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Solid-Liquid Work of Separation Rafael Tadmor, Ratul Das, Semih Gulec, Jie Liu, Hartmann N’guessan, Meet Shah, Priyanka Wasnik, and Sakshi B. Yadav Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b04437 • Publication Date (Web): 25 Jan 2017 Downloaded from http://pubs.acs.org on February 17, 2017

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Solid-Liquid Work of Separation Rafael Tadmor*, Ratul Das†, Semih Gulec†, Jie Liu, Hartmann N'guessan†, Meet Shah, Priyanka Wasnik, Sakshi B. Yadav Dan F. Smith Department of Chemical Engineering, Lamar University, Beaumont TX 77710

Abstract We establish a tool for direct measurements of the solid-liquid work of separation. This method mimics a drop that is subjected to a gravitational force that is slowly increasing until the solidliquid contact area starts to shrink spontaneously. The work of separation is then calculated based on Tate’s law. The values obtained for the work of separation are independent of drop size and are in agreement with Dupré’s theory suggesting that it may equal the work of adhesion.

Introduction Surface tension was established as a measurable property in the nineteenth century. The work of adhesion, which is of great importance for solid-liquid contacts, was conceptualized thermodynamically at that time but did not achieve measurability till today. Specifically, in 1863 Wilhelmy introduced measurement of surface tension via Wilhelmy plate method;1 in 1864 Tate2 laid the foundation for measuring surface tension from a falling drop weight; and in 1869 Dupré

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constituted the conceptual relationship between the solid-liquid work of adhesion and the surface tension via contact angle measurements. These three methods are still extensively used, with the work of adhesion being restricted to an estimate via the Young - Dupré equation.3-26 The contact angle values needed in the Young - Dupré equation are obscured by contact angle hysteresis, and by an unknown difference between macroscopic and nano-scopic contact angle values. Thus, many papers use it qualitatively (see a good discussion by Staykova et al.27). When quantification is required, gaps appear between the calculated and otherwise expected values. For example, Kuna et al.11 suggested more than 100% error in the absolute work of adhesion value obtained by the Young-Dupré equation, while the results of Voitchovsky et al.24 suggested about 200% error in some cases, and so did Heepe et al.28 These papers show reasonable qualitative correlation to the Young- Dupré equation, but Defante et al.29 found it failing to provide suitable qualitative predictions. Therefore, "In the absence of any data on the energy of adhesion",4 the literature mentioned above demonstrates the need for independent experimental determination of the absolute value of the work of adhesion. To obtain the work of adhesion directly and independently from contact angle measurements one needs to separate the liquid from the solid. This was realized by Boreyko et al.30 who induced this separation by adding vibrational energy to the system. This allowed to obtain the work of adhesion as a proportionality because the intensity of the vibrations transferred to the drop was known only as a proportionality. We follow a similar logic but allow a controlled gradual increase of a force pulling the drop, and then calculate the work of separation based on Tate’s law.2 We call it work of separation rather than work of adhesion as more work needs to be done before this can be considered main stream work of adhesion.


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We first consider here Tate’s law for a falling drop weight method5 in which one forms liquid drops at an end of a tube, allowing them to fall into a container until enough have been collected to accurately determine the weight per drop. Tate’s law then determines the surface tension, γ. The ideal Tate’s law is5:

γ =

mg π Dtube

(1)

Where m is the mass of the liquid under the tube as the drop is just about to fall, g, the gravitational acceleration and Dtube is the diameter of the tube. Note, eq. (1) considers the entire weight of the liquid under the tube31 (see Supporting Information). Here we consider a system of a drop on a flat surface for which the detachment starts from the solid-liquid interface. Unlike the falling drop weight technique in which the drop weight is increased by inflating the drop, here we increase the weight by increasing the force field. In the Drop Weight method, the diameter is prescribed but the drop weight is measured (and is the main reason for the error in that system), while we prescribe a drop weight and measure the drop diameter (which is the main source of error in our system). In the Drop Weight method, the pinning of the liquid to the solid capillary dictates that the onset of the liquid-liquid separation starts from the width of the capillary. In our method, we look for a critical de-pinning beyond which, no pinning can stop the reduction in drop width (the stop in the triple line shrinkage is due to creation of a bell shape, which, as explained later, is an outcome of a spontaneous drop width reduction). To increase the drop’s weight, we use gravitational and centrifugal forces such that their lateral components cancel each other as their normal components are gradually increased. This is done


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with a modified Centrifugal Adhesion Balance (CAB) 18, 32 (see Supporting Information). Briefly, a CAB, presented schematically in fig. 1, consists of a centrifugal arm at the end of which there is a chamber with a camera and a sample holder (goniometer) in which a surface and a drop are placed. The sample holder can tilt perpendicular to the rotation. In the past, this tilt was done manually,32 and the new model includes a motorized, automated tilt that is synchronized with the centrifugal rotation. The CAB allows the user to measure forces and obtain visual drop data (drop diameter, drop height, contact angle etc.), as the camera rotates together with the drop, capturing live images and storing them in a computer nearby in the lab. Comparing the CAB work of separation to a regular goniometer we note that a goniometer is capable of measuring contact angles which suffer from contact angle hysteresis and an unknown difference between the molecular and macroscopic contact angles while the CAB measures the work of separation directly. Comparing the CAB to a Wilhelmi plate we note that a Wilhelmi plate can measure the advancing and receding contact angles for known liquid surface tension. This technique represents the force for moving a contact line of constant length along a surface. On the other hand, our technique represents the force required to shrink the triple line length up to a point beyond which the triple line length shrinks spontaneously. The constant triple line length of the Wilhelmi plate is sensitive to blemishes on the solid surface.6 The spontaneously shrinking triple line at the end of the CAB experimental run represents the stage beyond which the blemishes stopped influencing the retraction and therefore no extra force is required for the triple line to continue shrinking.


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Theory: The CAB, shown schematically in fig. 1, combines gravitational and centrifugal forces to manipulate normal and lateral forces according to eq. (2) and eq. (3)32:

f || = m(ω 2 R cosα − g sin α )

(2)

f ⊥ = m (ω 2 R sin α + g cos α )

(3)

Where f ⊥ and f || are the normal and lateral force acting on the drop, ω is the CAB angular velocity, R is the drop's distance from the CAB's center of rotation, α is the tilt angle with respect to the horizon, and m is the drop’s mass.

A

!

f || = 0

B

Fig. 1: A. Schematics of CAB alignment for total zero lateral force ( ω 2 R cos α = gsin α ). At this alignment the drop can only move (fly) normal to the surface. B. Some drop parameters used in this study.

Note that the Bond number,33 (e.g. Bo = ∆ ρ gr 2 γ L for regular gravitational filed), needs to be modified for our system to:


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Bo =

(

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)

∆ ρ ω 2 R sin α + g cos α r 2 or simply ∆ρ ( f ⊥ / m )r 2 Bo =

γL

γL

(4)

where ∆ ρ is the difference between the drop’s density to the medium’s one, and r is the height of the droplet. The Bo values vary from one experimental run to the other over a spectrum that ranges from 0.5 at the beginning of some experimental runs to 5 towards the end some other experimental runs. There is no Bo value that can be correlated with our experiment. In contrast, there is a single value for the work of separation for different drop sizes of the same system. This is not a proof that the work of separation is the work of adhesion, yet it suggests that it may be the work of adhesion. For our purpose, it is required to change the normal force when the centrifugal and gravitational components cancel each other in the lateral direction but add up in the normal direction. Such an alignment, seen in fig. 1, shows that f|| = 0 when:

tanα =

ω2R

(5)

g

Increasing ω while simultaneously changing α according to eq. (5) makes sure that the drop cannot move laterally while the combined normal force field increases (mimicking a drop that is subjected to a gravity field that increases gradually). This setup is similar to that of Boreyko et al.30 except the force inducing the solid-liquid separation is quantifiable. Both setups follow the Dupré gedanken experiment4 according to which, the solid-liquid work of adhesion, WSL, is given by: WSL = γS + γL – γSL

(6)


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Where γS, γL and γSL are the solid-liquid, liquid-vapor, and solid-vapor interfacial energies respectively. The Dupré equation (Eq. 6) combined with the Young-Laplace equation (Eq. 7),

cosθ =

γ S − γ SL γL

(7)

results in eq. (8), where θ is the contact angle that the liquid makes with the surface: W SL = γ L (1 + cos θ )

(8)

Eq. (8), which was derived by Dupré,3 is often called the Young-Dupré equation. It relates the work of adhesion to the equilibrium contact angle. In accordance with the falling drop weight technique, the work of separation per area equals the pull off (separation) force per triple line circumference. The separation force is not necessarily the adhesion force. For the separation force to equal the adhesion force, we need to require that the analogy to Tate’s law will be insensitive to the direction of the separation process, since the liquid-liquid separation is vertical to the solid-liquid separation. While such a requirement may be justified if we consider adhesion studies done on adhesive tapes34 (where peeling force is insensitive to the peeling direction for tapes with low elastic modulus), more studies are needed to justify it theoretically. Considering the adhesive tape understanding, in analogy to Tate law for measuring surface tension, the work of separation per area equals the pull off (adhesion) force per triple line circumference 5 i.e.:

WSL =

FD π DP

(9)


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where FD is the pull-off force, or the Dupré force and DP is the pull off diameter of the triple line: D represents the drop's diameter (see fig. 1(B)), and the index P stands for pull off. Eq. (6) shows that the work of adhesion per unit area is related to the contact area (π r2) just as surface energy per unit area is related to the surface area. Similarly, both properties can also be described as force per unit length and in both cases the length is perpendicular to the force35. This results in an equality of the force per length to the energy per area for the two properties. Since WSL is an intensive property, it does not depend on the length, i.e.: ∂ (FD (π D ) ) =0 ∂ (π D ) D = D

(10)

P

Graphically, this is presented schematically in fig. 2(A).

B

A

P Fig. 2: Schematics plotting the Dupré force variation with (A) the drop’s pull off circumference. (B) The drop’s circumference as a negative abscissa, superimposed on the drop retention force,

f ⊥ . Following f ⊥ intersection with FD (the negative abscissa represents a positive time axis), the circumference will need to continue decreasing spontaneously without further force investment as represented by the horizontal green line.


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Experimental Materials Silicon wafers were obtained from Virginia Semiconductor, VA (diameter: 76.2 mm ± 0.3 mm, orientation: ± 0.9°, dopant: Boron, resistivity: 0.0034-0.0046 Ω-cm, center thickness: 381 µm ± 25 µm) and cut into rectangular slides of 2 cm x 2 cm. Hydrogen peroxide (50 wt% in water) was obtained from Acros Organics. Ethanol (99.5%, 200 proof absolute), distilled water (0.1 µm filtered Molecular Biology Reagent), Ammonium Hydroxide (99.99%), Hydrochloric acid (37%), Toluene (99.5%), and Octadecyltrimethoxysilane (90% technical grade, CAS No. 3069-42-9) were obtained from Sigma Aldrich and used for the self-assembly process. 36

Centrifugal Adhesion Balance (CAB) The Centrifugal Adhesion Balance (CAB) used was a Wet Scientific model CAB15G14. CAB pictures are shown in fig. 3. The right side of fig. 3 shows a snapshot of the CAB while it is rotating. The CAB contains a centrifugal arm which can rotate perpendicular to the gravitational field using a DC motor. At one end of the arm there is a chamber with a plate on which a CCD camera is fixed together with a light source and a holder to place the substrate surface. This chamber can rotate around an axis orthogonal to the centrifugal rotation and concurrently with the centrifugal rotation allowing any combination of gravitational and centrifugal forces and hence independent manipulation of normal and lateral forces according to the equations given in the main text. Note that at any time during the rotation the chamber keeps changing as the centrifugal acceleration increases so that at every moment the lateral force on the drop is zero according to eq. (5). The CCD camera transfers the images wirelessly in real time to a computer nearby in the lab.


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Figure 3. Pictures of CAB model CAB15G14. Left: closed CAB; Right: the CAB interior.

Procedure Step 1: Surface hydrophilization The silicon wafers were made hydrophilic in one of the two methods below (both produced the same result). Method 1: The Silicon wafer substrate was rinsed in a copious amount of ethanol followed by distilled water and then dried in the oven at 100 °C for 30 minutes. From the oven the substrate was transferred to the UV/Ozone Cleaner for 45 minutes to remove any organic contaminants on the substrate. Alternatively, RCA® cleaning method can also be used. Method 2: To remove contaminants and unwanted particles (dust, silica, metals), the wafer was dipped in NH4OH: H2O2: H2O (1:1:5 v/v/v) at 70 °C for 15 minutes.37 Then, the surface was washed with DI water before being immersed in HCl: H2O2: H2O (1:1:6 v/v/v) at 70 °C for 5 min. After this, the surface was dipped in toluene three times for 30 s to create an organic environment for the silanization process. Both methods gave the same final results.


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Step 2: Silanization process Silanization took place by self-assembly process in a closed beaker. To achieve this, a solution of 1 volume % Octadecyltrimethoxysilane with 99 volume % toluene was prepared and heated up to 70°C. The silicon wafer substrate from step 1 was immediately immersed in this preheated solution and remained in it for 3 hours.37-39 The surface was then washed with water several times to remove any traces of toluene left on the surface before baking it in the oven at 80 °C for 45 minutes. Step 3: Experimental Procedure The experiments were conducted when the lab environment was at 23 ± 1 °C and 96% Relative Humidity inside the CAB chamber. The silanized silicon surface was placed in the CAB sample holder and near it a few satellite droplets were added to bring the system quicker to near saturation conditions.40-42 The water drops were dispensed on the surface and immediately covered with the hemispherical optical glass dome.

Results and Discussion In our experiment, the pull off force is one datum in a growing force curve, f ⊥ . The reasons for f ⊥ to grow are not related to the work of adhesion but rather to contact angle hysteresis whose

exact details18, 32 are not the topic of this paper which focuses on the work of separation and the work of adhesion. Nonetheless, we note that f ⊥ values increase as D decreases. Thus, if we superimpose the trend shown in fig. 2(A) on the curve of f ⊥ vs. D, we get qualitatively what is shown in fig. 2(B) (in which we also reversed the x axis so that it will be in the same direction as the time axis). To conceptualize the experimental procedure, we want to consider a decreasing


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circumference axis as shown in fig. 2(B). Once the functions cross, f ⊥ = FD and D = DP , the drop diameter, D, will decrease spontaneously, while the applied force-ramp will not have the time to increase significantly. This is marked as green line in fig. 2(B). To identify this value experimentally, we need to look for the first moment in the experimental plots in which: ∂f ⊥ =0 ∂ (π D )

(11)

At that point the force reaches the value of eq. (9), i.e.: (12)

f ⊥ = FD = π D PW SL

following which the triple line circumference will decrease at no additional force as implied from eq. (10). Further circumference reduction will be spontaneous. Fig. 4 shows selected pictures from the experimental run presented in supporting movie 1. There are two processes that occur in tandem: first, reduction in the solid-liquid interfacial area and second, drop elongation, namely increase in liquid-air interfacial area. The reason for this order is that the reduction in solid-liquid interfacial area forces a drop elongation due to mass conservation while the opposite is not true: drop elongation does not force a reduction in solidliquid surface area (unless the solid-liquid surface area is weaker which means that it retracts first). As the solid liquid area is reduced, the drop narrows mainly at the vicinity of the solid, and less at the drop apex (this is due to hydrostatic considerations: the lower hydrostatic pressure at higher locations equals the Laplace pressure at that point, and therefore the curvature is smaller or even negative (ending up in a bell shape)). This results in a new drop shape that has a narrower neck. At some point the force pulling on the drop above the neck will equal the neck


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capillary pulling force, and a liquid-liquid snap will occur. This happens long after the time at which a spontaneous reduction in the solid-liquid interfacial area is initiated (several frames). The point considered for the pull off is when the solid-liquid area starts to reduce spontaneously, namely without an increase in the force. The liquid-liquid separation occurs a few frames later as a result of the change in the drop shape that the solid-liquid retraction induces. In analogy to two springs in series (see Supporting Information) in which treating one of the springs can be done irrespective of the other, we treat only the solid-liquid area change, which is of importance for work of adhesion studies, leaving the drop elongation for another study. As the effective gravity pulling on the drop reaches -4.0 g (for this particular drop), the drop's diameter starts decreasing spontaneously.

Fig. 4: Pictures of water drops during a CAB run of an increasing effective gravity field which pulls on the drop from the silanized (C18) silicon surface (see Supporting Information) from which it is suspended.

As expressed in eq. (12), the important parameter is not the acceleration, but rather the force and the circumference. These are plotted in fig. 5: 5(A) and 5(C) show the overall trend, while 5(B) and 5(D) magnify the final stages. The first point in the experimental plot which obeys eq. (11) is marked with an arrow in fig. 5(B) and fig. 5(D). Taking values from the plot and substituting in eq. (9), we get from fig. 5(B):


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WSL =

f⊥ 487 µ N mJ = = 50.8 2 m π DP 9.58 mm

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(13)

and from fig. 5(D):

WSL =

f⊥ 361 µ N mJ = = 50.2 2 m π DP 7.19 mm

(14)

Fig. 5: Water drop triple line circumference on silanized (C18) silicon surface versus the effective gravitational force pulling on the drops. Drop sizes are 10.5 µL (A and B); 9.2 µL (C and D).


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The forces and the circumferences differ significantly,43 but their quotients, i.e. both W SL 's, remain similar. This is expected according to eq. (10) and fig. 2(A). Thus, the set of circumference and force couples of different experimental runs should make a straight line similar to fig. 2(A). This is shown in fig. 6. The linear trend of fig. 6 supports the Dupré theory, and provides a unique W SL value (which for our particular system is: 51.9 mJ/m2).

Fig. 6: A set of points for which different experimental runs like those shown in fig. 5 obey eq. (11) for the first time, together with a fit based on eq. (9) using WSL= 51.9 mJ/m2.

From eq. (8), the contact angle that corresponds to the work of separation above is 106°. This value is close to the apparent measured advancing angle (107°) suggesting that the nanoscopic value of the contact angle may be higher than the macroscopic (observed) one. This is in line with references,11, 24, 28, 29 which show measured apparent contact angles that are significantly lower than the angles back calculated from the work of adhesion. An apparent contact angle that is lower than the theoretically predicted one was also observed by Fan et al. who showed that the apparent macroscopic experimental cutoff to distinguish between hydrophobic and hydrophilic surfaces is lower than the theoretical microscopic 90° value.44


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A

90 87 84 81 78 100

200 300 400 Normal Force (µN)

500

Contact Angle (deg)

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Contact Angle (deg)

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96

B

90 84 78 72 120 180 240 300 360 Normal Force (µN)

Fig. 7. The apparent contact angle of (A) 10.5 µl and (B) 9.2 µl water drop on a silanized (C18) silicon versus force pulling on the drop.

Contact angle hysteresis is influenced, among other things, by surface roughness and surface heterogeneity. These parameters also influence the process of the liquid-solid separation. One can see in fig. 5 that the initial part of the curve (before the blue arrow) follows an irregular shape. In turn, this irregularity is related to irregular contact angles (see fig. 7) Nonetheless, the point at which the spontaneous separation occurs is the same, regardless of the way the drop made to that critical value. The surface used for the plots above is rather smooth and has a low contact angle hysteresis of 13.8º when measured under normal gravity conditions (with θA(1g) = 103º and θR(1g) = 89.2º). It is only when we modify the effective gravity that we obtain a higher contact angle hysteresis. From the above discussion, it seems that the visible (or apparent) contact angle hysteresis which is associated with various surface inhomogeneities, defects, or blemishes,6 can vary from drop to drop due to the large area of a typical drop (order of mm2). Yet, if the surface still has a majority of blemish free area at the triple line, once the pulling force is higher than the work of adhesion


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associated with the majority (clean) solid area, the triple line will start shrinking spontaneously regardless of the hysteretic way it made. The above discussion suggest that the measured work of separation may be close to the work of adhesion. To test this, we consider a solid-liquid interface of known work of adhesion: glass is known to form a nanometric water layer on it.45 Therefore, for a glass – water system, we are in practice separating water from water and expect to have the water surface tension as the work of adhesion (see Supporting Information). An example of such an experiment is shown in fig. 8, and the average value obtained for that system is 71.3 ± 2.4 mJ/m2.

Fig. 8: Water drop triple line circumference on a glass surface versus the effective gravitational force pulling on the drops (zoomed in on the end of the run).

The value obtained, 71.3 ± 2.4 mJ/m2, is in agreement with the classic Tate experiment and literature values. The macroscopic (observed) contact angle value of this system is roughly 20°


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which is in agreement with measurements of Pashley et al.45 and lower than the back calculated contact angle based on the work of separation experiments (but again corresponds well with references11, 24, 28, 29). Therefore, we conclude that our work of separation measurements correlate well with the thermodynamic work of adhesion. We also made some measurements with rough systems. Surface roughness plays a significant role in wetting phenomena. Similar to the way it influences spontaneous spreading (see for example the elegant studies in ref 46-47), it should also influence spontaneous triple line retraction, namely work of adhesion measurements. As in other wetting properties, it is expected to depend on whether the roughness results in a Wenzel or in a Cassie regime. It is expected that a Wenzel regime will result in a higher work of adhesion, while Cassie regime will result in a lower work of adhesion. Preliminary results that we obtained show that this is indeed the case, though a more detailed separate study should be devoted to this aspect. In the experiments shown above, a smaller droplet is left on the solid surface behind the flying drop, but sometimes the departing drop leaves a clean surface behind. In both cases the critical diameter is calculated in the same way, namely the point at which the drop starts shrinking spontaneously without the need to further increase the force. The spontaneous nature of the drop shrinking shows that the force pulling on it has just become higher than the solid-liquid adhesion. The existence, or lack, of a remainder drop, as explained above, is related to a later stage after the spontaneous solid-liquid area reduction which is already commenced and the work of separation which is already determined. In the few systems that we considered so far, we found for water drops that adhere to solids with work of separation that is lower than 30 mJ/m2 there is no drop left behind, and when it is higher than 30 mJ/m2 there is a drop left behind. For example


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we show in fig. 9, frames from a CAB experiment with water drops on a microporous layers (MPL) of polytetrafluoroethylene (PTFE), and in fig. 10 we show that for this system WSL < 30 mJ/m2 :

Figure 9. Pictures of water drops on a microporous layers polytetrafluoroethylene surface during a CAB run of an increasing effective gravity field. No droplet is left after the detachment.

Normal Force (µN)

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75

Triple line shrinks to 0

72 69 66 3.6

3.2 2.8 2.4 2.0 Circumference (mm)

Fig. 10. The force pulling a 4 µL water drop from MPL-PTFE surface versus drop's circumference at CAB run. (only the end of the run is shown). The work of separation that correspond to this series of images is 25 mJ/m2. Conclusion We apply an ever increasing effective gravity using Centrifugal Adhesion Balance, thereby forcing a drop to detach from a solid surface in the normal direction. From this we demonstrate


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how to directly obtain the work of separation. The values of work of separation correlate well with the expected work of adhesion and are irrespective of drop size or initial conditions in agreement with the Dupré equation. Below we compare our work of separation results with literature estimates for the work of adhesion. We consider these categories: (1) the work of adhesion based on the contact angle measurements (Young-Dupre equation) or theoretically predicted value (when exist); (2) surface tension of the liquid, and (3) work of adhesion comparisons that exists in the literature. These are summarized in the table below. Table 1: Comparing our work of separation with existing work of adhesion literature System /

Theoretical prediction work of adhesion, WSL

for Is WSL different Agreement from the liquid with Ref 11, Work of separation (WCAB) surface tension*? 24, 29 that: Wthermo < Wθ 2 2 Water drop separated from 50.3 mJ/m < WSL < 85.7 mJ/m Yes: Yes***: trimethoxy(octadecyl)silane (corresponding to the Young2 monolayer on silicon Dupre equation solved for 51.9 ± 1.5 mJ/m 51.9 2 < 66 mJ/m θA_max = 107.5º, θR_min = 79º)** 2 2 ≠ 72.5 mJ/m for WCAB = 51.9 ± 1.5 mJ/m water at 96% i.e. W(95º). relative humidity Water drop separated from WSL = 72.5 mJ/m2 if the water No: water nanolayer on Glass layer covering the glass can 2 71.3 ± 2.4 mJ/m2 slip; or 145 mJ/m if the water WCAB = 71.3 ± 2.4 mJ/m2 layer covering the glass cannot ≈ 72.5 mJ/m2 slip; for water at 96% relative humidity

Yes***: 71.3

SolidâLiquid Work of Adhesion - ACS Publications - American

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SolidâLiquid Work of Adhesion - ACS Publications - American