Styrene-co-butadiene Rubber Blends by

Tapping mode atomic force microscopy (TMAFM) measurements were performed ... elastomers, cis-1,4-butadiene rubber (BR) and styrene-co-butadiene rubber...
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Langmuir 2000, 16, 5702-5711

Examination of Butadiene/Styrene-co-butadiene Rubber Blends by Tapping Mode Atomic Force Microscopy. Importance of the Indentation Depth and Reduced Tip-Sample Energy Dissipation in Tapping Mode Atomic Force Microscopy Study of Elastomers G. Bar,* M. Ganter, R. Brandsch, and L. Delineau Freiburger Materialforschungszentrum and Institut fu¨ r Makromolekulare Chemie, Albert-Ludwigs Universita¨ t, Stefan Meier-Strasse 21, 79104 Freiburg, Germany

M.-H. Whangbo* Department of Chemistry, North Carolina State University, Raleigh, North Carolina, 27695-8204 Received October 18, 1999. In Final Form: April 3, 2000

Tapping mode atomic force microscopy (TMAFM) measurements were performed for blends of two elastomers, cis-1,4-butadiene rubber (BR) and styrene-co-butadiene rubber (SBR) containing silica filler particles. To help interpret the TMAFM phase and height images of the BR/SBR blends, transmission electron microscopy (TEM) measurements were carried out for the BR/SBR blends, and dynamic mechanical analysis (DMA) as well as frequency-sweep/force-probe TMAFM measurements were carried out for BR and SBR homopolymers. TEM images show that silica filler particles of BR/SBR blends are present mainly in the SBR component, and DMA results reveal that BR has a lower glass transition temperature than does SBR. In the phase images of BR/SBR blends the less stiff component BR is brighter than is the stiffer component SBR. For the rational interpretation of TMAFM phase images of viscoelastic materials, it is crucial to consider the indentation depth of the tip into samples as well as the reduced tip-sample energy dissipation, not the total tip-sample energy dissipation. At a given set-point ratio the indentation depth is smaller on the stiffer component SBR than on the less stiff component BR, but at a given indentation depth the phase shift is larger on the stiffer component SBR. The phase shift increases almost linearly with increasing the reduced tip-sample energy dissipation. The reduced tip-sample sample energy dissipation is larger for SBR than for BR in agreement with DMA results.

1. Introduction In recent years the morphology and nanostructures of polymers have been extensively studied1 by tapping mode atomic force microscopy (TMAFM).2 Phase imaging3 of TMAFM is very sensitive to local materials properties and provides enhanced image contrasts. However, there are still a number of unanswered questions concerning how to interpret phase and amplitude images, mainly because the tip-sample force is a nonlinear function of the tip-sample distance.4-8 The height and phase images of TMAFM depend sensitively on experimental parameters such as the free amplitude A0, the set-point ampli(1) For some recent reviews, see: (a) Kiselyova, O. I.; Yaminsky, I. V. Colloid J. 1999, 61, 1. (b) Jandt, K. D. Mater. Sci., Eng. 1998, 21, 221. (c) Magonov, S. N.; Reneker, D. H. Annu. Rev. Mater. Sci. 1997, 27, 175. (d) Tsukruk, V. V. Rubber Chem. Technol. 1997, 70, 430. (2) Zhong, Q.; Innis, D.; Kjoller, K.; Elings, V. B. Surf. Sci. Lett. 1993, 290, L688. (3) Chernoff, D. A. Proceedings Microscopy and Microanalysis; Jones and Begell: New York, 1995. (4) Kru¨gger, D.; Anczykowski, B.; Fuchs, H. Ann. Phys. 1997, 6, 341. (5) Anczkowski, B.; Kru¨gger, D.; Babcock, K. L.; Fuchs, H. Ultramicroscoy 1996, 66, 251. (6) Anczkowski, B.; Kru¨gger, D.; Babcock, K. L.; Fuchs, H. Phys. Rev. B 1996, 53, 15485. (7) Burnham, N. A.; Behrend, O. P.; Oulevey, F.; Gremaud, G.; Gallo, P.-J.; Gourdon, D.; Dupas, E.; Kulik, A. J.; Pollock, H. M.; Briggs, G. A. D. Nanotechnology 1997, 8, 67. (8) Chen, J.; Workman, R. K.; Sarid, D.; Ho¨rper, R. Nanotechnology 1994, 5, 199.

tude Asp, the tip shape, the cantilever force constant, etc. This leads to difficulties in interpreting image contrasts of heterogeneous polymer samples. It is a crucial issue of TMAFM studies how to relate contrasts of height and phase images to tip-sample interactions and eventually to the physical properties of samples under examination. The vibrational characteristics of a cantilever tapping on a compliant sample such as poly(dimethylsiloxane) (PDMS) are quite different from those on a stiff sample such as Si.9,10 A cantilever tapping on a compliant sample behaves like a simple harmonic oscillator and is well described by the harmonic approximation.9,11-14 On a stiff sample, a tapping cantilever exhibits a bistable behavior.5,6,10,15,16 According to our recent TMAFM study of PDMS samples of different cross-link density,17 the tip (9) Whangbo, M.-H.; Brandsch, R.; Bar, G. Surf. Sci. Lett. 1998, 411, L794. (10) Bar, G.; Brandsch, R.; Whangbo, M.-H. Surf. Sci. Lett. 1998, 411, L802. (11) Bar, G.; Brandsch, R.; Whangbo, M.-H. Langmuir 1998, 14, 7343. (12) Bar, G.; Brandsch, R.; Bruch, M.; Delineau, L.; Whangbo, M.-H. Surf. Sci. Lett. 2000, 444, L11. (13) Magonov, S. N.; Elings, V.; Whangbo, M.-H. Surf. Sci. Lett. 1997, 375, L385. (14) Winkler, R. G.; Spatz, J. P.; Sheiko, S.; Mo¨ller, M.; Reineker, P.; Marti, O. Phys. Rev. B 1996, 54, 8908. (15) Marth, M.; Maier, D.; Honerkamp, J.; Brandsch, R.; Bar, G. J. Appl. Phys. 1999, 85, 7030. (16) Bar, G.; Brandsch R.; Whangbo, M.-H. Surf. Sci. Lett. 1999, 422, L192.

10.1021/la9913699 CCC: $19.00 © 2000 American Chemical Society Published on Web 05/20/2000

Examination of Elastomer Blends

deeply penetrates into the compliant samples, and a more compliant sample leads to a larger indentation such that at a given set-point ratio the indentation force is nearly constant on samples of different elastic moduli, in agreement with the prediction18 that phase contrast acquired at constant set-point amplitude should not depend on the sample’s modulus. However, PDMS samples of different cross-link density are distinguished when the amplitude and phase curves are examined in terms of the indentation depth.17 Simulations19 performed by numerically solving the equation of motion are in support of the observations that bistability may or may not occur depending on the nature of tip and sample employed and that indentation is an important factor for understanding phase images of compliant samples. Elastomer blends containing fillers are one class of composite materials playing an important role in rubber industry and technology. Blending is undertaken to improve the technical properties of the components, achieve a better processing behavior, or simply to reduce costs. Fillers such as carbon black or silica are often added to the blends to improve the mechanical properties of the compound.20 It is crucial to investigate the morphological and structural aspects of such blends, which is usually carried out using such microscopy techniques as optical microscopy and transmission electron microscopy (TEM). In the present work we carry out TMAFM studies on butadiene/styrene-co-butadiene (BR/SBR) rubber blends modified with silica fillers. Thus given samples of BR/ SBR blends, it is important to ask whether the BR and SBR components can be distinguished and identified by TMAFM height/phase images and, if so, what causes the contrast difference between the two components. To probe this question, we carried out TMAFM studies on BR/SBR rubber blends containing silica filler particles. To help analyze the height and phase images of BR/SBR blends, we performed TEM measurements of BR/SBR blends and also carried out frequency-sweep/force-probe measurements and dynamic mechanical analysis (DMA) on BR and SBR homopolymers. Our work demonstrates that for the rational interpretation of the observed image contrasts, it is necessary to perform such systematic measurements and consider the indentation depths. 2. Experimental Section cis-1,4-Butadiene rubber (BR) and styrene-co-butadiene rubber (SBR) were obtained from Bayer AG (CB 24 and Krylene 1500 trademarks, respectively). The styrene content in SBR was 15 mol %, i.e., 25 wt %. The 1:1 BR/SBR blends were prepared by mechanical mixing and contained 10 phr silica filler. The blend samples were annealed at 120 °C for 2 days to promote phase separation. TMAFM experiments were performed using a Nanoscope III scanning probe microscope. All TMAFM measurements were conducted on cryogenically cut surfaces in order to study the bulk morphology. We used three different types of commercial Si cantilevers. The resonance frequencies ω0 and corresponding cantilever spring constants, k0, of these cantilevers were ω0 ) 2π × 70 kHz and k0 ) 1 N/m, ω0 ) 2π × 160 kHz and k0 ) 30 N/m, and ω0 ) 2π × 330 kHz and k0 ) 40 N/m. All TMAFM experiments were carried out by driving the cantilever at its resonance frequency. The height and phase images presented were recorded simultaneously using the free amplitude A0 ) 60 nm and the set-point ratios, rsp ) Asp/A0, ranging from 1.0 to 0.2. (17) Bar, G.; Delineau, L.; Brandsch, R.; Bruch, M.; Whangbo, M. H. Appl. Phys. Lett. 1999, 75, 4198. (18) Tamayo, J.; Garcia, R. Appl. Phys. Lett. 1997, 71, 2394. (19) Behrend, O. P.; Odoni, L.; Loubet, J. L.; Burnham, N. A. Appl. Phys. Lett. 1999, 75, 2551. (20) Maiti, S.; De, S. K.; Bhowmick, A. K. Rubber Chem. Technol. 1992, 65, 293.

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Figure 1. TEM image of a BR/SBR blend with silica fillers. The sample was stained with RuO4. The horizontal bar corresponds to 1 µm. Both force-probe and frequency-sweep measurements were carried out with A0 ≈ 30, 50, and 60 nm. In the force-probe method, the lateral position of the tip is fixed, and the amplitude and phase angle of a tapping cantilever are measured as a function of the tip-sample distance z. Force-probe measurements lead to amplitude vs distance and phase vs distance curves, hereafter referred to as A(z) and Φ(z) curves. In the frequency-sweep method, the lateral position of the tip is fixed, and the amplitude and phase angle of a tapping cantilever are measured as a function of the driving frequency ω at a certain tip-sample distance z. The latter is fixed by first engaging the cantilever to the surface with a certain Asp value and then turning off the feedback control during the frequency sweep. Frequency-sweep measurements lead to amplitude vs frequency and phase vs frequency curves, hereafter referred to as A(ω) and Φ(ω) curves. Young’s storage (E′) and loss moduli (E′′) of the vulcanized polymers were determined by dynamic mechanical analysis (DMA) experiments using a Rheometrics Solids Analyzer (RSA) II in a film geometry (1.5 × 6 × 22 mm3) with strains of 0.0010.050 at a frequency of 1 Hz and at a cooling rate of 2 K/min. The shear storage (G′) and loss moduli (G′′) of the unvulcanized polymers were measured using a Rheometrics Mechanical Spectrometer (RMS) in a plate-plate geometry (1.5 mm thickness, 25 mm diameter) with strains of 0.005-0.050 at a frequency of 0.5 Hz and at a cooling rate of 2 K/min. For (TEM) measurements ultrathin sections of a BR/SBR blend were obtained using an ultramicrotome at cryogenic temperatures. These sections were stained with RuO4 as a staining agent for SBR. The TEM images were taken with a Zeiss CEM 902 transmission electron microscope in the bright field mode applying an acceleration voltage of 80 kV at a sample temperature of 100 K.

3. Results A. TEM and AFM Images. Prior to discussing our TMAFM data, we first consider the TEM results to unambiguously identify the components of BR/SBR blends. Figure 1 shows the TEM image obtained for an ultrathin section of a BR/SBR sample. The silica filler particles are clearly distinguished and appear in the darkest contrast. The staining agent RuO4 is selectively incorporated into the SBR component because of its phenyl rings. The SBR appears in darker contrast than the BR component due to the staining, although the contrast difference between the two polymer components is weak. Figure 1 shows that

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Figure 2. TMAFM height and phase images of a BR/SBR blend with silica fillers. The images were taken on a cryogenically cut surface with A0 ≈ 60 nm and ω0 ) 2π × 334.3 kHz. The cantilever force constant was 40 N/m. The set-point ratios rsp ) Asp/A0 were rsp ) 0.75 for (a) and (b), rsp ) 0.5 for (c) and (d), and rsp ) 0.25 for (e) and (f). The scan size was 5 µm in all images. In the height images (a), (c), and (e), the gray contrast covers height variations in the 150 nm range. In the phase images (b), (d), and (f), the gray contrast covers phase angle variations in the 25° range for (b) and in the 50° range for (d) and (f).

the silica filler particles are mainly present within the SBR component. Figure 2 presents the TMAFM height and phase images recorded using A0 ≈ 60 nm and several different rsp values.

Parts a and b of Figure 2 and show the height and phase images, respectively, recorded at rsp ) 0.75. The silica filler particles are clearly distinguished in the phase image and appear in the brightest contrast. Larger agglomerates

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Figure 3. A(ω) and Φ(ω) curves obtained for BR in (a) and (b), respectively, and for SBR in (c) and (d), respectively. The curves were recorded with A0 ≈ 50 nm at several rsp values using a cantilever with force constant of 40 N/m. The corresponding rsp values are indicated in (a) and (c). The vertical axis at 334.3 kHz indicates the resonance frequency (i.e., ω0 ) 2π × 334.3 kHz) of the free cantilever. In (b) and (d) the horizontal axis is located at a phase angle of 90°.

are seen in the lower left corner of the image. The contrast difference between the BR and SBR components is weak in the phase image. However, the SBR component containing the silica filler particles shows a slightly darker contrast than does the BR component. It is not possible to deduce the morphology of the BR and SBR phases from the height image (Figure 2a) although the BR region has a brighter contrast and appears as “higher” lying. The silica filler particles appear in the darkest contrast in the height image, i.e., “lowest” lying. Parts c and d of Figure 2 show the height and phase images, respectively, recorded at rsp ) 0.5. Compared with the case of rsp ) 0.75, the image contrast changed dramatically in both the height and phase images. In the height image (Figure 2c), the dark filler particles disappeared, and the morphology and topography cannot be discerned. The phase image (Figure 2d) still shows the filler particles in the bright contrast, but there is a strong contrast difference between the BR and SBR components with the BR and SBR components in bright and dark contrasts, respectively. A reduction of the set-point ratio to rsp ) 0.25 leads to further contrast changes in the height and phase images (Figure 2e,f). In the height image, the morphology of the BR and SBR components can be clearly distinguished with the BR region appearing in darker contrast (i.e., “lower” lying). In the phase image, the BR region still shows a brighter contrast than does the SBR region. However, the silica filler particles cannot be distinguished anymore. B. Amplitude and Phase Curves. As described above, the contrasts of the height and phase images depend sensitively on the measurement conditions and thus on the nature of the tip-sample interaction. Thus, without

further systematic studies, it is difficult to understand the cause for the image contrast variation, identify the BR and SBR regions from the TMAFM images alone, or deduce the “true topography” from the height images. To explore the factors affecting the image contrast further, we performed frequency-sweep and force-probe measurements on BR and SBR homopolymers. Representative A(ω) and Φ(ω) curves determined for BR and SBR are shown in Figure 3. The data were obtained using the drive frequency ω0 ) 2π × 334.3 kHz and the free amplitude A0 ≈ 50 nm. Similar curves were obtained using other free amplitudes (A0 ≈ 35 and 45 nm). The A(ω) and Φ(ω) curves determined for BR are shown in parts a and b of Figure 3, respectively, and those determined for SBR in parts c and d of Figure 3, respectively. As found in our previous studies of PDMS,7,17 the A(ω) curves show no amplitude peak truncation. That is, there is a peak rising above the set-point amplitude Asp, which is given in parts a and c of Figure 3 by the intercept of the A(ω) curve with the vertical line at ω0. Hysteresis with respect to the frequency-sweep direction (i.e., bistability) was not observed. For both BR and SBR, the peak position of the A(ω) curve, which is close to the frequency at which the phase angle Φ(ω) becomes π/2,9,10 shifts to a higher frequency as the set-point ratio rsp is decreased below 0.9. That is, the resonance frequency of a tapping cantilever shifts to higher frequencies, ωeff ) ω0 + ∆ω (∆ω > 0). The amplitude peaks become also broader with decreasing rsp, which indicates an enhancement of damping. The A(z) curves obtained for the BR and SBR samples with A0 ≈ 60, 45, and 35 nm are presented in Figure 4a, and the corresponding Φ(z) curves are presented in Figure

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Figure 4. (a) Amplitude A as a function of z for BR and SBR, and (b) phase shift ∆Φ as a function of z for BR and SBR. The squares, circles, and triangles represent the data obtained using A0 ≈ 60, 50, and 30 nm, respectively. The filled symbols represent the values for BR, and the open symbols represent those for SBR. The driving frequency was ω0 ) 2π × 334.3 kHz, and cantilever force constant was 40 N/m.

Figure 5. Phase shift, ∆Φ, as a function of rsp for BR and SBR. The values were derived from the A(z) curves. The squares, circles, and triangles represent the values derived from the data recorded with A0 ≈ 60, 50, and 30 nm, respectively. The filled symbols represent the values for BR, and the open symbols represent those for SBR, respectively.

4b. The A(z) curves show that the amplitudes do not decrease linearly as the tip-sample distance z is decreased. The A(z) and Φ(z) curves of the BR and SBR samples are not distinguished as the tip-sample distance z begins to decrease below zero where the tip-sample interaction is weak. As the tip-sample interaction is increased by decreasing the tip-sample distance further, the BR and SBR sample become clearly distinguished, and the amplitude at a given z and at a fixed A0 is larger for BR. As z is decreased, the phase shifts ∆Φ are all positive, i.e., the tip-sample interaction is dominated by the repulsive indentation force. At given z and at a fixed A0, the phase shift ∆Φ is smaller for SBR. To compare the height and phase images with the data obtained from ∆Φ(ω) curves or from ∆Φ(z) curves, it is necessary to plot the corresponding ∆Φ values as a function of the set-point ratio rsp because images are usually recorded at a constant set-point ratio rsp. Such ∆Φ vs rsp plots can be obtained from the phase images recorded at different rsp values, from the ∆Φ(ω) curves determined at different rsp values, or from ∆Φ(z) curves taken at different A0 values. Figure 5 plots the phase shift ∆Φ for the BR and SBR samples as a function of rsp. To a good approximation, ∆Φ is a linear function of rsp for 0.1 < rsp < 0.8. In the region of rsp < 0.8, ∆Φ is positive and is larger for BR than for SBR. This is in agreement with the darker

and brighter contrasts for the SBR and BR regions, respectively, observed in the phase images of panels b, d, and f of Figure 2. It should be noted that the ∆Φ values depend on the set-point ratio rsp, but not much on the free amplitude A0. As already pointed out,12,16 this means that a tapping cantilever is strongly affected by the tip-sample force whose gradient changes sharply while the cantilever goes through the lower turning point of oscillation (LTPO) and ∆Φ is proportional to the amount of time the tip spends in the vicinity of the LTPO. C. DMA Measurements. Parts a and b of Figure 6 present the storage modulus E′, loss modulus E′′, and tan δ ) E′′/E′ as a function of temperature for the BR and SBR samples, respectively. The data have been obtained for a vulcanized BR sample in the -120 to -40 °C temperature range (filled symbols), and for an unvulcanized BR sample in the -10 to +100 °C temperature range (open symbols). For SBR the data were obtained for a vulcanized sample in the -60 to +20 °C temperature range (filled symbols) and for an unvulcanized sample in the -10 to +100 °C temperature range (open symbols). Vulcanized and unvulcanized samples were used to avoid the difficulty of covering the entire temperature and modulus range (-100 to +100 °C, and 104 to 1010 Pa, respectively) of interest in one experimental test-geometry setup. The DMA data show a typical rubber-like behavior: for high temperatures far above the glass transition temperature Tg, both the loss and the storage moduli are low and show little dependence on temperature. As the temperature is decreased, E′ and E′′ increase, and the loss tangent, tan δ ) E′′/E′, shows a maximum at the glass transition temperature, Tg. The SBR sample has a greater Tg ≈ -39 °C than does the BR sample (Tg ≈ -95 °C). For the BR system there is a gap in the data in the -40 to -10 °C temperature range because the compound was found to crystallize in this regime giving rise to unphysical data. The expected behavior is indicated by a broken line based on the reported data from the literature.21 It is important to note that at any given temperature in the -60 to +20 °C range the storage and loss moduli are both greater for SBR that for BR. This is evident in the temperature regime where the glass transition of the SBR component occurs. At +20 °C, for example, E′ ) 1.3 × 106 Pa and E′′ ) 3.7 × 105 Pa for SBR, and E′ ) 5.2 × 105 Pa and E′′ ) 2.5 × 105 Pa for BR. (21) Kramer, O.; Hvidt, S.; Ferry, J. Science and Technology of Rubber, 2nd ed.; Mark, J. E., Erman, B., Eirich, F. R., Eds.; Academic Press: San Diego, 1994.

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Figure 6. Storage modulus E′, loss modulus E′′, and tan δ ) E′′/E′ as a function of temperature for (a) BR and (b) SBR. The squares, circles, and triangles represent the E′, E′′, and tan δ data, respectively. The values represented by the open symbols were obtained for vulcanized samples using a Rheometrics Solids Analyzer RSA in the -120 to -40 °C temperature range, and those represented by the filled symbols were obtained for unvulcanized samples using a Rheometrics Mechanical Spectrometer RMS in the -10 to +100 °C temperature range. The dashed lines in (a) represent the expected behavior of E′ and E′′ in the -40 to -10 °C temperature range.

4. Discussion A. Sample Stiffness and Damping. Our DMA results show that the glass transition temperature Tg is higher for SBR than for BR. Even at temperatures far above the Tg of SBR, the storage and loss moduli are slightly larger for SBR than for BR. It is known that due to the timetemperature-superposition principle,22 the relaxation times and hence moduli depend on the frequency. It is reasonable to assume that the BR and SBR samples appear “stiffer”, i.e., closer to Tg, due to the high oscillation frequency of the cantilever. According to our DMA results, the SBR sample should be stiffer than the BR samples in the TMAFM experiments. Thus if the indentation depth were the same on SBR and BR samples at a given rsp, one would expect that SBR gives rise to a greater repulsive indentation force, hence a larger frequency shift, and hence a greater phase shift. However, in the phase images of BR/SBR blends (Figure 2b,d,f), the less stiff component BR is brighter than the stiffer component SBR. In addition, the ∆Φ-vs-rsp curves of BR and SBR presented in Figure 4 reveal that at a given rsp below 0.8, the phase shift is larger on the less stiff component BR. To understand this contrast difference between the two, it is necessary to examine the phase shift, frequency shift, and quality factor on the BR and SBR samples in some detail. Our previous studies showed that the harmonic approximation provides a semiquantitative description of the phase shift for compliant elastomeric samples.9 This approximation assumes that the vibration of a tapping cantilever is harmonic and that the force constant keff and the resonance frequency ωeff of a tapping cantilever deviate only slightly from those of the free cantilever, k0 and ω0, respectively. Then the phase shift ∆Φ measured at the drive frequency ω0, i.e., the phase angle of a free cantilever, π/2, minus that of the corresponding tapping cantilever, Φ(ω0), is expressed as9

∆Φ )

(

)

ω0 ∆ω π - arctan ≈ 2Qeff 2 ω0 2Qeff∆ω

(1)

The ∆ω values can be directly determined from the Φ(ω) curves. The Qeff values can be determined from the A(ω) (22) Ferry, J. Viscoelastic Properties of Polymers, 3rd ed.; John Whiley & Sons: New York, 1980.

curves.9 Namely, the quality factor Q0 of a free cantilever is given by

Q0 ) ω0/B

(2)

where B is the bandwidth of the amplitude curve at its half-power point. For the case of weak damping the effective quality factor Qeff can be obtained from eq 2 by replacing Q0 and ω0 and with Qeff and ωeff, respectively. For the case of moderate to strong damping, the Qeff values can be determined from eq 3

A(ωeff) ) a0Qeff

(3)

where a0 is the amplitude of the bimorph driving the cantilever and A(ωeff) is the amplitude at the effective resonance frequency ωeff of the tapping cantilever. To determine the a0 value, we first find the quality factor of the free cantilever Q0 from eq 2 and then use the relationship A(ω0) ) a0Q0 to calculate a0. The ∆ω and Qeff values thus determined are plotted as a function of the set-point ratio rsp in parts a and b of Figure 7, respectively. As already reported,9,17 the ωeff and Qeff values deviate from ω0 and Q0, respectively, as soon as the tip-sample interaction sets in. For both BR and SBR, the ∆ω value increases and the Qeff value decreases when the tip-sample interaction is enhanced. For a given rsp the frequency shift ∆ω is larger for BR than for SBR (about twice as large at rsp ) 0.3, see Figure 7a). The quality factor Qeff is similar for BR and SBR in the rsp > 0.6 region, but Qeff is smaller for SBR than for BR in the rsp < 0.6 region (Figure 7b). From the ∆ω and Qeff values, one can calculate the ∆Φ values using eq 1, which we referred to as ∆ΦH.A. The plots of ∆ΦH.A values as a function of rsp (Figure 7c) have a very good correspondence to the rsp-dependence of the ∆Φ values (Figure 4). This is in support of the harmonic approximation, in which two factors contribute to the phase shift, i.e., ∆ω and Qeff (eq 1). The Qeff term is related to the viscous damping and energy dissipation caused by the tip-sample interaction (see below). The ∆ω term is related to the force constant change ∆k ) keff - k0, namely, ∆ω ) ∆k(ω0/2k0). The ∆ω value is larger on the less stiff component BR than on the stiffer component SBR at a given rsp below 0.8 (Figure 7a). This would be counterintuitive if the indentation depths on the SBR and BR samples were the same at a

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Figure 7. (a) ∆ω, (b) Qeff, and (c) ∆ΦHA as a function of rsp. The squares and circles represent the values for BR and SBR, respectively. The data in (a) and (b) were derived from the A(ω) and Φ(ω) curves obtained with A0 ≈ 60 and 50 nm, and ω0 ) 2π × 334.3 kHz. The ∆ΦHA data in (c) were calculated from the ∆ω and Qeff plotted in (a) and (b) using eq 1. The straight lines represent the linear fit.

Figure 8. (a) Amplitude A as a function of z for BR and SBR, and (b) indentation depth δ as a function of rsp for BR and SBR. The solid line in (a) shows the amplitude Ais(z) for an infinitely stiff surface with zero indentation. The squares and circles represent the values for BR and SBR, respectively. The data were obtained using A0 ≈ 60 nm and ω0 ) 2π × 334.3 kHz.

given rsp. However, the indentation depth on a compliant sample should increase with decreasing the stiffness of the sample.17,18 To relate the difference in ∆Φ, ∆ω, and Qeff of BR and SBR to that in their stiffness, it is necessary to examine the ∆Φ, ∆ω, and Qeff values as a function of the indentation depth δ. B. Phase Shift and Indentation Depth. Figure 8a shows representative A(z) curves for BR and SBR obtained with A0 ≈ 60 nm, where the solid line represents the amplitude Ais(z) for an infinitely stiff sample on which the indentation depth δ is zero. The A(z) curves observed for the BR and SBR samples lie above the Ais(z) curve because of the indentation on these samples. The deformation of the stiff silicon tip will be negligible compared with the

sample indentation so that the indentation depth δ(z) at a given z can be estimated from the difference δ(z) ) A(z) - Ais(z).17 The δ(rsp) curves obtained this way are also plotted in Figure 8b, which reveals that δ(rsp) increases with decreasing rsp, in the rsp > 0.7 region δ(rsp) is nearly identical for BR and SBR, and in the rsp < 0.7 region δ(rsp) becomes larger for BR than for SBR. It should be noted that the indentation depth is in the range of several tens of nanometers, i.e., δ ≈ 30 nm at rsp ≈ 0.8 for BR and SBR and δ ≈ 45 and 85 nm at rsp ≈ 0.2 for SBR and BR, respectively. Since we know the indentation depth as a function of the set-point ratio (Figure 8b), the ∆Φ(rsp), ∆ω(rsp), and Qeff(rsp) curves can be converted to the corresponding curves as a function of the indentation depth

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Figure 9. (a) ∆ω, (b) Qeff, and (c) ∆Φ as a function of indentation depth δ for BR and SBR. The squares and circles represent the values for BR and SBR, respectively. The data were obtained using A0 ≈ 60 nm and ω0 ) 2π × 334.3 kHz. The numbers on the plots represent the corresponding rsp values.

δ, i.e., ∆Φ(δ), ∆ω(δ), and Qeff(δ), as shown in parts a-c of Figure 9, respectively. For a given sample, the indentation force increases with increasing indentation depth23 and so does the frequency shift ∆ω(δ) (Figure 9a). For a small indentation δ < 30 nm, the tip-sample interaction is dominated by attractive forces, as can be seen from negative ∆ω and ∆Φ values (Figure 9a,c). For a large indentation δ > 30 nm, however, the tip-sample interaction is dominated by the repulsive indentation force, as can be seen from positive ∆ω and ∆Φ values. For a given sample, the effective quality factor Qeff decreases with increasing the indentation depth (Figure 9b). This behavior is expected because a tapping cantilever dissipates energy through the viscous damping and the tip-sample interaction,9,12 and the latter should increase with increasing the indentation depth. Figure 9b shows that with increasing the indentation depth, the effective quality factor Qeff decreases faster for a stiffer sample SBR than for a less stiff sample BR. As a consequence of the fact that the phase shift is affected by both ∆ω and Qeff, BR and SBR have similar ∆Φ values at a given indentation depth below 35 nm (Figure 9c). As shown in Figure 9c, BR and SBR allow a given indentation depth at different rsp values, so the values of their phase shifts at a given rsp become different. C. Phase Shift and Energy Dissipation. The studies by Tamayo and Garcia,18 and by Cleveland et al.24 showed (23) Israelachivili, J. Intermolecular Forces, 2nd ed.; Academic Press: San Diego, 1992. (24) Cleveland, J. P.; Anczykowski, B.; Schmid, A. E.; Elings, V. B. Appl. Phys. Lett. 1998, 72, 2613.

the importance of energy dissipation in understanding observed phase contrasts. A tapping cantilever driven at ω0 to have the set-point amplitude Asp possesses the maximum kinetic energy given by W0′ ) keffAsp2/2, where keff is the effective force constant of the tapping cantilever. A tapping cantilever is affected by the tip-sample interaction and hence leads to additional energy dissipation. Suppose that Wt-s is the energy dissipation of the tapping cantilever associated with the tip-sample interaction, and Wvis′ is that associated with the viscous damping in air. Then the effective quality factor Qeff of the tapping cantilever driven at ω0 is given by12

Qeff ≈

2πW0′ Wvis′ + Wt-s

(4)

The viscous dissipation energy in air, Wvis′, of the tapping cantilever can be estimated as Wvis′ ) 2πW0′/Q0. Thus one can calculate the tip-sample dissipation energy Wt-s from eq 4 once the effective quality factor Qeff is determined. Our recent work showed that for compliant, viscoelastic materials, the phase shift is related to the reduced tipsample energy dissipation, Wt-s/W0′, and not to the total energy dissipated by the tip-sample interaction, Wt-s. Thus, for the discussion of the phase shift, it is important to consider the fraction of the maximum kinetic energy of a tapping cantilever that is dissipated by the tip-sample interaction.12 Figure 10 a plots the Wt-s/W0′ values for BR and SBR as a function of rsp, and Figure 10b plots the phase shift ∆Φ for BR and SBR as a function of Wt-s/W0′. For each

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Figure 10. (a) Reduced tip-sample energy dissipation Wt-s/W0′ as a function rsp. (b) ∆Φ as a function of the reduced tip-sample energy dissipation Wt-s/W0′. The squares and circles represent the values derived from the data recorded with A0 ≈ 60 and 50 nm, respectively. The filled symbols represent the values for BR, and the open symbols represent the values for SBR, respectively.

sample the reduced tip-sample power dissipation increases continuously with decreasing rsp. This is understandable because the extent of the tip-sample interaction, and hence the associated tip-sample energy dissipation, should increase with increasing the tipsample contact time, i.e., with decreasing rsp. In the Wt-s/ W0′ vs rsp plots the BR and SBR samples are distinguished when rsp < 0.7. At a given rsp below 0.7 the Wt-s/W0′ value is larger on SBR than on BR, i.e., more energy is dissipated on the SBR sample. The ∆Φ vs Wt-s/W0′ plot in Figure 10b shows clearly that ∆Φ increases almost linearly with increasing Wt-s/W0′. This is not surprising because both quantities increase with increasing the tip-sample contact time. The phase shift ∆Φ is larger for BR at a given value of Wt-s/W0′, and is larger for BR at a given rsp. However, the value of Wt-s/W0′ is larger for SBR at a given rsp. The relationship between ∆Φ and Wt-s/W0′ is almost linear and closely resembles the ∆Φ vs rsp plot (Figure 5). For a given Wt-s/W0′ value the phase shift is larger for BR, and for a given rsp ∆Φ is larger for BR but Wt-s/W0′ is larger for SBR. In the process of reducing the amplitude to a desired set-point ratio rsp in imaging and frequencysweep experiments, the tip indents the sample and energy is dissipated by the tip-sample interaction. The required set-point ratio is achieved with smaller indentation depth, greater reduced energy dissipation, and smaller frequency shift on the stiffer sample SBR than on the less stiff sample BR. The phase shift ∆Φ is affected by both ∆ω and Qeff with the result that the phase shift is larger for the less stiff sample BR at a given rsp. D. Image Analysis. The above findings can be used to analyze the height and phase images in more detail. The phase images can be understood in terms of the indentation depth and the reduced energy dissipation, as discussed above. This consideration allows one to analyze the height images as well. It is noted from Figure 8b that at rsp ) 0.8 the indentation depth is about 30 nm for BR and SBR, but at rsp ) 0.3 the indentation depths are about 40 nm for SBR and 60 nm for BR. Thus it will be quite difficult to acquire the “true” topographical images on such compliant samples. The height image presented in Figure 2e (recorded at rsp ) 0.25) can be understood as a consequence of the different indentations on BR and SBR. The tip indents much more on BR than on SBR regions, so the feedback mechanism makes the tip move much closer to the sample surface on the BR region so as to reduce the amplitude to the desired set-point value. This makes the BR regions appear lower lying in the height image. Thus one may hope to obtain the correct topography information

by employing a large rsp value so as to reduce the extent of indentation. However, success of this approach is not necessarily guaranteed. For example, the height image of Figure 2a was recorded at rsp ) 0.75. For rsp > 0.7, the indentation depth is nearly the same for BR and SBR (Figure 8b), and so is the phase shift ∆Φ (Figure 4). However, the phase shift ∆Φ is negative at rsp > 0.7 for both BR and SBR hence indicating that the tip-sample interaction is dominated by attractive forces (Figure 4). In contrast, the phase shift ∆Φ on the filler particles is positive at rsp > 0.7 indicating that the tip-sample interaction is dominated by repulsive forces. Our TMAFM studies on self-assembled monolayers demonstrated11 that anomalous height images are obtained on a heterogeneous surface where the nature of the tip-sample interaction is not uniform throughout the surface: the region dominated by attractive tip-sample forces appears higher lying, because of a larger amplitude reduction in that region, than the region dominated by repulsive tip-sample forces. In a similar way, the filler particles (with repulsive tip-sample interaction) appear lower lying and the BR/ SBR surroundings (with attractive tip-sample interaction) higher lying in the height image (Figure 2a). It is not surprising that the silica filler particles show much brighter contrast in the phase images, because they are much stiffer than BR or SBR. Therefore this is consistent with the observation that for a given z or rsp, the phase shift is generally greater on stiff materials (such as silicon and mica) than on compliant materials. It should be pointed out that the phase contrast observed on the rubber components is not much influenced by the presence of the small filler particles. This was confirmed by comparing the values of the phase shifts obtained on filler containing blends with those obtained on the homopolymers that were identical within the experimental error. Finally we note that large and small domains are distinguished in Figure 2. The phase contrast and shape of the small domains are affected by the rsp value, i.e., by the extent of tip-sample interaction. The small domains become clearly distinguished at small rsp values only, and the phase contrast of the small domains can be slightly different from that of the large domains (compare Figure 2d,f). This may be caused by stiffer SBR domains lying underneath the less stiff BR component. Such domains are clearly distinguished at small rsp values only, i.e., under strong tip-sample interaction. However, the phase contrast and shape of the large domains do not appear to be affected by the rsp value.

Examination of Elastomer Blends

5. Concluding Remarks This TMAFM study is based on BR/SBR blends with silica filler particles that are incorporated mainly in the SBR component. In the phase images of BR/SBR blends, the less stiffer component BR is brighter than the stiffer component SBR. This finding would be puzzling if the indentation depths on BR and SBR were the same at a given set-point ratio. However, force probe measurements show that the indentation depth is larger on BR than on SBR. When the phase shift and frequency shifts are examined as a function of the indentation depth, it is found that at a given indentation depth the phase and frequency shifts are larger on the stiffer component SBR than on the less stiff component BR and that with increasing the indentation depth the effective quality factor Qeff decreases faster for the stiffer sample SBR than for the less stiff sample BR. For viscoelastic materials, it is the reduced tip-sample energy dissipation, not the total tip-sample energy dissipation, that is relevant for the discussion of

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phase shift. The phase shift increases almost linearly with increasing the reduced tip-sample energy dissipation. The reduced tip-sample sample energy dissipation is larger for SBR than for BR in agreement with DMA results. For the rational interpretation of TMAFM phase images, it is necessary to take the indentation depth and the reduced tip-sample energy dissipation into consideration. The present study is quite general and should be easily transferred for the analysis of other elastomers. Acknowledgment. G. Bar wishes to thank the Deutsche Forschungsgemeinschaft for the financial support under Grant BA 1285/4-1. Work at North Carolina State University was supported by the Office of Basic Energy Sciences, Division of Materials Sciences, U.S. Department of Energy, under Grant DE-FG05-86ER45259. M. Ganter acknowledges a grant from the Deutsche KautschukGesellschaft under project 5/96. LA9913699