620
Langmuir 1986,2, 620-625
Solid Surface Tension: The Interpretation of Contact Angles by the Equation of State Approach and the Theory of Surface Tension Components J. K. Spelt,t D. R. Absolom,tJ,§and A. W. Neumann*tJl§ Department of Mechanical Engineering, University of Toronto, Toronto, Ontario M5S 1A4, Canada, Institute of Biomedical Engineering, University of Toronto, Toronto, Ontario M5S l A 4 , Canada, and Research Institute, Hospital for Sick Children, Toronto, Ontario M5G 1x8,Canada Received August 7, 1985. I n Final Form: May 28, 1986 The two methods which are frequently used to determine solid surface tensions, the equation of state approach and the theory of surface tension components, often yield conflicting results and represent two completely different ways of conceptualizing interfacial tension problems. In this report an experiment is described which permits the independent evaluation of these two theories as part of an effort to establish the relative merits of each. The contact angles of two different liquids on a single solid substrate are found to be identical when the total liquid surface tensions are equal. This result, which was obtained for five liquid pairs on different surfaces, is independent of the relative magnitudes of the dispersion forces within the liquids of a given pair. This fiiding implies a basic deficiency of the theory of surface tension components and supports the equation of state approach.
Introduction The determination of solid and solid-liquid surface tensions is of importance in a wide range of problems in pure and applied science. Since it is not possible to measure directly surface tensions involving a solid phase, there exist, a t present, many indirect approaches for obtaining these values. These various methods are often in considerable disagreement, both quantitatively and from a theoretical standpoint. The problem persists because most of these approaches have not been objectively tested through the prediction of physical phenomena which could be independently observed and thus used to validate the various theories. The purpose of the present investigation was to apply one such independent test to the following two theories: (1)the Fowkes theory of surface tension components;l (2) the equation of state approach to interfacial tensions.2 These two approaches for evaluating solid surface tension are briefly outlined below. (1)The theory of surface tension components was pioneered by Fowkesl who proposed that surface tension should be considered in terms of components, each due to a particular kind of intermolecular force. Thus, a given organic liquid may have discrete surface tension components attributable to London dispersion forces, dipoledipole (Keesom) forces, induction (Debye) forces, and hydrogen-bonding forces. Such surface tension components, although not thermodynamically defined, are, nevertheless, regarded by Fowkes as unique physical properties of the material.' Liquid-solid interactions are considered only between those surface tension components which arise from the same types of forces. Therefore, at a water-Teflon interface, for example, since only dispersion forces are present in the Teflon, the large polar and hydrogen-bonding forces in the water will not act across the interface to affect the interfacial tension directly. Thus, in this approach the solid-liquid interfacial tension is a function of the types and relative magnitudes of the intermolecular forces in the solid and the liquid. The Fowkes equation and methdology is used to measure only the dispersion component of surface tension of 'Department of Mechanical Engineering,-University of Toronto. Institute of Biomedical Engineering, University of Toronto. 8 Research Institute, Hospital for Sick Children.
*
0743-7463/86/2402-0620$01.50/0
a solid (or of a liquid). There are no widely accepted methods for determining nondispersion components of surface tension and, therefore, little consensus exists regarding the magnitudes of total solid surface tensions. (2) The equation of state approach is based on thermodynamic arguments3 which lead to the conclusion that the solid-liquid interfacial tension is only a function of the total solid and liquid surface tensions. Unlike the Fowkes approach, the types and relative magnitudes of the intermolecular forces in either phase are not considered to be directly relevant. The interfacial tension is believed to be completely defined by the total surface tensions of the separate phases. In the case of both of these theories, solid surface tensions are evaluated by contact angle measurements. From Young's equation, YSL = Ysv - YLV cos 0 (1) it is seen that if yLvand ysv, the liquid-vapor and solidvapor surface tensions, respectively, are fixed for a series of solids and liquids, then the contact angle is directly related to ysL, the solid-liquid interfacial tension. This concept forms the basis for a direct experimental comparison of the predictions of the two theories. Consider first two different pure liquids that are chosen to have equal overall surface tensions, as measured by, for example, the Wilhelmy plate technique. These same liquids are, however, also selected to have widely disparate compositions of intermolecular forces. In other words, one liquid may be an alkane (a liquid which has only dispersion forces) while another may be characterized by a large dipole moment and perhaps significant hydrogen bonding. According to the theory of surface tension components, the contact angles of these two liquids on a single solid surface should differ in proportion to the differences in the make-up of the intermolecular forces. In contrast, the equation of state approach predicts that the contact angles be equal since both the total liquid and solid surface tensions are constant. This simple experiment provides a direct test of the basic premise of each of the two theories, and, moreover, it is independent of the specific form (1) Fowkes, F. M. Znd. Eng. Chem. 1964, Dec, 40-52. (2) Neumann, A. W.; Good, R. J.; Hope, C. J.; Sejpal, M.J. Colloid
Interface Sci. 1974, 49, 291. (3)Ward, C.A.; Neumann, A. W. J. Colloid Interface Sci. 1974, 49, 286.
0 1986 American Chemical Society
Langmuir, Vol. 2, No. 5, 1986 621
Solid Surface Tension Table I. Liquid Properties dipole moment: surface tension,* D mJ/m2 liquid pentadecane 0.0 28.93 - 0.085312' 0.97 42.14 - 0.10542' dibenzylamine 0.23 41.82 - 0.11882' 1-methylnaphthalene 2.77 43.24 - 0.11952' benzaldehyde ethyl caprylate 1.68 29.12 - 0.10182' 2.58 28.50 - 0.07662' heptaldehyde 2.23 41.84 - 0.12012' methyl salicylate
6d/6T x l O O C
100 71
79 60 50 47 44
Reference 18. *Measured by the Wilhelmy plate techniqueB with an uncertainty of k0.15 mJ/m2. Fraction of total solubility parameter ( 6 ~ attributed ) to dispersion forces at 25 O C . Calculated by using the solubility parameters in ref 5 and the correlations suggested in ref 4 (for details see ref 9).
Table 11. Predictions of the Beerbower Correlation of Liquid Surface Tension, yLV,with Solubility Parameter Components (&, ,6, and tih). Comparison of Predicted and Measured Surface Tensions (25 "C) and the Percentage of the Total Predicted Surface Tension due to the Dispersion Solubility Parameter Component (hd) Beerbower measured Beerbower YLV, YLV, YLV due to liquid mJ/m2 mJ/m2 6d, 70 pentadecane 29.6 26.8 100 dibenzylamine 41.0 39.5 94 I-methylnaphthalene 38.8 38.8 97 benzaldehyde 39.7 40.2 76 32.5 26.6 58 ethyl caprylate heptaldehyde 31.4 26.6 56 methyl salicylate 39.2 38.8 56
Liquids. In order to interpret the significance of the final contact angle results correctly, it is desirable to characterize each liquid in terms of the relative magnitudes of dispersion and nondispersion forces. In keeping with the goals of the experiment, this should be done independently of the methodology of Fowkes. A semiquantitative, relative assessment of the magnitudes of nondispersion forces may be achieved either by comparing the dipole moments or the empirical solubility parameters of the various liquids. The solubility parameter concept has been used successfully as a practical tool in a wide variety of areas: Solubility between two liquids is predicted on the basis of the degree of matching encountered among three components of the solubility parameter; viz., the dispersion (&), polar (8J, and hydrogen-bonding (&) components. This is analogous to the familiar adage that "like dissolves like", with the three empirically determined components defining the molecular character of a liquid. Although such solubility parameters lack a rigorous theoretical basis, they continue to be widely used in practice. Therefore, it is possible, with some confidence, to assume that at least a semiquantitative measure of the relative importance of dispersion forces can be obtained through the consideration of the relative magnitudes of published solubility parameters. The first three liquids in Table I were selected to be significantly more "dispersive" than the remaining four liquids, which are characterized by much larger dipole moments and by relatively smaller dispersion components of the solubility parameters. In addition, the prediction of the Burrell "hydrogen-bonding" classification: which is another empirical aid for the prediction of solubility, is "moderate" for the last four liquids and "poor" for the rest. This is not meant to imply the actual existence of hydrogen bonding in our systems but in the present context serves to indicate that independent experimental observation has established significant differences in the character of the intermolecular forces. Taken together, the information in Table I indicates that, relative to the last four liquids, dispersion forces in pentadecane, dibenzylamine, and I-methylnaphthalene are responsible for a significantly larger fraction of the total intermolecular binding energy. For the purpose of the present investigation, the exact magnitudes of such differences are unimportant. It is only necessary to establish that there are appreciable differences in the relative degree of "dispersion" in the first three liquids as compared to the last four liquids. BeerboweP has developed a correlation between liquid surface tension and the dispersion, polar, and hydrogen-bonding components of the solubility parameter. Table I1 compares the
predictions of the Beerbower correlation with the measured surface tensions for the seven liquids. The third column of this table lists the percentage of the total predicted surface tension which is due to the dispersion component of the solubility parameter. It should be noted, as Beerbower himself did: that this dispersive fraction bears no relation to the "dispersion component of surface tension" as presented in the Fowkes theory. The purpose of Table I1 is simply to provide another indication that pentadecane, dibenzylamine, and I-methylnaphthalene are characterized by a substantially higher fraction of dispersion forces than are the other four liquids. In order to minimize the potential for vapor adsorption, the seven liquids were chosen to have relatively high boiling points, the lowest being that of heptaldehyde at 153 "C. The sources of the liquids and the purities were as follows: benzaldehyde, Fluka, Puriss grade; dibenzylamine, Aldrich, 99% grade; ethyl caprylate (octanoic acid ethyl ester), Aldrich, 99+% grade, 99.9% pure; heptaldehyde, Aldrich, 95% grade, 99.5% pure; 1methylnaphthalene and pentadecane, API Standard Reference Materials (Carnegie Mellon University), 99.78 and 99.93 mol %, respectively; methyl salicylate (2-hydroxybenzoic acid methyl ester), Fluka, Purum grade, 99+%. The ethyl caprylate and heptaldehyde commercial samples were further purified by preparative gas chromatography prior to the contact angle experiments. Solid Surfaces. The acquisition of thermodynamically significant contact angle data is largely dependent on the quality of the substrate surface. The effects of roughness and heterogeneity can easily overshadow the influence of interfacial energ e t i c ~ . ~I t is, therefore, important in a study of this type to produce solid surfaces of sufficient quality to ensure that the observed contact angles accurately reflect the interaction between the solid and liquid surface tensions as given by Young's equation, eq 1. Contact angle measurements were performed on two surfaces. The first is heat-pressed Teflon FEP (Du Pont), a surface which is exceptionally smooth and homogeneous. At 24 "C the surface gave rise to advancing and receding contact angles of 5 2 O and 49", respectively, for hexadecane, and 46" and 43", respectively, for undecane. The method of preparation of this surface is summarized in ref 8, with greater detail supplied in ref 9. In the present work, two F E P samples (designated A and B) were employed, each having been prepared in a different way and each having a unique thermal history. The latter fact caused the surface tensions of the samples to be slightly different. A second solid surface, which was used for only one pair of liquids, was siliconized glass (details of dimethyldichlorosilane treatment given in ref 9). The advancing contact angle with water was 105", while the receding angle was between 95" and 100". Contact Angle Measurements. Sessile-drop contact angles were measured by a new technique (axisymmetric drop shape analysis or ADSA) which fits the Laplace equation of capillarity to an arbitrary m a y of coordinate points selected from the profiie of a drop."l' This approach is unique because it does not depend
Barton, A. F. M. Chem. Reu. 1975, 75, 731. Barton, A. F. M. CRC Handbook of Solubility Parameters and Other Cohesion Parameters; CRC Press: Boca Raton, FL, 1983. (6) Beerbower, A. J. Colloid Interface Sci. 1971, 35, 126.
(7) Neumann, A. W. Adu. Colloid Interface Sci. 1974, 4, 105. (8) Spelt, J. K.; Rotenberg, Y.; Absolom, D. R.; Neumann, A. W. Colloids Surf., in press. (9) Spelt, J. K. Ph.D. Thesis, University of Toronto, 1985.
of any Fowkes-type equation or of any particular equation of state. The materials, methods, and results of this experiment are outlined below.
Experimental Section
(4) (5)
622 Langmuir, Vol. 2, No. 5, 1986
Spelt et al.
Table 111. Grand Average Advancing Contact Angles of All Available Experments on Substrate FEP A grand avb errorC contact angled exptl liquid surface no. of liquids" contact angle limits (i) difference temp, OC tension, mJ/m2 expts/drops 24 39.0 1.4 M 72.6 -0.2 24 39.0 0.7 MS 72.8 41.8 3 0.6 75.4 D 42.9 +2.0 3 0.4 73.4 B 3 41.8 0.6 75.4 D 41.5 +2.5 3 0.6 72.9 MS 25.6 39 0.7 52.4 P 25.5 -0.8 39 0.3 53.2 H 14 27.7 0.3 53.6 P +0.6 14 27.7 0.4 53.0 EC
B, benzaldehyde; D, dibenzylamine (predominantly dispersive); EC, ethyl caprylate; H, heptaldehyde; M, 1-methylnaphthalene (predominantly dispersive); MS, methyl salicylate; P, pentadecane (totally dispersive). * Grand average contact angle: the average of the mean contact angles (the average contact angle for a single experiment) for the number of experiments indicated. CErrorlimits: The "worst possible case" values required to encompass all mean contact angles from the grand average contact angle. In cases where only one experiment was performed, the 95% student-t confidence limits on the mean contact angle are quoted. dContact angle difference: The contact angle of the predominantly dispersive liquid (the first one listed in each pair) minus that of the significantly nondispersive liquid. Table IV. Grand Average Advancing Contact Angles of All Available Experiments on Substrate FEP B grand avb errorC contact angled exptl liquid surface no. of liquids" contact angle limits (i) difference temp, OC tension, mJ/m2 expts/drops 3 41.8 4/12 D 72.4 3.2 0.6 +3.1 3 41.5 4/12 MS 69.3 39 25.6 1/3 P 49.1 0.5 H 50.3 0.4 -1.2 39 25.5 113 n-d
See footnotes of Table 111. Table V. Grand Average Advancing Contact Angles of All Available Experiments on the Siliconized Glass Substrate grand avb errorc contact angled exptl liquid surface no. of lisuids" contact angle limits (i) difference temp, "C tension, mJ/m2 expts/drops 24 39.0 215 M 58.3 1.1 0.3 -2.7 24 39.0 215 MS 61.0
a-dSee footnotes of Table 111. on the location of specific points of features of the drop shape, and it is generally applicable to all axisymmetric liquid-fluid interfaces; i.e., sessile or pendant drops and contact angles both greater than or less than 90'. The technique has an uncertainty of less than f0.4' (standard error of the mean for a sample size of three). I t is also objective, being independent of the skill and experience of the operator, and is relatively straightforward, both in terms of the apparatus and the details of its use. Drops are photographed in the horizontal plane and approximately 40 coordinate points are selected arbitrarily from the profile utilizing either a manual digitizing tablet or a digital image analyzer. This array of points is then fitted, in a least-squares sense, to the Laplace equation which yields both the contact angle and the liquid surface tension (for details see ref 8 or 9). Apparatus and Procedure. Table I lists the measured surface tension-temperature relation for each of the seven liquids. By controlling the temperature of the contact angle experiment, it was possible to match more exactly the total surface tensions of the various liquids. All of the experiments were, therefore, performed in a temperature-controlled chamber. Advancing contact angles were produced by growing sessile drops through a small hole in the center of the solid substrate with a motorized syringe drive.g Care was taken to eliminate vibrations in the system and to ensure that a given solid substrate was always oriented in the same direction so that each drop was photographed on the same portion of the surface. The same substrate was used for each liquid in a given pair (one "dispersive" and one "nondispersive" liquid). Prior to an experiment, the test surfaces were soaked for 20 min each in two changes of ethanol (absolute) and were then transferred to methanol (Fisher 99.9 mol %) and sonicated for 15 min. After two final rinses in methanol, the surfaces were placed in a small (10) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. J. Colloid. Interface Sci. 1983, 93, 169. (11) Boyce, J. F.; Schurch, S.;Rotenberg, Y.; Neumann, A. W. Colloids Surf. 1984, 9,307.
desiccator and dried under vacuum by using a water aspirator. The substrates were finally placed in a second desiccator and left under vacuum for at least 1.5 h prior to use. Similar cleaning procedures were employed for all syringes and needles used in the handling of the liquid samples. An experiment was begun by growing a drop on a substrate disk and then taking a series of photographs of the meridional profile. The drop volume was then increased by adding liquid through the hole in the center of the disk and this larger drop was in turn photographed. In this way a single experiment consisted of photographing a series of successively larger drops (usually three) on a given substrate. Individual drops were photographed 3 times, refocusing the microscope/camera each time, and the contact angles from these three photographs were averaged to provide a mean contact angle for that particular drop. The mean contact angle for a single experiment, usually consisting of three differently sized drops, was simply the average of the individual mean contact angles for each drop. In other words, the contact angle reported for a single experiment, of one liquid or a given substrate, was the average of (usually) nine ADSA results, comprising three replications for three distinct drops. In some cases, only two different drops were photographed in a given experiment.
Results and Discussion The results of the contact angle experiments are rep o r t e d in Tables 111, IV, and V for the solid substrates Teflon FEP sample A, FEP sample B, and siliconized glass, respectively. The data are grouped i n pairs according to the matched surface tensions of the liquids used. The first liquid i n each pair is the one which is completely or overwhelmingly composed of London dispersion forces, and the second liquid has relatively large nondispersion forces. The f o u r t h column i n these tables, the contact angle difference, is defined as the contact angle of the first liquid minus that of the second liquid. In four of the eight cases,
Langmuir, Vol. 2, No. 5, 1986 623
Solid Surface Tension this difference exceeds the range of the combined error limits, indicating the possible influence of some systematic factor, distinct from the random error which contributes to the error limits. The average of the eight contact angle differences is +0.4”. The following is a brief discussion of the possible explanations for these results, in terms of both the theory of surface tension components and that of the equation of state. The Fowkes equation for solid-liquid interfacial tensions, YSL
= 7s
+ YL - 2(YsdYLd)’/2
is strictly applicable only to situations in which a t least one phase is a saturated hydrocarbon (n-alkane, paraffin wax, etc.) since this ensures that only dispersion forces are operative within that phase. Here, ys and yL are, respectively, the solid and liquid surface tensions (neglecting, as is customary, equilibrium spreading pressures); ysL is the solid-liquid interfacial tension; and ysd and yLdare the dispersion components of the solid and liquid surface tension, respectively. The presence of the two different dispersion components under the square root sign in eq 2 should not be construed as implying the ability to treat the interaction of nondispersion forces in the two phases in a similar fashion. Equation 2 predicts that if ys and yL are fixed, then ysL will vary inversely with yLd. With respect to the contact angle experiments, the “dispersive“ liquid in each pair should, therefore, have the smaller contact angle. As was mentioned above, however, the average contact angle difference for the eight liquid pairs was +0.4O, indicating that the opposite trend was more prevalent. On the average, the “dispersive” liquid had a slightly larger contact angle than the more “nondispersive” liquid, in direct contradiction with the predictions of eq 2. Considering the four cases where the contact angle difference exceeds the error limits, in two of these (dibenzylamine with benzaldehyde and with methyl salicylate on FEP A) the difference is positive (contrary to eq 2), while in the other two cases it is indeed negative (pentadecane and heptaldehyde on FEP B and 1-methylnaphthalene and methyl salicylate on siliconized glass). Equation 2 may be combined with the Young equation, eq 1, to yield
+ COS e)
2(7Sd)1/2= (yL/yLd)’/2yD1/2(1
(3)
For a given pair of liquids (denoted “1” and “2”) on a single substrate, the left-hand side of eq 3 is constant so that -=--
yL:
YL:
YL*
YL1 YL1
YL*(
1 cos e 2
1 + cos
)2
(4)
el
Considering liquid “1”to be the dispersive liquid (the first liquid listed in each pair in Tables 111-V) and assuming for these liquids that the dispersion fraction is that listed in the last column of Table I1 (from the Beerbower correlation a t 25 “C), eq 4 may be used to calculate the implied dispersion fraction of liquid “2” (the left-hand side of eq 4). Note that eq 4 can also be used to give the ratio of the dispersive fractions of liquids “1”and “2”, without regard to the Beerbower correlation. Equation 4 is applicable to situations where the solid substrate is comprised only of London dispersion forces. This condition is satisfied by the use of both Teflon FEP’ and siliconized glass which has a surface consisting of methyl groups and thus behaves as a saturated hydrocarbon. Table VI presents the results of these calculations for the nondispersive liquids on the three substrates. The last
Table VI. Fowkes Equation Predictions of the Fraction of the Total Surface Tension due to Dispersion Forces for the Nondispersive (“2”) Liquids in Each Pair
liquids“
exptl temp, OC 24 24 3 3 3 3 39 39 14 14
(Beerbower) (Table 11) FEP A 0.97 0.56 0.94 0.76 0.94 0.56 1.00 0.56 1.00 0.58
y~:/r~,
(eq 4) 0.97 1.02 1.00 0.98 1.01
FEP B 3
0.94 0.56 1.00 0.56
0.98
Siliconized Glass 24 0.97 24 0.56
0.92
3
39 39
1.01
Liquid symbols as in Table 111.
column in this table is the Fowkes-theory prediction of the dispersive fraction of the “2” liquid (the nondispersive one) within each liquid pair. In all cases, this dispersive fraction is very close to 1.00, indicating that eq 2 predicts that the “2” liquids are just as dispersive as are the “1” liquids. This is clearly contrary to the predictions of the Beerbower correlation and, in general, to the expectations based on solubility parameters, molecular structure, and molecular properties. Within the context of the Fowkes approach, it therefore needs to be asked why the apparently significant differences in the relative magnitudes of dispersion forces have not manifested themselves in concomitant differences in the observed contact angle measured with each pair of liquids. One possible answer is that the “2“ liquids are, in effect, almost completely dispersive in behavior with the nondispersion contributions being too small to affect the contact angle noticeably. As was mentioned above, however, this is in considerable disagreement with the independent measures of the relative importance of nondispersion forces; viz., solubility parameters, the Beerbower correlation, and dipole moments. Nevertheless, if the “2” liquids are indeed accepted as being almost completely dispersive, then the conclusions remain significant within the context of the Fowkes approach. If liquids as apparently nondispersive as the “2” liquids of Table VI are found to behave as if they were overwhelmingly dispersive (as are the “1” liquids), it in effect means that in many practical situations it is unnecessary to evaluate the nondispersion components of surface tension; the wetting behavior is well modeled on the basis of a single (dispersion) component of surface tension equal to the total surface tension. In other words, the equation of state approach is applicable. Alternatively, if it is agreed that there is a significant difference between the liquids with regard to the types and relative magnitudes of the intermolecular forces, then it must be concluded that eq 2 has failed to detect these differences in terms of surface tension components. Therefore, within the context of the theory of surface tension components there are primarily two possible responses to the observed contact angles. The first may be to repudiate the independent measures of a liquid’s
624 Langmuir, Vol. 2, No. 5, 1986
Spelt et al.
Table VII. Equilibrium Spreading Pressures Required To Make the Contact Angles Equal in Each Liquid Pair” liquidb exptl Ad,‘ Ad,,‘ AB,,‘ Ke,e pair temp, “C deg deg deg mJ/m2 FEP A 24 -0.2 0.0 -0.2 0.1 M+MS +3.4 1.4 D+B 3 +2.0 -1.4 +0.4 +2.1 0.9 +2.5 D+MS 3 -1.0 -0.8 +0.2 0.3 39 P+H P + EC 14 +0.6 0.0 +0.6 0.1 FEP B
D + MS P+H
3
+3.1
39
-1.2
M+MS
39
+0.4 +0.2
+2.7 -1.4
1.2 0.4
Siliconized Glass -2.7 0.0
-2.7
1.0
” Calculations based on the Neumann equation of state. Liquid symbols as in Table 111. The first liquid in each pair is the “1” (dispersive) liquid and the second is the “2” liquid. A6 = d1 - d2; Ad,, contact angle difference due to the difference between y~~and yL2; Adr, contact angle difference due to K,, equilibrium spreading pressure responsible for Adr. “dispersive”character such as solubility parameters, dipole moments, and molecular structure. The argument would then be that the liquids in each polar-nonpolar pair are equally dispersive and hence the contact angles should indeed be the same. The second possible response would acknowledge the differences in the liquids within each pair and would conclude that the Fowkes equation does not correctly identify the anticipated nondispersion components of surface tension. In contrast to the above dichotomy, the present contact angle results are fully consistent with the equation of state approach to interfacial tensions. Recall that since the total liquid surface tensions are constant within a given pair of liquids, the contact angles are predicted (by an equation of state) to be equal on a single solid substrate. This does appear to be largely the case, although explanations must be found for the small, but finite, contact angle differences which persist. There are several ways to account for these discrepancies: (1) vapor adsorption leading to small equilibrium spreading pressures; (2) liquid contamination; (3) nonmaximal advancing contact angles. With respect to the last of these points, dynamic contact angle experiments12 have demonstrated that a static “advancing”contact angle may be as much as 3 O below the true Young contact angle encountered at very low threephase line velocities. Regarding the first possible explanation, although it is customary to neglect vapor adsorption (and, hence, equilibrium spreading pressures) in all practical contact angle measurements, it is important to appreciate that this is an approximation, albeit a good one, for most low-energy s01ids.l~ It is widely accepted that surfaces such as Teflon and polyethylene contain a small fraction of hydrophilic sites which may lead to spreading pressures on powdered Teflon of over 3 mJ/m2 with octane and approximately 2 mJ/m2 with water.13 The manner in which these powder measurements relate to solid surfaces of Teflon is in question, but it seems plausible to expect, under certain circumstances, equilibrium spreading pressures of the order of 1 mJ/m2. Table VI1 provides an estimate of the equilibrium spreading pressure required to make the contact angles equal in each liquid pair. The observed contact angle (12) Cain, J. B.; Fancis, D. W.; Venter, R. D.; Neumann, A. W. J. Colloid Interface Sci. 1983, 94, 123. (13) Good, R. J. A.C.S. Symp. Ser. 1975, No. 8.
difference, AO, between two liquids in a pair may be considered in two distinct parts, one due to the small differences in the liquid surface tension (AO,) and the other due to vapor adsorption (Ae,). A0 is defined as O1 - O2 where “1”and “2” denote respectively the dispersive and nondispersive liquids in a given pair. In order to calculate AO, and then AOr it is necessary to make use of an equation of state for interfacial tensions, ysL = ysL(ysv,yLv). Although an explicit formulation of such an equation has not yet been achieved analytically, there do exist empirical equations of state, of which only one has been widely used and t e ~ t e d . ~ ,This ~ J ~particular equation, due to Neumann et al., is based on a wide variety of contact angle data on low-energy surfaces, and in practice, it is implemented as a computer program2(which has been adapted to hand-held calculator~l~) or in the form of tables.16 The evaluation of AO, begins with the calculation of the solid surface tensions of the three substrates using the contact angle data in Tables 111-V. The least-squares relations for ysv, from the Neumann equation of state, are as follows: 19.3 - (0.0632)T mJ/m2 and 20.4 - (0.0722)T mJ/m2 for FEP A and FEP B, respectively. Knowing the solid surface tension at each experiment temperature, it is possible to predict the contact angle difference (AO,) due to the known difference in the measured liquid surface tensions yL1- yL2where the subscripts have the same meaning as above. The contact angle diffference attributable to adsorption is then given by AO, = A0 - AO,. If AO, is positive (the dispersive, “1”liquid is considered to be adsorbed) then K, is estimated as follows: K, = ys, - ysvl, where ysv, and ys, are calculated with the Neumann equation of state and the contact angle-liquid surface tension data, 01,yLvland 61 - AOT, yLvl, respectively. Here, O1 and yLvl are the contact angle and the surface tension, respectively, of the dispersive liquid in each pair listed in Tables 111-V. An analagous procedure, utilizing O2 and yLv2,is employed to estimate K, if AO, is negative. Of the eight hypothetical equilibrium spreading pressures listed in Table VII, six are less than or equal to 1 mJ/m2. As demonstrated by Good,13it is not unreasonable to assume that such spreading pressure can occur on surfaces of Teflon FEP and siliconized glass. It is, therefore, concluded that the observed differences in the contact angles within a given liquid pair may reasonably be attributed to experimental error and specifically to vapor adsorption. The present contact angle data are, thus, seen to be consistent with the predictions of the equation of state approach and provide an independent experimental verification of this theory. Finally, mention should be made of a second source of independent experimental evidence which may be used to evaluate the theory of surface tension components and that of the equation of state. The rejection or inclusion of microscopic particles at advancing solidification fronts may be predicted thermodynamically and then verified by direct experimental ob~ervation.’~This type of experiment, thermodynamic prediction followed by direct observation, has consistently confirmed the accuracy of the (14)Neumann, A. W.; Spelt, J. K.; Smith, R. P.; Francis, D. W.; Rotenberg, y.;Absolom, D. R. J. Colloid Interface Sci. 1984, 102,278. (15) Taylor, C. P. S. J . Colloid Interface Sci. 1984, 100, 589. (16) Neumann, A. W.; Absolom, D. R.; Francis, D. W.; van Oss, C. J. Sep. Purif. Methods 1980, 9, 69. (17) Neumann, A. W., Omenyi, S. N.; van Oss, C. J. J. Phys. Chem. 1982, 86, 1267. (18) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman: San Franciso, 1963.
Langmuir 1986,2,625-630 Neumann equation of state.17 The application of eq 2, on the other hand, is known to result in false predictions of particle behavior in a number of ~ y s t e m s . ~ ~ ' ~ The findings reported here give rise to some regrets. The idea of subdividing surface tensions into components which arise from the action of the individual intermolecular forces is very appealing. A completely successful theory of this nature would be an immensely valuable link between macroscopic and microscopic thinking. It should be understood that the experimental results presented here do not preclude the existence of such a theory. While it has become apparent that present day values are not dispersion components of surface tension, such components might well exist and contribute to the overall surface tension, although probably not in an additive fashion. We see the Fowkes approach as a decisive first step in the development of this area of surface science. (19) Smith, R. P. Ph.D. Thesis, University of Toronto, 1984.
625
Conclusions The contact angles of pairs of liquids on a single solid substrate were found to be equal when the surface tensions of the liquids were the same, regardless of the relative magnitudes of the dispersion forces comprising each of the two liquids. This observation is in direct conflict with the theory of surface tension components. It is, however, consistent with the expectations of the equation of state approach, in which the solid-liquid interfacial tension is only a function of the total solid and liquid surface tensions. Acknowledgment. Supported in part by the Natural Science and Engineering Research Council of Canada (A8278), the Medical Research Council (MT 5462, M T 8024, MA 9144), and the Ontario Heart and Stroke Foundation (4-12, AN-402). D.R.A. acknowledges gratefully support of the Ontario Heart Foundation through the receipt of a Senior Fellowship.
Interactions in Concentrated Nonaqueous Polymer Latices Ivana Markovie, R. H. Ottewill,* and Sylvia M. Underwood+ School of Chemistry, University of Bristol, Bristol B S 8 1 TS, U.K.
Th. F. Tadros ICI Plant Protection Division, Jealott's Hill Research Station, Bracknell, Berkshire, U.K. Received February 25,1986. I n Final Form: June 25, 1986 Particles of poly(methy1methacrylate) stabilized by poly(l2-hydroxystearicacid) can be used to form dispersions of high volume fraction in dodecane. In the present work volume fractions between 0.23 and 0.42 were examined by small-angleneutron scattering. From these measurements both the structure factor, S(Q),and the pair correlation function,g(r), were derived. By use of a model interaction potential function, based on the mean spherical approximation, it was found that the particle-particle interaction was soft at low volume fractions and became harder at high volume fractions, indicating that in the latter condition some compression of the stabilizing layer occurred.
Introduction Following the introduction of the concept of dispersion polymerization in nonaqueous media1g2methods have been developed for the preparation of stable monodisperse polymer latices in hydrocarbon^.^-' These have proved useful model colloidal dispersions for fundamental studies in media of low dielectric constant. A system of this type, which we have used in previous s t ~ d i e s ~is, ~composed ,~*~ of a core particle of poly(methy1 methacrylate) with an outer layer of a "comb" polymer, poly( 12-hydroxystearic acid), covalently attached to the core particle so that the oleophilic "teeth" project into the dispersion medium. In hydrocarbon media such as dodecane it seems reasonable to conclude that electrostatic effects are absent and hence the particles are sterically stabilized. Consequently, the range of interaction forces between these particles would not be expected to be significant beyond a range of about twice the length of the stabilizer chains,1° in the present case the "teeth" of the comb polymer. Although a significant number of theories have been proposed to account for the phenomena of steric stabili-
* To whom correspondence should be addressed. t Present
address: Dulux Australia Limited, Clayton, Victoria,
Australia.
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zation, and these have been well surveyed by Napper," there is still a sparsity of direct experimental information on the nature of the interaction potentials between sterically stabilized particles. However, our previous preliminary study on this type of system using small-angle neutron scattering4 and subsequent theoretical developm e n t ~ ' ~has - ~ indicated ~ that this technique provides a (I) Osmond, D. W. J.; Walbridge, D. J. J. Polym. Sci. 1970, (230,381.
(2) Barrett, K. E. J. Dispersion Polymerization I n Organic Media; Wiley: London, 1975. (3) Cairns, R. J. R.; Ottewill, R. H.; Osmond, D. W. J.; Wagstaff, I. J. Colloid Znterface Sci. 1976,54, 45. (4) Cebula, D. J.; Goodwin, J. W.; Ottewill, R. H.; Jenkin, G.; Tabony, J. Colloid Polym. Sci. 1983,261,555. (5) Antl, L.; Goodwin, J. W.; Hill, R. D.; Ottewill, R. H.; Owens, S. M.; Papworth, S.;Waters, J. A. Colloids Surf. 1986, 17,67. (6) Dawkins, J. V.; Taylor, G. Colloid Polym. Sci. 1980,258, 79. (7) Everett, D. H.; Stageman, J. F. Faraday Discuss. Chem. SOC.1978,
--.(8) Cairns, R. J. R.; van Megen, W.; Ottewill,R. H. J.Colloid Interface
65. 2.70.
Sci. 1981, 79, 511.
(9) van Megen, W.; Ottewill, R. H.; Owens, S. M.; Pusey, P. N. J. Chem. Phys. 1985,82, 508. (10)Koelmans, H.: Overbeek, J. Th. G. Discuss. Faraday SOC.1954. 18,52. (11) Napper, D. H. Polymeric Stabilization of Colloidal Dispersions;
Academic Press: London, 1983. (12) Hayter, J. B.; Penfold, J. Mol. Phys. 1981, 42, 109. 0 1986 American Chemical Society
