Gradient theory for structural forces in thin fluid films near the critical point

We consider a general form of the local gradient theory for structural forces in thin fluid films near the critical point. A complete analytical solution of this problem at separation distances substantially larger than the molecular size is presented. That is, pi= -[330Psi(-4)H(8.8923-Psi) + 384exp(-Psi)H(Psi-8.8923)]H(-Gamma)+[1134.36Psi(-4)H(8.8923-Psi + 192exp(-Psi)H(Psi-8.8923)]H(Gamma) where Gamma <0 for similar (both attractive or both repulsive) and Gamma >0 for dissimilar (one attractive, another repulsive) bounding surfaces. Here pi and Psi are the structural force and the separation distance scaled in a certain way, and H(.) is a unit step function. For binary polymer films, the results are further elaborated to include a scaling dependence of the structural force on polymerization degrees of components.     

DLVO forces in thin liquid films beyond the conventional DLVO theory

Further progress has taken place in the theory of surface forces beyond the conventional DLVO theory. The major recent advances are related to more accurate accounting for the ionic nature of liquid interlayer in the calculations of van der Waals forces and for the impact of dispersion interaction of ions with other ions or confining phases on the peculiarities of ion-electrostatic interactions in liquid films.     

Challenges in the structural characterization of thin organic films

This review addresses the special problems associated with the micro-structural characterization of thin and ultrathin organic films, primarily by optical spectroscopies. Films which are deposited by Langmuir-Blodgett techniques, self-assembly chemistry, and bulk film deposition techniques are considered. The use of enhanced optical excitation using surface phasma resonances and integrated optical structures is discussed extensively, as is the use of ellipsometry. Discussion of the spectroscopies used is broken into a section on electronic spectroscopies and an extensive discussion of vibrational spectroscopies. Vibrational information may be obtained with photons (absorption or scattering) or electrons (loss spectra), and the types of experimental systems amenable to each, along with the advantages and disadvantages of each are explored.     

Surface structural evolution in iron oxide thin films

Ordered iron oxide ultrathin films were fabricated on a single-crystal Mo(110) substrate under ultrahigh vacuum conditions by either depositing Fe in ambient oxygen or oxidizing preprepared Fe(110) films. The surface structure and electronic structure of the iron oxide films were investigated by various surface analytical techniques. The results indicate surface structural transformations from metastable FeO(111) and O-terminated Fe(2)O(3)(0001) to Fe(3)O(4)(111) films, respectively. The former depends strongly on the oxygen pressure and substrate temperature, and the latter relies mostly upon the annealing temperature. Our experimental observations are helpful in understanding the mechanisms of surface structural evolution in iron oxides. The model surfaces of Fe-oxide films, particularly O-terminated surfaces, can be used for further investigation in chemical reactions (e.g., in catalysis).     

The critical thickness of thin free liquid films

Summary A numerical method based onVrij's theory is described to calculate the critical thickness of rupture or of formation of black spots in thin liquid films. Special care is taken to account for the fact that wave growth and drainage occur simultaneously. The influence of double layer repulsion, film dimensions and hydrostatic pressure on the critical thickness of films is investigated. A survey is given of the conditions for which black spot formation, rupture or continuous drainage in films is expected.It is shown that the dependence of the critical thickness on electrolyte concentration and film radius found byManev et al. can be conveniently explained qualitatively on the basis ofVrij's theory, in contradiction to the assertions ofManev et al.

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Zusammenfassung Aufbauend auf die Theorie vonVrij wird eine Methode zur Berechnung der kritischen Dicken für das Zerbrechen dünner flüssiger Filme oder für die Bildung schwarzer Flecken beschrieben. Insbesondere wird der gleichzeitige Verlauf der Verdiinnung des Filmes und des Wachsens der Oberflächenwellen beachtet. Es wird der Einfluß der Doppelschichtabstoßung, der Abmessungen des Filmes und des hydrostatischen Druckes untersucht und ein Überblick gegeben, unter welchen Bedingungen man Bildung schwarzer Flecken, Zerbrechen oder ununterbrochene Verdünnung in den Filmen erwarten darf.Es wird gezeigt, daß die Abhängigkeit der kritischen Dicke von der Elektrolytkonzentration unter dem Filmradius, gefunden vonManev u. a., qualitativ erklärt werden kann auf der Basis der Theorie vonVrij.

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With 9 figures und 1 table     

On autophobing in surfactant-driven thin films

Recent experiments (Afsar-Siddiqui, A. B.; Luckham, P. F.; Matar, O. K. Langmuir 2004, 20, 7575-7582) on the spreading of aqueous droplets containing cationic surfactants over thin aqueous films supported by negatively charged substrates demonstrated trends in the spreading behavior with either increasing surfactant concentration or increasing film thickness. Although the substrate is initially hydrophilic and the droplet spreads, surfactant adsorption at the substrate renders it hydrophobic leading to droplet retraction. We generate a model here using lubrication theory that allows the effect of the surfactant on the wettability to be taken into account. Our numerical results show that due to basal adsorption of surfactant at the interface, the initially hydrophilic solid substrate is rendered hydrophobic. This then drives droplet retraction and dewetting, which is in agreement with the experimentally observed trends.     

The effect of gravity on thin fluid films

The effect of gravity on the existence at equilibrium of thin fluid films is studied. The equilibrium conditions under the effect of gravity are developed and applied to specific cases of practical significance. It is concluded that, in contrast to the nongravitational situation, the effect of gravity allows in some cases the existence of a thin film at equilibrium with a bulk phase of a different curvature. However, for soap films, the effect of gravity prevents their equilibrium existence for almost any macroscopic size, again, in contrast to the nongravitational case.     

Contact angles in thin liquid films : III. Interaction forces in Newton black soap films

The interaction parameters of Newton black soap films stabilized by NaDS, as derived from contact angle experiments, have been interpretated in terms of the structure and the interaction forces in the films. From the film thickness and the difference between the surface excess of the salt in the film and at the bulk surface it is concluded that (a) the diffuse double-layer overlap in the film is practically complete; (b) the film only contains absorbed DS⁻ ions and an equal amount of Na⁺ counterions, but no salt; and (c) the double layer at the bulk surface is still partly diffuse. A model for the structure of the NB films is proposed according to which the adsorbed DS⁻ ions with their counterions form a two-dimensional square lattice at each film surface. It is found that the interaction free energy of the NB films can be explained by taking into account the electrostatic interactions between the discrete ions in the two opposing surface lattices. The model of the NB film is qualitatively in agreement with the experimental results of other workers.     

Surface forces measurements of spin-coated cellulose thin films with different crystallinity

A systematic study of the surface forces between a cellulose sphere and cellulose thin films of varying crystallinity has been conducted as a function of ionic strength and pH. Semicrystalline cellulose II surfaces and amorphous cellulose films were prepared by spin-coating of the precursor cellulose solutions onto oxidized silicon wafers before regeneration in water. Crystalline cellulose I surfaces were prepared by spin-coating wafers with aqueous suspensions of sulfate-stabilized cellulose I nanocrystals. These preparation methods produced thin, smooth films suitable for surface forces measurements. The interaction with the cellulose I was monotonically repulsive at pH 3.5, 5.8, and 8.5 and at 0.1, 1, and 10 mM ionic strengths. This was attributed to the presence of strongly ionizable sulfur-containing groups on the cellulose nanocrystal surfaces. The amorphous film typically showed a steric interaction up to 100 nm away from the interface that was independent of the solution conditions. A range of surface forces were successfully measured on the semicrystalline cellulose II films; attractive and repulsive regimes were observed, depending on pH and ionic strength, and were interpreted in terms of van der Waals and electrostatic interactions. Clearly, the forces acting near cellulose surfaces are very dependent on the way the cellulose surface has been prepared.     

Calculations of van der Waals forces in thin liquid films using Lifshitz' theory

For the study of thin, free liquid films (soap films) van der Waals dispersion forces were calculated from Lifshitz' theory for some three-layer models with film thicknesses between 5 and 150 nm. The complete expression as given by [2.] was used to calculate the force, the energy, and the second derivative of the energy after the thickness, as a function of film thickness. The second derivative of the energy after the thickness is needed in light scattering of soap films. The calculations are based on the dielectric data of [14.]. Some effects of the hydrocarbon layers on and electrolyte in the aqueous layer are considered. In order to make the results readily usable, the calculations are presented in the form of accurate empirical equations.     

NMR probing of structural peculiarities in ionic solutions close to critical point

(1)H, (23)Na, (35)Cl, (79)Br, and (81)Br NMR chemical shifts (delta) and signal half widths (Delta(12)) have been measured in aqueous electrolyte mixtures [tetrahydrofuran/H(2)ONaCl and 3-methylpyridine (3MP)H(2)ONaBr] at different mass fractions of salt (X) in the one-phase region, close to their lower critical solution points (T(CL)). Discontinuous changes in slope of delta=f(X) and Delta(12)=f(X) have been found in (23)Na and (81)Br NMR spectra of 3MP/water/NaBr solution at X approximately 0.1 and T=301 K. The dependency of (1)H NMR signals of 3MP is continuous over the whole investigated range of X=0.002-0.2, whereas changes in the slope of H(2)O chemical shifts are hardly noticeable. In the two-phase region, i.e., at T>T(CL), a doubling of all NMR signals has been observed. The sensitivity of NMR parameters depends more on composition of solution for anions (Cl(-) and Br(-)) than for cations (Na(+)). A very strong relaxation effect for (81)Br nuclei with relaxation rates reaching 14 000 s(-1) was observed. The results are interpreted in terms of ion-molecular clustering and changes in coherency of dipole configurations of water molecules during supramolecular restructuring of solutions.     

Interaction forces in thin liquid films stabilized by hydrophobically modified inulin polymeric surfactant. 1. Foam films

Using the interferometric method of Scheludko-Exerowa for investigation of foam films, we have obtained results using a hydrophobically modified inulin polymeric surfactant (INUTEC SP1). Measurements were carried out at constant INUTEC SP1 concentration of 2 x 10(-)(5) mol.dm(-)(3) and at various NaCl concentrations (in the range 1 x 10(-)(4) to 2 mol.dm(-)(3)). At constant capillary pressure of 50 Pa, the film thickness decreased gradually with an increase in NaCl concentration up to 10(-)(2) mol.dm(-)(3) NaCl above which the film thickness remains virtually constant at about 16 nm. This reduction in film thickness with an increase in NaCl concentration is due to the compression of the double layer and at the critical electrolyte concentration (C(el,cr) = 10(-)(2) mol.dm(-)(3)) the electrostatic component of the disjoining pressure is completely screened and the remaining pressure is due to the steric interaction between the adsorbed polymer layers. Disjoining pressure-thickness (Pi-h) isotherms were obtained at C(el) < C(el,cr) (10(-)(4) - 10(-)(3) mol.dm(-)(3)) and C(el) > C(el,cr) (0.5, 1, and 2 mol.dm(-)(3)). In the first case, the disjoining pressure isotherms could be fitted using the classical DLVO theory, Pi = Pi(el) + Pi(vw), and using the constant charge model. At C(el) > C(el,cr), the main repulsion is due to the steric interaction between the polyfructose loops that exist at the air-water interface, i.e., Pi = Pi(st) + Pi(vw). Under these conditions, there is a sharp transition from DLVO to non-DLVO forces. In the latter case, the interaction could be described using the de Gennes' scaling theory. This gave an adsorbed layer thickness of 6.5 nm which is in reasonable agreement with the values obtained at the solid-solution interface. The Pi-h isotherms showed that these foam films are not very stable and they tend to collapse above a critical capillary pressure (of about 1 x 10(3) Pa), and these results could be used to predict the foam stability.     

Interaction forces in thin liquid films stabilized by hydrophobically modified inulin polymeric surfactant. 2. Emulsion films

The interaction forces in emulsion films stabilized using hydrophobically modified inulin (INUTEC SP1) were investigated by measuring the disjoining pressure of a microscopic horizontal film between two macroscopic emulsion drops of isoparaffinic oil (Isopar M). A special measuring cell was used for this purpose whereby the disjoining pressure Pi was measured as a function of the equivalent film thickness hw. The latter was determined using an interferometric method. In this way Pi-hw curves were established at a constant INUTEC SP1 concentration of 2x10(-5) mol.dm-3 and at various NaCl concentrations. At a constant disjoining pressure of 36 Pa, a constant temperature of 22 degrees C, and a film radius of 100 microm, hw decreased with an increase in the NaCl concentration, Cel, and reached a constant value of 11 nm at Cel=5x10(-2) mol.dm-3. This reduction in film thickness is due to the compression of the electrical double layer, and at the above critical NaCl concentration any electrostatic repulsion is removed and only steric interaction remains. This critical electrolyte concentration represents the transition from electrostatic to steric interaction. At a NaCl concentration of 2x10(-4) mol.dm-3 the Pi-hw isotherms showed a gradual decrease in hw with an increase in capillary pressure, after which there was a jump in hw from approximately 30 to approximately 7.2 nm when Pi reached a high value of 2-5.5 kPa. This jump is due to the formation of a Newton black film (NBF), giving a layer thickness of the polyfructose loops of approximately 3.6 nm. The film thickness did not change further when the pressure reached 45 kPa, indicating the high stability of the film. Pi-hw isotherms were obtained at various NaCl concentrations, namely, 5x10(-2), 5x10(-1), 1.0, and 2.0 mol.dm-3. The initial thicknesses are within the range 9-11 nm, after which a transition zone starts, corresponding to a pressure of about 0.5 kPa. In this zone all films transform to an NBF with a jump, after which the thickness remains constant with a further increase in the disjoining pressure up to 45 kPa, with no film rupture. This indicates the very high stability of the NBF in the presence of high electrolyte concentrations. The high emulsion film stability (due to strong steric repulsions between the strongly hydrated loops of polyfructose) is correlated with the bulk emulsion stability.     

Systematic study on structural phase behavior of CdSe thin films

Cadmium selenide (CdSe) thin films were chemically deposited at room temperature, from aqueous ammoniacal solution using Cd(CH(3)COO)(2) as Cd2+ and Na(2)SeSO(3) as Se2- ion sources. The as-deposited films were uniform, well adherent to the glass substrate, specularly reflective, and red-orange in color. The as-deposited CdSe layers grew with nanocrystalline sphalerite cubic structure along with the amorphous phase present in it, with optical band gap E(g) = 2.3 eV. The films were annealed in air atmosphere for 4 h at different temperatures and characterized for compositional, structural, morphological, and optical properties. XRD and SEM studies clearly revealed the systematic phase transformation of CdSe films from metastable nanocrystalline cubic (zinc blende type) to a mixture of cubic and hexagonal (wurtzite type), and finally into stable hexagonal through different intermediate phases with an improvement in the crystal quality. The films showed a red shift in their optical spectra after annealing.     

Instability of the interface between thin fluid films subjected to electric fields

The effect of an externally applied electric field on the stability of the interface between two thin leaky dielectric fluid films of thickness ratio and viscosity ratio ris analyzed using a linear stability analysis in the long-wave limit. A systematic asymptotic expansion is employed in this limit to derive the coupled nonlinear differential equations describing the evolution of the position of the interface between the fluids and the interfacial free charge distribution. The linearized stability of these equations is determined and the effect of the ratio of the conductivities, dielectric constants, thicknesses, and viscosities on the wavenumber of the fastest growing mode, kmax, and the growth rate of the most unstable mode, smax, is examined in detail. Specific configurations considered in previous studies, such as a perfect dielectric-air interface, leaky dielectric-air interface, etc., emerge as limiting cases from the general formulation developed in this paper. Our results show that the viscosity ratio, mur, does not have any significant effect on kmax for the interface between perfect and leaky dielectric fluids. In marked contrast, however, mur is shown to have a significant effect on the interface between two leaky dielectrics. Increasing mur from 0.1 to 10 could decrease kmax up to a factor of 5. In general, our results show that the presence of nonzero conductivity in either one or both of the fluids has a profound influence on the length-scale characteristic of the linear instability: a reduction even by a factor of 1/50 in the length scale can be effected when compared to the interface between two perfect dielectrics. These predictions could have important implications in pattern formation applications in thin fluid films that employ electric fields. The variation of kmax and smax on the thickness ratio, beta, indicates in general that kmaxalpha(beta-apha), and smaxalpha(beta-theta), where the exponents alpha and theta (both >0) are found to depend only on the ratio of conductivities, and are largely independent of other system parameters.     

Crystallization at the glass transition in supercooled thin films of methanol

The stability of an amorphous material depends on how fast and by what mechanism crystallization occurs. Based on crystallization rate measurements through optical reflectivity changes in supercooled methanol thin films, it is observed for the first time that there is a definitive and detectable change of the crystallization mechanism at the glass transition temperature T(g). For methanol glasses below T(g)=103.4 K, crystallization occurs as an interface controlled, one-dimension process at frozen-in embryo sites, while in the deep supercooled liquid phase above T(g) crystallization is diffusion controlled in two dimensions with a constant nucleation rate and an activation energy of 107.8(+/-4.7) kJ/mol.     

On the structure of evaporated bismuth oxide thin films

The bismuth oxide films evaporated from bulk Bi₂O₃ are shown to vary in stoichiometry. The as-evaporated low rate (1–5 Å/sec) films are microcrystalline and bismuth rich, relative to Bi₂O₃, and their optical absorption edge broadens and shifts to lower energies. High rate (15–25 Å/sec) films are morphous and oxygen-rich with an absorption edge shifted to higher energies. Thermal decomposition of the Bi₂O₃ during evaporation produces the variations in film stoichiometry. The high temperature δ-Bi₂O₃ observed in the as-evaporated low rate films and thermally treated amorphous films indicates the melt and the films are structurally similar. Thermal treatment of the low rate films results in the formation of the β-form. Comparison of X-ray and stoichiometry results suggests that β-Bi₂O₃ be expressed as β-Bi₂O_±3x, where x is the deviation from trioxide stoichiometry.     

Surface forces in wetting films

A short review of various components of surface forces acting in a non-symmetrical system such as wetting films is presented here. Experimental results are compared with modified DLVO theory, which includes, besides dispersion and electrostatic, structural (solvation) forces caused by a change in liquid structure in conditions of confined geometry. The peculiarities of disjoining pressure isotherms and conditions of the film stability of non-polar and polar simple liquids, as well as of aqueous solutions of electrolytes and surfactants, are systematically considered from a historical perspective.     

Optical birefringence in a fluid near its critical point with stratification under gravity

Electromagnetic wave propagation in an inhomogeneous medium is discussed in the context of light propagation in a fluid near its critical point, stratified under gravity. The system exhibits birefringence, where the transverse electric (te) and the transverse magnetic (tm) waves travel with different phase-velocities, depending upon the density-gradients with height set up in the system. The possibility of experimentally detecting the predicted phenomenon is also discussed.     

Triple point of Lennard-Jones fluid in slit nanopore: solidification of critical condensate

We report the results of a molecular dynamics simulation that looked for the triple point of Lennard-Jones fluid in slit-shaped nanopores. The simulation method employed for this purpose is able to maintain vapor-liquid coexistence in a nanopore at a specific equilibrium bulk-phase pressure. The triple point is the freezing point of the critical condensate. The triple-point temperature could be higher or lower than the bulk triple point, depending on the pore size. This is thought to be due to two opposing factors: the elevating effect of the pore-wall potential energy, and the depressing effect of the capillary condensate's tensile condition. Because of the cancellation, the deviation of the triple-point temperature from the bulk triple-point temperature was not considered significant. The pressure of the triple point, however, was significantly different from that of the bulk triple point. A simple model to describe the triple point is developed and shown to agree well with the results of the simulation. The importance of the two factors in nanoscale pores, which cannot be described by the classic Gibbs-Thomson equation, is emphasized.