Analytical expressions have been derived relating the length, surface area, volume, and Laplace excess pressure of a liquid drop adhering to a cylindrical fiber to linear drop dimensions and the contact angle. Extensive tables of dimensionless forms of these quantities have been computed. The calculations form the basis of a precise and accurate method for measuring contact angle in such systems. A description of experimental technique for contact angle measurement is given, together with results for some well-defined systems.

Contact angle measurements have been carried out on various solid substrates using water-propanol mixtures and α-bromonaphthalene as wetting liquids. These substrates were: polytetrafluorethylene, Parafilm, polyethylene, polyurethane, polystyrene, polymethylmethacrylate, fluorapatite, and hydroxyapatite. The dispersion and the polar components of the surface free energy, γ_s^d and γ_s^p have been calculated from the geometric mean equation. Two approaches have been considered: (1) neglecting the spreading pressure π_e and (2) taking π_e into account (Dann's method). The results show that both approaches actually yield the same results for the surface free energy, γ_s, if a proper interpretation of the approaches is considered. All data indicate, that approach (1) gives γ_s values determined on the adsorbed liquid layer, whereas in approach (2) the free energies of the bare solid surfaces are found.

The wettability of a number of low energy solid surfaces, including hoof keratin and human skin, has been examined using two liquids, water and methylene iodide, and employing Wu's empirical approach to obtain γ_s^d and γ_s^P, the dispersion and polar components of the solid “surface tension.” The sum of these parameters, (γ_s^d + γ_s^p) was found to be in good agreement with reported values of γ_c, the critical surface tension, based on Zisman plots. Using the latter method, γ_c values of solids selected from the above group were determined using aqueous ethanol solutions. The values were lower than those obtained using nonpolar liquids, thus confirming earlier findings. A compilation of our own data and data from the literature reveals that the derived values of γ_c show little or no dependence on the type of solid surface, the type of alcohol or its chain length. The results can be explained in terms of adsorption of alcohol at the surface of the solid.

Ellipsometrically determined adsorption isotherms are reported for water, bromobenzene, nitro-methane, benzene, amyl, butyl, propyl, and ethyl alcohols, carbon tetrachloride, n-octane, and n-hexane on a polished polytetrafluoroethylene surface. These are nonwetting systems, and contact angles were also measured. In addition, isotherms were determined for two wetting systems, carbon tetrachloride on oxide-coated stainless steel and n-hexane on oxide-coated chromium-plated glass. For most of the nonwetting cases, the film pressure of the adsorbed film was not negligible, and should not not be omitted in semiempirical treatments of contact angle. The isotherms may be fitted by a previously proposed potential-distortion model, the choice of parameters also giving the observed contact angle. Alternatively, the isotherms are found to be segments of a single characteristic isotherm of the Polanyi type and thus obey a corresponding state principle. This characteristic isotherm for nonwetting systems does not fit the data for the two wetting cases, and the possibility is discussed that in the nonwetting cases the adsorbed state consists of bulk-like liquid in the form of micropatches or lenses rather than as a film of uniform thickness.

The finding that the dispersion force contributions to the surface free energies of octane and water are equal enabled a simple method to be developed to characterize the hydrophilic nature of solid surfaces. This technique involves measuring octane contact angles on solid surfaces under water. Nonhydrophilic solids unable to interact by polar forces exhibit a predicted 50° contact angle, whereas those able to interact by polar forces give values greater than 50°. The greater the contact angle, the stronger are the polar interactions. The deviation of the contact angle from 50° can be used to evaluate, Isw, defined as the interfacial stabilization energy from the nondispersion (polar) forces.

The surface tensions of a series of poly(isobutylenes) in the molecular weight range 400–3000 have been determined at 24°C. These results, together with surface tension values from the literature for poly(dimethyl siloxanes) and three series of different pure chain-molecule homologues, are found to exhibit a linear dependence on (molecular weight)^{$\text{−2}\text{2}$}. A simple free-volume argument seems to be consistent with this empirical observation.

Six solid surfaces were compared with respect to their surface quality, by measuring advancing contact angles along the solid surfaces (in the vertical and horizontal directions) at constant immersion rate. It was found that surfaces of mica, dip coated in FC-721, Teflon (FEP) heat pressed against mica, and siliconized glass yield essentially constant advancing contact angles at different locations of the solid surfaces and, thus, are well suited to dynamic contact angle measurements. Static and low rate dynamic contact angles of a number of pure liquids were therefore measured on these solid surfaces. Low rate dynamic contact angles were found to be identical with the static contact angles and independent of the velocity of the three-phase contact line (up to 0.5 mm/min).

Contact angles of water, glycerol, formamide, ethylene glycol, 1-bromonaphthalene, and bromobenzene were measured in the temperature range 5–160° on surfaces of polyethylene, polystyrene, polyacetal, polycarbonate, poly(ethylene terephthalate), and poly(tetrafluoroethylene-co-hexafluoropropylene). Stable advancing and receding angles were found and these varied linearly with temperature except in the range where solubility or swelling was evidence. Superheated water wet all the polymers to a greater degree than predicted. For the fluoropolymer all the liquids showed a negative temperature coefficient of the contact angle, both advancing and receding, ranging from 0.03 to 0.1 deg/°C. For the other polymers coefficients for advancing angles were nearly all negative and ranged from 0.03 to 0.18 but most receding angle values were positive; several liquid-polymer pairs showed a negligible coefficient. Temperature coefficients of the critical surface tension and of the dispersion surface tension of each solid were evaluated. Correlations of these derived quantities are discussed.

The critical velocity of engulfing V_c of acetal, nylon-6,6, and nylon-12 particles when encountered by the solidification front of salol is reported as a function of particle size. Using the dimensional analysis derived previously, the free energy of adhesion ΔF^adh for the attachment of these particles to the salol solid/melt interface is determined. These values of ΔF^adh, together with the known surface tension values γ_PV of the particles, are used to determine the salol solid/melt interfacial tension γ_SL to be γ_SL = 0.0053 ± 0.0025 erg/cm². Similarly, the free energies of adhesion ΔF^adh for PMMA particles to the solid/melt interfaces of naphthalene, biphenyl, and salol are determined. As all the γ_SL values for these systems are known—in the case of naphthalene and biphenyl from the temperature dependence of contact angles—γ_PV for the PMMA particles is determined. Using the equation of state for interfaces, the contact angle for the system PMMA/water is predicted. This value is in excellent agreement with the contact angle of water on a film of PMMA obtained by solvent casting. It is concluded that measurement of the critical velocity of engulfing represents a unique method for contact angle determinations on small particles.

The surface free-energies of the polyethers, polyethylene glycol, polypropylene glycol, polyepichlorohydrin, and polybutylene glycol, their mixtures and their random and block copolymers were determined by means of the pendant drop method. In all cases, except that of random copolymers, surface excesses of the low surface-energy component have been found. In the mixtures of homopolymers the behavior of surface excess isotherms depends on the molecular weight of the two components, while in block copolymers it depends on the degree of polymerization of the base unit. The Belton and Evans Equation for perfect solutions and the Prigogine equation for r-mer solutions have been applied to the experimental data.

The surface tension and surface entropies of different molecular weight polyethylene glycols and polypropylene glycols have been measured. The surface entropy of a mixture of polyethylene glycol and polypropylene glycol and that of block copolymers have also been determined. In the case of homopolymers, there is no effect of molecular weight on surface free energy and the increase in free energy on passing from the interior to the surface is due mainly to the heat content with the entropic contribution being very small.

In the case of a mixture of homopolymers and block copolymers, a minimum is observed when surface entropy is plotted against composition. At any particular composition, the surface entropy of a mixture is higher than that of a block copolymer of the same composition.

The dispersion force component of surface tension γ_S^d and the nondispersive interaction energy at the water/solid interface (or the nondispersive work of adhesion) I_SWⁿ were evaluated for poly-(tetrafluoroethylene) (PTFE), poly(vinylchloride) (PVC) and poly(methylmethacrylate) (PMMA) by the analysis of the contact angles of water drops in hydrocarbon (the two-liquid-contact-angle method). The results were compared with those obtained by the one-liquid-contact-angle method with α-bromonaphthalene and methylene iodide as probe liquids, which is the method usually adopted. The values of γ_S^d from the two-liquid method were considerably larger than those from the one-liquid method, whereas their high sensitivity to error in the measurement of contact angles was taken into account. This discrepancy may be attributed to the neglect of the surface pressure π in the one-liquid method and the π values of the liquids used on the sample solids were calculated.

Ellipsometrically determined adsorption isotherms are reported for water on two types of pyrolytic carbon, on polyethylene, and on stearic acid-coated copper, for relative pressures up to close to the saturation pressure, P⁰, and for various temperatures. Contact angle data for bulk water on the same solids are included; advancing angles of 60°–90° were found. The adsorbed film thickness reaches 40–80 Å in the first two systems, but only a few angstroms in the second two; correspondingly, the surface pressures of P⁰, π⁰, are large in the first two cases and small in the second two. Large contact angle thus does not necessarily imply low π⁰. The data are fitted to a previously published potential-distortion model, which allows adsorption and contact angle behavior to be related.

The spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid–vapor interfacial tension and hydrophilize the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by our experimental observations.

A technique was developed to rapidly measure surface tensions (γ) of viscous molten polymers and polymer solutions. The usual problems of slow meniscus equilibration and low signal-to-noise levels due to thermal convection currents at elevated temperatures have been overcome. Small-diameter fibers were used as vertical probes in the Wilhelmy technique to facilitate rapid equilibration of the wetting meniscus, and a “baffle tube” surrounding the electrobalance wire was implemented to suppress noise from thermal convection currents from the oven. Even with the baffle tube, it was found that computer averaging of the measured wetting force was necessary to obtain the desired precision precision atT 250°C. Measurements of γ up to ∼400°C were routinely made with η> 50 P polymers. Data are given for a molten fluoropolymer, a thermoplastic, and a liquid crystalline polymer. Room-temperature polymer fluids with viscosities extending to η = 500,000 P were studied; at η ⩽ 5000 P the precision was better than 0.04mNm. The dynamic contact angle versus time was measured as a function of fiber diameter, giving a relationship between the rate of meniscus equilibration and fiber diameter. Contact angles of polymer fibers immersed in water and methylene iodiode were used to calculate the surface free energies of the polymer in the solid state. These values are consistent with the extrapolated molten surface tension data and help to characterize the trend in γ over a wide range ofT.

The critical surface tension γ_c of polyvinyl butyral has been measured with polyhydric alcohols and halogenated hydrocarbons. Despite variations in polymer composition (residual OH content) and modes of preparation, γ_c is found to be 24–25 dynes/cm. with the former class of liquids. The —CH₃ groups appears to predominate over —CH₂, ether oxygen, and OH groups present. Steric effect may account for this biasing of the γ_c values toward the lowest surface energy group present. Fowkes' relation based on dispersion force interactions only is found to fit the data reasonably well. Comparative data on polyethylene are also presented.

Dielectric barrier discharge (DBD) technologies have been used to treat a polypropylene film. Various parameters such as treatment speed or electrical power were changed in order to determine the treatment power impact at the polypropylene surface. Indeed, all the treatments were performed using ambient air as gas to oxidize the polypropylene surface. This oxidation level and the surface modifications during the ageing were studied by a wetting method and by X-ray photoelectron spectroscopy (XPS). Moreover polypropylene film surface topography was analyzed by atomic force microscopy (AFM) in order to observe the surface roughness modifications. These topographic modifications were correlated to the surface oxidation by measuring with a lateral force microscope (LFM) the surface heterogeneity. The low ageing effects and the surface reorganization are discussed.

The thermodynamic aspects of the evolution of surface free energy of acrylic acid grafted polyethylene films have been examined as a function of time of contact on water. The dispersive and polar components vary with time and the interfacial free energy reaches a minimal value. Two terms participate in these variations: adsorption of water molecules and reorientation of polar acrylic groups at the water-polymer interface. Irreversible process thermodynamics has been applied to these phenomena. The surface can be characterized by a phenomenological coefficient relating the orientation rate and the orientation affinity of the polar groups at the interface.

It is demonstrated that extraneous electric charge can produce a large variation in contact angle for water drops on polytetrafluoroethylene surfaces.

The London dispersive component of surface free energy γ_s^d and the nondispersive interactions with polar liquids W I_swⁿ were determined for hydrophilic polymers S, that is, cellulose, poly(vinyl alcohol) (PVA), and poly(methylmethacrylate) (PMMA). On applying the geometric-mean relation $\text{2(γ}{}_{\mathrm{s}}{}^{\mathrm{d}}\text{γ}{}_{\mathrm{w}}{}^{\mathrm{d}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ to the dispersive interaction with W I_sw^d, the γ_s^d values were found to be 30, 29, and 37 erg·cm⁻² for cellulose, PVA, and PMMA, respectively. Each of them is completely independent of the nature of the testing liquids W, indicating that the geometric-mean equation is appropriate for representing the dispersive interaction. On the contrary, such a geometricmean expression is shown to be inapplicable to the nondispersive interactions. It is suggested that Fowkes' approach, in which intermolecular forces are regarded to be dominated by dispersion force interactions and electron donor-acceptor interactions, is more reasonable than the popular approach.

“Intrinsic contact angle hysteresis” is defined as hysteresis that cannot be ascribed to roughness, heterogeneity, or penetrability of the solid surface. It can be explained if we postulate that the layer of liquid immediately adjacent to the solid surface has an ordered structure similar to that of a liquid monocrystal. This structure is fluid (zero yield point in shear) in the plane of the solid surface and presents no obstacle to an increase of the solid—liquid interfacial area (advancing of the three-phase boundary line). In planes normal to the solid surface the structure has a positive yield point in shear, which prevents decrease of the solid—liquid interfacial area (receding of the three-phase line) until the yield point is exceeded by the surface pressure π_SL. Mechanical stability of the system at all values of the contact angle between the “advancing” and “receding” angles θ_A and θ_R is ascribed to a continuously changing value of π_SL and of the corresponding specific interfacial free energy γ_SL in this interval. This change reflects the elastic response in shear of the solid—liquid interfacial film in planes normal to the solid surface in this interval.

The contact angle (θ) of a sessile liquid drop on a horizontal solid surface can be calculated from the drop volume and the radius of the contact circle at the liquid/solid interface. A simple apparatus which allows simultaneous estimation of these two parameters is described, and tests of the method for two systems are reported. The first system is a 3.25 mole liter⁻¹ solution of 1-propanol in water on paraffin wax. The advancing (θ_a) and receding (θ_r) contact angles at 20°C are found to be (59.5 ± 1.0)° and (54.3 ± 0.3)°, respectively, in good agreement with the literature values and those found by direct measurement. The second system chosen is cyclohexane (a volatile liquid) on cleaved mica at 20°C. Two mica sheets were used. Mean contact angles of cyclohexane on the first mica sheet are θ_a = (7.45 ± 0.10)°, θ_r = (6.99 ± 0.12)°. For cyclohexane on the second sheet the mean contact angles are θ_a = (6.48 ± 0.31)°, θ_r = (5.56 ± 0.06)°. The difference between advancing and receding contact angles is statistically significant (P < 0.01) for both sheets. Other methods of comparable accuracy exist for θ ⪆ 30°, but the accuracy of most of these methods diminishes rapidly if θ ⪅ 30°. If calculation of the contact angle from the spacing between interference fringes is not appropriate, then estimation from drop volume and contact circle radius becomes the method of choice if θ <~ 30°.

1. It is to be expected that the hysteresis of contact angles on polystyrene would be the effect of a number of simultaneous causes. Whatever the interpretation, the differences in the observed angles found with surfaces that had been formed in different ways point to structural differences among the samples; and the existence of structural differences would indicate that all the surfaces depart appreciably from ideality, e.g., from ideal flatness, rigidity, and homogeneity.

2. We have shown that effects due to film pressure, πe, would be in the opposite direction from those observed in hysteresis. Hence film pressure is not responsible for contact angle hysteresis.

A remarkable agreement between Weber's linear analysis and experiment makes it possible to determine the dynamic surface tension of viscous liquids from the growth rate of axisymmetric disturbances on excited capillary jets. The method is very accurate and can be used to determine the surface tension at as short as 10⁻⁴ sec surface age. Aqueous glycerol solution and inks developed for inkjet printing were used as test liquids in the experiments. While a dye base ink showed time-dependent surface tension, the surface tension of inks which were colloid suspensions of small pigment particles and contained surfactant micelles equalled their equilibrium value at 10⁻⁴ sec surface age. In the tentative explanation of this phenomenon, the dynamic equilibrium between surfactant molecules in solution and in micelles was substituted for long-range surfactant transport by diffusion. A result of this assumption is that surface tension in nonequilibrium states depends only on the composition of the surface layer.

Contact angles have been measured as a function of the three-phase-boundary velocity. Large velocity effects observed with other techniques were not seen using the plate method. It is possible to relate the dependence of contact angles on velocity to surface heterogeneity.

A new method has been developed for calculating surface free energies of polymeric materials using a simplified solution to the Fowler equation and polarizabilities and diamagnetic susceptibilities for polymer constituent groups. Comparison of this new method with estimates from group parachors, contact angle measurements, or extrapolation of data for melts indicates generally good agreement among the different methods. Discussions are also included on the effect of limited rotation on dipolar interactions and on the proper application of Good and Girifalco's method for estimating surface free energies of solids.

The contact angle may be measured by magnifying the projected image of a sessile drop, assuming the profile is elliptical, and finding the Cartesian coordinates of selected points on the profile. By selecting groups of three such points the mean equation to the outline can be determined and thus the tangent at the observed point of contact. The method was tested using water drops on various steel surfaces and using mercury on glass. Results showed generally satisfactory agreement with those obtained using the tilting plate method and also with those obtained by other investigators who have employed analytical methods to define the drop shape. If the sessile drop shape is assumed to be a part-oblate spheroid, a minimum free-energy analysis illuminates several experimentally observed features of its shape.

ESCA and contact angle measurements have been combined in a detailed study of the effect of surface-to-volume ratio or thickness on the surface composition of coatings of a mixture of two fluoroalkyl methacrylate polymers which differ in the length of their fluoroalkyl side chains. These measurements show that the polymer component with the longer side chain is surface active in the mixture. The surface concentration of this component was found to decrease with increasing surfaceto-volume ratio of the coating.

The temperature effect on the wettability of oxidized polyethylene films with known surface densities shows a decrease in the free energy of adhesion at about 85°C for different liquids employed with varying numbers of OH groups. The thermograms obtained by differential thermal analysis show that the beginning of the melting transition is at about 85°C. The close agreement between the temperature at the beginning of the melting transition and the decrease of the wettability of oxidized polyethylene films is interpreted by the increase of the chain mobility leading to the redistribution of external polar groups initially located at the solid—air interface. We express the observed phenomenon as a degree of the overturn of macromolecular chains. The results obtained are discussed in relation to the number of OH groups present in the liquids and their ability to form hydrogen bonds.

The wettability of stereospecific poly(methacrylates) was studied. In the wettability of poly(methacrylates) having bulky substituents such as phenyl and chloroethyl groups, it was found that the critical surface tensions for isotactic polymers were low compared to those for attactic polymers. The steric effect of the bulky substituent on wetting was also discussed.

The dispersion force contributions to the surface free energies of octane and water are equal—21.8 dyn/cm. Octane's surface free energy has no polar component, whereas water has a polar contribution of 50.2 dyn/cm. Therefore, the increase in the contact angle of octane on various polar polymer surfaces underwater is a quantitative measure of the interfacial stabilization energy from polar forces. Octane contact angles were measured underwater on polyethylene, polytetrafluoroethylene, and polyethyleneglycolterephthalate surfaces before and after surface oxidation in a low temperature asher. The octane contact angles increased in each case as the surfaces became oxidized. When simple lap joints were prepared from these polymers and then broken in an Instron Tester, the measured breaking forces correlated well with the octane contact angles. Breaking strength increases of 1.1, 1.2, and 1.8 psi were realized with the polyethylene, polytetrafluoroethylene, and polyethyleneglycolterephthalate, respectively, when the polar forces were increased by 1 erg/cm².