Langmuir 1998, 14, 2201-2207
2201
Wetting and Spreading of Styrene-Butadiene Latexes on Calcite W. N. Unertl† Laboratory for Surface Science and Technology, Sawyer Research Center, University of Maine, Orono, Maine 04469 Received August 8, 1997. In Final Form: January 20, 1998 The wetting behavior of individual styrene-butadiene latex particles on the cleavage surface of calcite is described for latexes with glass transition temperatures above and below room temperature. Contact angles of the spread particles, as determined from scanning force microscope images corrected for tip artifacts, were measured. Both types of latex spread with a slight anisotropy, resulting in a continuous variation of the local contact angle by (6° around the particle edges. Pull-off force measurements were used as a transfer standard to show that the surface energy of the latex particles, after spreading, was the same as that of continuous films made from the same latex. The work of adhesion W, as determined by the Young-Dupre´ equation, was found to be 80-85 mJ/m2 for the latex with a high glass transition temperature. Lifshitz theory was used to show that nondispersive interactions make a large contribution to W. Individual particles of the latex with a low glass transition temperature had a large variation in spreading behavior.
1. Introduction Latex particles with diameters of a few hundred nanometers are widely used as binders in coatings in a wide variety of applications including paints and coated papers. The coatings are usually applied as a water suspension of the latex and other constituents and then dried. This process is called consolidation. If the latex content is high, as in paints, the individual latex particles bind together to form a continuous network, as illustrated in Figure 1a. This binding process has been extensively studied.1-6 Many of the properties of the resulting coatings are controlled by the characteristics of the interactions between latex particles. This is not true in the case of low latex content, say 10% by weight or less. For these coatings, which are widely used on papers, the latexlatex interaction is not significant. Rather, as shown in Figure 1b, it is the interactions of individual latex particles with the other constituents that determine the properties of the coating.7 Only recently have the consolidation processes in coatings with low latex content received detailed study.8 In spite of their importance, the interactions between individual latex particles and various other materials used in coatings have received little attention.9,10 The wetting and spreading of individual latex particles is the subject of this paper. There are two previous qualitative SFM studies of the wetting and spreading of individual latex particles. Granier and Sartre9 used latex particles of styrenebutadiene (SB) copolymers with a surface layer containing †
E-mail:
[email protected].
(1) Eckersley, S. T.; Rudin, A. J. Appl. Polym. Sci. 1994, 53, 1139. (2) Dobler, F.; Pith, T.; Lambda, M.; Holl, Y. J. Colloid Interface Sci. 1992, 152, 1 and 12. (3) Wang, Y.; Juhue, D.; Winnik, M. A.; Leung, O. M.; Goh, M. C. Langmuir 1992, 8, 760. (4) Goh, M. C.; Juhue, D.; Leung, O. M.; Wang, Y.; Winnik, M. A. Langmuir 1993, 9, 1319. (5) Lin, F.; Meier, D. J. Langmuir 1995, 11, 2726. (6) Juhue, D.; Wang, Y.; Lang, J.; Leung, O. M.; Goh, M. C.; Winnik, M. J. Polym. Sci. B 1995, 33, 1123. (7) Lepoutre, P.; Hiraharu, T. J. Appl. Polym. Sci. 1989, 37, 2077. (8) Stanislawska, A.; Lepoutre, P. Tappi J. 1996, 79 (5), 117. (9) Granier, V.; Sartre, A. Langmuir 1995, 11, 2179. (10) Butt, H. J.; Gerharz, B. Langmuir 1995, 11, 4735.
Figure 1. Structure of coatings with low- and high-latex content.
varying amounts of acrylic acid segments. Particle diameters were 100-125 nm, and glass transition temperatures Tg were 5 or 41 °C. The latexes were deposited on the surfaces of silicon wafers, mica, and calcite as drops of diluted water suspension and then dried and imaged in air at room temperature. The degree of spreading of latexes with Tg ) 5 °C increased in proportion to the amount of acrylic acid in the surface layer. Adhesion, as indicated by the ability of the SFM tip to move the spread particles, was found to be stronger on the more basic calcite surface and weaker on the acidic silicate surface of the silicon wafer. Deformation and sliding induced by the SFM tip were reported for some of the latex formulations. Butt and Gerharz10 studied spreading of latexes composed of different proportions of n-butyl acrylate and methyl methacrylate, including nonhomogeneous compositions, deposited onto mica substrates. Particles with Tg below room temperature spread significantly, and their shapes were influenced by the latex composition. Even particles with high Tg appeared to be slightly deformed. In this paper, we describe a more quantitative application of SFM than that of previous studies. In particular, we extract the contact angle θ and determine the work of adhesion W of individual styrene-butadiene latex particles on calcite cleavage surfaces. These materials were chosen because SB latexes are widely used in paper coatings that have calcium carbonate particles as an important pigment. The primary contribution of our work is a determination of the work of adhesion from an analysis of scanning force microscope images. We also present other data related to the wetting and spreading process and to imaging artifacts in SFM.
S0743-7463(97)00895-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 03/25/1998
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Figure 2. Definition of the parameters used to describe latex particles. Left: a free spherical particle with radius R0 and surface energy γl. Right: a particle after it has spread on a substrate to form a spherical cap with surface radius R, contact height h, contact radius a, contact angle θ, and surface energy γs. The work of adhesion between the latex and substrate is W.
Figure 3. Notation used to describe the deformed shape of two objects in contact. The local radii of curvature prior to contact under load F are Ri and Rj. The diameter of the contact is 2a, and the deformation induced by the contact is δ.
2. Descriptions of Adhesion The principal goal of the work presented here is to extract thermodynamic information from SFM images of wetting and spreading of initially spherical latex particles that have spread on a surface. We analyze our results in analogy with the thermodynamics of the equilibrium shapes of liquid drops on surfaces.11,12 The situation is illustrated in Figure 2. Prior to deposition, each latex particle is a sphere of radius R0 in water suspension. The surface energy, in air, is γl. If the glass transition temperature Tg of the latex is low enough, it will spread spontaneously. After spreading to equilibrium on an undeformable surface, the shape is a spherical cap of height h, radius of curvature R, base radius a, contact angle θ, and surface energy γs. Gravitational effects are negligible for particles of the size of interest here. The work of adhesion W for the interface is given by
W ) γs + γl - γsl ) γl(1 + cos θ)
(1)
where γsl is the interfacial energy. Equation 1 is known as the Young-Dupre´ equation. If the interactions are due entirely to dispersion forces,12
W ) A/12πD2
(2)
reduction of molecular symmetry at the surface are usually of second order.12,14 If Tg is too high, the latex will not spread unless the system is heated. The particle-substrate interaction can be described using the contact mechanics of bodies in which interfacial adhesion is significant. The situation is illustrated in Figure 3, where bodies i and j, with local radii of curvature Ri and Rj, are brought into contact by an applied load F. The mechanical properties of each body are described in terms of its Young modulus E and Poisson ratio ν. This problem has been treated theoretically by Johnson, Kendall, and Roberts,15,16 whose treatment is known as JKR theory. The radius a of the contact area is given by
a3 )
Reff [F + 3πReffW + x6πReffWF + (3πReffW)2] (4) E*
where W is given by eq 1, the reduced modulus E* is defined as
E* ≡
[
]
2 2 4 (1 - νi ) (1 - νj ) + 3 Ei Ej
-1
(5)
and the reduced radius is where A is the Hamaker constant and D is the atomic spacing between the substrate and the latex and is typically an intermolecular spacing. The Hamaker constant can be calculated from macroscopic quantities using Lifshitz theory13 as described by Israelachvili12 and yields
( )( )
s - 1 l - 1 3 + A ≈ kT 4 s + 1 l + 1 3x2hfs 16
(ns2 - 1)(nl2 - 1) (3) fl 2 2 2 (ns + 1)xnl - 1 1 + xnl - 1 fs
(
)
where n, , and f are the index of refraction, dielectric constant, and electronic absorption frequency, respectively. The first term is about 2-3% of the second term for the materials considered in this paper. Corrections to eq 3 due to neglect of molecular-scale graininess and (11) Good, R. J.; van Oss, C. J. In Modern Approaches to Wettability; Schrader, M. E., Loeb, G. I., Eds.; Plenum Press: New York, 1992; p 1. (12) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1992. (13) Lifshitz, E. M. Sov. Phys. JETP (Engl. Transl.) 1956, 2, 73.
1 1 1 ≡ + Reff Ri Rj
(6)
Two special cases of eq 4 are of interest. If there is no applied load (F ) 0), then the contact radius becomes
a0 )
(
)
6πReff2W E*
1/3
(7)
The critical force Fp required to separate the bodies, which makes the square root in eq 4 zero, is also called the pulloff force and is given by
3 Fp ) - πReffW 2
(8)
The pull-off force does not depend on the mechanical properties of the bodies. (14) Chaudhury, M. K. Mater. Sci. Eng. 1996, R16, 97. (15) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1975, 53, 314. (16) Johnson, K. L. Contact Mechanics; Cambridge University Press: Cambridge, U.K., 1985.
Styrene-Butadiene Latexes on Calcite
Langmuir, Vol. 14, No. 8, 1998 2203 Table 1. Physical Properties of Materials material
property Young modulus E* (GPa) poisson ratio ν index of refraction n surface energy γ (mJ/m2) dielectric constant absorption frequency f (1015 Hz)
calcite
SiO2
Si3N4
SB latex
25031 0.2731
1.65,d 1.44e 33 23022 8.04,e 8.5e 4.535
70,a 72b 30 0.17-0.2330 1.4512 78-205f 23 4.5b 3.2h 12
0.1-1c 32 ≈1/3 1.5534 44.827 2-4g 12 2.3i 12
a Soda-lime glass. b Fused silica. c Values measured about 20 °C or more below T . g glass. g Typical values for polymers. h Fused quartz. i Polystyrene.
Finally, the deformation depth δ (Figure 3) is given by
δ)
[ ()]
a2 2 a0 1Reff 3 a
3/2
(9)
We shall also use JKR theory to analyze the contact between (i) the SFM tip and a latex particle or (ii) a latex particle and the calcite substrate. 3. Materials and Methods The calcite substrates were cleaved from uncut, transparent, natural calcite (Atomagic Chemical Corp.) to expose the (101h 4) surface using a razor blade. The orientation was confirmed by X-ray diffraction. Samples were typically about 1 cm on a side by 1-2 mm thick. The cleavage surface was characterized in the SFM and consisted of large atomically flat regions separated by steps ranging from single atomic heights up to about 60 nm high. Physical properties of calcite needed for the analysis of the experiments are given in Table 1. The majority of the work used a carboxylated styrenebutadiene latex (Dow Chemical RAP107NA) with a glass transition temperature of Tg ) 45 °C and a mean particle diameter of 150 nm. This latex will be referred to as the high-Tg latex. Since this latex does not spread at room temperature, it was possible to study the deposited particles prior to spreading. These latex particles were induced to spread by heating in air to approximately 90 °C. The other latex (Dow Chemical CP620NA) had Tg ≈ 5 °C and a mean diameter of 145 nm. This latex will be referred to as the low-Tg latex. Both latexes were supplied as suspensions of about 50 wt % latex in water and contained other unspecified additives. In order to deposit submonolayer quantities, the suspensions were diluted with distilled water to a concentration in the range 1 × 10-5 to 1 × 10-4 by volume. All of the samples described here were prepared by the drop method.17,18 In this method, a drop of about 1-µL volume is deposited onto freshly cleaved calcite from a pipette. For the low-Tg latex, the drop was allowed to dry in two different ways. In one case, the drying was kept slow by maintaining ≈95% relative humidity for 1 week followed by storage in a vacuum desiccator to remove the remaining water. In the second case, the sample was dried as rapidly as possible by placing it into a vacuum desiccator that was evacuated to about 300 mTorr by a mechanical pump within a few minutes. The high-Tg latex was allowed to dry at room temperature in air for about 30 min at a relative humidity of about 25% and then stored in a vacuum desiccator. In order to make this latex spread, the sample was heated to about 90 °C for 1 h on a Peltier hot stage mounted in the SFM.19 The drop method results in very nonuniform distributions (including clumping) of the latex particles on the surface15 due to the mass transport and capillary effects that occur during the drying process.20 However, there were always a sufficient number of isolated particles for the measurements reported here. (17) El Bediwi, A. B.; Kulnis, W. J.; Luo, Y.; Woodland, D. D.; Unertl, W. N. Mater. Res. Soc. Symp. Proc. 1995, 372, 277. (18) El Bediwi, A. B. Ph.D. Thesis, University of Mansoura, Mansoura, Egypt, 1995, unpublished. (19) Kulnis, W. J.; Unertl, W. N. Mater. Res. Soc. Symp. Proc. 1994, 332, 105. (20) Vanderhoff, J. W.; Bradford, E. B.; Carrington, W. K. J. Polym. Sci. Symp. 1973, 41, 155.
d
Ordinary ray. e Extraordinary ray. f Values for float
A Park Scientific Instruments Universal SFM was used to image the calcite substrate and latex particles deposited onto it. Commercial Si3N4 cantilever-tip assemblies were used, although in the analysis below, we will assume that the surface of the tip is actually a layer of oxidized silicon. All images were obtained in the constant force mode with an applied load on the tip of e1 nN. Height measurements along the sample normal (z-direction) were calibrated using a 91.4 ( 0.5 nm step height standard (Veeco, Sloan Technology Division, Santa Barbara, CA). Lateral distances in the surface (x and y directions) were calibrated using a grating standard with 463-nm line spacing (Ted Pella, Inc., model 16112, Redding, CA). In the analyses presented below, we assume the nominal values of tip radius r and cantilever force constant κ given by the manufacturer. However, the actual values of these quantities can easily differ by a factor of 2 or more from their nominal values, and results derived using them should be considered to be semiquantitative, at best. Forces are calculated using Hooke’s law
F ) κ∆z
(10)
where ∆z is the displacement of the cantilever due to force F acting on the tip. The SFM was not equipped to measure lateral forces. The SFM was also used to measure force-distance curves (see Figure 4a).21 In this measurement, the cantilever deflection is recorded as a function of sample displacement. Initially, at point A, the tip is not in contact with the sample. The sample is moved toward the tip at a constant speed until contact is achieved (B) and a predetermined maximum load is reached (C). The sample is then withdrawn along CDE until the adhesive bond between the tip and the sample is broken (E) and the cantilever returns to its undeflected state (F). The force required to break this adhesive bond is the pull-off force Fp (eq 8).
4. Results (a) Pull-off Force on Cleaved Calcite (101 h 4). The Fp required to separate the SFM tip from a freshly cleaved calcite surface was found to be less than 0.2 nN, which was the limit of sensitivity of our measurements. We used the softest cantilever (κ ) 0.01 N/m) available to us with a nominal tip radius of 20 nm. Figure 4b shows a typical measurement. The slight displacement between the loading and unloading data is due to hysteresis in the piezotube displacement. Equation 8 relates Fp to the work of adhesion W. Using the measured Fp = 0.2 nN and r ) Reff ) 20 nm, we find W = 2 mJ/m2; i.e., there is very little energy gain in forming the calcite-SFM tip interface. Even with the very conservative assumption that the force measurement is low by a factor of 10 and the tip radius high by a factor of 2, W e 42 mJ/m2. The surface energy of the cleavage face of calcite is γc ) 230 mJ/m2.22 However, the surface energy of the SFM tip is not known. We estimate below that the surface energy of our tips is about γt = 200 mJ/ m2. This is in the range expected for a surface layer of (21) Burnhan, N. A.; Colton, R. J.; Pollock, H. M. Nanotechnology 1993, 4, 64. (22) Gilman, J. J. J. Appl. Phys. 1960, 31, 2208.
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Figure 5. Image of isolated particles of high-Tg latex showing artifacts due to tip shape: (a) gray-scale image, (b) contour image with 10-nm contour line spacing (the image is 2.5 µm on a side); (c) histogram showing the height distribution measured for 58 particles of the high-Tg latex on calcite.
F)-
Figure 4. (a) A typical force-distance curve showing the pulloff force. (b) Force-distance curve for a freshly cleaved (101h 4) surface of calcite. The pull-off force is less than 0.2 nN. (c) Forcedistance curves for a continuous latex film and an isolated individual latex particle after it has spread on calcite.
oxidized silicon that should have a surface energy in the range found for glass (78-205 mJ/m2 23). Using the Young-Dupre´ equation, we calculate the interfacial energy between the tip and calcite to be γct ≈ 430 mJ/m2. Assuming very conservative assumptions about the uncertainties, this value of γct is reduced by only 10%. Alternatively, for the case of van der Waals dispersion forces, the force between a sphere and planar substrate is given by12 (23) Schultz, J.; Nardin, M. In Modern Approaches to Wettability; Schrader, M. E., Loeb, G. I., Eds.; Plenum Press: New York, 1992; p 82.
Ar 12D2
(11)
where A is the Hamaker constant and D the spacing between the tip and substrate in contact. We assume that D has the value of a typical interatomic spacing (0.20.3 nm) and use eq 3 and the quantities from Table 1 to estimate A = (6-9) × 10-20 J. This yields F < 7 nN. Thus, the interaction between the tip and calcite appears to be dominated by dispersion forces. These very weak forces also provide strong evidence that capillary forces due to the presence of a condensed water layer are not important in the tip-calcite interaction. (b) High-Tg Latex. Figure 5a is a gray-scale image of high-Tg latex particles after drying but before spreading. Figure 5b is a contour plot of the same data. The pyramidal shapes of the imaged particles are caused by the bluntness of the SFM tip as illustrated in Figure 6, which is drawn approximately to the scale of the images in Figure 5. Consider the tip as it moves over the particle from left to right and assume for the moment that all surfaces are perfectly rigid. The pyramidal side of the tip makes first contact with the sphere. As the tip slides upward to pass over the latex sphere, the contact point on the sphere remains stationary. In effect, the point on the sphere images the side of the tip. Once the rounded end of the tip makes contact, the tip follows a circular arc of radius r + R until the opposite side of the pyramid starts to slide down the sphere. The resulting image profile (lower trace in Figure 6) is a blunted pyramid tilted at the same angle θtilt as the tip. This is particularly evident in the contour plots of the individual particles in Figure 5b. Similar images of small spheres of known radius have been used to measure the tip shape.24-26 We point out two features of the image profile. First, below the point of initial contact, no information is obtained about the shape of the sphere or the underlying substrate. Second, the height (24) Markiewicz, P.; Goh, M. C. Langmuir 1994, 10, 409. (25) Villarrubia, J. S. J. Res. Natl. Bur. Stand. Technol. 1997, 102, 425. (26) Odin, C.; Aime, J. P.; El Kaakour, Z.; Bouhacina, T. Surf. Sci. 1994, 317, 321.
Styrene-Butadiene Latexes on Calcite
Langmuir, Vol. 14, No. 8, 1998 2205
Figure 6. Illustration of image artifacts caused by the tilt and shape of an SFM tip that influence the dimensions of images of a spherical particle and a spherical cap.
h of the image profile is equal to the height of the sphere. Thus, if deformation can be neglected, h can be measured directly from the image profile to obtain the sphere diameter. In the case of Figure 5a,b, the heights of the three isolated latex particles are 162, 149, and 157 nm; these heights are all near the nominal diameter 150 nm quoted by the manufacturer. Figure 5c shows the distribution of the heights measured by SFM for 58 particles. The average height is 137 ( 13 nm. Two factors can cause the measured height to be reduced from the expected value. These are (i) deformation due to the load on the SFM tip and (ii) deformation due to adhesion between the latex and substrate. The magnitudes of both effects can be estimated by calculating the deformation δ parameter (eq 9). To minimize deformation by the SFM tip, the applied load was kept as close to zero as possible. As we show below, the work of adhesion between the SFM tip and the latex is about 76 mJ/m2. From eqs 4-9, assuming a tip radius of 50 nm, a modulus of 0.1 GPa, and a latex radius of 75 nm, we obtain δ < 6 nm, for applied loads up to about 1 nN. Similarly, the deformation due to adhesion of the latex sphere to the calcite substrate is δ < 9 nm. Thus, the total deformation due to interactions with the tip and substrate is expected to reduce the height measurement by roughly 15 to about 135 nm. This value is in good agreement with the measured result and also indicates that the modulus of the high-Tg latex is near 0.1 GPa, as expected. Figure 7 shows gray-scale and contour map views of three high-Tg latex particles that have spread after heating to 92 °C for 1 h. The two particles labeled a and b are on the flat cleavage surface and particle c sits astride a cleavage step 1.5 nm high, which is about two unit cells of the calcite. The position of the step edge is indicated by the diagonal line in the contour map and is only weakly visible in the gray-scale image. After spreading, the latex particles have noncircular contacts with the calcite surface; i.e., spreading is not isotropic. Additional heating had no effect on the noncircular shapes. This result supports our assumption of thermodynamic equilibrium needed to apply the Young-Dupre´ equation. Since the orientation of the anisotropy varies from particle to particle, it cannot be an artifact of the SFM imaging process. Furthermore, the anisotropy is not correlated with the crystal structure of the calcite surface. We discuss this anisotropy later.
Figure 7. Image of high-Tg latex particles following spreading on calcite. Particles a and b are on an atomically flat terrace, and particle c is astride a 1.5 nm step. The image is 2.5 µm on a side, and the contour line spacing is 10 nm.
Also apparent in Figure 7 are a number of smaller particles. Such small particles were commonly observed with both the high- and low-Tg latexes. They were not studied in detail, but we note that agglomeration of one or more small particles with a single larger particle might account for the nonisotropic spreading. (c) Low-Tg Latex. Parts a and b of Figure 8 show two views of a typical image of the low-Tg latex deposited on calcite by the drop method at room temperature and dried at ≈95% relative humidity for 24 h before storing in a vacuum desiccator. This latex spreads at room temperature, and, like the high-Tg latex, the spreading is not isotropic. However, unlike the high-Tg latex, there is a large variation in the shapes of spread particles. For example, the low-Tg particles, labeled a and b in Figure 8, have the same height h even though particle a obviously has a much smaller volume than particle b. Either the low-Tg latex is not able to reach equilibrium at room temperature (≈25 °C) or its properties, such as surface energy or internal structure, vary significantly from particle to particle. Parts c and d of Figure 8 show a low-Tg latex particle after spreading in vacuum. The “particles” shown in the image are actually aggregates of several latex particles and have an even larger range of contact angles than individual particles spread at high humidity. Clearly, drying in high humidity enhances the spreading and reduces the agglomeration. (d) Surface Energy after Spreading. Pull-off force measurements were made on individual low-Tg latex
2206 Langmuir, Vol. 14, No. 8, 1998
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Fp1 γ1 = Fp2 γ2
(14)
We thus conclude that the surface energies of the latex particle and continuous film are identical with γ1 = γ2 = 44.8 mJ/m2. Combining eqs 6, 8, and 13, the surface energy of the tip can be written as
γt =
( )
Fp 2 -1 γ 3πr l
(15)
Using the quantities above, this yields γt = 200 mJ/m2. Although this value is highly dependent on nominal values assumed for κ and r, it is consistent with the low pull-off force values measured on the clean calcite surface as described above. 5. Analysis and Discussion
Figure 8. (a and b) Low-Tg latex particles following spreading on calcite in a high-humidity environment. The image is 2 µm on a side, and the contour line spacing is 10 nm. (c and d) Low-Tg latex particles after spreading on calcite in vacuum. The image is 2.02 µm on a side, and the contour line spacing is 20 nm.
particles and on continuous latex films cast from the lowTg latex suspension. These measurements were used to deduce that the surface energy was identical for the individual latex particles and the continuous film. The continuous films were made from a undiluted latex suspension cast on calcite, dried in air, and rinsed in deionized water to remove any water-soluble constituents that exude to the surface. The surface energy of films cast from the low-Tg latex was previously reported to be γl ) 44.8 mJ/m2.27 Figure 4c shows typical force-distance curves. The Fp are identical with average values of 18 ( 2 nN for the particles and 18 ( 3 nN for the film. All of the measurements were made with the same tip and cantilever force sensor that had a nominal κ ) 0.05 N/m. The smallest possible z-displacements were used to minimize the effects of piezotube creep and hysteresis; i.e., withdrawal was started as soon as the cantilever reached the no-load condition. Using eqs 1, 6, and 8,
Fp1 R1 W 1 R1 γt + γ1 - γt1 ) ) Fp2 r + R1 W2 r + R1 γt + γ2 - γt2
(12)
where subscripts 1 and 2 refer to the latex particle and film, respectively. Since the tip radius r ≈ 20 nm is much smaller than the radius of the spread particle R1 ≈ 300 nm, Fp1 ≈ Fp2 implies W1 ≈ W2. If the tip-latex interaction is entirely due to dispersion forces, then11
W ) γi + γj - γij ) 2xγtγl
(13)
is exactly correct. Equation 13 is also satisfied empirically by many polymers.12,14 Thus, (27) Al-turaif, H.; Unertl, W. N.; Lepoutre, P. J. Polym. Mater. Sci. Eng. 1993, 70, 295.
These experiments were undertaken to determine whether SFM measurements of the shapes of the spread latex particles might be a useful method to determine the contact angle θ and thus, using the Young-Dupre´ equation, to extract the interfacial energy W. In this section, we analyze the results from this perspective. (a) Origins of Anisotropic Spreading. We find that the latex particles all spread anisotropically on the cleavage surface of calcite. A few of the possible causes can be ruled out. However, others cannot and further study will be required before the mechanism can be determined. Artifacts in the SFM imaging process cannot be the cause of the asymmetry, since the particles have neither the same shape nor the same orientation with respect to the scanning direction. Figure 7 clearly demonstrates this. One possible explanation is that thermodynamic equilibrium has not been reached. This is unlikely since the contact angles were not changed when the 45/150 latex was heated for various times and the 5/145 latex did not spread further over periods of weeks after the samples were initially prepared. In fact, noncircular shapes are allowed in thermodynamic equilibrium. For example, the Laplace equation for the pressure difference P across the surface12
(
P ) γl
)
γl 1 1 + ) R1 R2 R
(16)
shows that the radii of curvature, R1 and R2, can take on any values, including negative ones, as long as the mean radius of curvature remains constant. Our data are not good enough to test whether this condition is fulfilled for the asymmetric shapes we observed. Capillary forces acting during water removal can also be ruled out as a cause of anisotropy because the 45/150 latex also spread anisotropically following heating after it was completely dried in a vacuum desiccator. The substrate is itself a possible source of anisotropy because the surface unit mesh of the (101h 4) surface is oblique. However, this must be an insignificant effect since the orientations of the spread particles have no correlation with the substrate lattice. But we cannot entirely rule out the possibility that the latex particles adsorb at point defects or small pits on the calcite surface and that the sizes or spatial distributions of these defects influence the spreading. Such defects are known to form on the calcite surface when it is immersed in water,28,29 but we never observed defects after drying. We cannot rule out several other possible causes of anisotropy
Styrene-Butadiene Latexes on Calcite
Langmuir, Vol. 14, No. 8, 1998 2207 Table 2. Interfacial Properties of 150-nm-Diameter, High-Tg Latex Particles Following Spreading on Calcium Carbonate (Calcite) contact angle (deg)
work of adhesion (mJ/m2)
work of adhesion per particle (J)
26-38
82-85
1 × 10-14
latex obtained after heating to 90 °C. The same range of values was obtained for the 5/145 latex spread under high humidity. Also shown in Table 2 is the work of adhesion W, calculated by the Dupre´ equation (eq 1) and the work of adhesion per particle E, defined by
E ≡ WA Figure 9. Polar plot of the contact angle variation around the edge of particle a in Figure 7. For comparison, the shape of the particle is superimposed in the center as a contour plot of 10nm contour line spacing.
including anisotropic distribution of additives from the latex suspension, nonuniform surface energy of the latex particle perhaps due to variations in the distribution of carboxylate groups on the surface, and internal structure such as cross-linking inside the latex particle itself. Additional experiments will be required. (b) Contact Angles and Work of Adhesion. Contact angles and their variations around the perimeters of the spread particles were estimated from the SFM data. Profiles were measured perpendicularly to the particle edge at intervals around the edge. The portion of the profile with downward curvature was fit to a circle and the effective contact angle was calculated at the intersection of this circle with a straight line fit to the calcite surface outside the latex particle. This effective contact angle underestimates θ by δθ, as illustrated in the lower right of Figure 6. Assuming a spherical cap and a spherical tip, we estimate δθ ≈ 1.3° for the 45/150 latex. Figure 9 shows a polar plot of the contact angles extracted from the 45/150 particle labeled a in Figure 7. In this case, θ varies between 26° and 38° with a mean value of 31° ( 3°. The 12° variation in θ around a spread particle is larger than the uncertainty in measuring θ or correcting it for the tip size. The smallest θ are found at the elongated ends and the largest θ at the narrowest cross section. Table 2 gives the values of θ for the 45/150 (28) Liang, Y.; Baer, D. R.; Lea, A. S. Mater. Res. Soc. Symp. Proc. 1995, 335, 409. (29) Park, N. S.; Kim, M. W.; Langford, S. C.; Dickinson, J. T. J. Appl. Phys. 1996, 80, 2680. (30) Oliver, W. C.; Pharr, G. M. J. Mater. Res. 1992, 7, 1564. (31) Ceram. Source 1989, 5. (32) Kan, C. S.; Blackson, J. H. Macromolecules 1996, 29, 6853. (33) CRC Handbook of Chemistry and Physics, 60th ed.; Weast, R. C., Astle, M. J., Eds.; CRC Press, Inc.: Boca Raton, FL, 1979. (34) Polymer Handbook; Brandrup, J., Immergut, E. H., Eds.; Wiley: New York, 1989. (35) Ishigame, M.; Sato, T.; Sakurai, T. Phys. Rev. B 1971, 3, 4388.
(17)
where A is the contact area calculated after correcting the image for tip bluntness. The magnitude of W is relatively insensitive to the variations in θ around the particle edge. The (3° variation results in only a ( 2 mJ/m2 spread in W. The contribution of dispersion forces to W is estimated to be in the range 22-49 mJ/m2 using eq 2, with the spacing D assumed to be in the range 0.2-0.3 nm and the Hamaker constant calculated using eq 3. Thus, the nondispersion component is in the range 37-64 mJ/m2 and is a substantial component of the total work of adhesion of 86 mJ/m2. 6. Conclusions The major result of the research reported here is a demonstration of how the scanning force microscope can be used to determine the work of adhesion for particles with submicrometer dimensions. This is a valuable addition to SFM analysis since there are no other techniques capable of making contact angle measurements on nonconducting materials with submicrometer dimensions. The caboxylated styrene-butadiene latex particles that were studied do not spread isotropically on the calcite surface. Although the cause of the anisotropy is not understood at present, we can rule out a geometrical effect due to the underlying oblique surface lattice of the calcite. The contact angle anisotropy results in a variation of only a few percent in the interfacial work of adhesion as calculated from the Dupre´ equation. Finally, it must be emphasized that the numerical results reported are characteristic of the specific latexes studied and should not be extrapolated to latexes of different formulations. Acknowledgment. The industrial sponsors of the Paper Surface Science Program at University of Maine provided financial support for this research. Yiren Luo is thanked for acquiring the data and the Dow Chemical Corp. for providing the latex samples. I thank D. Woodland for assistance in preparation of the figures and P. Lepoutre, N. Triantifilopolous, and W. Istone for useful discussions. LA9708952
