Comment pubs.acs.org/Langmuir
Comment on “Solid−Liquid Work of Adhesion” ABSTRACT: In a recent article, Tadmor and co-workers (Tadmor, R., et al. Langmuir 2017, 33, 3594−3600) used a centrifugal adhesion balance (CAB) to detach liquid drops from solid surfaces. By orienting solid surfaces in their CAB such that normal and lateral surfaces were balanced, the debonding force acted perpendicularly to the surface and drops detached by the axisymmetric retraction of their contact line. The detachment force was used to estimate the work of adhesion. To match the work of adhesion values from CAB to those calculated from the Young−Dupré equation, relatively large contact angles were required. Here, an alternative interpretation of their results is offered. Receding contact angles were estimated from their data and then used to predict the work of adhesion. These alternative predictions of the work of adhesion agreed with their estimates from the CAB.
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n a recent article, Tadmor and co-workers1 showed how a centrifugal adhesion balance (CAB) can be used to detach liquid drops from solid surfaces. Three types of solid surfaces were used: clean hydrophilic glass, silicon rendered hydrophobic by treating with octadecyl trimethoxysilane, and microporous polytetrafluoroethylene (mPTFE). After attaching a solid surface to the rotary arm of their CAB,2 a water drop was deposited. The arm was rotated at progressively higher speeds. With increasing centrifugal force, the sessile water drops distorted. By orienting the solid surface in the CAB such that normal and lateral surfaces were balanced, the debonding force acted perpendicularly to the solid surface and drops detached by the axisymmetric retraction of their contact line. Figure 1 shows images of distorted water drops captured at the onset of detachment.
Table 1. Experimentally Determined Values of the Critical Normal Force ( fc), Critical Drop Radius (R), and Work of Adhesion (wf) from the CAB for Hydrophilic Glass, Hydrophobic Silicon, and mPTFE, along with Estimates of the Receding Contact Angle (θr) and Work of Adhesion (wθ) from Contact Anglesa Solid surface Hydrophilic glass Hydrophobic silicon Microporous PTFE
R (mm)
wf (mJ/m2)
θr (deg)
wθ (mJ/m2)
1377 361 487 74.5
2.93 1.14 1.52 0.47
71 50 51 25
0 46 45 111
72 50 51 26
a
wf values were computed by Tadmor and co-workers with eq 1. Values of θr were estimated here using eqs 5 and 6. Values of wθ are from eqs 8 and 9.
the hydrophobic silicon and mPTFE may be realistic advancing values, θ = 90° seems too large for clean glass. Here, an alternative interpretation of these important new results is offered. Detachment of drops occurred as the contact line receded. Therefore, it seems that the appropriate contact angle to consider is the receding contact angle (θr).8 Values of θr were not reported but can be estimated from their data as follows. Figure 2 depicts a distorted sessile drop on their CAB at the inception of detachment. To retract the contact line, the critical normal force (fc) must first equal and then exceed the lateral surface force ( fs) that anchors the perimeter of the drop to the solid surface,
Figure 1. Images of sessile water drops in a CAB. The images show distorted drops that have begun to detach from a solid surface: (a) hydrophilic glass, (b) hydrophobic silicon, and (c) mPTFE.
From the critical normal force required to initiate detachment ( fc) and the critical drop radius (R) where the contact line began to recede, Tadmor and coworkers estimated the work of adhesion (wf) as 1 wf = fc R /πR2 = fc /2πR (1) 2 Results from their CAB experiments are listed in Table 1. Their estimates of wf from normal force seem reasonable, ranging from 71 mJ/m2 for clean glass to 25 mJ/m2 for mPTFE. The authors compared their estimates of wf to work of adhesion values calculated using the Young−Dupré equation and contact angles (θ),3−7 wSL = γ(1 + cos θ )
fc (mN)
(2) Figure 2. Depiction of a sessile drop distorted by a CAB.
To match wSL to wf, relatively large contact angles were required. In the case of clean glass, wSL equaled wf only if θ = 90°. For the hydrophobic silicon and mPTFE, agreement required θ = 107° and 131°. Although the contact angles for © XXXX American Chemical Society
Received: July 16, 2017
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DOI: 10.1021/acs.langmuir.7b02476 Langmuir XXXX, XXX, XXX−XXX
Langmuir
fc = fs
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(3)
(4)
Combining eqs 3 and 4 and rearranging yields an expression for estimating θr ≤ 90° from the CAB, cos θr = fc /2πRγ
(5)
For θr > 90°, cos θr = −fc /2πRγ
(6)
Estimated values of θr are listed in Table 1. They range from θr = 0° for glass to 111° for mPTFE. These values are consistent with both the images of the receding drops shown in Figure 1 and with values reported in the literature for these types of surfaces.9−12 Now that we have estimates of the receding contact angles, those can be used to estimate the work of adhesion. Rather than employing the generic Young−Dupré equation, i.e., eq 2, an expression is developed for predicting the work of adhesion for this specific geometry (wθ). The work done in peeling the liquid from the solid (W) can be assessed by integrating the lateral surface force ( fs) along the retraction path (r) and dividing by the area of retraction (A),13,14 0
∫ fs ∂r W wθ = = 0R A ∫R 2πr ∂r
(7)
Substituting eq 4 into eq 7, integrating from r = R to r = 0, and simplifying produces an expression for the work of adhesion where θr < 90°,
wθ = γ cos θr
REFERENCES
(1) Tadmor, R.; Das, R.; Gulec, S.; Liu, J.; N’guessan, H. E.; Shah, M.; Wasnik, P. S.; Yadav, S. B. Solid−Liquid Work of Adhesion. Langmuir 2017, 33 (15), 3594−3600. (2) Tadmor, R.; Bahadur, P.; Leh, A.; N’guessan, H. E.; Jaini, R.; Dang, L. Measurement of Lateral Adhesion Forces at the Interface between a Liquid Drop and a Substrate. Phys. Rev. Lett. 2009, 103, 266101. (3) Young, T. An Essay on the Cohesion of Fluids. Philos. Trans. R. Soc. Lond 1805, 95 (1), 65−87. (4) Dupré, A. Théorie Mécanique del la Chaleur; Gauthier-Villars: Paris, 1869; Chapitre IX. (5) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; Wiley: New York, 1990. (6) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1992. (7) Schrader, M. E. Young-Dupré Revisited. Langmuir 1995, 11 (9), 3585−3589. (8) Gao, L.; McCarthy, T. J. Teflon is Hydrophilic. Comments on Definitions of Hydrophobic, Shear versus Tensile Hydrophobicity, and Wettability Characterization. Langmuir 2008, 24 (17), 9183−9188. (9) Johnson, R. E., Jr.; Dettre, R. H.; Brandreth, D. A. Wettability as a Measure of Contamination. Contam. Control 1968, 7 (8), 14−6. (10) Chen, W.; Fadeev, A. Y.; Hsieh, M. C.; Ö ner, D.; Youngblood, J.; McCarthy, T. J. Ultrahydrophobic and Ultralyophobic Surfaces: Some Comments and Examples. Langmuir 1999, 15 (10), 3395−3399. (11) Fadeev, A. Y.; McCarthy, T. J. Self-Assembly Is Not the Only Reaction Possible between Alkyltrichlorosilanes and Surfaces: Monomolecular and Oligomeric Covalently Attached Layers of Dichloro- and Trichloroalkylsilanes on Silicon. Langmuir 2000, 16 (18), 7268−7274. (12) Extrand, C. W. Contact Angles and Hysteresis on Surfaces with Chemically Heterogeneous Islands. Langmuir 2003, 19 (9), 3793− 3796. (13) Extrand, C. W.; Moon, S. I. Experimental Measurement of Forces and Energies Associated with Capillary Rise in a Vertical Tube. J. Colloid Interface Sci. 2013, 407 (1), 488−492. (14) Extrand, C. W. Forces, Pressures and Energies Associated with Liquid Rising in Nonuniform Capillary Tubes. J. Colloid Interface Sci. 2015, 450 (1), 135−140.
The lateral surface force can be estimated from the critical radius (R), surface tension (γ), and receding contact angle (θr) of the liquid drop, fs = 2πR(γ cos θr)
Comment
(8)
If θr > 90°, then wθ = −γ cos θr
(9)
Predictions of the alternative work of adhesion (wθ) from eqs 8 and 9 are listed in Table 1. They agree well with wf values from Tadmor’s CAB measurements. The findings described here provide additional evidence that the work of adhesion depends on the geometry of both the solid and liquid, which implies that a single equation cannot universally define the work done in wetting or dewetting. (In previous work, it was also shown that the work of adhesion for liquid rising in homogeneous and heterogeneous capillary tubes does not equate to values from the Young−Dupré equation.13,14)
C. W. Extrand*
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CPC, 1001 Westgate Drive, St. Paul, Minnesota 55114, United States
AUTHOR INFORMATION
Corresponding Author
*Tel: +1-651-999-1859. E-mail: chuck.extrand@cpcworldwide. com. ORCID
C. W. Extrand: 0000-0002-0330-9236 Notes
The author declares no competing financial interest. B
DOI: 10.1021/acs.langmuir.7b02476 Langmuir XXXX, XXX, XXX−XXX
