Osmotic compression of mixtures of polymers and particles

Aqueous dispersions of nanometric ceria particles have been concentrated through osmotic stress. Mixed dispersions of ceria with small adsorbing macromolecules of poly (vinylpyrrolidone) have been prepared by the same method. The osmotic pressure of pure ceria dispersions results from electrostatic repulsions between particles. The osmotic pressure of dispersions containing a non-saturating amount of PVP is the same as that of pure dispersions, and the colloidal stability is depressed with respect to the pure dispersions. The osmotic pressure of dispersions containing an excess of PVP is increased by the free macromolecules, and the colloidal stability is enhanced. The organization of particles in these dispersions has been examined by small-angle x-ray scattering and cryotransmission electron microscopy. In pure ceria dispersions and in saturated dispersions, a liquid-like short-range order was found; when the concentration is increased, this short-range order follows a three-dimensional swelling law. In dispersions containing a non-saturating amount of PVP, the structure shows an alternance of clusters and voids, and the separations of clusters follow an unusual one-dimensional swelling law.     

Synthesis of spherical polymer and titania photonic crystallites

The fabrication of small structured spherical particles that are essentially small photonic crystals is described. The particles are 1-50 microm in diameter and are porous with nearly close-packed monodisperse pores whose size is comparable to the wavelength of light. The solid matrix of the particles is titania, which provides a large refractive index contrast between the particle matrix and pores. The particles are made by encapsulating polymer colloidal particles in emulsion droplets of hexanes in which a titanium alkoxide precursor is dissolved. Subsequent osmotic removal of the hexanes from the droplets and condensation of the alkoxide precursor leads to spherical aggregates of polymer spheres with titania filling the spaces between the polymer spheres. The polymer particles are then burned out leaving behind the desired porous titania particles. The size and structure of the pores and high refractive index of the titania matrix are expected to produce particles that are very efficient scatterers of light, making them useful as pigments.     

A universal approach to fabricate ordered colloidal crystals arrays based on electrostatic self-assembly

We present a novel and simple method to fabricate two-dimensional (2D) poly(styrene sulfate) (PSS, negatively charged) colloidal crystals on a positively charged substrate. Our strategy contains two separate steps: one is the three-dimensional (3D) assembly of PSS particles in ethanol, and the other is electrostatic adsorption in water. First, 3D assembly in ethanol phase eliminates electrostatic attractions between colloids and the substrate. As a result, high-quality colloidal crystals are easily generated, for electrostatic attractions are unfavorable for the movement of colloidal particles during convective self-assembly. Subsequently, top layers of colloidal spheres are washed away in the water phase, whereas well-packed PSS colloids that are in contact with the substrate are tightly linked due to electrostatic interactions, resulting in the formation of ordered arrays of 2D colloidal spheres. Cycling these processes leads to the layer-by-layer assembly of 3D colloidal crystals with controllable layers. In addition, this strategy can be extended to the fabrication of patterned 2D colloidal crystals on patterned polyelectrolyte surfaces, not only on planar substrates but also on nonplanar substrates. This straightforward method may open up new possibilities for practical use of colloidal crystals of excellent quality, various patterns, and controllable fashions.     

Free isotropic-nematic interfaces in fluids of charged platelike colloids

Bulk properties and free interfaces of mixtures of charged platelike colloids and salt are studied within the density-functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model. The charges of the particles are concentrated in their center. The density functional is derived by functional integration of an extension of the Debye-Hückel pair distribution function with respect to the interaction potential. For sufficiently small macroion charges, the bulk phase diagrams exhibit one isotropic and one nematic phase separated by a first-order phase transition. With increasing platelet charge, the isotropic and nematic binodals are shifted to higher densities. The Donnan potential between the coexisting isotropic and nematic phases is inferred from bulk structure calculations. Nonmonotonic density and nematic order parameter profiles are found at a free interface interpolating between the coexisting isotropic and nematic bulk phases. Moreover, electrically charged layers form at the free interface leading to monotonically varying electrostatic potential profiles. Both the widths of the free interfaces and the bulk correlation lengths are approximately given by the Debye length. For fixed salt density, the interfacial tension decreases upon increasing the macroion charge.     

Concentration Polarization of Interacting Solute Particles in Cross-Flow Membrane Filtration

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein-Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute-solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted. Copyright 1999 Academic Press.     

微扰理论非原始模型用于1:1价单一电解质水溶液

本文采用微扰理论非原始模型, 以带电硬球混合物为参考体系, 考虑粒子间各种作用能(色散、静电、偶极、四极、诱导), 首次取相对介电常数为1, 拟合了12处1:1价电解质水溶液的渗透系数, 获得了成功, 得到了7种1价离子Na^+,K^+, Rb^+, Cs^+, Cl^-, Br^-, I^-的微观参数(软球直径σ和色散能常数ε/k)。计算得到的电解质水溶液渗透系数的总平均绝对偏差是0.041。这些离子的微观参数在不同体系中维持不变。计算中未引入混合参数。     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

Sedimentation–diffusion profiles and layered sedimentation of charged colloids at low ionic strength

We report the formation of strongly inflated sedimentation–diffusion concentration profiles for charged monodisperse colloidal spheres in absolute ethanol. Various additional experiments, such as light scattering, confirm that the very dilute supernatants, left behind by the majority of settling colloids, contain spheres that repel each other at distances of micrometers. We attribute these unusual profiles to a significant counter-ion contribution to the osmotic pressure and to the Debye screening length. An approximate osmotic equation-of-state at the level of the second virial coefficient for dispersions at very low ionic strength indeed implies an algebraic long-distance decay of sedimentation–diffusion profiles, together with significant lowering of the effective colloid mass by an entropic lift due to counter-ions. We have also observed that sedimenting dispersions sometimes demix into two layers, which are both disordered fluids. Since the colloids are clearly repulsive on the DLVO pair level, this layering possibly manifests a phase transition driven by many-body attractions.     

Microscopic observation of ordered colloids in sedimentation equilibrium and the importance of Debye-screening length. 8. Unsymmetrical ordering and inclusion of anisotropic particles

Unsymmetrical crystal-like ordering of anisotropic-shaped particles are observed directly by a metallurgical microscope in sedimentation equilibrium and in deionized suspensions. The anisotropic colloids are polydispersed gold sols, rectangular tungstic acid, ellipsoidal poly(tetrafluoroethylene)(PTFE), aggregated (dimer, trimer, ...) polystyrene spheres, and bowl-shaped polymers. The distribution of the particles is analyzed by the two-dimensional distance distribution function. The interparticle distance continues to decrease as the initial concentration of the particles increases. Young's elastic modulus for the crystal-like structures is estimated to be 3.1 Pa for PTFE particles. The transformation from the unsymmetrical ordering to the symmetrical (hexagonal) array takes place as the concentration of diffusible ions decreases, which shows that the electrostatic interparticle repulsion and the elongated Debye-screening length around the particles play a key role. Furthermore, a bowl-shaped particle is observed to include a sphere in its cavity. This inclusional association is influenced greatly by the delicate changes in the effective sizes of the host and guest molecules containing the electrical double layers. These results show that electrostatic interparticle repulsion and the elongated Debye-screening length around the particles are essential for the ordering.     

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.     

Guest-host colloid crystals: experimental study and simulations

Disorder in colloid crystals was induced by doping them with a different number of large or small guest particles, which had a different deviation in size from the host colloids. The change in optical properties of the guest-host colloid crystals was assessed by using optical transmission spectroscopy while the variation in crystal structure was examined using scanning electron microscopy (SEM). The disruption in the crystalline lattices depended on the relative deviation in sizes of the guest and host particles and the concentration of the guest colloids. In parallel with experiments, the packing of spheres in guest-host crystals was modeled with a simulated annealing algorithm. A good correlation was found between the changes in crystal structure observed by SEM imaging and the simulated sphere packing. The experimental and simulated changes in the transmission spectra of guest-host colloid crystals were in good agreement.     

Thermal control over the electrophoresis of soft colloidal particles

We study the electrophoresis of surface-charged thermosensitive microgel particles based on poly-N-isopropylacrylamide (PNIPAM); these deswell with increasing temperature T. Our results show that the electrophoretic mobility mu is affected by the temperature-induced volume phase transition. It increases with increasing temperature, as a result of the charge density increase induced by particle deswelling. Temperature thus allows control of mu, in contrast to the more conventional charged hard spheres for which mu is T independent. Salt also affects the mu behavior and gives rise to rich phenomenology, sharing common characteristics with charged hard spheres and polyelectrolyte-coated colloids depending on whether the microgels are swollen or deswollen. We interpret the effects of salt concentration n by considering that particle charges are located in an external shell, as confirmed by titrations, and that it is this shell-salt-induced compression that affects the resulting mu behavior.     

Surface properties of fluids of charged platelike colloids

Surface properties of mixtures of charged platelike colloids and salt in contact with a charged planar wall are studied within density functional theory. The particles are modeled by hard cuboids with their edges constrained to be parallel to the Cartesian axes corresponding to the Zwanzig model [J. Chem. Phys. 39, 1714 (1963)] and the charges of the particles are concentrated at their centers. The density functional applied is an extension of a recently introduced functional for charged platelike colloids. It provides a qualitative approach because it does not determine the relation between the actual and the effective charges entering into the model. Technically motivated approximations, such as using the Zwanzig model, are expected not to influence the results qualitatively. Analytically and numerically calculated bulk and surface phase diagrams exhibit first-order wetting for sufficiently small macroion charges and isotropic bulk order as well as first-order drying for sufficiently large macroion charges and nematic bulk order. The asymptotic wetting and drying behaviors are investigated by means of effective interface potentials which turn out to be asymptotically the same as for a suitable neutral system governed by isotropic nonretarded dispersion forces. Wetting and drying points as well as predrying lines and the corresponding critical points have been located numerically. A crossover from monotonic to nonmonotonic electrostatic potential profiles upon varying the surface charge density has been observed. Nonmonotonic electrostatic potential profiles are equivalent to the occurrence of charge inversion. Due to the presence of both the Coulomb interactions and the hard-core repulsions, the surface potential and the surface charge do not vanish simultaneously, i.e., the point of zero charge and the isoelectric point of the surface do not coincide.     

Amorphous solid-like distribution of polydisperse particles of colloidal clay and microcrystalline cellulose in deionized suspension

A metallurgical microscope is used to directly observe the amorphous solid-like structures of deionized suspensions of highly polydispersed colloids in sedimentation equilibrium. The colloids used are colloidal clay of bentonite and microcrystalline cellulose (MCC). The two-dimensional distance distribution functions of the amorphous solid-like structures at relatively diluted and concentrated suspensions resemble those of the liquid-like and gas-like structures of monodispersed spheres, respectively. The center-to-center interparticle distances (D) in the amorphous solid-like structures are explained by the effective hard-sphere model; a colloidal particle is coated with electrical double layers. The maximum length of the width of the double layers (Debye length,D ₁) observed is ca. 1n at very dilute suspensions.D andD ₁ continue to decrease as the initial concentration of the particles increases, and from these data rigidities are estimated to be 0.12 and 0.09 Pa for bentonite and MCC suspensions, respectively. The log [viscosity] of bentonite suspensions begins to increase linearly as log [shear rate] decreases with a slope close to –1, which supports the solid-like nature of the suspensions. These experimental results show that electrostatic interparticle repulsion and the elongated Debye-screening length around the particles are both essential for the appearance of the amorphous solid-like structures.     

Effect of added free polymer on the swelling of neutral microgel particles: a thermodynamic approach

Microgel particles based on poly (N-isopropylacrylamide) have been shown to display an initial swelling behavior, followed by a collapse, with increasing concentration of added poly(ethylene oxide), PEO, chains. This paper considers the thermodynamic reasons for the observed expansion and subsequent shrinkage of the particles. At low concentrations of PEO, the free chains permeate into the microgel particles and cause an increase in osmotic pressure, expanding the particles. At higher concentrations of PEO, the particles are saturated and an increase in osmotic pressure in the external phase causes the particles to collapse again. The calculated magnitude of swelling and the effect of PEO molecular weight are, at least qualitatively, in agreement with the experimental observations reported elsewhere.     

Equivalent temperature and specific ion effects in macromolecule-coated colloid interactions

Ensemble total internal reflection microscopy is used to measure reversible temperature- and specific-ion-mediated interaction potentials between macromolecule-coated colloids and surfaces. Potentials are measured between PEO-PPO-PEO (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)) block copolymers adsorbed to hydrophobically modified silica colloids and glass or gold planar surfaces. Conditions investigated include temperatures from 20 to 47 degrees C and MgSO4 concentrations from 0.2 to 0.5 M. The solvent-quality-mediated copolymer layer collapse inferred by comparing measured potentials and the predicted van der Waals attraction, including effects of the adsorbed copolymer and surface roughness, displays good agreement with expected limits based on the PEO block contour length and the bulk PEO density. Superposition of all PEO layer collapse measurements onto a single universal curve, via a transformed temperature scale relative to a reference temperature in each case, indicates an equivalence of increasing temperature and increasing MgSO4 concentration when layer interactions and dimensions are mediated. Accurate knowledge of nanometer- and kT-scale interactions of copolymer-coated colloids as a function of temperature and MgSO4 concentration provides the ability to reversibly control the stability, phase behavior, and self-assembly of such particles.     

Charged micelle depletion attraction and interfacial colloidal phase behavior

Ensemble total internal reflection microscopy (TIRM) is used to directly measure the evolution of colloid-surface depletion attraction with increasing sodium dodecyl sulfate (SDS) concentration near the critical micelle concentration (CMC). Measured potentials are well described by a modified Asakura-Oosawa (AO) depletion potential in addition to electrostatic and van der Waals contributions. The modified AO potential includes effects of electrostatic interactions between micelles and surfaces via effective depletant dimensions in an excluded volume term and partitioning in an osmotic pressure term. Directly measured colloid-surface depletion potentials are used in Monte Carlo (MC) simulations to capture video microscopy (VM) measurements of micelle-mediated quasi-two-dimensional phase behavior including fluid, crystal, and gel microstructures. Our findings provide information to develop more rigorous and analytically simple models of depletion attraction in charged micellar systems.