2548
Langmuir 1998, 14, 2548-2553
Evaluation of the Lifshitz-van Der Waals/Acid-Base Approach To Determine Interfacial Tensions. 2. Interfacial Tensions of Liquid-Liquid Systems D. Y. Kwok,† Y. Lee, and A. W. Neumann* Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8 Received May 5, 1997. In Final Form: January 21, 1998 The Lifshitz-van der Waals/acid-base (van Oss) approach is tested using experimental interfacial tensions of a large number of liquid-liquid mixtures, as suggested by several researchers3,24,27-30 who wish to see wetting theories validated from liquid-liquid interfacial tensions. It is found that the van Oss approach does not predict correct interfacial tensions of virtually any liquid pairs in question. For example, the calculated interfacial tension of 1-bromonaphthalene-pentane is 7.0 mJ/m2; but this liquid combination is found to be miscible. It is also shown that the liquid surface tension components recently suggested by Lee40 have no impact on the calculated interfacial tension values. The van Oss approach is flawed, giving erroneous results, regardless of whether one employs the set of components from van Oss et al.3 or Lee.40
Introduction Recently, we have shown1 that the Lifshitz-van der Waals/acid-base (van Oss) approach2,3 gives inconsistent solid surface tension components and false values of solid surface tension from contact angles. The failure of this and similar surface tension component approaches4,5 is probably most easily understood in terms of experimental contact angle patterns: on one and the same solid, the contact angle changes smoothly with liquid surface tension, independent of intermolecular forces and liquid structure.6-15 Hence, contact angles do not contain information about putative surface tension components. * Author to whom correspondence should be addressed. Fax: (416) 978-7753. E-mail:
[email protected]. † This paper represents, in part, the Ph.D. thesis of D. Y. Kwok. E-mail:
[email protected]. (1) Kwok, D. Y.; Li, D.; Neumann, A. W. Langmuir 1994, 10, 1323. (2) van Oss, C. J.; Good, R. J.; Chaudhury, M. K. J. Colloid Interface Sci. 1986, 111, 378. (3) Good, R. J.; van Oss, C. J. In Modern Approaches to Wettability: Theory and Applications; Schrader, M., Loeb, G., Eds.; Plenum Press: New York, 1992; pp 22-23. (4) Fowkes, F. M. Ind. Eng. Chem. 1964, 56, 40. (5) Owens, D. K.; Wendt, R. C. J. Appl. Polym. Sci. 1969, 13, 1741. (6) Li, D.; Neumann, A. W. J. Colloid Interface Sci. 1992, 148, 190. (7) Kwok, D. Y.; Li, D.; Neumann, A. W. Colloids Surf., A 1994, 89, 181. (8) Kwok, D. Y.; Lin, R.; Mui, M.; Neumann, A. W. Colloids Surf., A 1996, 116, 63. (9) Kwok, D. Y.; Gietzelt, T.; Grundke, K.; Jacobasch, H.-J.; Neumann, A. W. Langmuir 1997, 13, 2880. (10) del Rı´o, O. I.; Kwok, D. Y.; Wu, R.; Alvarez, J. M.; Neumann, A. W. Contact Angle Measurements by Axisymmetric Drop Shape Analysis and an Automated Polynomial Fit Program. Colloid Surf., A (accepted). (11) Kwok, D. Y.; Lam, C. N. C.; Li, A.; Leung, A.; Wu, R.; Mok, E.; Neumann, A. W. Measuring and Interpreting Contact Angles: A Complex Issue; Colloids Surf., A (accepted). (12) Kwok, D. Y.; Lam, C. N. C.; Li, A.; Zhu, D.; Wu, R.; Neumann, A. W. Low-Rate Dynamic Contact Angles on Polystyrene and the Determination of Solid Surface Tensions. Polym. Eng. Sci. (accepted). (13) Kwok, D. Y.; Leung, A.; Li, A.; Lam, C. N. C.; Wu, R.; Neumann, A. W. Low-Rate Dynamic Contact Angles on Poly(n-butyl methacrylate) and the Determination of Solid Surface Tensions. Colloid Polym. Sci. (accepted). (14) Kwok, D. Y.; Lam, C. N. C.; Li, A.; Leung, A.; Neumann, A. W. Low-Rate Dynamic Contact Angles on Non-Inert Poly(propene-alt-N(n-alkyl)maleimide) Copolymers by an Automated Axisymmetric Drop Shape Analysis (ADSA-P). Langmuir 1998, 14, 2221.
The interfacial tensions of the van Oss approach2,3 were postulated both for liquid-liquid and solid-liquid systems as
γ12 ) γ1 + γ2 1/2 - 1/2 + 1/2 2(γLW γLW - 2(γ+ - 2(γ(1) 1 2 ) 1 γ2 ) 1 γ2 )
The total surface tension of any phase was postulated as - 1/2 + 2(γ+ γi ) γLW i i γi )
(2)
where γi denotes the interfacial tension of the ith phase and the superscripts LW, +, and - denote the Lifshitzvan der Waals, acid, and base surface tension components, respectively. In this paper, we pursue a different approach to test the van Oss approach. Apart from experimental contact angles, there are two frequently used ideas with respect to testing wetting theories: one is connected with the idea of using the phase rule to calculate the number of degrees of freedom;16-26 the other is to use experimental interfacial tensions of liquid-liquid systems.3,24,27-30 (15) Kwok, D. Y.; Lam, C. N. C.; Li, A.; Neumann, A. W. Low-Rate Dynamic Contact Angles on Poly(methyl methacrylate/n-butyl methacrylate) and the Determination of Solid Surface Tensions. J. Adhes. (accepted). (16) Defay, R. In Etude Thermodynamique de la Tension Superficielle; Gauthier Villars: Paris, 1934. (17) Defay, R.; Prigogine, I. In Surface Tension and Adsorption; Bellemans, A. (collab.); Everett, D. H. (trans); Longmans Green & Co.: London, 1954; p 222. (18) Crisp, D. J. Surface Chemistry: Proc. of Joint Meeting of Faraday Society and Societe de Chimie Physique; Bordeaus, 1947. See also: Crisp, D. J. Discuss. Faraday Soc. 1948, 3, 98. (19) Kirkwood, J. G.; Oppenheim, I. In Chemical Thermodynamics; McGraw-Hill: New York, 1961. (20) Dufour, L.; Defay, R. In Thermodynamics of Clouds; Smyth, M., Beer, A. (trans); Academic Press: New York, 1963. (21) Li, D.; Gaydos, J.; Neumann, A. W. Langmuir 1989, 5, 1133. (22) Li, D.; Neumann, A. W. Adv. Colloid Interface Sci. 1994, 49, 147. (23) Morrison, I. D. Langmuir 1989, 5, 540. (24) Morrison, I. D. Langmuir 1991, 7, 1833. (25) Gaydos, J.; Neumann, A. W. Langmuir 1993, 9, 3327. (26) Li. D.; Neumann, A. W. Langmuir 1993, 9, 3728. (27) van Oss, C. J.; Good, R. J.; Chaudhury, M. K. Langmuir 1988, 4, 884.
S0743-7463(97)00460-5 CCC: $15.00 © 1998 American Chemical Society Published on Web 04/04/1998
Interfacial Tensions of Liquid-Liquid Systems
Langmuir, Vol. 14, No. 9, 1998 2549
Table 1. Surface Tensions and Components (mJ/m2) Suggested by van Oss et al.,3 and the Purity and Supplier for the Liquids Used liquid
γ
γLW
γAB
γ+
γ-
supplier
purity (%)
glycerol formamide ethylene glycol dimethyl sulfoxide (DMSO) diiodomethane 1-bromonaphthalene hexadecane tetradecane dodecane decane pentane
64 58 48.0 44 50.80 44.4 27.5 26.6 25.4 23.8 16.1
34 39 29 36 50.8 44.4 27.5 26.6 25.4 23.8 16.1
30 19 19.0 8 0 0 0 0 0 0 0
3.92 2.28 1.92 0.5 0 0 0 0 0 0 0
57.4 39.6 47.0 32 0 0 0 0 0 0 0
Baker analyzed Aldrich Aldrich Sigma-Aldrich Aldrich Aldrich Aldrich Aldrich Aldrich Caledon Aldrich
99.8 99.5+ 99+ 99.9 (HPLC) 99 98 99+ 99 99 99.98 99+
With respect to the second point, van Oss et al.,27 Johnson and Dettre,28 Fowkes et al.,29 Morrison,24 Good and van Oss,3 and Lee30 all have suggested that approaches for solid-liquid capillary systems must also be applicable to liquid-liquid systems and that wetting theories should be tested using interfacial tensions of liquid-liquid systems. For example, Johnson and Dettre28 claimed that “Liquid-liquid systems are extremely useful for testing wetting theories because all the surface and interfacial tensions are measurable”.28 Similarly, Morrison24 claimed that “Data taken on liquid-liquid systems is thermodynamically equivalent to data taken on liquid-solid systems”.24 While these and similar claims conflict with thermodynamics (phase rule)16-22,25,26,31,32 as well as experimental results,33 the Lifshitz-van der Waals/acidbase approach,2,3 that is, eq 1, should be tested in this way in view of the persistence of the above claims. It is, therefore, the purpose of this paper to examine the validity of the van Oss approach to predict interfacial tensions of liquid-liquid systems using experimental interfacial tensions and miscibility information. Materials and Methods Thirty-three liquid-liquid pairs obtained from the following liquids with different molecular properties are chosen to perform interfacial tension measurements: pentane, decane, dodecane, tetradecane, hexadecane, dimethyl sulfoxide (DMSO), 1-bromonaphthalene, diiodomethane, formamide, ethylene glycol, and glycerol. It should be noted that water is not selected here for testing purposes because water-alkanes interfacial tensions are always used to determine the surface tension components of water.4 In a previous study,34 interfacial tensions of the following water-liquid pairs have been employed to test eq 1: watertrans-decalin, water-cis-decalin, and water-1-bromonaphthalene. The results suggested that eq 1 does not predict the correct interfacial tensions for these systems. The surface tension components postulated by van Oss et al.3 and the purities of the liquids used are shown in Table 1. The choice of these “calibration” liquids reflects our intention to follow the van Oss approach as closely as possible. Before interfacial tension measurements, each liquid-liquid mixture is allowed to equilibrate overnight in a number of test tubes in an approximately one-to-one volume ratio. For those liquid pairs which are immiscible, pendant drop experiments are employed to determine interfacial tensions by axisymmetric drop shape analysis-profile (ADSA-P). Briefly, ADSA is a technique to determine liquid-fluid interfacial tensions and contact angles from the shape of (28) Johnson, R. E., Jr.; Dettre, R. H. Langmuir 1989, 5, 293. (29) Fowkes, F. M.; Riddle, W. E.; Pastore, W. E.; Weber, A. W. Colloids Surf. 1990, 43, 367. (30) Lee, L. H. Langmuir 1993, 9, 1898. (31) Li, D.; Moy, E.; Neumann, A. W. Langmuir 1990, 6, 885. (32) Gaydos, J.; Moy, E.; Neumann, A. W. Langmuir 1990, 6, 888. (33) Kwok, D. Y.; Hui, W.; Lin, R.; Neumann, A. W. Langmuir 1995, 11, 2669. (34) Kwok, D. Y.; Neumann, A. W. Can. J. Chem. Eng. 1996, 74, 551.
Table 2. Measured Densities (g/cm3) at 23.0 ( 0.1 °C for the Immiscible Liquid-Liquid Mixtures Used liquid(1)-liquid(2)a
F1(2)
F2(1)
gly-pentane gly-decane gly-dodecane gly-tetradecane gly-hexadecane gly-diio gly-bromo form-pentane form-decane form-dodecane form-tetradecane form-hexadecane form-diio form-bromo diio-pentane diio-dodecane diio-hexadecane diio-ethylgly ethylgly-pentane ethylgly-decane ethylgly-dodecane ethylgly-hexadecane ethylgly-bromo DMSO-pentane DMSO-decane DMSO-dodecane DMSO-tetradecane DMSO-hexadecane
1.2547 1.2581 1.2558 1.2566 1.2555 1.2570 1.2553 1.1249 1.1300 1.1273 1.1283 1.1271 1.1673 1.1303 3.1043 3.2471 3.2695 3.2856 1.1059 1.1123 1.1093 1.1083 1.1165 1.0776 1.0946 1.0942 1.0954 1.0931
0.6180 0.7258 0.7563 0.7575 0.7679 3.2840 1.4802 0.6197 0.7266 0.7574 0.7581 0.7683 3.2844 1.4804 0.8030 0.9358 0.9609 1.1735 0.6201 0.7274 0.7581 0.7687 1.4780 0.6226 0.7289 0.7589 0.7603 0.7703
a gly, glycerol; form, formamide; diio, diiodomethane; ethylgly, ethylene glycol; bromo, 1-bromonaphthalene; DMSO, dimethyl sulfoxide.
axisymmetric menisci, that is, from sessile as well as pendant drops. The strategy employed is to fit the shape of an experimental drop to the theoretical drop profile calculated from the Laplace equation of capillarity, using surface tension as one of the adjustable parameters. The best fit identifies the correct, that is, operative, surface or interfacial tension.35,36 The experimental procedures and setup have been described elsewhere.33 Since ADSA-P requires the density difference across the liquid-fluid phases to determine interfacial tensions and since the density of pure liquids will be affected by solubility, accurate measurement of the density difference between the two phases is required. A digital density meter (Anton Paar DMA 45) was used to measure the densities of the mutually saturated liquids at 23.0 ( 0.1 °C; the results are shown in Table 2. For the interfacial tension measurements, the temperature was 23.0 ( 0.5 °C. For each measurement, at least 10 different drops were used. The interfacial tensions were then averaged from the results, giving 95% confidence limits for an averaged interfacial tension value. To illustrate the accuracy and (35) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. J. Colloid Interface Sci. 1983, 93, 169. (36) Cheng, P.; Li, D.; Boruvka, L.; Rotenberg, Y.; Neumann, A. W. Colloids Surf. 1990, 43, 151.
2550 Langmuir, Vol. 14, No. 9, 1998
Kwok et al.
Table 3. Comparison between the Experimental Interfacial Tensions (mJ/m2) (with the 95% Confidence Limits) and Those Calculated from Eq 1a liquid-liquid pairsb
exp γ12
calc γ12 from eq 1
% error
1. gly-pentane 2. gly-decane 3. gly-dodecane 4. gly-tetradecane 5. gly-hexadecane 6. gly-diio 7. gly-bromo 8. form-pentane 9. form-decane 10. from-dodecane 11. form-tetradecane 12. form-hexadecane 13. form-diio 14. form-bromo 15. diio-pentane 16. diio-dodecane 17. diio-hexadecane 18. diio-ethylgly 19. ethylgly-pentane 20. ethylgly-decane 21. ethylgly-dodecane 22. ethylgly-hexadecane 23. ethylgly-bromo 24. bromo-pentane 25. bromo-decane 26. bromo-dodecane 27. bromo-tetradecane 28. bromo-hexadecane 29. DMSO-pentane 30. DMSO-decane 31. DMSO-dodecane 32. DMSO-tetradecane 33. DMSO-hexadecane
26.50 ( 0.007 28.03 ( 0.004 24.74 ( 0.005 26.40 ( 0.04 31.91 ( 0.20 21.70 ( 0.01 16.78 ( 0.18 25.97 ( 0.02 27.73 ( 0.02 26.10 ( 0.006 24.82 ( 0.01 27.25 ( 0.03 16.73 ( 0.01 16.56 ( 0.005 4.99 ( 0.01 4.09 ( 0.004 5.44 ( 0.01 10.84 ( 0.01 15.73 ( 0.02 17.89 ( 0.002 17.30 ( 0.03 18.10 ( 0.02 9.72 ( 0.02 miscible miscible miscible miscible miscible 8.67 ( 0.01 9.20 ( 0.02 11.03 ( 0.09 11.13 ( 0.02 11.53 ( 0.002
33.3 30.9 30.6 30.5 30.3 31.7 30.7 24.0 20.9 20.0 20.2 20.0 19.8 19.2 9.7 4.4 3.6 22.0 20.9 19.3 19.1 19.0 20.6 7.0 3.2 2.6 2.3 2.0 12.0 9.3 8.9 8.7 8.6
25.7 10.2 23.7 15.5 -5.0 46.1 83.0 -7.6 -24.6 -23.4 -18.6 -26.6 18.4 16.7 94.4 7.6 -33.8 103.0 32.9 7.9 10.4 5.0 111.9
38.4 1.1 -18.4 -21.8 -25.4
a
The surface tensions and components suggested by van Oss et (in Table 1) are used to calculate the interfacial tensions from eq 1. The set of components from Lee40 have no impact on the calculated values; see text. The % error varies from 34% too low to 112% too high. b gly, glycerol; form, formamide; diio, diiodomethane; ethylgly, ethylene glycol; bromo, 1-bromonaphthalene; DMSO, dimethyl sulfoxide.
al.3
consistency of the results, we show in Table 5 the raw experimental data of diiodomethane-hexadecane for multiple (newly formed) drops. It can be seen that the accuracy of the experimental interfacial tensions is better than 0.01 mJ/m2. A repeat experiment on a different date is shown in Table 6. Clearly, the experimental interfacial tensions obtained from the two different dates differ by only less than 0.1 mJ/m2, as expected from the possible temperature fluctuations of (0.5 °C.
Results and Discussion Table 3 summarizes the observed miscibility, the experimental interfacial tensions, and the interfacial tensions calculated from eq 1. The calculated interfacial tensions are based on the surface tension components postulated by van Oss et al.3 (in Table 1). It can be seen in Table 3 that, for liquid pairs which are immiscible, the predicted interfacial tensions range from 34% lower to 112% higher than the experimental values. Several liquid pairs are found to be miscible: they are 1-bromonaphthalene-pentane, 1-bromonaphthalene-decane, 1-bromonaphthalene-dodecane, 1-bromonaphthalene-tetradecane, and 1-bromonaphthalene-hexadecane. Obviously, the interfacial tensions of these systems should be zero or, according to the van Oss approach, “negative”.3,37 (37) van Oss, C. J.; Good, R. J.; Chaudhury, M. K. J. Protein Chem. 1986, 5, 385.
Figure 1. Comparison between the interfacial tensions γ12 calculated from eq 1 and those determined experimentally, where a diagonal line represents perfect agreement. The numbers designate the liquid pairs in Table 3. Liquid pair nos. 24-28 have been excluded from this figure because experimental γ12 values (zero or negative) are not available; nevertheless, the van Oss approach predicts false (i.e. positive) γ12 values for these miscible liquid pairs. Table 4. Comparison between the Experimental (Miscibility) Observation and Those Calculated from Eq 1 for the Liquid Pairs Studied in Ref 34a calc γ12 from eq 1b liquid-liquid pairsc
miscibility observation
van Oss et al.
Lee
water-gly water-form water-ethylgly water-DMSO gly-form gly-ethylgly gly-DMSO form-ethylgly form-DMSO diio-bromo diio-DMSO ethylgly-DMSO bromo-DMSO
miscible miscible miscible miscible miscible miscible miscible miscible miscible miscible miscible miscible miscible
-14.2 -6.3 -12.7 -3.5 1.4 1.1 4.9 0.6 1.1 0.2 9.3 2.0 8.4
-14.0 -6.0 -12.5 -3.6 1.4 1.0 4.7 0.6 0.9 0.2 9.3 1.8 8.4
a The surface tensions and components suggested by van Oss et al.3 and Lee40 are used to calculate the interfacial tensions from eq 1. Equation 1 does not predict the correct interfacial tensions for all liquid-liquid pairs, except those of water-liquid pairs. b Calculated interfacial tension based on the surface tension components suggested by van Oss et al.3 and Lee.40 c gly, glycerol; form, formamide; diio, diiodomethane; ethylgly, ethylene glycol; bromo, 1-bromonaphthalene; DMSO, dimethyl sulfoxide.
Equation 1, however, predicts these interfacial tensions to be all positive, varying from 2.0 to 7.0 mJ/m2. It is apparent that, for the immiscible as well as miscible liquid pairs in question, the interfacial tensions calculated from eq 1 are false. Figure 1 illustrates a comparison between the measured and predicted interfacial tensions, where a diagonal line represents perfect agreement. In this figure, the numbers designate the liquid pairs in Table 3. Several miscible liquid pairs (nos. 24-28 in Table 3) have been excluded from this figure because experimental interfacial tension values (zero or negative) are not available; nevertheless, eq 1 predicts false (i.e. positive) interfacial tension values for these miscible liquid pairs.
Interfacial Tensions of Liquid-Liquid Systems
Langmuir, Vol. 14, No. 9, 1998 2551
Table 5. Summary of the Raw Experimental Results for Diiodomethane-Hexadecane Using ADSA-P Performed on Date 1 time (s)
γ12
95% confidence (mJ/m2)
area (cm2)
0.0 10.0 20.0 30.0 40.0 50.0
5.469 920 5.458 640 5.464 264 5.462 230 5.458 698 5.463 850
0.014 661 1 0.012 047 0 0.009 760 3 0.013 396 5 0.010 565 9 0.010 887 4
0.028 899 0 0.029 065 1 0.029 226 1 0.029 363 0 0.029 495 1 0.029 632 1
Drop No. 1 0.000 565 4 60.0 0.000 568 2 70.0 0.000 571 0 80.0 0.000 573 2 90.0 0.000 575 3 mean 0.000 577 6
0.0 10.0 20.0 30.0 40.0 50.0
5.470 599 5.459 328 5.462 689 5.462 055 5.464 848 5.460 845
0.010 126 4 0.012 476 8 0.009 118 3 0.011 596 6 0.010 685 3 0.010 956 2
0.028 796 5 0.029 039 0 0.029 261 9 0.029 488 7 0.029 687 8 0.029 888 1
Drop No. 2 0.000 563 6 60.0 0.000 567 8 70.0 0.000 571 6 80.0 0.000 575 3 mean 0.000 578 5 0.000 581 6
0.0 10.0 20.0 30.0 40.0 50.0
5.462 564 5.468 154 5.465 038 5.463 337 5.466 350 5.461 735
0.009 489 8 0.013 100 0 0.013 604 9 0.011 175 7 0.010 272 0 0.012 402 8
0.028 598 2 0.028 836 6 0.029 046 4 0.029 260 1 0.029 455 0 0.029 636 9
Drop No. 3 0.000 559 8 60.0 0.000 564 2 70.0 0.000 567 8 80.0 0.000 571 5 90.0 0.000 574 8 mean 0.000 577 7
0.0 10.0 20.0 30.0 40.0 50.0
5.465 081 5.467 189 5.465 915 5.465 818 5.466 539 5.466 539
0.010 226 8 0.005 509 2 0.008 640 3 0.013 846 6 0.012 046 1 0.012 046 1
0.027 946 8 0.028 213 4 0.028 458 9 0.028 671 9 0.029 046 2 0.029 046 2
Drop No. 4 0.000 547 5 60.0 0.000 552 5 70.0 0.000 557 2 80.0 0.000 561 2 90.0 0.000 567 9 mean 0.000 567 9
0.0 10.0 20.0 30.0 40.0 50.0
5.461 143 5.468 948 5.468 928 5.463 028 5.462 319 5.462 661
0.011 240 5 0.013 226 2 0.015 294 1 0.015 555 7 0.010 930 2 0.010 049 5
0.028 658 5 0.028 805 1 0.028 922 8 0.029 024 0 0.029 135 7 0.029 448 5
Drop No. 5 0.000 560 9 60.0 0.000 563 6 70.0 0.000 565 8 80.0 0.000 567 5 90.0 0.000 569 4 mean 0.000 574 5
0.0 10.0 20.0 30.0 40.0 50.0
5.465 719 5.463 341 5.461 180 5.464 482 5.467 567 4.563 458
0.006 306 1 0.009 457 3 0.011 780 7 0.011 580 0 0.008 983 4 0.009 342 4
0.028 749 3 0.029 073 1 0.029 381 5 0.029 656 8 0.029 924 3 0.030 176 9
Drop No. 6 0.000 562 7 60.0 0.000 568 4 70.0 0.000 573 6 80.0 0.000 578 0 90.0 0.000 582 1 mean 0.000 585 8
0.0 10.0 20.0 30.0 40.0 50.0
5.467 944 5.467 111 5.458 927 5.462 635 5.465 445 5.463 030
0.013 139 8 0.011 392 9 0.011 295 3 0.014 655 8 0.006 878 1 0.010 292 0
0.028 895 5 0.029 201 2 0.029 477 3 0.029 739 9 0.029 980 3 0.030 203 8
Drop No. 7 0.000 565 3 60.0 0.000 570 6 70.0 0.000 575 0 80.0 0.000 579 3 90.0 0.000 583 0 mean 0.000 586 2
0.0 10.0 20.0 30.0 40.0 50.0
5.460 245 5.461 042 5.459 084 5.461 008 5.462 815 5.464 257
0.009 400 5 0.010 706 3 0.011 099 5 0.011 473 0 0.009 437 2 0.011 302 5
0.029 126 3 0.029 246 0 0.029 371 2 0.029 481 8 0.029 583 0 0.029 682 0
Drop No. 8 0.000 569 3 60.0 0.000 571 2 70.0 0.000 573 3 80.0 0.000 575 2 90.0 0.000 576 8 mean 0.000 578 4
0.0 10.0 20.0 30.0 40.0 50.0
5.464 582 5.461 266 5.464 957 5.459 361 5.462 055 5.462 068
0.009 901 2 0.011 595 1 0.009 374 6 0.009 710 5 0.008 719 3 0.009 441 4
0.029 609 6 0.029 840 1 0.030 050 1 0.030 259 6 0.030 445 8 0.030 634 7
Drop No. 9 0.000 577 3 60.0 0.000 580 9 70.0 0.000 583 9 80.0 0.000 586 9 mean 0.000 589 3 0.000 591 6
0.0 10.0 20.0 30.0 40.0 50.0
5.465 142 5.462 565 5.464 904 5.464 438 5.463 797 5.461 961
0.011 582 8 0.011 011 4 0.013 483 9 0.010 587 3 0.009 037 9 0.010 525 0
0.028 740 8 0.028 966 5 0.029 158 1 0.029 337 8 0.029 506 8 0.029 654 4
Drop No. 10 0.000 562 5 60.0 0.000 566 5 70.0 0.000 569 9 80.0 0.000 572 9 90.0 0.000 575 7 mean 0.000 578 0
volume (cm3)
time (s)
γ12
95% confidence (mJ/m2)
area (cm2)
volume (cm3)
5.463 660 5.458 072 5.456 294 5.463 753
0.009 022 3 0.010 915 5 0.011 012 1 0.010 245 8
0.029 736 3 0.029 841 6 0.029 934 8 0.030 035 8
0.000 579 2 0.000 580 8 0.000 582 2 0.000 583 8
0.008 266 5 0.010 233 8 0.009 159 1
0.030 075 3 0.030 261 6 0.030 446 6
0.000 584 4 0.000 586 8 0.000 589 2
0.011 420 0 0.010 501 4 0.009 658 1 0.008 373 0
0.029 819 5 0.029 998 4 0.030 162 5 0.030 337 9
0.000 580 6 0.000 583 2 0.000 585 4 0.000 587 8
0.012 814 2 0.008 425 6 0.012 312 5 0.010 229 5
0.029 201 7 0.029 342 7 0.029 485 7 0.029 606 8
0.000 570 6 0.000 572 8 0.000 575 2 0.000 577 1
0.011 455 5 0.010 049 5 0.008 665 0 0.010 518 7
0.029 343 2 0.029 448 5 0.029 553 5 0.029 624 5
0.000 572 9 0.000 574 5 0.000 576 4 0.000 577 4
0.009 073 7 0.012 098 6 0.010 861 0 0.011 192 8
0.030 408 5 0.030 657 4 0.030 917 0 0.031 262 8
0.000 588 7 0.000 591 9 0.000 594 4 0.000 597 6
0.008 894 5 0.011 122 1 0.010 786 0 0.010 552 9
0.030 428 1 0.030 665 2 0.030 900 6 0.031 158 6
0.000 589 1 0.000 592 0 0.000 594 4 0.000 596 7
0.010 441 1 0.010 953 8 0.014 482 7 0.009 892 5
0.029 801 6 0.029 881 8 0.030 002 3 0.030 106 5
0.000 580 2 0.000 581 5 0.000 583 3 0.000 584 7
0.010 666 0 0.010 385 8 0.012 608 6
0.030 846 9 0.031 056 0 0.031 328 3
0.000 593 9 0.000 595 8 0.000 598 0
0.013 155 0 0.011 448 0 0.011 814 3 0.009 439 7
0.029 793 8 0.029 915 0 0.030 036 9 0.030 146 8
0.000 580 1 0.000 582 0 0.000 583 6 0.000 585 2
γ12 ) 5.46 5.464 856 5.458 725 5.457 939 γ12 ) 5.46
5.463 547 5.464 157 5.457 043 5.463 516 γ12 ) 5.46 5.462 716 5.464 366 5.461 838 5.464 185 γ12 ) 5.47 5.458 886 5.462 661 5.464 491 5.462 750 γ12 ) 546 5.458 243 5.457 456 5.499 242 5.455 850 γ12 ) 546 5.461 481 5.461 570 5.452 819 5.454 865 γ12 ) 5.46 5.460 357 5.464 187 5.462 086 5.462 724 γ12 ) 5.46 5.455 987 5.453 174 5.453 034 γ12 ) 5.46
5.459 700 5.464 717 5.460 250 5.458 731 γ12 ) 5.46
2552 Langmuir, Vol. 14, No. 9, 1998
Kwok et al.
Table 5 (Continued) time (s)
γ12
95% confidence (mJ/m2)
area (cm2)
0.0 10.0 20.0 30.0 40.0 50.0
5.458 953 5.462 016 5.464 275 5.457 844 5.463 922 5.46 0537
0.009 251 4 0.014 203 3 0.010 441 8 0.011 602 5 0.010 080 7 0.011 046 9
0.029 327 8 0.029 478 7 0.029 630 1 0.029 780 9 0.029 930 8 0.030 080 8
Drop No. 11 0.000 572 6 60.0 0.000 575 1 70.0 0.000 577 6 80.0 0.000 579 9 90.0 0.000 582 2 mean 0.000 584 4
0.0 10.0 20.0 30.0 40.0
5.464 306 5.462 589 5.461 318 5.459 692 5.459 925
0.009 610 3 0.008 881 2 0.010 517 6 0.007 740 9 0.009 710 6
0.029 718 4 0.029 922 9 0.030 140 7 0.030 359 1 0.030 599 8
Drop No. 12 0.000 579 0 50.0 0.000 582 1 60.0 0.000 585 2 mean 0.000 588 1 0.000 591 3
0.0 10.0 20.0 30.0 40.0 50.0
5.460 084 5.463 458 5.460 113 5.463 880 5.460 274 5.459 551
0.011 251 3 0.009 386 3 0.011 876 6 0.013 150 7 0.011 727 6 0.008 113 0
0.029 050 1 0.029 307 2 0.029 536 1 0.029 773 4 0.029 976 7 0.030 195 7
Drop No. 13 0.000 568 0 60.0 0.005 725 5 70.0 0.000 576 1 80.0 0.000 579 9 90.0 0.000 582 9 mean 0.000 586 1
0.0 10.0 20.0 30.0 40.0 50.0
5.460 459 5.462 125 5.461 376 5.465 676 5.458 801 5.465 216
0.008 426 2 0.014 586 3 0.009 999 8 0.012 597 8 0.010 310 0 0.008 182 6
0.029 280 0 0.029 424 0 0.029 565 0 0.029 716 4 0.029 839 1 0.029 980 5
Drop No. 14 0.000 571 9 60.0 0.000 574 3 70.0 0.000 576 6 80.0 0.000 579 0 90.0 0.000 580 8 mean 0.000 583 0
0.0 10.0 20.0 30.0 40.0 50.0
5.460 361 5.462 714 5.462 612 5.462 851 5.461 909 5.466 342
0.008 979 9 0.010 091 0 0.010 205 8 0.014 147 6 0.012 462 7 0.011 008 4
0.029 301 4 0.029 441 7 0.029 576 1 0.029 710 5 0.029 829 0 0.029 946 3
Drop No. 15 0.000 572 2 60.0 0.000 574 6 70.0 0.000 576 7 80.0 0.000 578 9 90.0 0.000 580 7 mean 0.000 582 5
0.0 10.0 20.0 30.0 40.0 50.0
5.458 546 5.465 957 5.465 508 5.467 144 5.460 802 5.460 173
0.011 8071 0.009 773 1 0.007 933 2 0.010 525 7 0.007 403 8 0.011 079 9
0.029 129 0 0.029 436 8 0.029 710 8 0.029 989 7 0.030 257 1 0.030 524 0
Drop No. 16 0.000 569 4 60.0 0.000 574 5 70.0 0.000 578 8 80.0 0.000 583 1 mean 0.000 586 8 0.000 590 3
0.0 10.0 20.0 30.0
5.469 419 5.463 805 5.465 551 5.461 989
0.012 436 4 0.011 672 1 0.012 514 6 0.011 404 7
0.028 952 9 0.029 404 3 0.029 820 2 0.030 213 3
Drop No. 17 0.000 566 3 40.0 0.000 574 0 50.0 0.000 580 7 mean 0.000 586 3
volume (cm3)
These results provide strong evidence that the van Oss approach is flawed, as suggested by several researchers.3,24,27-30 It should be noted that the deficiency of eq 1 is not limited to the liquid pairs shown in Table 3 and those studied in our previous paper.34 For example, the interfacial tension of squalene-diiodomethane can be easily calculated from eq 1 because they are claimed to be nonpolar liquids.3,29 Equation 1 predicts an interfacial tension of 3.0 mJ/m2; Fowkes, the pioneer of surface tension component approaches, however, reported that this system is miscible.29 We wish to point out that the so-called liquid surface tension components as reported by van Oss et al. have been modified, from time to time since 1986. Kloubek38 has argued that the van Oss approach,2,3 as used to combine the acid and base components, is incorrect. The surface tension components suggested by van Oss et al.3 are also different from those found by Kloubek.39 Lee,40 (38) Kloubek, J. Langmuir 1989, 5, 1127.
time (s)
γ12
95% confidence (mJ/m2)
area (cm2)
volume (cm3)
5.457 748 5.456 191 5.465 620 5.463 684
0.008 310 3 0.007 876 6 0.011 619 6 0.010 689 4
0.030 228 6 0.030 363 7 0.030 513 3 0.030 650 5
0.000 586 3 0.000 588 1 0.000 590 3 0.000 591 9
0.012 802 3 0.009 529 9
0.030 857 8 0.031 162 5
0.000 594 0 0.000 596 6
0.008 611 5 0.012 759 0 0.011 961 0 0.011 427 3
0.030 401 4 0.030 608 8 0.030 824 4 0.031 064 5
0.000 588 8 0.000 588 8 0.000 593 9 0.000 595 9
0.010 987 1 0.007 491 9 0.011 660 0 0.010 456 2
0.030 094 0 0.030 214 4 0.030 337 5 0.030 454 2
0.000 584 6 0.000 586 3 0.000 587 9 0.000 589 4
0.013 249 0 0.008 319 9 0.005 658 8 0.012 551 2
0.030 071 0 0.030 180 6 0.030 294 1 0.030 403 1
0.000 584 4 0.000 585 9 0.000 587 4 0.000 588 8
0.011 746 0 0.010 870 6 0.011 344 1
0.030 805 6 0.031 119 9 0.031 760 5
0.000 593 6 0.000 596 4 0.000 599 9
0.009 982 4 0.011 920 5
0.030 613 7 0.031 066 8
0.000 591 4 0.000 595 9
γ12 ) 5.46 5.458 764 5.448 994 γ12 ) 5.46
5.461 003 5.460 439 5.458 267 5.452 164 γ12 ) 5.46 5.462 112 5.462 747 5.462 325 5.458 646 γ12 ) 5.46 5.463 692 5.459 803 5.462 658 5.460 225 γ12 ) 5.46 5.457 969 5.452 422 5.449 022 γ12 ) 5.46
5.461 091 5.451 059 γ12 ) 5.46
in a recent publication, claimed that the reference values 3 of water γ+ w and γw, as used by van Oss et al., are false. All of these contradictory findings and claims have seriously flooded the literature. Other researchers41-43 have started to note the inconsistency of the van Oss approach.2,3 Be that as it may, “adjustment” in the values of γ+ and γ- for the polar liquids does not affect the results shown in Table 3. This lies in the fact that each liquid pair consists of at least one nonpolar liquid. This is indeed the preferred arrangement of van Oss et al., as claimed in a rebuttal44 to contact angle studies using only polar liquids.1 Clearly, recent values of γ+ and γ- suggested by Lee40 have no impact on the calculated values shown in Table (39) Kloubek, J. Collect. Czech. Chem. Commun. 1991, 56, 277. (40) Lee, L. H. Langmuir 1996, 12, 1681. (41) Berg, J. C. In Wettability; Berg, J. C., Ed.; Marcel Dekker: New York, 1993; p 75. (42) Holla¨nder, A. J. Colloid Interface Sci. 1995, 169, 493. (43) Morra, M. J. Colloid Interface Sci. 1996, 182, 312. (44) Wu, W.; Giese, R. F., Jr.; van Oss, C. J. Langmuir 1995, 11, 379.
Interfacial Tensions of Liquid-Liquid Systems
Langmuir, Vol. 14, No. 9, 1998 2553
Table 6. Summary of the Raw Experimental Results for Diiodomethane-Hexadecane Using ADSA-P Performed on Date 2 time (s)
γ12
0.0 20.0 40.0 60.0 80.0 100.0
5.382 121 5.402 884 5.384 289 5.386 453 5.445 793 5.362 194
mean 0.0 10.0 20.0 40.0 60.0 80.0 100.0 120.0
95% confidence (mJ/m2)
area (cm2)
volume (cm3)
Drop No. 1 0.024 962 4 0.019 259 8 0.028 910 8 0.019 675 9 0.029 995 6 0.028 318 9
0.026 137 1 0.026 392 9 0.026 291 4 0.026 512 4 0.026 496 1 0.026 518 2
0.000 513 8 0.000 519 7 0.000 517 3 0.000 522 8 0.000 522 1 0.000 522 8
Drop No. 2 0.020 182 2 0.015 578 9 0.022 228 4 0.028 956 9 0.029 133 4 0.022 204 6 0.021 556 5 0.039 138 8
0.027 276 6 0.027 179 9 0.027 386 0 0.027 311 2 0.027 483 0 0.027 495 4 0.027 333 9 0.027 511 2
0.000 539 5 0.000 537 0 0.000 542 1 0.000 539 8 0.000 544 0 0.000 544 4 0.000 540 3 0.000 544 9
Drop No. 3 0.024 462 4 0.020 057 3 0.020 320 9 0.011 548 7 0.017 473 8
0.029 360 4 0.029 413 7 0.029 259 5 0.029 444 4 0.029 473 9
0.000 581 3 0.000 582 0 0.000 578 1 0.000 582 5 0.000 583 3
Drop No. 4 0.014 376 2 0.021 495 5 0.013 928 7 0.020 552 6
0.029 746 7 0.029 571 1 0.029 536 1 0.029 711 3
0.000 589 1 0.000 584 6 0.000 583 9 0.000 588 7
Drop No. 5 0.011 477 3 0.024 329 9 0.025 181 5 0.019 874 5 0.013 265 2
0.029 787 5 0.029 757 5 0.029 799 7 0.029 777 5 0.029 761 0
0.000 588 7 0.000 588 2 0.000 588 8 0.000 589 1 0.000 588 0
Drop No. 6 0.011 595 9 0.029 834 0 0.022 944 9 0.029 773 2 0.032 244 9 0.029 711 2
0.000 590 9 0.000 589 4 0.000 588 3
Drop No. 7 0.021 000 7 0.028 755 1 0.010 215 8 0.028 667 7 0.015 180 0 0.028 634 5
0.000 570 5 0.000 568 5 0.000 560 8
Drop No. 8 0.030 524 7 0.028 583 6 0.021 328 1 0.028 441 6 0.019 520 0 0.028 433 1
0.000 567 3 0.000 563 9 0.000 563 8
Drop No. 9 0.034 580 1 0.019 599 6 0.022 184 6 0.027 523 1
0.000 548 5 0.000 551 2 0.000 546 0 0.000 547 2
γ12 ) 5.39 5.390 408 5.376 983 5.371 496 5.366 475 5.364 729 5.371 176 5.399 140 5.366 308
mean
γ12 ) 5.37
0.0 20.0 40.0 60.0 80.0
5.337 993 5.390 372 5.371 123 5.391 988 5.361 879
mean
γ12 ) 5.37
20.0 40.0 60.0 80.0
5.376 498 5.379 555 5.382 346 5.385 288
mean
γ12 ) 5.38
0.0 20.0 40.0 60.0 80.0
5.378 003 5.386 747 5.385 625 5.388 526 5.389 560
mean
γ12 ) 5.39
30.0 50.0 70.0
5.419 519 5.388 651 5.432 482
mean
γ12 ) 5.41
30.0 60.0 90.0
5.380 247 5.393 917 5.395 432
mean
γ12 ) 5.39
30.0 60.0 90.0
5.366 596 5.397 109 5.382 655
mean
γ12 ) 5.38
0.0 20.0 40.0 60.0
5.350 181 5.396 211 5.356 721 5.444 227
mean
γ12 ) 5.39
polar-polar liquid pairs previously studied.34 In that paper, it was found that eq 1 cannot predict the interfacial tensions (i.e. zero) of virtually any miscible liquid pairs in question. For this reason, we show these liquid pairs in Table 4 together with the calculated interfacial tensions using the sets of components by van Oss et al.3 as well as those of Lee.40 Again, it is apparent that, other than those for the water-liquid pairs, all interfacial tensions predicted from the van Oss approach are false for both sets of components. Of course, this does not imply that the approach may be applicable for water-liquid pairs: the interfacial tensions calculated from eq 1 for water-transdecalin, water-cis-decalin, and water-1-bromonaphthalene have been shown to conflict with the experimental values.34 The Lifshitz-van der Waals/acid-base approach2,3 has been shown to fail the “test” postulated by those who wish to validate wetting theories from liquid-liquid interfacial tensions. The van Oss approach cannot be used to predict liquid-liquid interfacial tensions. Conclusions
0.027 708 6 0.027 831 0 0.027 606 2 0.027 646 4
(1) van Oss’s treatment of the acid-base approach does not predict the correct interfacial tensions of a large number of arbitrarily chosen miscible and immiscible liquid-liquid systems. (2) Since van Oss treatment does not predict the correct interfacial tension values of liquid-liquid systems, according to van Oss,27 Johnson and Dettre,28 Fowkes,29 Morrison,24 Good and van Oss,3 and Lee,30 caution should be exercised when this approach is used to determine solid surface tension components from contact angles. Acknowledgment. This research was supported by the Natural Science and Engineering Research Council of Canada (Grant Nos. A8278 and EQP173469), Ontario Graduate Scholarships (D.Y.K.), and University of Toronto Open Fellowships (D.Y.K.). Appendix
3. However, the question may arise whether the set of components by Lee40 could make eq 1 applicable for the
The accuracy and reproducibility of the experimental interfacial tensions are shown in Tables 5 and 6 for diiodomethane-hexadecane on two different dates. Typically, as soon as each drop is formed, at least 3 and up to 10 pictures are taken for about 90 s. These procedures allow one to observe any time dependence of the interfacial tensions due to, for example, the presence of impurities which will lower the interfacial tensions. Since the interfacial tensions are quite constant, that is, essentially independent of time, these results can be averaged. It is apparent that the accuracy of the experimental interfacial tensions is better than 0.01 mJ/m2 for multiple drops obtained on the same date and is better than 0.1 mJ/m2 for drops obtained on the two different dates. Clearly, an uncertainty of, say, (0.5 °C in the temperature does not affect the resulting interfacial tensions appreciably. Averaging over all interfacial tension values, because of the large number of data, results in γ12 for diiodomethanehexadecane. The reproducibility is similar for the other liquid-liquid pairs. LA970460E
