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Dynamic Viscoelastic Properties of Liquid Polymer Films Studied by Atomic Force Microscopy Matthew C. Friedenberg† and C. Mathew Mate* IBM Almaden Research Center, San Jose, California 95120 Received April 8, 1996. In Final Form: September 13, 1996X Atomic force microscopy is used to investigate the dynamic viscoelastic response of a low-molecularweight polymer liquid, poly(dimethylsiloxane) (PDMS), constrained between a flat silicon wafer and a tip made from a glass sphere. Capillary forces dominate the response at low frequency, and viscous forces dominate at high frequency. The magnitude of the capillary interaction between the AFM tip and the polymer liquid is determined by the thickness of PDMS deposited onto the silicon wafer. The frequency spectrum can be effectively described by a simple mechanical model that assumes the polymer film responds as a Newtonian liquid. The model demonstrates that viscous forces can lead to a predominantly in-phase response due to the compliance of the AFM cantilever. Measurements of the viscous damping coefficient as a function of the separation between the tip and the substrate allow a quantitative determination of the viscosity of the polymer constrained between the two surfaces; this value for viscosity agrees well with the bulk viscosity for separations greater than about 25 nm. For smaller separations, the microroughness of the glass spheres used as tips prevents an accurate determination of the viscosity.
Introduction The use of thin polymer films to modify surface properties is important in many applications, including lubrication, biomaterials, sensors, and displays. Such films can be prepared by Langmuir-Blodgett deposition, self-assembly, adsorption, spin-coating, dip-coating, sputtering, etc. Although many techniques exist to characterize the material properties of such films, it can be difficult to obtain quantitative information about the viscoelastic properties using conventional techniques. These properties are particularly important for understanding friction, lubrication, and adhesion,1 where variation of temperature and sliding speed can have a dramatic effect on the response of the polymer due to the different time scales accessed. Of the available techniques to study viscoelasticity in ultrathin films constrained between two surfaces, the surfaces forces apparatus (SFA) has been used most extensively. This device measures the force between a pair of crossed mica cylinders separated by a liquid at a distance of as little as a few molecular diameters. The SFA has been used to measure the shear viscosity of a wide variety of thin polymer films. Horn and Israelachvili2 found that, for separations greater than 5 nm, the viscosity of a poly(dimethylsiloxane) (PDMS) film is equivalent to the bulk viscosity. When the separation of the mica surfaces is on the order of a few molecular diameters or less, confinement effects are frequently encountered, appearing as oscillations in force as molecular layers are squeezed out of the gap or as yield stresses, indicating a transition from liquid-like to solid-like behavior.3 The atomic force microscope (AFM)4 was introduced in 1986 to enable imaging of the surface topography of insulating materials with atomic resolution. On the basis of a desire to image with sensitivity to properties other than topography, many variations of atomic force mi† Present address: Gen-Probe Incorporated, 9880 Campus Pt. Drive, San Diego, CA 92121. X Abstract published in Advance ACS Abstracts, November 15, 1996.
(1) Moore, D. F. The Friction and Lubrication of Elastomers; Pergamon Press: New York, 1972. (2) Horn, R. G.; Israelachvili, J. Macromolecules 1988, 21, 2836. (3) Homola, A. M. In Surface Diagnostics in Tribology; Miyoshi, K., Chung, Y. W., Eds.; World Scientific: River Edge, NJ, 1993; p 271. (4) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930.
S0743-7463(96)00331-9 CCC: $12.00
croscopy have been developed: lateral-force microscopy, force-modulation microscopy, magnetic force microscopy, electric field microscopy, etc. One of these new microscopies, force-modulation microscopy forms images by mapping quantities related to the viscosity and elasticity of the sample.5-7 Typically, the sample (or the base of the tip) is modulated sinusoidally, and the resulting sinusoidal displacement of the tip is resolved into an in-phase and out-of-phase response or, alternatively, into an amplitude and phase-shift. Often, the in-phase or amplitude responses are interpreted as “elasticity”, and the out-ofphase or phase-shift responses are interpreted as “viscosity”. For example, Overney and Leta8 have generated an “elasticity map” of a lipid bilayer with molecular resolution by measuring the spatially-resolved amplitude response of the AFM tip during a two-dimensional scan of the film. Also, Akari and co-workers9 have imaged mixed self-assembled monolayers containing dodecanethiol and a thiol-terminated poly(styrene) on gold by measuring the amplitude of the tip response as the tip was rastered across the surface. Akari et al. claimed the ability to image single poly(styrene) molecules on the basis of their “elasticity” contrast with respect to dodecanethiol. Unfortunately, the contact geometry is not generally known for these systems, nor is the cantilever spring constant known to any precision. Furthermore, as we will show in this paper, the compliance of the AFM cantilever can lead to a viscous response that is largely in-phase, causing it to be confused with elasticity. This inability to readily interpret results in terms of a true viscosity and elasticity greatly reduces the usefulness of force-modulation microscopy as it is currently operated. Moreover, since these experiments are typically performed at a select frequency, only a single time scale of the material is investigated. Because the viscoelastic properties of polymers depend quite strongly on shear rate and (5) Radmacher, M.; Tillman, R. W.; Fritz, M.; Gaub, H. E. Science 1992, 257, 1900. (6) Kajiyama, T.; Tanaka, K.; Ohki, I.; Ge, S.-R.; Yoon, J.-S.; Takahara, A. Macromolecules 1994, 27, 7932. (7) Overney, R. M.; Bonner, T.; Meyer, E.; Ruetschi, M.; Luthi, R.; Howald, L.; Frommer, J.; Guntherodt, H.-J.; Fujihira, M.; Takano, H. J. Vac. Sci. Technol. B 1994, 12, 1973. (8) Overney, R. M.; Leta, D. P. Tribology Lett. 1995, 1, 247. (9) Akari, S. O.; van der Vegte, E. W.; Grim, P. C. M.; Belder, G. F.; Koutsos, V.; ten Brinke, G.; Hadziioannou, G. Appl. Phys. Lett. 1994, 65, 1915.
© 1996 American Chemical Society
Viscoelastic Properties of Liquid Polymer Films
oscillation frequency,10 one can gain additional insight into the dynamic properties of thin polymer films by studying their viscoelastic responses on a variety of time scales. Haugstad and co-workers11 have highlighted the importance of polymer dynamics in their studies of gelatin films using friction-force microscopy, where they relate the observed velocity dependence of the friction force to molecular relaxations in the gelatin film. In this paper, we use atomic force microscopy with force modulation to study the dynamic viscoelastic response of thin films of a low-molecular-weight polymer liquid, poly(dimethylsiloxane) (PDMS). Our objective is to demonstrate the ability of this technique to measure quantitatively the dynamic response of a simple Newtonian liquid. A 44 µm diameter glass sphere is used as an AFM tip to define a precise contact geometry for the tip-sample interaction. The frequency response is measured as a function of the separation between the tip and substrate for several thicknesses of PDMS films deposited on silicon wafers. The results are interpreted with a simple mechanical model that takes into account the viscous forces of the liquid between the tip and the substrate and the capillary forces of the liquid around the tip.
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Figure 1. (a, top) Schematic of the atomic force microscope (AFM) used in the present work. (b, bottom) Detailed view of the contact area for the tip-sample interaction.
Experimental Methods Materials. Poly(dimethylsiloxane), viscosity ) 350 cP, was obtained from Dow Corning (Midland, MI). Silicon (100) wafers (1in. diameter) were purchased from Virginia Semiconductor, Inc. (Fredericksburg, VA). Preparation of PDMS Films. The silicon wafers were subjected to a cleaning procedure prior to depositing the PDMS film: First, the wafers were rinsed with isopropyl alcohol (Baker), dried with filtered nitrogen, then rinsed in FC-72 fluorocarbon solvent (3M), and, finally, exposed to a UV-created ozone for 10 min. Following this treatment, the thickness of the native silicon oxide layer was 17.0 ( 0.5Å as measured by ellipsometry (Rudolph Research). PDMS was deposited by placing a drop of the polymer liquid on the wafer and then wiping the drop with a clean-room wiper to obtain a fairly uniform thickness of polymer. Three different samples were prepared with PDMS thicknesses of 35 ( 8, 82 ( 28, and 188 ( 28 nm as determined by ellipsometry. We also used atomic force microscopy to determine the thickness of deposited PDMS at the actual point of viscoelastic property measurement;12 the values so obtained were 32, 92, and 128 nm for the three samples. Atomic Force Microscope. Our AFM, described previously,12 is shown schematically in Figure 1. The cantilever is prepared from a 2 mm long, 50 µm diameter tungsten wire (California Fine Wire Company, Grover City, CA), bent to a right angle at the tip. A 44 µm diameter glass sphere (Duke Scientific, Mountain View, CA) is glued to the tip of the tungsten wire using a UV-cured epoxy (Loctite). The radius of curvature of the sphere is determined through optical microscopy. The cantilever-sphere assembly is rinsed in toluene and ethanol before use to ensure surface cleanliness. The spring constant of the cantilever is calculated to be 40 N/m from its measured resonance frequency, f0 ) 7.8 kHz. Force Modulation. An HP3325A function generator (Hewlett-Packard, Palo Alto, CA) is used to drive the PDMScoated substrate along the z-axis with a sinusoidal motion. The resulting tip deflection, measured interferometrically, is reduced in amplitude and shifted in phase with respect to the modulation of the substrate. The amplitude and phase of the tip response are obtained from the raw signal with an SR850 lock-in amplifier (Stanford Research Systems, Sunnyvale, CA) and measured as a function of modulation frequency and separation between the tip and substrate. The amplitude ratio is defined as the ratio of the amplitude of the tip response to that of the substrate (10) Ferry, J. D. Viscoelastic Properties of Polymers; John Wiley & Sons: New York, 1980. (11) Haugstad, G.; Gladfelter, W. L.; Weberg, E. B.; Weberg, R. T.; Jones, R. R. Tribology Lett. 1995, 1, 253. (12) Mate, C. M.; Lorenz, M. R.; Novotny, V. J. J. Chem. Phys. 1989, 90, 7550.
Figure 2. Mechanical model for the dynamic response of the AFM tip in a force-modulation experiment. oscillation. The DC force on the tip is measured separately. Frequency sweeps are performed between 1.8 and 1000 Hz with a modulation amplitude of 1 nm. All experiments are performed at ambient temperature (23 °C), pressure, and humidity.
Modeling We have developed a simple mechanical model to describe the dynamic response of our experimental system. In this model (Figure 2), the tip and substrate are coupled by three mechanical elements that represent the viscoelastic and meniscus forces that mediate the interaction. The motion of the tip is also influenced by the spring constant of the cantilever, kL. The viscoelastic properties of the polymer liquid are described by a Maxwell model, containing a series combination of a spring (elastic element) with spring constant kP and a dashpot (viscous element) with damping coefficient bP. As discussed by Mate and Novotny,13 the force of a liquid meniscus on a spherical tip can comprise several interactions, including the capillary pressure over the area where the meniscus contacts the tip and the surface tension around the annulus of the meniscus. If the effective capillary radius r is much smaller than the tip radius R and the liquid wets the tip surface as shown in Figure 1b, the force arising from capillary pressure is the dominant contribution to the meniscus force F:
(
F = -4πRγL 1 +
u 2r
)
(1)
where γL is the surface tension and u is related to the separation of tip and substrate: positive values of u correspond to the penetration depth of the tip in the polymer liquid, and negative values represent the tip distance above the liquid film surface. From this equation, it can be seen that the capillary force is linear with separation; therefore, it is represented in our model by a spring with spring constant -kM: (13) Mate, C. M.; Novotny, V. J. J. Chem. Phys. 1991, 94, 8420.
6140 Langmuir, Vol. 12, No. 25, 1996 -kM )
dF = -2πRγL/r du
Friedenberg and Mate (2)
Here, the spring constant is negative because the attractive force decreases with increasing separation. We make several simplifying assumptions: First, we assume that the polymer film behaves as a purely viscous liquid; i.e., the spring constant of the polymer, kP, is set to zero. In addition, we assume that the viscous damping coefficient bP is independent of frequency; i.e., the response is Newtonian. Finally, we assume that the meniscus spring constant kM is independent of both frequency and separation. With these assumptions, the model is reduced to two parameters: the meniscus spring constant kM and the viscous damping coefficient of the polymer bP. We can independently determine kM by measuring the response at low frequency and large separation, where viscous forces are negligible. Then, the model contains only a single adjustable parameter, bP, that is varied to fit the experimentally-determined amplitude ratio A and phase shift δ. Accordingly, we derive the following two equations:
A)
tan δ )
ωbp sin δ - kM cos δ kL - kM - mω2 ωbP(kL - mω2) 2
(ωbP) - kM(kL - kM - mω2)
(3)
(4)
where ω is the modulation frequency in rad/s and m is the effective mass of the cantilever:
m)
kL (2πf0)2
(5)
If the modulation frequency is much smaller than the resonance frequency of the cantilever, then kL - mω2 = kL. Then, neglecting capillary forces, eqs 3 and 4 reduce to
A)
ωbP sin δ kL
tan δ )
kL ωbP
(6)
(7)
Thus, for a purely viscous sample oscillating well below the cantilever resonance frequency, the tip response will be predominantly in-phase (δ = 0°) if kL , ωbP and predominantly out-of-phase (δ = 90°) if kL . ωbP. Since force modulation experiments are typically performed with weak cantilevers (approximately 0.05-0.5 N/m) and modulation frequencies on the order of 1-10 kHz,6,8,9 the viscous response will be primarily in-phase for all but the lowest viscosity samples. Consequently, one must exercise great caution when interpreting the in-phase and out-of-phase responses of force modulation microscopy as simply “elasticity” and “viscosity”.
Results and Discussion Viscosity Determination by AFM. We can take advantage of the observed dependence of the damping coefficient on separation to calculate the viscosity of the PDMS between the tip and substrate surfaces. It is wellknown from fluid mechanics that the motion of an oscillating sphere in a fluid becomes highly damped as it approaches a plane wall. Moore1 discusses this phenomenon in the context of the lubrication of elastomers and provides an equation for the damping coefficient, b, as a function of the separation between the sphere and wall, h:
b ) 6πηR2/h
(8)
where η is the viscosity of the fluid and R is the radius of curvature of the sphere. From this equation, it can be
Figure 3. AFM response of the 92 nm PDMS film as a function of separation at a modulation frequency of 10 Hz. (a, top) DC force as a function of separation. Smaller values of the force represent increasing attraction or decreasing repulsion. (b, bottom) Amplitude ratio (0) and phase shift (4) as a function of separation.
seen that a plot of 1/b versus h should be linear, with the slope proportional to 1/η. A similar analysis has previously been used in conjunction with the surface forces apparatus to measure the viscosity of thin liquid films14 and liquid bridges formed by capillary condensation.15 In Figure 3, we show the DC force on the tip, the amplitude ratio, and the phase shift as a function of the tip-substrate separation with an initial separation of approximately 60 nm. This experiment was performed at a modulation frequency of 10 Hz. Zero separation is arbitrarily defined as the point at which the DC force is a minimum, corresponding to the greatest attractive force. At positive separations the DC force becomes more attractive as the separation is reduced, while at negative separations the DC force becomes more repulsive (Figure 3a). In Figure 3b, the amplitude ratio and phase shift of the tip response are shown as a function of separation. As the separation is decreased from 60 nm, the phase initially undergoes a slow decrease and then rapidly drops to zero when hard-wall contact is reached at zero separation. The amplitude ratio increases slightly as the separation decreases and then rapidly jumps to unity at the hard wall. Figure 4 shows the reciprocal of the damping coefficient calculated from the amplitude ratio and phase (using eq 3) as a function of separation. We use a meniscus spring constant of -0.80 N/m for this calculation, determined independently from the tip response at low frequency and large separation. The plot is linear down to a separation near zero. Below this point, we observe that the reciprocal of the damping coefficient drops sharply to zero. We believe this decrease arises from hard-wall contact by asperities on the sphere (see below). From the slope of (14) Tonck, A.; Georges, J. M.; Loubet, J. L. J. Colloid Interface Sci. 1988, 126, 150. (15) Crassous, J.; Charlaix, E.; Gaywallet, H.; Loubet, J.-L. Langmuir 1993, 9, 1995.
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Figure 4. Reciprocal of the viscous damping coefficient bP as a function of separation for the 92 nm PDMS film. The dotted line represents an extrapolation of the linear portion of the curve to the x-axis.
Figure 6. Amplitude ratio (a, top) and phase shift (b, bottom) of the tip response as a function of modulation frequency for a 92 nm PDMS film at separations of 500 nm (4), 250 nm (0), and 50 nm(O). The three solid curves correspond to the predictions of the mechanical model (eqs 3 and 4) using the parameters discussed in the text.
Figure 5. Influence of modulation frequency and deposited film thickness on the measured viscosity of thin PDMS films. Each data point is calculated from measurements of the reciprocal damping coefficient as a function of separation. The three thicknesses are 128 nm (0), 92 nm (O), and 32 nm (4), and the initial separation is approximately 60 nm. The dashed line corresponds to the bulk value of 350 cP.
the line prior to hard-wall contact and our knowledge of the macroscopic radius of curvature of the sphere, we calculate a viscosity of 430 ( 40 cP, in reasonable agreement with the bulk value of 350 cP. In separate experiments, we also measure a viscosity near 430 cP for larger separations of 250 and 500 nm. Looking at the form of eq 8, one might expect a plot of 1/damping vs separation to go through the origin; yet in this case, the x-intercept is approximately -25 nm. We have found the value of the x-intercept to be consistent for all experiments with a given sphere but to vary greatly between spheres. We believe that the source of this deviation is the nanometer-scale roughness of the glass sphere. We have measured the surface topography of several glass spheres with a Nanoscope-3 AFM (Digital Instruments, Santa Barbara, CA) and found them to contain protrusions as tall as 75 nm with radii of curvature up to 200 nm. This microroughness prevents us from obtaining data at very small separations, limiting our ability to compare these results with SFA measurements, where the atomic smoothness of the mica surfaces allows the investigation of angstrom-scale separations. Using the procedure described in this section, we have investigated the effect of modulation frequency and deposited film thickness on the PDMS viscosity measured by AFM (Figure 5). We observe a slight decrease in viscosity (approximately 20%) as the modulation frequency increases from 10 to 500 Hz. Although the effect is too weak to say with confidence that it arises from shear thinning, we note that PDMS fluids with viscosities as low as 1000 cst have been found to undergo shear thinning
at high frequencies.16 In addition, the measured viscosity of the 32 nm PDMS film appears to be smaller than that of the two thicker films at all frequencies. We believe this effect to be an artifact that arises because the microscopic radius of curvature of the glass sphere, that wetted by the PDMS film, may not be identical to the macroscopic radius. As the area wetted by the film decreases, it becomes more likely that inhomogeneities on the glass surface will contribute to the hydrodynamic radius of curvature that is probed by this experiment. Since the viscosity depends on the square of the radius, the influence of such inhomogeneities can be significant. Frequency Response. In Figure 6, the amplitude ratio and phase shift of the tip response are shown for three different tip-substrate separations: 500, 250, and 50 nm. The solid curves in the figure correspond to the predictions of the Newtonian model described earlier (using eqs 3 and 4). At low frequencies and large separations, we find that the amplitude ratio (Figure 6a) decreases to a finite, nonzero value and the phase shift (Figure 6b) approaches 180°. We attribute this lowfrequency response to the change in capillary force with separation. This is an important difference between the present AFM work and prior studies using the surface forces apparatus (SFA). With the SFA, the capillary interaction is negligible compared to other forces, but with the smaller contact geometry of the AFM, the capillary forces dominate the low-frequency response for finite separations. As the frequency increases, the amplitude ratio increases to unity and the phase shift decreases to zero because of enhanced viscous coupling between the tip and the polymer liquid. This is exactly the behavior predicted by eqs 6 and 7 of our model. Even with our relatively stiff AFM cantilever and using a low-viscosity Newtonian liquid, the force-modulation response possesses a large in-phase response. For the modeling results, we have used a value of -0.80 N/m for the meniscus spring constant for all three separations and a viscous damping coefficient bP of 0.065, 0.015, and 0.0057 N‚s/m at separations of 50, 250, and 500 nm, respectively. These damping coefficients were selected to provide reasonable fits to both the amplitude (16) Johnson, G. C. J. Chem. Eng. Data 1961, 6, 275.
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Since kM describes the capillary interaction of the polymer liquid with the AFM tip, it can be used to calculate the effective capillary radius of the meniscus around the glass sphere, r. Using eq 2 and a surface tension of 19.7 × 10-3 N/m for PDMS at 23 °C,17 the effective capillary radius is determined to be 1.4 µm for the 32 nm film, 3.4 µm for the 92 nm film, and 7.7 µm for the 128 nm film. Furthermore, as discussed by Mate and Novotny,13 the capillary pressure P ) γL/r is in equilibrium with the pressure of the liquid film on the silicon substrate, i.e. the disjoining pressure Π, which represents the strength of the interaction between the polymer molecules and the surface. Thus, we obtain disjoining pressures of 14 kPa for the 32 nm film, 5.8 kPa for the 92 nm film, and 2.5 kPa for the 128 nm film. These low pressures indicate a weak attraction between the polymer and substrate for the film thicknesses investigated. Figure 7. Amplitude ratio (a, top) and phase shift (b, bottom) of the tip response as a function of modulation frequency for deposited PDMS thicknesses of 128 nm (4), 92 nm (0), and 32 nm (O). The tip is approximately 250 nm from hard-wall contact. The three solid curves correspond to the fits of the mechanical model using the parameters discussed in the text.
and phase response at a given separation. The mechanical model provides good agreement with the experimental data, predicting both the shape of the amplitude response and the more subtle features of the phase response. Moreover, the coefficient for the 50 nm separation, 0.065 N‚s/m, agrees well with the value calculated independently in Figure 4, approximately 0.056 N‚s/m. Effect of Film Thickness. Figure 7 shows the amplitude ratio and phase shift as a function of frequency at a tip-substrate separation of approximately 250 nm for the three samples with different thicknesses of PDMS. As the film thickness decreases, the amplitude ratio increases at low frequencies. The phase response also shows a strong thickness dependence at low frequencies. At high frequencies, the model predicts that the responses should be dominated by the PDMS viscosity and should therefore superpose for the three thicknesses, as they do in Figure 7. For the model predictions, we have used a damping coefficient bP of 0.015 N‚s/m for all three film thicknesses and a meniscus spring constant of -0.35, -0.80, and -2.0 N/m for the 128, 92, and 32 nm thicknesses of deposited PDMS, respectively. Slight deviations from the model at high frequency probably arise from discrepancies in the exact separation for these three samples due to drift. The dominant effect of decreasing the PDMS film thickness is therefore to increase the capillary interaction between the AFM tip and the polymer. Mate and Novotny13 reported a similar thickness dependence of capillary forces in force vs distance curves of perfluoropolyether films.
Summary We have determined the dynamic viscoelastic response of a low-molecular-weight poly(dimethylsiloxane) film constrained between a flat silicon wafer and a glass sphere using atomic force microscopy. Measurements of the viscous damping coefficient as a function of the separation between the AFM tip and the substrate allow a quantitative determination of the viscosity of the polymer film, which agrees well with the bulk value. The observed frequency response, obtained with sample modulation, is dominated by capillary forces at low frequencies and viscous forces at high frequencies. A decrease in film thickness leads to a marked change in the low-frequency response because of the resulting enhancement of capillary forces. The experimental data can be effectively modeled by accounting for the capillary interaction and by assuming that the polymer film responds as a Newtonian liquid. The model demonstrates that viscous forces can lead to a predominantly in-phase response because of the compliance of the AFM cantilever. Our current plans are to investigate materials with a more pronounced viscoelastic response. Acknowledgment. The authors would like to acknowledge Tony Logan for his assistance with AFM measurements of the topography of the glass spheres. The authors are also grateful to C. Singh Bhatia for his enthusiastic support of this project. This work was funded, in part, by the National Storage Industry Consortium (NSIC). LA960331I (17) Sperling, L. H. Introduction to Physical Polymer Science; John Wiley & Sons: New York, 1992.
