheres near a charged wall

An exact formula for the contact value of the density of a system of charged hard spheres near a charged hard wall is obtained by means of a general statistical mechanical argument. In addition, a formula for the contact value of the charge profile in the limit of large field is obtained. Comparison with the corresponding expressions in the Poisson-Boltzmann theory of Gouy and Chapman shows that these latter expressions become exact for large fields, independent of the density of the hard spheres.     

Self-assembled double-shelled ferrihydrite hollow spheres with a tunable aperture

Novel double-shelled hierarchical ferrihydrite hollow spheres (Fe(10)O(14)(OH)(2).4H(2)O) were successfully synthesized on a large scale by using a facile medicine-inspired solution-phase approach. Sodium nitroprusside (SNP), an ordinary and inexpensive medicine for expanding blood vessels, served as both a ferric source and an in situ formed gas-bubble template with the presence of sodium dihydrogen phosphate as a pH regulator, coordinator, and stabilizer. A twice-gas-bubble template model has been proposed for the formation of the double-shelled hollow spheres to take advantage of the dissociation and hydrolyzation of the two kinds of ligands in the SNP precursor. The size of the double-shelled ferrihydrite hollow spheres can be tuned by varying the experimental parameters. As-obtained ferrihydrite is highly sensitive to ethanol gas, which indicates potential applications in the field of sensing devices.     

Phase diagram of mixtures of hard colloidal spheres and discs: a free-volume scaled-particle approach

Phase diagrams of mixtures of colloidal hard spheres with hard discs are calculated by means of the free-volume theory. The free-volume fraction available to the discs is determined from scaled-particle theory. The calculations show that depletion induced phase separation should occur at low disc concentrations in systems now experimentally available. The gas-liquid equilibrium of the spheres becomes stable at comparable size ratios as with bimodal mixtures of spheres or mixtures of rods and spheres. Introducing finite thickness of the platelets gives rise to a significant lowering of the fluid branch of the binodal.     

Large attractive depletion interactions in soft repulsive-sphere binary mixtures

We consider binary mixtures of soft repulsive spherical particles and calculate the depletion interaction between two big spheres mediated by the fluid of small spheres, using different theoretical and simulation methods. The validity of the theoretical approach, a virial expansion in terms of the density of the small spheres, is checked against simulation results. Attention is given to the approach toward the hard-sphere limit and to the effect of density and temperature on the strength of the depletion potential. Our results indicate, surprisingly, that even a modest degree of softness in the pair potential governing the direct interactions between the particles may lead to a significantly more attractive total effective potential for the big spheres than in the hard-sphere case. This might lead to significant differences in phase behavior, structure, and dynamics of a binary mixture of soft repulsive spheres. In particular, a perturbative scheme is applied to predict the phase diagram of an effective system of big spheres interacting via depletion forces for a size ratio of small and big spheres of 0.2; this diagram includes the usual fluid-solid transition but, in the soft-sphere case, the metastable fluid-fluid transition, which is probably absent in hard-sphere mixtures, is close to being stable with respect to direct fluid-solid coexistence. From these results, the interesting possibility arises that, for sufficiently soft repulsive particles, this phase transition could become stable. Possible implications for the phase behavior of real colloidal dispersions are discussed.     

Adsorption of polymer chains onto charged spheres: Experiment and theory

A self-consistent field (SCF) theory for the adsorption of polyelectrolyte chains onto oppositely charged spheres is considered. It is demonstrated that the criterion for critical adsorption shows a different behavior for small and large curvature of the surface. Experiments give indeed evidence for the power-law behavior as theoretically predicted for large curvature.