Bounding film drainage in common thin films

A review of thin film drainage models is presented in which the predictions of thinning velocities and drainage times are compared to reported values on foam and emulsion films found in the literature. Free standing films with tangentially immobile interfaces and suppressed electrostatic repulsion are considered, such as those studied in capillary cells. The experimental thinning velocities and drainage times of foams and emulsions are shown to be bounded by predictions from the Reynolds and the theoretical MTsR equations. The semi-empirical MTsR and the surface wave equations were the most consistently accurate with all of the films considered. These results are used in an accompanying paper to develop scaling laws that bound the critical film thickness of foam and emulsion films. (c) 2005 Elsevier B.V. All rights reserved.

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.

Assessment of P availability in heavily fertilized soils using the diffusive gradient in thin films (DGT) technique

Phosphorus-availability tests typically provide an indication of quantity of P available (Colwell bicarbonate-extractable P), or of the intensity of supply (0.01 M CaCl2-extractable P). The soil's capacity to buffer P is more difficult to assess, and is generally estimated using a P-adsorption curve. The diffusive gradient in thin films (DGT) approach may provide a simpler means of assessing a soil's ability to maintain soil solution P. Optimal extraction conditions were found to be 24 h exposure of DGT samplers to saturated soil. The DGT approach was evaluated on a range of 24 soils, some of which had high Colwell- (>100 mu g g(-1)) and Bray 1- (>30 mu g g(-1)) extractable P content, but showed a tomato (Lycopersicon esculentum Mill.) yield response to the addition of P fertilizer. The DGT approach provided an excellent separation of soils on which tomato showed a yield response, from those where fertilizer P did not increase dry-matter yield. Phosphorus accumulation was strongly correlated with soil solution P concentration and anion exchange resin-extractable P, but showed poor correlation with Colwell- or Bray 1-extractable P. The DGT P accumulation rate of 3.62 x 10(-7) to 4.79 x 10(-5) mol s(-1) m(-3) for the soils tested was comparable to the uptake rate of roots of tomato plants that were adequately supplied with P (2.25 x 10(-5) mol s(-1) m(-3)).

Application of edge-to-edge matching model to understand the in-plane texture of TiSi2 (C49) thin films on (001)(Si) surface

The edge-to-edge matching model, which was originally developed for predicting crystallographic features in diffusional phase transformations in solids, has been used to understand the formation of in-plane textures in TiSi2 (C49) thin films on Si single crystal (001)si surface. The model predicts all the four previously reported orientation relationships between C49 and Si substrate based on the actual atom matching across the interface and the basic crystallographic data only. The model has strong potential to be used to develop new thin film materials. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Mixed thin films of a cationic amphiphilic porphyrin and n-alkanes

Langmuir and Langmuir-Blodgett (LB) films of a cationic amphiphilic porphyrin mixed with n-alkanes octadecane and hexatriacontane were prepared and characterized, to examine the influence of the alkanes on film structure and stability. While the structure present in these films was controlled primarily by the porphyrin, the addition of the alkanes resulted in significant changes to both the phase behavior of the Langmuir films and the molecular arrangement of the LB films. These changes, as well as the observed chain length effects, are explained in terms of the intermolecular interactions present in the films.

Evaluation of elastic modulus and hardness of thin films by nanoindentation

Simple equations are proposed for determining elastic modulus and hardness properties of thin films on substrates from nanoindentation experiments. An empirical formulation relates the modulus E and hardness H of the film/substrate bilayer to corresponding material properties of the constituent materials via a power-law relation. Geometrical dependence of E and H is wholly contained in the power-law exponents, expressed here as sigmoidal functions of indenter penetration relative to film thickness. The formulation may be inverted to enable deconvolution of film properties from data on the film/substrate bilayers. Berkovich nanoindentation data for dense oxide and nitride films on silicon substrates are used to validate the equations and to demonstrate the film property deconvolution. Additional data for less dense nitride films are used to illustrate the extent to which film properties may depend on the method of fabrication.

Determination of mechanical properties of PECVD silicon nitride thin films for tunable MEMS Fabry-Pérot optical filters

This paper reports an investigation on techniques for determining elastic modulus and intrinsic stress gradient in plasma-enhanced chemical vapor deposition (PECVD) silicon nitride thin films. The elastic property of the silicon nitride thin films was determined using the nanoindentation method on silicon nitride/silicon bilayer systems. A simple empirical formula was developed to deconvolute the film elastic modulus. The intrinsic stress gradient in the films was determined by using micrometric cantilever beams, cross-membrane structures and mechanical simulation. The deflections of the silicon nitride thin film cantilever beams and cross-membranes caused by in-thickness stress gradients were measured using optical interference microscopy. Finite-element beam models were built to compute the deflection induced by the stress gradient. Matching the deflection computed under a given gradient with that measured experimentally on fabricated samples allows the stress gradient of the PECVD silicon nitride thin films introduced from the fabrication process to be evaluated.

Thin films of a tetracationic porphyrin

Langmuir-Blodgett films of the tetracationic porphyrin tetrakis( octadecyl-4-pyridinium) porphinatozinc(ii) bromide transferred from subphases containing different salts were studied using X-ray photoelectron spectroscopy (XPS) and X-ray reflectometry. In contrast to previous results at the air/water interface, we found that the porphyrin adopted a fixed conformation at the air/solid interface regardless of composition of the subphase or whether the films were transferred above or below the primary phase transition. This conformation was assigned to the formation of an interdigitated bilayer structure.

Multiple ordered phases in Langmuir-Blodgett films of cadmium arachidate at elevated temperatures

Using synchrotron X-ray grazing incidence diffraction, superlattice structures have been observed to develop in Langmuir-Blodgett films of cadmium arachidate as the temperature is raised. The previously reported superstructure in the stacked lamellae at room temperature changes at about 70 degreesC and there are further changes at about 90 and 103 degreesC before the major phase transition from stacked lamellae to hexagonally packed rods occurs at 107 degreesC (Langmuir 1997, 13, 1602). Between 70 and 103 degreesC there is a 1 x 10 one-dimensional in-plane superstructure, which is commensurate with the local structure and has an interlayer shift along [01] by a distance of b (of the local structure) at lower temperatures, and a further shift at about 90 degreesC. At lower (

Hydrothermal deposition of cerium hydroxycarbonate thin films on glass

The first success in the preparation of rare earth hydroxycarbonate thin films has been achieved. Cerium hydroxycarbonate films were prepared by a hydrothermal deposition method, the sample of a single orthorhombic phase was deposited at a lower temperature while those of orthorhombic and hexagonal phases were obtained at higher temperatures. The crystals in the films could be ellipsoidal, prismatic, or rhombic, depending on the deposition conditions applied. The thin films could be candidates for developing novel optical materials and for advanced ceramics processing. (C) 2003 Elsevier Science B.V. All rights reserved.

Formation of mesostructured titania thin films using iospropoxide precursors

Mesostructured titania thin films were prepared by an evaporation-induced self-assembly process. The highly acidic sot precursors contained titanium(IV) tetraisopropoxide (TTIP) as a titanium source, a tri-block copolymer Pluronic P123 as a template, and acetylacetonate and HCl as hydrolysis inhibitors. Characteristics of the resultant titania thin films were studied using X-ray diffraction (XRD) analysis, N-2-adsorption/desorption analysis, and transmission electron microscopy (TEM). XRD and TEM investigations on the as-synthesised films revealed the appearance of cubic-like, pseudohexagonal, and lamellar mesophases; depending on the amount of water in the sols of film precursors. Template removal by a calcination process yields high surface area (320-360 m(2)/g) mesoporous materials with crystalline anatase frameworks. Water content also influences the degree of anatase crystallinity of the calcined films. Higher water content resulted in improved anatase crystallinity. These nanostructured materials are of interest for photocatalysts, pbotoelectrochemical solar cells and other photonic devices. (C) 2003 Elsevier B.V. All rights reserved.

Scaling laws for the critical rupture thickness or common thin films

Despite decades of experimental and theoretical investigation on thin films, considerable uncertainty exists in the prediction of their critical rupture thickness. According to the spontaneous rupture mechanism, common thin films become unstable when capillary waves. at the interfaces begin to grow. In a horizontal film with symmetry at the midplane. unstable waves from adjacent interfaces grow towards the center of the film. As the film drains and becomes thinner, unstable waves osculate and cause the film to rupture, Uncertainty sterns from a number of sources including the theories used to predict film drainage and corrugation growth dynamics. In the early studies, (lie linear stability of small amplitude waves was investigated in the Context of the quasi-static approximation in which the dynamics of wave growth and film thinning are separated. The zeroth order wave growth equation of Vrij predicts faster wave growth rates than the first order equation derived by Sharma and Ruckenstein. It has been demonstrated in an accompanying paper that film drainage rates and times measured by numerous investigations are bounded by the predictions of the Reynolds equation and the more recent theory of Manev, Tsekov, and Radoev. Solutions to combinations of these equations yield simple scaling laws which should bound the critical rupture thickness of foam and emulsion films, In this paper, critical thickness measurements reported in the literature are compared to predictions from the bounding scaling equations and it is shown that the retarded Hamaker constants derived from approximate Lifshitz theory underestimate the critical thickness of foam and emulsion films, The non-retarded Hamaker constant more adequately bounds the critical thickness measurements over the entire range of film radii reported in the literature. This result reinforces observations made by other independent researchers that interfacial interactions in flexible liquid films are not adequately represented by the retarded Hamaker constant obtained from Lifshitz theory and that the interactions become significant at much greater separations than previously thought. (c) 2005 Elsevier B.V. All rights reserved.

Observation of a cubic phase in mesoporous silicate films grown at the air/water interface

X-Ray diffraction is reported from mesoporous silicate films grown at the air/water interface. The films were studied both as powdered films, and oriented on silicon or mica sheets. At early stages of growth we observe Bragg diffraction from a highly ordered cubic phase, with both long and short d-spacing peaks. We have assigned this as a discontinuous micellar Pm3n phase in which the silica is partly ordered. Later films retain only the known hexagonal p6m peaks and have lost any order both at short d-spacings and the longer d-spacing Bragg peaks characteristic of the cubic structure. The silica framework is considerably expanded from that in bulk amorphous silica, average Si Si distances are some 30% greater. Incorporation of glycerol or polyethylene glycol preserves the earlier cubic structure. To be consistent with earlier, in situ, X-ray and neutron reflectivity data we infer that both structures are produced after a phase transition from a less-ordered him structure late in the induction phase. The structural relations between the film Pm3n and p6m phase(s) and the known bulk SBA-1 and MCM-41 phases are briefly discussed.