A.W. Neumann

Contact angle measurement and contact angle interpretation

Recent progress in the correlation of contact angles with solid surface tensions are summarized. The measurements of meaningful contact angles in terms of surface energetics are also discussed. It is shown that the controversy with respect to measurement and interpretation of contact angles are due to the fact that some (or all) of the assumptions made in all energetic approaches are violated when contact angles are measured and processed. For a large number of polar and non-polar liquids on different solid surfaces, the liquid–vapor surface tension times cosine of the contact angle, γlvcosθ, is shown to depend only on the liquid–vapor surface tension γlv, and the solid–vapor surface tension γsv when the appropriate experimental techniques and procedures are used. Equations which follow these experimental patterns and which allow the determination of solid surface tensions from contact angles are discussed. Universality of these experimental contact angle patterns is illustrated; other reasons which may cause data to deviate from the patterns slightly are discussed. It is found that surface tension component approaches do not reflect physical reality. Assuming the fact that 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 Youngs equation for determining solid surface tensions. The explicit form of such a relation is obtained by modifying Berthelots 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 from like pairs. Existing static contact angles for 34 different types of solid surfaces from Zisman et al. are evaluated in terms of their solid surface tensions using experimental contact angle patterns. A FORTRAN computer program has been implemented to automate these procedures. It is 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.

Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces

Drop shape techniques, such as axisymmetric drop shape analysis, are widely used to measure surface properties, as they are accurate and reliable. Nevertheless, they are not applicable in experimental studies dealing with fluid configurations that do not present an apex. A new methodology is presented for measuring interfacial properties of liquids, such as surface tension and contact angles, by analyzing the shape of an axisymmetric liquid-fluid interface without use of apex coordinates. The theoretical shape of the interface is generated numerically as a function of surface tension and some geometrical parameters at the starting point of the interface, e.g., contact angle and radius of the interface. Then, the numerical shape is fitted to the experimental profile, taking the interfacial properties as adjustable parameters. The best fit identifies the true values of surface tension and contact angle. Comparison between the experimental and the theoretical profiles is performed using the theoretical image fitting analysis (TIFA) strategy. The new method, TIFA-axisymmetric interfaces (TIFA-AI), is applicable to any axisymmetric experimental configuration (with or without apex). The versatility and accuracy of TIFA-AI is shown by considering various configurations: liquid bridges, sessile and pendant drops, and liquid lenses.

An equation-of-state approach to determine surface tensions of low-energy solids from contact angles

Abstract An equation of state is developed which allows the surface tension of a low-energy solid to be determined from a single contact angle formed by a liquid which is chemically inert with respect to the solid and whose liquid surface tension is known. The equation of state is obtained using two independent methods. In the first one, similar arguments to those in previous papers are used; however, the qualitative argument, based on the general appearance of plots, is replaced by computer curve fitting and statistical analysis. The second method, which has not been employed heretofore, treats the solid surface tension as an adjustable parameter. Molecular arguments in conjunction with the interaction parameter Φ are used to eliminate poor choices of the solid surface tension. The results are in excellent agreement with the first method. The range of validity of the equation of state and practical points in its application are discussed.

Automation of axisymmetric drop shape analysis for measurements of interfacial tensions and contact angles

Abstract Axisymmetric drop shape analysis-profile (ADSA-P) was developed to determine liquid-fluid interfacial tensions and contact angles by fitting the Laplace equation of capillarity to an arbitrary array of coordinate points selected from the drop profile. The data acquisition method, which consisted of the manual measurement of a number of coordinate points of a photographic image of a drop, was found to be time consuming and inaccurate. An automatic digitization technique utilizing recent developments in digital image acquisition and analysis to achieve rapid and accurate data acquisition and preprocessing is presented. The technique eliminates errors due to the optical distortions. It was found that high accuracy could be obtained through the use of sub-pixel resolution in determining the drop profile coordinates. The results obtained not only compared well with the conventional methods, but also considerably outstripped the accuracy of conventional methods.

Contact angles and their temperature dependence: thermodynamic status, measurement, interpretation and application

A_ Introduction 106 B. Thermodynamic status of tontact angles 109 (i) The vertical plate model 111 (a) The driving force Ierm _ . _ _ . . _ . _ _ _ _ _ _ _ _ _ 112 (b) The liquid/ vapour interface 113 (c) Work done against gravity 114 (d)Derivation of Young’s equntion I15 (ii) Application to smooth and heterogeneous rolid surfxrs 116 (a) Smooth, homogeneous solid surftice 116 (b)Heterogeneoussurface consisting of horizontal strips 116 (c) Heterogeneous solid surface consisting of vertic-i strips . . 120 (iii) Contact angles on homogeneous and rough solid surfaces 126 (a) The driving force term 127 (b) The liquid/vapour interface 128 cc) Work done against gravity ...... 129 (d) Application to idealized rough surfaces 130 C. hfeasurement of contact anglesand their temperature dependence _ . _ _ _ . _ . 134 0) The technique of the capillary rise at a vertical plate 135 (ii) Sample preparation 138 (iii) Experimental results 140 (a) Siliconed glass against various liquids . _ _ _ . . _ . . _ _ _ . . 140 (b) Hexatriacontane/water c) Cholesteryl acetate/water : : : : : : : : : : : : : : : : : : 141 147 (di Polytetrafluoroe&ylene/n-decane .. . . .. .. (e) A vinyl acetate/vinyl chloride copolymer and a ehlori&tea ribber ai&nst water and 142

Contact angles on hydrophobic solid surfaces and their interpretation

Abstract Contact angles of 17 liquids on 3 hydrophobic solid surfaces, FC721, fluorinated ethylene propylene, and polyethylene terephthalate, were measured by using the Axisymmetric Drop Shape Analysis-Profile (ADSA-P) technique. Details of the surface preparation and the experiments are presented. The accuracy of these contact angle data is better than 0.2° in most cases. These data were used to calibrate an equation of state for interfacial tensions of solid—liquid systems. The end results of the analysis is an equation of state for interfacial tensions with a single parameter β = 0.0001247 (m2/mJ)2, cf., Eqs. [22]–[24]. Within the experimental limitations, there is no evidence for the notion that β might change from system to system.

Thermodynamics of contact angles. II. Rough solid surfaces

Abstract The thermodynamics of an idealized rough surface is treated, using the geometry of a vertical plate partially immersed in a liquid. Gravity is included explicitly in the theory. The results of this treatment are more general than those of previous studies and are more easily extended to other surface topographies. Some novel results are found, such as a delineation of the conditions under which a macroscopic contact angle of 180° will result from geometric properties of the solid surface. On rough surfaces consisting of material for which, if smooth, the equilibrium contact angle would be different from 90°, the slopes of the asperities will be a very important factor in determining the effective equilibrium contact angles.

The dependence of contact angles on drop size and line tension

Abstract We report contact angle measurements of five n-alkanes, dodecane through hexadecane, on Teflon (FEP) as a function of drop size. In all cases the contact angles decreased by approximately 5° when the drop size was increased from approximately 1 to 4 mm contact radius. A complete solution to the problem of mechanical equilibrium of a sessile drop on a solid surface indicates that the dependence of the contact angle on drop size may be explained by including the effect of line tension in the Young equation. The observed drop size dependence of the contact angle yields a line tension of (2.5 ± 0.5) × 10−6 J/m. Over the range of n-alkanes studied it was not possible to discern any dependence of the line tension on liquid surface tension.

Contact angle interpretation in terms of solid surface tension

Abstract 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.

Equation of state for interfacial tensions of solid-liquid systems

The surface tensions of the solid-vapour interface and the solid-liquid interface, f and f’, are important parameters in many areas of applied science and technology. These interfacial tensions are responsible for the behaviour and properties of commonly used materials such as paints, adhesives, detergents and lubricants. As well, many interfacial phenomena, such as adhesion of biological cells to biomaterials and synthetic materials, are not only governed by specific chemical interactions, but are frequently dominated by changes in the overall free energy of the process of adhesion, which is a function of the surface tensions involving a solid phase. In order to perform a thermodynamic analysis of interfacial phenomena, such as cell adhesion, one has to know the solid surface tensions, r and y’, involved in that system. Generally, the liquid-fluid inter-facial tension can be measured directly by many different methods; however, because of tbe absence of mobility, a solid interface is very different in this respect from a liquid-fluid interface, and hence the solid