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angles corresponding to a slowly advancing and receding contact line. ... until now only for static contact angle measurements, i.e. at constant drop volumes. We.
Colloids and Surfaces A: Physicochemical and Engineering Aspects 206 (2002) 469– 483 www.elsevier.com/locate/colsurfa

Contact angle hysteresis on dentin surfaces measured with ADSA on drops and bubbles Hartmut Alexander Wege a,*, Juan Antonio Holgado-Terriza b, Juan Ignacio Rosales-Leal c, Raquel Osorio c, Manuel Toledano c, ´ ngel Cabrerizo-Vı´lchez a,* Miguel A a

Department of Applied Physics, Biocolloid and Fluid Physics Group, Uni6ersidad de Granada, C/Fuentenue6a s/n, 18071 Granada, Spain b Department of Informatic Languages and Systems, Uni6ersidad de Granada, 18071, Granada, Spain c Department of Stomatology, Biomaterials Group, Uni6ersidad de Granada, 18071 Granada, Spain

Abstract Contact angle measurement on biological surfaces is difficult due to substrate hydration, porosity and heterogeneity. The former promotes very low contact angles, and the latter leads to irregular drop shapes and contact angle hysteresis, being meaningful in terms of surface energetics only low rate dynamic contact angles, i.e. the extreme angles corresponding to a slowly advancing and receding contact line. ADSA-CD has been developed to take into account the drop shape irregularity. It requires as input the liquid surface tension and density, the co-ordinates of some contact line points and the drop volume, yielding a mean contact angle. Due to the latter requirement ADSA-CD has been used until now only for static contact angle measurements, i.e. at constant drop volumes. We present an upgrade of the method that permits to control very precisely the drop volume, and to capture simultaneously drop images for contact angle determination, permitting this way to use ADSA-CD for hysteresis measurements. Low contact angles lead to difficulties in their measurement, being the captive bubble technique a known method to overcome this shortcoming. As our system is also capable to measure captive bubble low rate dynamic contact angles, we performed an experimental study with Teflon and bitumen model surfaces, which permits to identify the advancing bubble angles with the receding drop angles. We were therefore able to measure hysteresis on dentin tissue, which has a too low receding drop angle to be measured by ADSA-CD. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Contact angle hysteresis; Non-ideal surfaces; Dentin; Axisymmetric Drop Shape Analysis and captive bubble

1. Introduction It is well known [1] that the Young equation, * Corresponding author. Fax: + 34-958-24-3214. E-mail address: [email protected] (H.A.Wege).

klf cos q= ksf − ksl,

0927-7757/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 7 7 5 7 ( 0 2 ) 0 0 0 8 8 - 2

(1)

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is the thermodynamic equilibrium condition for an ideal solid–liquid – fluid capillary system, being the contact angle qYoung uniquely determined by the three interfacial tensions klf, ksf and ksl as an equilibrium property of the system. However, the key condition for the derivation of Youngs equation, the requirement to the solid surface to be ideal, i.e. smooth, homogeneous, inert, nonporous and non-deformable, usually is not met by real surfaces which always present, at least to some extent and on some scale, roughness and heterogeneity. As a consequence, the observed contact angle is not unique but falls into a more or less wide interval, which is in some way characteristic for the system. The major and minor observable contact angle values, respectively occur at the contact line of an advancing and receding liquid front and are called the advancing and receding contact angle, respectively. The difference between them is the width of the scatter interval and is called contact angle hysteresis. Due to this scatter and despite of the apparent simplicity of the contact angle measurement, contact angle measurement and interpretation and especially its use in conjunction with the Young equation for solid interfacial energy determination is at least very delicate [2], and contact angles are often used merely as empirical parameters to quantify wettability. Notable pioneer work to find the appropriate equivalent to Young’s equation for rough surfaces was done by Wenzel [3], although Wenzel’s equation predicts the rough solid contact angles to be always smaller than the smooth solid ones and therefore showed up to contradict experiment. An analogue treatment for heterogeneous surfaces was performed by Cassie [4], but the resulting Cassie angle is not very useful as it is not identifiable among all other possible angles. To overcome this, the concept of several metastable states corresponding to different contact angles was introduced [5] and confirmed by several thermodynamic model considerations able to predict heterogeneity-induced hysteresis [1,7] and stickand-slip-behavior [8]. Gibbs’s [6] concept of line tension and the one of contact line corrugation [9,10] was introduced to explain roughness-induced contact angle scatter and drop size depen-

dence. The same concepts were used to explain how heterogeneities of different size (from atomic over micrometric up to millimetric scale) have different effects on contact angle behavior (from no effect at all over intrinsic hysteresis to contact line contortion). Further model considerations [10,11] confirmed the experimental evidence [12] that in the case of a smooth surface with heterogeneities of appropriate size the advancing and receding angle characterize the surface component with the lowest and highest interfacial energy, respectively. This is a very important result as it permits to use dynamic contact angles to estimate the interfacial energy of the components of a heterogeneous surface. In the case of biological surfaces analysis is even more complicated, as for a meaningful measurement they usually have to be in their native, hydrated state. Hydrated surfaces present an aqueous film who’s thickness may vary from a few nm up to several mm [13], and beside the practical difficulty to obtain precise measurements of the normally very low contact angles, it may be necessary for their interpretation, at least at microscopic scale, to take into account the film disjoining pressure [14] and double-layer forces [15–17] in the case of static contact angles, and precursor film effects [13,18] for the case of dynamic contact angles. Also in the experimental field great progress has been made, i.e. in drop profile detection. This was achieved at macroscopic scale (\ 10 mm), where drop shape obeys the Laplace equation of capillarity as well as at microscopic scale (around the contact line), where the interface shape is governed by long-range molecular interactions across the interface [19] or by hydrodynamic forces in the case of a moving contact line. In the latter case interferometric [20] and ellipsometric [21] techniques were used successfully, and in the former case as well as in the transition between them drop micrograph digitization techniques helped to improve data quality. Among them, beside the capillary-rise-based techniques [22,23] specially the techniques based on fitting experimental drop profiles to the Laplace equation as Axisymmetric Drop Shape Analysis (ADSA) [24] showed to be a powerful instrument.

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2. The dentinal surface Modern dental restorative treatments are based on the composite polymeric materials. The success of the composite restorations is based, on the one hand, in the physical and chemical properties of composite resins and, on the other hand, on the adhesion to the dental tissues. While the adhesion

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to enamel is a reliable technique due to its mainly mineral composition, bonding to dentin represents a greater challenge because dentin is a complex heterogeneous and an intrinsically wet organic tissue. The dentin is composed by 50 vol% mineral (primarily apatite crystallites in the form of a carbonate rich, calcium deficient apatite), 30 vol%

Fig. 1. Scanning electron micrographs showing the dentinal tissue: (a) dentin far from the pulp, with a low tubule density (original magnification× 1000); (b) dentin near the pulp, with a high tubular density (original magnification× 1000); (c) lateral view of dentin in which it can be observed the dentin covered by the smear layer (original magnification× 3000). (Abbreviations: DT, dentin tubule; PD, pertitubular dentin; ID, intertubular dentin; SL, smear layer).

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organic material (largely type I collagen), and 20 vol% fluid (similar to plasma) [25]. The histological characterization of the dentinal tissue reveals it to be a porous and inhomogeneous tissue, as shown in Fig. 1. Dentin is penetrated by a tubular labyrinth containing the odontoblastic cells. The tubules converge on the pulp chamber and therefore tubule density and orientation vary from location to location. Tubule number is incremented closer to the pulp (Fig. 1(a and b)) [26]. The tubule lumen is lined by the peritubular dentin, which is highly mineralized containing mostly apatite crystals with little organic matrix. The tubules and peritubular dentin are separated by intertubular dentin composed of a matrix of type I collagen reinforced by apatite. Dentin is hydrated in the vital state due to the pulpal pressure, estimated to be approximately 15 cm H2O [27], which causes an outward flow of dentinal fluid. Its permeability is variable and location dependent, being greater near the pulp [28]. In addition, when dentin is instrumented or grounded, a thin layer of debris partially covers the surface and occludes the dentin tubules (Fig. 1(c)). This layer is named smear layer and was demonstrated to consist of calcium and phosphate plus organic material [29]. Current adhesive systems modify the dentin surface to change the energetic characteristics and to allow adhesive resins infiltrate the biological tissue. The process of adhesion consists in a first demineralizing acid treatment, followed by the infiltration of the demineralized dentin by the adhesive resin. The result is the formation of the named hybrid layer, a mixture of the demineralized biological tissue and the adhesive resin, as shown in Fig. 2. The dynamic nature of dentin, its histological structure and its intrinsically wetness, configure a substrate that is responsible of bonding failure and marginal leakage, which occurs with all resinbased adhesives. Improved understanding of its nature should have important consequences for today’s dental procedures and should lead to new methods to preserve and protect teeth, and repair defects brought on by disease or trauma.

Fig. 2. Scanning electron micrograph of the hybrid layer formed after dentin demineralization and infiltration by an adhesive resin (original magnification×500). (Abbreviations: HL, hybrid layer; D, dentin; A, adhesive).

3. Contact angle measurement with ADSA

3.1. ADSA-Profile The original version of ADSA, ASDA-Profile, was developed to determine liquid–fluid interfacial tensions and contact angles from the profile of Axisymmetric menisci, i.e. from drops and bubbles, from pendant as well as from sessile (captive) ones. Using as input local gravity and the fluid density difference it fits the experimental profile to the Laplace equation of capillarity, 1 1 DP = k + , (2) R1 R2 and using the interfacial tension k as adjustable parameter, it yields as outputs among others k, the drop volume and the contact angle q. R1 and R2 are the principal radii of curvature, and DP the difference of pressure along the interface. Details can be found elsewhere [24]. Apart from the above inputs, it requires only a set of several arbitrary but accurate points selected from the drop profile. An automatic digitization technique using digital image acquisition and analysis has been used [30], and an upgrade has been developed [31].





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3.2. ADSA-diameter With decreasing contact angle, and especially for rough surfaces, the drop profile image appears more and more fuzzy near the surface, and it become increasingly difficult to locate the point where the profile meets the surface, and therefore to extract contact angle with precision. Furthermore, if the surface presents heterogeneities of macroscopic size they will lead to contact line corrugation. In this case the condition of axisymmetry is not fulfilled anymore and the drop contact angle ceases to be unique but varies with contact line location. ADSA-D has been developed to overcome these shortcomings. Instead of side-view profiles, top-view drop micrographs are captured. For contact angles smaller than 90° the contact line is visible on them, and a set of contact point co-ordinates are obtained from it to calculate the average contact diameter (ADSA-CD). For contact angles greater than 90° the drop equator is visible, and a set of extracted point co-ordinates yield the maximum diameter (ADSA-MD). Beside local gravity and the fluid density difference, the above diameter data, the liquid surface tension and the drop volume are used as additional inputs, and the best fit to the Laplace equation yields the average contact angle as output. 4. Materials and methods

4.1. Materials The asphaltic bitumen (a mixture of asphaltenes and resins, hardness 150– 200) was kindly released by REPSOL YPF DERIVADOS. All reagents and liquids were purchased by PANREAC QUI´MICA SA. All chemicals in contact with the surfaces were analytical grade. The water used was Milli-Q+ de-ionized water with conductivity of 0.054 mS. All the tubing is made of Teflon. Tubing and micro-injector were cleaned by successive through-flow of acetone, propanol and water. Tube cleanness and water purity were checked with independent measures of the surface tension using the pendant-drop technique.

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All experiments were performed in a clean laboratory with 99.99% filtered air supply, placed in the basement of the building.

4.2. Set-up A schematic view of the set-up, similar to that used by Rodrı´gez et al. [32], is shown in Fig. 3. For the ADSA-P measurements a horizontally orientated SONY CCD B&W camera (SSCM370CE) with a resolution of 752×582 pixels equipped with a LEICA APOZOOM objective is fixed to an optical bench together with the light source, the light diffuser and specimen cell containing the drop/bubble. For the ADSA-D measurements drop images were acquired from the top of the cell with a vertically mounted LEIZ APOZOOM microscope fitted with a monocular phototube, and a COHU 4910 CCD monochrome camera. A Leica CLS fiber-optic system with a concentric ring lamp are used to illuminate the surface being analyzed, providing a uniform field of background light. Vertical alignment of the camera assembly above the surface was performed maximizing the magnitude and uniformity of reflected light from the gauge-ring. All the set-up is mounted on a vibrationdamped, self-leveling MELLES GRIOT table, which assures horizontal alignment. The specimen cells are thermostatized HELMA standard photo spectrometer cells, saturated with vapor for drop measurements, and firmly closed in any case to control temperature and to minimize drop contamination and evaporation. They were placed on an adjustable platform, permitting to find the best surface inclination, compromise between horizontality and optimal image contrast, which is necessary for profile edge detection in ADSA-P measurements. A PC (Pentium III-MMX 450 MHz), equipped with a Data Translation DT 3155 frame grabber, receives and stores the CCD signal with a resolution of 768× 576 pixels and 256 gray levels per pixel at a maximum steady state rate of five pictures per second. For ADSA-P the drop/bubble type determination and meniscus profile detection is fully auto-

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mated using local gradient operators. But for the ADSA-D top-view drop images, a complete automation of contact line detection, applicable to diverse liquids and biological substrate surfaces is a very complex task, due to low contrast and different image textures. The difficulty to improve contrast and at the same time the textural unifor´ lvarez et al. to the addition of a dye to mity lead A the water placed on a biological surface [33]. But as key requirement, the selected dye must not interact with the liquid neither with the surface. This condition may be problematic, especially in the case of receding liquid fronts. Therefore, in our device a semi-automated contact line detection proceeding is used. Once the profile/contact line data are obtained, the fit process is fully automated. The ADSA-D algorithm uses the drop volume as a parameter in the contact angle calculation, which must be known beforehand. For this reason the former has been used until now only for static contact angle measurements, where stringent control over drop volume is easily achieved with a micropipette.

But in hysteresis-presenting systems only the extreme angles corresponding to a slowly advancing or receding contact line are identifiable and therefore meaningful for contact angle interpretation. This is why for the case of ADSA-P, where drop volume is an output and no strict control over it is necessary, these dynamic contact angles were successfully obtained using the following method: the specimen surfaces are provided with a hole in the center, and connected to a motordriven syringe. This allows to move the contact line gently, growing or shrinking the drop by liquid injection or extraction, respectively, without any external distortion of the fluid-fluid interface. We developed the following upgrade of the method: the perforated specimens are connected to a Hamilton Microlab 500 micro-injector equipped with a syringe of suitable volume by Teflon capillaries. As the micro-injector output data permit exact knowledge of the injected fluid volume, it is possible to perform dynamic contact angle measurements also with ADSA-D.

Fig. 3. Schematic representation of the set-up.

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Fig. 4. Schematic representation of the specimen preparation.

The complete set-up is computer controlled by a user-friendly program (DINATEN) which is fully Windows integrated.

4.3. Specimen preparation In order to obtain reliable contact angle data extreme care in specimen preparation and storage and experimental proceedings is of primordial importance. Virtually ubiquitous contaminant molecules and particles readily adsorb spontaneously onto any surface except maybe extreme low-energy surfaces, and therefore the contact angle data often may characterize surface properties of the principal contaminants rather than of the material in study. To avoid surface exposure to contamination final surface preparation was always performed immediately before contact angle measurement.

4.3.1. The dentin surfaces Human third molars were used and prepared as follows: the middle of the root was sectioned and the pulp tissue was eliminated. Two stainless steel cannula tips were introduced in the radicular portion to provide a through-flow that allows cleaning and air bubbles elimination, and to apply the intrapulpal pressure. The tips were cemented with glass ionomer cement Aqua-Cem (Dentsplay, Konstanz, Germany). After this, the coronal upper third of specimens was sectioned parallel to the oclusal plane and a flat dentin surface was obtained. Then, a perpendicular perforation was done in the center of the dentin surface and a third stainless steel cannula was inserted and cemented with the above cement, as shown in Fig. 4. Then they were stored at 4 °C in physiologic solution for up to 2 weeks. Immediately before use, they were ground down gently by hand with sandpaper under a jet of water, successively from 500 to 4000 grit. After

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a soft final polish with water-soaked cellulose tissues they were cleaned with a jet of water under pressure. Intrapulpal pressure was attained filling the pulp chamber with saline solution and connecting the mounted tooth to a saline column. The column height was adjusted to 15 cm to provide the intrapulpal pressure [27].

4.3.2. The Teflon surfaces The teflon surfaces were chosen and prepared as model surfaces to be as chemically homogeneous as possible but rough: 2 cm cubic Teflon blocks were cut and 2 mm holes drilled perpendicularly in the centers of two adjacent faces, joining at the center of the cube. Next a Teflon tube with 2 mm outer diameter was pushed through the right-angled hole, connecting this way the top surface with one of the sides. The whole block was sonicated during 24 h in chromic-sulphuric acid and another 24 h in acetone. Next it was rinsed with propanol and with water, dried with filtered nitrogen and stored in propanol. Immediately before use the top surface was first ground gently by hand with 1200 grit sandpaper immersed in a fresh acetone– water emulsion, then ground with 4000 grit sandpaper under a jet of propanol. A part of the surfaces received directly the final cleaning with a jet of water under pressure, and the other part was previously polished, first with propanol-soaked cellulose tissues and then with water-soaked ones. 4.3.3. The bitumen surfaces The bitumen surfaces were chosen and prepared as model surfaces to be chemically heterogeneous but as smooth as possible: a 2 mm hole was drilled in the center of a small metal plate with border, and it was fixed on one of the above-mentioned Teflon blocks, pushing the Teflon tube through the hole until it protrudes about 3 mm. A small amount of bitumen was placed on plate, surrounding the capillary tip, and the whole block was placed in a clean glass cylinder and blown out with filtered nitrogen. Next the whole cylinder was closed and kept during 1 h at 90 °C in a clean, non-ventilating oven. At this temperature the bitumen is completely molten, and a perfectly smooth and horizontal surface is formed. After

this the whole cylinder is cooled in the refrigerator down to 60– 70 °C, a temperature at which the bitumen is still somewhat soft. As the contact angle of the liquid bitumen on Teflon is significantly higher than 90°, a small depression will have formed around the vertically protruding Teflon tube. Therefore, the tube was carefully pulled out a bit with clean pincers under a jet of nitrogen, and cut directly above the bitumen– Teflon contact line. Then the tube was pulled in again until leveling the contact line exactly with the bitumen surface. After this the whole glass cylinder was cooled in the refrigerator down to laboratory temperature.

5. Results and discussion The aim of this work was to develop a methodology able to produce reliable measures of lowrate contact angle hysteresis on dentin or other highly problematic, biologic surfaces. First of all, it is natural to ask if the contact line motion speed does not affect the measured contact angles. In fact, Hervert and deGennes’ model of a one-dimensional edge of a spreading drop [18], based on molecular considerations, predicts bending of the edge close to the contact line, which was confirmed experimentally by Chen and Wada [20]. Dussan et al., developed a model for moving contact lines in the limit of low capillary numbers Ca = 6v/k (6 is the contact line speed, v the viscosity and k the surface tension), which predicts microscopic viscous deviations from the static Laplace shape as well, and also confirmed it experimentally [23,34]. However, the magnitude of this deviation from the Laplace drop shape and the distance from the contact line where it is still noticeable, depend on the capillary number. As in our experiments the liquid was water and speed varied between 0.002 and 0.008 mm s − 1, Ca was always less than 10 − 7, and deviation from the Laplace-shape is expected to occur at distances in the order of microns, which are clearly below the optical resolution of our device (about 10 microns). Even a deviation up to, say, 100 microns, which has been measured only for capillary numbers in the range 0.01B Ca B 0.1 [22], would not

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significantly affect the obtained result, as it would affect no more than some tens of the about 1000 extracted profile points, which are fitted to the Laplace equation. Furthermore, in previous, independent experiments on Teflon model surfaces we could establish that the measured water contact angles were independent of the speed of contact line movement up to velocities of approximately 1 mm s − 1. In Fig. 5, you can see typical results of an ADSA-P measurement for pure water on dentin at T =23 °C. The whole experiment is divided in

Fig. 5. Typical result of an ADSA-P measurement of a water drop on dentin polished 4000 grit at T= 23 °C. The experiment is divided in three parts that correspond to drop growing, drop relax at constant volume, and drop shrinking. Contact angle, contact radius and drop volume are plotted as function of time. The latter is represented as given by the injector (injector) and as calculated by ADSA-P (ADSA-P). The uniform decrease of the shrinking contact angle at constant contract radius indicates line pinning: no real receding angle is obtained.

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three blocks corresponding to growing, relaxing and shrinking drop, and the contact angle, the contact radius and the drop volume are plotted as a function of time. The latter is represented as given by the injector (--) and as calculated by ADSA-P (--). For a perfectly axisymmetric drop and without any liquid loss due to evaporation or absorption the two measures should coincide. In the growing zone, meaningful contact angles do not start at zero volume, but only at a contact radius significantly greater than that of the drop alimentation cannula. Therefore, the first contact angle data not corresponding to uniform movement of the contact line should not be considered as representing the dentin properties. At times \ 30 s, a relatively uniform contact line movement yields an almost constant contact angle of qadvancing = (69.490.5)°. At t= 90 s the volume calculated by ADSA-P starts to deviate from the one given by the injector and remains smaller for the rest of the experience. This probably indicates that axisymmetry was lost and that the obtained contact angles are not average angles. But even if— at least from this point on— the numeric value of qadvancing is not trustworthy any more, it is still possible to extract some important qualitative information of the experiment. So, in the constant volume zone, the drop is relaxing towards slightly lower contact angle by increasing the contact radius up to a certain value where the contact line gets ‘pinned’, and both magnitudes remain constant until drop shrinking starts. Then a uniform decrease of contact angle at constant contact radius is observed, indicating that the contact line is still pinned and none of the measured angles is a (true) receding angle. For qB 25°, due to practical problems in edge detection, no reliable data could be obtained. Fig. 6 exhibits the results of a typical ADSA-D measurement under the same conditions, where axisymmetry is not a requirement. As here the volume is no output, only the volume given by the micro-injector is plotted. It exhibits exactly the same general features as the ADSA-P experiment: In the growing zone, from a certain minimum contact radius on the contact line moves uniformly, corresponding to a constant advancing

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Fig. 6. ADSA-D measurement of a water drop on dentin polished 4000 grit at T= 23 °C. The volume is plotted as given by the micro-injector. Due to line pinning no receding angle is obtained.

contact angle qadvancing =(77.9 90.9)°, which is reasonably independent of the actual contact line position, and may therefore be considered as characteristic for the dentin substrate. Further we observe a slight drop relaxation in the constant volume zone, and line pinning in the shrinking zone. For qB 10° no more data could be obtained due to drop collapse: as shown in Fig. 7, the drop splits in several droplets of unknown volume and therefore incomputable contact angle. So it can be concluded that the axisymmetry requirement of ADSA-P is probably too strong for the dentin surface. With ADSA-D dynamic drop experiments we can obtain a trustworthy advancing contact angle, but for the receding angle only an upper bound (12°) could be found. As the Laplace equation describes menisci of

drops as well as for bubbles, and as the solid–liquid –fluid system thermodynamics are in principle analogue for sessile drops and captive bubbles, it is natural to ask if: (a) the sessile drop receding angle is identical to the captive bubble advancing angle; and if (b) the sessile drop advancing angle equals the captive bubble receding angle. In (a), both cases correspond to a receding liquid front, i.e. the solid–liquid-interface is substituted by a solid–gas-interface, and we would expect both surfaces to be fully hydrated, and would suppose virtually no different behavior even for systems that naturally occur in a hydrated state. In (b), both cases correspond to an advancing liquid front. But while the captive bubble front is presumed to move on a fully hydrated surface, for the sessile drop front this is not necessarily the case. To verify experimentally these questions, one needs surfaces, on which measurement of advancing as well as receding angles for drops as well as for bubbles is technically possible. As hysteresis is believed to be caused basically by surface roughness and heterogeneity, two different model surfaces were chosen: the first should be as chemically homogeneous as possible but rough, and the second should be heterogeneous but as smooth as possible.As the first model surface Teflon was chosen, and prepared in the above-described manner in order to obtain a surface with a

Fig. 7. Micrograph of a collapsed water drop on dentin.

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Fig. 8. ADSA-P hysteresis measurement of first a sessile drop (squares), followed immediately by a captive bubble (circles) on the same homogeneous but rough Teflon model surface at T= 23 °C. The test liquid is water. The experiment is divided in two parts, corresponding to drop/bubble growing and shrinking, respectively. The computed drop (- -) and bubble (--) contact angle, contact radius and volume are plotted as function of time. As a check for axisymmetry, the volume plot also contains drop (solid line) and bubble (dotted line) volume, as given by the injector: (a) ground with 1200 +4000 grit sandpaper only; (b) ground with sandpaper and polished with cellulose tissue.

controlled and uniform roughness, as well as to rigorously eliminate any contaminant who may adhere to the surface during its preparation. For the second we selected an asphaltic bitumen, composed of a mixture of asphaltenes and resins and therefore inherently heterogeneous. The above-described melting/freezing procedure provided very smooth and flat surfaces. As the rigidity of these surfaces is limited (150– 200), surface deformation, probably due to the vertical component of the liquid surface tension, occurred if the contact line was allowed to stay at rest for sufficient time. For instance, a few hours lead to deformations visible to the nude eye, and on these surfaces a very large initial stick-and-slip step was observed. Rest times up to 1 min caused no

deformation detectable with our optical resolution, although sometimes a moderate initial stickand-slip step occurred. For that reason the drop/bubble relaxation part at constant volume was skipped of the experiments. For both surface types, immediately after final surface preparation a drop experiment was carried out, followed without delay by a bubble experiment. In Fig. 8(a) the typical result of such a ADSA-P drop-vs.-bubble experiment for water at T= 23 °C on a Teflon surface without final polish is shown. It is divided in two blocks corresponding to growing and shrinking drop/bubble; the contact angle, the contact radius and the drop volume are plotted as a function of time, for the

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drop as well as for the bubble. First of all, the volume plot now contains four curves: the drop volume as given by the injector (solid line) and as calculated by ADSA (solid - -), and the bubble volume as given by the injector (dotted line) and as calculated by ADSA (dotted --). The good agreement between the former two as well as between the latter two suggests that the drops as well as the bubbles are adequately axisymmetric. The growing drop angle grows with the drop volume at constant contact radius until contact line movement sets on. From this moment qadvancing drop is fairly constant and position-independent. At the start of drop shrinking the contact line gets pinned first and contact angle diminishes until the onset of contact line movement. Then qreceding drop remains reasonably invariable. The growing bubble contact line starts to move immediately, yielding a quite steady qadvancing bubble, only perturbed by a slight stickand-slip behavior visible in the small kinks in the angle and radius plots at t = 60 s. The bubble contact line also gets slightly pinned at the start of shrinking, but less, and contact angle increases until reaching a more or less constant qreceding bubble. The same experiment was repeated several times on the same surface, but rotating the specimen each time a bit, viewing it from a different orientation. The resulting contact angles were identical within the experimental error, indicating that in this type of surfaces the axisymmetry condition is fulfilled satisfactorily. The important feature is that qreceding drop and qadvancing bubble are identical within the experimental error, while qadvancing drop and qreceding bubble are not. The latter may be explained by different hydration states of the surface. Fig. 8(b) shows an analogue experiment for a Teflon surface with final polish. At the onset of growing, both drop and bubble exhibit an initial contact angle ‘overshot’: due to line pinning the growing contact angle increases/decreases beyond the corresponding qadvancing, towards which it relaxes by quick contact line movement during the following 15/45 s, respectively. At the start of volume extraction no ‘overshot’ is observed. The

shrinking drop angle decreases uniformly until it reaches a certain value, at which drop contact line movement sets on, and which is identical to the qadvancing bubble value. The shrinking bubble angle increases in an analogue manner until it attains the value of qadvancing drop, where the bubble contact line movement begins. But while qreceding drop remains constant within the experimental error and virtually identical to qadvancing bubble during the rest of the withdrawing process, qreceding bubble does not: it remains steady during the first part of the receding process, but once reached a certain contact radius it diminishes until attaining the advancing bubble value at the end of shrinking. This behavior, although unexplained, is perfectly reproducible. Again, the important conclusion is that for this homogeneous but rough model surfaces qreceding drop and qadvancing bubble are virtually identical in the whole measured contact radius interval. The same type of experiments was performed on the smooth-but-heterogeneous bitumen surfaces. The contact angles exhibited larger scatter, mainly due to stick-and-slip behavior. In Fig. 9(a), where a typical result of a bubble experiment is shown, you can observe the step-function-like discontinuities in the contact radius plot, and the corresponding saw-tooth-like ones in the contact angle plot, characteristic for stick-and-slip behavior. Nevertheless, the fair agreement between the volume as given by the injector (line) and the calculated one (- -) suggests that axisymmetry is acceptably fulfilled. Furthermore, as this technique permits to distinguish between meaningful and meaningless contact angles, it was possible to extract the most meaningful ones from every experiment, i.e. the ones corresponding to a more or less uniform contact line movement. So from this experiment, only the contact angles highlighted by the hatched squares were used for averaging with the results from other analogue experiments. In Fig. 9(b) these averages of over 800 individual angles corresponding to 16 experiments from four different view angles on four different surfaces are shown. Here, qadvancing drop and qreceding bubble agree quite well, and qreceding drop and qadvancing bubble coincide perfectly within the experimental error.

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Extrapolating from these model surfaces to real, i.e. rough and heterogeneous surfaces, we conclude that at least qreceding drop and qadvancing bubble coincide sufficiently to identify one with the other. In the case of qadvancing drop and qreceding bubble the situation is more complicated, and a more profound analysis should be made. The former allows us to use the advancing bubble angle on dentin surfaces to determine the hysteresis. In Fig. 10(a) typical result of a dynamic bubble measurement with ADSA-P for pure water on dentin 4000 grit at T = 23 °C is shown. The most striking feature is that contact angle behavior is symmetrical with respect to the direction of contact line movement, i.e. q depends

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slightly on contact radius, but no hysteresis is observed. The experiment was repeated on several specimens, and this behavior is perfectly reproducible. We also tested axisymmetry by rotating the specimen, and found that for bubbles on dentin this condition is fulfilled satisfactorily. The contact radius dependence could be interpreted in terms of line tension, using the wellknown modified Young equation [9]: klv cos q= ksv − ksl − kslvsgs, (3) where kslv is the line tension and sgs is the geodesic curvature of the contact line, which is equal to the inverse of contact radius for axisymmetric menisci. So the line tension is readily obtained from the slope of a plot of cos q vs. 1/R according to the dependence,

Fig. 9. (a) Typical ADSA-P bubble hysteresis measurement result on a bitumen model surface. The step-function-like discontinuities in the contact radius plot with the corresponding saw-tooth-like ones in the contact angle plot are characteristic for stick-and-slip behavior. As only contact angles corresponding to a more or less uniform contact line movement are meaningful, from this experiment only the contact angles highlighted by the hatched squares where extracted for averaging with the results from other analogue experiments. (b) Comparison of the advancing/receding drop/bubble contact angle of water on smooth but heterogeneous bitumen model surfaces at T= 23 °C. The angles are averages of over 800 individual ADSA-P dynamic contact angle measurements, obtained by selecting only the meaningful values from 16 experiments, each performed in the same way as in Fig. 9, on four different surfaces, each from four different view angles.

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contact angle has a fairly constant and contact line position-independent value of (6.99 0.9)°. The lack of hysteresis is probably related to the fact that under these conditions the highly hydrophilic dentin surface is completely hydrated.

6. Summary and conclusions

Fig. 10. Typical result of a captive bubble ADSA-P measurement at T= 23 °C on dentin polished 4000 grit. Same plot as in Figs. 5 and 6.

cos q = cos qr = −

ksl6 1 . kl6 R

(4)

But the plot of cos q vs. 1/R (not shown) shows a quite poor linear correlation (r =0.58), a commonly observed feature of non-ideal surfaces [35], which lead to the introduction of the non-thermodynamic pseudo line tension term [36]. In any case, for the magnitude of the line tension term expected from theoretical considerations as well as from other experimental studies [35], the effect of line tension on contact angle drop size dependence should be negligibly small for radii ] 1 mm. Furthermore, as the radius of the injection cannula is 1 mm, the contact angles corresponding to a contact radius less than 1 mm probably do not reflect exclusively the dentin surface properties but also those of the cannula material (steel). So if we consider only the q values for R \1 mm,

An experimental technique capable to measure accurately low-rate dynamic contact angles of drops and bubbles on highly non-ideal, biologic surfaces has been developed. It has been proved experimentally that on homogeneous-but-rough as well as on smooth-butheterogeneous model surfaces there is a correspondence between receding drop angles and advancing bubble angles. Identifying the advancing bubble contact angle with the receding drop angle, we are able to compute a measure of the drop contact angle hysteresis on biologic surfaces, where the receding drop angle is too low to be measured accurately. Namely, contact angle hysteresis of pure water at T= 23 °C on superficial dentin tissue ground down to 4000 grit and polished, was found to be (72.99 1.8)°. Taking into account that of the thermodynamic work of adhesion is given by the relation Wadh = klv(1+cos q), it follows that if qR B qA and klv does not vary as in our experiments, WR must be greater than WA, i.e. that contact angle hysteresis implies adhesion hysteresis [37]. Adhesion hysteresis is the part of the adhesion energy that cannot be recovered and is given by, DWadh = klv(cos qR + cos qA). Therefore, we can compute the adhesion hysteresis of our system to be DWadh = (589 1) mJ m − 2.

Acknowledgements This work was supported MAT98-0937-C02-01/02.

financially

by

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