A model of electrowetting, reversed electrowetting, and contact angle saturation

While electrowetting has many applications, it is limited at large voltages by contact angle saturation, a phenomenon that is still not well understood. We propose a generalized approach for electrowetting that, among other results, can shed new light on contact angle saturation. The model assumes the existence of a minimum (with respect to the contact angle) in the electric energy and accounts for a quadratic voltage dependence ～U(2) in the low-voltage limit, compatible with the Young-Lippmann formula, and an ～U(-2) saturation at the high-voltage limit. Another prediction is the surprising possibility of a reversed electrowetting regime, in which the contact angle increases with applied voltage. By explicitly taking into account the effect of the counter-electrode, our model is shown to be applicable to several AC and DC experimental electrowetting-on-dielectric (EWOD) setups. Several features seen in experiments compare favorably with our results. Furthermore, the AC frequency dependence of EWOD agrees quantitatively with our predictions. Our numerical results are complemented with simple analytical expressions for the saturation angle in two practical limits.     

Development of diffuse double layers in column-wicking experiments: Implications for pH-dependent contact angles on quartz

The pH dependence of contact angles in quartz powder beds was studied by column wicking. The rate of capillary penetration was found to be highest at the isoelectric point of quartz which, by applying the classical Washburn equation, results in a minimum contact angle at the isoelectric point. Direct contact angle measurements however show that the contact angle is at a maximum at the point of zero charge (see e.g. [1], [2], [3], [4], [5] and [6]). By measuring the permeability of powder columns with aqueous solutions of varying pH, it is shown that the permeability reaches a maximum at the isoelectric point. This suggests that the rate of capillary penetration is influenced by the permeability of the powder columns towards respective aqueous solutions. The difference in permeability can be explained by the notion of an electroosmotic counter-pressure which was already recognized by Klinkenberg [7]. An approach is presented that involves the calculation of capillary constants from permeability measurements of the corresponding aqueous solutions. An equation is derived that takes direct account for the electroosmotic counter-pressure. Application of this equation combined with capillary constants calculated from permeabilities of the corresponding aqueous solutions results in the expected contact angle-pH relationship.     

Impact of pinning of the triple contact line on electrowetting performance

Pinning of the triple contact line adversely affects electrowetting on dielectric. Electrowetting response of substrates with contact angle hysteresis ranging from 1° to 30° has been characterized, and the results are interpreted within the framework of electromechanics corrected for pinning. The relationship between contact angle hysteresis, threshold potential for liquid actuation, and electrowetting hysteresis is quantified. Our results demonstrate that a modified electrowetting equation, based on balance of forces (including the pinning forces) acting on the triple contact line and on the drop, describes the electrowetting response of substrates with significant contact angle hysteresis. Finally, the surface properties of PDMS Sylgard 184 were found to be influenced by the electric field.     

An empirically validated analytical model of droplet dynamics in electrowetting on dielectric devices

Explicit analytical models that describe the capillary force on confined droplets actuated in electrowetting on dielectric devices and the reduction in that force by contact angle hysteresis as a function of the three-dimensional shape of the droplet interface are presented. These models are used to develop an analytical model for the transient position and velocity of the droplet. An order of magnitude analysis showed that droplet motion could be modeled using the driving capillary force opposed by contact angle hysteresis, wall shear, and contact line friction. Droplet dynamics were found to be a function of gap height, droplet radius, surface tension, fluid density, the initial and deformed contact angles, contact angle hysteresis, and friction coefficients pertaining to viscous wall friction and contact line friction. The first four parameters describe the device geometry and fluid properties; the remaining parameters were determined experimentally. Images of the droplet during motion were used to determine the evolution of the shape, position, and velocity of the droplet with time. Comparisons between the measured and predicted results show that the proposed model provides good accuracy over a range of practical voltages and droplet aspect ratios.     

Physical significance of contact angles

Summary The physical significance of contact angles has been interpreted on the basis of a model derived from known surface energy relationships. The degrees of non-spreading and spreading have been expressed in terms of the magnitude of contact angles. On the basis of the physical picture, hysteresis of contact angle has been calculated from the experimental values of equilibrium contact angle and surface tension of the liquid. It has been suggested that it is not necessary to assume that hysteresis of contact angles is due to surface roughness of solids. The picture also explains why apparent contact angle on a non-flat solid surface is more than that on a flat solid.With 2 figures and 1 table     

Effect of three-phase contact line topology on dynamic contact angles on heterogeneous surfaces

Cassie-Baxter theory has traditionally been used to study liquid drops in contact with microstructured surfaces. The Cassie-Baxter theory arises from a minimization of the global Gibbs free energy of the system but does not account for the topology of the three-phase contact line. We experimentally compare two situations differing only in the microstructure of the roughness, which causes differences in contact line topology. We report that the contact angle is independent of area void fraction for surfaces with microcavities, which correspond to situations when the advancing contact line is continuous. This result is in contrast with Cassie-Baxter theory, which uses area void fraction as the determining parameter, regardless of the type of roughness.     

Model and experimental studies for contact angles of surfactant solutions on rough and smooth hydrophobic surfaces

Despite the practical need, no models exist to predict contact angles or wetting mode of surfactant solutions on rough hydrophobic or superhydrophobic surfaces. Using Gibbs' adsorption equation and a literature isotherm, a new model is constructed based on the Wenzel and Cassie equations. Experimental data for aqueous solutions of sodium dodecyl sulfate (SDS) contact angles on smooth Teflon surfaces are fit to estimate values for the adsorption coefficients in the model. Using these coefficients, model predictions for contact angles as a function of topological f (Cassie) and r (Wenzel) factors and SDS concentration are made for different intrinsic contact angles. The model is also used to design/tune surface responses. It is found that: (1) predictions compare favorably to data for SDS solutions on five superhydrophobic surfaces. Further, the model predictions can determine which wetting mode (Wenzel or Cassie) occurred in each experiment. The unpenetrated or partially penetrated Cassie mode was the most common, suggesting that surfactants inhibit the penetration of liquids into rough hydrophobic surfaces. (2) The Wenzel roughness factor, r, amplifies the effect of surfactant adsorption, leading to larger changes in contact angles and promoting total wetting. (3) The Cassie solid area fraction, f, attenuates the lowering of contact angles on rough surfaces. (4) The amplification/attenuation is understood to be due to increased/decreased solid-liquid contact-area.     

Drop size dependence of contact angles on two fluoropolymers

Young’s equation predicts that the contact angle of a liquid drop is independent of its size. Nevertheless, large drop size dependences of contact angles have been observed, especially for millimetre-sized drops, on a variety of solid surfaces. We report new measurements of drop size dependence of contact angles for several liquids on two fluoropolymer surfaces, Teflon AF 1600 and EGC-1700. We demonstrate a new strategy for contact angle measurement that allows detection of approximately 0.1° changes in the contact angle during the growth of a drop. We find that on the surfaces examined, drop size dependence of contact angles is ten times smaller than on all previously studied fluoropolymers at the millimetre scale. The data are insensitive to various attempted surface modifications. We discuss the interpretation of the data and possible physical sources.     

Vapour adsorption and contact angles on hydrophobic solid surfaces

To test the effects of vapour adsorption on contact angle measurements, contact angles of high-vapour-pressure liquids and low-vapour-pressure liquids on a hydrophobic solid surface (FC721) were measured by using the axisymmetric drop shape analysis-profile (ADSA-P) technique. Details of the surface preparation and the experiments are presented. By plotting the experimental data in terms of _1v cos vs. _1v, this study shows that the vapour adsorption on a fluorocarbon surface, FC721, is negligible.     

Influence of electronic properties of naphthalene compounds on contact angles

Contact angles of a homologous series of naphthalene compounds on films of a fluorinated acrylate polymer (EGC-1700) deviate from an ideal pattern of contact angles. The deviations increase with the electronegativity of the constituent atoms of the liquid molecules. The results suggest that an uneven distribution of electrostatic charges over the molecules creates strong dipole moments, giving rise to fairly strong dipole-dipole and dipole-induced dipole interactions between liquid molecules and the EGC-1700 chains, which have large dipole moments. In comparison, contact angles of the same probe liquids on the films of Teflon AF 1600, which have small dipole moments, fall on a smooth curve representing the surface tension of the polymer film.     

The contact angles of surfactant solution on the quartz surface

Summary The contact angles formed on the quartz surface by 0,1 N NaCl aqueous solution at different pH were measured. The effect of surfactants such as anion-active sodium dodecyl sulphate (NaDS) and cation-active cetyltrimethylammonium bromide (CTAB) was investigated. The results are interpreted in terms of the Frumkin-Derjaguin theory of wetting.With 4 figures and 1 table     

Thermodynamic modeling of contact angles on rough, heterogeneous surfaces

Theoretical modelling for contact angle hysteresis carried out to date has been mostly limited to several idealized surface configurations, either rough or heterogeneous surfaces. This paper presents a preliminary study on the thermodynamics of contact angles on rough and heterogeneous surfaces by employing the principle of minimum free energy and the concept of liquid front. Based on a two-dimensional regular model surface, a set of relations were obtained, which correlate advancing, receding and system equilibrium contact angles to surface topography, roughness and heterogeneity. It was found that system equilibrium contact angles (theta(ES)) can be expressed as a function of surface roughness factor (delta) and the Cassie contact angle (theta(C)): costheta(ES) = deltacostheta(C). This expression can be reduced to the classical Wenzel equation.: theta(ES) = theta(W) for rough but homogeneous surfaces, and the classical Cassie equation theta(ES) = theta(C) for heterogeneous but smooth surfaces. A non-dimensional parameter called surface feature factor (omega) was proposed to classify surfaces into three categories (types): roughness-dominated, heterogeneity-dominated and mixed-rough-heterogeneous. The prediction of advancing and receding contact angles of a surface is dependent on which category the surface belongs to. The thermodynamic analysis of contact angle hysteresis was further extended from the regular model surface to irregular surfaces; consistent results were obtained. The current model not only agrees well with the models previously studied by other researchers for idealized surfaces, but also explores more possibilities to explain the reported experimental results/observations that most existing theories could not explain.     

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.     

Water contact angles and hysteresis of polyamide surfaces

The wetting behavior of a series of aliphatic polyamides (PAs) has been examined. PAs with varying amide content and polyethylene (PE) were molded against glass to produce surfaces with similar roughness. After cleaning, chemical composition of the surfaces was verified with X-ray photoelectron spectroscopy. Advancing and receding contact angles were measured from small sessile water drops. Contact angles decreased with amide content while hysteresis increased. Hysteresis arose primarily from molecular interactions between the contact liquid and the solid substrates, rather than moisture absorption, variations in crystallinity, surface deformation, roughness, reorientation of amide groups, or surface contamination. Free energies of hysteresis were calculated from contact angles. For PE, which is composed entirely of nonpolar methylene groups, free energies were equivalent to the strength of dispersive van der Waals bonds. For PAs, free energies corresponded to fractional contributions from the dispersive methylene groups and polar amide groups.     

Stick-slip of the three-phase line in measurements of dynamic contact angles

Contact angles of a series of n-alkanes (i.e., n-heptane to n-hexadecane) are studied on two functionalized maleimide copolymers (i.e., poly(ethene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ETMF) and poly(octadecene-alt-N-(4-(perfluoroheptylcarbonyl)aminobutyl)maleimide) (ODMF)). On the homogeneous ETMF films, all liquids show a smooth motion of the three-phase line. In contrast, on ODMF surfaces that are found to consist of mainly fluorocarbons and small patches of hydrocarbons, short-chain n-alkanes show a stick-slip pattern. By increasing the chain length of the probe liquids, stick-slip is reduced significantly. The phenomenon is discussed in the framework of the Cassie equation. It is found that the upper limit of contact angles in the stick-slip pattern is given by the advancing angle that would be obtained on the pure fluorocarbon surface, whereas the lower limit of the stick-slip pattern is given by the Cassie angle.     

Determination of contact angles on microporous particles using the thin-layer wicking technique

The properties of particle-stabilized emulsions, especially with regard to phase inversion, are very dependent on the contact angle that the particles experience at the oil-water interface. For the very small particles used for such emulsions (often a few tens of nm), it is impossible to measure this contact angle directly. Its value could be calculated if it were possible to determine the components of the solid surface free energy. To establish a method suitable for such particles, we have investigated the imbibition of five probe liquids into a porous bed of silica (commercial TLC plates) using the thin-layer wicking technique. For all liquids, the difference between wicking rate for bare plates and for those pre-contacted with the vapors is large but it is not due to an advancing angle effect on bare plates. Our analysis shows that it is due to the diversion of flowing liquid into blind pores which are already filled in the pre-contacted case. Thus a new model is proposed describing wicking in a porous medium with very small blind pores by introducing a parameter into the Washburn equation that corrects for this capillary condensation effect. The parameter needed is determined independently using gravimetric adsorption measurements. When this modified Washburn equation is used, the difference between advancing and receding contact angle is actually quite small. When the averages are used as the Young's contact angles, values for the surface energy components of silica are obtained that are completely consistent between the five liquids and have magnitudes expected for this type of silica surface.     

Specific heat and dielectric relaxations in ultra-thin polystyrene layers

The effect of thickness on the glass transition dynamics in ultra-thin polystyrene (PS) films (4 nm < L < 60 nm) was studied by thin film ac-calorimetry, dielectric spectroscopy (DRS) and capacitive dilatometry (CD). In all PS-films, a prominent α-process was found in both the ac-calorimetric and dielectric response, indicating the existence of cooperative bulk dynamics even in films as thin as 4 nm. Glass transition temperatures (T_g) were obtained from ac-calorimetric data at 40 Hz and from capacitive dilatometry, and reveal a surprising, marginal thickness dependence T_g(L). These results, which confirm recent data by Efremov et al. [Phys. Rev. Lett. 91 (2003)] but oppose many previous observations, is rationalized by differences in film annealing conditions together with the fact that our techniques probe exclusively cooperative dynamics (ac-calorimetry) or allow the effective separation of surface and “bulk”-type mobility (CD). Two other observations, a significant reduction in c_p towards lower film thickness and the decrease in the contrast of the dilatometric glass transition, support the idea of a layer-like mobility profile consisting of both cooperative “bulk” dynamics and non-cooperative surface mobility.     

A refractive tilting-plate technique for measurement of dynamic contact angles

The contact angle is a critical parameter in liquid interface dynamics ranging from liquid spreading on a solid surface on earth to liquid motion in partially filled containers in space. A refractive tilting-plate technique employing a scanning laser beam is developed to conduct an experimental study of a moving contact line, with the intention of making accurate measurements of the contact angle. The technique shows promise as an accurate and potentially fully automated means to determine the velocity dependence of the contact angle at the intersection of the interface between two transparent fluids with a transparent solid surface. Ray tracing calculations are included to reinforce the measurement concept. The principal experiments were conducted at speeds ranging from 0.05 to 1.00 mm/s, both advancing and receding, using an immiscible liquid pair (nonane/formamide) in contact with glass. The contact angle was found to depend for practical purposes only on the sign of the velocity and not on its magnitude for the range of velocities studied. Other observations revealed a bimodal behavior of the contact line that depends on which liquid first contacts the glass, with resulting drift in the dynamic contact angle with time.     

A technique for measurement of pretilt angles arising from alignment layers

A well-controlled, reproducible alignment with or without a pretilt angle is a basic need for the development of any kind of liquid crystal display. We have built an optical set-up based on the crystal rotation method. With this system we can measure the pretilt angle in nontwisted liquid crystal samples. Presentation of the experimental set-up and first results of these measurements (obtained with a precision of 0.3 ) are given for several compounds and alignment layers.