Formation and thermodynamic stability of a novel class of useful materials: Close-packed monolayers of submicron monodisperse spheres just below a polymer surface

When certain materials such as Se or Sn are vacuum-deposited onto heated polymers under appropriate conditions, a most unusual structure can form, consisting of a nearly close-packed monolayer of submicron, almost monodisperse spheres embedded a few tens of nanometers under the polymer surface. The size of the spheres can be controlled, at constant surface packing density, simply by controlling the quantity of material deposited. A similar structure can often be formed if small particles of many substances (including elements and both inorganic and organic compounds) are deposited as a smoke or are merely spread in a suitable manner over the surface of a polymer which is subsequently softened by heat or by an appropriate vapor. Structures of this kind may have a wide range of applications. A basic thermodynamic discussion is presented to show first that a tendency to form particulate subsurface structures is a rather general property of most metals and inorganic compounds, the tendency being frustrated in many cases (at least with vacuum deposition) by kinetic factors. Second, a model is proposed to explain the tendency for the particles to remain in a monolayer near the polymer surface; in this case, detailed calculations are limited to the case of a single sphere embedded in a polymer half-space, although it is shown that neighboring spheres tend to stabilize the equilibrium. A long-range Van der Waals force acts to pull the sphere deeper into the polymer; on the other hand, consideration of the entropy of the polymer in the vicinity of particle and air interfaces, on the basis of free infinite polymer chains and of Fowkes' view of interfacial properties, shows that there is a novel and substantial entropic force tending to push the sphere back toward the surface. The balance of these two forces produces a minimum in the free energy of the system when the sphere is a specific distance from the surface. When the appropriate interaction parameters are used, the equilibrium distances predicted for Se and Sn in polystyrene, and their relative magnitudes, are in good agreement with those observed experimentally. Simple physical interpretations are given both for the formation of subsurface particulate structures and for the tendency for the particles to remain in a monolayer.     

Existence of fluid layers in the corners of a capillary with non-uniform wettability

Based on free energy variation we derive the criterion for displacement during water invasion of oil layers, sandwiched between water in corners and in the centre of a capillary with partly altered wettability. This displacement may arise in combination with a piston-like displacement in which the layers are formed, or, alternatively, these two displacements do not occur and a single piston-like displacement arises removing all oil from the pore cross-section at once. The free energy differentials associated with the three displacements determine exactly which displacement(s) happen during water invasion. Depending on the area and the (advancing) contact angle on the surface of altered wettability, as well as on the half-angles of the pore corners, layers may or may not exist. We compare the criterion for the displacement of oil layers with the existing geometrical criterion. The latter always allows a larger range of contact angles and pressure combination for which layers may exist than the presently derived criterion, hence the geometrical criterion is insufficient and is now superceded.     

Liquid-vapor isotherm in a closed single-component system with curved interfaces

A thermodynamic model to obtain the radius of bubbles or droplets in a single-component system for a given temperature, total volume, and phase distribution is developed. The general formulation of the model includes bubbles or droplets in the form of spheres, truncated spheres on a flat solid surface or inside conical walls. In these three geometries the liquid-vapor curvature radius is positive but in the case of conical walls it can be also negative. States with different dispersed-phase distributions are compared using the total free energy of the system. When the curvature radius is positive, it has a minimum nonvanishing value and the occurrence of the Ostwald ripening is energetically favorable. On the other hand, when the curvature radius is negative, it is energetically more favorable to find the dispersed phase even in the expected single-phase region, and the occurrence of an anti-ripening phenomenon. The PV isotherms obtained from the model and the applicability of the results to the nucleation process are discussed.     

Strong and Weak Interactions of Colloidal Particles with High Surface Potentials

A simple method for calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential presented. Using Derjaguin's method and the improved Derjaguin' method, the expressions of the interaction free energy between two dissimilar spheres with high surface potentials are derived. These formulae may be divided into two groups: those for the strong interaction and those for the weak interaction. The juncture of strong and weak interactions is at kappah=4 for dissimilar plates and at kappah=2.8 for spheres The relative error is largest at this point, about 10%. Copyright 2001 Academic Press.     

Some aspects of hydrate formation and wetting

Experimental observations of gas hydrate formation have shown that, in the initial nucleation and crystallization process, water-oil emulsions may be generated, destabilized or even inverted. These phenomena are consistent with the effects of particles on emulsions. In this work we relate experimental observations of hydrate formation to the phenomenon of wettability. It is shown that details of hydrate wetting are important for both the morphology and the kinetics of the formed hydrates. For the cases of hydrate lenses and spheres, it is shown that the various wetting states can be illustrated and analyzed by using wetting diagrams. Metastability is a function of the surface energies of the hydrate formation, i.e., the wetting state, and it is shown that in some cases metastability vanishes, and thus hydrates nucleates instantly at all positive driving forces. The magnitude of buoyancy and turbulence forces acting on a hydrate sphere are compared to the capillary force and it is concluded that capillary energy dominates when the hydrate spheres is less than 1 mm.     

Coordination numbers for rigid spheres of different size—estimating the number of next-neighbour interactions in a mixture

The maximum number of rigid spheres which can be attached to a central sphere of different diameter is calculated numerically. It is shown that this coordination number is not proportional to the surface ratio of the spheres, but roughly to power 1.2 of the diameter ratio. This has consequences for the methods by which averages of molecular properties are calculated; for several binary liquid mixtures it is shown that replacing molar fractions by contact fractions makes plots of excess properties versus concentration appear more symmetrical, thereby reducing the number of terms required in Redlich-Kister correlations.     

Fabrication of hybrid nanostructured arrays using a PDMS/PDMS replication process

In the study, a novel and low cost nanofabrication process is proposed for producing hybrid polydimethylsiloxane (PDMS) nanostructured arrays. The proposed process involves monolayer self-assembly of polystyrene (PS) spheres, PDMS nanoreplication, thin film coating, and PDMS to PDMS (PDMS/PDMS) replication. A self-assembled monolayer of PS spheres is used as the first template. Second, a PDMS template is achieved by replica moulding. Third, the PDMS template is coated with a platinum or gold layer. Finally, a PDMS nanostructured array is developed by casting PDMS slurry on top of the coated PDMS. The cured PDMS is peeled off and used as a replica surface. In this study, the influences of the coating on the PDMS topography, contact angle of the PDMS slurry and the peeling off ability are discussed in detail. From experimental evaluation, a thickness of at least 20 nm gold layer or 40 nm platinum layer on the surface of the PDMS template improves the contact angle and eases peeling off. The coated PDMS surface is successfully used as a template to achieve the replica with a uniform array via PDMS/PDMS replication process. Both the PDMS template and the replica are free of defects and also undistorted after demoulding with a highly ordered hexagonal arrangement. In addition, the geometry of the nanostructured PDMS can be controlled by changing the thickness of the deposited layer. The simplicity and the controllability of the process show great promise as a robust nanoreplication method for functional applications.     

A cell model of a liquid droplet

An expression for the free energy of a droplet composed of attracting hard spheres is found using a simple cell model. The hard-sphere repulsion is assumed to act only between molecules in the same cell, whereas attraction extends over many cells. A maximum term analysis gives rise to a mean-field free energy which includes terms proportional to the first and second power of the droplet radius R with coefficients which can be related to the planar surface tension and Tolman length. Certain Gaussian fluctuations about the maximum term are also considered, corresponding to droplet translation and capillary wave fluctuations. Inclusion of these fluctuations is necessary to ensure that the nucleation rate is proportional to the system volume. They also reduce the planar surface tension and introduce a logarithmic term, -4/3 ln R, into the free energy. The inclusion of other fluctuations and the relationship between these equations and those arising in density-functional theories of nucleation is discussed.     

Concentration‐Dependent Self‐Assembly of a Novel Comb Oligomer Having Rigid Binaphthyl Macrocyclic Pendants

Summary: The synthesis and self‐assembly of a comb oligomer having rigid racemic binaphthyl macrocyclic pendant groups are described. The coupling of two structural motifs at the molecular level, e.g., a nanometer‐size chiral cavity, and a flexible polymeric backbone, could lead to new opportunities in molecular recognition and separation. The macrocyclic monomers were synthesized followed by introduction of an acrylate side‐group, and through free‐radical polymerization, they yielded a comb oligomer. Most importantly, this novel oligomer can self‐assemble into solid or hollow spheres when tetrahydrofuran (THF) solutions of the oligomer at different concentrations are dropped onto the surface of water. The morphology of the solid or hollow spheres was observed by TEM, ESEM and DLS.

A schematic illustration of the processes of self‐assembly of the oligomer.     

Structure of inhomogeneous polymer solutions: a density functional approach

The structure of polymer solutions confined between surfaces is studied using a density functional theory where the polymer molecules have been modeled as a pearl necklace of freely jointed hard spheres and the solvent as hard spheres. The present theory uses the concept of universality of the free energy density functional to obtain the first-order direct correlation function of the nonuniform system from that of the corresponding uniform system, calculated through the Verlet-modified type bridge function. The uniform bulk fluid direct correlation function required as input has been calculated from the reference interaction site model integral equation theory using the Percus-Yevick closure relation. The calculated results on the density profiles of the polymer as well as the solvent are shown to compare well with computer simulation results.     

Effective interaction of nonuniformly charged colloid spheres in a bulk electrolyte

The interaction energy between two like-charged colloid spheres with nonuniformly distributed surface charges immersed in a bulk electrolyte is calculated under the linearized Poisson-Boltzmann equation. The calculated results are sensitive to the relative orientations of the spheres due to the anisotropy of the distribution of charges on the sphere surface. The effective repulsive interaction after thermal average is weaker than the case when charges are uniformly distributed on the spheres, and with the increase of the nonuniformity, an attractive interaction between the two spheres emerges.     

Long-Range Electrostatic Interaction between a Charged Wall and Two Similarly Charged Colloidal Spheres at Low Surface Potentials

The long-range electrostatic interaction between a pair of similarly charged colloidal spheres and a charged planar wall at low surface potentials is theoretically investigated. The linear Poisson-Boltzmann equation (PBE) and the point charge approximation of the charged sphere are used. The electrical potential distribution in the electrolyte solution is found from the PBE at the constant surface potentials using the image charge method. The electrostatic forces acting on the spheres are then calculated. The results show that the repulsive interaction between a pair of similarly charged colloidal spheres clearly decreases when a charged wall appears nearby, but it is impossible for an attractive force to emerge at the scaled surface potentials less than 1. There is, however, an attractive force between the charged wall and the similarly charged colloidal spheres, when the surface potential zetap on the wall is sufficiently higher than the surface potential zetas on the spheres to make zetap > zetasexp(kappah) (h is the distance from the wall to the sphere center). In this case, there are negative surface charges on the spheres at positive surface potential zetas. It is these negative charges that produce the above attraction. Copyright 1999 Academic Press.     

Electrophoresis of Spherical Particles with a Random Distribution of Zeta Potential or Surface Charge

Electrophoresis is often used to measure the "average" zeta (zeta) potential on particles. However, it has been found by previous researchers that in making predictions of colloidal forces and stability, the distribution of zeta potential on the particles is important. This paper provides a straightforward method for measuring charge nonuniformity on colloidal spheres. It is shown that if the charge or zeta potential is random on a group of spheres, each covered with N equal-area patches, then the average magnitude of the dipole moment on the spheres is 0.92sigma(zeta)/N, and the average magnitude of the quadrupole moment is 1.302sigma(zeta)/N, where sigma(zeta) is the standard deviation of zeta potential over the surface of individual spheres. This is true for any random distribution of zeta potential, and the results emphasize that "random" implies nonuniform. It is demonstrated that since typical translational mobility measurements are much less sensitive to random charge nonuniformity than rotational mobility measurements, the latter measurement is better suited for measuring the second moment (sigma(zeta)) of zeta potential. Monte Carlo simulations were done to confirm and extend the analytical results. Copyright 2000 Academic Press.     

Texture dependence of capillary instabilities in nematic liquid crystalline fibres

Static and dynamic linear analyses of axisymmetric capillary instabilities in textured nematic liquid crystalline fibres are performed using the equations of nemato-statics and inviscid nemato-dynamics. Three representative textures, viz. axial, onion, and radial, are analysed to show all possible effects of Frank gradient elasticity on the wavelength selection and growth rate of peristaltic modes driven by surface area reduction. It is found that Frank elasticity may tend to stabilize or destabilize the fibre, depending on the initial fibre texture. Axial textures tend to stabilize the fibre through the director splay-bend distortions driven by surface tilting. Onion textures are destabilized by decreasing azimuthal bend elastic energy caused by surface displacement. Radial textures exhibit a stabilizing tilt mechanism due to bend modes and a destabilizing displacement mechanism due to splay modes, but the former is predicted to be dominant. The static analysis provides good estimates of the instability thresholds while the transient energy balance provides information on the fastest growing modes. The static and dynamic results are compared and shown to be fully consistent. The couplings between splay and/or bend distortions, surface tilting, and surface displacement in nematic fibres are characterized and used to explain the deviations from the classical Rayleigh instability.     

Electrophoresis of two identical rigid spheres in a charged cylindrical pore

The electrophoresis of two identical spheres moving along the axis of a long cylindrical pore under the conditions of low surface potential and weak applied electric field is investigated. The geometry considered allows us to examine simultaneously the effects of boundary and the presence of a nearby entity on the behavior of a particle. The influences of the separation distance between two spheres, the thickness of a double layer, the ratio (radius of sphere/radius of pore), and the charged conditions on the surfaces of the spheres and the pore on the mobility of a particle are investigated. Several interesting results that are not reported in the literature are observed. For instance, although for the case of two positively charged spheres in an uncharged pore the qualitative behavior of a sphere depends largely on its size relative to that of a pore and the thickness of the double layer, this might not be the case when two uncharged spheres are in a positively charged pore. In addition, in the latter, the mobility of a sphere increases with the increases in the separation distance between two spheres, and this effect is pronounced when the ratio (radius of sphere/radius of pore) takes a medium value or the thickness of the double layer is either sufficiently thin or sufficiently thick.     

Diffusion and trapping in a suspension of spheres with simultaneous reaction in the continuous phase

Much progress has been made in modeling the reaction of Brownian particles with spherical traps. Previously, work has focused on the effective reaction rate of systems of particles that diffuse freely until they are trapped by spheres in the dispersion. A particularly effective and efficient method to describe the reacting system is based on first-passage time distributions, from which an effective reaction rate coefficient of the suspension can be determined. The analysis presented here addresses reaction and diffusion in systems in which particles can undergo reaction in the continuous phase as well as reaction at the sphere surface. The first-passage method is extended to allow reaction or decay of the diffusing species in the continuous phase. The diffusion path is divided into a series of first-passage regions and is considered the probability of the particle being consumed in each of these regions. This allows the determination of the total reaction rate of the suspension (continuous phase reaction plus trapping) and the relative consumption rate in each phase. The extended method is applied to a model system of concentric spheres with a known continuum solution. It is shown to be accurate for consumption of reactant in the continuous phase from approximately 0 to approximately 100%. The method then is applied to a suspension of spheres.     

Colloidal dynamics near a particle-covered surface

How the diffusive dynamics of colloidal spheres changes in the vicinity of a particle-coated surface is of importance for industrial challenges such as fouling and sedimentation as well as for fundamental studies into confinement effects. We addressed this question by studying colloidal dynamics in a partially coated surface layer, using video microscopy. Particle mean squared displacement (MSD) functions were measured as a function of a (local) effective volume fraction (EVF), which was varied by making use of gravity settling. Comparison of MSDs at the bare and coated surfaces for EVF of 0.2-0.4 revealed that at the latter surface the motion amplitudes are strongly reduced, accompanied by a sharp transition from diffusive to nearly caged motion. This clearly indicates that the surface-attached particles cannot be taken into account via volume fraction and that their immobility has a distinct effect. For EVF > 0.45, the caging becomes dominated by the suspended particles, making the dynamics at the bare and coated surfaces similar.     

Free silver nanoparticles synthesized by laser ablation in organic solvents and their easy functionalization

Stable colloidal solutions of free silver nanoparticles (AgNPs) have been synthesized without reducing and stabilizing agents in pure acetonitrile and N,N-dimethylformamide by laser ablation of the bulk metal. Synthesis in tetrahydrofuran and dimethyl sulfoxide gave nanoparticles surrounded by a carbon shell or included in a carbon matrix. Mie theory for free and core@shell spheres accounts for the UV-vis spectra of the nanoparticles and allows their structural characterization. Transmission electron microscopy confirms the structure of the synthesized AgNPs. It is shown that free nanoparticles can be immediately functionalized, without further treatments, in the organic solvent used for the synthesis with molecules which are soluble in the same solvent.     

Fabrication of superhydrophobic surfaces from binary colloidal assembly

In this work, superhydrophobic surfaces were derived from binary colloidal assemblies. CaCO(3)-loaded hydrogel spheres and silica or polystyrene ones were consecutively dip-coated on silicon wafers. The former assemblies were recruited as templates for the latter self-assembly. Due to the hydrophilicity difference between silicon wafers and CaCO(3)-loaded hydrogel spheres, the region selective localization of silica or polystyrene spheres leads to irregular binary structures with a hierarchical roughness. The subsequent modification with low surface energy molecules yields a superhydrophobic surface. The heating treatment may largely enhance the mechanical stability of the resulting binary structures, which allows regeneration of the surface superhydrophobicity, providing a good durability in practice.     

Electrostatic interaction between two spherical colloidal particles

Explicit exact analytic expressions are obtained in the form of infinite series for the potential distribution and the potential energy of the electrostatic interaction for the system of two dissimilar spheres in an electrolyte solution on the basis of the linearized Poisson—Boltzmann equation without recourse to Derjaguin's approximation. The leading term of the expression for the interaction energy (the zeroth order approximation) corresponds to the interaction energy that would be obtained if both spheres were ion-penetrable spheres (“soft” spheres). This term is a screened Coulomb interaction due to a simple linear superposition of the unperturbed potentials of the respective spheres, which is proportional to the product of their unperturbed surface potentials. The first-order approximation corresponds to the interaction energy that would be obtained if either sphere were a soft particle (the other being hard). The first-order correction term consists of two sub-terms, each of which is proportional to the square of the unperturbed surface potential of either sphere and does not depend on the unperturbed surface potential of the other sphere, can be interpreted as the interaction between the soft sphere and its image with respect to the hard sphere. This image interaction is attractive if the surface potential of the hard sphere is constant and repulsive if the surface charge density of the sphere is constant. It is shown that Derjaguin's method as well as its extension to the interaction of unequal spheres by Hogg, Healy and Fuerstenau (HHF) is quite a good approximation.