A model for the stability of films stabilized by randomly packed spherical particles

Particle stabilized thin films occur in a range of industrial applications where their properties affect the efficiency of the process concerned. However, due to their dynamic and unstable nature they are difficult to observe experimentally. As such, a tractable way of gaining insight into the fundamental aspects of this complicated system is to use computer simulations of particles at interfaces. This paper presents modeling results of the effect of nonuniform packing of spherical particles on the stability of thin liquid films. Surface Evolver was used to model cells containing up to 20 particles, randomly packed in a thin liquid film. The capillary pressure required to rupture the film for a specific combination of particle arrangement, packing density, and contact angle was identified. The data from the periodic, randomly packed models has been used to find a relationship between particle packing density, contact angle, and critical capillary pressure which is refined to a simple equation that depends on the film loading and contact angle of the particles it contains. The critical capillary pressure for film rupture obeys the same trends observed for particles in regular 2D and 3D packing arrangements. The absolute values of P*(crit), however, are consistently lower than those for regular packing. This is due to the irregular arrangement of the particles, which allows for larger areas of free film to exist, lowering the critical capillary pressure required to rupture the film.     

A model for investigating the behaviour of non-spherical particles at interfaces

This paper introduces a simple method for modelling non-spherical particles with a fixed contact angle at an interface whilst also providing a method to fix the particles orientation. It is shown how a wide variety of particle shapes (spherical, ellipsoidal, disc) can be created from a simple initial geometry containing only six vertices. The shapes are made from one continuous surface with edges and corners treated as smooth curves not discontinuities. As such, particles approaching cylindrical and orthorhombic shapes can be simulated but the contact angle crossing the edges will be fixed. Non-spherical particles, when attached to an interface can cause large distortions in the surface which affect the forces acting on the particle. The model presented is capable of resolving this distortion of the surface around the particle at the interface as well as allowing for the particle's orientation to be controlled. It is shown that, when considering orthorhombic particles with rounded edges, the flatter the particle the more energetically stable it is to sit flat at the interface. However, as the particle becomes more cube like, the effects of contact angle have a greater effect on the energetically stable orientations. Results for cylindrical particles with rounded edges are also discussed. The model presented allows the user to define the shape, dimensions, contact angle and orientation of the particle at the interface allowing more in-depth investigation of the complex phenomenon of 3D film distortion around an attached particle and the forces that arise due to it.     

The effect of particle hydrophobicity, separation distance and packing patterns on the stability of a thin film

Hydrophobic particles attached to bubble films in foams can increase the capillary pressure required to cause coalescence or bursting. Previous studies have considered the effects of changing particle spacing and contact angle in 2 dimensions (2D), but there are limitations to this approach; in 2D when the separation distance is zero and the particles are touching, the critical capillary pressure tends to infinity as there is no exposed film. In 3 dimensions (3D) spherical packing ensures that there are always exposed sections of film between particles even when they are close packed. Using Surface Evolver, the effects of contact angle and particle separation on the stability of a particle laden film were investigated in 2D and 3D. The 2D model was compared and validated with an analytical approach developed by Ali et al. [Ind. Eng. Chem. Res. 39 (2000) 2742-2745] and a 3D model was used to investigate the critical capillary pressures of square and hexagonal packing of monodisperse particles. It was found that when the stability of the film was compared with the area of film per particle both packing patterns have the same stability.     

Effect of hydrophobicity on the stability of the wetting films of water formed on gold surfaces

We have developed a methodology that can be used to determine disjoining pressures (Π) in both stable and unstable wetting films from the spatial and temporal profiles of dynamic wetting films. The results show that wetting films drain initially by the capillary pressure created by the changes in curvature at the air/water interface and subsequently by the disjoining pressure created by surface forces. The drainage rate of the film formed on a gold surface with a receding contact angle (θ(r)) of 17° decreases with film thickness due to a corresponding increase in positive Π, resulting in the formation of a stable film. The wetting film formed on a hydrophobic gold with θ(r)=81° drains much faster due to the presence of negative Π in the film, resulting in film rupture. Analysis of the experimental data using the Frumkin-Derjaguin isotherm suggests that short-range hydrophobic forces are responsible for film rupture and long-range hydrophobic forces accelerate film thinning.     

Fabrication of flexible gold films with periodic sub-micrometer roughness and their wettability control by modification of SAM

Flexible honeycomb gold films supported by polymer sheets are fabricated by using polystyrene particle monolayers. The surfaces of the flexible gold films are covered with self-assembled monolayers (SAMs) of hydrophobic or hydrophilic thiol compounds, and the wettability of the modified surface is evaluated by measurements of the contact angles of water droplets. The contact angle of the film covered with hydrophobic SAM is ca. 150 degrees, which is greater than the value of 112 degrees for a flat gold surface, while the values for hydrophilic SAM are below 10 degrees.     

Particle zips: vertical emulsion films with particle monolayers at their surfaces

Vertical emulsion films with particle monolayers at their surfaces have been studied by direct microscope observations. The effects of particle wettability and surface coverage on the structure and stability of water films in octane and octane films in water have been investigated. Monodisperse silica particles (3 microm in diameter) hydrophobized to different extents have been used. It is found that the structure and stability of emulsion films strongly depend on the film type (water-in-oil or oil-in-water), the particle contact angle, the interactions between particles from the same and the opposite monolayer, and the monolayer density. Stable films are observed only when the particle wettability fulfills the condition for stable particle bridges--in agreement with the concept that hydrophilic particles can give stable oil-in-water emulsions, whereas hydrophobic ones give water-in-oil emulsions. In the case of water films with dilute disordered monolayers at their surfaces, the hydrophilic particles are expelled from the film center toward its periphery, giving a dimple surrounded by a ring of particles bridging the film surfaces. In contrast, the thinning of octane films with dilute ordered monolayers at their surfaces finally leads to the spontaneous formation of a dense crystalline monolayer of hydrophobic particles bridging both surfaces at the center of the film. The behaviors of water and octane films with dense close-packed particle monolayers at their surfaces are very similar. In both cases, a transition from bilayer to bridging monolayer is observed at rather low capillary pressures. The implications of the above finding for particle stabilized emulsions are discussed.     

Study on aluminium-based single films

In the present paper the authors studied isolated metallic films made from the same material used for making metallic foams, and then characterised their properties. Metal films were made from a liquid aluminium alloy reinforced with ceramic particles of known concentration. Melts without such particles were also investigated. It is shown that stable films could not be made from Al-Si alloy having no particles, and just extremely thin and fragile films could be made from commercially-pure Al. In contrast, aluminium alloys containing particles such as SiC and TiB(2) allowed pulling thin, stable films, which did not rupture. Significant thinning of films was observed when the particle concentration in the melt decreased. By in situ X-ray monitoring of liquid films during pulling, film thickness and drainage effects within the liquid film could be studied. The morphology and microstructure of films was characterised after solidification. Our work shows that the question of how foams are stabilised can be studied using a simplified system such as a film, instead of having to deal with the multitude of different structural elements present in a foam.     

Disjoining pressure,contact angles and line tension in free thin liquid films

Three are the main thermodynamic quantities which characterize the physical behaviour of the thin liquid films: the disjoining pressure, the macroscopic contact angle between the film and its adjacent bulk liquid phase, and the line tension of the film contact perimeter. All these quantities manifest the action of the long-range interaction surface forces which take place in any small capillary system. The rigorous introduction of such quantities is closely related to the Gibbs concept of surface of tension. For the case of a thin plane parallel liquid film there exist three surfaces of tension. By making use of them the thickness of the film would also be defined. There are several experimental methods for determining the tension of film, the contact angles. the line tension. Some important details of these methods. some experimental results together with important features of the thermodynamic theory of the thin liquid films are the subject of the present paper.     

Thin wetting films from aqueous solutions of surfactants and phospholipid dispersions

The microscopic thin wetting film method was used to study the stability of wetting films from aqueous solution of surfactants and phospholipid dispersions on a solid surface. In the case of tetradecyltrimethylammonium bromide (C(14)TAB) films the experimental data for the receding contact angle, film lifetime, surface potential at the vapor/solution and solution/silica interface were used to analyze the stability of the studied films. It is shown that with increasing C(14)TAB concentration charge reversal occurs at both (vapor/solution and solution/silica) interfaces, which affects the thin-film stability. The spontaneous rupture of the thin aqueous film was interpreted in terms of the earlier proposed heterocoagulation mechanism. The presence of the mixed cationic/anionic surfactants was found to lower contact angles and suppresses the thin aqueous film rupture, thus inducing longer film lifetime, as compared to the pure amine system. In the case of mixed surfactants hetero-coagulation could arise through the formation of ionic surfactant complexes. The influence of the melting phase-transition temperature T(c) of the dimyristoylphosphatiddylcholine (DMPC) on the stability of thin films from dispersions of DMPC small unilamellar vesicles on a silica surface was studied by measuring the film lifetime and the TPC expansion rate. The stability of thin wetting films formed from dispersions of DMPC small unilamellar vesicles was investigated by the microinterferometric method. The formation of wetting films from diluted dispersions of DMPC multilamellar vesicles was studied in the temperature range 25-32 degrees C. The stability of thin film of lipid vesicles was explained on the basis of hydrophobic interactions. The results obtained show that the stability of wetting films from aqueous solutions of single cationic and mixed cationic-anionic surfactants has electrostatic origin, whereas the stability of the phospholipid film is due to hydrophobic interaction.     

Determination of the molecular orientation of very thin films on solid substrates: surface liquid crystal layers and rubbed polyimide films

The molecular orientation of very thin films on solid substrates can be determined quantitatively by measuring the polarized infrared (IR) absorption spectra of samples as a function of angle of incidence. The quantitative molecular orientation is derived by fitting the incident angle dependence and the dichroic ratio with theoretical calculations. We applied this method to a technologically important system: liquid crystal (LC)/rubbed polyimide film. To understand the alignment mechanism of LC molecules in contact with rubbed polyimide films, we have quantitatively determined the molecular orientation of rubbed polyimide films and a surface LC layer in contact with a rubbed polyimide film. In this paper two relations are discussed: (1) correlation between the inclination angle of polyimide backbone structures in rubbed films and the pretilt angle of bulk LC in contact with them, and (2) relation among the molecular orientation of a rubbed polyimide film and those of surface and bulk LC layers in contact with it.     

Capillary Pressure in Thinning Emulsion Film Stabilized with Solid Spherical Particles

Stability and coalescence of emulsions stabilized with solid particles is determined by the energy of particle attachment at the liquid–liquid interface (the energy of adhesion) and by the value of capillary pressure arising in the emulsion film in the process of its thinning under the lower pressure when two layers of solid particles (on the opposite film sides) draw together up to their direct contact and formation of menicsi in the porous space between particles. We calculated maximal (critical) capillary pressure P _{c, max} whose exceeding leads to the film rupture as a function of contact angle and the size of solid particles needed to form the adsorption layer of monodisperse spherical particles with a dense hexagonal packing. Capillary pressure isotherms P _c(h) (h is the thickness of emulsion film) were also calculated. The deviation of meniscus shape from spherical was considered using the Mayer, Stowe, and Princen method. Determination of capillary pressure in a model emulsion film containing hexagonal-packed transparent glass spheres demonstrated that, at various degrees of particle hydrophobicity, experimental data are in good agreement with theoretical calculations of the P _{c, max} value and P _c(h) isotherm.     

Submicron films prepared from aqueous dispersions of nanoscale polymer crystals

Thin and ultrathin films of polyethylene of variable thickness are obtained from aqueous dispersions of prefabricated nanoscale crystals by spin‐coating. Continuous films with a thickness of only 15 nm, up to 220 nm, homogeneous over hundreds of μm, or assembled discontinuous monolayers of flat‐on lamella particles were prepared, depending on the solids content of the dispersion employed, as revealed by AFM and TEM. The morphology of melt‐recrystallized films was not affected by the surfactant present. Homogeneous continuous films without undesirable dewetting were retained upon melting and recrystallization of the films upon cooling, composed of polygonal spherulites for a thicker film (220 nm), randomly grown edge‐on lamella for a 40 nm film, and dominant flat‐on lamella for a 15 nm thick film. Annealing below T_m resulted in lamella thickening, without changes of crystal orientation or structure of the particle assemblies for discontinuous monolayers. Surfactant adsorbed to the nanocrystals in the aqueous dispersion desorbs at least partially during formation of the nascent films, and upon annealing below the melting point surfactant migrates to the film‐air interface to form aggregates, which can be removed by rinsing, during which the film stays intact and structurally unaltered as revealed, amongst others, by water contact angles. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6420–6432, 2009     

Contact angles of colloid silica and gold particles at air-water and oil-water interfaces determined with the gel trapping technique

We have used the recently developed gel trapping technique (GTT) to determine the three-phase contact angles of submicrometer silica particles partially coated with octadecyl groups. The particles were spread at air-water and decane-water surfaces, and the aqueous phase was subsequently gelled with a nonadsorbing polysaccharide. The particles trapped at the surface of the aqueous gel were lifted by molding with curable poly(dimethylsiloxane) and imaged with scanning electron microscopy (SEM) to determine the particle contact line diameter which allows their contact angle at the original air-water or oil-water interface to be estimated. We report for the first time the use of the GTT for characterizing the contact angle of individual submicrometer particles adsorbed at liquid interfaces. The SEM images also reveal the structure of the particle monolayer at the interface and the structure of adsorbed particle aggregates. We have also determined the contact angles of agglomerated gold powder microparticles at the air-water and the decane-water interfaces. It was found that agglomerated gold particles demonstrate considerably higher contact angles than those on flat gold-coated surfaces.     

Direct catalytic route to superhydrophobic polyethylene films

Polyethylene films grow on a flat silica surface modified by the bis(imino)pyridyl iron(II) catalyst during ethylene polymerization in toluene solvent. The resulting films show superhydrophobic properties. Advancing water contact angle as high as 169 degrees and sliding angles as low as 2 degrees are obtained on these films. SEM images reveal special surface structures of these films containing micrometer-sized islands, submicrometer particles on the islands, and stress nanofibers between the islands, which render superhydrophobicity to the polyethylene surfaces. After the submicrometer particles and stress nanofibers are removed by annealing, the superhydrophobic properties of the polymer films disappear.     

Critical capillary pressure for destruction of single foam films and foam: effect of foam film size

Foams and single foam films stabilised by ionic and amphiphile polymer surfactants are studied with foam pressure drop technique (FPDT) and thin liquid film-pressure balance technique (TLF-PBT). A pressure is reached at which the single foam films rupture and the foams destruct very fast (avalanche-like). For film rupture we named this pressure—critical capillary pressure of film rupture, P_cr,film while for foam destruction, we introduced a new parameter—critical capillary pressure of foam destruction, P_cr,foam. The surfactant kind and foam film type (common thin, common black and Newton black) affect the values of both parameters. When below 20 kPa, P_cr,film and P_cr,foam are close by value, when over 20 kPa, there is a significant difference between them. The P_cr,film versus film size and P_cr,foam versus foam dispersity dependences, indicate that the film size and foam dispersity strongly affects the critical capillary pressure values. Film size distribution histograms reveal that a foam always contains films that are of a larger than the most probable size. They rupture at lower pressures, does initiating the destruction of the whole foam, which can be an explanation why higher than 20 kPa there is a difference between P_cr,film and P_cr,foam values. This parameter, P_cr,foam is considered of significant with respect to foam stability and could find use in industry.     

Capillary forces between chemically different substrates

Motivated by experimental results, we present numerical and analytical calculations of the capillary force exerted by a capillary bridge spanning the gap between two parallel flat plates of asymmetric wettability. Depending on whether the sum of the two contact angles is smaller or larger than 180 degrees, the capillary force is either attractive or repulsive at small separations D between the plates. In either cases the magnitude of the force diverges as D approaches zero. The leading order of this divergence is captured by an analytical expression deduced from the geometry of the meniscus of a flat capillary bridge. The results for substrates with different wettability reveal an interesting behavior: with the sum of the contact angles fixed, the magnitude of the capillary force and the rupture separation decreases as the asymmetry in contact angles is increased. In addition, we present the rupture separation, i.e., the maximal extension of a capillary bridge, as a function of the contact angles. Our results provide an extensive picture of surface wettability effects on capillary adhesion.     

Spreading of liquid drops over dry surfaces

Spreading of thin, axisymmetric, non-volatile, Newtonian liquid drops over a dry, smooth, flat solid surface is considered both theoretically and experimentally in the case of complete wetting. The drop profile is solved analytically by matching the “outer” solution for large film thicknesses, where only the capillary effects are important, with the “inner” solution for small film thicknesses, where the viscous and disjoining pressure effects are comparable to capillary effects. It is shown that the apparent radius of the wetted spot, the apex height of the drop, and the apparent advancing dynamic contact angle follow different power laws in time and the advancing dynamic contact angle follows a power law in capillary number. Both the prefactor and the exponent of each power law are derived theoretically. Good agreement between the theory predictions and experimental measurements is shown for both the prefactor and exponent of each power law. It is necessary to emphasize that the theory suggested does not include any fitting parameters.     

疏水型SiO2光学增透膜的制备

以正硅酸乙酯（TEOS）为有机醇盐前驱体,采用溶胶-凝胶技术,通过酸/碱二步法控制实验条件,结合三甲基氯硅烷（TMCS）对胶粒表面的修饰过程,制备出结构可控的疏水型SiO2薄膜.采用椭偏仪、FTIR、接触角测试仪、SEM等对薄膜的折射率、红外特性、接触角以及表面形貌等进行了测量.研究结果表明,疏水型SiO2薄膜的折射率在1.33～1.18之间连续可调;SiO2胶粒表面的亲水性－OH中的H已部分被非活性－Si(CH3)3基团取代;接触角由表面未修饰膜的40°左右增加到表面修饰膜的120°左右.     

Stable drop shapes under disjoining pressure. II. Multiplicity and stability

The stability of the contact line region as affected by the disjoining pressure has been analyzed by solving the augmented Young-Laplace equation. Because of the results in Part I (Zhang, X., Neogi, P., and Ybarra, R. M., J. Colloid Interface Sci.), we have concentrated on obtaining multiple solutions for the same set of conditions. As many as five solutions were obtained: drops that end in a thin film with uniform thickness and where the film shape oscillates, drops that end with microscopic contact angles, as well as uniform thin films of two different thicknesses. The results of linear stability analysis were used to show that most cases were unstable to infinitesimal disturbances. Only two stable drop shapes for the particular disjoining pressure investigated are stable, a thin film of constant thickness and a thin drop that ends in a film of same thickness. Both multiplicity and stability have been discussed here for the first time and shed considerable light on the role of the attractive and repulsive forces.     

Orientation of pentacene molecules on SiO2: from a monolayer to the bulk

Near edge x-ray absorption fine structure (NEXAFS) spectroscopy is used to study the orientation of pentacene molecules within thin films on SiO2 for thicknesses ranging from monolayers to the bulk (150 nm). The spectra exhibit a strong polarization dependence of the pi* orbitals for all films, which indicates that the pentacene molecules are highly oriented. At all film thicknesses the orientation varies with the rate at which pentacene molecules are deposited, with faster rates favoring a thin film phase with different tilt angles and slower rates leading to a more bulklike orientation. Our NEXAFS results extend previous structural observations to the monolayer regime and to lower deposition rates. The NEXAFS results match crystallographic data if a finite distribution of the molecular orientations is included. Damage to the molecules by hot electrons from soft x-ray irradiation eliminates the splitting between nonequivalent pi* orbitals, indicating a breakup of the pentacene molecule.