DETERMINATION OF SOLID SURFACE TENSION FROM CONTACT ANGLES: THE ROLE OF SHAPE AND SIZE OF LIQUID MOLECULES

Accurate surface tension of Teflon® AF 1600 was determined using contact angles of liquids with bulky molecules. For one group of liquids, the contact angle data fall quite perfectly on a smooth curve corresponding to γ_sv = 13.61 mJ/m², with a mean deviation of only ±0.24 degrees from this curve. Results suggest that these liquids do not interact with the solid in a specific fashion. However, contact angles of a second group of liquids with fairly bulky molecules containing oxygen atoms, nitrogen atoms, or both deviate somewhat from this curve, up to approximately 3 degrees. Specific interactions between solid and liquid molecules and reorientation of liquid molecules in the close vicinity of the solid surface are the most likely causes of the deviations. It is speculated that such processes induce a change in the solid–liquid interfacial tension, causing the contact angle deviations mentioned above. Criteria are established for determination of accurate solid surface tensions.     

Low-rate Dynamic Contact Angles on Poly(methyl methacrylate/n-butyl methacrylate) and the Determination of Solid Surface Tensions

Low-rate dynamic contact angles of 12 liquids on a poly(methyl methacrylate/n-butyl methacrylate) P(MMA/nBMA) copolymer are measured by an automated axisymmetric drop shape analysis-profile (ADSA-P). It is found that 6 liquids yield non-constant contact angles, and/or dissolve the polymer on contact. From the experimental contact angles of the remaining 6 liquids, it is found that the liquid- vapour surface tension times the cosine of the contact angle changes smoothly with the liquid-vapour surface tension, i.e., γ_iv cos θ depends only on γ_iv for a given solid surface (or solid surface tension). This contact angle pattern is in harmony with those from other inert and noninert (polar and non-polar) surfaces [34-42, 51 -53]. The solid-vapour surface tension calculated from the equation-of-state approach for solid -liquid interfacial tensions [14] is found to be 34.4 mJ/m², with a 95% confidence limit of \pm 0.8mJ/m², from the experimental contact angles of the 6 liquids.     

Contact angle measurements and interpretation: wetting behavior and solid surface tensions for poly(alkyl methacrylate) polymers

Low-rate dynamic contact angles of a large number of liquids were measured on a poly(ethyl methacrylate) (PEMA) polymer using an automated axisymmetric drop shape analysis profile (ADSA-P). The results suggested that not all experimental contact angles can be used for the interpretation in terms of solid surface tensions: eight liquids yielded non-constant contact angles and/or dissolved the polymer on contact. From the experimental contact angles of the remaining four liquids, we found that the liquid-vapor surface tension times the cosine of the contact angle changes smoothly with the liquid-vapor surface tension, i.e. γlv cos ζ depends only on γlv for a given solid surface (or solid surface tension). This contact angle pattern is again in harmony with those from other methacrylate polymer surfaces of different compositions and side-chains. The solid-vapor surface tension of PEMA calculated from the equation-of-state approach for solid-liquid interfacial tensions was found to be 33.6 ± 0.5 mJ/m2 from the experimental contact angles of the four liquids. The experimental results also suggested that surface tension component approaches do not reflect physical reality. In particular, experimental contact angles of polar and nonpolar liquids on polar methacrylate polymers were employed to determine solid surface tension and solid surface tension components. Contrary to the results obtained from the equation-of-state approach, we obtained inconsistent values from the Lifshitz-van der Waals/acid-base (van Oss and Good) approach using the same sets of experimental contact angles.     

Low-rate dynamic contact angles on polystyrene and the determination of solid surface tensions

Low-rate dynamic contact angles of 13 liquids on a polystyrene polymer are measured by an automated axisymmetric drop shape analysis – profile (ADSA-P). It is found that 7 liquids yielded non-constant contact angles, and/or dissolved the polymer on contact. From the experimental contact angles of the other 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_lvcosθ 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 (7–13, 24–26). The solid-vapor surface tension calculated from the equation-of-state approach for solid-liquid interfacial tensions (33) is found to be 29.8 mJ/m², with a 95% confidence limit of ±0.5 mJ/m² from the experimental contact angles of 6 liquids.     

On the Predominant Electron-Donicity of Polar Solid Surfaces

The reasons for the predominant electron-donicity of almost all solid polar surfaces and its implications are discussed in this paper. By contact angle or interfacial tension measurements, the electron-accepting as well as the electron-donating properties of polar liquids can be ascertained, through the interplay between their energies of adhesion and cohesion. For the solid-liquid interface, direct interfacial tension measurements are not possible, but indirectly, solid/liquid interfacial tensions of polar systems can be obtained by contact angle measurement. However, as the energy of cohesion of a solid does not influence the contact angle formed by a liquid drop placed upon its surface, one can only measure the solid surface'ks residual polar property, manifested by the energy of adhesion between solid and liquid. This residual polar property is of necessity the dominant component; in most cases this turns out to be its electron donicity. When, by means of contact angle measurements with polar liquids, both electron-accepting and electron-donating potentials are found on a polar solid, it is most likely still partly covered with a polar liquid: usually water. The amount of residual water of hydration of a polar solid follows from its polar (Lewis acid-base) surface tension component (γ^AB). The degree of orientation of the residual water of hydration on a polar solid can be expressed by the ratio of the electron-donating to electron-accepting potentials (γ^⊖/γ^⊕), measured on the hydrated surface.     

On the interpretation of contact angle hysteresis

The determination of solid surface free energy is still an open problem. The method proposed by van Oss and coworkers gives scattered values for apolar Lifshitz-van der Waals and polar (Lewis acid-base) electron-donor and electron-acceptor components for the investigated solid. The values of the components depend on the kind of three probe liquids used for their determination. In this paper a new alternative approach employing contact angle hysteresis is offered. It is based on three measurable parameters: advancing and receding contact angles (hysteresis of the contact angle) and the liquid surface tension. The equation obtained allows calculation of total surface free energy for the investigated solid. The equation is tested using some literature values, as well as advancing and receding contact angles measured for six probe liquids on microscope glass slides and poly(methyl methacrylate) PMMA, plates. It was found that for the tested solids thus calculated total surface free energy depended, to some extent, on the liquid used. Also, the surface free energy components of these solids determined by van Oss and coworkers' method and then the total surface free energy calculated from them varied depending on for which liquid-set the advancing contact angles were used for the calculations. However, the average values of the surface free energy, both for glass and PMMA, determined from these two approaches were in an excellent agreement. Therefore, it was concluded that using other condensed phase (liquid), thus determined value of solid surface free energy is an apparent one, because it seemingly depends not only on the kind but also on the strength of interactions operating across the solid/liquid interface, which are different for different liquids.     

A study of the applicability of the capillary rise of aqueous solutions in the measurement of contact angles in powder systems

The rate of wetting of a powder bed was studied in terms of the wetting parameters, liquid surface tension and powder/liquid contact angle, using three carbon black powders and aqueous solutions of surfactants and organic liquids. The rate of capillary rise of pure organic liquids through a powder bed can be described by the Washburn equation, and when compared with the behavior of aqueous surfactant solutions, it showed that deviations from linearity of the latter are attributable to adsorption of surfactant on the solid surface with resultant depletion of solute from the liquid phase. Agreement between Washburn capillary rise results and sessile drop results was observed whenever adsorption was absent.     

THE EFFECT OF SUBSTRATE GEOMETRY ON DYNAMIC CONTACT ANGLES IN SURFACE WETTING

Dynamic contact angles play a central role in the problem of wetting of surfaces. A solid surface is moving steadily through the free surface of a liquid. The angle between the plunging solid surface and the liquid free surface at the line of solid-liquid contact is the dynamic contact angle. This work compares experimentally measured dynamic contact angles of horizontally rotating rolls of different diameters with those of circular fibers, and tapes. The comparison also includes dry and pre-wet surfaces. Dynamic contact angles depend on the geometry of the wetted substrate. Specifically the geometry through its curvatures affects the surface tension forces at the contact line. Smaller diameter rolls generate smaller angles. In wetting of circular fibers the angles are the smallest compared to tapes and rolls. Flat dry tapes form the largest angles when they are wetted. This implies that the curvatures of the circular rolls and fibers contribute to the balance of surface energies at the contact line. Pre-wet surfaces generate considerably smaller angles at the same wetting speeds. In contrast with that, the diameter of rolls does not affect the critical speed of air entrainment.     

On the Predominant Electron-Donicity of Polar Solid Surfaces

The reasons for the predominant electron-donicity of almost all solid polar surfaces and its implications are discussed in this paper. By contact angle or interfacial tension measurements, the electron-accepting as well as the electron-donating properties of polar liquids can be ascertained, through the interplay between their energies of adhesion and cohesion. For the solid-liquid interface, direct interfacial tension measurements are not possible, but indirectly, solid/liquid interfacial tensions of polar systems can be obtained by contact angle measurement. However, as the energy of cohesion of a solid does not influence the contact angle formed by a liquid drop placed upon its surface, one can only measure the solid surface'ks residual polar property, manifested by the energy of adhesion between solid and liquid. This residual polar property is of necessity the dominant component; in most cases this turns out to be its electron donicity. When, by means of contact angle measurements with polar liquids, both electron-accepting and electron-donating potentials are found on a polar solid, it is most likely still partly covered with a polar liquid: usually water. The amount of residual water of hydration of a polar solid follows from its polar (Lewis acid-base) surface tension component (γ^AB). The degree of orientation of the residual water of hydration on a polar solid can be expressed by the ratio of the electron-donating to electron-accepting potentials (γ^?/γ^⊕), measured on the hydrated surface.     

Spreading of liquid drops over solid substrates: 'like wets like'

The classic hydrodynamic wetting theory leads to a linear relationship between spreading speed and the capillary force, being determined only by the surface tension of the liquid and its viscosity. Both equilibrium and dynamic processes of wetting are important in adhesion phenomena. The theory appears to be in good agreement with the results generated from experiments conducted on the spreading of poly(dimethylsiloxane) (PDMS) on soda-lime glass substrate and fails to account for the behavior of other liquids. In this study, the spreading kinetics of four different liquids (hexadecane, undecane, glycerol and water) was determined on three different solids, namely, soda-lime glass, poly(methyl methacrylate) (PMMA) and polystyrene (PS). Droplets from the same liquid allowed to spread under identical conditions on three different substrates produce distinctly different behaviors. The results show that the equilibrium contact angles are qualitatively ranked in accordance with the critical surface tension of wetting (γ _c) of the respective solid, i.e., high-γ _c solids caused the low surface tension liquids to assume the least equilibrium spreading (largest contact angle). On the other end, low-γ _c solids with the lowest surface tension liquid produce the most wetting (smallest contact angle). The results suggest that equilibrium spreading could be explained on the basis of the axiom 'like wets like'; in other words, polar surfaces tend to be wetted by polar liquids and vice versa.     

On the use of Washburn's equation for contact angle determination

A systematic study on the possibility of Young's contact angle determination from Washburn's equation was performed using the so-called thin-layer wicking technique in which the rate of penetration of a liquid into the porous layer of a solid is measured. Commercial (Merck) SiO₂ deposited on the glass plate for thin-layer chromatography was used as a model solid and n-alkanes (from pentane to hexadecane), diiodomethane, and α-bromonaphthalene were employed as the probe liquids. It was shown that the contact angle calculated from Washburn's equation was not equal to Young's contact angle of a drop of the same liquid, placed on a flat surface of the solid. Consequently, the solid surface free energy components calculated using contact angles from Washburn's equation are not the true values. However, the approach previously suggested by us has been verified again, as it gives consistent values of the surface free energy components determined from all the liquids used.     

The multiple roles of interfacial tension in fluid phase equilibria and fluid–solid interactions

The tension at the interfaces separating the three phases of matter is a unique property in that it can reveal a great deal of information about the phases in contact, including the direction and extent of mass transfer of components, their proximity to equilibrium, the nature of fluids distribution relative to one another, the contact angle, and the spreading and adhesion behavior of liquids on solid surfaces. In this paper we examine, with supporting experimental data, the multitude of roles played by interfacial tension in establishing (1) the phase behavior characteristics of solubility, miscibility, and the associated mass transfer mechanisms in multicomponent fluid systems, (2) the nature of fluids distribution in gas–oil–water systems in porous solid substrates and (3) the spreading and adhesion characteristics in solid–liquid–liquid systems through dynamic contact angles.     

Evaluation of surface energy of solid polymers using different models

In the present work, contact angles formed by drops of diethylene glycol, ethylene glycol, formamide, diiodomethane, water, and mercury on a film of polypropylene (PP), on plates of polystyrene (PS), and on plates of a liquid crystalline polymer (LCP) were measured at 20°C. Then the surface energies of those polymers were evaluated using the following three different methods: harmonic mean equation and geometric mean equation, using the values of the different pairs of contact angles obtained here; and Neumann's equation, using the different values of contact angles obtained here. It was shown that the values of surface energy generated by these three methods depend on the choice of liquids used for contact angle measurements, except when a pair of any liquid with diiodomethane was used. Most likely, this is due to the difference of polarity between diiodomethane and the other liquids at the temperature of 20°C. The critical surface tensions of those polymers were also evaluated at room temperature according to the methods of Zisman and Saito using the values of contact angles obtained here. The values of critical surface tension for each polymer obtained according to the method of Zisman and Saito corroborated the results of surface energy found using the geometric mean and Neumann's equations. The values of surface energy of polystyrene obtained at 20°C were also used to evaluate the surface tension of the same material at higher temperatures and compared to the experimental values obtained with a pendant drop apparatus. The calculated values of surface tension corroborated the experimental ones only if the pair of liquids used to evaluate the surface energy of the polymers at room temperature contained diiodomethane. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1831–1845, 2000     

Analysis and surface energy estimation of various model polymeric surfaces using contact angle hysteresis

Wetting of hydrophobic polymer surfaces commonly employed in electronic coatings and their interaction with surfactant-laden liquids and aqueous polymer solutions are analyzed using a contact angle hysteresis (CAH) approach developed by Chibowski and co-workers. In addition, a number of low surface tension acrylic monomer liquids, as well as common probe liquids are used to estimate solid surface energy of the coatings in order to facilitate a thorough analysis of surfactant effects in adhesion. Extensive literature data on contact angle hysteresis of surfactant-laden liquids on polymeric surfaces are available and are used here to estimate solid surface energy for further understanding and comparisons with the present experimental data. In certain cases, adhesion tension plots are utilized to interpret wetting of surfaces by surfactant and polymer solutions. Wetting of an ultra-hydrophobic surface with surfactant-laden liquids is also analyzed using the contact angle hysteresis method. Finally, a detailed analysis of the effect of probe liquid molecular structure on contact angle hysteresis is given using the detailed experiments of Timmons and Zisman on a hydrophobic self-assembled monolayer (SAM) surface. Hydrophobic surfaces used in the present experiments include an acetal resin [poly(oxymethylene), POM] surface, and silane, siloxane and fluoro-acrylic coatings. Model surfaces relevant to the literature data include paraffin wax, poly(methyl methacrylate) and a nano-textured surface. Based on the results, it is suggested that for practical coating applications in which surfactant-laden and acrylic formulations are considered, a preliminary evaluation and analysis of solid surface energy can be made using surfactant-laden probe liquids to tailor and ascertain the quality of the final coating.     

On the determination of the surface energetics of porous polymer materials

The solid surface tension γsv of hydrophobic polymer powders has been determined using the capillary penetration technique. By plotting Kγlv cos ζ, where K is a geometric factor, versus the liquid surface tension γlv, the following values of γsv were directly derived from the curves: poly(tetrafluoroethylene) γsv = 20.4 mJ/m², polypropylene γsv = 30.2 mJ/m², polyethylene γsv = 34.4 mJ/m², and polystyrene γsv = 27.5 mJ/m². These values are in good agreement with the γsv values obtained from contact angle measurements on flat and smooth solid surfaces of the same materials. If the contact angles were first calculated from the capillary penetration experiments, which is the usual procedure applied in the literature, distinctly higher contact angles were obtained. Obviously these angles are affected by the powder morphology and are therefore meaningless contact angles in terms of a surface energetic interpretation.     

Estimation of interfacial tension components for liquid–solid systems from contact angle measurements

A technique has been developed for estimating the hydrogen bonding and London dispersion force components of liquid surface tension and solid surface free energy levels. The technique relies on (a) measuring contact angles generated by sessile drops of liquids on solids and (b) performing calculations based on theories of thermodynamic wetting of solids by liquids. The technique is used to estimate interfacial force components of certain liquids and papers typical of those used in xerographic processing.     

WETTABILITY AND SURFACE ENERGETICS OF ROUGH FLUOROPOLYMER SURFACES

Hydrophobic solid surfaces with controlled roughness were prepared by coating glass slides with an amorphous fluoropolymer (Teflon® AF1600, DuPont) containing varying amounts of silica spheres (diameter 48 μm). Quasi-static advancing, θ_A, and receding, θ_R, contact angles were measured with the Wilhelmy technique. The contact angle hysteresis was significant but could be eliminated by subjecting the system to acoustic vibrations. Surface roughness affects all contact angles, but only the vibrated ones, θ_V, agree with the Wenzel equation. The contact angle obtained by averaging the cosines of θ_A and θ_R is a good approximation for θ_V, provided that roughness is not too large or the angles too small. Zisman's approach was employed to obtain the critical surface tension of wetting (CST) of the solid surfaces. The CST increases with roughness in accordance with Wenzel equation. Advancing, receding, and vibrated angles yield different results. The θ_A is known to be characteristic of the main hydrophobic component (the fluoropolymer). The θ_V is a better representation of the average wettability of the surface (including the presence of defects).     

AN ARTIFICIAL NEURAL NETWORK APPROACH TO CAPILLARY RISE IN POROUS MEDIA

An artificial neural network (ANN) was used to analyze the capillary rise in porous media. Wetting experiments were performed with 15 liquids and 15 different powders. The liquids covered a wide range of surface tension (15.45-71.99 mJ/m²) and viscosity (0.25-21 mPa.s). The powders also provided an acceptable range of particle size (0.012-45 μm) and surface free energy (25.5-62.2 mJ/m²). An artificial neural network was employed to predict the time of capillary rise for a known given height. The network's inputs were density, surface tension, and viscosity for the liquids and particle size, bulk density, packing density, and surface free energy for the powders. Two statistical parameters, the product moment correlation coefficient (r²) and the performance factor (PF/3), were used to correlate the actual experimentally obtained times of capillary rise to: (i) their equivalent values as predicted by a designed and trained artificial neural network; and (ii) their corresponding values as calculated by the Lucas-Washburn equation as well as the equivalent values as calculated by its various other modified versions. It must be noted that for a perfect correlation r² = 1 and PF/3 = 0. The results showed that only the present ANN approach was able to predict with superior accuracy (i.e., r² = 0.92, PF/3 = 51) the time of capillary rise. The Lucas-Washburn calculations gave the worst correlations (r² = 0.15, PF/3 = 1002). Furthermore, some of the modifications of this equation as proposed by different workers did not seem to conspicuously improve the relationships, giving a range of inferior correlations between the calculated and experimentally determined times of capillary rise (i.e., r² = 0.27 to 0.48, PF/3 = 112 to 285).     

Experimental determination of capillary forces by crushing strength measurements

Mechanisms that lead to powder agglomeration are in many cases controlled by capillary forces. Indeed, in the earliest stage of agglomeration, minute amounts of liquid join solid particles by liquid bridges. Spontaneous formation of the bridge at contact points is caused by capillary condensation. Depending on solid/liquid interactions, particularly contact angle and spreading, liquid bridges may attract or repel individual particles. Undesired agglomeration may appear during storage and is called caking. On the other hand, powder agglomeration process is often required, for example, in enlargement of the particle size, i.e. granulation. A simple experimental device, designed from usual caking tests, was developed in order to estimate capillary forces transmitted by attracting liquid bridges joining particles. Crushing strength of wet cylindrical agglomerates was estimated. Influence of the low saturations of the void space (0<S<25%) and the surface tension of a liquid have been investigated. A normalised force which does not depend on the surface tension contribution has been calculated from experimental measurements and compared to Rumpf's model. It is possible to roughly estimate the solid/liquid contact angle by comparison with the model.