Low-rate dynamic and static contact angles and the determination of solid surface tensions

COLLOIDS AND ELSEVIER

Colloids and Surfaces A: Physicochemicaland EngineeringAspects 116 (1996) 63-77

A

SURFACES

Low-rate dynamic and static contact angles and the determination of solid surface tensions D.Y. Kwok, R. Lin, M. Mui, A.W. Neumann * Department of Mechanical Engineering, Universityof Toronto, 5 King's College Road, Toronto, Ont. MSS 3G8, Canada Received 29 November 1995; accepted 1 February 1996

Abstract

Low-rate dynamic contact angles of 17 liquids on a carefully prepared solid surface (FC-722 dip-coated on a mica surface) were measured by axisymmetric drop shape analysis-profile. It was found that low-rate dynamic contact angles are essentially independent of the velocity of the three-phase contact line and identical to the static advancing angles. The mean contact angles for each liquid were determined by averaging the contact angles at 10 different advancing rates. These angles were used to test different contact angle approaches for solid surface tensions. It was found that these experimental contact angles on the inert solid surface are consistent with the equation of state approach for interfacial tensions. The Fowkes and the Lifshitz-van der Waals/acid-base approaches were shown to contradict experimental contact angles.

Keywords: Axisymmetric drop shape analysis; Dynamic contact angle; Solid surface tension; Static contact angle

1. Introduction

In the vast majority of contact angle studies in the literature, the method used is direct measurement on sessile drops using a goniometer [ 1], by placing a tangent on the drop profile at the base of a solid surface. However, such a technique normally gives a contact angle accuracy of 0nly ___2 °. In addition, with respect to dynamic contact angle measurements, it is virtually impossible for this technique to determine contact angles at different velocities of the three-phase contact line. Recently, Li and Neumann [2] and Li et al. [3] have published accurate static contact angles of various polar and non-polar liquids on three wellprepared inert solid surfaces: a non-polar fluorocarbon (FC-721) dip-coated on mica, a non-polar * Corresponding author. 0927-7757/96/$15.00© 1996 ElsevierScienceB.V. All rights reserved PII 0927-7757(96)03590-X

heat-pressed Teflon (FEP) and a polar poly(ethylene terephthalate) (PET). These contact angle data are plotted in Fig. 1, where Ylv and 0 are, respectively, the liquid-vapour surface tension and the contact angle. As can be seen in this figure, the curves for the three solids are so smooth that one has to conclude that Ylv cos 0 depends only on two independent variables, y~ and Vsv ~lv COS 0 ~---F

(Yl~, Ys~)

(1)

There is no evidence for an additional and independent effect of intermolecular forces on contact angles. Because of Young's equation Ylv COS 0 = 7sv -- 7sl

(2)

the solid-liquid surface tension Ys~ can be shown to be a function of only Y~vand hv Y~ =f(7,v, Y~)

(3)

64

D. Y. Kwok et al./Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77

40.0 20.0

DFC721[21 OFC721[31 m F E P 12) APETI2]

~k...~. A

DMSO II-J~ _

0.0 Hexme /

/

\ l-B~monaphthalene ~

x,

"t4..~.~ " x ~ `ethyleneGlyc°l DMS

DiethyleneGlycol

-40.0

~

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Fig. 1. A plot of ?iv cos 0 versus Vlvon a FC-721 surface;data are from Refs. [2] and I-3]. The smoothness of the curves indicates that the values of Ylvcos 0 depend only on 7iv and 7s~.

These experimental results indeed confirm the existence of an equation of state relationship, i.e. Eq. (3). In addition, the values of 7,v calculated from the equation of state approach, using the contact angles of different polar and non-polar liquids, were found to be essentially constant. This further highlights the validity of this approach to determine solid surface tensions from contact angles. In comparison with other contact angle approaches for the same contact angle data, Kwok et al. [4,5] have shown that the Fowkes as well as the Lifshitz-van der Waals/acid-base approach are untenable. It should be noted that the experimental patterns shown in Fig. 1 are not always observed in the literature; curves far less smooth or no unique curves at all are sometimes reported. Such patterns can have a variety of causes. Accurate contact angle measurements require extreme experimental care. Even very minor vibrations can cause advancing contact angles to decrease, resulting in errors of several degrees. Surface roughness can affect contact angles and make Young's equation inapplicable. Swelling of the solid by the liquid can change the chemistry of the solid and hence the value of 7,v and 0 in an unpredictable manner. Therefore,

scatter due to such causes prohibits the application of all contact angle approaches; i.e. the equation of state approach as well as the surface tension component approaches. Because of their importance with respect to the 7sv determination and the present controversy in contact angle research, we want to double-check the results of Li and Neumann [2] and Li et al. [3] (who worked with static contact angles) by measuring low-rate dynamic contact angles at different velocities of the three-phase contact line using axisymmetric drop shape analysis-profile (ADSA-P) [-6-8]. ADSA-P is a versatile surface tension/contact angle technique, applicable to both pendant and sessile drops; it provides high accuracy and consistency for surface tension and contact angle measurements. It has been applied to ultralow liquidliquid interfacial tensions [9,10], the pressure dependence of liquid-liquid interfacial tensions [ 11 ], film balance experiments with insoluble films [12] and soluble films [13], a variety of studies on the time dependence of liquid-liquid interfacial tensions in the presence of surface-active materials [14-16], the drop-size dependence of contact angles and line tension [-17-19], contact angle

D. Y. Kwoket aL/ColloidsSurfacesA: Physicochem.Eng. Aspects116 (1996) 63-77

measurements with an accuracy exceeding other methods by an order of magnitude [2,3], and contact angle kinetics of protein solution [20]. ADSA-P has also been employed by other laboratories in various surface tension and contact angle measurements [21,22]. On carefully prepared solid surfaces, the measurements of contact angles using ADSA-P typically yield a contact angle accuracy of better than 0.3 ° [2,3]. In this work, a series of low-rate dynamic contact angles of 17 polar and non-polar liquids on a fluorocarbon (FC-722) dip-coated mica surface are reported. As will be seen later, these low-rate dynamic contact angles are identical to the static angles and hence, they reconfirm the soundness of the experimental protocol used by Li and Neumann [2] and by Li et al. [3]. The reason why we choose FC-722 (which is very similar to the FC-721 used by Li and Neumann and Li et al.) as our test solid is not because it is a non-polar surface, but because (1) it is a very smooth and inert surface; and (2) it has a low solid surface tension, allowing us to measure contact angles of various liquids with different surface tensions and molecular properties (intermolecular forces). It should be noted that the equation of state approach [23,24] as well as the surface tension component approaches [25,26] for determining solid surface tensions are all symmetrical, i.e. either of the two phases in the governing equation of these approaches can be chosen as the solid or the liquid phase.

2. Materials (solid surface and liquids) A near-perfect surface was chosen for the dynamic contact angle experiments: a fluorocarbon, FC-722, dip-coated on a mica surface. FC-722, a 3M company "Fluorad" brand "fluorochemical" coating, available as a 2% solution, was used as supplied; using a dip-coating technique [2] it was coated on freshly cleaved mica surfaces. Before dip-coating, the mica surfaces were prepared by the following procedure. (1) Mica sheets were cut into small mica plates about 1 in x 2 in in size; (2) a hole about 1 mm in diameter was made by drilling, in the centre of each mica surface; (3) each

65

mica surface was then cleaved by a sharp knife, cleaned with ethanol and acetone, and dried in the air before dip-coating. The mica sheets were supplied by Asheville-Schoonmaker Mica Co. (Newport News, VA). It should be noted that the hole in the centre of each mica surface was made in order to allow the formation of the sessile drop by pumping the liquid from below the solid surface using a motorized syringe mechanism (see below). This is to ensure that the measured angles are indeed the advancing contact angles. In the literature, it is customary to first deposit a drop of liquid on a given solid surface using a syringe or a Teflon needle; the drop is then made to advance by supplying more liquid from above using a syringe or a needle in touch with the drop profile. Such experimental procedures cannot be used for axisymmetric drop shape analysis (ADSA), since ADSA determines the contact angles and surface tensions based on the complete and undisturbed drop profile. Seventeen liquids were chosen in this study. The selection of these liquids was based on the following criteria: the liquids (1) should include a wide range of intermolecular forces; (2) they should be nonreactive with the solid surface; and (3) they should be non-toxic. They are, in the order of increasing surface tension: decane, 1-pentanol, trans-decalin, hexadecane, 1-decanol, cis-decalin, ethyl cinnamate, dibenzylamine, dimethyl sulfoxide (DMSO), 1-bromonapthalene, diethylene glycol, ethylene glycol, diiodomethane, thiodiethanol, formamide, glycerol and water. The physical properties and surface tensions of these liquids are shown in Table 1.

3. Methods and procedures 3.1. Axisymmetric drop shape analysis-profile (ADSA-P )

ADSA-P is a technique for determining liquidfluid interfacial tensions and contact angles from the shape of axisymmetric menisci, i.e. from sessile as well as pendant drops. The strategy employed is to fit the shape of an experimental drop to the theoretical drop profile according to the Laplace

D. Y. Kwok et al./Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77

66

Table 1 Density, purity and surface tension of the liquids used Liquids

Supplier

Decane l-Pentanol

trans-Decalin Hexadecane 1-Decanol

cis-Decalin Ethyl cinnamate Dibenzylamine DMSO 1-Bromonapthalene Diethylene glycol Ethylene glycol Diiodomethane Thiodiglycol Formamide Glycerol Water

Caledon Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Sigma-Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Baker analyzed LAST s

Purity

99.98% 99 + % 99% 99 + % 99 + % 99% 99% 97% 99.9% (HPLC) 98% 99% 99 + % 99% 99 + % 99.5 + % 99.8% Doubly distilled

Density (g cm-3)

~lv (mJ m-2)

Surface tension

0.730 0.811 0.870 0.773 0.829 0.897 1.049 1.026 1.101 1.489 1.118 1.113 3.325 1.221 1.134 1.258 0.997

23.88 + 0.008 26.01 + 0.09 27.19 ± 0.08 27.62 ± 0.005 28.99 + 0.004 32.32 ± 0.01 37.17 + 0.02 40.80 __+0.06 42.68 ___0.09 44.31 + 0.05 44.68 ± 0.03 47.55 ± 0.02 49.98 ± 0.02 56.26 ± 0.004 59.08 ± 0.01 65.02 ± 0.04 72.70 ± 0.09

No. of drops

10 10 10 10 10 7 10 9 10 7 9 10 10 10 10 8 10

" Laboratory of Applied Surface Thermodynamics.

3.2. Experimentalprocedures

equation of capillarity Ae =

+

(4)

using the surface (interfacial) tension 7 and, in the case of a sessile drop, the contact angle as the adjustable parameters; AP is the pressure difference across the liquid and fluid phases, and R~ and Rz are the two principal radii of curvature of the drop. The best fit identifies the correct surface (interfacial) tension and, in the case of a sessile drop, the contact angle. Details of the methodology can be found elsewhere [6]. The experimental set-up for ADSA-P pendant and sessile drops is shown in Fig. 2. Sessile drop experiments were performed by ADSA-P to determine the contact angles. However, it has been found that, since ADSA assumes an axisymmetric drop shape, the values of the liquid surface tensions measured from sessile drops are very sensitive to even a very small amount of surface imperfection, such as roughness and heterogeneity, while contact angles are less sensitive. Therefore, in order to obtain more accurate results, the liquid surface tensions used in this study were measured by applying ADSA to a pendant drop.

In pendant drop measurements, a liquid drop was formed at the tip of a Teflon capillary inside a sealed quartz cuvette, so as to prevent evaporation and vibration due to air currents in the laboratory. Usually 10 drops for one liquid were measured, and at least 20 pictures were taken for each drop. These pictures were automatically stored in the computer. Subsequently, the surface tension of each liquid was calculated from each picture by ADSA-P. The averaged surface tensions of each liquid are shown in Table 1. To perform dynamic contact angle measurements for sessile drops, a motor-driven syringe is employed in the experimental set-up shown in Fig. 2. The dynamic advancing and receding contact angle measurements can be performed, respectively, by pushing or pulling the syringe plunger of a motorized syringe mechanism, leading to an increase or decrease in the drop volume. A schematic of this mechanism is shown in Fig. 3. In this work, dynamic contact angle measurements at ten different velocities of the three-phase contact line were studied for each liquid. In the actual experiments, an initial liquid drop

67

D. Y. Kwok et al./Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77

ADSA-P Pendant Drop digitizer

monitor

computer

terminal

diffuser

light ~ source

pendant drop

microscopeand videocamera

ADSA-P Sessile Drop diffuser I sessill~ light

source

~

> ~--~2:2~--] microscopeand videocamera

digitizer

:>

monitor

--

computer

terminal

MotorDrivenSyringe Fig. 2. A schematicof the experimentalset-upfor ADSA-Ppendantdrop and sessiledrop experiments. about 0.3 cm in radius was carefully deposited, covering the hole on the surface. This is to ensure that the drop will increase axisymmetrically in the centre of the image field when liquid is supplied from the bottom of the surface using a motorized syringe mechanism. The motor in the motorized syringe mechanism was then set to a specific speed by adjusting the voltage by means of a voltage controller. Such a syringe mechanism pushes the syringe plunger, leading to an increase in the drop volume and hence the three-phase contact radius. This advancing drop was then recorded in a sequence of pictures by the computer until the three-phase contact radius is about 0.5cm or larger. Since ADSA-P determines the contact angle and the three-phase contact radius simultaneously for each picture, the advancing dynamic contact angles as a function of the three-phase contact radius (i.e. location of the surface) can be obtained.

The actual rate of advancing was determined by linear regression, by plotting the three-phase contact radius over time. Different advancing rates were studied by adjusting the voltage by means of a voltage controller. The mean contact angle for a specific advancing rate was obtained by averaging the measured contact angles after the three-phase contact radius reached 0.4-0.5 cm (see below). The purpose of choosing these relatively large drops was to avoid any line tension effects on the measured contact angles. It should be noted that measuring contact angles as a function of the three-phase contact radius has an additional advantage: the quality of the surface is observed indirectly in the measured contact angles. If a solid surface is not very smooth, irregular and inconsistent contact angle values will be seen as a function of the three-phase contact radius.

68

D. Y. Kwok et al./Colloids Surfaces A." Physicochem. Eng. Aspects 116 (1996) 63-77

I E a. Liquid b. Solid c. Stage d. Syringe e. Motor f. Driving Mechanism

C

Forward

e

I

•

"

Backward

I

Fig. 3. A schematic of a motorized syringe m e c h a n i s m for dynamic contact angle experiments.

In this work, a total of more than 150 pieces of mica surfaces were prepared and used; a new mica surface was always used for each dynamic contact angle experiment. Furthermore, at least 40 pictures were acquired for each experiment by ADSA-P, i.e. more than 7000 pictures were acquired and analyzed. This amount of contact angle data cannot be obtained easily by a conventional goniometer technique.

4. Results and discussion

Fig. 4 shows a typical example of a low-rate dynamic contact angle experiment: 1-bromonapthalene on a FC-722 surface. As can be seen in this figure, increasing the drop volume V linearly from 0.8 to 0.9 cm 3 by means of the motorized syringe mechanism increases the contact angle 0 from about 90 to 94 ° at an essentially constant three-phase contact radius R. This is due to the fact that even carefully placing an initial drop from above on a solid surface can result in a

contact angle somewhere between advancing and receding. Therefore, it takes time for the initial drop front to advance. Further increase in the drop volume causes the three-phase contact line to advance, with 0 remaining essentially constant as R increases. Increasing the drop volume in this manner ensures the measured 0 to be an advancing contact angle. The advancing rate for this experiment can be determined by linear regression from the linear region of the plot of the three-phase contact radius vs. time; it was found that the drop periphery was being advanced at a rate of 0.270 mm min -1 in the specific example given in Fig. 4. The regression coefficient for the advancing rate was found to be 0.999; this indicates that the rate of change of the three-phase contact line was very constant, even though it was controlled only by manipulating the drop volume. As can be seen in Fig. 4, the measured contact angles are essentially constant as R increases. This indicates good surface quality of the solid used in this experiment. It turns out that averaging the measured contact angles after R reaches 0.45 cm is

D. Y. Kwok et aL /Colloids Surfaces A." Physicochem. Eng. Aspects 116 (1996) 63 77

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0,80 100.0

200.0

Time [sec.] Fig. 4. Results of the low-rate dynamic contact angle experiment involving 1-bromonapthalene on a FC-722 surface. The

0.0

100.0

200.0

Time [sec.]

advancing rate for the three-phase contact line is 0.270 mm min-1. The mean contact angle is found to be 93.84°.

Fig. 5. Results of the low-rate dynamic contact angle experiment involving thiodiethanol on a FC-722 surface. The advancing rate for the three-phase contact line is 0.289 mm min-1. The mean contact angle is found to be 104.61°.

convenient, since the drop is guaranteed to be in the advancing mode and that line tension effects are negligible [ 1 7 - 1 9 ] . Averaging the measured contact angles, after R reaches 0.45 cm, yields a mean contact angle of 93.84 ° for 1-bromonapthalene. While a three-phase contact radius of 0.45 cm seems to be an arbitrary value, it turns out that there is virtually no difference between averaging 0 for R larger than 0.45 and 0.5 cm; the contact angles are essentially constant after R = 0.45 cm. Fig. 5 shows a similar dynamic contact angle experiment with thiodiethanol. As can be seen in this figure, increasing V from 0.9 to 1.4 cm 3 by means of the motorized syringe increases R from 0.4 to 0.52 cm, with an essentially constant 0. The advancing rate for this experiment was determined, by linear regression from the plot of the R vs. time, to be 0.289 m m min-1; the regression coefficient was found to be 0.999. Averaging the contact angles

after R reaches 0.45 cm yields a mean 0 value of 104.61 o. It was found that a slight slip and stick occurred for water and 1-pentanol. Fig. 6 shows dynamic contact angle results for water. Again, after an initial increase of the drop volume at constant R, 0 reaches its appropriate advancing value, i.e. as the drop volume increases from 1.3 to 1.4 cm 3, the water contact angle increases from about 108 to 120 °. Suddenly, 0 decreases from 120 to about 118 ° and the three-phase contact line starts to move as V increases. This indicates that the water drop was initially sticking on the FC-722 surface. Further increase in V causes the three-phase contact line to advance at an essentially constant 0 of about 118 ° . From linear regression, it was found that the drop was advancing at 0.143 m m min -1 (regression coefficient, 0.999); averaging the contact angles after R reaches 0.5 cm yields a mean water contact angle of 118.41 ° Another example of slip/stick behaviour is

D. Y. Kwok et al./Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77

70 125.0

78.0

~

120.0

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74.0

110.0

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.

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i

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0.90

1.20

0.70

0.0

[~ 100.0

200.0

300.0

400.0

500.0

Time [sec.]

Fig. 6. Results of the low-rate dynamic contact angle experiment involving water on a FC-722 surface. The advancing rate for the three-phase contact line is 0.143 mm rain-1 The mean contact angle is found to be 118.41°. shown in Fig. 7 for 1-pentanol. As the drop volume increases from 0.8 to 0.85 cm 3, 0 increases linearly from 70 to 76 ° at essentially constant R, and then suddenly decreases to 75 ° and the three-phase contact line starts to move. Further increase in V causes slight slip/stick behaviour, as can be seen from the inconsistency of the contact angles and the non-linearity of the plots of the three-phase contact radius versus time and the apparent volume versus time. After R reaches 0.5cm, slip/stick behaviour becomes less prominent; averaging the contact angles, after R reaches 0.5 cm, yields a mean 0 value of 74.20 °. The advancing rate for this experiment was found to be 0.286 m m m i n - 1 by linear regression (regression coefficient,

0.997). It should be noted that 1-pentanol could stick severely on the FC-722 surface; Fig. 8 shows such an experiment. As the drop volume increases initially, 0 increases from about 72 to 75 ° at constant R. Suddenly, the three-phase contact line jumps to

0.0

i

50.0

_

,

h 100.0 Time [sec.]

J 150.0

L 200J

Fig. 7. Results of the low-rate dynamic contact angle experiment involving 1-pentanol on a FC-722 surface, with slightly slip and stick behaviour. The advancing rate for the threephase contact line is 0.286 m m m i n - 1. The mean contact angle is found to be 74.20 ° (see text).

the next location, and the contact angle decreases from 75 to about 73 °. As V continues to increase, 0 increases from 73 to about 76 ° at essentially constant R. This slip/stick behaviour repeats itself several times. Obviously, these observed contact angles cannot all be the Young contact angle, since ~sv, 7lv (and ~sl) are constant, so that because of Young's equation, 0 ought to be a constant. Therefore, such contact angle results were not used to deduce solid surface tensions. The experimental patterns in Fig. 8, of course, cannot be easily observed and determined using a conventional goniometer technique. Thus, if one performs such an experiment using a goniometer technique, the slip/stick behaviour (in Fig. 8) may not be observable; hence a contact angle incompatible with Young's equation may result, leading to an experimental pattern slightly different from those shown in Fig. 1. Experimental patterns different from those shown in Fig. 1 therefore do not necessarily

D. Y. Kwok et aL/Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77 t O l U

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imply that the equation of state relationship is invalid or the surface tension component approaches are correct. Other experimental patterns of contact angle data could be caused by surface roughness and non-inertness of solids which may result in contact angles incompatible with Young's equation. It should be noted that such contact angles prohibit the application of all contact angle approaches, since all approaches assume the validity of Young's equation. We have also performed dynamic/static contact angle experiments. A liquid drop is first selected to advance at a specific advancing rate and is then halted, while a sequence of images are recorded. A typical experiment is shown in Fig. 9 for cis-decalin. As the drop volume increases from 0.56 to 0.72 cm 3, the three-phase contact line advances from about 0.36 to 0.41 cm at a rate of 0.412 mm min-1 (regression coefficient, 0.999). A sequence of drop images was acquired after the motor was stopped at R=0.41 cm. As can be seen in Fig. 9,

0.0

50.0

100.0

150.0

Time [see.] Fig. 9, Results of the dynamic/static contact angle experiments involving cis-decalin on a FC-722 surface. This result suggests that the dynamic contact angle 0dy. is identical to the static contact angle 0st~t. It also reconfirms the experimental protocol used by Li and Neumann 1-2] and Li et al. E3] to measure static contact angles.

the contact angle is independent of the low advancing rate; this result suggests that the low-rate dynamic contact angle Ody, is identical to the static contact angle 0,tat. This result reconfirms the experimental protocol used by Li and Neumann [2] and Li et al. I-3] to measure static contact angles and is also in good agreement with recent work to determine low-rate dynamic contact angles by the automated capillary rise technique [27]. A summary of the low-rate dynamic contact angles for the 17 liquids is shown in Table 2. With each liquid, 10 different measurements (i.e. 10 different advancing rates on 10 new surfaces) were performed. It can be seen that these dynamic contact angles are essentially independent of the velocity of the three-phase contact line, as is, in principle, obvious from Fig. 9. Since the low-rate dynamic contact angles in Table 2 are essentially independent of the velocity of the three-phase

D. Y. Kwok et al./Colloids Surfaces A. Physicochem. Eng. Aspects 116 (1996) 63-77

72

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contact line, a mean dynamic contact angle for each pure liquid was determined by averaging the contact angles at 10 different advancing rates. Fig. 10 shows the low-rate dynamic contact angle results in Table 2, in a plot of ?iv cos 0 versus 7~v. It can be seen that the values of 7~v cos0 change smoothly as 7~v increases. Thus, the values of 71v cos 0 are a function of only 7~v and 7sv. Because of Young's equation, the value of 7s~ can be expressed as a function of only Ylv and Ys~, in good agreement with the equation of state approach for interfacial tensions. The Fowkes [25] and the Lifshitz-van der Waals/acid-base [26] approaches, on the other hand, stipulate that the value of 7~ cos 0 should be a function of not only 71~ and Y~, but of surface tension components (intermolecular forces) as well. This stipulation is contradicted by the data summarized in Fig. 10. Using the experimental contact angles in Table 2 and liquid surface tensions in Table 1, the values of ?s~ for a FC-722 dip-coated mica surface, calculated from the equation of state approach, are shown in Table 3. It can be seen that the calculated values of the solid-vapour surface tensions 7~ are essentially constant. The consistency in the values of 7s~ further reconfirms the validity of the equation of state approach for determining solid surface tensions. It should be noted that the empirical equation of state was not calibrated using these data. It was calibrated using the contact angle data of Li and Neumann [2] (also shown in Table 3). Averaging the ys~ values for FC-722 yields a mean Y~ of 12.11 ___0.25 mJ m -2. Let us now focus on the experimental contact angles in Table 2. Since alkanes and FC-722 are non-polar, according to the Fowkes approach [25], the solid surface tension can be determined from the experimental contact angles and surface tensions. Table 4 shows the 7s values of FC-722 using the Fowkes approach. They were calculated using the experimental contact angles and surface tensions of decane, hexadecane, cis-decalin, transdecalin, 1-bromonapthalene and diiodomethane in Table 2. It turns out that the calculated 7~ values vary from 8.3 to 11.2; a mean 7~ value of 10.4 was obtained by averaging these values. Knowing this ?s value, the putative dispersive liquid surface tension components yd, for the polar liquids in Table 2,

74

D. Y. Kwok et al./Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77 30.0

/ Decane [ l-Pentanol

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80.0

7,,

Fig. 10. A plot of ~lv cos 0 versus ~)lvon a nearly perfect FC-722 surface. This experimental result suggests that the values of Y~v depend on only 7iv and 7,v, and not directly on intermolecular forces. Table 3 A summary of the surface tensionsa and mean low-rate dynamic contact angles of 17 pure liquids on FC-722 dip-coated mica surface Liquid

Decane 1-Pentanol

trans-Decalin Hexadecane 1-Decanol

cis-Decalin Ethyl cinnamate Dibenzylamine DMSO

1-Bromonapthalene Diethylene glycol Ethylene glycol Diiodomethane Thiodiethanol Formamide Glycerol Water

This work, FC-722

Li and Neuman I-2], FC-721

~21v

0

~)sv

~"v

0

~sv

(mJ m -2)

(Deg)

(mJ m -z)

(mJ m 2)

(Deg)

(mJ m-2)

23.88 26.01 27.19 27.62 28.99 32.32 37.17 40.80 42.68 44.31 44.68 47.55 49.98 56.26 59.08 65.02 72.70

67.36 72.95 73.38 75.94 78.84 79.56 86.54 90.70 90.95 93.81 94,22 97.87 10 I. 18 104.56 108.49 111.73 118.69

11.87 11.46 11.92 11.39 11.18 12.44 12.21 12.21 12.88 12.44 12.43 12.11 11.70 12.67 11.98 12.75 12.23

23.43 -29.50 27.76 -31.65 38.37 40.63 43.58 44.01 45.04 47.99 -54.13 57.49 63.11 72.75

65.97 -76.71 75.32 -79.87 88.20 92.06 94.47 95.29 96.84 99.03 -103.73 107.32 111.38 119.05

11.98 -12.03 11.63 -12.04 12.11 11.64 11.90 11.75 11.56 11.82 -12.20 11.90 12.17 12.06

Mean

12.11 + 0.25

11.91 __+0.12

a The values of 7,v were determined using the equation of state approach for interfacial tensions. c a n be c a l c u l a t e d f r o m t h e F o w k e s a p p r o a c h a n d are s h o w n in T a b l e 5. It c a n be seen in T a b l e 5 t h a t the c a l c u l a t e d 71a

v a l u e s for 1 - p e n t a n o l , 1 - d e c a n o l , ethyl c i n n a m a t e , dibenzylamine and DMSO are essentially identical to t h e m e a s u r e d t o t a l l i q u i d surface tensions. T h e

D. Y. Kwok et aL /Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77 Table 4 The solid surface tensions calculated from the Fowkes approach, using dispersive liquids Liquid

Y~v" (mJ m -2)

0b (Deg)

~s = ya (mJ m -2)

Decane trans-Decalin Hexadecane cis-Decalin 1-Bromonapthalene Diiodomethane

23.43 27.19 27.62 32.32 44.31 51.00

67.36 73.38 75.94 79.56 93.81 101.18

11.24 11.24 10.67 11.27 9.65 8.29

Mean

10.39

The Lifshitz-van der Waals acid-base approach reverts to the Fowkes approach for totally dispersive systems and hence it yields the same 7s value, a From Table 1. b From Table 2.

Fowkes model, however, stipulates the y( values of polar liquids, such as alcohols and DMSO, to be much less than the total liquid surface tensions 71, depending on the polarity or non-dispersivity of the liquids. The Fowkes approach is clearly contradicted by these experimental results. Since the dispersive components of some liquids have been reported by Fowkes, it is instructive to compare these values with those in Table 5. These liquids are DMSO, diethylene glycol, formamide and water; the liquid surface tension components claimed by Fowkes are also reproduced in Table 5.

75

It can be seen that there are large differences between the yld values expected by Fowkes and those we obtained from experimental contact angles. For example, the putative dispersive surface tension component of water, according to Fowkes, should be 21.1; however, the y( value of water from the experimental contact angle is 34.4. The implications of the contact angle data of alcohols and water should be confronted with a claim of Fowkes [28] that we did not choose properly polar liquids in our previous work: "If water or alcohols, or any members of classes 1 or 2 had been used, the conclusions would have been in perfect agreement with the theories under attack" [28]. The results presented here re-affirm that this claim of Fowkes is false. Since the Lifshitz-van der Waals/acid-base approach [26] reverts to the Fowkes approach for a dispersive solid surface, it suffers the same deficiency as the Fowkes approach. However, only a few LW surface tension components for polar liquids have been reported by Good and van Oss 1-26] (see Table 5); they were given for DMSO, ethylene glycol, formamide, glycerol and water. It should be noted that, conceptually, the Fowkes' dispersive and non-dispersive surface tension components, respectively, are the same as the LW and AB surface tension components of the acid-base approach. Therefore, a similar test can be performed for the acid-base approach. In Table 5, the

Table 5 Comparison of the dispersive surface tension components Liquid

Ylv (mJm -2)

Calculated values based on Ys= 10.39 mJ m -2 y~ (mJm -2)

1-Pentanol 1-Decanol Ethyl cinnamate Dibenzylamine DMSO Diethylene glycol Ethylene glycol Thiodiethanol Formamide Glycerol Water

26.01 28.99 37.17 40.80 42.68 44.68 47.55 56.26 59.08 65.02 72.70

27.22 28.81 37.38 39.08 42.39 41.17 40.52 42.68 39.16 40.34 34.38

Fowkes et al. 1-29] y~ (mJ m -2)

Good and van Oss [26] ~w (mJ m -z)

D

m

m

29 32.3 -

-

28 -

-

21.1

36 29 39 34 21.8

76

D. Y. Kwok et al./Colloids Surfaces A: Physicochem. Eng. Aspects 116 (1996) 63-77

LW surface tension components calculated from experimental contact angles are far away from those which Good and van Oss claimed, except formamide. For example, the LW surface tension component for DMSO was claimed to be 36; however, for a constant 7s value of 10.4, the Lifshitz-van der Waals/acid-base approach predicts the LW surface tension components to be 42.4. It is apparent - - and in principle obvious from Figs. 1 and 10 - - that the surface tensions determine the contact angles completely, contrary to the basic assumptions of the Fowkes as well as the Lifshitz-van der Waals/acid-base model. Clearly, this does not mean that intermolecular forces are irrelevant; they determine the primary surface tensions 71v, ]?sv (and Y~l). However, intermolecular forces do not have an additional, independent effect on contact angles.

5. Conclusions (1) Axisymmetric drop shape analysis-profile (ADSA-P) is a very suitable technique for determining dynamic contact angles. Measuring dynamic contact angles as a function of surface location yields important information about the solid-liquid system that is not easily assessable by means of a conventional goniometer technique. (2) Low-rate dynamic contact angles are shown to be essentially identical to the static advancing contact angles. This reconfirms the experimental protocol used by Li and Neumann [2] and Li et al. [3], who worked with static contact angles. (3) Low-rate dynamic contact angles for various polar and non-polar liquids on a well-prepared FC-722 dip-coated mica surface are consistent with the equation of state approach for interfacial tensions. The 7sv values for FC-722 calculated from the equation of state approach are essentially identical, independent of the liquids chosen. (4) The Fowkes and the Lifshitz-van der Waals/ acid-base approaches for determining solid surface tensions are shown to clash with experimental contact angles.

Acknowledgements This research was supported by the Natural Science and Engineering Research Council of Canada (grants no. A8278 and no. EQP173469) and a University of Toronto Open Fellowship (D.Y.K.).

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[25] F.M. Fowkes, Ind. Eng. Chem., 12 (1964) 40. [26] R.J. Good and C.J. van Oss, The Modern Theory of Contact Angles and the Hydrogen Bond Components of Surface Energies; in. M. Schrader and G. Loeb (Eds.), Modern Approaches to Wettability: Theory and Applications, Plenum Press, New York, 1992, pp. 1-27. [27] D.Y. Kwok, C.J. Budziak and A.W. Neumann, J. Colloid Interface Sci., 173 (1995) 143. [28] F.M. Fowkes, J. Adhesion Sci. Technol., 1 (1987) 7. [29] F.M. Fowkes, F.L. Riddle, Jr., W.E. Pastore and A.A. Weber, Colloids Surfaces, 43 (1990) 367.