Stability in Colloidal Mixtures Containing Particles with a Large Disparity in Size

An experimental approach, based on turbidity measurements, is proposed for studies of the stability in colloidal mixtures containing particles with large disparity in size. The main advantage of this approach is that it permits investigations even under conditions of comparable particle number concentrations of the two colloidal populations. Binary mixtures containing a poly(vinyl acetate) (PVAc) latex and a Ludox AS-40 silica sol were investigated. The silica particles were much smaller than the latex ones. The experimental stability factors were compared with the theoretical values computed on the basis of the Kihira-Ryde-Matijevic model (J. Chem. Soc., Faraday Trans. 88(16), 2379 (1992)) for interaction between spherical particles with unevenly distributed surface charges. All the experimental results support the idea that, even when both sols are negatively charged, the small silica particles are adsorbed onto the latex surface. Under these conditions, the heteroaggregates, which are composed of PVAc cores surrounded with silica particles, can be modeled as PVAc particles having "modified" surface characteristics (i.e., average Stern potential and varying extents of the surface charge segregation). Copyright 2001 Academic Press.     

Shear effects in interfacial rheology and their implications on oscillating pendant drop experiments

Adsorbed molecules that associate or entangle with one another at the fluid interface will give rise to shearing resistance (i.e., resistance to shape change at constant area) on the continuum scale. Where these shear effects occur, familiar theoretical constructs, such as the Young-Laplace equation or the complex dilational modulus, are rendered invalid. In this work, we report numerical simulations of an oscillating pendant drop with a surface that is a shear-resisting film. Specifically, the drop surface is treated as a Boussinesq fluid (i.e., one that possesses independent viscous coefficients for dilation and shearing). We show that the frequency response of the apparent dilational modulus (based on tensions determined from the Young-Laplace equation) is remarkably consistent with the Maxwell model of viscoelasticity. It is argued, however, that usage of the Maxwell model, in the context of dilational rheology, is unphysical; as such, the apparent "Maxwellian behavior" is likely due to shear resistance within the Boussinesq material (i.e., the interface may not be undergoing any internal relaxation at all). Our results also predict an apparent "softening" of the adsorbed layer as the interfacial structure becomes more developed.     

Aggregation phenomena in the suspension polymerization of VCM

In the suspension polymerization of VCM, insoluble polymer particles are formed inside the monomer droplets. The growth and aggregation of these particles are responsible for important polymer properties, such as porosity. It is well established that the most characteristic polymer particles, the primary particles, are of a narrow distribution with a size (diameter) ranging from 0.10–0.20 m. This work studied the formation of primary particles based on the aggregation phenomena that take place inside a monomer droplet. This was done by formulating a population balance equation, which was based on the following considerations: a) polymerization occurs in both the monomer and the polymer phases; b) there is continuous formation of the basic particles in the monomer phase; c) the growth of the polymer particles occurs as a result of both polymerization in the polymer phase and aggregation of the particles; d) the colloidal properties of the particles that are responsible for the aggregation phenomena were considered to be the net result of attraction and repulsion energies.It was shown that for particles carrying a constant charge it was not possible to predict the formation of primary particles of size 0.10–0.20 m. The particle size distribution had a mode diameter equal to the diameter of the basic particles. Consequently, the particle charge was allowed to vary in a way proportional to the particle radius raised to a power coefficient. For values of the coefficient greater than zero, i. e., when the particle charge increased during polymerization, the aggregation of the basic particles was efficient enough to result in the formation of large primary particles.     

Phase behavior of colloidal hard tetragonal parallelepipeds (cuboids): a Monte Carlo simulation study

The impact of particle geometry on the phase behavior of hard colloidal tetragonal parallelepipeds (TPs) was studied by using Monte Carlo simulations in continuum space. TPs or "cuboids" of aspect ratios varying from 0.25 to 8 were simulated by approximating their shapes with multisite objects, i.e., via rigid clusters of hard spheres. Using equation of state curves, order parameters, radial distribution functions, particle distribution functions along three directions, and visual analysis of configurations, an approximate phase diagram for the TPs was mapped out as a function of aspect ratio (r) and volume fraction. For r > 3 and intermediate concentrations, the behavior of the TPs was similar to that of spherocylinders, exhibiting similar liquid crystalline mesophases (e.g., nematic and smectic phases). For r = 1, a cubatic phase occurs with orientational order along the three axes but with little translational order. For 1 < r < 4, the TPs exhibit a cubatic-like mesophase with a high degree of order along three axes where the major axes of the particles are not all aligned in the same direction. For r < 1, the TPs exhibit a smectic-like phase where the particles have rotational freedom in each layer but form stacks with tetratic order. The equation of state for perfect hard cubes (r = 1) was also simulated and found to be consistent with that of the rounded-edge r = 1 TPs, except for its lack of discontinuity at the cubatic-solid transition.     

Three-dimensional discrete charge effects on the electrostatic interaction between two soft particles

An expression for the electrostatic interaction energy between two parallel plate-like soft particles (i.e., hard particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution is derived by using the linearized Poisson-Boltzmann equation. This expression is based on a discrete charge model in which the surface layer consists of a cubic lattice of fixed point charges. We show that the deviation of the results of the discrete charge model from those of the conventional smeared charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large. As this ratio decreases, on the other hand, the discrete charge model approaches a smeared charge model, leading to the Donnan-potential regulated interaction model.     

Diffusion and Brownian motion in Lagrangian coordinates

In this paper we consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. Both the convection-diffusion partial differential equation and the Langevin equation are expressed in Lagrangian coordinates and are shown to be equivalent for uniform, isotropic diffusion. The Lagrangian diffusivity is proportional to the square of the relative change of surface area and is related to the Eulerian diffusivity through the deformation gradient tensor. Associated with the initial value problem, we relate the Eulerian to the Lagrangian effective diffusivities (net spreading), validate the relation for the case of linear flow fields, and infer a relation for general flow fields. Associated with the boundary value problem, if the scalar transport problem possesses a time-independent solution in Lagrangian coordinates and the boundary conditions are prescribed on a material surface/interface, then the net mass transport is proportional to the diffusion coefficient. This can be also shown to be true for large Peclet number and time-periodic flow fields, i.e., closed pathlines. This agrees with results for heat transfer at high Peclet numbers across closed streamlines.     

Discrete charge effects on the Donnan potential and surface potential of a soft particle

The Donnan potential and surface potential of soft particles (i.e., polyelectrolyte-coated hard particles) in an electrolyte solution play an essential role in their electric behaviors. These potentials are usually derived via a continuum model in which fixed charges inside the surface layer are distributed with a continuous charge density. In this paper, for a plate-like soft particle consisting of a cubic lattice of fixed point charges, on the basis of the linearized Poisson–Boltzmann equation, we derive expressions for the electric potential distribution in the regions inside and outside the surface layer. This expression is given in terms of a sum of the screened Coulomb potentials produced by the point charges within the surface layer. We show that the deviation of the results of the discrete charge model from those of the continuous charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large.     

Multiscale theory of collective and quasiparticle modes in quantum nanosystems

A quantum nanosystem (such as a quantum dot, nanowire, superconducting nanoparticle, or superfluid nanodroplet) involves widely separated characteristic lengths. These lengths range from the average nearest-neighbor distance between the constituent fermions or bosons, or the lattice spacing for a conducting metal, to the overall size of the quantum nanosystem (QN). This suggests the wave function has related distinct dependencies on the positions of the constituent fermions and bosons. We show how the separation of scales can be used to generate a multiscale perturbation scheme for solving the wave equation. Results for electrons or other fermions show that, to lowest order, the wave function factorizes into an antisymmetric (fermion) part and a symmetric (bosonlike) part. The former manifests the short-range/exclusion-principle behavior, while the latter corresponds to collective behaviors, such as plasmons, which have a boson character. When the constituents are bosons, multiscale analysis shows that, to lowest order, the wave function can also factorize into short- and long-scale parts. However, to ensure that the product wave function has overall symmetric particle label exchange behavior, there could, in principle, be states of the boson nanosystem where both the short- and long-scale factors are either boson- or fermionlike; the latter "dual fermion" states are, due to their exclusion-principle-like character, of high energy (i.e., single particle states cannot be multiply occupied). The multiscale perturbation analysis is used to argue for the existence of a coarse-grained wave equation for bosonlike collective behaviors. Quasiparticles, with effective mass and interactions, emerge naturally as consequences of the long-scale dynamics of the constituent particles. The multiscale framework holds promise for facilitating QN computer simulations and novel approximation schemes.     

Effect of pulp composition on the characteristics of residuals in CMC made from such pulps

Four different spruce sulphite pulp samples were used for the preparation of carboxymethylcellulose (CMC). The characteristics of the unreacted fibre and particle residuals obtained in the CMC-preparation were used to establish a correlation between the hemicellulose in the pulp and the intrinsic viscosity, i.e.,␣cellulose chain length and the occurence of unreacted residuals. It was shown that the residual particles in the CMC consisted of fibres, fibre fractions and gel particles of different degrees of substitution. The results suggested that pulps with long cellulose chains, i.e., pulps with high intrinsic viscosities, resulted in particles that were more substituted and more swollen. These pulps also resulted in more substituted hemicelluloses in the CMC and more substituted residuals. It was also suggested that galactoglucomannan in the cellulose pulps is favourable for the swelling which results in more substituted hemicelluloses in the CMC and more swollen residuals. The amount of residuals was influenced mainly by the characteristics of the cellulose in the pulp. It is therefore believed that a combination of high viscosity and a suitable combination of hemicelluloses is the most favourable way of eliminating the occurrence of undissolved residuals in CMC.     

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.     

Surfactant-induced Marangoni eddies alter the coffee-rings of evaporating colloidal drops

The influence of the small ionic surfactant sodium dodecyl sulfate (SDS) on the evaporation of drying colloidal droplets is quantitatively investigated. The addition of SDS leads to a significantly more uniform deposition of colloidal particles after evaporation (i.e., the so-called "coffee-ring effect" is dramatically altered). We understand this phenomenon in the context of circulating radial Marangoni flows induced by the variation of SDS concentration along the air-water interface. Video microscopy permits the direct visualization of the colloidal particles involved in these flows, revealing a surprisingly stable "Marangoni eddy" that prevents particle deposition at the drop perimeter.     

Structure of nanocrystalline particles of metallic cobalt formed during the reduction of Co<Subscript>3</Subscript>O<Subscript>4</Subscript> oxide

X-ray diffraction is applied to investigate metallic cobalt obtained by the reduction of nanocrystalline particles of Co₃O₄. The particles of metallic cobalt have a high concentration of stacking faults, i.e., violations of the layer packing sequence ABABAB..., which is seen in X-ray diffraction patterns as anisotropic broadening of diffraction peaks. Simulation of the diffraction patterns of α-Co with a different concentration of stacking faults is carried out.     

Structure determination of CdS and ZnS nanoparticles: direct modeling of synchrotron-radiation diffraction data

We introduce a modified method of powder-diffraction data analysis to obtain precise structural information on freestanding ZnS and CdS nanoparticles with diameters well below 5 nm, i.e., in a range where common bulk-derived approaches fail. The method is based on the Debye equation and allows us to access the crystal structure and the size of the particles with high precision. Detailed information on strain, relaxation effects, stacking faults, and the shape of the particles becomes available. We find significant size differences between our new results and those obtained by established methods, and conclude that a mixed zinc-blende/wurtzite stacking and significant lattice distortions occur in our CdS nanoparticles. Our approach should have direct impact on the understanding and modeling of quantum size effects in nanoparticles.     

Single particle jumps in a binary Lennard-Jones system below the glass transition

We study a binary Lennard-Jones system below the glass transition with molecular dynamics simulations. To investigate the dynamics we focus on events (jumps) where a particle escapes the cage formed by its neighbors. Using single particle trajectories we define a jump by comparing for each particle its fluctuations with its changes in average position. We find two kinds of jumps: "reversible jumps," where a particle jumps back and forth between two or more average positions, and "irreversible jumps," where a particle does not return to any of its former average positions, i.e., successfully escapes its cage. For all investigated temperatures both kinds of particles jump and both irreversible and reversible jumps occur. With increasing temperature, relaxation is enhanced by an increasing number of jumps and growing jump lengths in position and potential energy. However, the waiting time between two successive jumps is independent of temperature. This temperature independence might be due to aging, which is present in our system. We therefore also present a comparison of simulation data with three different histories. The ratio of irreversible to reversible jumps is also increasing with increasing temperature, which we interpret as a consequence of the increased likelihood of changes in the cages, i.e., a blocking of the "entrance" back into the previous cage. In accordance with this interpretation, the fluctuations both in position and energy are increasing with increasing temperature. A comparison of the fluctuations of jumping particles and nonjumping particles indicates that jumping particles are more mobile even when not jumping. The jumps in energy normalized by their fluctuations are decreasing with increasing temperature, which is consistent with relaxation being increasingly driven by thermal fluctuations. In accordance with subdiffusive behavior are the distributions of waiting times and jump lengths in position.     

Triethylaluminum as a concentration-dependent coinitiator and chain-transfer agent of free-radical polymerization of methyl methacrylate in the presence of benzoquinone

Yields in methyl methacrylate (MMA) polymerization as a function of triethylaluminum (TEA) concentration have been determined at a constant benzoquinone (BQ) concentration. The polymerization is negligible at [TEA]/[BQ] concentration ratios smaller than 1, but reaches a maximum yield and then decreases for larger TEA concentrations. Molecular weight measurements show a similar trend, although the maximum is shifted with respect to that corresponding to polymer yield. The existence of two reaction mechanisms is shown by rate measurements at constant initial concentrations. One is a fast reaction, over in a few minutes, which accounts for most of the yield after 30 min reaction time. The other is a slower photoinitiated reaction of the products of the fast reaction. The mechanism proposed is based on a chain-transfer reaction between the inhibitor radical, formed by the addition of the polymer radical (M·) to BQ and TEA, giving a reactive ethyl radical: The competition between a pair of reactions of TEA and BQ, i.e., a free-radical reaction corresponding to the conjugate addition and a molecular reaction leading to the BQ reduction product, is held responsible for the observed yield maximum, since the molecular reaction prevails at larger TEA concentrations. The observed drop in the molecular weight is the result of a chain-transfer reaction on TEA, i.e., the substitution of an ethyl group by the growing polymer radical.     

Patterned assembly of colloidal particles by confined dewetting lithography

We report the assembly of colloidal particles into confined arrangements and patterns on various cleaned and chemically modified solid substrates using a method which we term "confined dewetting lithography" or CDL for short. The experimental setup for CDL is a simple deposition cell where an aqueous suspension of colloidal particles (e.g., polystyrene spheres) is placed between a floating deposition template (i.e., metal microgrid) and the solid substrate. The voids of the deposition template serve as an array of micrometer-sized reservoirs where several hydrodynamic processes are confined. These processes include water evaporation, meniscus formation, convective flow, rupturing, dewetting, and capillary-bridge formation. We discuss the optimal conditions where the CDL has a high efficiency to deposit intricate patterns of colloidal particles using polystyrene spheres (PS; 4.5, 2.0, 1.7, 0.11, 0.064 microm diameter) and square and hexagonal deposition templates as model systems. We find that the optimization conditions of the CDL method, when using submicrometer, sulfate-functionalized PS particles, are primarily dependent on minimizing attractive particle-substrate interactions. The CDL methodology described herein presents a relatively simple and rapid method to assemble virtually any geometric pattern, including more complex patterns assembled using PS particles with different diameters, from aqueous suspensions by choosing suitable conditions and materials.     

Flow-induced patterning of Langmuir monolayers

Insoluble monolayers on water have been patterned at the macroscopic scale (i.e., at the centimeter scale of the flow apparatus) as well as the mesoscopic scale (i.e., down to the micron scale resolvable via optical microscopy). The macroscopic patterning at the air/water interface results from a hydrodynamic instability leading to a steadily precessing flow pattern. The velocity field is measured, and the associated shear stress at the interface is shown to be locally amplified by the flow pattern. The resulting hydrodynamic effects on two different monolayer systems are explored: (1) the pattern in a model monolayer consisting of micron-size, surface-bound particles is visualized to show that the particles are concentrated into isolated regions of converging flow with high shear, and (2) Brewster angle microscopy of a Langmuir monolayer (vitamin K1) shows not only that the monolayer is patterned at the macroscopic scale but also that the localized high-shear flow further patterns the monolayer at the mesoscale.     

Phase Behaviors of Soft-core Particle Systems

This paper reviews some of our recent works on phase behaviors of particulate systems with a soft-core interaction potential.The potential is purely repulsive and bounded,i.e.,it is finite even when two particles completely overlap.The one-sided linear spring(harmonic) potential is one of the representatives.This model system has been successively employed to study the jamming transition,i.e.,the formation of rigid and disordered packings of hard particles,and establish the jamming physics.This is actually based on the 4"hard,:aspect of the potential,because at low densities and when particle overlap is tiny the potential resembles the hard sphere limit.At high densities,the potential exhibits its"soft"aspect:with the increase of density,there are successive reentrant crystallizations with many types of solid phases.Taking advantage of the dual nature of the potential,we investigate the criticality of the jamming transition from different perspectives,extend the jamming scenario to high densities,reveal the novel density evolution of two-dimensional melting,and find unexpected formation of quasicrystals.It is surprising that such a simple potential can exhibit so rich and unexpected phenomena in phase transitions.The phase behaviors discussed in this paper are also highly regarded in polymer science,which may thus shed light on our understanding of polymeric systems or inspire new ideas in studies of polymers.     

Stick-slip of the three-phase line in measurements of dynamic contact angles

Contact angles of a series of n-alkanes (i.e., n-heptane to n-hexadecane) are studied on two functionalized maleimide copolymers (i.e., poly(ethene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ETMF) and poly(octadecene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ODMF)). On the homogeneous ETMF films, all liquids show a smooth motion of the three-phase line. In contrast, on ODMF surfaces that are found to consist of mainly fluorocarbons and small patches of hydrocarbons, short-chain n-alkanes show a stick-slip pattern. By increasing the chain length of the probe liquids, stick-slip is reduced significantly. The phenomenon is discussed in the framework of the Cassie equation. It is found that the upper limit of contact angles in the stick-slip pattern is given by the advancing angle that would be obtained on the pure fluorocarbon surface, whereas the lower limit of the stick-slip pattern is given by the Cassie angle.     

Film Growth and Surface Roughness with Effective Fluctuating Covalent Bonds in Evaporating Aqueous Solution of Reactive Hydrophobic and Polar Groups: A Computer Simulation Model

Summary: A computer simulation model is proposed to study film growth and surface roughness in aqueous (A) solution of hydrophobic (H) and hydrophilic (P) groups on a simple three dimensional lattice of size with an adsorbing substrate. Each group is represented by a particle with appropriate characteristics occupying a unit cube (i.e., eight sites). The Metropolis algorithm is used to move each particle stochastically. The aqueous constituents are allowed to evaporate while the concentration of H and P is constant. Reactions proceed from the substrate and bonded particles can hop within a fluctuating bond length. The film thickness ( ) and its interface width ( ) are examined for hardcore and interacting particles for a range of temperature ( ). Simulation data show a rapid increase in and followed by its non‐monotonic growth and decay before reaching steady‐state and near equilibrium ( ) in asymptotic time step limit. The growth can be described by power laws, e.g., with a typical value of in initial time regime followed by at . For hardcore system, the equilibrium film thickness ( ) and surface roughness ( ) seem to scale linearly with the temperature, i.e., at low and at higher . For interacting functional groups in contrast, the long time (unsaturated) film thickness and surface roughness, and decay rapidly followed by a slow increase on raising the temperature.

Growth of the average film thickness at a temperature .