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Collapse of a Polymer Brush in a Poor Solvent Probed by Noise Analysis of a Scanning Force Microscope Cantilever Andreas Roters, Martin Schimmel, Ju¨rgen Ru¨he, and Diethelm Johannsmann* Max-Planck-Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany Received December 23, 1997. In Final Form: April 27, 1998 We have investigated the swelling of a polystyrene polymer brush in mixtures of toluene and methanol. We varied the solvent quality for polystyrene via the methanol weight fraction. As the solvent quality decreases, the brush collapses. The brush was synthesized by the “grafting from” method and has a thickness of 66 nm in the dry state. The brush’s viscoelastic profile was probed by analyzing the noise spectrum of a scanning force microscope (SFM) cantilever. The noise power spectrum displays the cantilever resonance. By fitting Lorentz curves to the spectra, one obtains an effective spring constant and a friction coefficient, which are measures of the elastic and the viscous interaction between the cantilever and the sample. The effective spring constant of the cantilever increases, when it comes into contact with the brush. This allows for an assessment of the brush thickness. The thickness in the swollen state (pure toluene) is about five times larger than the thickness in the dry state.
Introduction Polymeric adsorbates at surfaces play an important role in many areas of technology such as colloid stabilization,1 adhesion,2 lubrication,3 tribology,4 chromatography,5 and rheology.6 The structure and dynamics of such polymeric adsorbates as well as their response to perturbations have therefore attracted a lot of scientific interest.7 “Tethered layers” in particular, which are systems of terminally grafted linear polymer chains, have been intensely investigated.8-11 For systems with sufficiently high grafting density (“brushes”) there is strong lateral chain overlap and the osmotic pressure leads to chain stretching.12,13 The peculiar boundary conditions of terminal attachment result in a polymer conformation and dynamics which are different from those for polymers in the bulk. The degree of swelling of polymer brushes is largely determined by the solvent quality in the ambient medium. In bad solvents, brushes collapse to form a dense layer on the substrate. It is now well established that this collapse proceeds continuously as a function of solvent quality. Various theoretical14,15 and experimental16 studies have * Author for correspondence. Phone: 49-6131-379 163. Fax: 496131-379 360. E-mail:
[email protected]. (1) Napper, D. H. Steric Stabilization of Colloidal Dispersions; Academic Press: London, 1983. (2) Raphae¨l, E.; de Gennes, P. G. J. Phys. Chem. 1992, 96, 4002. (3) Klein, J. Annu. Rev. Mater. Sci. 1996, 26, 581. (4) Klein, J.; Kumacheva, E. Science 1995, 269, 816. (5) van Zanten, J. H. Macromolecules 1994, 27, 6797. (6) Parnas, R. S.; Cohen, Y. Rheol. Acta 1994, 33, 485. (7) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: London, 1993. (8) Halperin, A.; Tirell, M.; Lodge, T. P. Adv. Polym. Sci. 1991, 100, 31. (9) Halperin, A. In Soft Order in Physical Systems; Rabin, Y., Bruinsma, R., Eds.; NATO ASI Series Vol. 323 of Series B: Physics; Plenum Press: New York and London, 1994; pp 33-56. (10) Szleifer, I.; Cariggnano, M. A. Adv. Chem. Phys. 1996, XCIV, 165. (11) Grest, G. S.; Murat, M. In Monte Carlo and Molecular Dynamics Simulations in Polymer Science; Binder, K., Ed.; Clarendon Press: Oxford, 1994. (12) Alexander, S. J. Phys. (Paris) 1977, 38, 983. (13) de Gennes, P. G. J. Phys. (Paris) 1976, 37, 1443. (14) Halperin, A. J. Phys. (Paris) 1988, 49, 547. (15) Zhulina, E. B.; Borisov, O. V.; Pryamitsyn, V. A.; Birshtein, T. M. Macromolecules 1991, 24, 140.
resulted in a fairly consistent picture. This gradual collapse contrasts with the behavior of bulk polymers of high molecular weight which discontinuously phase separate into a dense and a dilute phase for solvent qualities just below the θ-point.17 Isolated polymer chains of high molecular weight also abruptly change their conformation from a Gaussian chain (Rg ∼ N1/2) to a globular sphere (Rg ∼ N1/3) just below the θ-condition.18 In brushes, the collapse is smoothened because the elastic energy associated with chain stretching enters the free energy as a new term. In previous publications19,20 we have shown that by analyzing the noise spectrum of a scanning force microscope (SFM), one can measure the elastic and viscous coupling between a cantilever and a polymer brush as a function of the brush-cantilever separation. Figure 1 illustrates the principle of the measurement. The analysis relies on fitting resonance curves to the noise power spectral density (PSD). From the eigenfrequency ω0, the damping constant γ, and the oscillator strength A, one can calculate the effective spring constant κ, the friction coefficient ξ, and the effective mass m. These are local measurements in the sense that they probe the environment of the cantilever only. However, it should be kept in mind that all of the cantilever takes part in the interaction. The term “local” implies a spatial scale in the range of some microns, not the molecular scale. When the sample approaches the cantilever from below, this affects the resonance parameters and thereby gives experimental access to the dynamics of the cantileverbrush interaction. Swollen and collapsed brushes are easily distinguished. Here, we present the application of SFM noise analysis to the collapse of a polystyrene brush immersed in mixtures of toluene and methanol. Whereas toluene is a good solvent, methanol does not dissolve polystyrene. The (16) Karim, A.; Satija, S. K.; Douglas, J. F.; Ankner, J. F.; Fetters, L. J. Phys. Rev. Lett. 1994, 73, 3407. (17) Einaga, Y.; Tong, Z.; Fujita, H. Macromolecules 1985, 18, 2258. (18) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (19) Roters, A.; Johannsmann, D. J. Phys.: Condens. Matter 1996, 8, 7561. (20) Roters, A.; Gelbert, M.; Schimmel, M.; Ru¨he, J.; Johannsmann, D. Phys. Rev. E 1997, 56, 3256.
S0743-7463(97)01409-1 CCC: $15.00 © 1998 American Chemical Society Published on Web 06/30/1998
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Figure 1. Schematic description of the experimental setup.
variation of solvent quality with composition serves our purpose to study the brush collapse.
other hand, are usually determined with good accuracy even for highly overdamped spectra.
Theory
Materials
We model the cantilever as an elastically suspended sphere which experiences random forces from its environment.21 The statistical motion of such a particle is described by the Langevin equation:
m
d2u(t) dt
2
+ξ
du(t) + κu(t) ) R(t) dt
(1)
where u(t) is the displacement, m is the effective mass, ξ is the friction coefficient, κ is the spring constant, and R(t) is the random force. In Newtonian liquids, the power spectrum of the random force does not depend on frequency. When the cantilever’s environment displays viscoelastic dispersion, the friction must be replaced by a term describing friction with memory. This aspect is treated in a separate publication.22 Here, we confine ourselves to a description where the spring constant κ and the friction coefficient ξ are independent of frequency. According to the fluctuation dissipation theorem, the noise power spectral density (PSD) is given by resonance curves
d|u(ω)2| ) dω (ω
2 0
Aγ ) - ω2)2 + γ2ω2 kBT ξ (2) π (κ - mω2)2 + ξ2ω2
with A the oscillator strength, kBT the thermal energy, ω0 ) (κ/m)1/2 the eigenfrequency, and γ ) ξ/m the damping constant. The parameters m, κ, and ξ are determined through fitting. A fourth quantity automatically obtained is the time-averaged displacement of the cantilever ∆zDC, which is proportional to the static force FDC. For highly overdamped spectra the error bar on the effective mass becomes quite large. The inertial term in the Langevin equation is negligible for situations dominated by friction. The spring constant and the friction coefficient, on the (21) Kubo, R.; Toda, M.; Hashitsume, H. Statistical Physics; Springer: Heidelberg, 1985; Vol. 2. (22) Gelbert, M.; Roters, A.; Schimmel, M.; Ru¨he, J.; Johannsmann, D. In preparation.
The synthesis of the polymer brush followed the “grafting from” approach,23,24 as depicted in Figure 2. Briefly, the first step is the formation of a self-assembled monolayer of an initiator for free radical polymerization at the surface of a silicon wafer. Other oxidic substrates with free surface hydroxyl groups can be used as well. The initiator is a derivative of AIBN which is attached to the wafer via a monochlorosilyl moiety. Subsequently, the polymerization is thermally initiated in a 4/1 v/v solution of styrene monomer in CHCl3. After polymerizing for 6 h at 60 °C, the samples are rinsed with solvent and undergo Soxhlet extraction with toluene for 15 h to remove physisorbed polymer. The dry thickness of the polymer monolayer, as determined by surface plasmon resonance spectroscopy,25 was 66 nm. There are two separate ways to assess the molecular weight. First, one can infer the molecular weight from other experiments using large substrates as well as high surface area silica gels, where similar polymerization conditions have been chosen. In these cases, the grafted polymer was cleaved off the surface by acid-catalyzed transesterification of the ester break-seal of the initiator after polymerization. This material was investigated with size exclusion chromatography and static light scattering. Second, one can calculate the polymer grafting density from the initiator grafting density and its decomposition kinetics. From the number of chains per unit area and the brush thickness in the dry state, the molecular weight can be assessed as well. The grafting distance for the brush investigated here is between 26 and 48 Å. This results in molecular weight Mn between 0.3 × 106 and 1 × 106 g/mol. The corresponding number of segments per chain is between 3000 and 10 000. The polydispersity is in the range Mw/Mn ) 2-3. As a consequence of this rather large polydispersity, one expects the segment density profile to be rather smooth.26 In particular, it strongly deviates from the parabolic profile given in the literature.27 The dimensionless grafting density σ, which is the ratio of the minimum area per segment divided by the area per chain, is between 0.02 and 0.07. As solvents, we used mixtures of methanol and toluene with methanol volume fractions of 0%, 10%, 17%, 30%, 60%, and 100%. For bulk polystyrene, the θ-condition is fulfilled at a methanol fraction of about 20%.26,27 The use of solvent mixtures to adjust the solvent quality has a slight drawback in the sense that one strictly speaking has a ternary system. One expects an enrich(23) Prucker, O.; Ru¨he, J. Macromolecules 1998, 31, 592. (24) Ru¨he, J. Nachr. Chem., Tech. Lab. 1994, 42, 1237. (25) Knoll, W. Makromol. Chem. 1991, 192, 2827. (26) Bianchi, U.; Magnasca, V. Chim. Ind. 1940, 40, 263. (27) Oth, J.; Desreux, V. Bull. Soc. Chim. Belg. 1954, 63, 285.
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Figure 2. Synthesis of tethered polymer layers by the “grafting from” approach. The initiator is self-assembled on a silicon oxide surface. The polymer grows in situ by free radical polymerization from the surface-bound initiator. ment of the good solvent (toluene) inside the brush. This does not qualitatively change the picture.
Experimental Procedure and Data Analysis Details of the experimental procedure have been published elsewhere.19,20 Figure 1 sketches the principle of the measurement. Briefly, we used a TMX 2010 instrument from TopoMetrix. The tip of the V-shaped silicon nitride cantilevers is a pyramid with a height of 2.9 µm and an opening angle of about 70°. It should be kept in mind that a large part of the tip interacts with the polymer layers. Therefore the radius of the tip apex is of minor importance. The thermal rms-noise 1/2 is about 3 Å. It is well above the detection limit. Only the fundamental resonance was in the accessible range of frequencies. In air the resonance frequencies typically are about 40 kHz with a Q-factor of about 20. In liquids the resonance frequencies decrease to about 10 kHz and the Q-factor is about 2. For determining the viscoelastic profile, we worked in a liquid cell. The vertical tip-sample distance is controlled by the z-piezo of the scanner, while the x- and the y-piezo are disconnected. We had to include a low pass filter with a cutoff around 150 Hz into the driving electronics of the z-piezo in order to eliminate the noise from the piezodriver. The “pictures” taken in that configuration contain only noise. All data were taken in the approach mode; that is, the profiles were measured with the height decreasing between successive data points. We were not interested in the adhesion between the tip and the brush at this point. The spectral noise power density is obtained by Fourier transformation of 128 data strings of 1024 pixels each. Parallel to data acquisition we monitor the noise with a Fourier Analyzer (HP 35670A) connected to the analog output of the quadrant detector. After moving the sample stage, we observed some irregular excess noise, which usually disappeared within a few seconds. Therefore we waited 4 s after each movement of the sample stage to allow for equilibration. Data acquisition for a z-profile as displayed in Figure 3 takes about 4 min. Distance calibration is not trivial. For sufficiently dilute layers, there is a well-defined kink in the force-distance curve which is a natural choice for z ) 0. At that same height the thermal noise discontinuously disappears
(bottom spectrum in Figure 3a), leaving only nonthermal noise. The interpretation is that, for sufficiently dilute layers, the tip can dive into the layer until it touches the substrate at some discrete height z ) 0. For dense brushes, like the one investigated here, this point is less well defined. There always remains a polymer cushion below the tip which allows for some noise, although the static force onto the cantilever is considerable. Ultimately, the static cantilever displacement is so large that it leaves the range of the instrument, while the noise is still different from the contact situation on a bare glass slide. There is no well-defined kink in the static force-distance curve either. Therefore a certain ambiguity remains with regard to the offset of the distance scale. We estimate the uncertainty to be in the range of a few nanometers for swollen brushes (methanol fractions of up to 17%). For collapsed brushes, the uncertainty in the height calibration may amount to a substantial fraction of the total thickness. In particular, the brush in pure methanol behaved exactly as a bare glass surface. In this case, we assume that “contact” is achieved, when the tip touches the top of the brush. The thickness of the brush in methanol given in Figure 5 is the dry thickness as measured with surface plasmon resonance spectroscopy.25 Results and Discussion Figure 3a shows a set of noise spectra taken in pure toluene on an empty glass surface. The numbers indicate the distance between the tip and the sample surface. In Figure 3b analogous data are displayed for the polystyrene brush in pure toluene. As part 3a shows, the presence of a solid surface affects the noise of the SFM tip even if it is not coated with a brush.19 After fitting the data, one finds that the main change is an increase in the friction coefficient ξ. This effect has been calculated by Reynolds as early as 1886.28 The corresponding force is sometimes called the “lubrication force”3 and serves as the contrast mechanism in the “scanning near field acoustic microscope (SNAM)”.29 As the gap between the tip and the sample narrows, the flow of solvent is diverted and this increases the friction coefficient. In the presence of a swollen brush, (28) Reynolds, O. Philos. Trans. R. Soc. London 1886, 177, 157. (29) Gu¨thner, P.; Fischer, U. Ch.; Dransfeld, K. Appl. Phys. B 1989, 48, 89-92.
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Figure 3. Noise spectra obtained during approach to the sample surface. The numbers give the tip-sample distance: (a) empty glass slide; (b) polystyrene brush in toluene; (c) polystyrene brush in toluene for close approach; (d) polystyrene brush in methanol for close approach.
the increase of friction is much stronger than that for the empty glass slide, as evidenced by the highly overdamped spectra (Figure 3b). Figure 3c and d displays detailed spectra obtained when the cantilever comes close to the substrate. We show spectra taken in pure toluene and spectra taken in pure methanol. While the spectra taken in toluene vary rather continuously with tip-sample distance, there is a discontinuity between 0.34 and 0.23 µm in methanol. This difference is the central result of our work. In toluene, the viscoelastic interaction between tip and sample varies rather continuously with distance because the brush is swollen, whereas in methanol there exists an interface which abruptly changes the interaction once the tip touches it. From the fits such as the ones shown in Figure 3b-d, we obtain profiles of the effective spring constant κ, the friction coefficient ξ, and the effective mass m. The static
force FDC is also obtained from the average cantilever displacement. Figure 4 shows the derived profiles for the various parameters.30 The distance z was derived from the driving voltage of the z-piezo, where a correction for the cantilever displacement was applied. The profile of the friction coefficient and the effective mass (Figure 4a and b) are quite similar. They show a long-range interaction mediated by the liquid environment, which is present even for an empty glass slide. In ref 20, we argue that the friction coefficient increases for a cantilever suspended above a brush (compared to a tip above a bare glass surface) because a vertical motion of the cantilever couples to the “breathing modes” of the (30) Because the spectra for the bare glass surface were taken with a different cantilever, quantitative comparison to the other data sets is difficult. Qualitatively, the profile for the bare glass surface resembles the profile for 100% methanol.
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Figure 5. Thickness derived from the elastic profiles. The apparent thickness varies only a little with solvent quality better than the θ-condition (methanol fraction e 17%). For poorer solvents, the brush collapses. For pure methanol, the brush thickness was taken as being identical to the dry thickness measured with surface plasmon resonance microscopy.
Figure 4. Profiles of friction coefficient ξ (a), effective mass m (b), effective spring constant κ (c), and static force FDC (d).
brush.31,32 Vertical flow of solvent can compress the brush and thereby dissipate energy. The effective mass closely correlates to the friction coefficient. This can be rationalized by assuming that the amount of ambient medium moving with the cantilever scales as the penetration depth of shear sound. Shear stress evanescently decays in liquids with a decay length proportional to η1/2. As the viscosity increases, the amount of material dragged along by the movement of the cantilever increases as well. (31) de Gennes, P. G. Adv. Colloid Interface Sci. 1987, 27, 189. (32) Fytas, G.; Anastasiadis, S. H.; Seghrouchni, R.; Vlassopoulos, D.; Li, J.; Factor, B. J.; Theobald, W.; Toprakcioglu, C. Science 1996, 274, 2041.
The fact that the range of the viscous interaction is so large makes it difficult to extract any information about the density profile from it. The decay of the spring constant κ and the static force FDC, on the other hand, are much steeper. Apparently, the elastic interactions are intrinsically short-ranged. We do not find any long-range elastic interaction between a bare glass surface and an SFM tip, either. Elastic interactions are therefore more suited to infer structural information. A comparison of the profiles of the static force FDC and spring constant κ shows that the excess effective spring constant (κ - κ∞) is not equal to the derivative of the static force ∇FDC. This equality is usually observed in a vacuum and is used as the contrast mechanism in the noncontact mode of the SFM.22 The inequality of the static force gradient and the spring constant is explained by the fact that the spring constant is measured at kilohertz frequencies, whereas the characteristic frequency for the measurement of the static force is about 1 Hz. This is an indication of viscoelastic behavior, which will be dealt with in more detail in a separate publication.22 Taking the elastic interaction (static or dynamic) as an indicator of swelling, one clearly observes that for methanol concentrations above 17%, the brush collapses. In Figure 5, we have plotted the thickness as given by the onset of the elastic interaction versus methanol content. Generally speaking, the dynamic interaction, as given by the spring constant, yields a larger thickness than the static force. Presumably, the spring constant is more sensitive to the dilute outer tails of the brush. In the swollen state the brush is expanded by a factor of about 5, with respect to the collapsed state. The reason certainly is viscoelastic dispersion which results in a situation where the kilohertz elastic modulus is higher than the static modulus. This swelling ratio is in agreement with previous experiments using neutron reflectometry,33 ellipsometry,34 and quartz resonators.35 Although one may be tempted to infer detailed structural information on the brush’s segment density profile from (33) Bunjes, N.; Habicht, J.; Prucker, O.; Paul, S.; Ru¨he, J.; Knoll W. Submitted. (34) Domack, A.; Prucker, O.; Ru¨he, J.; Johannsmann, D. Phys. Rev. A 1997, 56, 680. (35) Habicht, J.; Schmidt, M.; Ru¨he, J.; Johannsmann, D. In preparation.
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the profile of the elastic interaction as shown in Figure 4c and d, this task proved to be prohibitively difficult. The effective forces are a complicated convolution of various interactions involving different parts of the brush and the cantilever. However, the profile of viscoelastic interactions should be of interest on its own because the brush-cantilever system can be considered as a model for the dynamic interaction between a brush and a colloidal particle in its immediate environment. Presumably, the Brownian motion of that particle will be similar to the Brownian motion of the SFM tip. Conclusions We have probed the collapse of a polystyrene brush in solvents of varying quality by measuring the noise
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spectrum of a SFM cantilever suspended above it. The profiles of the elastic interactions strongly differ between swollen and collapsed brushes. The increase in the effective spring constant is much smoother for swollen brushes than for collapsed ones. The brush-cantilever system can be viewed as a model system for the dynamic interaction between a brush and a colloidal particle. Acknowledgment. We thank Volker Scheumann for technical support and acknowledge helpful discussions with Hans-Ju¨rgen Butt. LA971409D
