Estimation of the Surface Tension Components of Thiodiglycol

The estimation of the solid surface free energy from contact angle ... This subject was addressed before by other authors,15 and will not be focused o...
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Langmuir 1998, 14, 4198-4203

Estimation of the Surface Tension Components of Thiodiglycol Maria Helena Ada˜o,†,‡ Benilde Saramago,† and Anabela C. Fernandes*,† Centro de Quı´mica Estrutural, Complexo I, IST, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal, and Instituto Superior de Cieˆ ncias da Sau´ de-Sul, Quinta da Granja, 2825 Monte Caparica, Portugal Received August 5, 1997. In Final Form: April 8, 1998 The total surface tension of thiodiglycol was determined experimentally, and its surface tension components were estimated: γLW ) 42 ( 1 mJ m-2, γ+ ) 1.1 ( 0.5 mJ m-2, and γ- ) 25.0 ( 0.5 mJ m-2. The Lifshitz-van der Waals component was estimated from experimental values of thiodiglycol/n-alkane interfacial tensions, measured by the pendant drop method. The γ+ and γ- were estimated using the additional information of the contact angle of thiodiglycol on a solid substrate with known surface energy components. Three polymeric substrates were used independently with this purpose: PS, SAN2, and PMMA. The most consistent set of values was obtained using PMMA. The final establishment of the values for the surface tension components of thiodiglycol involved a trial and error procedure where the parameters were slightly changed to reproduce the previously calculated surface energy components of the three polymer substrates. This study reinforced the idea that the estimation of the surface free energy components of a liquid (or solid) is highly dependent on the calculation method and on the systems used to perform the calculations.

Introduction The separation of the liquid surface tension into a dispersion and a nondispersion component was first suggested by Fowkes.1 Since then, several approaches have been used to divide the liquid and solid surface free energy into independent components.2-5 One of the most widely used treatments, developed by Van Oss et al.,5 assumes the existence of two main components, the Lifshitz-van der Waals component, γLW, and the acidbase component, γAB. The γLW component includes not only the contribution due to the dispersion (London) interactions but also the contributions due to the induction and dipole-dipole (Keesom) interactions, which are generally small in comparison to the dispersion contribution. The acid-base component, γAB, includes the contributions due to all electron acceptor-electron donor interactions. The special case of the hydrogen bonding interactions are part of the acid-base component. It is generally accepted that the dispersion component of interfacial free energy between two phases i and j may be expressed as the geometric mean of the dispersion components of the surface free energy of phases i and j. Van Oss et al. extended the geometric mean rule to all the interactions included in γLW, according to

γLW ij

)

γLW i

+

γLW j

-

LW 1/2 2(γLW i γj )

(1)

The geometric mean combining rule, however, is not applicable to γAB. Van Oss et al.,5 considered that the acid-base component is divided into a electron acceptor (γ+) and electron donor (γ-) surface parameters that have * To whom correspondence should be addressed. † Centro de Quı´mica Estrutural. ‡ Instituto Superior de Cie ˆ ncias da Sau´de-Sul. (1) Fowkes, F. M. J. Phys. Chem. 1962, 66, 682. (2) Fowkes, F. M. Ind. Eng. Chem. 1964, 56 (12), 40. (3) Kaelble, D. H.; Uy, K. C. J. Adhes. 1970, 2, 50. (4) Wu, S. J. Polym. Sci. 1971, C34, 19. (5) van Oss, C. J.; Chaudhury, M. K.; Good, R. J. Chem. Rev. 1988, 88, 927.

a complementary nature and are related through the equation:

γAB ) 2(γ+γ-)1/2

(2)

According to these authors the interfacial free energy between two phases i and j may be described in terms of the surface free energy components, γLW, γ+, and γ-, of the two phases in contact + - 1/2 - 1/2 1/2 1/2 2 - (γLW + (γ+ γij ) [(γLW i ) j ) ] + 2[(γi γi ) j γj ) - 1/2 + 1/2 (γ+ - (γi γj ) i γj ) ] (3)

When the two phases in contact are a solid and a liquid, eq 3 may be combined with Young’s equation leading to: LW 1/2 - 1/2 + 1/2 + (γ+ + (γ) (1 + cos θ) γL ) 2((γLW S γL ) S γL ) S γL ) (4)

where AB AB + - 1/2 γL ) γLW L + γL with γL ) 2(γL γL )

(5)

According to eq 4 the surface free energy components of a solid may be estimated from the contact angles of a set of three liquids of known surface tension components and, inversely, the surface tension components of a liquid may be determined from the contact angle of the liquid on three substrates with known surface free energy components. The estimation of the solid surface free energy from contact angle measurements is a very controversial subject. Fowkes,6 for instance, states that “... is thermodynamically impossible to determine γS from contact angle measurements ...”. This point of view is not partitioned by other authors3-5,7,8 who suggested several approaches to estimate γS using the contact angles of a set of testing (6) Fowkes, F. M.; Riddle, F.L., Jr.; Pastore, W. E.; Weber, A. A. Colloids Surf. 1990, 43, 367.

S0743-7463(97)00878-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/24/1998

Surface Tension Components of Thiodiglycol

liquids. In this paper we will use the van Oss, Chaudhury, and Good5,9 approach described above, bearing in mind its limitations, that have been recently pointed out by Della Volpe et al.10 and previously by other authors.11-13 Despite the unsolved problems and the inconsistencies encountered in the acid-base approach, at present, there is no better alternative to estimate the surface free energy of a solid or of a liquid. Neumann’s7 equation of state, for instance, can only be applied successfully in systems where the interactions through the interface have only a dispersive nature.14 One of the difficulties in the application of the acidbase approach to find the surface free energy components of a solid is the choice of the liquid trio that is more adequate to characterize the surface under study. The necessary basic requirements to be fulfilled by the test liquids are the absence of chemical reaction with the substrate (the inertia of the liquids with respect to the substrate), the existence of a finite contact angle on the substrate, and the knowledge of their surface tension components. Further conditions are necessary concerning the relative magnitude of the different surface tension components of the three liquids. This subject was addressed before by other authors,15 and will not be focused on here. Water, glycerol, and diiodomethane are a commonly used set of liquids that fulfill the above requirements. Diiodomethane is particularly useful because its acidbase component is assumed to be zero, and this fact simplifies the calculations. Unfortunately, in a few cases, diiodomethane reacts with the surface and cannot be used. One example just encountered by the authors16 is the surface of pure acrylonitrile and of random copolymers containing its monomer. Thiodiglycol proved to be a good probe liquid in what concerns its chemical stability and wetting properties, but the LW and the AB components of its surface tension are not available in the literature. The main objective of this paper is to report the evaluation of the three components, γLW, γ+ and γ-, in which the surface tension of thiodiglycol may be divided. To our knowledge, the only reported values of the surface tension components of thiodiglycol refer to the dispersion and polar components.17 Essentially, two methods are used to estimate the LW and the AB surface tension components of a liquid.18-23 (7) Li, D.; Neumann, A. W. Adv. Colloid Interface Sci. 1992, 39, 299. (8) Lee, L.-H. Langmuir 1996, 12, 1681. (9) van Oss, C. J.; Chaudhury, M. K.; Good, R. J. Adv. Colloid Interface Sci. 1987, 28, 35. (10) Della Volpe, C.; Siboni, S. J. Colloid Interface Sci. 1997, 195, 121. (11) Fowkes, F. M. In Acid-Base Interactions; Mittal, K. L., Anderson, H. R., Jr., Eds.; VSP: Utrecht, The Netherlands, 1991; p 93. (12) Berg, J. C. In Wettability; Berg, J. C., Ed.; Marcel Dekker: New York, 1993; p 75. (13) Kwok, D. Y.; Li, D.; Neumann, A. W. Langmuir 1994, 10, 1323. (14) Lee, L.-H. Langmuir 1993, 9, 1898. (15) Hollander, A. J. Colloid Interface Sci. 1995, 169, 493. (16) Ada˜o, M. H. V. C.; Saramago, B. J. V.; Fernandes, A. C. In preparation. (17) Ko, Y. C.; Ratner, B. D.; Hoffman, A. S. J. Colloid Interface Sci. 1981, 82 (1), 25. (18) van Oss, C. J.; Good, R. J.; Busscher, H. J. J. Dispersion Sci. Technol. 1990, 11, 75. (19) van Oss, C. J.; Good, R. J.; Chaudhury, M. K. Langmuir 1988, 4, 884. (20) Janczuk, B.; Bialopiotrowicz, T.; Wo´jcik, W. J. Colloid Interface Sci. 1989, 127 (1), 59. (21) Janczuk, B.; Bialopiotrowicz, T. J. Colloid Interface Sci. 1989, 127 (1), 189. (22) Janczuk, B.; Wo´jcik, W.; Zdziennicka, A. J. Colloid Interface Sci. 1993, 157, 384. (23) van Oss, C. J.; Lu, J.; Chaudhury, M. K. J. Colloid Interface Sci. 1989, 128 (2), 313.

Langmuir, Vol. 14, No. 15, 1998 4199 Table 1. Liquids Used in Interfacial Tension Measurements liquids

% purity

boiling point (°C)

heptane octane decane hexadecane 1-bromonaphthalene thiodiglycol

>99 >99 >99 >99 98 >99

98 125-127 174 287 279-281 166 (20 mmHg)

Table 2. Densities of Liquids (g cm-3) at 25 °Ca saturated with liquid

HPT

OCT

DEC

HXD

BNF

HPT * OCT * DEC * HXD * BNF * TDG 1.178 1.176 1.177 1.204 W 0.9970 0.9969 0.9969 0.9970 0.9967

TDG

W

pure liquids

0.679 0.6799 0.680 0.699 0.6987 0.703 0.7267 0.730 0.770 0.7702 0.773 1.477 1.4759 1.489 * 1.177 * 0.9970

a HPT, heptane; OCT, octane; DEC, decane; HXD, hexadecane; BNF, 1-bromonaphthalene; TDG, thiodiglycol; W, bidistilled water.

One is based on the knowledge of liquid-liquid interfacial tensions between the liquid and a series of test liquids showing a wide spectrum of polarities. The other one is based on the knowledge of the contact angle of the liquid on well-characterized surfaces. Both methods were used in this paper to estimate the surface tension components of thiodiglycol. To our knowledge there are no reported values in the literature on liquid-liquid interfacial tensions, γll, involving thiodiglycol. It is the second objective of this paper to report accurate experimental values for the interfacial tensions of thiodiglycol with a series of n-alkanes and with 1-bromonaphthalene. Experimental Section Materials. The liquids used for the surface and interfacial tension measurements, supplied by Aldrich, are listed in Table 1 and were all used as received. The water was deionized in a Millipore purification system, yielding a resistivity of 18 MΩ cm at 25 °C. The polymers used in the contact angle measurements were poly(methyl methacrylate) (PMMA), from Aldrich Chemical Co. with M h w ) 120 000, polystyrene (PS), from Aldrich Chemical Co. with M h w ) 280 000, and a styrene/acrylonitrile (2 wt % in acrylonitrile), random copolymer (SAN2), from Asahi Chemical Industry Co. Ltd., with M h w ) 204 000. Dichloromethane, pro analysis, from Merck was used to produce PS, SAN2, and PMMA films. Methods. The mutual solubility of the liquids studied, although small, is different from zero, and the densities of the pure liquids as well as the liquid-liquid interfacial tensions are affected by this fact. To take into account this mutual solubility, each pair of liquids was allowed to come in contact with each other in a separator funnel before the interfacial tension measurements, for a period not less than 24 h, to ensure that equilibrium had been attained. The accurate densities of the pure as well as of the mutually saturated liquids were measured using the pycnometer technique at 25 ( 0.1 °C. The results are shown in Table 2. The surface tensions, γlv, and the interfacial tensions, γll, were determined from the shape of pendant drops using ADSA-P, axisymmetric drop shape analysis, previously developed by Neumann and co-workers.24,25 The same program was used to determine the contact angle of sessile drops on the polymer films. This software allows the determination of interfacial tensions and contact angles by fitting (24) Cheng, P.; Li, D.; Boruvka, L.; Rotnberg, Y.; Neumann, A. W. Colloids Surf. 1990, 43, 151. (25) Cheng, P.; Neumann, A. W. Colloids Surf. 1992, 62, 297.

4200 Langmuir, Vol. 14, No. 15, 1998

Ada˜ o et al. Table 3. Surface Tension of Mutually Saturated Liquids Measured at 25 ( 0.1 °C

Figure 1. Experimental setup for interfacial tension measurements, when liquid 1 is heavier than liquid 2. the shape of an experimental drop, pendant or sessile, to a theoretical drop profile obtained with the Laplace equation. Using the acceleration of gravity and the density difference between the two phases in contact, the interfacial tension is calculated as an adjustable parameter of the best fit of the profile. Besides the interfacial tension, the computer program provides the drop volume, surface area, and, in the case of a sessile drop, the contact angle and the radius of the three-phase contact line. The image of the drop was recorded with a JVC TK-1070 color video camera mounted on a Wild-Heerbrugg M3Z microscope. The video signal was transmitted to a Video Pix Framegrabber from Sun Microsystems, which performs the frame grabbing and the digitalization of the image with 256 gray level for each pixel. A Sun Sparcstation IPC was used to acquire the image from the image processor and to perform the image analysis and computation. Both the sessile drop and pendant drop measurements were carried out inside an environmental chamber where the temperature was controlled to (0.1 °C. The liquid/liquid interfacial tension measurements were carried out using the experimental setup shown schematically in Figure 1, where liquid 1 is heavier than liquid 2. The glass cell has two quartz windows and a volume large enough to avoid the wall effects. When liquid 1 is less dense than liquid 2, the interfacial tension measurement is only possible using an inverted needle. The inverted drops were analyzed using a different software, designated by G-Contact, which was developed by de Coninck and co-workers.26 The main difference between ADSA-P and G-Contact lies on the method used for edge detection.27 The contact angle and the interfacial tension results presented are always average values over, at least, 20 drops. The dependence of the liquid-liquid interfacial tension on the volume of the drop was studied by using either a pendant drop or an inverted drop. The PS, SAN2, and PMMA polymer films were obtained by spin coating from dichloromethane solutions onto carefully cleaned glass substrates. The films were placed in a vacuum oven at room temperature. Afterward the temperature was gradually raised, during 2 days, to a temperature slightly above the glass transition temperature of each polymer and kept at this temperature for more 2 days, to ensure the evaporation of the solvent. Finally, the films were cooled slowly to room temperature, always inside the vacuum oven, and were stored in a desiccator.

Results and Discussion Liquid-Vapor and Liquid-Liquid Interfacial Tensions. The experimental surface tensions of the mutually saturated liquids and the liquid-liquid interfacial tensions necessary for this study are reported in Tables 3 and 4, respectively. The γll for the systems water/n-heptane, water/n-decane, and water/bromonaphthalene were determined and are reported here for comparison purposes. These values are slightly different from those obtained by Kwok et al.28 (using a number of drops between 5 and (26) De Coninck, J. Private communication. (27) Serro, A. P.; Ada˜o, M. H.; Fernandes, A. C.; Saramago, B.; de Ruijter, M. J.; Voue´, M.; Semal, S.; De Coninck, J. Proceedings of the 4th International Symposium on Evaluation of Reservoir Wettability and Its Effects on Oil Recovery, 1996. (28) Kwok, D. Y.; Hui, W.; Lin, R.; Neumann, A. W. Langmuir 1995, 11, 2669.

liquid

saturated with

γ (mJ m-2)

σm/N1/2

HPT OCT HXD HPT DEC BNF BNF TDG TDG TDG TDG W W W

TDG TDG TDG W W W TDG BNF HXD OCT HPT HPT DEC BNF

20.0 20.9 26.1 20.0 23.8 43.6 42.7 48.2 50.2 52.6 54.1 71.0 71.5 71.9

0.2 0.1 0.1 0.1 0.9 0.2 0.2 0.5 0.5 0.2 0.2 0.6 0.7 0.4

Table 4. Liquid-Liquid Interfacial Tensions, Measured at 25 ( 0.1 °C liquid 1

liquid 2

γ (mJ m-2)

σm/N1/2

HPT HPT DEC OCT HXD BNF BNF

TDG W W TDG TDG TDG W

15.48 49.42 47.24 14.20 16.24 4.38 37.77

0.15 0.43 0.57 0.05 0.08 0.09 0.47

Figure 2. Interfacial tension for the water/bromonaphthalene system as a function of the volume of the drop, when: 4 bromonaphthalene is a pendant drop, and 2 water is an inverted drop.

11): 50.66 mJ m-2 for water/n-heptane, 51.07 mJ m-2 for water/n-decane, and 37.95 mJ m-2 for water/1-bromonaphthalene although the liquids used came from the same source and the method of measurement, including the software, was the same. For the water/1-bromonaphthalene system an unexpected behavior was observed which, to our knowledge, was not reported before. If, in the experimental setup shown in Figure 1, liquid 1 is 1-bromonaphthalene and liquid 2 is water, the measured γll depends on the volume of the drop. However, if liquid 1 is water and liquid 2 is 1-bromonaphthalene, the measured γll, from an inverted drop, is independent of the volume of the drop, as shown in Figure 2. This behavior was not observed in any of the other systems studied in this work, where the liquidliquid interfacial tensions were found to be independent of the volume of the drop, when using either a pendant or an inverted drop. The value shown in Table 4 for the water/1-bromonaphthalene interfacial tension is the maximum value obtained with a pendant drop. The single value reported by Kwok et al.28 for this system is close to this maximum value. We believe that this behavior is related to the relative order of magnitude of the surface tensions and densities

Surface Tension Components of Thiodiglycol

Langmuir, Vol. 14, No. 15, 1998 4201

Table 5. Relative Values of the LW Components of Thiodiglycol (TDG), Glycerol (G), and Ethylene Glycol (EG) from Interfacial Tension Measurements with n-Alkanes n-alkane C7 C8 C16 a

γLW TDG/mJ

m-2 a t ) 25 °C 42.94 42.04 34.54

γLW G /mJ

m-2 a t ) 20 °C 35.50 35.55 31.74

γLW EG /mJ

m-2 b t ) 20 °C 33.69 32.81 29.79

of the mutually saturated liquids. In fact, among the pairs of liquids studied, this is the only one where the relative values of the surface tension and density do not vary in the same direction. In this system the 1-bromonaphthalene saturated with water shows a lower surface tension than the water saturated with 1-bromonaphthalene. However, the 1-bromonaphthalene rich phase has the highest density. The observed behavior suggests that in this system there is a competition between gravity and interfacial forces. As shown in Table 4 the liquid-liquid interfacial tension between thiodiglycol and the n-alkanes studied is almost constant. For the thiodiglycol/1-bromonaphthalene system the interfacial tension is lower, which is in accordance with the high degree of mutual solubility shown by these two liquids. Evaluation of the Surface Tension Components of Thiodiglycol. As mentioned before the LW and the AB components of the surface tension of a liquid can be determined from liquid-liquid interfacial tensions or from contact angle measurements on solid surfaces whose surface free energy components are known, according to eqs 2 and 3. Taking into account that dispersion forces are the only source of aliphatic hydrocarbons surface tension, Fowkes2 stated that it is possible to determine the LW component of the surface tension of polar liquids, on the basis of interfacial tension measurements with aliphatic hydrocarbons, whereas the AB component is equal to the difference between the total surface tension and the LW component. When component 1 is an aliphatic hydrocarbon, γLW 1 ) γ1, eq 3 reduces to

(6)

and the LW component for thiodiglycol may be evaluated

γLW ) (γ1 + γ2 - γ12)2/4γ1 2

PS SAN2 PMMA

diiodomethane (D)

water (W)

glycerol (G)

thiodiglycol (TDG)

34.8 32.3 39.9

86.6 83.3 70.1

76.2 74.5 65.6

51.1 49.6 46.2

Table 7. Surface Free Energy Components (mJ m-2) of the Polymers Obtained with W/D/G

Our results. b Reference 22.

1/2 γ12 ) γ1 + γ2 - 2(γ1γLW 2 )

Table 6. Static Contact Angles (deg) for Various Liquids on Polymers

(7)

Using for γ1 and γ2, the values of the surface tensions of the mutually saturated liquids and for γ12 the experimental liquid-liquid interfacial tensions, shown in Tables 3 and 4, respectively, the LW component of thiodiglycol is obtained. Table 5 shows that the LW component of thiodiglycol, resulting from experimental interfacial tensions with the n-alkanes, decreases as the chain length of the n-alkane increases. This trend was also observed with other polar liquids, like ethylene glycol or glycerol.22 These values are also included in Table 5 for comparison purposes. It is interesting to note that, for water, probably due to the small size of the molecules, this dependence of the LW surface tension component on the chain length of the n-alkane is not so clear and the usually accepted value for γLW, 21.8 ( 0.7 mJ m-2, was averaged over several hydrocarbons with longer chain lengths.2 In this study, the low value obtained with n-hexadecane, which is mainly

PS SAN2 PMMA a

γLW

γ+

γ-

ref

42.1 42 43.2 39.7 39-43

0.07 (0) 0.09 0.02 (0)

3.6 1.1 5.2 13.5 9.5-22.4

our study 29a our study our study 29a

Based on advancing angles.

a consequence of the lowering of the surface tension of thiodiglycol when saturated with n-hexadecane, was not considered relevant to the estimation of the dispersion component of thiodiglycol. As a consequence, γLW TDG was assumed to be 42 ( 1 mJ m-2. The surface tension of thiodiglycol was found to be 54.6 ( 0.6 mJ m-2 at 25 °C, using the pendant drop method. The value for the AB component of thiodiglycol surface tension is then determined as =12.6 mJ m-2. To estimate γ+ and γ- for thiodiglycol, at least two polar liquids, with known γ- and γ+ and not miscible or slightly miscible with thiodiglycol, are needed. All the polar liquids tested, including 1-bromonaphthalene which is only slightly polar, are partially or totally miscible with thiodiglycol and this approach could not be further used. As previously mentioned, the surface tension components of a given liquid may also be estimated using the contact angle values on three solids with known surface free energy components, according to eq 4. The surface tension components of thiodiglycol may be then estimated from the thiodiglycol contact angle measured on PS, SAN2, and PMMA substrates by solving a system of three equations to three unknowns. The surface free energy components of PS and SAN2 were determined in this laboratory as part of a more general study on the surface energetics of a series of random styrene-acrylonitrile copolymers.16 The literature values on the surface energy components of PMMA are not unique and vary within a wide range. In view of this we decided to determine those components ourselves. The static contact angles of water, glycerol, and diiodomethane on PS, SAN2, and PMMA polymer films are reported in Table 6 and were used together with eqs 4 and 5 to find the surface free energy components of these polymers, γLW, γ+, and γ-. The contact angles shown in Table 6 are always average values over at least 20 drops, and the maximum standard deviation was not larger than 2°. The values obtained for the surface free energy components of PMMA, PS, and SAN2 together with the values obtained by other authors for PMMA and PS are presented in Table 7. The liquid surface tension components for water, glycerol, and diiodomethane used in the calculations were previously reported.29 It should be emphasized here that the reaction of diiodomethane with the styreneacrylonitrile copolymers was observed only in the cases where the percentage of acrylonitrile was larger than 11 (29) Good, R. J.; van Oss, C. J. In Modern Approaches to Wettability. Theory and Applications; Schrader, M. E., Loeb, G. I., Eds.; Plenum Press: New York, 1992.

4202 Langmuir, Vol. 14, No. 15, 1998

Ada˜ o et al.

Table 8. Thiodiglycol Electron-Acceptor and Electron-Donor Parameters Based on Contact Angle Measurements on Polymer Substrates (with γLW TDG ) 42 mJ m-2) set no.

polymer substrate

1 2 3

PS SAN2 PMMA

γ+ TDG (mJ 0.83 0.76 1.62

m-2)

γTDG

(mJ

m-2)

43.0 43.5 24.5

wt %, and consequently it is legitimate to use SAN2 as one of the polymer substrates. We also would like to refer that static contact angles were always used in this study. A static contact angle is defined here as the contact angle extrapolated to t ) ∞, where t is the time of the spontaneous spreading of an advancing drop after being deposited on the substrate. These contact angles have intermediate values between the advancing and receding contact angles reported by us30 and by other authors.31 The use of a static contact angle leads to a unique set of surface free energy components. Although some information may be lost using this procedure, the value obtained for the surface free energy and its components reflects the average characteristics of the surface. The consideration of an advancing and receding contact angle would result in two sets of values for the same surface,32 introducing an additional complexity to the estimation of the surface tension components of thiodiglycol. With the surface free energy components of the three polymer surfaces and the contact angle of thiodiglycol known, the system of three equations to three unknowns may now be solved. The values obtained for the surface tension components of thiodiglycol, γLW ) 49.65 mJ m-2, γ+ ) 0.88 mJ m-2, and γ- ) 134.40 mJ m-2, leading to a γtotal ) 71.40 mJ m-2, do not have any physical meaning. Remember that the measured surface tension for thiodiglycol is 54.6 mJ m-2. It should be referred that if in the calculations a slightly different value is considered for the electron-acceptor component of the surface free energy of PMMA, γ+) 0.00 mJ m-2, instead of γ+ ) 0.02 mJ m-2, for example, a different set of values is obtained γLW ) 48.9 mJ m-2, γ+ ) 0.35 mJ m-2, and γ- ) 59.5 mJ m-2, leading to a γtotal ) 58.00 mJ m-2. This kind of inconsistency was also observed by Neumann et al.13 when determining the surface free energy components of polymer surfaces using different sets of liquids. In a recent study Della Volpe et al.10 pointed out that the equation system whose solution provides the surface free energy components can be ill-conditioned by an improper choice of solvents that do not represent all acid-base typologies: prevalently dispersive, acid, or basic. This may be one of the reasons for the inconsistencies in the results obtained in this study. The three solids used are not representative of all the acid-base typologies. In fact the surface free energy components evaluated for these polymers are quite similar: they have a mainly dispersive nature. Among the three, PMMA is the one having the larger acid-base component. Another possible origin of the inconsistencies observed is the mathematical instabilities of the model, as suggested by Hollander.15 In view of the previous results another approach has to be used. As we already know γLW and γtotal, only the (30) Ada˜o, M. H. V. C.; Saramago, B. J. V.; Fernandes, A. C. Colloids Surf., A 1998, 132, 181. (31) Lloyd, T. B.; Ferreti, K. E.; Lagow, J. J. Appl. Polym. Sci. 1995, 58, 291. (32) Good, R. J.; Srivatsa, N. R.; Islam, M.; Huang, H. T. L.; van Oss, C. J. In Acid-Base Interactions; Mittal, K. L., Anderson, H. R., Jr., Eds.; VSP: Utrecht, The Netherlands, 1991; p 79.

Table 9. Surface Free Energy Components (mJ m-2) of PS Recalculated Using γ+ TDG and γTDG Shown in Table 8 set no.

γLW (mJ m-2)

γ+ (mJ m-2)

γ- (mJ m-2)

1 2 3

58.4 55.8 48.4

1.17 0.91 0.35

2.73 2.85 3.22

Table 10. Surface Free Energy Components (mJ m-2) of the Polymers and of the Test Liquids PS SAN2 PMMA thiodoglycol water glycerol

γLW

γ+

γ-

42.0 42.1 39.7

0.06 0.06 0.01

3.6 5.2 15.6

γLW

γ+

γ-

ref

42.0 ( 1 21.8 34

1.1 ( 0.5 25.5 3.92

25.0 ( 0.5 25.5 57.4

our work 29 29

additional information relative to the contact angle of thiodiglycol on a single, well-characterized solid surface is needed. The electron-acceptor, γ+ TDG, and the electrondonor, γTDG, components are evaluated through the resolution of the following system of equations: LW LW 1/2 - 1/2 (1 + cos θ) γTotal + (γ+ + TDG ) 2[(γTDGγS ) TDGγS ) + 1/2 (γTDGγS ) ] (8) LW + 1/2 γTotal TDG ) γTDG + 2(γTDGγTDG)

(9)

Our three polymeric substrates, PMMA, PS, and SAN2, were used independently and three sets of surface tension parameters, γ+ and γ-, shown in Table 8, were evaluated for thiodiglycol using eqs 8 and 9. The values obtained with PS and SAN2 are similar but quite different from those obtained with PMMA. To test these three sets of γ+ and γ- components of thiodiglycol, we decided to recalculate the surface free energy components of PS using thiodiglycol instead of diiodomethane. The surface free energy components obtained for PS are shown in Table 9. Comparing these values with those obtained previously with diiodomethane and shown in Table 7, one may conclude that none of the three sets of values used for γ+ and γ- of thiodiglycol is able to reproduce the PS surface free energy components. However, set no. 3 obtained with PMMA is the one that reproduces better the previously estimated values. The calculation procedure revealed that the final results obtained for the surface free energy components of a polymer surface are highly sensitive to small changes in the γ+ and γ- of the testing liquids. In fact, the surface free energy components of PS are well reproduced if we use γ+ ) 1.10 mJ m-2 and γ- ) 25.0 mJ m-2, instead of γ+ ) 1.62 mJ m-2 and γ- ) 24.5 mJ m-2 as the surface tension components of thiodiglycol. Table 10 shows the surface free energy components obtained for PS, SAN2, and PMMA using water, glycerol, and thiodiglycol together with the values taken for γLW, γ+, and γ- of the test liquids. The above set of values may be compared to the equivalent surface free energy components, obtained with water, glycerol, and diiodomethane, presented in Table 7. Although there are slight differences, the agreement between the values for γLW, γ+, and γ- of SAN2 and PMMA is quite good. In view of this analysis we propose for thiodiglycol γLW ) 42 ( 1 mJ m-2, γ+ ) 1.1 ( 0.5 mJ m-2, and γ- ) 25 ( 0.5 mJ m-2, which reproduce the surface free energy

Surface Tension Components of Thiodiglycol

components of the testing solids and simultaneously the experimental surface tension of the liquid. It should be referred that the estimated surface tension components for thiodiglycol (γLW ) 42 ( 1 mJ m-2 and γAB ) 10.5 ( 2 mJ m-2) are not contradictory to the usually accepted surface tension components for glycerol (γLW ) 34 mJ m-2 and γAB ) 30 mJ m-2) and ethylene glycol (γLW ) 29 mJ m-2 and γAB ) 19 mJ m-2), two similar molecules. Among the three, thiodiglycol has the highest value for γLW and shows the lowest acid-base character. This is in accordance with the fact that thiodiglycol is the largest molecule, and the groups responsible for the acid-base interactions are more diluted. The use of the estimated surface tension components of thiodiglycol in other systems must be carried out with care. It was not possible, with the kind of systems used in this study, to attribute a rigorous, single value to the surface tension components of thiodiglycol that could statisfy simultaneously the experimental surface tension of the liquid and the surface tension components of the solids. As a consequence, the values estimated in this study must be used taking into account the associated uncertainties. The difficulty in getting a single set of values for the surface tension components of liquids and solids is one of the major flaws of the surface tension components method and is reflected in the fluctuation of values that appear in the literature, even for the most common polymers and solvents.10,11,22,29,31,33 It is clear from the above discussion that the division of the surface tension of a liquid or a solid, according to van Oss’s approach must be considered with great care. Independently of the validity of this treatment, it must be emphasized that meaningless surface tension components can be obtained if a poor choice of the testing liquids or solids has been made. Conclusions The surface tension components of thiodiglycol, defined in accordance to van Oss et al. were estimated using a (33) Wu, S. Polymer Interface and Adhesion; Dekker: New York, 1982.

Langmuir, Vol. 14, No. 15, 1998 4203

combined approach. The Lifshitz-van der Waals component was estimated on the basis of experimental liquidliquid interfacial tensions between thiodiglycol and n-alkanes. The electron-acceptor, γ+, and the electron-donor, γ-, surface parameters were determined from contact angle measurements of thiodiglycol on polymer substrates with known surface free energy components. With this purpose polystyrene, a random copolymer of styreneacrylonitrile, SAN2, and poly(methyl methacrylate) was used. The final set of values γLW ) 42 ( 1 mJ m-2, γ+ ) 1.1 ( 0.5 mJ m-2, and γ- ) 25.0 ( 0.5 mJ m-2, proposed for thiodiglycol, was adjusted to fit the surface free energy components of polystyrene obtained with water, glycerol, and diiodomethane. The surface free energy components of SAN2 and PMMA, calculated using water, glycerol, and thiodiglycol as test liquids, compared well with the surface free energy components obtained with water, glycerol, and diiodomethane determined either in this study or by other authors. As a general conclusion one may say that thiodiglycol, despite having a nonzero acid-base component, can be used as a test liquid, in particular, in polymer surfaces that react with diiodomethane. Further use of thiodiglycol as a test liquid in other systems is needed to completely confirm the above statements. Finally, it was demonstrated from the above calculation procedure that the division of the surface tension into components, according to van Oss’s approach, has to be performed in a critical way to avoid erroneous results. Acknowledgment. Maria Helena V. C. Ada˜o acknowledges the financial support of Praxis XXI, BD9497/ 96. We are grateful to Professor Joel De Coninck for allowing us to use the G-Contact software, developed by him and co-workers. LA970878C