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Influence of Film-Substrate Adhesion on the Mechanical Properties of Thin Polymer Films D. Silbernagl, H. Sturm, and B. Cappella* Federal Institute for Material Research and Testing (BAM), Unter den Eichen 87, 12205 Berlin, Germany Received December 12, 2008. Revised Manuscript Received February 11, 2009 The mechanical properties of mechanical double layers (thin amorphous films of poly(n-butyl methacrylate) on considerably stiffer silicon substrates) were investigated by force-displacement curves acquired with an atomic force microscope. The substrate surface was modified to provide a hydrophilic and a hydrophobic moiety. Such a modification affects the adhesion between film and substrate, since the polymer film adheres strongly on the hydrophilic side and weakly on the hydrophobic one. In this way, we were able to investigate the influence of the adhesion between the polymer film and substrate on the mechanical properties of the mechanical double layer. We were able to show that force-displacement curves on the two moieties of the sample have a different shape, and we propose an interpretation of the mechanisms determining the force-deformation curves on films with small adhesion to the substrate. This experiment can also provide an approach to the question of how the mechanical properties of a bulk material change with the volume to surface ratio, since a film with vanishing adhesion to the substrate is the only experimental accessible setup approximating a free-standing thin film.
Introduction The investigation of nanomechanical properties is crucial for advancing in many technologies and applications, since several materials are implemented in a micro- to nanoscale or are solely obtainable as thin films or colloids. When examining mechanical properties in the nanoscale, atomic force microscopy is the analytical method with the best lateral and vertical resolution. It has been shown that by means of atomic force microscope (AFM) force-distance curves the mechanical properties of a homogeneous material can be determined, if the adequate continuum elastic theory is applied.1,2 The high resolution of these measurements is due to the fact that only a small portion of the sample volume is probed. This probed volume is defined as the portion of the bulk material in which the applied force is spread, and its size is primarily determined by the probe size, in the case of an AFM, the tip radius, which is in the range of tens of nanometers. Despite the high resolution an AFM provides, there are sample geometries in which the probed volume is inhomogeneous, for example, when an interface is present in the probed volume. In this case, the elastic continuum theories, valid for homogeneous samples, cannot be applied and a new description of the acquired force-distance curves in dependence of the geometry of the sample and of the properties of the involved materials has to be developed. In order to shed light on this subject, we examined in detail the case of a mechanical double layer, that is, when the interface is perpendicular to the applied load. As a model system, we used a compliant film on a rigid substrate. In previous experiments, the dependency of the force-distance curves on the Young’s modulus of the involved materials and on the film thickness was shown and a semiempirical theory describing this dependency was developed.3,4 In these (1) Cappella, B.; Kaliappan, S. K.; Sturm, H. Macromolecules 2005, 38(5), 1874–1881. (2) Kaliappan, S. K.; Cappella, B. Polymer 2005, 46(25), 11416–11423. (3) Cappella, B.; Silbernagl, D. Langmuir 2007, 23(21), 10779–10787. (4) Cappella, B.; Silbernagl, D. Thin Solid Films 2008, 516(8), 1952–1960.
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experiments, the same materials and procedures were used in order to obtain the same adhesion between the polymer film and the substrate. Yet, it has to be assumed that the adhesion has a fundamental influence on the mechanical properties of the double layer5,6 as well as the film thickness. This assumption is plausible when considering that an interface with little interaction conducts also little of the applied stress. This changes significantly the probed volume and thus the measured mechanical properties. Hence, the adhesion cannot be disregarded when extending and completing our semiempirical theory. In order to briefly explain our semiempirical theory, we first examine the force-distance curves on homogeneous materials. A force-distance curve is a plot of the cantilever deflection δ versus the distance Z, which is the distance between the sample surface and the rest position of the cantilever. Using the cantilever spring constant kc, the force F can be derived via Hooke’s law: F ¼ -kc δ
ð1Þ
In all the following force-distance curves, we will plot the deflection versus Z instead of plotting the force versus Z, since kc is known. The deformation D of a sample can be derived from the difference between the distance Z and the deflection δ: D ¼ Z -δ
ð2Þ
For homogeneous samples, when sample adhesion to the tip can be neglected when compared to the load F, Hertz theory applies.7 In Hertz theory, the dependency (5) Blackman, G. S.; Mate, C. M.; Philpott, M. R. Phys. Rev. Lett. 1990, 65 (18), 2270–2273. (6) Chadwick, R. S. SIAM J. Appl. Math. 2002, 62(5), 1520–1530. (7) Butt, H. J.; Cappella, B.; Kappl, M. Surf. Sci. Rep. 2005, 59(1-6), 1–152.
Published on Web 3/18/2009
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In order to describe the shape of such a deformation curve D3/2 as a function of the cantilever deflection δ, we use a hyperbolic fit: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ D3=2 ¼ βδ þ ε - R2 δ2 þ 2εðβ -γÞδ þ ε2 with the parameters R, β, γ, and ε. In Figure 1 the hyperbola function (black line), together with its asymptotes (dashed lines), is shown. The parameters R and β define the slopes of the asymptotes of the hyperbola, that is, the minimal and maximal value of the first derivative, which is described by a sigmoid function: DD3=2 R2 δ þ εðβ -γÞ ¼ β - qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dδ R2 δ2 þ 2εðβ -γÞδ þ ε2 Figure 1. Plot of the deformation D3/2 versus cantilever def-
lection δ. Experimental curves (circles) were taken on a mechanical double layer and on the involved bulk materials. Fits are shown as solid lines. Asymptotes of the hyperbolic fit are shown as dashed lines.
of the deformation D on the load F is described as follows: kc D3=2 ¼ pffiffiffiffi δ RK
ð3Þ
with the tip radius R and the reduced Young’s modulus K. The reduced modulus K is a function of the modulus E, the Poisson ratio ν, and the mechanical properties of the AFM tip (Et, νt): ! 1 3 1 - ν2 1 - νt 2 ¼ ð4Þ þ K 4 E Et So, when plotting the deformation D3/2 of a homogeneous material versus pffiffiffiffi the deflection δ, we get a straight line with a slope kc = RK (see eq 3). Figure 1 shows such curves, measured on bulk polymer (gray circles) and on substrate (black circles). The spring constant kc and the tip radius R are the same in both cases, because both measurements were performed with the same cantilever. The difference in the slopes of the curves is due to the difference of the Young’s moduli of the polymer and substrate, Ep and Es. A deformation curve taken on a mechanical double layer (Figure 1, gray-black circles) cannot be described by the Hertz theory, since the sample is inhomogeneous. The curve is not a line; that is, the Young’s modulus of the double layer Ef depends on the load F and on the deformation D. Ef is a composition of the Young’s moduli of the involved materials Ep and Es. The contribution of each elastic modulus depends on D/t, the ratio of the deformation to the film thickness. This is understandable if the polymer film is pictured as a mechanical shielding of the substrate. The effectiveness of the shielding decreases with increasing deformation D or decreasing film thickness t. At a large D/t ratio, the influence of the Young’s modulus of the substrate Es is dominant, that is, Ef ≈ Es. For the limiting case t f 0, that is, the blank substrate, D/t tends to an infinite value and Ef = Es. At a small D/t ratio, the contribution of the Young’s modulus of the polymer is dominant, that is, Ef ≈ Ep. For the limiting case t f ¥, that is, bulk polymer, D/t tends to zero and Ef = Ep. 5092
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ð6Þ
These limits are inversely proportional to the elastic moduli of the materials building the double layer: kc β - R ¼ pffiffiffiffi , RKs
kc β þ R ¼ pffiffiffiffi RKp
ð7Þ
The parameter γ is the first derivative of the hyperbola at δ = 0, and its value is between β - R and β + R. If the geometry of a double layer tends to that of a homogeneous sample, that is, t tends to zero (substrate) or t tends to an infinite value (bulk polymer), then γ tends to β - R or to β + R, respectively. In these cases, the hyperbola degenerates to one of its asymptotes. The limiting cases of the hyperbolic fit are hence the Hertz fit. The parameter ε, together with γ, defines the width of the force interval, in which the mechanical properties of the double layer differ significantly from the mechanical properties of the involved materials. In particular, the width of the sigmoid function (eq 6), that is, the width of the transition from one plateau value (β + R) to the other (β - R), is given by ε b R
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðβ -γÞ2 1R2
ð8Þ
In order to estimate the influence of the adhesion on the mechanical properties of the double layer, we consider the limiting case in which there is no adhesion between the polymer film and the substrate. This is the case, for example, for liquid polymer films, which were examined by Mate and co-workers by means of force distance curves.5,8 The deformation curve of such a sample, schematically shown in Figure 2, has no transition region but rather a transition point. Hence, it can be described by two lines, that is, a hyperbola with b = 0. A particular consequence of these deformation characteristics is that, regardless of the film thickness t, the deformation curve of the double layer (gray solid curve) matches for small loads the deformation curve of the liquid polymer (black dashed curve). In other words, for deformations smaller than the film thickness, the substrate does not influence the mechanical properties of the double layer and is completely shielded by the polymer. The lack of a transition region is due to the missing adhesion, which allows the polymer to move aside under the (8) Mate, C. M.; Lorenz, M. R.; Novotny, V. J. J. Chem. Phys. 1989, 90 (12), 7550–7555.
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Figure 3. Structure of PnBMA.
Figure 2. Schematic plot of a deformation curve of a liquid polymer film (gray solid line) which coincides with the deformation curves of the bulk materials (black dashed line). pressure of the indenting tip. If there were adhesive forces between the polymer and substrate, the stress exerted by the tip would be transmitted to the substrate and hybrid mechanical properties would result in a transition region. For double layers with a weak adhesion, we expect a deformation behavior intermediate between both limiting cases, that of an adherent polymer film (Figure 1) and that of a nonadherent liquid polymer film (Figure 2). Hence, the deformation of a double layer with weak adhesion between the film and substrate should approach the deformation of the bulk polymer for small forces. In other words, a decreasing adhesion should make the deformation curve insensitive to the substrate for small loads. This expected behavior of a mechanical double layer has to be verified experimentally. For this purpose, an experimental setup is chosen, in which neither the mechanical properties of the involved materials nor the film thickness are altered, but the adhesion between the film and substrate can be changed. In order to achieve a variation of the adhesion between polymer film and substrate, the substrate surface properties have to be altered by adequate means. The adhesion force is a composition of long-range and short-range interactions (van der Waals force), acting between the molecules at the substrate surface and the polymeric groups (side groups, end groups, loops of the main chain).The van der Waals force is the sum of three forces: (a) the Keesom force acting between dipoles, (b) the Debye force acting between permanent dipoles and induced dipoles and (c) the London force or dispersion force acting between instantaneous dipoles.7 The largest contribution to the adhesion force is the interaction between dipoles, and consequently, a reduction of the polar bonds at the surface of the substrate leads to a reduction of the adhesion. As substrate material, we used silicon wafers, whose surfaces are oxidized (SiO2). Such an oxygen terminated surface is polar (ΔENSi-O 1.5). Upon etching the surface with hydrofluoric acid (HF), the oxidation layer is removed and the residual surface reacts to silicon hydride (ΔENSi-H 0.36). Thus, the etched surface is hydrogen terminated, nonpolar, and hydrophobic. Measurements yielded a contact angle between water and hydrogen terminated surfaces larger than 52. On oxygen terminated surfaces, the contact angle is smaller than 6.9 The functionalization of the surface is not stable, and thus, the polarity of the surface changes with time, but this method provides important advantages. The mechanical properties of the substrate are not affected. No third layer between the polymer and substrate is formed, which is what (9) Kissinger, G.; Kissinger, W. Phys. Status Solidi A 1991, 123(1), 185–192.
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would occur when using a separating agent. Such a separation layer would alter the mechanical properties of the whole sample. As a polymer we have chosen poly(n-butyl methacrylate) (PnBMA, Figure 3) for several reasons. First, a large number of experiments concerning mechanical double layers have been already performed with this polymer. Thus, data for comparison are available, and the deposition of thin PnBMA films by spin-coating is a well-known process. From past experience, it is also known that PnBMA films adhere well to hydrophilic surfaces (glass and amorphous SiO2). Second, PnBMA includes besides a nonpolar main chain a side group, the butylmethacrylate, with a polar group (carbon acid ester COOR) and a nonpolar aliphatic group (CHn). This is necessary to achieve a variation of the adhesion. The carboxylic acid ester, as Noel et al. could show with ester terminated surfaces, has a lower contact angle and a stronger adhesion with polar media and surfaces as compared to methyl terminated surfaces.10 Clear and Nealy could show that in a nonpolar medium the adhesion force between nonpolar/nonpolar and nonpolar/polar surfaces is smaller than that between two polar surfaces.11 In our sample preparation, the medium is nonpolar (toluene or air) and the surface can be polar (oxygen terminated) or nonpolar (hydrogen terminated). The nonpolar groups of PnBMA (aliphatic groups) show a weak adhesion with both kinds of surfaces, polar as well as nonpolar. The adhesion between the polar groups of PnBMA and nonpolar surfaces is also small. In contrast, the adhesion between the polar groups and the polar surface is significantly higher. In summary, the polymeric film adheres better on polar surfaces than on nonpolar surfaces. This mechanism would indeed be more effective with a polymer with a stronger polar character; however, the balance between polar and nonpolar properties of the chosen polymer is crucial for the realization of the desired sample design. In order to obtain a uniform polymeric film from solution on a surface with different polarities, the solvent has to be able to wet polar and nonpolar surfaces alike. In ambient atmosphere (air), this is only possible with a nonpolar solvent. Thus, the polymer has to be soluble in a nonpolar solvent, which would be unfeasible for a polymer with a predominant polar character.
Experimental Section In a first step, polished silicon wafers, sized ∼2 2 cm (Wacker AG, Freiberg, Germany), were completely etched with a solution of 2% HF and 6% NH4F in water at room temperature for 20 s. Thereby, the oxide on the wafer surface was completely stripped. This first step was followed by rinsing with deionized water. With this pretreatment, a clean and uniform surface was obtained. In a second step, the silicon surfaces were oxidized by exposing them to plasma (air, 13 MHz) for 20 min, resulting in (10) Noel, O.; Brogly, M.; Castelein, G.; Schultz, J. Langmuir 2004, 20(7), 2707–2712. (11) Clear, S. C.; Nealey, P. F. J. Colloid Interface Sci. 1999, 213(1), 238–250.
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oxygen termination. In a third step, one half of each sample surface was again etched to obtain the hydrogen termination and then successively rinsed and dried. In doing so, the oxygen termination of the nonetched surface moiety was maintained. The regions of different surface termination were clearly distinguishable on all samples by wetting the surfaces with water. The oxygen terminated surfaces were wetted with a small contact angle, whereas hydrogen terminated surfaces were barely wetted at all. In an immediate fourth step, polymer films were spin-coated onto the wafers. Despite a spin time of 1 min, the polymeric film is not completely solvent-free. This influences significantly the mechanical properties of the PnBMA and leads to a decrease of the Young’s modulus and to the occurrence of plastic deformations at small loads. From previous experiments, we know that a drying period of several days up to 1 week is necessary to achieve reproducible, meaningful force-distance curves. Thus, two time dependent mechanisms had to be considered: the drying of the sample and the fading of the substrate surface termination. However, a further wetting test after removing the polymer film after 14 days showed that the desired surface properties, although reduced, were still present. It has to be assumed that, because of the polymer covering the substrate, undesired fading of the surface termination has been suppressed or at least slowed down. As expected for a spin-coated film of a polymer with Tg = 22 C, the films are extremely even with very small roughness ( D* the liquid polymer film has been squeezed out of the contact area and no longer contributes to the mechanical properties of the double layer, which are then completely determined by the substrate. On the contrary, the amorphous polymer film cannot be further elastically deformed after D* and remains as a mechanical barrier between the AFM tip and the substrate, that is, D* < t. Hence, for deformations greater than D*, the weak adherent film behaves as a strong adherent film (the adhesion is coerced) and the mechanical properties of the double layer are a combination of the mechanical properties of the two involved materials. Comparing the deformation curves on hydrophobic and hydrophilic substrates, it is clear that the first derivative of D3/2 for D > D* is smaller in the latter case, that is, the film on the hydrophilic substrate appears to be stiffer. It can be reasoned that the lateral mobility of the polymer on a hydrophobic substrate, for D > D*, although strongly limited, is still higher than in the case of an adherent polymer film. At this point of the analysis, a possible artifact of the measurement must be excluded, namely, the presence of an air cushion at the interface between the polymer and hydrophobic substrate. Several arguments can be raised against this assumption. If the characteristics of the curves on the hydrophobic substrate were determined by an air cushion, this air layer should be present on the whole hydrophobic part of the sample. In particular, since D* always has the same value for a given sample, the thickness of the air cushion should be the same all over the hydrophobic moiety. Considering the size of the sample and the sample preparation, the formation of such a uniform air layer is highly improbable. If such an air cushion underneath the film exists, the film should not adhere at all to the substrate and parts of the film, which were isolated through scratching, should fall off. On the contrary, we were able to acquire the topography of such portions of the sample and to take force-distance DOI: 10.1021/la8041007
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Figure 6. Deformation D3/2 versus cantilever deflection δ. Curves were taken on hydrophilic (solid markers) and hydrophobic (empty markers) parts of samples A (t = 30 nm, circles), B (t = 65 nm, squares), and C (t = 120 nm, triangles).
curves on them, which would be impossible for a loose film. Moreover, the stiffness of a polymer film on an air cushion would be orders of magnitude lower than that of the bulk polymer, since the air layer acts as a compliant substrate leading to a softening of the sample. On the contrary, in all our measurements, the initial stiffness of the film on the hydrophobic substrate was comparable to the stiffness of the bulk polymer. The characteristics of a deformation curve taken on a weakly interacting double layer can be summarized as follows: (1) For D < D*, Ef = Ep, and D3/2 is a line. (2) For D > D*, Ef is intermediate between Ep and Es, and D3/2 is a hyperbola. These criteria are independent of the thickness of the polymer film t, and the deformation curves on the hydrophobic parts of samples A, B, and C show a similar behavior, as can be seen in Figure 6 (empty markers). For comparison, the deformation curves on the hydrophilic parts of the same samples are shown as well (solid markers). The latter show the typical behavior of deformation curves taken on double layers with strong adhesion at the polymer/substrate interface. Comparing the deformation curves on hydrophobic areas, it is clear that the deformation D* correlates with the film thickness t. The thicker the polymer film, the larger is D*. D* is for sample A (t = 30 nm) ∼8 nm, for sample B (t = 65 nm) ∼12 nm, and for sample C (t = 120 nm) ∼16 nm. Likewise, the first derivative of the deformation curves correlates for D > D* with the film thickness t. Furthermore, it correlates with the first derivative of the deformation curve of the hydrophilic part of the same sample. Thus, the characteristics of a deformation curve on an amorphous polymer film with weak adhesion to the substrate can be extended by the properties depending on the film thickness: (3) For t1 < t2, D*1 < D*2. (4) For t1 < t2 and D > D*i , Ef1 g Ef2. Up to now, we treated cases of deformation curves acquired on polymer films with either a weak or a strong interaction with the substrate and therefore either barely or strongly restricted in their lateral mobility. Assuming a correlation between the interactions at the interface and the mechanical properties of the double layer, it has to be expected that a deformation curve on a polymer film with an intermediate adhesion to the substrate is 5096
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Figure 7. Schematic oversight of sample A with hydrophilic (white), intermediate (light gray), and hydrophobic (dark gray) regions. Corresponding deformation curves are shown versus deflection δ. a hybrid of the curves shown up to now. In order to demonstrate such a hybrid behavior, sample A was examined at different spots. An oversight of sample A is sketched in Figure 7, where the hydrogen terminated (oxygen terminated) regions are marked dark gray (white). Between these two areas, there is a change-over area, where the etching of the silicon oxide is incomplete. This is due to the procedure of hydrophobization, which does not take place in an exactly delimited area of the sample surface. Because of solvent vapor and changing wetting meniscus during etching, the hydrophobization is nonuniform and decreases gradually in the change-over area. In this change-over area, an intermediate adhesion is expected. Figure 7 shows the deformation curves taken on the change-over area of the sample (dash-dotted lines). They indeed show a hybrid behavior between the curves taken on hydrophilic (solid line) and hydrophobic (dotted lines) parts of the substrate. The hybrid behavior can be seen in the intermediate initial slope and in the intermediate overall mechanical properties: Ef,hydrophil > Ef,intermediate > Ef,hydrophob.
Conclusion In this initial experiment, we were able to create mechanical double layers with different adhesion at the interface by modification of the substrate surface without altering the mechanical properties of the involved materials and the film thickness of the compliant film. In order to verify the modification of the sample surface, we measured the adhesion between the tip and the two moieties of the substrate in water, and we were able to show that the adhesion is larger on the hydrophobic moiety. As expected, the mechanical properties of the involved materials are not altered by the modifications. Force-distance curves acquired on the hydrophilic moiety showed the typical shape of force-distance curves on an adherent mechanical double layer as already seen in previous experiments. Such curves could be fitted by taking advantage of our semiempirical theory. Curves on adherent films are dominated by the polymer (substrate) for small (large) deformations. These two regimes are connected by a broad transition region. Measured values of the elastic moduli of the constituents are in agreement with the literature and with previous measurements. With this sample setup, we were able to investigate the influence of the adhesion on the shape of force-distance Langmuir 2009, 25(9), 5091–5097
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curves. With decreasing adhesion at the interface, (a) at small loads, the curve approximates the force-distance curve of the bulk polymer, that is, the deformation is insensitive to the substrate; (b) at higher loads, the film behaves like an adherent film and the curve is a hyperbola; and (c) these two regimes are separated by a critical deformation D*. One goal of this experiment was to investigate the possibility of estimating the adhesion at an interface of a mechanical double layer by means of AFM force-distance curves. As a matter of fact, we were able to show and explain characteristics of a force-distance curve which can provide a
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qualitative approach to estimate the interfacial adhesion. For further steps toward a quantitative approach, a more precise “tuning” of the adhesion at the interface will be required. The second goal of this experiment was to show that a mechanical double layer with little adhesion to the substrate is a suitable approximation for a free-standing film, which actually cannot be realized in an experimental setup. Further investigation of such mechanical double layers with smaller film thickness is thus a promising approach to study materials with a high surface to volume ratio.
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