Langmuir 1994,10, 2006-2009
2006
Calculation of Spreading Pressure from Contact Angle Data on Polymer Surfaces H. Yildirim Erbil TUBITAK, Marmara Research Center, Department of Chemical Engineering, P.O. Box 21, 41470 Gebze-Kocaeli, Turkey Received August 27,1993. In Final Form: January 14,1994' A novel analysis to determine the spreading pressure, r,, for water-polymer interactions from contact angle data is proposed by using Van Oss et al.'s interfacialLifshitz-van der Waals and acidtbaseinteractions method. In this analysis, first measurements of the contact angles of water drops on the polymer in different hydrocarbons in the two-liquid method are performed; then the contact angle determination of a water drop on the same polymer sample in the one-liquid method is carried out. The data obtained from the one-liquid method are evaluated by using the data obtained from the two-liquid method in order to calculate T,. The precise contact angle data on poly(tetrafluoroethy1ene)(PTFE),poly(methy1methacrylate) (PMMA),and poly(viny1chloride) (PVC) reported by Tamai et al. are used in the calculations and good agreement is obtained with the x, data obtained from independent adsorption measurements.
Introduction The surface free energy of polymers cannot be measured directly because of the elastic and viscous restraints of the bulk phase, which necessitates the use of indirect methods. Several approximations are currently available to evaluate the surface free energy of polymers from contact angle data.' These semiempirical approximations were derived from the works of Girifalco and Good: F ~ w k e sOwens ,~ and Wendt,4 and Wu6 and resulted in large controversy in this field. The use of nonlinear programming methods did not give satisfactory results.The above approximations depend on the data obtained by measuring the contact angle of liquids on the polymer surface under its vapor atmosphere, which is also called the "one-liquid" method. Tamai et al.9J0have extended this method to high-energy surfaces such as metals as well as to low-energy surfaces such as polymers by measurements of the contact angles of water drops in different hydrocarbons which is called the "two-liquid" method. However, it is a common fact that in all of these approaches, the spreading pressure, re, which is the equilibrium film pressure of the adsorbed vapor of the liquid on the polymer, is assumed to be zero for low-energy surfaces. In contrast, there have been several experimental studies which have shown large values for low-energy surfaces, and it was suggested that, to some extent, a spreading pressure might exist even if finite contact angles were ~bserved.'l-~~ In our previous study,'aa novel analysis was used to determine the spreading pressure from contact ~~
~
Abstract published in Advance ACS Abstracts, April 1, 1994. (1) Adamson, A. W. In Physical Chemistry of Surfaces, 5th ed.; Wiley-Interscience: New York, 1990; Chapter 10. (2) Girifalco, L. A,; Good, R. J. J.Phys. Chem. 1967, 61, 904. (3) Fowkes, F. M. Ind. Eng. Chem. 1964,56, 40. (4) Owens, D. K.; Wendt, R. C. J. Appl. Polym. Sci. 1969, 13, 1741. (5) Wu, S. J. Phys. Chem. 1970, 74, 632. (6) Erbil, H. Y. J. Appl. Polym. Sci. 1987, 33, 1397. (7) Erbil, H. Y.; Merip, R. A. Colloids Surf. 1988, 33, 85. (8) Erbil, H. Y.; Merip, R. A. Angew. Makromol. Chem. 1988,163,101. (9)Tamai, Y.; Makuuchi, K.; Suzuki, M. J. Phys. Chem. 1967, 71, 4176. (10)Tamai, Y.; Mataunaga, T.; Horiuchi, K. J. Colloid Interface Sci. 1977, 60, 112. (11) Melrose, J. C. In Contact Angle, Wettability and Adhesion; Advances in Chemistry Series No. 43; American Chemical Society: Washington, DC, 1964; p 158. (12) Zettlemoyer, A. C. J. Colloid Interface Sci. 1968,28, 343. (13) Tadros, M. E.; Hu, P.; Adamson, A. W. J. Colloid Interface Sci. 1974, 49, 184. (14) Dann, J. R. J. Colloid Interface Sci. 1970, 32, 302. @
angle data by the combination of the two-liquid contact angle method with the one-liquid contact angle method using Good's interaction parameter (0)formalism. In that method, first measurements of the contact angles of water drops on the polymer in different hydrocarbons in the two-liquid method were performed; then the contact angle determination of a water drop on the same polymer sample in the one-liquid method was carried out. The data obtained from the one-liquid method were evaluated by using the data obtained from the two-liquid method in order to calculate r e . This method did not require the use of (a)values calculated in terms of statistical mechanics, due to the fact that the product (0ysJ2) can be readily calculated from experimental data. The precise contact angle reported by Tamai et al.l0 were used in the calculations and good agreement was obtained with the re data obtained from independent adsorption measurements.18 Recently, Van Oss, Good, and co-workers introduce a theory and a practical methodology to estimate the interfacial tensions between apolar and electron acceptor/ electron donor molecules.1g-21 They assume that surface and interfacial tensions consist of two components; an apolar or a Lifshitz-van der Waals component (indicated by superscript LW) of electrodynamic origin and a polar component (indicated by superscript AB) caused by Lewis acid-base interactions. The two components are additive: yjj = yi;w
+ yij-
They suggested that LW forces include not only the London dispersion forces (d) but also the Keesom orientation (p) and Debye induction (I) forces:
+ yiip + yi;
(2) This methodology was successfully applied to polymer and protein interactions with liquids, surface free energy y i y = yijd
(15) Good, R. J. J. Colloid Interface Sci. 1976,52, 308. (16) Buascher, H. J.; Kip, G. A. M.; Van Silfhout, A.; Arende, J. J. Colloid Interface Sci. 1986, 114, 307. (17) Janczuk, B.; Wojcik, W.; Zdziennicka,A.; Gonzalez-Caballero,F. J. Mater. Sci. 1992,27,6447. (18) Erbil, H. Y. J. Adhes. Sci. Technol. 1989, 3, 29. (19)Van Om, C. J.; Chaudhury, M. K.; Good, R. J. Adu. Colloid Interface Sci. 1987,8, 35. (20) Van Oss, C. J.; Chaudhury, M. K.; Good, R. J. Chem. Rev. 1988, 88, 927. (21) Van 0 8 8 , C. J.; Good, R. J. J.Macromol. Sci., Chem. 1989, A26, 1183.
0743-7463/94/2410-2006$04.50/00 1994 American Chemical Society
Langmuir, Vol. 10, No. 6,1994 2007
Calculation of Spreading Pressure determination of polymers, polymer solubility predictions of solvents, and critical micelle concentration estimation of surfactants.l%= This methodology was also tested with liquid-liquid interactions% and the calculated results agreed well with independent interfacial tension data from mercury interactions.27 More recently, Van Oss et al. methodology was applied to the two-liquid method2s in the determination of the galena surface free energy components, and the results were compared with the Hamilton,29 Ruckenstein,30 and S ~ h u l t z linear ~ ~ t ~equation ~ extrapolation approach. In the present study, the methodology of Van Oss et al. is applied to determine the spreadingpressure from contact angle data obtained by using both "one-liquid"and "twoliquid" methods. Since Tamai et al.lo reported precise contact angle data for the same polymer samples prepared by the same procedure with the one-liquid and the twoliquid methods, these data are used in calculations.
Theory (1) One-LiquidMethod. Young's equations3describes the thermodynamic equilibrium of the three surface free energies ysv, YSL, and YLV existing at the phase boundaries of a drop of liquid at rest on a solid surface (3) YLV cos 6 = Ysv - YSL where YLV, YSV, and YSL are, respectively, the surface free energiesof liquid and of solid against their saturated vapor, and the surface free energy of the interface between solid and liquid; subscripts L, S, and V refer to liquid, solid and vapor respectively. The work required to pull the liquid away from the surface (i.e., the total work of adhesion) is given by DuprB's equation34 as follows
(W (W
S L ~and ~ )the acid-base work of adhesion contributions S L ~are ) the main components of WSLA. WSLA= WSLLW + WSLD
The additivity of intermolecular forces is accepted for both surface and interfacial free energies as in eq 1 and for all exclusively LW interactions, i.e., interactions between two completely apolar compounds; the GoodGirifalco-Fowkes combining rule35is applicable
In many liquid-solid interfaces, in addition to LW interactions, polar interactions of the hydrogen bonding type often occur. All electron acceptor-electron donor interactions or Lewis acid-base (AB)interactions are this type. Unlike LW interactions, AB interactions are essentially asymmetrical and can only be satisfactorily treated by taking that asymmetry into account.20 The electron acceptor and electron donor parameters of the yzm are thus expressed as, respectively, Yi+ and Yjso that yiAB =-2 (10) The work of adhesion contribution of the acid-base interactions can then be expressed as19920
By combining eqs 4 and 9 in LW form one obtains
Consequently,the total work of adhesion will be as from eqs 8, 11, and 12
(4) WSLA= Yso + YLV - YSL where yso is the surface tension of the solid in vacuum. Combining eqs 3 and 4 yields (5) wSLA= (ys0- ySv) + YLv(l + COS 0) where the first term is the spreading pressure, which is the equilibrium film pressure of the adsorbed vapor of the liquid on the solid (6) = Yso - Ysv and correspondsto the reduction of the surface free energy of the solid when in contact with the saturated vapor of the wetting liquid. Combining eqs 5 and 6 yields =Tg
WSL" = 7re + Y L V ( l + cos 0) (7) According to the method of van Oss et al.1@-21the Lifshitz-van der Waals work of adhesion contributions (22)Van Oss, C. J.; Arnold, K.; Good, R. J.; Gawrisch, K.; Ohki, J. Macromol. Sci., Chem. 1990,A27,563. (23)Van Ose, C. J.; Good, R. J. J. Dispersion Sci. Technol. 1991,12, 95. (24)Van Oss, C. J.; Good, R. J. Langmuir 1992,8,2877. (25)Chibowski, E.;Bolivar, M.; Gonzalez-Caballero, F. J. Colloid Interface Sci. 1992,154, 400. (26)Erbil, H. Y. Langmuir 1994,10,286. (27)Erbil, H. Y. J. Colloid Interface Sei. 1989,129,384. (28)Janczuk, B.; Wojcik, W.; Zdziennicka, A.; Gonzales-Caballero, F. Mater. Chem. Phys. 1992,31,235. (29)Hamilton, W. C. J. Colloid Interface Sei. 1971,40, 219. (30)Ruckenstein, E.; Lee, H. S. J. Colloid Interface Sci. 1987,120, 153. (31)Schultz, J.; Toutaumi, K.; Dounet, J. B. J. Colloid Interface Sci. 1977.59. 272. ----, (32)Shanahan,M.E.R.;Canzeneuve,C.;Carre,A.;Schultz, J. J. Chem. Phys. 1982, 79,241. (33)Young, T. Philos. Trans. R . SOC.London 1805,95,65. (34)JhprB, A. In Theorie Mecanique de la Chaleur;Gauthier-Villars: Paris, 1869;p 368.
--.
(13) Then by combining eqs 7 and 13, one obtains 7re
+ YLV(1 + cos 0) =
+ z/y,.'y,,+)(14) (2) Two-Liquid Method. Young's equation for the contact angle (0) of a water drop (W) on a plain solid (S) in a hydrocarbon (H) is cos e = YSH - YSW (15) The interfacial free energy equation in the Van Oss et al. approach iszo YHW
712
=
(0+ l.&+)(G 6) (16)
2(* when applied to a two-liquid system one obtains TSH
=
(e
2 ( d 7-
- -1'
+
z/rH+ - 6) )(G - x,(H) (17)
Ysw = ( d & = - d p ) 2 +
6)
2(2/r,' - G I ( & - - aH(W) (18) In the two-liquid method, hydrocarbon and water are mutually soluble to some extent and it may be possible (35)Reference 1, p 407.
Erbil
2008 Langmuir, Vol. 10, No. 6, 1994
that water is adsorbed onto the solid surface from the hydrocarbon phase a d H ) , or conversely, the hydrocarbon is adsorbed onto the solid surface from the water phase
Table 1. Surface Free Energies and the Interfacial Free Energiea of the Liquids Used in the Two-Liquid Method (mJ/mVO ~~
TH(w).
On the other hand, since all the used aliphatic hydrocarbons are apolar, by definitionm LW = YH+=YH-=O and YH YH Then eq 17 becomes
Combining eqs 15, 18, and 19 yields YHW COS
e = YH - yWLw -
cyclohexane isooctane n-hexane water
YLV
YHW
25.0 18.9 18.7 72.8
50.3 49.7 49.3
Table 2. Water Contact Angles (e) on the Polymerdo(deg) two-liquid method one-liquid method cyclohexane isooctane n-hexane PMMA 73.1 f 1.2 118.8 i 1.0 112.5 i 1.1 NIP 113.9 i 0.8 174.7 i 0.9 173.4 f 0.8 175.0i 0.7 PTFE 84.0 i 1.5 139.9 & 1.5 134.2i 1.0 134.1 i 0.8 PVC ND = not determined.
‘ d x -
- [Tw(H)- a H ( w ) ] (20)
When only two hydrocarbon-water sets are considered, eq 20 becomes
Table 3. One-Liquid Contact Angle Results for the Polymers Used*‘ (deg) glyc- ethylene form- methylene a-bromowater erol glycol amide iodide naphthalene PTFE 112 105 87 91 85 76 74 67 52 57 34 11 PMMA 50 55 40 16 PVC 83 69
In the one-liquid method, for water drops on polymers eq 14 can be rewritten as aw
+ Y w ( i + cos e) = 2d-
+ G+ -1
(27)
Since most polymers are monopolar, that is, they only accept or donate electronsthrough acid-base interactions, one of the terms of ys+ and ys- is equal to zero. Accordingly, when one uses a ypLWvalue obtained from the two-liquid method, and yw, yw+, yw-, yp+, and y s o values from literature, it is possible to calculate the spreading pressure of water on polymers from eq 27.
Since
eq 23 becomes
so, even aw(H) and TH(W) cannot be neglected, the difference between the a’s of the hydrocarbons can be considered to be negligible, A*H(W)
0,
3 :
A*w(H)
0
3 :
(25)
and consequently one obtains YH,W
cos
- YH,W cos e2 = YH, - YH, -
Since, the left-hand side of eq 26 and YH, and YH, are all known experimentally, yseLW can be calculated from this equation.
Results and Discussion The surface and interfacial free energies of the liquids reported by Tamai et al.l0 are presented in Table 1. The contact angle measurement results of water drops on poly(methylmethacrylate)(PMMA),poly(tetrafluoroethy1ene) (PTFE), and poly(viny1 chloride) (PVC) are taken from ref 10 both for the one- and two-liquid methods and are given in Table 2. Since, PTFE is an apolar polymer, its ypLWand awvalues can be directly calculated from eqs 26 and 27 using ys- = ys+ = 0. The results are presented in Table 6. The water spreading pressure on PTFE is not equal to zero, it is 6.2 mJ/m2 and is in good agreement with the published data from ellipsometricmeasurements and the results obtained from different calculation routes.W827 For PMMA and PVC, which are interacting with water via acid/base electron donor/acceptor interactions, a problem exists. Since eq 27 has two unknowns, the value of y s o - of the water-polymer interaction is required to calculate awon this polymer. For the nearest approximation, we used ysv- instead of yp-. Dann’s precise results are presented in Table 314 and van Oss et al.’s liquid parameters are presented in Table 4.3s The values of the ysVLw and ysv- parameters calculated from Tables 3 and 4 using A, = 0 in eq 14 are presented in Table 5. Then a,,,values are calculated from (36)Van Ow, C. J.; Giese, R. F.; Li, Z.;Murphy, K.;Norrie, J.; Chaudhury, M. K.;Good, R. J. J. Adhes. Sci. Techno!. 1992,6,413. (37) Hu, P.; Adamson, A. W.J. Colloid Interface Sci. 1977,59, 605.
Calculation of Spreading Pressure
Langmuir, Vol. 10,No. 6,1994 2009
Table 4. Values of the Surface Tension Components and ParameteraM (mJ/mZ) water glycerol ethylene glycol formamide methylene iodide a-bromonaphthalene
YLV
YLVLW
YL+
YL-
72.8 64.0 48.0 58.0 50.8 44.4
21.8 34.0 29.0 39.0 50.8 44.4
25.5 3.92 1.92 2.28 0 0
25.5 57.4 47.0 39.6
0 0
Table 5. Values of the Parameters Calculated from Tables 3 and 4 Using re = 0 in Equation 14 (mJ/m2) PTFE PMMA PVC
YSVLW
Ysv-
17.12 43.04 41.15
0 9.79 4.65
Table 6. Values of the Parameters Calculated from Tables 1,2, and 5 Using Equations 26 and 27 (mJ/mZ) PTFE PMMA PVC
YSOLW
mv
28.11 75.13 60.00
6.20 18.58 13.70
Table 7. Values of the Water Spreading Pressure on Polymers from Published Literature (mJ/mZ)
mv PTFE PTFE PTFE PMMA PMMA PVC
8.8 9.0 6.6 26.0 16.3 6.4
ref 37 16 18 16 18 18
Tables 1, 2, and 5 using eqs 26 and 27 and are given in Table 6. Water has a spreading pressure of 18.58 mJ/m2 on PMMA which is in good agreement with values reported in Table 7. It is approximately 71 % of the value reported by Busscher et al. from ellipsometrically measured adsorption isotherms.l6 We found no experimental adsorption data for water-PVC interactions in the literature to compare. The rw value for water-PVC interaction calculated in this method is nearly twice the value calculated via interaction parameter (a) formalism.18 This larger value seems to be more consistent if we compare the difference between ysoLWand ysvLWwhich is 18.85 mJ/ m2.
The main controversy was derived from the Fox and Zisman study38 on the effect of the partial vapor pressure of the liquid-phase component on the contact angles of several organic liquids on PTFE. No difference was observed between the angles measured in air having a negligible partial vapor pressure and those measured in air saturated with vapor. This result led to the conclusion that the film pressures were of vanishing magnitude for the cases studied. Many researchers had also adopted this assumption in their discussions. However, experimental measurement of contact angles involves a liquid drop resting on a solid surface forming a three-phase confluent zone. The vapor space in the immediate neighborhood of this region is saturated or nearly saturated with the liquid vapor. Hence, the solid-vapor interface, which is effective in establishing the value of the contact angle, is subjected to a film pressure corresponding to saturation conditions. Therefore, the insensitivity of the contact angles reported by Fox and Zisman to the saturation conditions of the bulk vapor is to be expected. Consequently, the results are not conclusive evidence for negligible values of the film pressures.ls This point, not usually discussed in the literature, has been emphasized in the publications of Adam and Livingston39 and Melrose.'l In this study, we have determined only rw values for water-polymer interactions. However, it is also possible to calculate revalues of hydrophobic liquids on polymers when the reverse two-liquid method (Le. hydrocarbon drops formed by inverted needles in water, which is well known for characterizing hydrophilic polymers) is applied simultaneously with the one-liquid method in which hydrocarbon drops are used.
Conclusions (1) In the one-liquid method reshould not be neglected. (2) The results obtained from both the one-liquid and the two-liquid methods can be combined to determine re values using Van Oss et al. methodology. The rw values for water-polymer interaction obtained by this method are in agreement with the values reported in the literature which were determined from ellipsometrically measured adsorption isotherms. (38)Fox, H.W.;Zisman,A. W.J. Colloid Sci. 1950,5, 514. (39)Adam, N. K.;Livingston, H.K.Nature 1958,182,128.
