Langmuir 1994,10, 1323-1328
1323
Evaluation of the Lifshitz-van der Waals/Acid-Base Approach To Determine Interfacial Tensions D.Y.Kwok,t D.Li,t and A. W. Neumann*tt Department of Mechanical Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 1A4, and Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8 Received August 6,1993.I n Final Form: December 21,199P In an attempt to determine the solid surface tension components of the solid surfaces FC721, FEP, and PET, by using the Lifshitz-van der Waals/acid-base approach from the measurement of contact angles of different polar and apolar liquids, the solid surface tension components, ysLW, yse, and yse, were found to be inconsistent and strongly dependent on the liquids used. Accordingly, these solid surface tension components are not unique material properties of the solid surfaces and the acid-base approach is not applicable for the determination of solid surface tension components from contact angles. In addition, occurrence of negative values for the square root of 7.p and yse suggests questionable physical meaning of the solid surface tension components, 7s. and yse. It is also shown that the inconsistent and negative e yse are not a consequence of contact angle errors or errore in r~~~ values. values of y ~ and Introduction It is generally agreed that the measurement of the contact angle on a given solid surface is the most practical way to obtain the surface free energies or surface tensions, ysv and y s ~ the , solid-vapor and solid-liquid surface tension, respectively. The Fowkes and Lifshitz-van der Waaldacid-base approaches make use of contact angle measurements on a given solid surface to obtain the solid surface tension components,ysLw,yse, and yse and hence YSV and YSL. In this paper, previously published contact angle data are used in conjunction with the Lifshitz-van der Waals/ acid-base approach to determine the solid surface tension components, ysLW,yse, and yse, of three solid surfaces, fluorocarbon FC721, Teflon FEP, and PET. The FC721 and FEP surfaces are known to be dominated by the dispersive forces. This is, of course, of no consequence; there is no reason to use any specific kind of solid surfaces to test the Lifshitz-van der Waals/acidbase approach; the approach should be applicable to a variety of types of solids. Surface Tension Components The approach of surface tension components was pioneered by Fowkes.lP2 He proposed that the total surface tension can be expressed as a s u m of surface tension components, each of which arise due to a specific type of intermolecular forces:
y = yd
+ yn
That is, the total surface tension (y)is the sum of only the dispersive (yd) and nondispersive (yn) surface tension components. The dispersive and nondispersive surface tension components are often said to be the apolar and polar surface tension component, respectively; the apolar component includes the molecular interactions due to the London forces and the polar component includes all molecular interactions due to non-London forces. According to Fowkes? the solid-liquid interfacial tension y s can ~ be expressed by means of a geometric mean relation as (3) where the subscripts S and L refer to the solid and liquid phase, respectively. Equation 3 is supposed to be valid for the case where at least one of the phases (either solid or liquid) is completely dispersive. Under the assumption of negligible vapor adsorption (so that y ~ = v TL and ysv ys), the dispersive properties of either the liquid or solid can be calculated by combining eq 3 with the Young equation
-
cos e = Ysv - YSL
(4)
+ COS e) yL= 2(?,d y t ) 1 / 2
(5)
YLV
as (1
where y, yd, yh, and ydi are the total surface tension, dispersive surface tension component, and surface tension components due to hydrogen and dipole-dipole bonding, respectively. According to Fowkes, the dispersive surface tension component (yd)in eq 1is a result of the molecular interaction of the London forces. In practice, eq 1is often rearranged into the following form: t University of Toronto. 9
University of Alberta. Abstract published in Advance ACS Abstracts, March 1,1994.
(1) Fowkes, F. M.J. Phy8. Chem. 1962,66,382. (2) Fowkes, F. M. Ind. Eng. Chem. 1964,56,40.
0743-7463/94/2410-1323$04.50/0
(2)
where 0 is the contact angle and the subscripts LV and SV represent the liquid-vapor and the solid-vapor phase, respectively. To be specific,assumingthat the liquid phase is completely dispersive ( y = ~ y ~ ~eq) 5, becomes (1+ COS e) yL= 2(y,d yL)1/2
(6)
Consequently, the dispersive property of the solid, ysd, can be obtained from eq 6 if the liquid surface tension y~ and the contact angle 6 on that solid are known. The corresponding nondispersive property, ysn,can be calculated back from eq 2 if the total solid surface tension ys is known. The same methodology can be applied to 0 1994 American Chemical Society
Kwok et al.
1324 Langmuir, Vol. 10, No. 4,1994
determine the dispersive and nondispersive components of a given polar liquid on an apolar solid. Generalization of the Theory of Surface Tension Components More recently, van Osset a1.W proposed a generalization of the Fowkes surface tension component approach which they named the Lifshitz-van der Waalslacid-base approach or acid-base approach for short. They claimed that for any liquid or solid the total surface tension y can be uniquely characterized by three different surface tension componenta,e the Lifshitz-van der Waals (LW) surface tension component yLw, the acid (electron acceptor) surface tension component y", and the base (electron donor) surface tension component ye, such that yi= y y
+ yim
(7)
where yi is the total surface tension, TiLw is the Lifshitzvan der Waals surface tension component,y8- is the acidbase surface tension component, and yi' and yie are the electron acceptor and donor surface tension components, respectively, in the i phase. The interfacial tension between the solid and liquid phases is given by the acid-base approacha as
It is worth mentioning that eq 9 obtained from the acidbase approach is similar to if not identical with eq 3 of the Fowkes approach in the case of at least one apolar material. For an apolar liquid ( y ~ = e y~~ = 0) on a given solid, eq 9 would essentiallyreduceto the Fowkes approachas stated in eq 3. Determination of the Solid Surface Tension Components of the Acid-Base Approach There are two strategies proposed by van Oss et aLM which could be employed to determine the surface tension components of either the solid or the liquid. In order to calculate the so-called solid surface tension componenta from the acid-base approach, eq 9 combined with the Young equation (4) yields LW
yL (1 + COS e) = 2(ys
LW 112
yL
+ 2(ySeyLeF2+
apolar liquid. Then two other polar liquids can be used to determine the remaining properties of the solid. van Oss et aL6J stated that both methodologies in principle can be used; however, they are in favor of the second method, i.e. method I1 (see later); van Oss et aL7 pointed out that "we have found, in a considerable number of recent studies, that results appeared to be most consistent when one apolar and two polar liquids were used, and there are practical and theoretical reasons why such direct measurements of yLware the most accurate"; unfortunately, these practical and theoretical reasons were not given. Our study will present the calculated putative surface tension components of the solids by using both methods. Method I. For a polar liquid, with surface tension y ~ , LW surface tension component yLLW,acid and base surface tension components, y ~ ' and y ~ respectively, ~ , and a contact angle e on a given solid substrate, eq 10 can be written in the form of A = BysLW' I 2 + Cys@
(3)vanOse,C. J.;Chaudhury,M.K.;Good,R. J.Adu. Colloidlnterface Sci. 1987,28, 35. (4) van Oss, C. J.; Good, R. J.; Chaudhury, M. K. Langmuir 1988,4, w. --_. (5)van Oss, C.J.; Chaudhury, M. K.; Good,R. J. Chem. Reu. 1988,88, 927. (6) Good,R. J.; van Om, C. J. Wetting; Plenum Press: New York, 1992; Chaper 1. (7)van Ose, C. J.; Giese,R. F., Jr.; Good, R. J. Langmuir 1990,6,1711. (8) van Oss, C. J.; Good, R. J. J.Dispersion Sci. Technol. 1990,ll (l), 75.
(11)
where A = yL(i + COS e),
B = 2yLLw
c = 2yLe1/2,
D = 2yL@'1' (12)
Three equations of the form of eq 11 constitute a set of three simultaneous equations which can be solved for the three unknown properties of the solid, ysLw,yse, and yse, if the corresponding properties for all three liquids are known. Method 11. Now consider the approach favored by van Oss et al>J For an apolar liquid, with a surface tension y ~ 1LW , surface tension component y ~ 1zero ~ acid ~ , and the base surface tension components, YLI. and Y L I ~= 0, respectively, and a contact angle 01 on a given solid substrate, eq 10 results in
Therefore, the ysLwvalue can be determined directly and subsequently be used in eq 15; see later. For a second, polar liquid, eq 10 can be written as
where
E = yL(l + COS 0) - 2(ysLwyLLW)'I2
2(yseYLe)1/2 (10)
if it is assumed that vapor adsorption is negligible. In view of eq 10, the solid properties ysLw,yse, and yse, according to van Oss et 0 1 . , ~ can be calculated by simultaneous solution of three equations if the measurement of contact angles with respect to three different polar liquids is known on one solid substrate. However, y ~ y ~ ' ,and y~~ for these liquids must be known, a priori. Alternatively, ysLwcan be determined first by using an
+ Dyse ' I 2
(15)
C and D are defined as in eq 12. Two equations of the form of eq 14constitute a set of two simultaneous equations which can be solved for the two unknown properties of the solid, ys@ and yse. ~
~
,
Results Recently, Li et aLDpublished accurate contact angle data of various liquids on three different solid surfaces: a fluorocarbon (FC721), Teflon (FEP), and poly(ethy1ene teraphthalate) (PET). However, no dispersive liquids were used by Li et aLg for the PET surface. Therefore, the subsequent calculations of the solid surface tension components could only be performed with method I and not with the Fowkes approach and method I1 of the acidbase approach, for the PET surface. To calculate the ysd (9)Li,D.;Neumann, A. W.J. Colloid Interface Sci. 1992,148,1,190.
Determining Interfacial Tensions
Langmuir, Vol. 10, No. 4,1994 1325
Table 1. Contact Angle and Liquid Surface Tension Data for Dispersive Liquids Reproduced from References 9 and 10 for Three Solid Surfaces. FC721. FEP and PET* liquid pentaneb hexaneb decane0 dodecanec tetradecane' hexadecanec cis-decalin' 1-bromonaphthalenec 0
15.65 18.13 23.43 25.44 26.55 27.76 31.65 44-01
38.89 f 0.50 50.48 f 0.41 65.97 f 0.18 69.82 i 0.13 73.31 f 0.07 75.32 f 0.29 79.87 f 0.10 95.29 f 0.11
12.37 f 0.08 12.14 f 0.08 11.60 f 0.05 11.51 f 0.04 11.00 f 0.02 10.90 i 0.08 10.94 f 0.03 9.07 f 0.03
43.70 f 0.06 47.96 f 0.10 52.51 f 0.11 53.75 f 0.11 62.60 f 0.12 79.70 f 0.14
*
17.39 0.01 17.73 f 0.03 17.18 f 0.03 17.57 f 0.04 16.87 i 0.04 15.29 f 0.06
ysd values are calculated from eq 6. Taken from ref 10. Taken from ref 9.
Table 2. Summary of the Contact Angles, Liquid Surface Tensions, and Liquid Surface Tension Components To Calculate the Solid Surface Tension Components of the Solid Surfaces. FC721. FEP, and PET
DMSO 1-bromonaphthalene ethylene glycol formamide glycerol water 0
FC721 94.47 f 0.15 95.29 f 0.11 99.03 f 0.12 107.32 i 0.06 111.38 f 0.27 119.05 f 0.08
b (de@ FEP
PET
80.35 f 0.08 79.70 f 0.14 85.56 f 0.10 95.38 f 0.10 100.63 f 0.10 111.59 f 0.10
47.52 i 0.10 61.50 f 0.18 68.10 f 0.13 79.09 f 0.08
Taken from ref 9. Taken from ref 6 based on water
YLa
88
(mJ/m2) 43.58 44.01 47.99 57.49 63.11 72.75
YL.
'
(mJ/m2) 0.5 0 1.92 2.28 3.92 25.5
YLeb
rLmb
YLLWC
(mJ/m2) 32.0 0 47.0 39.6 57.4 25.5
(mJ/m2) 8.0 0 19.0 19.0 30.0 51.0
(mJ/m*) 35.58 44.01 28.99 38.49 33.11 21.75
a reference liquid (YW. = ywe = 25.5 mJ/m2). Calculated from eq 16.
Table 3. Summary of the Coefficients for Equations 11 values from the Fowkes approach for FC721 and FEP, the and 14 When Different Liquids Are Used for the T w o contact angle data of a number of dispersive liquids were Methods. taken from Lis and Xie et a1.10 and used in eq 6. The A E resulting ysd values, together with the liquid surface FC721 FEP PET B C D FC721 FEP tensions and contact angles, are shown in Table 1. In the case of the acid-base approach, there is a severe DMSO 40.18 50.89 11.93 11.31 1.41 4.26 4.24 limitation of the scope for testing purposes: only for a ethyleneglycol 40.46 51.71 80.40 10.77 13.71 2.77 8.03 9.60 40.37 52.10 84.92 12.41 12.59 3.02 3.01 3.58 limited number of liquids, the values of y ~ y ~ e~and , ~ ,formamide 40.10 51.47 86.65 11.51 15.15 3.96 5.44 6.47 glycerol y ~ are e available from van Oss et a1.61* Therefore only 37.42 45.98 86.52 9.33 10.10 10.10 9.33 9.51 water five polar liquids, DMSO,ethylene glycol, formamide, a Method I A = B&W 112 + C Y ~ * + Dyse glycerol, and water, and one apolar liquid, l-bromonaphMethod I 1 E I C@/2 + D@ W , thalene, could be used. In principle, other dispersive liquids from Li et aLg can be used as apolar liquids to determine ysLWfor FC721 and FEP in methdd 11, eq 13; values between the values calculated from eq 16 and those from van Oss et al.6: 0.9 mJ/m2 for glycerol and 0.5 mJ/m2 the choice of 1-bromonaphthalene reflects our intention to follow the prescriptions of van Oss et al. as closely as or less for all other liquids. It will become apparent later possible: van Oss et al.5suggested that "It usually is most that this is of no consequence in the determination of expedient to determine ysLwfirst,with the help of a high ysLW,ys', and me. energy apolar (or virtually apolar) liquid such as a-broFollowing the methodology stated as method I above monaphthalene and diiodomethane." , y~~~ and employing the contact angle 8, YL, Y L ~Y, L ~ and The most recent recommended values of LO and y ~ ~ for , the polar liquids on FC721, FEP, and PET, a number of different equations of the form of eqs 11and 12 were based on water as a reference liquid, taken from ref 6 for the above six liquids are summarized in Table 2. The obtained. The coefficients for these equations are shown liquid surface tension and contact angle data taken from in Table 3. It should be noted that if contact angle data ref 9 for these liquids on the three surfaces, FC721, FEP, for more than three polar liquids on the solid surfaces are and PET, are also shown in Table 2. It should be noted available, the excess information can be used for control , y~~ for the above polar purposes. For instance, simultaneous solutions of the that if the values of yLLW,y ~ eand liquids, obtained from van Oss et a1.F are used, the total equations for DMSO,ethylene glycol, and formamide for FC721 are sufficient to yield the solid properties, ysLW, liquid surface tensions y~ will not be identical with those e y~~ values were taken in Table 2. Therefore, only y ~ and yse, and yse, of FC721. However, simultaneous solution from van Oss et alS6and the corresponding y~~~ values of any three of the equations for the liquids in Table 3 should provide the proper ysLw,yse, and yse values for were obtained from FC721. Tables 4-6 give the square root values of ysLw, yse, and yse obtained for the solid surfaces FC721, FEP, (16) and PET, respectively, using different combinations of the liquids. This procedure may be preferable to simply using the We now employ the methodology previously designated values for y~ and y~~~ as given by van Oss et a1.,6 since as method 11. By use of contact angle data for the apolar they give only two significant figures in many cases and liquid, 1-bromonaphthalene, the values of ysLw were since the accuracy of our data is significantly higher. As determined directly, for both surfaces FC721 and FEP, it turns out, there is only a slight difference in the y~~~ by using eq 13: ysLW for FC721 was found to be 9.07 mJ/ m2, and 15.29 mJ/m2 for FEP. Then the polar liquid (10)Li,D.; Xie, M.;Neumann, A. W. Colloids Polym. Sci. 1993,271, properties and contact angles for FC721 and FEP were 573.
Kwok et al.
1326 Langmuir, Vol. 10, No. 4,1994 Table 4. Calculated Solid Surface Tension Components for FC721,Using Method 1. ysLW1/2b
FoGl-Wa FoGl-DM FoGl-EG Fo-Wa-DM Fo-Wa-EG Fc-DM-EG GI-Wa-DM GI-Wa-EG G1-DM-EG Wa-DM-EG Average S.D., u 95% confid limita
Ysml/2 b
ysel/2b
YsLW b
.@c
(mJ/m2) (mJ/m2) (mJ/m2) (mJ/mz) (mJ/m2) 2.56 0.48 0.86 0.83 7.38 1.22 -1.61 -4.16 1.30 2.32 -18.40 -14.12 -4.22 2.07 2.18 -9.96 39.88 -4.05 1.23 7.06 2.87 4.15 1.91 0.75 1.13 -8.28 -5.52 2.06 -2.01 1.66 4.14 11.28 -0.10 0.68 3.38 -0.78 7.38 106.98 9.98 -4.73 -30.69 -29.93 3.23 -4.75 0.87 1.03 6.74 0.97 0.53 2.39 3.34 12.90 f2.07
0.33 f2.66 fl.90
4.93 f2.17 f1.55
Table 7. Calculated Solid Surface Tension Components for FC721,Using Method 11.
-5.95 f11.43 18.18
12.81 f37.66 f26.94
FoGl Fo-Wa Fo-DM Fo-EG G1-Wa G1-DM G1-EG Wa-DM Wa-EG DM-EG
ysm1/20
ysel/2c
+Bd
yse
(mJ/m2) (mJ/m2) (mJ/mz) (mJlm2) (mJlm3 9.07 -1.10 5.58 -12.28 -3.21 9.07 0.02 0.90 0.04 9.11 0.53 -1.19 -1.26 7.81 9.07 9.07 2.44 -9.16 -44.70 -35.63 9.07 0.16 0.76 0.24 9.31 9.07 0.39 -0.13 -0.10 8.97 9.07 1.36 -3.82 -10.39 -1.32 9.07 0.30 0.63 0.38 9.45 0.50 0.42 0.42 9.07 9.49 9.07 0.04 2.70 0.22 9.29
average S.D., o 95% contiid limita
0.46
f0.92 fO.66
-0.33 13.93 12.81
-6.74 114.16 f10.13
2.33 f14.16 f10.13
a Key: DM, DMSO; EG, ethylene glycol; FO, formamide; G1, Glycerol; Wa, Water; u, standard deviation. Calculated by three equations of the form of eq 11. Calculated by eq 8. Calculated by eq 7.
'Key: DM, DMSO; EG, ethylene glycol; Fo, formamide; G1, glycerol;Wa, water; u, standard deviation. Calculated by eq 13 using 1-bromonaphthalene [see text]. Calculated by two equations of the form of eq 14. Calculated by eq 8. e Calculated by eq 7.
Table 5. Calculated Solid Surface Tension Components for FEP, Using Method 1.
Table 8. Calculated Solid Surface Tension Components for FEP, Using Method 11.
rsLW 112 b
FoG1-Wa FoGl-DM FoGl-EG Fo-Wa-DM Fo-Wa-EG Fo-DM-EG G1-Wa-DM GI-Wa-EG GI-DM-EG Wa-DM-EG average S.D., o 95% confidliiita
rsm
112 b
112 b
ysLW b
rsABc
(mJ/m2) (mJ/m2) (mJ/m2) (mJlm2) (mJ/mZ) 3.36 0.63 0.82 1.03 12.32 -3.27 6.72 1.32 -1.24 3.16 -5.09 -26.57 -18.79 2.61 2.79 -7.01 43.40 -3.13 1.12 7.10 6.02 0.68 3.13 2.30 1.70 -8.89 -4.14 2.43 -1.83 2.18 0.15 0.67 0.20 16.52 4.04 -5.42 -1.10 11.92 155.44 11.98 -48.84 -47.80 4.16 -5.87 1.02 0.49 1.41 9.48 2.84 1.44 4.02 f3.25 f2.32
0.65 f2.88 f2.06
-1.14 f2.51 11.80
*
-7.69 f17.62 f12.60
17.92 f53.84 138.51
FoGl Fo-Wa Fo-DM Fo-EG GI-Wa GI-DM GI-EG Wa-DM Wa-EG DM-EG average S.D., u 95% contid limits
ys*l/2c
ysel/2c
ysABd
(mJ/mz) (mJ/m2) (mJ/m2) (mJ/m2) (mJ/m2) 15.29 -1.31 6.63 -17.37 -2.08 15.29 0.08 0.86 0.14 15.43 15.29 0.47 4.79 -0.74 14.55 15.29 2.92 -10.99 -64.18 -48.89 15.29 0.24 0.70 0.34 15.63 15.29 0.33 0.38 0.25 15.54 15.29 1.63 -4.60 -15.00 0.29 15.29 0.29 0.65 0.38 15.67 15.29 0.64 0.30 0.38 15.67 15.29 -0.15 4.20 -1.26 14.03 0.51 fl.11 f0.79
-0.27 f4.78 f3.42
-9.71 f20.29 h14.51
5.58 120.29 f14.51
'Key: DM, DMSO; EG, ethylene glycol; Fo, formamide; G1, glycerol; Wa, water; u, standard deviation. Calculated by three equations of the form of eq 11. Calculated by eq 8. d Calculated by eq 7.
OKey: DM, DMSO EG, ethylene glycol; Fo, formamide; G1, glycerol;Wa, water; u, standard deviation. Calculated by eq 13 using 1-bromonaphthalene [see text]. c Calculated by two equations of the form of eq 14. Calculated by eq 8. e Calculated by eq 7.
Table 6. Calculated Solid Surface Tension Components for PET,Using Method 1.
in Table 2 should yield ys' and yse. van Oss et a1.8 agreed that uys' and yse can be entirely defined with two polar liquids, the availability of a third liquid could yield a useful set of control values." Tables 7 and 8 summarize the square root values of 7s' and yse and ys, obtained for the solid surfaces of FC721 and FEP, respectively, when different combinations of polar liquids are used.
FoG1-Wa Fdl-EG Fo-Wa-EG GI-Wa-EG average S.D., u 95% confid limita a Key:
4.80 4.49 3.89 9.58
1.34 2.43 2.26 -2.01
2.79 -0.49 2.71 1.73
7.48 -2.38 12.25 -6.95
30.52 17.78 27.38 84.83
5.69 12.62 f4.17
1.01 f2.07 f3.29
1.69 f1.53 f2.43
2.60 f8.81 114.02
40.13 130.29 f48.19
EG, ethylene glycol; Fo, formamide; G1, glycerol; Wa, water;
u, Standard deviation. b Calculated by three equations of the form
of eq 11. Calculated by eq 8. Calculated by eq 7.
used to obtain equations of the form of eqs 14 and 15. The coefficients of these equations are also given in Table 2 for the two solid surfaces; it should be noted that the coefficients E for the PET surface are not available since no dispersive liquid was used by Li et a1.9 on this surface. Once ysLwis determined by using one apolar liquid, the contact angle data for any two polar liquids on a given solid substrate are sufficient to find 7s' and yse. For instance, simultaneous solution of the equations for DMSO and ethylene glycol on FC721 are sufficient to yield the solid properties of ys' and y ~ for e FC721. However, simultaneoussolution of any two of the polar liquids shown
Discussion When vapor adsorption is negligible, it is expected that the total surface tension and solid surface tension components should be approximately constant and independent of the liquids used. The results obtained from the Fowkes approach and both methods I and 11, i.e. the Lifshitz-van der Waals/ acid-base approach, do not bear out this expectation. As can be seen in Table 1, there is a systematic trend for the ysd values: ?sd decreases as y~ increases, i.e., the ysd values vary in a very regular fashion by about 25% for FC721, suggesting a severe flaw in the Fowkes approach. The error limits for ysd values (Table 1)were calculated from the corresponding contact angle errors. The small errors in the ysdvalues suggest that the observed trend in ysdcannot be due to.contactangle errors. In the case of the acid-base approach, the solid surface tensions and the components were found to be inconsistent for all three surfaces using both methods I and 11; see Tables 4-8. In particular, methods I and I1 yield com-
Determining Interfacial Tensions
Langmuir, Vol. 10, No. 4,1994 1327
Table 9. Expected Contact Angle and y~~~ Values Using Method I1 for FC721.
94.47 0.15 100.11 5.64 DMSO 108.92 9.89 Ethylene glycol 99.03 t 0.12 107.32 0.10 110.49 3.17 Formamide 116.79 5.41 Glycerol 111.38 t 0.27 127.87 8.82 Water 119.05 t 0.08 Calculation based on the hypothesis that 7s. = yse = 0 [see text].
35.58 28.99 38.49 33.11 21.75
44.51 45.12 44.93 44.33 38.61
8.93 16.13 6.44 11.22 16.86
Table 10. Expected Contact Angle and y~~~ Values Using Method I1 for FEP. A8 =
liquids DMSO ethylene glycol formamide glycerol water
e0b-d
80.35 85.56 95.38 100.63 111.59
(de&
*
0.08 0.10 0.10 0.10 0.10
8-.
(deg)
OeIP
85.96 97.04 98.98 106.68 119.91
- Ooa(de& 5.61 11.48 3.60 6.05 8.32
YLLWlWd
YLLWOIpCtd
(mJ/m2)
(mJ/m2)
AYLLW = YLLWeXp Y L L W d
35.68 28.99 38.49 33.11 21.75
42.34 43.71 44.38 43.31 34.57
6.76 14.72 5.89 10.20 12.82
-
Calculation based on the hypothesis that 7s. = ys* = 0 [see text].
pletely different results. As can be seen in these tables, the standard deviations, S.D., and the 95% confidence limits (a Student t distribution is used) for the solid surface tensions and components, calculated from the acid-base approach, are huge; therefore, results obtained by averaging over such a large range is meaningless. The ys values for, e.g., FC721, using method I in Table 4, vary from -30.0 to 107.0 mJ/m2; using method I1 in Table 7, they vary from -35.6 to 9.5 mJ/m2. Also, for the FEP surface using method I in Table 5, the ys values vary from -47.8 to 155.4 mJ/m2; using method I1 in Table 8, they vary from -48.9 to 15.7 mJ/m2. Similarly, for the PET surface using method I in Table 6, the ys values vary from 17.8 to 84.8 mJ/m2. It is interesting to note what could be concluded from these tables if nothing were known about the properties of the surfaces, FC721, FEP, and PET. The acid-base approach would predict all kinds of different molecular properties: apolar, monopolar and bipolar acidic and basic properties as well as “negative” solid and solid-liquid interfacial surface tensions, depending on which combination of liquids is chosen, all for one and the same solid surface (Tables 4-8). Regardless of which of the two methods is chosen, negative square root values of the solid surface tension components and also negative total solid surface tension values are obtained frequently. van Oss et aL6 agreed that negative values of the total solid surface tension should not occur and that negative square root values of the solid surface tension components are anomalous: t h e g claimed that “A negative value of y l B is physically allowable for a mechanically stable condensed phase, provided ylB < yiLW, i.e., provided that the total surface free energy (surface tension) is positive.” It can be shown that the negative ys values calculated from the acid-base approach cannot be due to errors in the contact angles. To be specific, let us consider Table 7 and assume, for the sake of argument, that there is an error in the contact angles. For the liquid pair of glycerol and water, the ys value is in line with other positive ys values; it is expected that the contact angles for these two liquids are correct. Then, if we consider the liquid pair of glycerol and ethylene glycol,the negative ys value would be expected to be due to an error in the 8 for ethylene glycol, since 8 for glycerol for the liquid pair of glycerol and water “works well”. In order to bring this negative ys value in line with other positive y s values, “adjustment” in 6 for ethylene glycol is required. However, this “adjustment” in 8 would spoil the ys values for the liquid
pairs of water and ethylene glycol as well as DMSO and ethylene glycol, which “work well” without the “adjustment”. Therefore, the occurence of negative solid surface tension and surface tension components cannot be “adjusted” by corrections to the contact angles. Similar arguments can be applied not only to other liquid pairs, but to the data of Table 8 as well, with similar results: “Adjusting” the contact angles of one or several liquids in an ad hoc fashion is impossible in view of the experimental error limits; even if it were possible, it could not make the scheme of van Oss et alaMwork. Surprisingly, van Oss et aL6 have expressed a similar view: “In a number of cases, the fudging of the observations to bring dys’ from, say, -0.5 into the positive range was larger than 20°, which is quite implausible.” Let us step well back from the discussion of Tables 7 and 8, which represent the straightforward implementation of the acid-base approach for accurate contact angles measured on carefully prepared solid surfaces. It is wellknown from the molecular structure of FC721 and FEP and certainly accepted within the surface tension component approaches,2p6that these surfaces are dispersive (apolar) so that 7s’ as well as yse should be zero or close to zero. Thus, the Lifshitz-van der Waals/acid-base approach cannot predict the correct values of ys’ and yse for FC721 and FEP surfaces (see Tables 4 and 5 and 7 and 8). However, one might attempt to argue that there is a small contact angle error or error in the yLLWvalues leading to the erroneous, finite values of the ys’ and yse, for these surfaces. To explore this possibility, let us consider method I1 and assume that both the ys’ and yse are actually zero. The putative contact angle error and error in y~~~ values for FC721 and FEP were calculated and are shown in Tables 9 and 10, respectively. It can be seen in these tables that the error in the contact angle measurements leading to the erroneous, finite values of 7s’ and yse would have to be at least 3O and up to 11O. Such errors are not possible; cf. Table 2. Alternatively, the error in the y~~~ values would have to be a t least 6 mJ/m2 and up to 17 mJ/m2. While the authors of the surface tension components approaches have not provided guidance as to the likely magnitude of errors, deviations of up to nearly 100 5% ,in the case of water/FC721, seem impossible. Furthermore, ywLW cannot be simultaneously 38.6 mJ/m2 (Table 9) and 34.6 mJ/m2(Table 10). Thus “adjustments”in the contact angles and ~ L L Wvalues cannot make the acid-base approach “work”. These arguments present definitive proof that the erroneous values of the solid surface tension components calculated from the Lifshitz-van der Waals/
1328 Langmuir, Vol. 10,No.4,1994
acid-base approach are not due to errors in the y~~~ values or in the contact angle measurements; rather, they highlight the shortcomings of the approach. We conclude that the Lifshitz-van der Waalslacid-base approach gives neither reasonable and consistent solid surface tension components nor solid surface tensions from contact angle measurements.
Conclusions It has been shown that both the Fowkes and Lifshitzvan der Waals/acid-base approaches fail experimentally. On the basis of the Lifshitz-van der Waalslacid-base approach, it has also been shown that the calculated solid surface tension components show a strong dependence on the liquids used, in violation of agreed upon expectations.
Kwok et al.
Negative values for solid surface tension and square roots of surface tension components are obtained, also in violation of agreedupon expectations. Consequently,these solid surface tension components obtained from contact angle measurements using the Lifshitz-van der Waals/ acid-base approach are not material properties of the solid surfaces. It has also been shown that experimental contact angle errors are too small to save the Lifshitz-van der Waalslacid-base approach.
Acknowledgment. This research was supported by the Natural Science and Engineering Research Council of Canada (No. 8278) and a University of Toronto Open Thanks are due to Y. C. Chung for Fellowship (D.Y.K.). double checking the calculations in this paper.
