Langmuir 24(4)(2008)1476-1483 Forces between Polyethylene Surfaces in Oxyethylene Dodecyl Ether Solutions as Influenced by the Number of Oxyethylene Groups Jakub Nalaskowski*1, Jarosław Drelich2, Jan D. Miller1 1
Department of Metallurgical Engineering, University of Utah, 135 S 1460 E, Room 412, Salt Lake City, Utah 84112-0114, USA 2 Department of Materials Science and Engineering, Michigan Technological University, M&M Bldg 506, Houghton, MI 49931, USA Running Title: Forces between polyethylene surfaces Corresponding Author: Jakub Nalaskowski, Department of Metallurgical Engineering, University of Utah, 135 S 1460 E, Room 412, Salt Lake City, Utah 84112-0114, USA email:
[email protected], fax: (801)581-4937 Abstract The atomic force microscopy (AFM) colloidal probe technique was used to study the effect of oxyethylene dodecyl ethers, C12En (n=1-7), on interactions between hydrophobic polyethylene (PE) surfaces in aqueous solutions. Long-range (colloidal) and contact (pull-off) forces were measured between 10-20 µm PE spheres and a flat PE surface at concentrations of surfactant of 1×10-6 M and 1×10-4 M. Surface tension of the surfactant solutions and contact angles at PE surfaces were also studied. The influence of the number of oxyethylene groups in the surfactant molecule was examined. Initially longrange attractive (hydrophobic) forces between the PE surfaces were observed which decreased in range and magnitude with an increase in the number of oxyethylene groups in 1×10-4 M solutions. Above four oxyethylene groups per molecule, repulsive forces were observed. The measured pull-off force between PE surfaces decreased monotonically from approximately 500 mJ/m2 for C12E1 to 150 mJ/m2 for C12E7. The interfacial energy was calculated based on the JKR model, taking into account long-range forces operating outside the contact area. The interfacial energies decreased from 43-47 mJ/m2 for PE-water and PE-C12E1 (1×10-4 M) interfaces to ~18 mJ/m2 for PE-C12E7 (1×10-4 M). Interfacial energy was also calculated from measured contact angles and surface tensions using Neumann’s equation of state and Young’s equation. The relationship between interfacial energy and the number of oxyethylene groups, and the interfacial energy values were smaller, within 15-25 mJ/m2, to the relationship and interfacial energy values calculated from pull-off force measurements.
1
Keywords: adhesion, atomic force microscopy, colloidal forces, hydrophobic forces, interfacial energy, nonionic surfactant, oxyethylene dodecyl ethers, polyethylene
2
Introduction Nonionic surfactants from the group of oxyethylene alkyl ethers (CnEm) are widely used due to their unique interfacial activities. The adsorption of nonionic surfactants at the solid-liquid interface is a key to many important technical applications where wetting and interfacial forces play a decisive role, including emulsification and powder dispersion,1,2 detergency,3-5 mineral processing,6 and oil recovery.7 More recently, oxyethylene alkyl ethers have become important reagents in wastepaper deinking flotation, improving the dispersion of ink particles and foam stability.
8-10
In these
systems, surfactant molecules adsorb on hydrophobic surfaces, modifying their wetting characteristics and changing the interfacial forces between surfaces of particles, droplets and gas bubbles. Interfacial activity of oxyethylene alkyl ethers can be controlled by variation in the hydrocarbon and oxyethylene chain segments. The critical micelle concentration and phase behavior of these nonionic surfactants have been studied.11-14 Also significant effort was dedicated to study the surface behavior of oxyethylene alkyl ethers, including adsorption density and adsorption kinetic studies,15-19 influence on wetting, 20,21 and structure of adsorbed surfactant layers.22-24 Forces between hydrophobic surfaces in aqueous systems have received considerable attention during the past two decades.25-35 The atomic force microscopy (AFM) colloidal probe technique has been successfully used in the study of forces between particles and solid surfaces, particularly in systems closely related to mineral processing.28,32,36-39 Many important findings pertaining to the role of hydrophobic interactions, system stability, coagulation, and influence of surfactants have been reported. The colloidal probe technique has also been proven to be a valuable tool for quantification of adhesion
3
forces.40 Measurements of adhesion between colloidal probes and flat surfaces in both air 41-46
and aqueous solutions
47-50
have been reported in the literature. Systematic study of
the influence of oxyethylene alkyl ethers on these interactions has not been reported. The aim of this paper is to show how the number of oxyethylene groups of the surfactant molecule affects the hydrophobic interaction, pull-off force, and interfacial energy of the hydrophobic surface. In this study we examined the effect of a series of oxyethylene dodecyl ethers (C12En, where n = 1-7) on the long-range forces and adhesion between model hydrocarbon surfaces of low-molecular weight polyethylene (PE) in aqueous solutions using the AFM colloidal probe technique. These results are compared with wettability studies of PE surfaces in contact with C12En solutions. Interfacial energy was calculated from contact angle and surface tension measurements using Young’s equation,51 and compared with interfacial energy calculated from AFM adhesion measurement data using the JKR theory. 52
Materials and Methods Chemicals. Oxyethylene dodecyl ethers, CH3(CH2)11(OCH2CH2)nOH (n=1-7), also called surfactants in the next part of this communication, with a purity of >99% were purchased from Nikko Chemicals (Tokyo, Japan) and used without further purification. The surfactant solutions were prepared by using 1 mM solution of KCl (Alfa Aesar, AR grade) in deionized water (Milli-Q system, Millipore). The PE powder was a low-density polyethylene (Scientific Polymer Product, Inc.) with a molecular weight MW 1800 and melting point mp. 117 oC. Muscovite mica was purchased from Wards, Inc. Other reagents included: glycerol, ethylene glycol (certified ACS grade from Fisher Scientific),
4
nitrogen (reagent grade N2 -Mountain Airgas), and deionized water (18 MΩ·cm) obtained using a Milli-Q System (Millipore).
Polyethylene Surface Preparation. The flat PE substrate was prepared by melting low-density PE powder on a freshly cleaved surface of muscovite mica. After cooling, the PE sample was peeled from the mica surface and inspected to assure no mica remained on the PE surface. Mean surface roughness (RMS) of the PE sample was measured using contact mode AFM and was found to be 0.13 nm for a 0.25 µm2 surface area.
Contact Angle Measurement. The contact angles were measured using a G10 Krüss goniometer equipped with a CCD camera, and a computer with Drop Shape Analysis (DSA) software designed for calculating the value of contact angles from the shape of sessile drops using the Young-Laplace equation. The contact angle measurements in this study were done at room temperature (2022oC) using the sessile-drop technique53 as follows. In a rectangular glass chamber the PE sample was placed on stable supports. The chamber was partially filled with deionized water of pH 5.8 and covered with parafilm. A clean microsyringe filled with a surfactant solution and attached stainless steel needle was mounted to the goniometer stage. The needle was introduced through the parafilm cover and was located close to the PE surface. A drop of surfactant solution was produced at the tip of the needle using a microsyringe and placed on top of the PE substrate. The drop base was increased to a diameter of 7-9 mm to assure lack of drop size effect on contact angle.54 Because from 2
5
to 10 minutes was needed for the drop to reach a stable shape,55 the relaxed contact angles established after 10 minutes of drop equilibration at the PE substrate are reported in this paper. The detailed results on contact angle relaxation for drops of the oxyethylene dodecyl ethers solutions on PE and toner substrates are presented in another paper.55 In a separate experiment, a drop of diiodomethane or ethylene glycol was placed on the PE surface. The volume of the drop was increased to cause the drop base to advance until a drop base diameter of about 8 mm was reached. Then, the advancing contact angle was measured in 20-40 seconds.
Surface Tension Measurements. The surface tension measurements for surfactant solutions were performed at room temperature (20-22°C) using a pendant drop technique56 with the G10 Krüss instrument. The DSA program was used to calculate the surface tension from a contour of the pending drop based on the Young-Laplace equation. The drop was formed at the end of a 2 mm stainless steel needle in the transparent cell covered with a parafilm and partially filled with deionized water. The tip of the needle was made hydrophobic by rubbing it with the parafilm. Hydrophobic character of the needle tip is necessary to prevent the surfactant solution from climbing up the needle and to ensure a symmetrical shape for the pending drop. The formed drop equilibrated for 3060 seconds before its image was captured. At least 15 s was needed for the newly formed drop surface to saturate with surfactant molecules. The measurements were repeated three to five times for each solution and average values are reported.
6
Colloidal Probe Preparation. Spherical PE particles were obtained by suspending a PE powder in glycerol, heating the suspension above the melting point of the polymer, and then solidifying of the dispersed polymeric droplets at a reduced temperature.57 After appropriate filtration, washing and drying, this procedure was found not to change the surface properties of PE particles,57 which retained a high degree of hydrophobicity. These particles had a relatively smooth surface and were suitable for the AFM colloidal probes.57
Force Measurements. A Nanoscope IIIa (Digital instruments, Inc.) was used for force measurements. The freshly prepared PE substrate was mounted onto a stainless steel puck and placed under the fluid cell sealed by a silicone o-ring. An E-scanner with maximum Z-range of 5 µm was used. PE spherical particles with diameter from 10 µm to 20 µm were glued using 325 Speedbonder adhesive and 7075 Locquic activator (Loctite Corp.), on the tipless rectangular silicon cantilevers (Pointprobes NCL-16, Nanosensors, Germany) using a micromanipulator and CCD camera. With this procedure, particles of diameter from 1 µm to 200 µm can be precisely glued to the AFM cantilever. It has been established that there is no contamination of spherical particles with epoxy resin during gluing. Cantilevers were used for measurements after at least 24 hours of drying. An example of the cantilever with attached PE sphere is shown in Figure 1. After the surfactant solution was injected, the system was equilibrated for 10 minutes. For every concentration, at least 30 force measurements were taken at three different locations on the PE surface. After measurements, the system was washed with 1 mM KCl solution six times, and force measurements were repeated in 1 mM KCl solution. The 7
force curves were reproducible for the PE-KCl solution systems. Further the AFM measurements were reversible after washing the sample with water, indicating practically complete desorption of nonionic surfactant from the PE surface. The experiments were repeated for surfactant solutions in order of decreasing number of ethoxy groups, from C12E7 to C12E1. After measurements, the diameter of PE colloidal probe and dimensions of cantilever were measured with a scanning electron microscope (SEM) after sputtering them with ~10 nm film of gold. The spring constant of the cantilever (k) was calculated from the dimensions of the cantilever according to the formula:58 k=
Eh3 ( 2a + w ) 12 L3
(Eq. 1)
where a and w are the lengths of the parallel sides of the trapezoid, h is the height of the trapezoid, L is the length of the cantilever measured from the base to the center of glued particle, and E is Young’s modulus for the cantilever (1.5x1011 N/m2). The spring constant varied from about 30 to 40 (+10%) N/m. We are aware that this theoretical method used for determination of the cantilever’s spring constant may lead to an error in calculated force values. However, we also used Cleveland’s method61 in our laboratory and found no significant difference between spring constant values determined with both methods for several single-beam cantilevers. Zero separation between the probe and the substrate was determined from the slope of the linear compliance region of the curve representing the cantilever deflection versus expansion of the piezo. Due to the elasticity of PE, error in establishing the zero separation distance from the constant compliance region is likely to be present in the
8
range of up to a few nanometers. However, such deformations, even if they occurred, have a minor impact on the discussion presented in this communication. Recorded cantilever’s deflection curves were converted, and normalized with respect to radius of the PE sphere, to force by radius versus separation distance curves. Force curves were then averaged and presented for values of separation greater than the jump-tocontact distance. The adhesion force was obtained from measuring the deflection of the cantilever at the point where particle snaps off from the surface after contact, and averaged from at least 30 measurements. Maximum applied loads after contact were 5-10 µN and times of loading were 360-500 ms. These parameters were kept constant in all measurements in order to avoid variations in the adhesion force. The use of stiff cantilevers and high maximum loads were necessary to deform nano-asperities of polyethylene surfaces and to comply with the JKR contact mechanics model in the analysis of the adhesion forces.62-64 According to our analysis presented in Ref (63), the applied loads at a level of a few µN can initiate plastic deformations of asperities with a radius of curvature of up to ~200 nm on the PE surface. Such deformations are desirable in experiments with imperfect colloidal probes. In fact, our PE particles have nano-scaled surface irregularities as shown by an AFM image of one of the PE probes presented in Ref. (64). It should be added, however, that no significant trend in pull-off force for subsequent measurements was observed and no permanent deformation of the particle body was recorded for the loads used.
Contact Angle and Surface Tension Measurements and Discussion
9
Surface Energy of Polyethylene. An advancing contact angle measured for drops of diiodomethane on the PE substrate varied from 49 to 51 degrees. Because diiodomethane is an apolar liquid, the interaction of polyethylene with diiodomethane is due to Lifshitzvan der Waals interactions. In such systems Neumann’s equation of state65 (Eq. 2) can be used to estimate the surface energy of PE based on the measured advancing contact angle.66 Neumann’s equation of state is:65
cosθ = 2
γ SV − β (γ e γ LV
LV
−γ SV ) 2
−1
(Eq. 2)
where γSV is the solid surface energy, γLV is the liquid surface tension, θ is the advancing contact angle, and β is the constant, β=0.0001247 (m2/mJ)2. The γSV value for the PE substrate used in this study was determined to be 36.2 mJ/m2 and is comparable to the values reported in the literature (33.7-36.8 mJ/m2).66 We also measured the advancing contact angles for water and ethylene glycol and analyzed the surface energy of PE using the Lifshitz-van der Waals Lewis acid-base interaction model described in detail by van Oss.67 The value of γSV=35.0 mJ/m2 was obtained, in good agreement with the surface energy calculated from the Neumann’s equation of state. Therefore, the γSV =36.2 mJ/m2 value was used to calculate the interfacial energy between surfactant solutions and PE, presented in the next part of this communication.
Wetting of Polyethylene by C12En Solutions. The results from contact angle measurements showed that the hydrophobicity of PE is only slightly affected by 1×10-6 M solutions of oxyethylene dodecyl ethers (Figure 2). Also for 1×10-6 M solutions, no substantial effect of the ethylene oxide chain length on relaxed contact angles was
10
observed. An increase of oxyethylene dodecyl ether concentration to above 1×10-6 M caused the contact angle to decrease.55 As shown in Figure 2, the contact angles were substantially reduced for 1×10-4 M oxyethylene dodecyl ethers solutions as compared to 1×10-6 M solutions. The contact angle depended on the length of the ethylene oxide chain in the structure of oxyethylene dodecyl ether and decreased from 92+2 degrees to less than 20 degrees with increasing number of oxyethylene groups. In this communication, we only show the contact angle results for 1×10-6 M and 1×10-4 M solutions as these solutions were also used in the AFM studies of interfacial forces. According to the Young equation51 (Eq. 3), the contact angle changes can be affected by changes in surface tension of liquid (γLV), surface energy of solid (γSV) and/or solidliquid interfacial energy (γSL),
γ SV − γ SL = γ LV cosθ
(Eq. 3)
It is a well accepted fact that the surfactants do not migrate outside the surfactant solution drops placed on hydrophobic surfaces during contact angle measurements.68 As a result, the surface energy of PE was not affected by oxyethylene dodecyl ethers solutions in this study. In contrast, results from surface tension measurements shown in Figure 3 clearly indicate the adsorption of oxyethylene dodecyl ethers at the solution-air interface. Adsorption of surfactants also took place at the PE-solution interface as can be concluded from the adhesion tension (γLV⋅cosθ) data shown in Figure 4. Adhesion tension increased monotonically with increasing number of ethoxy groups in the surfactant structure. These changes do not follow the changes in surface tension of solutions shown in Figure 3, particularly for 10-4 M solutions. Additionally, if the contact angle changes could be affected by changes in the surface tension of liquid alone, the adhesion tension versus 11
surface tension should be a straight line, parallel to the x-axis.68 Such a straight line was not observed in this study (not shown).
Interfacial Energy from Contact Angle Data. The adsorption of oxyethylene dodecyl ethers at a hydrophobic surface, like PE, takes place mainly through the hydrocarbon chain segment of the surfactant. The adsorption of the hydrophobic surfactant chain segment to hydrophobic surface is certainly driven by the entropic effect associated with a reduction in the number of ordered structures of water molecules surrounding hydrophobic entities.69 The polar segment of the surfactant, composed of ethoxy groups, is oriented into the aqueous phase causing a reduction of interfacial tension between the aqueous solution of the surfactant and the polyethylene. The interfacial tension (γSL) between surfactant solutions and polyethylene was calculated based on Young’s equation (Eq. 3) and using 36.2 mJ/m2 as the value for the surface energy of PE. The results of these calculations for the 1×10-6 M and 1×10-4 M solutions are presented in Figure 5. The PE-solution interfacial energy remained essentially constant for 1×10-6 M solutions of C12En (n=1 to 7) and varied between about 33 to 37 mJ/m2. It decreased however, monotonically to less than 5 mJ/m2 with an increasing number of oxyethylene groups in the structure of the oxyethylene dodecyl ether for 1×10-4 M solutions (Figure 5). Because each ether used in this study has the same hydrophobic dodecyl chain segment, the effect shown in Figure 5 is strictly due to the polar (oxyethylene) segments. The data for the correlation between γSL and the number of oxyethylene groups (n=1-7) shown in Figure 5
12
were fit by the exponential trendline to obtain the following relationship between interfacial energy and number of oxyethylene groups:
γ SL = 33.0e −0.33n
for n=1 to 7
(Eq. 4)
Atomic Force Microscopy Measurements and Discussion Long-Range Surface Forces. AFM colloidal probe measurements between a PE sphere and a PE surface in oxyethylene dodecyl ether solutions revealed the existence of long-range, strong attractive forces as can be seen from Figure 6. These forces have been discussed in literature during the last two decades25-35 and have been referred to as longrange hydrophobic forces. Possible origins of these forces are discussed in a separate article.70 As can be seen from Figure 6, strongly attractive forces with an exceptional range, up to 100 nm, were observed for solutions of oxyethylene dodecyl ether with four and less oxyethylene groups in the molecule. For solutions of surfactant with more than four groups in the molecule, only repulsive forces were observed. These systems were characterized as having small contact angles, less than 25-30 degrees (Figure 2), and interfacial energy less than about 20 mJ/m2 (not shown). Although it has not been investigated during this work, it can be expected that the observed repulsive forces originate from charges present at the PE-solution interface. Overlap of force curves for solutions with C12En of n=5,6, and 7 support this speculation; no strong change in magnitude and range of the repulsive electrical double layer forces is expected for hydrophobic surfaces in solutions of pure nonionic surfactants. For example, it has been
13
shown that the zeta potentials of hydrophobic particles, such as coal, are almost insensitive to the concentration of oxyethylene dodecyl ethers.71 Despite extensive research in the field of long-range hydrophobic forces, accepted quantitative theory of these interactions does not exist and empirical equations are usually used to describe them.70 One of the most popular empirical equations is the double exponential function given in Eq. 5:73
H H F = C1 exp − + C2 exp − R D1 D2
(Eq. 5)
where F is the hydrophobic force, R is radius of curvature, C1, C2 are pre-exponential factors, H is separation distance, and D1, D2 are decay lengths. Figure 6 shows the experimental force versus distance curve recorded for 1×10-4 M C12E1-7 solutions, together with theoretical fits of the combined DLVO (electrical double layer and van der Waals) and hydrophobic forces using Eq. 6. H H 4π (0.035κ −1 sinh(ψ 0 / 51.4)) 2 F A = − + exp ( −κ H ) + C1 exp − + C2 exp − 2 εε 0κ R 6H D1 D2 (Eq.6) where A is Hamaker constant, ψ0 is surface potential, ε is dielectric constant of medium, ε0 is permittivity of vacuum, and κ is the Debye parameter. A Hamaker constant of 9.6×10-21 J and Debye parameter corresponding to the 1×10-3 KCl solution was used for the fit. A surface potential of -62 mV was used for the polyethylene, which seems to be acceptable magnitude in view of the literature results presented by Chibowski et al.72 C1 and D1 correspond to the long range component of hydrophobic force and were fitted for data above 25 nm, while C2 and D2 were fitted for the data below 25 nm and describe the short range component of hydrophobic force. Parameters for fitting of the
14
experimental data with Eq. 5 as a function of the number of ethoxy groups are given in Figure 7. As shown in Figure 6, experimental points fit the theoretical values over a wide range of distances for all systems. Adsorption of the oxyethylene dodecyl ether molecules with increasing number of oxyethylene groups at the surface caused a decrease in a hydrophobic character of the PE surface. It can be clearly seen that the magnitude of the long range component of the hydrophobic force (C1 parameter) decreases monotonically with an increase in the number of ethoxy groups in the surfactant molecule and reaches zero for 5 and more ethoxy groups (Figure 7). On the other hand, the decay length of the long range hydrophobic force component (D1 parameter) maintains a high and relatively constant value for the number of ethoxy groups below 5. While for 5 ethoxy groups only the short range hydrophobic interaction component is still observed (C2=-7.7 mN/m), there is no hydrophobic force component present for surfactants with more than 5 ethoxy groups in the molecule and the long-range forces measured for these surfactants can be fitted with the DLVO model. For these molecules, (E5-E7), a short range steric repulsion was also observed at separation distances of less than 5 nm. This short-range steric repulsion was not analyzed in detail during this study. As discussed earlier, adsorbed oxyethylene dodecyl ether reduced the interfacial energy of polyethylene. As a result, the hydrophobic attraction between PE surfaces decreased with an increasing number of oxyethylene groups and vanished for C12En with n>5. A similar dependence of long-range hydrophobic forces on the hydrophobic character of interacting surfaces, rendered hydrophobic by silanation, has been reported in the literature.28,33
15
Adhesion Forces and Interfacial Energy from AFM Studies. The results from measurements of the adhesion (pull-off) force (FA) between PE surfaces in the oxyethylene dodecyl ether solutions are shown in Figure 8. The surfactant at a concentration of 1×10-6 M had no significant effect on adhesion between PE surfaces. However, at a concentration of 1×10-4 M, a strong effect on adhesion was observed. An increase in the number of oxyethylene groups led to a significant reduction in the adhesion between PE surfaces from about 500 to 150 mJ/m2. Using one of the contact mechanics models, the adhesion forces measured can be used to calculate interfacial energy (γSL) between PE and surfactant solution. Two contact mechanics models derived by Johnson et al.52 and Derjaguin et al.,74 named JKR and DMT models, respectively, are frequently used by researchers to interpret the pull-off forces measured by the AFM technique. These analytical models have been reviewed in detail by many authors.40,75,76 In general, both JKR and DMT models apply to particlesubstrate systems which undergo elastic deformation during contact. The DMT model has been most successfully applied to systems with sub-microscopic particles of high Young’s modulus that interact with other surfaces through relatively weak surface forces. The JKR model is usually applied to micron-sized particles and larger, of low Young’s moduli and high surface energies. To decide on which model to use, either the Tabor number77 or the Maugis number75 must be calculated.64 For example, for the system under consideration, the Maugis number (λ) calculated according to Equation (7) is between 28 and 81.
16
λ=
2.06 3 RW 2 πK2 z0
(Eq.7)
where zo is the equilibrium separation distance between the probe and substrate (≈0.16 nm), R is the radius of the probe, W is the work of adhesion (from 20 to 70 mJ/m2, depending (K =
on
a
solution
used),
and
K
is
the
reduced
elastic
modulus
2E ≈ 0.25 GPa; E is the Young’s modulus and υ is the Poisson’s ratio). 3(1 −ν 2 )
Such a large Maugis number (λ>5) indicates that the JKR model should be used in the analysis of elastic deformations and pull-off forces for our PE-solution-PE system. According to the JKR model,52 the correlation between the normalized force of adhesion and the interfacial energy is given by the following equation: FA = 3πγ SL R
(Eq. 8)
Unfortunately, the JKR model was derived based on the assumption that the particlesurface interactions occur only in the area of contact and interactions outside the contact area were ignored. In the systems with a liquid, long-range forces including repulsive electrical double layer, attractive van der Waals, and attractive hydrophobic forces, operate between the AFM probe and substrate outside the adhesive contact area. If these long-range forces are comparable in the magnitude to the adhesion forces, they should not be neglected. For this reason, we subtracted the long-range forces operating outside the contact area ((F/R)outside) from the measured pull-off forces ((FA /R)AFM; Figure 8) before introducing the value of FA/R into Equation (8):
γ SL =
1 FA F − 3π R AFM R outside
(Eq. 9)
17
For simplicity, we calculated (F/R)outside value as a combination of all forces (van der Waals, electrical double layer, and hydrophobic forces) operating between PE particle and PE surface at a probe central displacement distance, δ (Figure 9). According to the JKR model, and considering our symmetrical PE-PE system, the central displacement δ at the moment of the particle pull off from the substrate surface is given by:
= δ
a 2 2 12π aγ SL − R 3 K
(Eq.10)
where: 3π R 2γ SL a= K 3
(Eq. 11)
and
1 3 1 −ν 2 = K 2 E
(Eq. 12)
υ is the Poisson’s ratio and E is the Young modulus for polyethylene. In our calculations, these parameters were set at υ=0.5 and E=0.5 MPa. Our crude, but simple, approach relies on a perfect sphere-flat geometry system with elastic particle, where the size of adhesive contact is negligible as compared to the diameter of the particle. Although this way we overestimate the F/Routside forces by a few percents, this error is comparable or smaller than the errors associated with experimental determination of forces at δ. More rigorous treatment of the system will be presented in a separate communication. It was found that the long-range hydrophobic forces contribute to adhesion at a level of up to 2-6%. And therefore, cannot be neglected in analysis of pull-off force. On the other hand, both van der Waals and electrostatic forces operating outside the contact area are of 18
negligible magnitude as compared to adhesion forces. Using Equation (9), γSL values were calculated and they are shown in Figure 10. The interfacial energy was practically constant for polyethylene surrounded by 10-6 M C12En solutions and equal to 45-52 mJ/m2. In 1×10-4 M surfactant solutions, the PE-liquid interfacial energy was influenced by the chemical structure of the surfactant molecules, and decreased monotonically from 47 mJ/m2 to 18 mJ/m2 for C12E7 as the number of oxyethylene groups increased from 1 to 7. It was also observed that interfacial energy values obtained from AFM measurements have a very similar trend but are higher (from 15 to 24 mJ/m2) than those calculated from contact angle measurements. The data from the correlation between the interfacial energy (γSL) and the number of oxyethylene groups (n=1-7) shown in Figure 10 were fit by an exponential function, and the relationship was found to be similar to the interfacial energy calculated from contact angle measurements (see Eq. 4):
γ SL = 51.9e −0.15 n
for n=1 to 7
(Eq. 10)
Summary and Conclusions Adsorption of the oxyethylene dodecyl ether (from C12E1 to C12E7) molecules from 1×10-4 M solutions has been found to change the wettability of a PE surface as shown from contact angle measurements. The contact angle depended on the length of the ethylene oxide chain in the structure of oxyethylene dodecyl ether and decreased from 92+2 degrees to less than 20 degrees with an increasing number of oxyethylene groups. The number of oxyethylene segments in the surfactant molecule also has a significant influence on long-range hydrophobic forces measured in 1×10-4 M solutions. The
19
experimental force curves were fit with an extended DLVO equation that includes a double exponential function describing hydrophobic forces. The magnitude of the long range component of the hydrophobic force was found to decrease monotonically from about -14 mN/m with an increase in number of ethoxy groups in the surfactant molecule, reaching zero for five and more ethoxy groups. The short range component of the hydrophobic force decreases from-30+20 mN/m to zero for ethers with six and seven ethoxy groups. The decay length of the long range hydrophobic force component maintains a high and relatively constant value of +35+5 nm for the number of ethoxy groups below 5, but drops to zero in C12E5-7 solutions. We also report the effect of the number of oxyethylene segments in the surfactant molecule on adhesion forces between PE surfaces. In 1×10-4 M solutions, the adhesion decreased from about 500 to 150 mJ/m2 with an increase in the number of oxyethylene group from 1 to 7. The interfacial energy was calculated from adhesion data using the JKR model, taking into account long-range forces operating outside the contact area. The interfacial energies decreased from 43-47 mJ/m2 for PE-water and PE-C12E1 (1×10-4 M) interfaces to ~18 mJ/m2 for PE-C12E7 (1×10-4 M). The interfacial energy values calculated from measured contact angles and surface tensions using both the Neumann’s equation of state and the Young’s equation were smaller, within 15-25 mJ/m2, to those calculated from adhesion force measurements.
Acknowledgment Financial support provided by the Department of Energy, Basic Science Division (Grant No. DE-FG-03-93ER14315) and from the U.S. National Science Foundation
20
(Grant No. CTS-9618582) is gratefully acknowledged. Although the research described in this article has been funded partially by these agencies, it has not been subjected to the agencies’ required peer and policy review and therefore does not necessarily reflect the views of these agencies and no official endorsement should be inferred.
References (1)
Rosen, M. J. Surfactants and Interfacial Phenomena, Wiley, New York, 1978.
(2)
Schick, M. J.; (Ed.) Surfactant Science Series, Vol. 23: Nonionic Surfactants: Physical Chemistry, Marcel Dekker, New York, 1987.
(3)
Schick, M. J. Surfactant Science Series 1987, 23, 753-833.
(4)
Schwuger, M. J. J. Am. Oil Chem. Soc. 1982, 59, 258-264.
(5)
Schwuger, M. J. J. Am. Oil Chem. Soc. 1982, 59, 265-272.
(6)
Leja, J. Surface Chemistry of Froth Flotation; Plenum Press: New York, 1982.
(7)
Fayers, F. J.; (Ed.) Developments in Petroleum Science, Vol. 13: Enhanced Oil Recovery [Proceedings of the 3rd European Symposium on Enhanced Oil Recovery Held in Bournemouth, U.K., September 21-23, 1981], 1981.
(8)
Azevedo, M. A. D.; Miller, J. D.; Borchardt, J. K.; Nalaskowski, J.; Drelich, J. TAPPI Pulping/Process and Product Quality Conference, Boston, MA, United States, Nov. 5-8, 2000, 750-761.
(9)
Borchardt, J. K.; Miller, J. D.; Azevedo, M. A. D. Curr. Opin. Colloid Interface Sci. 1998, 3, 360-367.
(10)
Pletka, J.; Gosiewska, A.; Chee, K. Y.; McGuire, J. P.; Drelich, J.; Groleau, L. Prog. Paper Recycl. 2000, 9, 40-48.
21
(11)
Meguro, K.; Takasawa, Y.; Kawahashi, N.; Tabata, Y.; Ueno, M. J. Colloid Interface Sci. 1981, 83, 50-56.
(12)
Huibers, P. D. T.; Lobanov, V. S.; Katritzky, A. R.; Shah, D. O.; Karelson, M. Langmuir 1996, 12, 1451-1459.
(13)
Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. 1: Phys. Chem. Cond. Phas. 1983, 79, 975-1000.
(14)
Lang, J. C.; Morgan, R. D. J. Chem. Phys. 1980, 73, 5849-5861.
(15)
Corkill, J. M.; Goodman, J. F.; Tate, J. R. Trans. Faraday Soc. 1966, 62, 979-986.
(16)
Ottewill, R. H.; Walker, T. Kolloid Zeitsch. Zeitsch Polym. 1968, 227, 108-116.
(17)
Partyka, S.; Zaini, S.; Lindheimer, M.; Brun, B. Colloids Surf. 1984, 12, 255-270.
(18)
Brinck, J.; Joensson, B.; Tiberg, F. Langmuir 1998, 14, 5863-5876.
(19)
Brinck, J.; Joensson, B.; Tiberg, F. Langmuir 1998, 14, 1058-1071.
(20)
Scales, P. J.; Grieser, F.; Furlong, D. N.; Healy, T. W. Colloids Surf. 1986, 21, 55-68.
(21)
Chander, S.; Mohal, B. R.; Aplan, F. F. Colloids Surf. 1987, 26, 205-216.
(22)
Patrick, H. N.; Warr, G. G.; Manne, S.; Aksay, I. A. Langmuir 1997, 13, 43494356.
(23)
Patrick, H. N.; Warr, G. G. Colloids Surf., A 2000, 162, 149-157.
(24)
Dong, J. P.; Mao, G. Z. Langmuir 2000, 16, 6641-6647.
(25)
Israelachvili, J. N.; Pashley, R. M. J. Colloid Interface Sci. 1984, 98, 500-514.
(26)
Herder, P. C. J. Colloid Interface Sci. 1990, 134, 336-345.
(27)
Rabinovich, Y. I.; Guzonas, D. A.; Yoon, R. H. Langmuir 1993, 9, 1168-1170.
(28)
Rabinovich, Y. I.; Yoon, R. H. Langmuir 1994, 10, 1903-1909.
22
(29)
Churaev, N. V. Colloid J. (Transl. of Kolloidn. Zh.) 1995, 57, 233-235.
(30)
Forsman, J.; Joensson, B.; Woodward, C. E. J. Phys. Chem. 1996, 100, 1500515010.
(31)
Yoon, R.-H.; Ravishankar, S. A. J. Colloid Interface Sci. 1996, 179, 403-411.
(32)
Yoon, R.-H.; Flinn, D. H.; Rabinovich, Y. I. J. Colloid Interface Sci. 1997, 185, 363-370.
(33)
Nalaskowski, J.; Veeramasuneni, S.; Hupka, J.; Miller, J. D. J. Adhes. Sci. Technol. 1999, 13, 1519-1533.
(34)
Nguyen, A. V.; Nalaskowski, J.; Miller, J. D.; Butt, H.-J. Inter. J. Miner. Process. 2003, 72, 215-225.
(35)
Yaminsky, V.; Ohnishi, S.; Ninham, B. in Handbook of Surfaces and Interfaces of Materials, Nalwa, H.S. (Ed.), Academic Press, San Diego 2001, vol. 4, 131-227.
(36)
Pazhianur, R.; Yoon, R. H. Processing of Complex Ores: Mineral Processing and the Environment, Proceedings of the UBC-McGill Bi-Annual International Symposium on Fundamentals of Mineral Processing, 2nd, Sudbury, Ont., Aug. 1719, 1997 1997, 247-256.
(37)
Yoon, R.-H.; Pazhianur, R. Colloids Surf., A 1998, 144, 59-69.
(38)
Toikka, G.; Hayes, R. A.; Ralston, J. Colloids Surf., A 1998, 141, 3-8.
(39)
Biggs, S.; Proud, A. D. Langmuir 1997, 13, 7202-7210.
(40)
Drelich, J.; Mittal, K.L. (Eds), Atomic Force Microscopy in Adhesion Studies, VSP, Leiden – Boston 2005.
(41)
Schaefer, D. M.; Gomez, J. J. Adhes. 2000, 74, 341-359.
23
(42)
Heim, L.-O.; Blum, J.; Preuss, M.; Butt, H.-J. Phys. Rev. Lett. 1999, 83, 33283331.
(43)
Fuji, M.; Machida, K.; Takei, T.; Watanabe, T.; Chikazawa, M. J. Phys. Chem. B 1998, 102, 8782-8787.
(44)
Segeren, L. H. G. J.; Siebum, B.; Karssenberg, F. G.; Van Den Berg, J. W. A.; Vancso, G. J. J. Adhes. Sci. Technol. 2002, 16, 793-828.
(45)
Beach, E.R..; Tormoen, G.W.; Drelich, J. J. Adhes. Sci. Technol. 2002, 16, 845868.
(46)
Beach, E.R.; Tormoen, G.W.; Drelich, J. J. Colloid Interface Sci. 2002, 247, 8499.
(47)
Freitas, A. M.; Sharma, M. M. J. Colloid Interface Sci. 2001, 233, 73-82.
(48)
Toikka, G.; Hayes, R. A.; Ralston, J. J. Colloid Interface Sci. 1996, 180, 329-338.
(49)
Bowen, W. R.; Hilal, N.; Lovitt, R. W.; Wright, C. J. Colloids Surf., A 1999, 157, 117-125.
(50)
Vakarelski, I. U.; Ishimura, K.; Higashitani, K. J. Colloid Interface Sci. 2000, 227, 111-118.
(51)
Young, T. Phil. Trans. 1805, 95, 65-87.
(52)
Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. Roy. Soc., Ser. A 1971, 324, 301-313.
(53)
Drelich, J.; Miller, J.D.; Good, R.J. J. Colloid Interface Sci. 1996, 179, 37-50.
(54)
Drelich, J. J. Adhesion 1997, 63, 31-51.
24
(55)
Drelich, J.; Zahn, R.; Miller, J., D.; Borchardt, J. K. in Contact Angle, Wettability and Adhesion; Mittal, K. L. (Ed.), VSP: Utrecht, Boston, 2002; Vol. 2, pp 253264.
(56)
Drelich, J.; Fang, Ch.; White, C.L. in Encyclopedia of Surface and Colloid Science, Hubbart, A.T. (Ed.), Marcel Dekker, Inc., New York 2002, pp. 31523166.
(57)
Nalaskowski, J.; Drelich, J.; Hupka, J.; Miller, J. D. J. Adhes. Sci. Technol. 1999, 13, 1-17.
(58)
Equation (1) was misprinted in Ref.(59), without factor 2 in front of a, and this error was also pasted into Ref. (60). The results in both of these references, however, are those calculated based on the correct equation presented in this paper.
(59)
Drelich, J.; Nalaskowski, J.; Gosiewska, A.; Beach, E.; Miller, J. D. J. Adhes. Sci. Technol. 2000, 14, 1829-1843.
(60)
Nalaskowski, J.; Drelich, J.; Hupka, J.; Miller, J.D. Langmuir 2003, 19, 53115317.
(61)
Cleveland, J. P.; Manne, S.; Bocek, D.; Hansma, P. K. Rev. Sci. Instrum. 1993, 64, 403-405.
(62)
Biggs, S.; Spinks, G. J. Adhes. Sci. Technol. 1998, 12, 461-478.
(63)
Tormoen, G.W.; Drelich, J. J. Adhes. Sci. Technol. 2005, 19, 181-198.
(64)
Drelich, J.; Tormoen, G.W.; Beach, E.R. J. Colloid Interface Sci. 2004, 280, 484497.
(65)
Li, D.; Neumann, A. W. J. ColloidInterface Sci. 1992, 148, 190-200.
25
(66)
Drelich, J.; Miller, J. D. J. Colloid Interface Sci. 1994, 167, 217-220.
(67)
van Oss, C.J. Interfacial Forces in Aqueous Media, Marcel Dekker, Inc., New York 1994.
(68)
Bargeman, D.; Van Voorst Vader, F. J. Colloid Interface Sci. 1973, 42, 467-472.
(69)
Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1992.
(70)
Nguyen, A.V.; Drelich, J.; Colic, M.; Nalaskowski, J.; Miller, J.D. in Encyclopedia of Surface and Colloid Science, 2nd ed., P. Somasundaran (Ed.), Taylor & Francis, London 2007, 1:1, 1-29 (DOI:10.1081/E-ESCS-120022194).
(71)
Nalaskowski, J. PhD Dissertation, Faculty of Chemistry; Gdansk University of Technology: Gdansk, 1999, p 218.
(72)
Chibowski, E.; Wiacek, A.E.; Holysz, L.; Terpilowski, K. Langmuir 2005, 21, 4347-4355.
(73)
Pashley, R. M.; McGuiggan, P. M.; Ninham, B. W.; Evans, D. F. Science 1985, 229, 1088-1089.
(74)
Derjaguin, B.V.; Muller, V.M.; Toporov, Y.P., J. Colloid Interface Sci. 1975, 53, 314-326.
(75)
Maugis, D., Contact, Adhesion and Rupture of Elastic Solids, Springer, Berlin 2000.
(76)
Maugis, D. J. Colloid Interface Sci. 1992, 150, 243-269.
(77)
Tabor, D. J. Colloid Interface Sci. 1977, 58, 2-13.
26
Figure 1. Scanning electron micrograph of 18 µm PE sphere at the end of AFM cantilever (2000× mag.).
27
100 90
Contact Angle [deg]
80 70 60 50 40 30 20 10
1E-6 M 1E-4 M
0 KCl
1
2
3
4
5
6
7
Number of Ethoxy Groups
Figure 2. Contact angles for KCl and C12En solutions at the PE surface.
28
80
Surface Tension [mN/m]
70
60
50
40
30 1E-6 M 1E-4 M 20 KCl
1
2
3
4
5
6
7
Number of Ethoxy Groups
Figure 3. Surface tension of KCl and C12En solutions.
29
40 1E-6 M
Adhesion Tension [mN/m]
1E-4 M 30
20
10
0 KCl
1
2
3
4
5
6
7
Number of Ethoxy Groups
Figure 4. Adhesion tension of KCl and C12En solutions at the PE surface.
30
Interfacial Energy [mJ/m2]
40
30
20
10 1E-6 M 1E-4 M 0 KCl
1
2
3
4
5
6
7
Number of Ethoxy Groups
Figure 5. Interfacial energy between KCl and C12En solutions and the PE surface calculated using Young’s equation and contact angle values.
31
5
0
F/R [mN/m]
-5
-10 Number of Ethoxy Groups 1 2 3 4 5 6 7
-15
-20
-25 0
10
20
30
40
50
60
70
80
Separation Distance [nm] Figure 6. Interaction forces between PE surfaces in 1×10-4 M C12En solutions. Every third experimental point is shown for clarity. Continuous lines are extended DLVO fits.
32
Double Exponential Function Parameters [C-mN/m, D- nm]
40
20
0
C1 D1 C2 D2
-20
-40
-60 KCl
1
2
3
4
5
6
7
Number of Ethoxy Groups
Figure 7. Pre-exponential (C), and decay length (D) parameters of double exponential function (Eq. 5) for interaction forces between PE surfaces in 1×10-4 M C12En solutions (n is the number of ethoxy groups).
33
600 550 500
FA/R [mN/m]
450 400 350 300 250 200 150
1E-6 M 1E-4 M
100 KCl
1
2
3
4
5
6
7
Number of Ethoxy Groups
Figure 8. Normalized adhesion force between PE surfaces in KCl and C12En solutions.
34
pull off force
R
δ
outside contact area interactions
aS Figure 9. Shape of an elastic adhering particle before its spontaneous separation from a substrate.
35
60 55
Interfacial Energy [mJ/m2]
50 45 40 35 30 25 20 15 10 5
1E-6 M AFM 1E-4 M AFM 1E-6 M CA 1E-4 M CA
0 KCl
1
2
3
4
5
6
7
Number of Ethoxy Groups
Figure 10. Interfacial energy between KCl and C12En solutions and a PE surface calculated using Eq. 9 and force of adhesion values. For comparison, the interfacial energy calculated from contact angle data are also included.
36
