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     

Microscopic studies of static and dynamic contact angles

Molecular dynamics simulations are used to test macroscopic theories for static and dynamic contact angles. Young's equation is verified by comparing observed static contact angles to angles calculated from the independently measured surface tensions between phases. Laplace's relation between the interfacial curvature and pressure is also checked. Both equations agree with simulation results within statistical errors. Hydrodynamic theories of dynamic contact angles are less well defined because they produce diverging stresses at the contact line between the solid and fluid interfaces if the usual no-slip boundary condition is assumed. Our simulations show that slip occurs within about two molecular diameters of the contact line, and that local hydrodynamics breaks down in the slip region. The slip results from large tangential stresses along the solid wall. A surprising result is that changes in the boundary condition for single-fluid flow at molecular scales produce dramatic changes in the dynamic contact angle.     

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.     

Contact angle of surfactant solutions on precipitated surfactant surfaces. II. Effects of surfactant structure,presence of a subsaturated surfactant,pH, and counterion/surfactant ratio

The contact angle of a saturated aqueous surfactant solution on the precipitate of that surfactant was measured by using the sessile drop method. The sodium and calcium salts of alkyl sulfates (C₁₂, C₁₄, and C₁₈) had advancing contact angles higher than those of alkyl trimethylammonium bromides (C₁₄, C₁₆, and C₁₈). The measured advancing contact angles for several surfactant solutions did not substantially change with varying surfactant/counterion ratios; therefore, the precipitating counterion concentration (e.g., water hardness) had little effect on the wettability. The contact angles of fatty acid (C₁₂ and C₁₆) solutions did not show any dependence on pH between a pH of 4 and 10. The contact angles of saturated calcium dodecanoate (CaC₁₂) solutions containing a second subsaturated surfactant (sodium dodecyl sulfate: NaDS) decreased with increasing NaDS concentrations until reaching the critical micelle concentration of the surfactant mixture. These results show that the second suractant can act as a wetting agent in this saturated surfactant system. Application of Young’s equation to contact angles showed that the solid/liquid surface tension can change substantially with surfactant concentration and be important in addition to the liquid/vapor surface tension in reducing contact angles. Application of the Zisman equation results in a “critical” surface tension for the CaC₁₂ or soap scum of 25.5 mN/m, which is comparable to difluoroethene.     

Arrangements of uniformly sized particles in a powder bed

The volume of the unit cell of a powder bed in a general case is calculated, and an equation is proposed for calculating the porosity of the bed consisting of uniformly sized ellipsoidal particles in contact and regularly arranged. In the case of uniformly sized spherical particles in contact, the equation can be simplified.Three dimensions and face angles of the unit cell are given for each regular arrangement both in cases of ellipsoidal and spherical particles. The values of the porosity are calculated by using the author's equation: the results for both ellipsoids and spheres are equal when tire particle arrangements are the same.The face angles of the unit cells proposed by Graton and Fraser are modified in two cases by the author's method of calculation and a system omitted from their classification is described. Other equations for calculation of the porosity are discussed.     

Contact Angles and Monolayer Depletion

Contact angles and contact angle hysteresis are very sensitive to surface heterogeneity. The degree of coverage of a surface by organic monolayers can be estimated by using the average of the cosines of advancing and receding angles in the equation of Cassie. This estimate can be refined by using a calibration curve computed from an idealized model of a heterogeneous surface.

Adhesion can be significantly influenced by the presence of monolayers and partial monolayers on adherends. These monolayers often control the rate of wetting by an adhesive and also the ultimate contact angle of the system. There is also some speculation that such monolayers might act as weak boundary layers.

Since contact angles are so sensitive to coverage by monolayers (1-2), the question arises as to what extent contact angles can be used to measure surface coverage. The work described in this paper was undertaken to answer that question. While the concepts developed here are applicable to any heterogeneous system, they were developed primarily to study the adsorption and depletion of organic monolayers on high energy surfaces.     

Contact Angles and Monolayer Depletion

Contact angles and contact angle hysteresis are very sensitive to surface heterogeneity. The degree of coverage of a surface by organic monolayers can be estimated by using the average of the cosines of advancing and receding angles in the equation of Cassie. This estimate can be refined by using a calibration curve computed from an idealized model of a heterogeneous surface.

Adhesion can be significantly influenced by the presence of monolayers and partial monolayers on adherends. These monolayers often control the rate of wetting by an adhesive and also the ultimate contact angle of the system. There is also some speculation that such monolayers might act as weak boundary layers.

Since contact angles are so sensitive to coverage by monolayers (1-2), the question arises as to what extent contact angles can be used to measure surface coverage. The work described in this paper was undertaken to answer that question. While the concepts developed here are applicable to any heterogeneous system, they were developed primarily to study the adsorption and depletion of organic monolayers on high energy surfaces.     

Interpretation of contact angle hysteresis

Hysteresis of the contact angle, i.e. the difference between the advancing and receding contact angles, is discussed in terms of the liquid film presence behind the drop when it has receded. It is shown that values of receding contact angles in many systems result from a well-defined free energy balance in the solid/liquid drop system. If a duplex film is present behind the drop, experimental receding contact angles up to 15° may be considered as lying in the range of the experimental error. In the case of low-energy solids (e.g. Teflon), it is possible to determine graphically the minimum value of the surface tension below which a liquid will leave a duplex film behind the drop when receding.     

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.     

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.     

Anisotropic Wetting of Liquids on Finely Grooved Surfaces

A photolithographically-prepared, parallel-grooved surface on silica has been employed as a model to study the influence of roughness on the spreading equilibrium of liquid drops. The equations generated by Oliver, Huh and Mason for cylindrically shaped drops were extended to account for wetting by liquid crystals. The observed drop shapes were dependent upon surface roughness. The equilibrium contact angles on a smooth surface can be calculated from the roughness, contact angles both parallel and perpendicular to the grooves, and the drop shape. Reasonably good agreement with experimental contact angles was obtained.     

Contact angle measurements using the Wilhelmy balance for asymmetrically treated samples

The Wilhelmy balance technique can be used to assess the wettability of rectangular samples with two differently treated faces. The contact angle on the treated face can be reliably deduced, provided that a consistent value for the contact angle on the untreated face has been obtained. As an example, a hydrophobic plate with various serrations on one face only is examined in detail. The agreement between the experimentally determined contact angles and the angles predicted by the Cassie equation is very good. We demonstrate that there are no methodological reasons to reject the use of the Wilhemy technique for samples which have received different physical or chemical treatments on the two faces.     

Compositional Dependence of Wetting and Contact Angles in Solid‐Liquid‐Liquid Systems under Realistic Environments

The Dual Drop Dual Crystal (DDDC) contact angle measurement technique has been used in this study with a high‐pressure high‐temperature optical cell apparatus to measure dynamic contact angles in rock‐oil‐brine systems at realistic reservoir conditions of temperature and pressure. The experimental observations with live, stocktank, de‐asphalted and de‐resined crude oils indicate that the stability of oil, which determines the precipitation of asphaltenes for wettability alteration, is controlled by the entire oil composition. The ionic interactions caused by the brine composition and surface charged behaviour of rock substrates have been identified as another main mechanism that can affect wetting and contact angles in solid‐liquid‐liquid systems.     

筛板上液体横向流动时气泡的形成特性

An apparatus,desinged to simulate bubbling of a sieve tray operated in froth regime,was employed. Bubble contact angles in and above the incipient weeping regimer for an air-water-plexiglas system were investigated. The influence of both liquid cross-flow and gas up-flow upon bubble contact angles was examined. A model considering the influence of liquid cross-flow was developed to predict bubble size from a sieve hole in froth operation regime.The comparison shows that the bubble sizes predicted by the present model are consistent with our experimental values and the available published experimental data.     

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).     

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).     

Fabrication of hydrophobic Ti3SiC2 surface with micro-grooved structures by wire electrical discharge machining

The near-superhydrophobic Ti₃SiC₂ surfaces with regular and controllable micro-grooved structures were fabricated by wire electrical discharge machining (WEDM). The surface topographies and chemical compositions of smooth and micro-grooved Ti₃SiC₂ surfaces were characterized. The micro removal mechanism of Ti₃SiC₂ in the process of electrical discharge machining was also analyzed. The wetting mechanism of micro-grooved Ti₃SiC₂ surface was discussed along with the static contact angle, anisotropic wettability and contact angle evolution versus time. The relationships between parallel and perpendicular contact angles, depth-width ratio of micro-grooved structures and surface roughness of textured surface were investigated. The experimental results show that the parallel contact angle on the textured Ti₃SiC₂ surface increased by about 164% compared with the one on the smooth surface, and near-superhydrophobic surface with obvious anisotropy was roughly achieved. The experimental parallel contact angles were very close to theoretical contact angles calculated by Cassie-Baxter formula. It is confirmed that the depth-width ratio may be used to predict the parallel contact angle with the average prediction error of 2.4%. The perpendicular contact angles had a good correlation with the depth-width ratio and surface roughness.     

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.     

Molecular mechanisms of hydrophobic transitions

This review article provides new insights into the molecular mechanisms of hydrophobicity that emerge within the phenomenological framework of classical capillarity. The thermodynamic analysis of surface phenomena via the Gibbs adsorption equation that forms the basis of the experimental physical chemistry of liquid-fluid interfaces extends with its rigorous implications towards the wetting of solid surfaces. Observations on equilibrium contact angles, contact angle hysteresis, and the dynamics of wetting hitherto based on qualitative results that received fragmentary and eclectic interpretations are accounted for in terms of the values of adsorption pressures that act at the three-phase line. Hydrophobic surfaces and hydrophobic transitions induced by reversible solute adsorption qualify as two distinct limiting cases in this thermodynamic context. The equilibrium and kinetic aspects of the wetting of uniform and chemically heterogeneous surfaces by pure liquids and surfactant solutions is discussed with reference to reversible liquid-fluid interfaces. The importance of the solvent and solute adsorption at the solid-vapor interface for proper assessment of static and dynamic dewetting transitions is particularly addressed.     

A new model to determine contact angles on swelling polymer particles by the column wicking method

The contact angle determination on swelling polymer particles by the Washburn equation using column wicking measurements may be problematic because swelling occurs during the wicking process. The objective of this research was to develop a new model to more accurately determine contact angles for polymer particles that undergo solvent swelling during the column wicking process. Two phenomena were observed related to the swelling effect during the wicking process: (1) a temperature rise was detected during the wicking process when the swelling polymer particles interacted with polar liquids, and (2) a smaller average capillary radius (r) was obtained when using methanol (polar liquid) compared to using hexane (non-polar liquid). The particle swelling will induce both particle geometry changes and energy loss which will influence the capillary rise rate. The model developed in this study considered the average pore radius change and the energy loss due to the polymer swelling effect. Contact angle comparisons were conducted on wood with formamide, ethylene glycol, and water as test liquids, determined by both the new model and the Washburn equation. It was shown that the contact angles determined by the new model were about 4-37° lower than those determined by the Washburn equation for water, formamide, and ethylene glycol. Todetermine whether the polymer particles are swelling, two low surface tension liquids, one polar (methanol) and the other non-polar (hexane), can be used to determine the average pore radius (r values) using the Washburn equation. If the same r values are obtained for the two liquids, no swelling occurs, and the Washburn equation can be used for the contact angle calculation. Otherwise, the model established in this study should be used for contact angle determination.