On the applicability of Young–Laplace equation for nanoscale liquid drops

Debates continue on the applicability of the Young–Laplace equation for droplets, vapor bubbles and gas bubbles in nanoscale. It is more meaningful to find the error range of the Young–Laplace equation in nanoscale instead of making the judgement of its applicability. To do this, for seven liquid argon drops (containing 800, 1000, 1200, 1400, 1600, 1800, or 2000 particles, respectively) at T = 78 K we determined the radius of surface of tension R_s and the corresponding surface tension γ_s by molecular dynamics simulation based on the expressions of R_s and γ_s in terms of the pressure distribution for droplets. Compared with the two-phase pressure difference directly obtained by MD simulation, the results show that the absolute values of relative error of two-phase pressure difference given by the Young–Laplace equation are between 0.0008 and 0.027, and the surface tension of the argon droplet increases with increasing radius of surface of tension, which supports that the Tolman length of Lennard-Jones droplets is positive and that Lennard-Jones vapor bubbles is negative. Besides, the logic error in the deduction of the expressions of the radius and the surface tension of surface of tension, and in terms of the pressure distribution for liquid drops in a certain literature is corrected.     

Kinetics of wetting of liquid on a solid surface

To consider a sessile drop on an ideal solid surface in equilibrium with a vapor phase, the classic Young equation was given. The derivation of the Young equation was based on both the mechanics and the energy knowledge. According to the constant volume of the liquid in the wetting process of the liquid on a smooth and homogeneous solid surface and the low energy law, Young equation was ob-tained through the mathematic method in this paper. The previous work indicated that the contact angle θ was a function...     

The surface energy of kaolinite

The surface energy of kaolinite was determined from the water adsorption isotherm, the water/kaolinite contact angle, and the surface tension of water, using a formula obtained by combining the Young equation with the general equation of pair interaction. This formula could be represented by a polynomial function whose roots gave one real value of 252.57±2.75 mJ m^–2 for the surface energy of kaolinite. An important feature of the procedure for obtaining this energy is the use of the Young equation to determine the range in which the value of the surface energy lies.     

Silicon-Modified Carbohydrate Surfactants V: The Wetting Behaviour of Low-Molecular-Weight Siloxane,Carbosilane, Silane and Polysilane Precursors on Low-Energy Surfaces

The surface tensions, wetting tensions, contact angles and solid/liquid interfacial tensions of defined siloxanes as well as those of analogous carbosilanes, polysilanes and neopentyl substituted silanes were determined. The wetting experiments were carried out on a glass plate coated with perfluoroalkyl methacrylate (FC 722^®). The siloxanes possess the lowest surface tensions. Due to the presence of oxygen atoms in the siloxane backbone, a donor–acceptor portion (γ^+/−_lv) of the surface tension of about 1–2 mN/m was determined. The solid/liquid interfacial tension also contains a donor–acceptor portion (γ^+/−_sl). Its value is almost identical to that of γ^+/−_lv. The γ^+/−_sl differences between individual molecules of the same surface tension are responsible for contact angle differences of up to 4°. © 1997 John Wiley & Sons, Ltd.     

Contact angle interpretation in terms of solid surface tension

Recent experimental (low-rate) dynamic contact angles for 14 solid surfaces are interpreted in terms of their solid surface tensions. Universality of these experimental contact angle patterns is illustrated; other reasons that can cause data to deviate from the patterns are discussed. It is found that surface tension component approaches do not reflect physical reality. Assuming solid surface tension is constant for one and the same solid surface, experimental contact angle patterns are employed to deduce a functional relationship to be used in conjunction with the Young equation to determine solid surface tensions. The explicit form of such a relation is obtained by modifying Berthelot’s rule together with experimental data; essentially constant solid surface tension values are obtained, independent of liquid surface tension and molecular structure. A new combining rule is also derived based on an expression similar to one used in molecular theory; such a combining rule should allow a better understanding of the molecular interactions between unlike solid–liquid pairs.     

Interfacial tension of liquids from the height and contact angle of a single sessile drop

The height of a sessile drop of liquid when placed on a smooth solid surface increases as the drop volume increases, until it reaches a limiting value for a very large drop. The magnitude of the height and the contact angle depends on the different physical properties of the system. A large value for the contact angle is often associated with a large value for height and vice versa. From the data of measured limiting height, Z _Θ ^∞ and contact angle,Θ, the surface or interfacial tension,γ, can be estimated using the following equation: $$\gamma = \Delta \rho \cdot g \cdot (Z_\Theta ^\infty )^2 /2(1 - \cos (\Theta ))$$ whereΔ? is the density difference between the sessile drop and that of its surrounding medium,g is the gravitational force of acceleration. In this study, the magnitude ofγ of water for various systems is estimated. These values agree with the literature values. Furthermore, the values ofγ for various liquid₁/ solid/liquid₂ systems agree with data from other methods. Thus, the above equation is valid for different liquid-solid systems. It is further shown that very accurate measurements of contact angle,Θ, can be carried out for systems in which Z _Θ Δ _? andγ are known. The variation ofΘ with the height and volume of the sessile drop is analyzed for different systems.     

On the modelling of the dynamic contact angle

The dynamic contact angle is a value of great significance for characterizing wetting processes. Three strategies have been developed for modelling this value; empirical models, models based on molecular kinetics and models based on flow mechanics.Models based on molecular kinetics start from the fact that the dynamic contact angle appears immediately at the Une of wetting, and that the curvature of the liquid surface can be neglected. Models based on flow mechanics show that near the line of wetting the curvature is very strong. These models require the presence of the static contact angle at the line of wetting and give a model of the dynamic contact angle as the slope of the interface. In the present paper, models based on flow mechanics are extended in two directions. For the case of flow in a tubular capillary, the model represents the effect of the adsorption kinetics of surfactants on the dynamic contact angle, assuming the adsorption to be kinetically controlled. Another model is concerned with the effect of the flow of the third phase on the dynamic contact angle and on the boundaries of dynamic wetting. It is demonstrated that coating under an inert liquid is possible only for small working ranges.Symbols A dimensionless number of adsorption - B dimensionless number of adsorption - c concentration - C curvature - D diffusion coefficient - D _s surface diffusion coefficient - h, H height above the solid surface - K ₁ ,K ₂ rate constants - l length of slippage - p pressure - q mass flow density - r, R radius - R viscosity ratio - R _G gas constant - t time - U, v velocity - , , angle - viscosity - y dimensionless surface concentration - surface concentration - stream function - density - surface tension - _LF liquid-fluid interfacial tension - shearing stress - dimensionless radius - Ca capillary number     

A simple preparation of stable,nonreactive surfaces for gas kinetic studies of reactions of hydrogen atoms

A quartz surface has been prepared for which γ, the mean collisional efficiency for removal of hydrogen atoms, is given by over the temperature range from 315 to 818 K. The preparation “cleans” the surface by contact with 10M aqueous NaOH for ? 15 hr and then deactivates it by contact with 10M aqueous HNO₃ for ?15 hr. The surface is stable and long-lived even after prolonged contact with air. Preliminary results show that a similar result can be obtained using Pyrex glass surfaces.     

Adsorption kinetics at air/solution interface studied by maximum bubble pressure method

A general dynamic surface adsorption equation (t) for maximum bubble pressure method was derived by solving Ficks diffusion equation for the bubbles under different initial and boundary conditions. Different from the planar surface adsorption(Ward-Tordai equation), the derived dynamic surface adsorption (t) for the short time consists of two terms, one of them reflects the geometric effect caused by the spherical bubble surface. This kind of effect was discussed.The equilibrium surface tension _eq and the dynamic surface tension (t) of aqueous C₁₀E₈ (CH₃(CH₂)₉(OCH₂CH₂)₈OH) solution at temperature 25 °C were measured by means of Wilhelmy plate method and maximal bubble pressure method respectively. In the region of t0 (short time limits) a good agreement of experimental results with the theory was reached and the adsorption was controlled by diffusion. However, for the long time limits, a mixed diffusion-kinetics controlled process was proved.     

Factors influencing the contact angle value. The contact angle,as a characteristic of the properties of solid surfaces

A survey of publications concerning the properties of solids in relation to wetting phenomena is presented. Factors influencing the contact angle value as well as problems of objective approach to research into wetting phenomena are discussed. Peculiarities of the direct and reverse processes during the formation of the solid—liquid—vapor three-phase contact and the inevitability of contact angle hysteresis for polar solids and liquids are analyzed. It is suggested that contact angle hysteresis is due to high energy of the interaction between the liquid and the solid and hence a long relaxation time of the three-phase contact system. Specific features of the response of a solid surface to all surface processes (“chemomechanics”) is discussed. Cleaning of solid surfaces as well as surface preparation for repeated measurements is considered. It is shown that good reproducibility of results is possible if conditions for sample preparation are met. The results of determination of the activation energy for wetting of glass surface with water are presented. The influence of the structure of solids (their hardness) on the contact angle values is demonstrated. Inevitability of the presence of different-type active sites characterized by different dissociation constants (pK_a) on the surface of solids is discussed. The pK_a values and content of these surface sites obtained from potentiometric titration and wetting data are estimated. The estimates thus obtained are in reasonable agreement with each other and can thus be used in practical applications. However, potentiometric titration is currently inappropriate for evaluating the content of individual surface sites as well as the surface charge.     

Adsorption kinetics of nonionic surfactants using the drop volume method

The kinetic results obtained for the nonionic surfactantsn-octyl,n-decyl, andn-dodecyl dimethyl andn-octyl, andn-decyl diethyl phosphine oxide show purely diffusion controlled adsorption. The drop volume technique applied in a static and dynamic version proves to be useful to measure the adsorption kinetics in the form of surface tensions in function of time. Comparisons of the results obtained from both the static and the dynamic measuring procedure confirm the validity of a theory applied to interpret the kinetic data.Nomenclature a Langmuir parameter - c ₀ surfactant bulk concentration - D diffusion coefficient - surface concentration - ₀ equilibrium surface concentration - ¯ (t)/ ₀ reduced surface concentration - maximum value of - R gas law constant - surface tension - ₀ surface tension of pure water - t time - T absolute temperature     

Experimental Study on Contact Angle Patterns: Liquid Surface Tensions Less Than Solid Surface Tensions

The interpretation of contact angles in terms of solid surface tensions is not trivial. In the past, we and others have postulated that contact angles should be measured with liquid of surface tension larger than the anticipated solid surface tension, i.e., gamma(lv)>gamma(sv). This has recently been disputed. It is also not entirely obvious how to proceed experimentally since gamma(sv) is not known initially. Typically, one starts with a liquid of high gamma(lv) (such as water) and goes lower. We have stopped in the past when the contact angles became small. A question arises as to what would happen if we would go on. Contact angles of liquids with gamma(lv) less than or near gamma(sv) were measured on eight polymer-coated solid surfaces. The experimental contact angle patterns for gamma(lv)gamma(sv) were compared. Results suggest that contact angle interpretation in terms of solid surface tensions requires contact angles to be measured for gamma(lv)>gamma(sv) because the Young equation is not applicable for gamma(lv)相似文献   

Studies of the wetting kinetics of liquid drops on solid surfaces

The viscosity _L and the surface tension _L of the liquid as well as the equilibrium contact angle _e are essential parameters governing the wetting kinetics of liquids on solids. By means of a contact angle apparatus with video image digitization, the dynamic contact angle and the radiusr of the contact area of sessile drops on solid surfaces have simultaneously been determined in dependence on time after drop application between about 3·10^–2 s and long times.The measurements were performed with series of liquids: polydimethylsiloxanes with different molecular masses and solutions of polyisobutylene in decalin and polyacrylic acid in water, covering a wide range of concentrations. The liquids in each series have a constant surface tension, but viscosities ranging over about four orders of magnitude, allowing the influence of _L and _L to be studied independently. Solids such as glass, polyethylene and polytetrafluoroethylene were chosen so that the cases of complete wetting (spreading) and partial wetting ( _e) could be studied.The curves of cos andr/R ₀ vs. time for the different liquids of a series can be superimposed to a master curve by plotting them against _L·t _L·R ₀, whereR ₀ is the radius of the original drop. All these master curves coincide at small wetting times, with exception of the data for the polysiloxanes. That means that the early stage of the wetting process is determined only by the properties of the wetting liquid. The influence of the solid surface, characterized by the equilibrium contact angle _e becomes significant only at the end of the wetting process.Dedicated to Professor Dr. H. Willersinn on the occasion of his 65^th birthday     

Adhesion of high polymers. II. Wettability of elastomers

Data on wettability of elastomers should be considered basic to the understanding of all phases of elastomer adhesion. However, no such data in the form of critical surface tensions were available for elastomers other than polydimethylsiloxane. For this study, 18 elastomers were selected to determine the effects of functional groups, of geometrical and structural isomerisms, of copolymerization, and of the induced orientation upon wettability. Most results support the constitutive law of wettability established by Shafrin and Zisman. The effect of structural isomerisms in the form of a vinyl side group and cyclization is discussed. An equation for the calculation of critical surface tension of a copolymer or of a mixture of isomers is proposed as follows: where N_i is the mole-fraction of the individual monomer in the copolymer and \documentclass{article}\pagestyle{empty}\begin{document}$ \gamma _{c_i } $\end{document} is the critical surface tension of each homopolymer. Most elastomer adhesion studies conducted in the past were concerned with the diffusion theory of adhesion. This study further supports the conclusion on the role of diffusion and adsorption in adhesion advanced in Part I, especially with respect to the physical state of polymer at the time of application. The wettability data in this study could shed some light upon major basic mechanisms involved in elastomer reinforcement.     

Wettability of Microstructured Hydrophobic Sol-Gel Coatings

The formation of appropriate surface patterns on hydrophobic surfaces leads to a general change in their wettability and the contact angle increases substantially. Such coatings are of great technical interest, especially if aqueous media are concerned as in the prevention of ice-adhesion. For this reason various fluorine containing nanocomposite coatings have been developed by sol-gel processing.The morphology of these hydrophobic surfaces has been controlled by varying the content of silica particles regarding size, degree of aggregation, and concentration. The wettability is characterized by the measurement of dynamic contact angles against water. The complete range of different wettability regimes is accessible, i.e. smooth surfaces (both low advancing contact angle and hysteresis between advancing and receding contact angle), surfaces within the Wenzel regime (high advancing contact angle and hysteresis), and superhydrophobic surfaces (high advancing contact angle and low hysteresis). The wettability is correlated with the surface roughness as determined using a profilometer or AFM.The wettability of superhydrophobic surfaces is greatly dependent on the surface tension of the liquid. By comparison of the tiltangle _t of a smooth and a superhydrophobic surface, a critical surface tension _c is identified, where _t (smooth surface) = _t (microstructured surface). The microstructured surface provides a better run-off of liquids _lg > _c 55 mN·m^–1.     

Generalized theory of capillarity for axisymmetric menisci

A high-curvature generalization of the Laplace equation of capillarity and the Young equation of capillarity (including line tension) is developed for an axisymmetric solid-liquid-fluid system. The most general expressions for the Laplace and Young equations do not assume a particular form for the specific surface free energy. However, when a particular form, i.e., ω^(A) = γ^(A)_∞+ C_JJ+ C_kK, which is related to Gibbs' expression for a highly curved menisci,¹ is assumed to hold for the specific surface free energy then we are able to recover the expected simplified form of the Laplace equation. The corresponding high-curvature Young equation includes a couple which balances the surface moments at the contact line. Unfortunately, the effect of this couple could be confused with the effect of line tension in experiments which attempt to measure the dependence of the contact angle on the contact line radius.     

Studies on the Effects of Additional Components on Micellization of CTAB via Surface Tension Measurements

The effects of Tris-HCl buffer solution on the cmc of cetyltrimethylammonium bromide (CTAB) were studied by surface tension measurement. The result shows that the effect of the buffer solution depends on the interaction between CTAB and NaCl and the structure accelerants of water, Tris. A series of parameters, including the critical micelle concentration (cmc), the surface tension at cmc (γ_cmc), the adsorption efficiency (pC₂₀), and the effectiveness of surface tension reduction (∏_cmc) were obtained from the surface tension measurements in the presence of glycine with different concentration in the Tris-HCl buffer solution at 27°C. In addition, maximum surface excess concentration (Γ _max) and minimum surface area per molecule (A_min) at the air-water interface were estimated according to the Gibbs adsorption isotherm. The thermodynamic parameters (Δ C _p,m , Δ H _m,tr , Δ C _p,m,tr ) of micellization for CTAB in the absence and presence of glycine at different temperature were also been obtained.     

Contact angle interpretation: re-evaluation of existing contact angle data

We have recently shown that static contact angles measured by conventional goniometer techniques could be meaningless in the context of the Young equation. There is an abundance of contact angles in the literature that are of unknown status. Here, we explored whether one should completely neglect the literature contact angle data. Existing static contact angles for 34 different types of solid surfaces from Zisman and co-workers were evaluated in terms of their solid surface tensions using experimental contact angle patterns. A fortran computer program was implemented to automate these procedures. It was found that literature contact angles do not have to be discarded completely; they can be used to determine solid surface tensions, with caution. The surface tensions for the 34 solid surfaces from Zisman et al. are also reported.