# Low-rate dynamic contact angles on polystyrene and the determination of solid surface tensions.

INTRODUCTIONThe interpretation of contact angles in terms of surface energetics relies on the validity of Young's equation,

[[Gamma].sub.lv]cos[[Theta].sub.Y] = [[Gamma].sub.sv] - [[Gamma].sub.sl] (1)

which interrelates the Young contact angle with the interfacial tensions of the liquid-vapor [[Gamma].sub.lv], solid-vapor [[Gamma].sub.sv], and solid-liquid [[Gamma].sub.sl] interfaces. [[Theta].sub.Y] is the Young contact angle, i.e. a contact angle that can be used in conjunction with Young's equation. While there are a number of thermodynamic equilibrium contact angles [[Theta].sub.e], they are not necessarily equal to [[Theta].sub.Y] (1-3).

Equation 1 implies a single, unique Young contact angle; in practice, however, contact angle phenomena are complicated (1-3). For example, the contact angle made by an advancing liquid ([[Theta].sub.a]) and that made by a receding liquid ([[Theta].sub.r]) are not identical; nearly all solid surfaces exhibit contact angle hysteresis (the difference between [[Theta].sub.a] and [[Theta].sub.r]). Contact angle hysteresis can be due to roughness and heterogeneity of a solid surface. If roughness is the primary cause, then the measured contact angles are meaningless in terms of Young's equation. It is well known that on very rough surfaces, contact angles are larger than on chemically identical smooth surfaces (4); such contact angles do not reflect material properties of the surface; rather, they reflect morphological ones. In a recent study using atomic force microscopy, we have shown that surface roughness of the scale present on the surfaces used here, i.e. roughness in the nanometer range, has virtually no effect on the advancing contact angles (5).

In general, the experimentally observed apparent contact angle, [Theta], may or may not be equal to the Young contact angle, [[Theta].sub.Y] (3):

1) On ideal solid surfaces, there is no contact angle hysteresis and the experimentally observed contact angle is equal to [[Theta].sub.Y];

2) On smooth, but chemically heterogeneous solid surfaces, [Theta] is not necessarily equal to the thermodynamic equilibrium angle. Nevertheless, the experimental advancing contact angle, [[Theta].sub.a], can be expected to be a good approximation of [[Theta].sub.Y]. Therefore, care must be exercised to ensure that the experimental apparent contact angle, [Theta], is the advancing contact angle in order to be inserted into Young's equation;

3) On rough solid surfaces, no such equality between advancing contact angle and [[Theta].sub.Y] exists. Thus, all contact angles on rough surfaces are meaningless in terms of Young's equation.

Recently, we have shown (6, 7) that measuring contact angles at very slow motion of the three-phase contact line allows direct observation of surface quality. In addition, when such procedures are interpreted by an automated axisymmetric drop shape analysis - profile (ADSA-P), complexities such as dissolution of the polymer by the liquid and slip/stick contact angles, which affect the contact angle interpretation in terms of surface energetics, can be identified (7-13).

In this study, we report low-rate dynamic contact angles of various liquids on a polystyrene (PS) polymer by ADSA-P. The PS-coated surface is prepared by a solvent casting technique that surface roughness is in the order of nanometers or less. These dynamic (advancing) contact angles are then employed for the interpretation in terms of solid surface tensions.

MATERIALS (SOLID SURFACE AND LIQUIDS)

Polystyrene (PS) was purchased from Polysciences (Warrington, P. A.; cat# 00574, MW 125,000-250,000, atatic beads). A 2% PS/toluene solution was prepared using toluene (Sigma-Aldrich, 99.8% HPLC grade) as the solvent. Silicon wafers <100> (Silicon Sense, Naschua, N.H.; thickness: 525 [+ or -] 50 micron) were selected as the substrate for contact angle measurements. They were obtained as circular discs of about 10 cm diameter and were cut into rectangular shapes of about 2.5 cm x 5 cm. Each rectangular wafer surface was then soaked in chromic acid for at least 24 h., rinsed with doubly distilled water, and dried under a heat lamp before polymer coating.

The PS-coated surfaces were prepared by a solvent casting technique: a few drops of the 2% PS/toluene solution were deposited on dried silicon wafers inside a vacuum desiccator at about 90 [degrees] C; the solution spread and a thin layer of the PS formed on the wafer surface after toluene evaporated. This preparation produced good quality coated surfaces, as manifested by light fringes, due to refraction at these surfaces, suggesting that surface roughness is in the order of nanometers or less.

With respect to the low-rate dynamic contact angle measurements by ADSA-P, liquid was supplied to the sessile drop from below the wafer surfaces using a motorized syringe device (7). In order to facilitate such an experimental procedure, a hole of about 1 mm diameter was made, by using a diamond drill bit from [TABULAR DATA FOR TABLE 1 OMITTED] Lunzer (New York, N.Y.; SMS-0.027), in the center of each rectangular wafer surface before soaking in chromic acid. This strategy was pioneered by Oliver et al. (14, 15) to measure sessile drop contact angles because of its potential for avoiding drop vibrations and for measuring true advancing contact angles without disturbing the drop profile. In order to avoid leakage between a stainless steel needle (Chromatographic Specialities, Brockville, Ont; N723 needles pt. #3, H91023) and the hole (on the wafer surface), Teflon tape was wrapped around the end of the needle before inserting into the hole. 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 contact with the drop. Such experimental procedures cannot be used for ADSA-P since ADSA determines the contact angles and surface tensions based on the complete and undisturbed drop profile.

Thirteen liquids were chosen in this study. Selection of these liquids was based on the following criteria: (1) liquids should include a wide range of intermolecular forces; (2) liquids should be non-toxic; and (3) the liquid surface tension should be higher than the anticipated solid surface tension (4, 16). They are shown in Table 1, together with the physical properties and surface tensions (measured at 23.0 [+ or -] 0.5 [degrees] C).

METHODS AND PROCEDURES

ADSA-P is a technique to determine liquid-fluid interfacial tensions and contact angles from the shape of axisymmetric menisci, i.e., from sessile as well as pendant drops. Assuming that the experimental drop is Laplacian and axisymmetric, ADSA-P finds a theoretical profile that best matches the drop profile extracted from an image of a real drop, from which the surface tension, contact angle, drop volume, surface area and three-phase contact radius can be computed. The strategy employed is to fit the shape of an experimental drop to a theoretical drop profile according to the Laplace equation of capillarity, using surface/interfacial tension as an adjustable parameter. The best fit identifies the correct surface/interfacial tension from which the contact angle can be determined by a numerical integration of the Laplace equation. Details of the methodology and experimental set-up can be found elsewhere (7,17-19).

Sessile drop experiments were performed by ADSA-P to determine contact angles. The temperature and relative humidity were maintained, respectively, at 23.0 [+ or -] 0.5 [degrees] C and at about 40%. It has been found that, since ADSA assumes an axisymmetric drop shape, the values of 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, the liquid surface tensions used in this study were independently measured by applying ADSA-P to a pendant drop, since the axisymmetry of the drop is enforced by using a circular capillary. Results of the liquid surface tension are given in Table 1.

In this study, at least 7 and up to 10 dynamic contact angle measurements were performed for each liquid, at velocities of the three-phase contact line in the range from 0.1 to 1.2 mm/min. The choice of this velocity range was based on previous studies (6, 7, 20), which showed that low-rate dynamic contact angles at this velocity range are essentially identical to the static contact angles, for these relatively smooth surfaces.

In actual experiments, an initial liquid drop of about 0.3 cm radius was carefully deposited, covering the hole on the surface. This is to ensure that the drop will increase axisymmetrically in the center of the image field when liquid is supplied from the bottom of the surface and will not hinge on the lip of the hole. The motor in the motorized syringe mechanism was then set to a specific speed, by adjusting the voltage from a voltage controller. Such a syringe mechanism pushes the syringe plunger, leading to an increase in drop volume and hence the three-phase contact radius. A sequence of pictures of the growing drop was then recorded by the computer typically at a rate of 1 picture every 2 seconds, until the three-phase contact radius was about 0.5 cm or larger. For each low-rate dynamic contact angle experiment, at least 50 and up to 100 images were normally taken. Since ADSA-P determines the contact angle and the three-phase contact radius simultaneously for each image, the advancing dynamic contact angles as a function of the three-phase contact radius (i.e. location on the surface) can be obtained. The actual rate of advancing can be determined by linear regression, by plotting the three-phase contact radius over time. For each liquid, different rates of advancing were studied, by adjusting the speed of the pumping mechanism.

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. When the measured contact angles are essentially constant at different surface locations, the mean contact angle for a specific rate of advancing can be obtained by averaging the contact angles, after the three-phase contact radius reaches 0.4 to 0.5 cm (see later). The purpose of choosing these relatively large drops is to avoid any line tension effects on the measured contact angles (21-23).

RESULTS AND DISCUSSION

Of the 13 liquids used, it was found that only 6 liquids yielded usable contact angles. They are water, glycerol, formamide, ethylene glycol, diethylene glycol, and dimethyl sulfoxide (DMSO). The rest of the 7 liquids either dissolved the polymer on contact or yielded non-constant contact angles during the course of the experiments.

Figures 1(a)-(f) show, respectively, typical experimental results of water, glycerol, formamide, ethylene glycol, diethylene glycol, and DMSO: all contact angles are essentially constant, as drop volume V increases and hence the three-phase contact radius. Increasing the drop volume in this manner ensures the measured [Theta] to be an advancing contact angle. In all cases, the measured contact angles are essentially constant as R increases. This indicates good surface quality of the surfaces used. It turns out that averaging the measured contact angles after R reaches 0.4 cm is convenient, since the drop is guaranteed to be in the advancing mode and that line tension effects are negligible. While a three-phase contact radius of 0.4 cm may seem to be an arbitrary value, it turns out that there is virtually no dependence on the choice of the starting point.

In Figs. 1 (a) and (f), there is an initial increase in the contact angle at essentially constant R as the drop volume increases. This is due to the fact that even carefully putting an initial liquid drop from above on a solid surface can result in a contact angle somewhere between advancing and receding. After reaching the proper advancing contact angle, further increase in the drop volume causes the drop front to advance, with [Theta] essentially constant as R increases.

Two liquids, 1, 1, 2, 2-tetrabromoethane and 1-iodonaphthalene were found to dissolve the PS-coated wafer on contact, resulting in very irregular and fiat drops. The remaining 5 liquids all show slip/stick behavior. Figure 2(a) shows the contact angle results of diiodomethane. It can be seen that initially the apparent drop volume, as perceived by ADSA-P, increases linearly, and [Theta] increases from 35 [degrees] to 60 [degrees] at essentially constant R. Suddenly, the drop front jumps to a new location as more liquid is supplied into the sessile drop. The resulting [Theta] decreases sharply from 60 [degrees] to 35 [degrees]. As more liquid is supplied into the sessile drop, the contact angle increases again. Such slip/stick behavior could be due to non-inertness of the surface. Phenomenologically, an energy barrier for the drop front exists, resulting in sticking, which causes [Theta] to increase at constant R. However, as more liquid is supplied into the sessile drop, the drop front possesses enough energy to overcome the energy barrier, resulting in slipping, which causes [Theta] to decrease suddenly. It should be noted that as the drop front jumps from one location to the next, it is unlikely that the drop is or will remain axisymmetric. Such a non-axisymmetric drop will obviously not meet the basic assumptions underlying ADSA-P, causing possible errors, e.g. in the apparent surface tension and drop volume. This can be seen from the discontinuity of the apparent surface tension and drop volume with time as the drop front sticks and slips. Obviously, the observed angles in Fig. 2(a) cannot all be the Young contact angles; since [[Gamma].sub.lv], [[Gamma].sub.sv] (and [[Gamma].sub.sl]) are constants, [Theta] ought to be a constant because of Young's equation. In addition, it is difficult to decide unambiguously at this moment whether or not Young's equation is applicable at all because of lack of understanding of the slip/stick mechanism. Therefore, these contact angles should not be used for the interpretation in terms of surface energetics.

The experimental results of other liquids, either incompatible with Young's equation or possibly with physico-chemical reaction with the solid surface, are shown in Figs. 2(b)-(e). It can be seen that all liquids yield slip/stick behavior and, for reasons discussed above, these angles cannot be used for the interpretation in terms of surface energetics.

The reproducibility of all solid-liquid systems is excellent. They are summarized in Table 2 for the 6 liquids with constant contact angles, at different rates of advancing and each on a newly prepared surface; a total of more than 70 freshly prepared PS-coated wafers were prepared and used; more than 4000 images were acquired and analyzed by ADSA-P. In the specific case of water in Table 2, a final value of 88.42 [+ or -] 0.28 was obtained, by averaging the contact angles from different rates of advancing (for different experiments). The 95% confidence limits calculated in this manner (in Table 2) include all possible errors, due to experimental technique, solid surface preparation, etc. A summary of the results is given in Table 3.

Disregarding the inconclusive contact angle data in Fig. 2, we show in Fig. 3 the contact angle results from Tab/e 2, by plotting [[Gamma].sub.lv]cos[Theta] vs. [[Gamma].sub.lv]. It can be seen that liquids with different molecular nature fall on a smooth curve, in good agreement with the patterns from previous studies (7-13, 24-27): the values of [[Gamma].sub.lv]cos[Theta] change smoothly with [[Gamma].sub.lv], so that we again conclude that

[[Gamma].sub.lv] = cos[Theta] = F([[Gamma].sub.lv], [[Gamma].sub.sv]) (2)

and hence because of Young's equation

[[Gamma].sub.sl] = F ([[Gamma].sub.lv], [[Gamma].sub.sv])(3)

Thus, the surface tension component approaches (28-31) clash directly with these experimental results: the surface tension component approaches (28-31) stipulate that [[Gamma].sub.sl] depends not only on [[Gamma].sub.lv] and [[Gamma].sub.sv], but also on the specific intermolecular forces of the liquids and solids. The above experimental results allow one to search for a relation in the form of Eq 3.

On phenomenological grounds, an equation-of-state approach for solid-liquid interfacial tensions has been formulated (32, 33):

[[Gamma].sub.sl] = [[Gamma].sub.lv] + [[Gamma].sub.sv] - 2[-square root of [[Gamma].sub.sv] [e.sup.-[Beta]([[Gamma].sub.lv] - [[Gamma].sub.sv]).sup.2]]] (4)

where [Beta] is a constant which was found to be 0.0001247 [([m.sup.2]/mJ).sup.2]. Combining this equation with

Young's equation yields

cos[[Theta].sub.Y] = 1 + 2 [-square root of [[Gamma].sub.sv]/[[Gamma].sub.lv]] [e.sup.-[Beta]([[Gamma].sub.lv] - [[Gamma].sub.sv]).sup.2] (5)

Thus, the solid surface tensions can be determined from experimental (Young) contact angles and liquid surface tensions.

The applicability of any approach having the form of Eq 3 can be tested using the criteria of the constancy of the calculated [[Gamma].sub.sv] values. Relations of the form of Eq 3 have been in the literature for a long time. Two examples are Antonow's role (34)

[[Gamma].sub.sl] = [[Gamma].sub.lv] + [[Gamma].sub.sv] - 2 [-square root of[[Gamma].sub.lv] [[Gamma].sub.sv]] (6)

and Berthelot's geometric mean relationship (35)

[[Gamma].sub.sl] = [[Gamma].sub.lv] + [[Gamma].sub.sv] - 2 [-square root of [[Gamma].sub.lv] [[Gamma].sub.sv]] (7)

Combining these or similar relationships with Young's equation yields a relation of the form of Eq 2, from which [[Gamma].sub.sv] can be calculated. We show in Table 4 the [[Gamma].sub.sv] values calculated from Antonow's rule (34), Berthelot's rule (35), and the equation-of-state approach for solid-liquid interfacial tensions (33), i.e. Eq 5; the underlying Eq 4 can be understood as a modified Berthclot rule (32). It can be seen that the values of [[Gamma].sub.sv] calculated from Antonow's rule increase as [[Gamma].sub.lv] increases; the [[Gamma].sub.sv] values calculated from Berthelot rule decrease as [[Gamma].sub.lv] increases. Only the [[Gamma].sub.sv] values from the equation-of-state approach for solid-liquid interfacial tensions are quite constant, essentially independent of the liquids used: the [[Gamma].sub.sv] value of PS was found to be 29.82 mJ/[m.sup.2] with a 95% confidence limit of [+ or -] 0.47 mJ/[m.sup.2].

It should be noted that the constant [Beta] value of 0.0001247 [([m.sup.2]/mJ).sup.2] used in the above calculations was determined only from the contact angle data on three well-prepared solid surfaces (25): FC-721-coated mica, heat-pressed Teflon (YEP), and poly(ethylene terephthalate) (PET). Alternatively, the [[Gamma].sub.sv] value of PS can be determined by a two-variable least-square analysis (25, 33), [TABULAR DATA FOR TABLE 2 OMITTED] [TABULAR DATA FOR TABLE 3 OMITTED] by assuming [[Gamma].sub.sv] and [Beta] in Eq 5 to be constant. Employing the set of contact angle data on PS, we obtain a [Beta] value of 0.0001197 [([m.sup.2]/mJ).sup.2] and a [[Gamma].sub.sv] value of 29.67 md/[m.sup.2]. It is evident that there is good agreement between the [[Gamma].sub.sv] values (29.82 [+ or -] 0.47 mJ/[m.sup.2] and 29.67 mJ/[m.sup.2]) determined from the two strategies. However, it might be argued that the two [Beta] values are different. To show that such a difference is of little consequence with respect to the determination of [[Gamma].sub.sv], we determined the [[Gamma].sub.sv] values of a hypothetical system having [[Gamma].sub.lv] 50 mJ/[m.sup.2] and [Theta] = 50[degrees] for the above [Beta] values. It turns out that there are virtually no differences in the calculated [[Gamma].sub.sv] values: [[Gamma].sub.sv] = 35.54 mJ/[m.sup.2] when [Beta] = 0.0001247 [([m.sup.2]/mJ).sup.2] and [[Gamma].sub.sv] = 35.48 mJ/[m.sup.2] when [Beta] = 0.0001197 [([m.sup.2]/mJ).sup.2]. The above results reconfirm the validity of the equation-of-state approach (33) to determine solid surface tensions from contact angles.

Alternatively, polymer melts experiments (36-38) have been widely used in the determination of [[Gamma].sub.sv] at room temperature by extrapolation. The [[Gamma].sub.sv] value of the atatic polystyrene reported here is in close agreement with that obtained recently from polymer melts (39). The polystyrene surface tension at 20 [degrees] C has been obtained by extrapolating the melt surface tension below the glass transition temperature, [T.sub.g].

However, such an extrapolated value could be in error, if d[Gamma]/dT changes significantly at [T.sub.g]. Thus, allowing for a change in d[Gamma]/dT by [+ or -] 20% and assuming that there is no step change in the surface tension at [T.sub.g], the upper and lower limits of the extrapolated surface tension at 20 [degrees] C would be, respectively, 34.4 and 32.8 mJ/[m.sup.2]. the fact that the value for the solid surface tension is slightly lower than the extrapolated melt surface tension represents a well-known pattern: it has been found, e.g., from solidification front experiments (40) that, for a large number of cases (with the exception of water), the extrapolated [[Gamma].sub.lv] values of the melt to room temperature are higher than the actual surface tensions of the solids, typically by a few percent. In light of this and given the fact that the polystyrenes used in the two studies are not identical, an average [[Gamma].sub.sv] value of 29.8 [+ or -] 0.5 mJ/[m.sup.2] for polystyrene, [TABULAR DATA FOR TABLE 4 OMITTED] determined from contact angles using the equation-of-state approach (33), is indeed very plausible.

CONCLUSIONS

(1) The values of [[Gamma].sub.lv] cos[Theta] change smoothly with [[Gamma].sub.lv] for polystyrene, in excellent agreement with those from other polar and non-polar surfaces (7-13, 24-26).

(2) The [[Gamma].sub.sv] values of polystyrene calculated from the equation-of-state approach (33) are quite constant, essentially independent of the liquids used; the average value is [[Gamma].sub.sv] = 29.8 [+ or -] 0.5 mJ/[m.sup.2]. This reconfirms the soundness of the approach to calculate solid surface tensions from contact angles.

ACKNOWLEDGMENTS

This research was supported by the Natural Science and Engineering Research Council of Canada (Grants: No. A8278 and No. EQP173469), Ontario Graduate Scholarships (D.Y.K.), and University of Toronto Open Fellowships (D.Y.K.).

REFERENCES

1. A.W. Neumann, Adv. Colloid Interface Sci., 4, 105 (1974).

2. A. Marmur, Colloids Surf. A, 116, 25 (1996).

3. D. Li and A. W. Neumann, "Thermodynamic Status of Contact Angles" in Applied Surface Thermodynamics, A.W. Newmann, J. K. Spelt, eds.; Marcel Dekker Inc.: New York, 1996; pp 109-168.

4. K. Grundke, T. Bogumil, T. Gietzelt, H.-J. Jacobasch, D. Y. Kwok, and A. W. Neumann, Prog. Colloid Polym. Sci., 101, 58 (1996).

5. K. Grundke, P. Weidenhammer, C. Werner, R. Trinowitz, A. Janke, D. Y. Kwok, K. Poschel, H.-J. Jacobasch, and A. W. Neumann (in preparation).

6. D. Y. Kwok, C. J. Budziak, and A. W. Newmann, J. Colloid Interface Sci., 173, 143 (1995).

7. D. Y. Kwok, R. Lin, M. Mui and A. W. Neumann, Colloids Surf. A, 116, 63 (1996).

8. D. Y. Kwok, T. Gietzelt, K. Grundke, H.-J. Jacobasch, and A. W. Neumann, Langmuir, 13, 2880 [1997).

9. O. I. del Rio, D. Y. Kwok, R. Wu, J. M. Alvarez, and A. W. Neumann, "Contact Angle Measurements by Axisymmetric Drop Shape Analysis and an Automated Polynomial Fit Program," Colloid Surf. A, (accepted for publication).

10. D. Y. Kwok, C. N. C. Lain, A. Li, A. Leurig, R. Wu, E. Mok and A. W. Neumann, "Measuring and Interpreting Contact Angles: A Complex Issue," Colloids Surf. A, (accepted for publication.)

11. D.Y. Kwok, A. Leung, A. Li C. N. C. Lam, R. Wu and A. W, Neumann, Colloid Poly. Sci., 276, 459 (1998).

12. D. Y. Kwok, C. N. C. Lam, A. Li A. Leung and A. W. Neumann, Langmuir, 14, 2221 (1998).

13. D. Y. Kwok, C. N. C. Lam, A. Li and A. W. Neumann, "LowRate Dynamic Contact Angles on Poly(methyl methacrylate/n-butyl methacrylate) and the Determination of Solid Surface Tensions", J. Adhes. (accepted for publication).

14. J. F. Oliver, C. Huh, and S. G. Mason, J. Colloid Interface Sci., 58, 568 (1977).

15. J. F. Oliver, C. Huh, and S. G. Mason, Colloids Surf., 1, 79 (1980).

16. W. A. Zisman, "Contact Angle, Wettability and Adhesion" in Advances in Chemistry Series, Vol. 43; American Chemical Society: Washington, D.C., (1964).

17. Y. Rotenberg, L. Boruvka, and A. W. Neumann, J. Colloid Interface Sci., 83, 169 (1983).

18. P. Cheng, C. Li, L. Boruvka, Y. Rotenberg, and A. W. Neumann, Colloids Surf., 83, 169 (1983).

19. S. Lahooti, O. I. Kel Rio, P. Cheng and A. W. Neumann, "Axisymmetric Drop Shape Analysis," in Applied Surface Thermodynamics, A. W. Newmann, J. K. Spelt, eds., Marcel Dekker Inc.: New York, 1996; pp. 441-507.

20. D. Y. Kwok, D. Li and A. W. Neumann, "Capillary Rise at a Vertical Plate as a Contact Angle Technique," in Applied Surface Thermodynamics, A. W. Neumann, J. K. Spelt, eds., Marcel Dekker Inc.: New York, 1996; pp. 413-440.

21. D. Duncan, D. Li, J. Gaydos, and A. W. Neumann, J. Colloid Interface Sci., 169, 256 (1995).

22. D. Li and A. W. Neumann, Adv. Colloid Interface Sci., 39, 347 (1992).

23. J. Gaydos and A. W. Neumann, "Line Tension In Multiphase Equilibrium Systems," in Applied Surface Thermodynamics, A. W. Neumann, J, K. Spelt. eds., Marcel Dekker Inc.: New York, 1996; pp. 169-238.

24. D. Y. Kwok, D. Li, and A. W. Neumann, Colloids Surf. A, 89, 181 (1994).

25. D. Li and A. W. Neumann, J. Colloid Interface Sci., 148, 190 (1992).

26. D. Li, M. Xie, and A. W. Neumann, Colloid Polym. Sci., 271, 573 (1993).

27. D. Y. Kwok and A. W. Neumann, "Contact Angles and Surface Energetics," Prog. Colloid Polym. Sci., 109, 170 (1998).

28. F. M. Fowkes, Ind. Eng, Chem., 12, 40 (1964).

29. D. K. Owens and R. C. Wendt, d. Appl. Polym. Sci., 13, 1741 (1969).

30. C. J. van Oss, M. K. Chaudhury, and R. J. Good, Chem. Revs., 88, 927 (1988).

31. R. J. Good and C. J. van Oss, "The Modern Theory of Contact Angles and the Hydrogen Bond Components of Surface Energies," in Modern Approaches to Wettability: Theory and Applications, M. Schrader, G. Loeb., eds.; Plenum Press: New York, 1992; pp. 1-27.

32. D. Li and A. W. Neumann, J. Colloid Interface Sci., 137, 304 (1990).

33. J. K. Spelt and D. Li, "The Equation of State Approach to Interfacial Tensions," in Applied Surface Thermodynamics, A. W. Neumann, J. K. Spelt, eds., Marcel Dekker Inc.: New York, 1996; pp 239-292.

34. G. Antonow, J. Chim. Phys., 5, 372 (1907).

35. D. Berthelot, Compt. rend., 126, 1703, 1857 (1898).

36. S. Wu, J. Colloid Interface Sci., 31, 153 (1969).

37. S. Wu, J. Phys. Cherry, 74, 632 (1970).

38. S. Wu, in: Polymer Interface and Adhesion, Marcel Dekker, New York (1982).

39. D.Y. Kwok, L. K. Cheung, C. B. Park, and A. W. Neumann, Polym. Eng. Sci., 38, 757 (1998).

40. D. Li and A. W. Neumann, "Behaviour of Particles at Solidification Fronts," in Applied Stiff ace Thermodynamics, A. W. Neumann, J. K. Spelt, eds.; Marcel Dekker Inc.: New York, 1996; pp. 557-628.

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Author: | Kwok, D.Y.; Lam, C.N.C.; Li, A.; Zhu, K.; Wu, R.; Neumann, A.W. |
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Publication: | Polymer Engineering and Science |

Date: | Oct 1, 1998 |

Words: | 4594 |

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