Thickness, stability and contact angle of liquid films on and inside nanofibres, nanotubes and nanochannels

While the stability of liquid films on substrates is a classical topic of colloidal science, the availability of nanostructured materials, such as nanotubes, nanofibres and nanochannels, has raised the question of how the stability of liquid films and their wetting behaviour is affected by nanoscale confinement. This paper will present the conditions for the stability of liquid films on and inside cylindrical solid substrates with nanometre scale characteristic dimensions. It is shown that the stability is determined by an effective disjoining/conjoining pressure isotherm which differs from the corresponding disjoining/conjoining pressure isotherm of flat liquid films on flat solid substrates. From the former, the equilibrium contact angles of drops on an outer or inner surface of a cylindrical capillary have been calculated as a function of surface curvature, showing that the expressions for equilibrium contact angles vary for different geometries, in view of the difference in thickness of the film of uniform thickness with which the bulk liquid (drops or menisci) is at equilibrium. These calculations have been extended to the case of glass nanocapillaries and carbon nanotubes, finding good agreement with experimental results in the literature.     

Investigation of the isotherms of the disjoining pressure of wetting films of binary nonionic solutions by the ellipsometric method

The paper deals with an experimental investigation into the influence of the second component on the thicknesses of the wetting films of a nonionic solvent. A technique has been developed for the production of pure, smooth, thin glass substrates for wetting liquid films.

The use of these glass substrates enabled us to exclude the influence on the experimental results of such noncontrollable factors as roughness and pollution of the substrate surface. The isotherms of the disjoining pressure of wetting films of a number of two-component mixtures of nonionic liquids on glass substrates were experimentally determined. The film thicknesses were measured by an ellipsometric method; the disjoining pressure for the film was preset by adjusting the pressure of solvent vapours. The results obtained demonstrate a qualitative agreement with the theory of the adsorption component of disjoining pressure developed by Derjaguin and Churaev.

It is also shown that even very small additions of a polar substance to a nonpolar solvent may cause a marked change in the thickness of films. In addition to adopting the theory of the adsorption component of disjoining pressure, certain assumptions are made about the formation of the structural component resulting from the addition of a polar component to quantitatively describe the results obtained. The contribution of the adsorption and structural components of disjoining pressure to the stability of films of solution is estimated.     

Wetting and surface forces

In this review we discuss the fundamental role of surface forces, with a particular emphasis on the effect of the disjoining pressure, in establishing the wetting regime in the three phase systems with both plane and curved geometry. The special attention is given to the conditions of the formation of wetting/adsorption liquid films on the surface of poorly wetted substrate and the possibility of their thermodynamic equilibrium with bulk liquid. The calculations of contact angles on the basis of the isotherms of disjoining pressure and the difference in wettability of flat and highly curved surfaces are discussed. Mechanisms of wetting hysteresis, related to the action of surface forces, are considered.     

Isotherms of Capillary Condensation Influenced by Formation of Adsorption Films

Isotherms of capillary condensation are often used to determine the vapor sorption capacity of porous adsorbents as well as the pore size distribution by radii. In this paper, for calculating the volume of capillary condensate and of adsorption films in a porous body, an approach based on the theory of surface forces is used. Adsorption isotherms and disjoining pressure isotherms of wetting films are presented here in an exponential form discussed earlier. The calculations were made for straight cylindrical capillaries of different radii and slit pores of different width. The mechanisms of capillary condensation differ in cylindrical and slit pores. In cylindrical pores capillary condensation occurs due to capillary instability of curved wetting films on a capillary surface, when film thickness grows. In the case of slit pores, coalescence of wetting films formed on opposite slit surfaces proceeds under the action of attractive dispersion forces. Partial volumes of liquid in the state of both capillary condensate and adsorbed films are calculated dependent on the relative vapor pressure in a surrounding media. Copyright 2000 Academic Press.     

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.     

Equilibrium thin liquid films

The latest results are reviewed and a number of new concepts of the thermodynamics of thin films are formulated. Current definitions of disjoining pressure and their applications for introducing disjoining pressure into thermodynamics of phase equilibria, as well as the new thermodynamic definition of the thickness of thin film, are considered. New approaches to the rigorous definition of disjoining pressure in curved films and films with nonuniform thickness, including transition zones of wetting films, are analyzed. The modulus of Gibbs’ elasticity is derived for the case of a thin film. The role of the elasticity of this type in thin films and its correlation with traditional transverse (Derjaguin) elasticity related to the disjoining pressure are explained.     

Wetting–dewetting films: The role of structural forces

The liquid wetting and dewetting of solids are ubiquitous phenomena that occur in everyday life. Understanding the nature of these phenomena is beneficial for research and technological applications. However, despite their importance, the phenomena are still not well understood because of the nature of the substrate's surface energy non-ideality and dynamics. This paper illustrates the mechanisms and applications of liquid wetting and dewetting on hydrophilic and hydrophobic substrates. We discuss the classical understanding and application of wetting and film stability criteria based on the Frumkin–Derjaguin disjoining pressure model. The roles of the film critical thickness and capillary pressure on the film instability based on the disjoining pressure isotherm are elucidated, as are the criteria for stable and unstable wet films. We consider the film area in the model for the film stability and the applicable experiments. This paper also addresses the two classic film instability mechanisms for suspended liquid films based on the conditions of the free energy criteria originally proposed by de Vries (nucleation hole formation) and Vrij–Scheludko (capillary waves vs. van der Waals forces) that were later adapted to explain dewetting. We include a discussion of the mechanisms of nanofilm wetting and dewetting on a solid substrate based on nanoparticles' tendency to form a 2D layer and 2D inlayer in the film under the wetting film's surface confinement. We also present our view on the future of wetting–dewetting modeling and its applications in developing emerging technologies. We believe the review and analysis presented here will benefit the current and future understanding of the wetting–dewetting phenomena, as well as aid in the development of novel products and technologies.     

Untersuchungen des spaltdruckes dünner filme, deren entwicklung, ergebnisse und zu lösende aktuelle probleme

Considered is the development of the notions of the equilibrium disjoining pressure, beginning from its first experimental discovery for the films between solid surfaces, wetting or free. Considered is also the role of the disjoining pressure in the thermodynamics of liquid films, which is regarded as the main thermodynamic characteristic of the latter. The application of the notion of the disjoining pressure to the hydrodynamics of thin films has been mentioned. Considered are the components of the disjoining pressure, dependent upon the dispersion forces, ionic-electrostatic forces, and upon the structural peculiarities of boundary layers. In conclusion, one has considered the importance of the disjoining pressure for the stability of colloids.     

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.     

Thin wetting films from aqueous electrolyte solutions on SiC/Si wafer

The stability and rupture of thin wetting films from aqueous NaCl or Na2SO4 solutions of different concentrations on silicon carbide were investigated. The flat surface of SiC was obtained by plasma-enhanced chemical vapor deposition (PE-CVD) on top of a silicon wafer. The microinterferometric method was used for measuring the film thickness with time. The light reflectance was calculated as a function of film thickness for the four-layer system: air/aqueous solution/SiC/Si wafer. The microinterferometric experiments showed that films from aqueous NaCl and Na2SO4 solutions with concentrations up to 0.01 M were stable independent of the pre-treatment of the substrate. The pre-treatment of the SiC surface was crucial for the wetting film stability at electrolyte concentrations greater than 0.01 M. The films were unstable and ruptured if SiC was washed with 5% hydrofluoric acid and concentrated sulfuric acid, while they were stable if washing was in sulfuric acid only, without immersing SiC in HF. The average equilibrium film thickness was determined as a function of electrolyte concentration. Measurements of the electrokinetic potential zeta were performed by electrophores of SiC powder in 0.001 M NaCl. It was shown that silicon carbide surface was negatively charged. The theory of heterocoagulation was used for the interpretation of the results. Besides the DLVO forces, the structural disjoining pressure (both positive and negative) has been included in the analysis.     

An experimental investigation of polymolecular solvate (adsorbed) films as applied to the development of a mathematical theory of the stability of colloids

After a critical discussion of the current concepts of solvation of surfaces and colloid particles, as well as of the methods of studying solvation, a new quantitative definition of solvation is advanced. This definition connects solvation with the disjoining action of thin layers of liquids, discovered and studied in earlier experiments described in the preceding papers of this series.

The present paper describes a new, more convenient method of measuring both the thickness and disjoining action of thin layers for cases when they separate gas bubbles from solids (wetting films).

Observations of non-equilibrium states of such wetting films are described.

Experimental data are quoted, which are used in establishing an equation of state of a solvate layer. This equation expresses the equilibrium pressure (disjoining action) of a solvate layer for aqueous and non-aqueous media as a function of the thickness of the layer.

The effect of electrolytes on the thickness of aqueous solvate films. as well as the influence of surface-active substances upon vaseline-oil films on steel surfaces, has been investigated.

A theory of interaction of micelles, taking into account the disjoining action of thin layers of dispersion medium between the micelle surfaces, is advanced.

In conclusion, the computations used in the latter theory are employed to elaborate a theory of slow coagulation and stability of colloids and disperse systems.     

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.     

Impact of surface forces on wetting of hierarchical surfaces and contact angle hysteresis

The influence of the long-range surface forces on the wetting of multi-scale partially wetted surfaces is discussed. The possibility of partial wetting is stipulated by a specific form of the Derjaguin isotherm. Equilibrium of a liquid meniscus inside a cylindrical capillary is used as a model. The interplay of capillary and disjoining pressures governs the equilibrium of the liquid in the nano- and micrometrically scaled pores constituting the relief of the surface. It is shown that capillaries with a radius smaller than a critical one will be completely filled by water, whereas the larger capillaries will be filled only partially. Thus, small capillaries will show the Wenzel type of wetting behavior, while the same liquid inside the large capillaries will promote the Cassie-Baxter type of wetting. Consideration of disjoining/conjoining pressure allows explaining of the “rose petal effect”, when a high apparent contact angle is accompanied with a high contact angle hysteresis.     

Thin film drainage: hydrodynamic and disjoining pressures determined from experimental measurements of the shape of a fluid drop approaching a solid wall

Accurate measurements of the shape of a mercury drop separated from a smooth flat solid surface by a thin aqueous film reported recently by Connor and Horn (Faraday Discuss. 2003, 123, 193-206) have been analyzed to calculate the excess pressure in the film. The analysis is based on calculating the local curvature of the mercury/aqueous interface, and relating it via the Young-Laplace equation to the pressure drop across the interface, which is the difference between the aqueous film pressure and the known internal pressure of the mercury drop. For drop shapes measured under quiescent conditions, the only contribution to film pressure is the disjoining pressure arising from double-layer forces acting between the mercury and mica surfaces. Under dynamic conditions, hydrodynamic pressure is also present, and this is calculated by subtracting the disjoining pressure from the total film pressure. The data, which were measured to investigate the thin film drainage during approach of a fluid drop to a solid wall, show a classical dimpling of the mercury drop when it approaches the mica surface. Four data sets are available, corresponding to different magnitudes and signs of disjoining pressure, obtained by controlling the surface potential of the mercury. The analysis shows that total film pressure does not vary greatly during the evolution of the dimple formed during the thin film drainage process, nor between the different data sets. The hydrodynamic pressure appears to adjust to the different disjoining pressures in such a way that the total film pressure is maintained approximately constant within the dimpled region.     

Instabilities of nematic liquid crystal films

We discuss instabilities exhibited by free surface nematic liquid crystal (NLC) films of nanoscale thickness deposited on solid substrates, with a focus on surface instabilities that lead to dewetting. Such instabilities have been discussed extensively; however, there is still no consensus regarding the interpretation of experimental results, appropriate modeling approaches, or instability mechanisms. Instabilities of thin NLC free surface films are related to a wider class of problems involving dewetting of non-Newtonian fluids. For nanoscale films, the substrate–film interaction, often modeled by a suitable disjoining pressure, becomes relevant. For NLCs, one can extend the formulation to include the elastic energy of the NLC film, leading to an ‘effective’ disjoining pressure, playing an important role in instability development. Focusing on thin film modeling within the framework of the long-wave asymptotic model, we discuss various instability mechanisms and outline problems where new research is needed.     

Rupture of thin liquid films induced by impinging air-jets

Thin liquid films on partially wetting substrates are subjected to laminar axisymmetric air-jets impinging at normal incidence. We measured the time at which film rupture occurs and dewetting commences as a function of diameter and Reynolds number of the air-jet. We developed numerical models for the air flow as well as the height evolution of the thin liquid film. The experimental results were compared with numerical simulations based on the lubrication approximation and a phenomenological expression for the disjoining pressure. We achieved quantitative agreement for the rupture times. We found that the film thickness profiles were highly sensitive to the presence of minute quantities of surface-active contaminants.     

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.     

Disjoining pressure measurements using a microfabricated groove for a molecularly thin polymer liquid film on a solid surface

A method for measuring disjoining pressure of a molecularly thin liquid film on a solid surface by using a microfabricated groove has been developed. The shape of the meniscus of a thin film in the microgroove was measured with an atomic force microscope, and the disjoining pressure was obtained from the capillary pressure obtained from the measured curvature of the meniscus. Our method is applicable to a film with a thickness greater than the diameter of gyration in the polymer molecule. Moreover, the method can detect the changes in the disjoining pressure caused by ultraviolet light irradiation, and it is effective in investigating the intermolecular interaction between a thin film and a solid surface.