Langmuir I995,11,379-379
Evaluation of the Lifshitz-van der Waals/ Acid-Base Approach To Determine Surface Tension Components Fowkesl showed an advantageous approach to treated polar materials, which is to separate the total surface or interfacial tension into two additive components, one for the apolar interactions and the other for the polar interactions. The nature of the polar interactions was unclear until the treatment by Lifshitz? which was more recently extended to surface interactions by Chaudhury3 and which allowed the distinction between electrodynamic Lifshitz-van der Waals (LW)interactions from Lewis acid base (AB) interactions. Subsequent work has shown this approach to be useful and to describe accurately the behavior of a wide variety of materials+-’ These include flocculation of clay the adsorption of organic moleculesg and biopolymers10onto silicate minerals, the quantitative determination of the critical micelle concentration,’l and the exclusion of hydrophilic c01loids’~J~ by an advancingice front, to name only a few applications. In spite of this success, there has not been universal agreement on the correctness of the Lewis acidmase description of the polar interfacial forces. In particular, Neumann and colleagues continued to describe interfacial and surface properties by an “equation of staten,14J5and Chibowski and c01leagues~~J’ (amongothers) grouped all polar interactions into a single parameter, yp. Recently, however, Chibowski18and colleagues have recognized the advantages of the Lewis acidmase approach. Neumann and c o - w ~ r k e r s , ’ ~ J however, ~ J ~ - ~ ~ have only been working with hydrophobic surfaces (e.g., FEP, FC 721, and PET) to calibrate their “equation of state”. This equation has been criticized by a number ofworkers. First, van de Ven et al. indicated that several of its original assumptions14J5were erroneous and its practical ap(1)Fowkes, F. M. J . Phys. Chem. 1963,67,2538. (2)Lifshitz, E. M. Zh. Eksp. Teor. Fiz. 1955,29,94. (3)Chaudhury,RM. ShortRange andLongRangeForcesinCoUoidal and Macroscopic Systems. Ph.D. Dissertation, S U N Y at Buf€alo, 1984, p 215. (4)Van Oss, C. J.: Good, R. J.: Chaudhury, M. K. Langmuir 1988, 4,884. (5)Van Oss, C. J.; Chaudhury, M. R ; Good, R. J. Chem. Rev. 1988,
379
plicability often t e n u o u ~ . Second, ~ ~ * ~ ~Morrison proved that the theory‘s claimed thermodynamic derivation is e r r o n e ~ u s(see ~ ~ ,also, ~ ~ Good;27Johnson and DettreZ8). Third, Fowkes et al.29and van Oss et al.4 demonstrated that there are a great many cases of gross experimental disagreement between predictions from Neumann’s “equation of state” and the observed interfacial tensions between water and organic liquids. Fourth, Neumann’s“equation of state” takes no account of hydrogen bonds or of the Lewis acid and Lewis base nature of hydrogen bondforming polar compounds. Fifth, the “equation of state” prohibits interfacial tensions to have a negative value, which is tantamount to stating that the free energy of interaction, AGsm, between particles or solids, S, immersed in a liquid, L, can never be p ~ s i t i v e .The ~ recent rebuttals by Neumann and c ~ - w o r k e r s ~have ~ - ~not ~ addressed any of these objections. More recently, Kwok et al. tested the surface tension component approach, using the same hydrophobic surfaces, and some mathematical prestidigitation, and claimed “the Lifshitz-van der Waaldacid-base approach gives neither reasonable and consistent solid surface tension components nor solid surface tensions from contact angle m e a s ~ r e m e n t s ” We . ~ ~demonstrate here why their conclusions are unwarranted, one of the main reasons (but not the only reason) being that it is not possible to derive the complete polar properties of a liquid from contact angle measurements on hydrophobic surfaces.
Theory and Methodology Fowkes first suggested that the surface tension could be resolved into components due to dispersion, induction and dipole-dipole forces, and hydrogen b o n d i n g . l ~ ~ ~ - ~ ~ Fowkes et al. also pioneered the explicit application of Lewis acid-base theory to interfaces between condensed phase^.^^,^^ Van Oss et a1.5proposed that if a solid surface involves both LW and AB interactions, the total surface tension (yTOT) should be the sum of two components,yLw and yAB instead of yd and ym as proposed by Fowkes (the superscript d stands for dispersion, indicating just the van der Waals-London interactions). Finally, the YoungGood-Girifalco-Fowkes equation was expanded by van Oss et al.5-6 to:
88.927. - - I
(6)Van os~, C. J.; Chaudhury, M. R ; Good,R. J.Adv.Colloid Interface Sci. 1987,28,35. (7) Good, R. J.; van Oss, C. J. Wettability;Plenum Press: New York, 1992; Chapter 1. (8)Van Oss, C. J.; Giese, R. F.; Costanzo, P. M. Clays Clay Miner. 1990. ~~. . 151-159. (SiNorris, J.; Giese, R. F.; van Oss, C. J.;Costanzo, P. M. Clays Clay Miner. 1992,327. (10) Costanzo, P. M.; Giese, R. F.; van Oss,C. J. J . Adhesion Sci. Tech. 1990,267-275. (11)Van Oss, C. J.; Costanzo, P. M. J.Adhesion Sci. Tech. 1992,477. (12)Van Oss. C. J.: Giese. R. F.: Wentzek, R.: Norris J.: Chuvilin, E.M.J . Adhesion Sci. Tech.’1992;503-516: (13)Van Oss, C. J.; Giese, R. F.; Nonis, J. Cell Biophys. 1992,253. (14)Ward, C. A.; Neumann, A. W. J . Colloid Interface Sci. 1974,49, ’
286. (15)Neumann, A. W.;Good, R. J.;Hope, C. J.;Sejpal, M. J . Colloid Interface Sci. 1974,49,291. (16)Janczuk, B.;Chibowski, E.; Staszczuk, P. J . Colloid Interface Sci. 1983,1-6. (17)Chibowski, E.; Staszczuk,P. Clays Clay Miner. 1988,455-461. (18)Holysz, L.; Chibowski, E. Langmuir 1992,303-308. (19)Spelt, J. JS.; Absolom, D. R.; Neumann, A. W. Langmuir 1987, 3. - ,588-591. (20)Spelt, J. K.;Neumann, A. W. Langmuir 1987,3,588-591. (21)Li,D.;Neumann,A.W. J.Col1oidZnterfmeSci. 1992,148,190~~~
200.
(22)Li, D.; Neumann, A. W. Adv. Colloid Interface Sci. 1992,39, 299-435.
When an apolar liquid and/or an apolar solid is used, eq (23)van de Ven, T. G. M.; Smith, P. G.; Cox, R. G.; Mason, S. G. J . Colloid Interface Sci. 1983,91,298. (24)van de Ven, T. G. M. J . Colloid Interface Sci. 1984,102,301. (25)Morrison, I. D. Langmuir, 1989,5,540. (26)Morrison, I. D. Langmuir 1991,7 , 1833. (27)Good, R. J. Chem. Eng. Educ. 1987,94-97. (28)Johnson, R. E.; Dettre, R. H. Langmuir 1989,5,283-285. (29)Fowkes, F. M.; Riddle, F. L.; Pastore, W. E.; Weber,A. L. Colloids Surfaces 1990,43,367. (30)Neumann, A. W.; Spelt, J. K.; Smith, R. P.; Francis, D. W.; Rotenberg, Y.; Absolsom, D. R. J . Colloid Interface Sci. 1984,102,298. (31)Gaydos, J.; Neumann, A. W. Langmuir 1993,9,3327. (32)Li, D.; Neumann, A. W. Langmuir 1993,9,3728. (33)Kwok,D.Y.;Li,D.;;Neumann,A.W.Langmuir1994,10,13231328. (34)Fowkes, F. M. J . Phys. Chem. 1962,66,382. (35)Fowkes, F. M. Znd. Eng. Chem. 1964,56,40. (36)Fowkes, F. M. J . Phys. Chem. 1968,72,3700. (37)Fowkes, F. M.; Mostafa, M. A. Znd. Eng. Che., Prod. Res. Deu. 1978,17,3. (38)Fowkes, F. M. In Physicochemical Aspects of Polymer Surfmes, Mittal, K.L., Ed.; Plenum Press: New York, 1983;Vol. 2,p 583.
0743-7463/95/2411-0379$09.00/00 1995 American Chemical Society
380 Langmuir, Vol. 11, No.1, 1995
Comments
Table 1. Values of the Surface Tension Components and Parameters (in mJ/M2)of Test Liquids Used for Contact Angle Measurements at 20 "Ca a-bromonaphthalene (a-Br) diiodomethane (DIM) dimethyl sulfoxide (DMSO) ethylene glycol (EG) glycerol (GLY) formamide (FO) water
44.4 50.8 44 48 64 58 72.8
=O
44.4 50.8 36 29 34 39 21.8
=O =O
0 8 19 30 19 51
=O 0 32b ~t47.0 57.4 39.6 25.5
0.5b =1.92 3.92 2.28 25.5
a From Good and van Oss, 1992. b Values of y+ for DMSO range from 0.07to 0.7mJ/M2. The extreme hygroscopic character of DMSO makes it a difficult liquid to use in contact angle measurement^.^
Table 2. Surface Tension Components and Parameters of FEP Obtained by Solving Eq 1. The Contact Angle Data from Table 2 in Kwok et aLSs
water-GLY water-FO water-EG water-DM mean SD least-squares a
15.76 15.59 15.79 15.79 15.74 fO.10 15.66
A
d YS (mJ/M2) (mJ/M2)
rim
(mJ/M2)
15.42 15.42 15.42 15.42 15.25
0.34 0.17 0.37 0.37 0.32 fO.10 0.41
0.06 0.01 0.39 0.09 0.14 f0.17 0.13
0.49 0.72 0.09 0.39 0.42 f0.27 0.34
ykW = 15.42 m J N 2 from 1-bromonaphthalene.
Table 3. Surface Tension Components and Parameters of FC 721 Obtained by Solving Eq 1. The Contact Angle Data from Table 2 in Kwok et aless
0.W
o.io
0.05
0.i5
0.20
0.25
1l(YL)'"
water-GLY water-FO water-EG water-DM mean SD least-squares a
9.41 9.15 9.57 9.51 9.41 f0.18 9.40
9.15 9.15 9.15 9.15 9.15
0.26 0.00 0.42 0.36 0.26 f0.18 0.34
0.03 0.00 0.24 0.09 0.09 fO.10 0.07
0.56 0.79 0.18 0.37 0.48 f0.27 0.44
viw = 9.15 mJ/M2 from 1-bromonaphthalene.
Figure 1. Contact angles of a number of apolar liquids on F C 721 a n d FEP. R is the linear correlation coefficient. 2.24
.
'
J
-
2.0
1.e1.61.4-
1takes the form of
1210-
oe-
where 0 is the contact angle, the subscripts L and S represent the liquid and the solid phases, y+ is the electronacceptor and y- the electron-donor parameter of the polar component of the surface tension, yAB, where yAB = 2(y+y-)1'2. In using eq 1,van Oss et al.5 recommended "It usually is most expedient to determine ykw first, with the help of a high-energy apolar (or virtually apolar ) liquid...", and Good and van Oss7 pointed out "Mathematically, it is possible to use three polar liquids and a set of three equations in the form of eq 1 rather than two equations in the form of eq 1together with eq 2. Such tactics work ifthe values ofthe parameters (e.g.,y - ) for the three liquids are not too close together. Ifthey are close, the calculated values of the three parameters for the solid will be unduly sensitive to small errors in the values of the parameters of the liquids, and in the measured contact angles". Both were cited in Kwok et al.'s paper.33 However, it can be seen from Table 1that the values of the electron-acceptor parameter of most polar-liquids used in contact angle measurements are very close. Thus, it is not surprising that they obtained strange results.
0604-
0200OW
I
, 002
.
, . , 004
006
,
, . , . , 008
010
012
.
, 014
. 016
Figure 2. Contact angles of a number of polar liquids on FC 721, FEP, and PET. R is the linear correlation coefficient.
Results and Discussion If one follows the preferred methodology given a b o ~ e , ~ . ~ clear and reasonable values are obtained for the Lifshitzvan der Waals and the Lewis acid-base surface tension components of FEPand IFC 721, as shown in Tables 2 and 3. FEP and FC 721 turn out to be very hydrophobic, as was well known to begin with. The authors Kwok et al. state "As can be seen in Table 1, there is a systematic trend for the ysd values: ysd decreases as y~ increases..., suggesting a severe flaw in the Fowkes approach".33In reaching this strange conclusion, however, they failed to analyze their own data in
Comments
Langmuir, Vol. 11, No. 1, 1995 381
Table 4. Surface Tension Componenta and Parameters of PET Obtained by Solving Eq 1. The Contact Angle Data from Table 7
water-GLY water-FO water-EG mean SD least-squares
44.21 43.48 44.01 43.90 f0.36 43.67
43.48 43.48 43.48 43.36
0.73 0 0.53 0.42 f0.36 0.31
0.02 Ob 44 0.01 0.01 fO.O1 0.003
6.67 6.63 6.97 6.76 f0.17 7.17
= 43.48 mJ/M2; averaging the results obtained with 1-bromonaphthalene and with diiodomethane. (y+)" = -0.079.
Table 6. Expected Contact Angles from the Lifshitz-van der WaaldAcid-Base Young Eq 1 Calculated by the Least-Squares Method and Observed Contact Angles Reproduced from Table 2 in Kwok et aLaa for FEP liauids 1-bromonaphthalene water glycerol formamide ethylene glycol
eobsdrved
eexpected
(ded 79.7 111.59 100.63 95.38 85.56
(deal 80.09 111.65 99.71 92.98 89.38
A0 = @exp - eobs (ded 0.39 0.06 -0.92 -2.40 3.82
Table 6. Expected Contact Angles for FC 721 from Lifshitz-van der WaaldAcid-Base Young Eq 1 Calculated by the Least-Squares Method and Observed Contact Angles Reproduced from Table 2 in Kwok et a1.= for FC 721 liquids 1-bromonaphthalene water glycerol formamide ethylene glycol
eobserved
@expected
(deg) 95.29 119.05 111.38 107.32 99.03
(deg) 95.54 119.12 110.50 105.19 102.33
A@= @exp
- @ob8
0.25 0.07 -0.88 -2.13 3.30
Tables 1and 2.33 For FC 721 and FEP, according to eq 2 or to eq 6 in Kwok et al.,33a linear relationship between (1 cos 6 ) and l/yL1/2exists ( 6 made by apolar liquids) and yields ysLW= 11.43 mJ/M2 for FC 721 and 17.14 mJ/M2 for FEP (Figure 1). Also, a linear relationship between (1 cos 6 )and ( y ~ ~ ~exists ) ~ for ~ these / y two ~ apolar solids (6 made by polar liquids) and yields ysLS = 12.28 mJM2 for FC 721 and 19.91 mJ/M2for FEP (Figure 2). Since PET is not a fluorocarbon like FC 721 and Teflon FEP and has a small value of electron-donor surface tension parameter, PET does not have a good linear relationship with polar liquids: R = 0.65 (Figure 2). Although 1-bromonaphthalene (1-Br) was used by Li and NeumannZ1(see also Kwok et al.33)to measure contact angles on FC 721 and FEP, somehow no data obtained with apolar liquids were given for PET. We measured contact angles on PET39(from IIMAK Co., NY)with polar liquids as well as apolar liquids: diiodomethane and 1-bromonaphthalene(Table 7, see also, Wu40and Dala141). The contact angles we obtained with polar liquids are very close to those found by Li and Neumann.21 The total surface tension of PET obtained by eq 1is yToT = ykw y y = 43.48 0.36 = 43.84 mJM2,which is significantly higher than the value (35.59 mJ/M2)derived by Li and Neumanq21using only an array of less appropriate polar liquids. It can be seen from Table 8 that the contact angles of apolar liquids do not fit into the "equation of state" derived from the polar liquids, i.e., the calculated contact angles for 1-Br and DIM by the "equation of state" (based on y s = 35.59 mJ/M2) are 20-25" higher than the observed contact angles (see Table 8). On the other hand,
+ +
+
+
Table 7. Observed and Expected Contact Angles from the Lifshitz-van der WaaldAcid-Base Young Eq 1 Calculated by the Least-Squares Method for PET
1-bromonaphthalene diiodomethane water glycerol formamide ethylene glycol
13.6 f 0.6 31.0 f 0.7 77.1 & 0.6 66.8 f 0.3 56.9 f 0.4 49.1 & 0.6
12.45 32.03 77.05 67.71 55.25 49.55
-1.15 1.03 -0.05 -0.91 -1.65 0.45
Table 8. Expected Contact Angles from Neumann's "Equation of State": Eq 24 in Ref 21 and Observed Contact Andes from Table 2 in Kwok et al.99for PET
liquids 1-Br DIM water GLY FO EG
@observed
@expectedb
(deg) 13.6a 31.P 79.09 68.10 61.50 47.52
(deg) 6.48 32.43 66.67 53.74 45.28 25.20
A0 = - @ob,
@expectedC eexpb
(deg) 38.49 51.21 79.77 68.50 61.17 46.40
(deg) -7.12 1.43 -12.42 -14.16 -16.22 -22.32
6,'
A0 = - @obs (de& 24.89 20.21 0.68 0.40 -0.33 -1.12
a From Table 7. Based on ySW = 43.73 mJ/M2 for PET, averaging the results ( y s = 43.18 mJ/M2, 1-Br; and ys = 44.27 mJ/M2, DIM) by solving Neumann's "equation of state", eq 24 in ref 21 with contact angles of 1-Br and DIM. Based on ys = 35.59 mJ/M2 for PET, averaging the results of the "equation of state" with the contact angles of polar liquids.
when ys is taken to be between 43.18 and 44.27 mJ/M2(as measured by the two apolar liquids), the contact angles for the polar liquids expected via the "equation of state" are 12"-22" lower than the observed contact a n g l e ~ ~ l , ~ ~ (see Table 8). In the Lifshitz-van der Waaldacid-base approach,there are three unknown values for the surface tension components. When contact angle measurements are performed with three or more liquids, these constitute a set of simultaneous equations which can be mathematically solved by the standard least-squares method. By using the contact angles data from ref 33, the surface tension components and parameters, solved by the leastsquares are shown in Tables 2-4. It can also been seen from Tables 5-7 that the observed contact angles and the contact angles expected via the Lifshitzvan der Waaldacid-base approach are very close for these liquids. Consequently, not only does the surface tension components approach work on polar systems but it also can describe apolar systems, to determine their surface properties, as well as correlate the contact angles. It should also be pointed out that in the surface tension component approach the occasional occurrence of small negative values of (usually) the square root of the y+ surface tension parameter is ~ e l l - k n o w n .When ~ , ~ ~these very small negative square roots" persist even after (39)PET smoothfilmswere cleanedwith methanol and acetone before contact angle measurements. (40) Wu, S. Polymer Interface and Adhesion; Marcel Dekker: New York, 1982. (41) Dalal, N. E. Langmuir, 1987,3,1009-1015. (42) Giese, R. F., Jr. Unpublished program for solving eq 1by the least-squares method. (43) Good, R. J. J. Adhesion Sci. Technol. 1992,6, 1269. (44) Negative values of (y+)", when they occur at all, are usually very small, e.g., (y+)" 0.1 (see e.g., Table 4). Such values may be taken to be effectively zero. However, when not calculated properly, rather fantastic values for (y+)" or for (y-)- can be obtained, e.g., (y+)" up to -5.42 and (y-)- up to -10.99 (mJ/M2)", as given by Kwok et a1.3S Q;
Comments
382 Langmuir, Vol. 11, No. 1, 1995
having been calculated properly,5g7they can be ascribed to small experimental errors in contact angle measurements, as well as to minor uncertainties that may still exist with respect to the exact y+ and y- values of some of the polar liquids used in the contact angle measurements. In contrast to the conclusionsofKwok et al.33it is shown on the basis of their contact angle data that the Lifshitzvan der Waaldacid-base approach is applicable for the determination of the solid surface tension for the apolar fluorocarbons FC 721 and FEP provided the limitations of the method are obeyed. Neumann’s “equation of state”is an empirical equation applicable to a selected range of apolar polymers only and not applicable to polar systems. In addition, as it prohibits interfacial tensions to have a negative value, the equation is thermodynamically unsound.
Acknowledgment. The authors gratefully acknowledges many useful suggestions from reviewer no. 3.
W.WU,+~*R. F.Giese, Jr.? and C. J. van OSS*~@*~~ Departments of Geology, Microbiology, and Chemical Engineering, State University of New York at Buffalo, Buffalo, New York 14214 Received July 18, 1994 In Final Form: September 26, 1994 LA940570A t Department of Geology.
Present address: Departments of Chemistry and Biomaterial, SUNY Buffalo, 750 NS&M complex, Buffalo, NY 14260. 8 Department of Microbiology. Department of Chemical Engineering.
