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   

Recent progress in the determination of solid surface tensions from contact angles

Advancing contact angles of different liquids measured on the same solid surface fall very close to a smooth curve when plotted as a function of liquid surface tension, i.e., gamma(lv)costheta versus gamma(lv). Changing the solid surface, and hence gamma(sv), shifts the curve in a regular manner. These patterns suggest that gamma(lv)costheta depends only on gamma(lv) and gamma(sv). Thus, an "equation of state for the interfacial tensions" was developed to facilitate the determination of solid surface tensions from contact angles in conjunction with Young's equation. However, a close examination of the smooth curves showed that contact angles typically show a scatter of 1-3 degrees around the curves. The existence of the deviations introduces an element of uncertainty in the determination of solid surface tensions. Establishing that (i) contact angles are exclusively a material property of the coating polymer and do not depend on experimental procedures and that (ii) contact angle measurements with a sophisticated methodology, axisymmetric drop shape analysis (ADSA), are highly reproducible guarantees that the deviations are not experimental errors and must have physical causes. The contact angles of a large number of liquids on the films of four different fluoropolymers were studied to identify the causes of the deviations. Specific molecular interactions at solid-vapor and/or solid-liquid interfaces account for the minor contact angle deviations. Such interactions take place in different ways. Adsorption of vapor of the test liquid onto the solid surface is apparently the only process that influences the solid-vapor interfacial tension (gamma(sv)). The molecular interactions taking place at the solid-liquid interface are more diverse and complicated. Parallel alignment of liquid molecules at the solid surface, reorganization of liquid molecules at the solid-liquid interface, change in the configuration of polymer chains due to contact with certain probe liquids, and intermolecular interactions between solid and liquid molecules cause the solid-liquid interfacial (gamma(sl)) tension to be different from that predicted by the equation of state, i.e., gamma(sl) is not a precise function of gamma(lv) and gamma(sv). In other words, the experimental contact angles deviate from the "ideal" contact angle pattern. Specific criteria are proposed to identify probe liquids which eliminate specific molecular interactions. Octamethylcyclotetrasiloxane (OMCTS) and decamethylcyclopentasiloxane (DMCPS) are shown to meet those criteria, and therefore are the most suitable liquids to characterize surface tensions of low energy fluoropolymer films with an accuracy of +/-0.2 mJ/m2.     

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.     

Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA)

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop). Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of original ADSA using a drop with an apex, it is still not as accurate as a surface tension measurement using a pendant drop suspended from a holder. In this article, the computational and experimental aspects of ADSA-NA were scrutinized to improve the accuracy of the simultaneous measurement of surface tensions and contact angles. It was found that the results are relatively insensitive to different optimization methods and edge detectors. The precision of contact angle measurement was enhanced by improving the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. To optimize the experimental design, the capillary was replaced with an inverted sharp-edged pedestal, or holder, to control the drop height and to ensure the axisymmetry of the drops. It was shown that the drop height is the most important experimental parameter affecting the accuracy of the surface tension measurement, and larger drop heights yield lower surface tension errors. It is suggested that a minimum nondimensional drop height (drop height divided by capillary length) of 1.7 is required to reach an error of less than 0.2 mJ/m(2) for the measured surface tension. As an example, the surface tension of water was measured to be 72.46 ± 0.04 at 24 °C by ADSA-NA, compared to 72.39 ± 0.01 mJ/m(2) obtained with pendant drop experiments.     

THE MECHANICAL VIEW OF THE SURFACE TENSION IS FALSE

The concept of surface tension is usually introduced as a force per unit length originated from the “stress tensor” at the liquid surface (and vaguely extended to solids). This mechanical model of the surface tension, a paradigm for many workers in the field, is wrong. The inferences from the model, however, are correct in the more common uses. Some contradictions may appear but not sufficient to abandon such a simple and intuitive concept. The origin of the surface tension, of a liquid or solid surface, is in the molecular interactions, when some other phase is put in contact with such a surface. Recent developments using the surface tension components allow to predict interfacial surface tensions and to measure surface tension of solids. Although the power of this approach is evident, its use is only incipient because some results, particularly the presence of negative interfacial tensions, are difficult to interpret using the erroneous vision of surface tension as a consequence of a “stress tensor” at the liquid (or solid) surface. We present here some properties of liquids useful to fundament the concept of surface tension and briefly refer to Laplace's equation, Young's equation and capillarity, attempting to correct some misinterpretations.     

On the Degree to which the Contact Angle is Affected by the Adsorption onto a Solid Surface of Vapor Molecules Originating from the Liquid Drop

ABSTRACT

From surface tensions of liquids and Lifshitz-van der Waals (LW) and Lewis acid-base (AB) surface tension components and the AB electron-acceptor γ⁺ and electron-donor γ^˙ parameters determined by contact angle (θ) measurements (using the Young-Dupré equation for polar systems), the interfacial work of salvation (W_st) between various contact angle liquids (L) and a moderately polar solid (S), such as polymethylmethacrylate (PMMA) could be determined. From these W_SL -values the maximum values of the equilibrium association constant, K_a, are obtained for the adsorption of molecules of liquids, L, onto a solid substratum, S. From the K_a-values and the vapor pressures of the various liquids, the maximum number of liquid molecules adsorbed from the gaseous phase onto the solid surface can be determined, at 20^°C and 76cm Hg ambient atmospheric pressure. This yields the maximum value for the fraction, ?, of the surface area of the solid that will be covered by molecules of the liquid, L, emanating from the liquid drop, via the gaseous state. From these ?-values, using Cassie's approach, the maximum amount, Δθ, can be determined by which the observed contact angle is lower than the ideal contact angle, as a consequence of the coverage of the solid substratum by adsorbed molecules originating from the contact angle liquid.

For most of the contact angle liquids used, the maximum deviation, Δθ, is well under 1^°; for water on PMMA it is about 1½^°.     

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 kinetics of human albumin solutions at solid surfaces

Contact angle kinetics of sessile drops of albumin solution on hydrophilic acetal and hydrophobic FC 721 surfaces were measured using axisymmetric drop shape analysis. Young's equation is used to calculate the solid/liquid interfacial tension from measured contact angles and surface tensions as a function of time. The change in solid/liquid interfacial tension is a result of protein adsorption. It indicates that at the hydrophilic acetal surface the albumin molecules, interact only weakly, whereas the interaction with the hydrophobic FC 721 surface is quite strong.     

Spreading of a fluid phase on a spherical surface

The adsorption between a liquid drop and a micro-particle in an air or an air bubble and a micro-particle in water is dominated by liquid-solid or air-solid interfacial tension and wetting area of the liquid or air on the particle surface. The wetting area is determined by the spreading of the liquid drop or the bubble on the micro-particle. To explore this spreading, a wetting model of a fluid phase on a spherical particle was built. According to the theoretical results, the contact angle is constant when a fluid phase spreads on a spherical solid surface; the micro-particle can not submerge under a fluid when only interfacial tensions are involved and the wetting is not a complete wetting. The corresponding experiments were performed to confirm the theoretical results.     

Prediction of solid-fluid interfacial tension and contact angle

Two simple equations have been developed using the lattice theory and the regular solution assumption to predict the solid-vapor and solid-liquid interfacial tension. The required parameters are the liquid critical temperature and volume, the solid melting temperature and the molar volume of liquid and solid compounds. To confirm the models, the predicted solid-fluid interfacial tension values have been used to predict the contact angle of the liquid drop on the solid surface applying Young's equation. Agreement of the predicted contact angle with the experimental data reveals the reliability of the developed models.     

Obtaining surface tension from contact angle data by the individual representation approach

Young equation is the fundamental equation of wetting theory in which the connection among the surface tensions, \(\gamma _{{\varphi \psi }} \) and the contact angle, θ _L, are given. The surface tension of solid surfaces, however, cannot be obtained directly from the Young equation. In this paper, the application of the individual representation theory is demonstrated for the determination of surface tensions of solids (or any phase pair) using experimentally obtained contact angle data. According to this approach, the state of the interfacial layers depends upon, by definition, the properties of the bulk phases in every heterogeneous system, and thus, it complements the traditional capillary theory.     

Validity of the "sharp-kink approximation" for water and other fluids

The contact angle of a liquid droplet on a solid surface is a direct measure of fundamental atomic-scale forces acting between liquid molecules and the solid surface. In this work, the validity is assessed of a simple equation, which approximately relates the contact angle of a liquid on a surface to its density, its surface tension, and the effective molecule-surface potential. This equation is derived in the sharp-kink approximation, where the density profile of the liquid is assumed to drop precipitously within one molecular diameter of the substrate. It is found that this equation satisfactorily reproduces the temperature-dependence of the contact angle for helium on alkali metal surfaces. The equation also seems be applicable to liquids such as water on solid surfaces such as gold and graphite, on the basis of a comparison of predicted and measured contact angles near room-temperature. Nevertheless, we conclude that, to fully test the equation's applicability to fluids such as water, it remains necessary to measure the contact angle's temperature-dependence. We hypothesize that the effects of electrostatic forces can increase with temperature, potentially driving the wetting temperature much higher and closer to the critical point, or lower, closer to room temperature, than predicted using current theories.     

Equilibrium contact angles of liquid droplets on ideal rough solids

This work proposes a theoretical model for predicting the apparent equilibrium contact angle of a liquid on an ideal rough surface that is homogeneous and has a negligible body force, line tension, or contact angle hysteresis between solid and liquid. The model is derived from the conservation equations and the free-energy minimization theory for the changes of state of liquid droplets. The work of adhesion is expressed as the contact angles in the wetting process of the liquid droplets. Equilibrium contact angles of liquid droplets for rough surfaces are expressed as functions of the area ratios for the solid, liquid, and surrounding gas and the roughness ratio and wetting ratio of the liquid on the solid for the partially and fully wet states. It is found that the ideal critical angle for accentuating the contact angles by the surface roughness is 48°. The present model is compared with existing experimental data and the classical Wenzel and Cassie-Baxter models and agrees with most of the experimental data for various surfaces and liquids better than does the Wenzel model and accounts for trends that the Wenzel model cannot explain.     

Contact angle hysteresis of bovine serum albumin (BSA) solution/metal (Au-Cr) coated glass substrate

Bovine serum albumin (BSA) has an extraordinary property to carry biomolecules. An experimental study on the wettability of BSA is presented in this study. The variations in the surface tension and the equilibrium contact angle with the change in BSA concentration are also reported. The surface tension and the contact angle are measured with pendant and sessile drop techniques, respectively. A nonlinear decrement in the surface tension with the increment in the BSA concentration is observed. An equilibrium contact angle of a BSA solution with particular concentration is determined by studying the hysteresis in the contact angle from dynamic contact angle measurements. The needle-in-drop technique is used to study the hysteresis of the contact angle. It is observed that the obtained surface tension and the equilibrium contact angle vary with the BSA concentration. In this reported study, for the considered combination of the BSA concentration and solid surface, the liquid drop does not recede as the drop volume decreases, which represents nonreceding contact angle condition. The increment in the contact angle with the increment in the BSA concentration is observed. Finally, it is observed that the inclusion of the proteins not only changes the surface tension but also changes the contact angle.     

Thermal healing of scratches and determination of solid surface tension of selenium

The healing of scratches on the surface of vitreous selenium was observed over a period of nine weeks, and from the data the solid surface tension of vitreous Se is estimated to be (100 ± 20) dyne/cm at 38.8°C, about the same as that of the liquid at the melting point. This value is three times as large as the critical surface tension determined from contact angle measurements, which indicates that for vitreous Se in contact with organic liquids, the solid—liquid interfacial tension is about two-thirds as much as the solid surface tension. The present method of measurement can probably be used to determine the solid surface tension of other polymers, and by measuring the healing of scratches on a solid immersed in a liquid the method could be used to determine the solid—liquid interfacial tension.     

Contact Angle Patterns on Low-Energy Surfaces

It is well-known that on a given low-energy solid surface, the contact angles of different organic liquids follow a regular pattern. The experimental evidence for this, and semi-empirical equations describing the pattern, are reviewed. Theoretical and computational efforts to explain the pattern are discussed, and a simplified analytical approach is presented. The main pattern of contact angles is seen to arise from two factors: a common combining rule for liquid-solid molecular interactions, and the reduced density of liquid molecules adjacent to a lower-energy solid surface. Irregular departures from the main pattern are due to chemical effects originating in molecular structure.     

Molecular simulation of fluid-solid interfaces at nanoscale

The equilibrium states of vapor and liquid coexistent phases in contact with a solid surface are studied at the nanoscale by molecular dynamics simulations for a temperature close to the fluid triple point. The characteristics of the solid-fluid interfaces are determined when the interaction strength between the fluid and the solid varies in order to go from a situation of complete drying to that of complete wetting. From the vapor-liquid density profiles of liquid drops lying on the substrate surface or menisci of liquid films confined in slit pores, the contact angles made by the vapor-liquid interface with the solid are computed. The angle values are similar for the drops and the films. They are also in good qualitative agreement with the estimates obtained through the Young's relation from the surface tensions associated with the vapor-solid, liquid-solid, and vapor-liquid interfaces. However, at this scale, the uncertainties inherent to the angle computation and, to a lesser extent, to size effects seem to preclude that the quantitative agreement between the angle estimates obtained from the interface geometry and calculated from the Young's relation can be better than few degrees.     

The surface energy of montmorillonite

By combining the relation that describes pair interaction in binary mixtures with the Young equation, a formula is obtained for calculating the surface energy of montmorillonite as a function of the surface pressure, the surface tension of water, and the liquid/solid contact angle. The formula is an equation of an inverted parabola, which could be represented by a polynomial function. Roots of the polynomial gave one real value of 205.066+/-2.764 mJm(-2) for the surface energy of montmorillonite. The value obtained is of the expected magnitude and probably is better than those obtained by previous approaches.     

Contact angle measurements with liquids consisting of bulky molecules

Well-measured contact angles with different solid-liquid systems fall approximately on smooth patterns when plotted versus liquid surface tension. However, there are deviations of 1 degrees -3 degrees , which are outside the error limits. It is the purpose of this paper to elucidate the reasons for such deviations. Two types of liquids were selected for advancing contact angle measurements on Teflon AF 1600 coated surfaces: a series of n-alkanes ranging from n-hexane to n-hexadecane and five liquids consisting of bulky molecules, octamethylcyclotetrasiloxane (OMCTS), methyl salicylate, tetralin, cis-decalin, and octamethyltrisiloxane (OMTS). It was found that contact angles of the liquids with bulky molecules fall on a perfectly smooth curve corresponding to a solid surface tension of 13.64 +/- 0.1 mJ/m2. However, contact angles of n-alkanes deviated from this curve by up to 3 degrees in a complicated fashion. The observed trend suggests that more than one mechanism is responsible for the deviations. Substrate-induced rearrangement of liquid molecules in the close vicinity of the surface in the case of long-chain n-alkanes and adsorption of vapor onto the solid surface in the case of short-chain n-alkanes are the most likely explanations. The results suggest that liquids with bulky molecules appear to be suitable for contact angle measurements to characterize energetics of polymeric surfaces.     

Low-rate dynamic contact angles on poly(n-butyl methacrylate) and the determination of solid surface tensions

 Low-rate dynamic contact angles of 22 liquids on a poly(n-butyl methacrylate) (PnBMA) polymer are measured by an automated axisymmetric drop shape analysis-profile (ADSA-P). It is found that 16 liquids yielded non-constant contact angles, and/or dissolved the polymer on contact. From the experimental contact angles of the remaining 6 liquids, it is found that the liquid–vapor surface tension times cosine of the contact angle changes smoothly with the liquid–vapor surface tension, i.e. γ_lv cos θ depends only on γ_lv for a given solid surface (or solid surface tension). This contact angle pattern is in harmony with those from other inert and non-inert (polar and non-polar) surfaces [34–37, 45–47]. The solid–vapor surface tension calculated from the equation-of-state approach for solid-liquid interfacial tensions [14] is found to be 28.8 mJ/m², with a 95% confidence limit of ±0.5 mJ/m², from the experimental contact angles of the 6 liquids. Received: 12 September 1997 Accepted: 22 January 1998