Steric Forces Measured with the Atomic Force Microscope at Various

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Steric Forces Measured with the Atomic Force Microscope at Various Temperatures Hans-Ju¨rgen Butt,* Michael Kappl, Henning Mueller, and Roberto Raiteri Institut fu¨ r Physikalische Chemie, Universita¨ t Mainz, 55099 Mainz, Germany

Wolfgang Meyer and Ju¨rgen Ru¨he Max-Planck-Institut fu¨ r Polymerforschung, 55099 Mainz, Germany Received October 26, 1998. In Final Form: January 8, 1999 Steric forces between polymer brushes and atomic force microscope tips were investigated. We studied two systems: polystyrene (PS) grafted to silicon in cyclohexane and poly(ethylene oxide)/poly(methacrylic acid) (PEO/PMAA) diblock copolymer adsorbed with the PMAA block to aluminum oxide in aqueous medium. On approach exponentially decaying repulsive forces were observed in both systems. With a homemade heat stage we could adjust the temperature. Increasing the temperature between 19 and 53 °C led to a linear increase of the decay length for PS in cyclohexane. Also the work required to bring the tip to a certain distance increased roughly linearly with temperature. This supports the view that the repulsion is of entropic origin. At the same time this demonstrates that the temperature dependence of surface forces could be routinely measured. For PEO in water the repulsive force was not significantly affected by a change in temperature. Approaching and retracting parts of force curves measured with PS in cyclohexane were in most cases indistinguishable. In contrast, for PEO in water a significant hysteresis was observed. This might be caused by an escape of polymers underneath the tip of the atomic force microscope. When retracting the tip in some cases the stretching of individual polymers was observed in both systems. Stretching force vs distance curves could be described by a wormlike chain model with typical persistence lengths of 1 nm.

* To whom correspondence may be addressed. E-mail: butt@ wintermute.chemie.uni-mainz.de.

are strongly bound to the surfaces9,10 or polymeric amphiphiles can be used. Examples of polymeric amphiphiles are diblock copolymers with one poorly and one strongly dissolved block.11-14 The first block adsorbes strongly to the surface while the other block extends into the solution. In the experiments described here we investigated two systems with the atomic force microscope (AFM): polystyrene (PS) in cyclohexane and poly(ethylene oxide) (PEO) in water. In the first case, PS monolayers consisting of chains covalently attached to the surfaces of silicon wafers were generated. Then we measured the force between the PS/silicon surface and a standard silicon nitride tip in cyclohexane. These measurements were done at temperatures ranging from 21 to 53 °C. With change of the temperature, the solvent was changed from a poor solvent below the Θ-temperature to a moderately good solvent at temperatures above Θ; the Θ-temperature of PS in bulk cyclohexane is 34.5 °C. Using grafted PS rather than physisorbed polymer offers the advantage that the amount of polymer on the silicon surface is constant and independent of the solvation properties of the medium. In addition, the steric force caused by PEO in aqueous medium was studied. Therefore a diblock copolymer with a long PEO block and a short poly(methacrylic acid) (PMAA) block was allowed to adsorb to an aluminum oxide substrate. In water the PMAA block is known to adsorb

(1) Patel, S. S.; Tirrel, M. Annu. Rev. Phys. Chem. 1989, 40, 597635. (2) Myers, D. Surfaces, Interfaces, and Colloids: Principles and Applications; VCH: Weinheim, 1991. (3) Klein, J. Nature 1980, 288, 248-250. (4) Klein, J.; Luckham, P. F. Macromolecules 1984, 17, 1041-1048. (5) Israelachvili, J. N.; Tirrel, M.; Klein, J.; Almog, Y. Macromolecules 1984, 17, 204-209. (6) Almog, Y.; Klein, J. J. Colloid Interface Sci. 1985, 106, 33-44. (7) Marra, J.; Hair, M. L. Macromolecules 1988, 21, 2356-2362. (8) Marra, J., Christenson, H. K. J. Phys. Chem. 1989, 93, 71807184.

(9) Roters, A.; Gelbert, M.; Schimmel, M.; Ru¨he, J.; Johannsmann, D. Phys. Rev. E 1997, 56, 3256-3264. (10) Roters, A.; Johannsmann, D. J. Phys.: Condens. Matter 1996, 8, 7561-7577. (11) Taunton, H. J.; Toprakcioglu, C.; Fetters, L. J.; Klein, J. Macromolecules 1990, 23, 571-580. (12) Hadziioannou, G.; Patel, S.; Granick, S.; Tirrell, M. J. Am. Chem. Soc. 1986, 108, 2869-2876. (13) Schillen, K.; Claesson, P. M.; Malmsten, M.; Linse, P.; Booth, C. J. Phys. Chem. B 1997, 101, 4238-4252. (14) Dai, L.; Toprakcioglu, C. Europhys. Lett. 1991, 16, 331-335.

Introduction Two solid surfaces bearing a high surface coverage of adsorbed flexible polymers repel each other as they approach in a good solvent medium. This effect is due to the osmotic repulsion between segments in the opposing layers. The use of this effect to stabilize colloids is well established.1,2 To gain insight into polymer-modified surface interaction, direct force measurements between surfaces bearing adsorbed flexible polymers have been carried out, mainly with the surface force apparatus.3-8 These experiments have provided evidence for at least three types of interactions: the osmotic repulsion in good solvents, osmotic attraction in poor solvent, and the attractive bridging effect due to polymer chains simultaneously adsorbed on both surfaces. The adsorption of the polymer to the surfaces of interest is one decisive parameter which determines the interaction. In general, homopolymers adsorb strongly in a poor solvent and little if at all in a good solvent. This makes it inherently difficult to study steric interactions in a good solvent with physisorbed homopolymers. There are two ways to get around this problem: Grafted polymers which

10.1021/la981503+ CCC: $18.00 © 1999 American Chemical Society Published on Web 03/02/1999

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strongly and practically irreversibly to aluminum oxide. In contrast, PEO is strongly solvated and adsorbs negligibly. The diblock copolymer shows an ideal amphiphile behavior. Like grafted polymers we can assume that over the time range of an experiment the amount of polymer adsorbed is constant. Another reason for choosing PEO/ PMAA diblock copolymers is their relevance to stabilize Al2O3 dispersions.15 Measured results were compared to results of calculations. For a relatively high surface coverage, de Gennes,16 based on a result of Alexander,17 calculated the force between two equal surfaces with adsorbed or grafted polymer using scaling arguments. For the force per unit area he obtained

f ≈ kBT Γ3/2

[( ) ( ) ] 2L0 D

9/4

-

D 2L0

3/4

(1) Materials and Methods

with kB being the Boltzmann constant and T the absolute temperature. Γ is the grafting or adsorption density in m-2, D is the distance between the two surfaces. L0 is the equilibrium thickness of the polymer brush. Equation 1 is valid for D/2L0 < 1. The first term comes from the osmotic pressure, which increases as the two surfaces approach each other, and the polymer concentration increases. The second term accounts for the decrease in elastic energy as the chains are compressed. In our case only one surface is coated with polymer. Assuming that neither PEO in water nor PS in cyclohexane shows a strong adsorption to the tip surface, we substitute D/L0 for D/2L0 to account for the reduced total layer thickness (as in ref 18). For 0.2 < D/L0 < 0.9 the above expression is roughly exponential and can be approximated by19,20

f ≈ 50kBT Γ3/2 e2πD/L0

local interactions should allow detection of variations in the interaction and detection of single molecule interactions.30 Recently an additional effect was discussed with respect to finite-sized objects approaching grafted polymers: the escape transition. AFM tips are so small that they interact with single or few polymer molecules. In this case part of the polymer chain might escape from under the tip. For an end-grafted fixed single chain in a Θ solvent, simple scaling theory predicts a change from F ∝ D-3 for a confined chain to F ∝ D-2 for an escaped chain.31,32 F is the force between tip and polymer-coated sample. The case of a mobile chain was considered by Subramanian et al.18 They mention that an escape might lead to a hysteresis in the force curve.33 One purpose of this study was to check whether escape transitions occurred or not.

(2)

Milner et al. derived a more complex expression based on self-consistent field approximation.21,22 This expression predicts a relatively similar force law to that of de Gennes.19 The experiments were done with an atomic force microscope (AFM) and uncoated silicon nitride tips. Using an AFM offers the advantage of being able to use various materials and to study local effects.20,23-29 “Local” means that the interacting areas are relatively small. The tips used had typical radii of curvature of 50 nm. Measuring (15) Orth, J.; Meyer, W. H.; Bellmann, C.; Wegner, G. Acta Polym. 1997, 48, 490-501. (16) de Gennes, P. G. Adv. Colloid Interface Sci. 1987, 27, 189-209. (17) Alexander, S. J. Phys. (Paris) 1977, 38, 983-987. (18) Subramanian, G.; Williams, D. R. M.; Pincus, P. A. Macromolecules 1996, 29, 4045-4050. (19) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: London, 1992; p 295. (20) O’Shea, S. J.; Welland, M. E.; Rayment, T. Langmuir 1993, 9, 1826. (21) Milner, S. T.; Witten, T. A.; Cates, M. E. Macromolecules 1988, 21, 2610-2619. (22) Milner, S. T. Europhys. Lett. 1988, 7, 695-699. (23) Lea, A. S.; Andrade, J. D.; Hlady, V. Colloids Surf., A 1994, 93, 349-357. (24) Zhang, J.; Uchida, E.; Uyama, Y.; Ikada, Y. J. Colloid Interface Sci. 1997, 188, 431-438. (25) Braithwaite, G. J. C.; Howe, A.; Luckham, P. F. Langmuir 1996, 12, 4224-4237. (26) Brown, H. G.; Hoh, J. H. Biochemistry 1997, 49, 115035-15040. (27) Chatellier, X.; Senden, T. J.; Joanny, J. F.; di Meglio, J. M. Europhys. Lett. 1998, 41, 303-308. (28) Senden, T. J.; di Meglio, J. M.; Auroy, P. Eur. Phys. J., B 1998, 3, 211-216. (29) Ortiz, et al. Submitted for publication in Macromolecules.

Polymer Synthesis and Sample Preparation. The surfaceattached polystyrene layers have been prepared following a “grafting-from” approach, where polymer molecules are grown directly at the surface of a substrate by using self-assembled monolayers of initiators. Details of the experimental procedures for the preparation have been described before.34,35 Briefly, the initiator was immobilized on silicon at room temperature under argon using anhydrous toluene as a solvent and dry triethylamine as a catalyst. The samples were kept overnight and then cleaned by extensive rinsing with methanol and chloroform. Polymerization was performed at 60 °C in a Schlenk-tube using toluene/styrene mixtures (1/2 v/v). All solutions were carefully degassed through at least three freeze-thaw cycles to remove oxygen traces. After polymerization all samples were extracted using a Soxhlet apparatus and toluene for at least 10 h to remove all nonbonded polymer material. The thickness of the polymer layers was measured by ellipsometry (Riess, Germany) to be 10 nm. In similar experiments it has been shown that by following this procedure polymers with a molecular weight of 5 × 105 g/mol and a polydispersity of about 1.5-2.0 are attached to the surfaces. The poly(ethylene oxide)/poly(methyacrylic acid) block copolymer was synthesized as described in ref 15. For the experiments we used block copolymers with an average of 6 MAA groups and 21 EO groups. Aluminum oxide samples were prepared by evaporating ≈10 nm of aluminum onto microscope cover glasses. After the samples were exposed to air, the aluminum oxidized. Adsorption of the diblock copolymer was allowed for at least 1 h. Atomic Force Microscopy. All measurements were done with a commercial AFM (Nanoscope 3, Digital Instruments, California) using standard V-shaped silicon nitride cantilevers of different stiffness and tip sharpness (Olympus sharpened tips, 100 µm length, 0.4 µm thickness, with a calculated spring constant of 0.09 N/m, Digital Instruments, Nanoprobes, 100 µm and 200 µm length, 0.6 µm thickness, with calculated spring constants of 0.05-0.29 N/m). The scanner was calibrated as described in ref 36. Force Measurements. In a force measurement the sample, which is mounted on the piezoelectric scanner, is moved continuously up and down. Deflection of the cantilever and height position of the sample are recorded. The force is obtained by multiplying the deflection of the cantilever, Dcant, with its spring constant. To obtain force-versus-distance curves, the original deflection-versus-position curves had to be converted by D ) Dscanner - Dcant. D is the distance between tip and sample surface, (30) Li, H. B.; Rief, M.; Oesterhelt, F.; Gaub, H. E. Adv. Mater. 1998, 10, 316-319. (31) Guffond, M. C.; Williams, D. R. M.; Sevick, E. M. Langmuir 1997, 12, 5691-5696. (32) Jimenez, J.; Rajagopalan, R. Langmuir 1998, 14, 2598-2601. (33) Subramanian, G.; Williams, D. R. M.; Pincus, P. A. Europhys. Lett. 1995, 29, 285-290. (34) Prucker, O.; Ru¨he, J. Macromolecules 1998, 31, 592-601. (35) Prucker, O.; Ru¨he, J. Macromolecules 1998, 31, 602-613. (36) Jaschke, M.; Butt, H.-J. Rev. Sci. Instrum. 1995, 66, 12581259.

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Figure 2. Abbreviations used to calculate the force from the force per unit area considering explicitly the tip shape. Figure 1. Schematic of the heat stage placed on top of the AFM scanner. The temperature could be increased by an electric current through a resistor heat plate. Dscanner is the piezo scanner position. The point of zero distance was determined from the linear part of the contact line. Forceversus-scanner position curves were continuously taken with a frequency of typically one per second. Temperature Control. The temperature was varied by a heat stage mounted on top of the scanner (Figure 1). The heat stage consisted of a resistance heating foil directly underneath the sample to allow for efficient heating. Electric current was provided by a set of batteries. A 1 mm thick spacer provided heat isolation to the piezoelectric scanner of the AFM. The temperature was monitored by a bimetal thermometer in the liquid cell on the sample surface. We estimate the error of the temperature to be 1-2 °C. Data Analysis. Repulsive forces measured during the approach and partly during the retraction were fitted with different functions. Equation 2 gives the force per unit area f between two parallel surfaces, one being coated with a polymer. To account for the tip shape, we approximate the total force by integrating f over the whole tip surface. For a rotational symmetric tip the cross-sectional areas over which to integrate are 2πr dr, with r being the radius of the tip at a given distance z from the surface (Figure 2). The total force on the tip is

F ≈ 2π

dr dz ∫ f r dr ) 2π ∫ f(z) r dz ∞

∞

0

D

(3)

The tip shape at the end is roughly parabolic.37 It can be described by z - D ) r2/2R. R is the radius of a sphere inscribed at the end of the tip with the same radius of curvature. It follows that dr/dz ) R/r. Inserting this and eq 2 into eq 3, we obtain

F ≈ 100πkBTR Γ3/2

∫e

∞ -2πz/L 0

D

dz ) 50kBTRL0 Γ3/2 e2πD/L0 (4)

To test if measured force curves decayed as predicted, they were fitted with an exponentially decaying function

F ) A e-D/λ

(5)

or with two exponentials. The amplitude A and the decay length λ were the fitting parameters. In addition, repulsive forces were fitted with a function predicted by Guffond et al., who calculated the force between a grafted polymer chain and a finite-sized flat obstacle in a Θ (37) Siedle, P.; Butt, H.-J.; Bamberg, E.; Wang, D. N.; Ku¨hlbrandt, W.; Zach, J.; Haider, M. Inst. Phys. Conf. Ser. 1993, 130, 361-364.

solvent.31 To test if the observed force showed the typical behavior of a confined chain, we fitted with a third power decay law

F)

(

)

P1 D - D0

3

(6)

An escaping chain is supposed to show a quadratic decay

F)

(

)

P1 D - D0

2

(7)

D0 accounts for a possible offset in determining the zero distance. P1 and D0 were the fitting parameters. Also a sum of eqs 6 and 7 was used to fit the approaching parts of force curves.

Results and Discussion A typical force curve measured on bare silicon in cyclohexane is shown in Figure 3. At distances larger than ≈4 nm, no force was observed. At closer distance, the tip was attracted, and at typically 1-2 nm, it jumped onto the sample. We attribute the attraction to van der Waals forces. When retracting the tip again after contact, it had to be pulled off of the sample with adhesion forces usually below 0.2 nN. Polystyrene in Cyclohexane. During the approach the force between polystyrene grafted to silicon and a silicon nitride tip was repulsive (Figure 3). The repulsion could usually be fitted with one exponentially decaying function as given by eq 5. At 21 °C the decay length λ was 20 nm. An amplitude A of roughly 1.5 nN was measured. With λ ) L0/2π ) 20 nm, an amplitude of 1.5 nN, and an estimated radius of curvature of R ) 50 nm, a grafting density of Γ ≈ 1.1 × 1016 m-2 is calculated with eq 4. This corresponds to a typical distance between grafting sites of 9 nm. From the polymerization time we estimate a grafting density of 6 × 1016 m-2, which corresponds to a mean distance between grafting sites of 4 nm.34,38 Considering the uncertainty in determining the tip radius (about a factor of 2), the inaccuracy of the spring constant of the cantilever (again a factor of 2), and the rough approximations which lead to eq 4, the two values agree. In a few cases an additional short-range component was required, and we had to use two exponentials to fit the repulsive force. At 21 °C the decay length of the shortrange component was 3.0 nm. Even then, the amplitude (38) Habicht, J.; Schmidt, M.; Ru¨he, J.; Johannsmann, D. Submitted.

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cated an escape transition of the polymer underneath the AFM tip, as was proposed by refs 31-33. One reason might be the relatively high grafting density. At such a high grafting density a polymer might not be able to escape because the space is already occupied by neighboring polymers. When the tip was retracted, usually completely reversible and hence repulsive forces curves were observed (Figure 3a). In some cases a hysteresis was observed between approach and retraction. In about 15% of the force curves, attractive peaks were detected when retracting the tip (Figure 3b). Such adhesion peaks were also observed by Courvoisier et al.39 and Senden et al.28 They can probably be attributed to a bridging effect of individual polymers. Part of the polystyrene adsorbes to the silicon nitride surface of the tip. To stretch and finally detach the polystyrene again, a certain force is necessary. To analyze these events quantitatively, we compared measured stretching force-versus-distance curves of what we think were traces of individual polymers with the result of two models: the wormlike chain (WLC) model and the freely jointed chain (FJC) model. In the WLC model, also known as the Porod-Kratky chain model,40,41 the entropic elasticity of a wormlike chain with continuous curvature is considered. The direction of curvature at any point of the trajectory is random. The force required to stretch a WLC in a solvent to a length D is given by42,43

Fst(D) ) Figure 3. Force curve measured between polystyrene grafted to silicon and silicon nitride AFM tip in cyclohexane at the Θ-temperature of 35 and at 52.5 °C. Usually approach and retraction showed an exponentially decaying repulsive force (a). For comparison a force curve measured on bare silicon in cyclohexane at 24 °C is shown. In about 15% of the force curves, adhesion peaks were observed when retracting the tip (b).

of the additional short-range component was small compared to the amplitude of the long-range component. The occasional appearance of two exponentials should not be overinterpreted. There could be several trivial reasons. First, eq 2 is strictly valid for 0.2 < D/L0 < 0.9. We fitted over a significantly larger range. Second, the additional exponential might have been necessary to account for the polydispersity of the grafted polymer and/or a heterogeneity due to variations of the layer thickness at different locations. The repulsive force could also be fitted with eqs 6 and 7. Then, however, unrealistically high distance offsets, D0, of 60-110 and 40-60 nm were obtained, respectively. At this point we would like to remind that with the AFM the zero distance cannot be measured independently. Zero distance is deduced from the linear part of the force-versusposition curve. It could well be that zero distance is assigned to a position above the silicon surface. If at a certain position the polymer brush is compressed so much by the tip that an additional increase of the force does not lead to a further compression, this position would be taken as zero distance. Hence, a certain offset was expected. We did, however, not expect such a high offset. An offset of 60 nm would imply that a practically incompressible polymer layer of 60 nm thickness existed on the silicon. This is in complete contrast to ellipsometric results. In conclusion we think that eqs 6 or 7 do not adequately describe the force observed. We always observed continuous, monotonically increasing repulsive forces during the approach. Nothing indi-

[

]

kBT D 1 1 + b L 4(1 - D/L)2 4

(8)

where b denotes the persistence length and L the contour length of the polymer. The formula is an approximate interpolation. For D , L it becomes Fst(D) ) 3kBTD/2bL. For forces beyond kBT/b, it converges to the expression Fst(D) ) kBT/(4b(1 - D/L)2).42 Reference 44 contains a more refined treatment. The WLC model was already successfully applied to analyze the stretching of DNA,43,45 polysaccharides,46 poly(dimethylsiloxane) in heptane,28 and the protein titin.47 The FJC model treats the polymer as a chain of statistically independent segments of length l whose orientations are uncorrelated in the absence of external forces.48 The force needed to stretch a FJC to a length D is given by (ref 41, p 320)

Fst )

kB T L l

(DL)

-1

(9)

L -1 is the inverse Langevin function. We approximated it by the first four terms of its series: (39) Courvoisier, A.; Isel, F.; Francois, J.; Maaloum, M. Langmuir 1998, 14, 3727-3729. (40) Kratky, O.; Porod, G. Recl. Trav. Chim. Pays-Bas 1949, 68, 1106. (41) Flory, P. J. Statistical Mechanics of Chain Molecules; Hanser: Mu¨nchen, 1989; p 401. (42) Marko, J. F.; Siggia, E. D. Macromolecules 1995, 28, 87598770. (43) Bustamante, C.; Marko, J. F.; Siggia, E. D.; Smith, S. Science 1994, 265, 1599-1600. (44) Kovac, J.; Crabb, C. Macromolecules 1982, 15, 537-541. (45) Baumann, C. G.; Smith, S. B.; Bloomfield, V. A.; Bustamante, C. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 6185-6190. (46) Rief, M.; Oesterheld, F.; Heymann, B.; Gaub, H. E. Science 1997, 275, 1295-1297. (47) Rief, M.; Gautel, M.; Oesterheld, F.; Fernandez, J. M.; Gaub, H. E. Science 1997, 276, 1109-1112. (48) Kuhn, W.; Gru¨n, F. Kolloid Z. 1942, 101, 248-271.

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Fst )

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kBT D 9 D 3 297 D 5 1539 D 3 + + + l L 5L 175 L 875 L

[

()

()

7

( )]

(10)

For a discussion see refs 49 and 50. The first two terms of expressions 8 and 10 are equal assuming that 2b ) l. Adhesion peaks could be fitted with the WLC model and with the FJC model (Figure 3b). However, when fitting with the FJC model, the calculated contour lengths were often lower than the distance of detachment. Otherwise the steep increase of the force at large distances was not reproduced. Since the contour length cannot be shorter than the detachment distance, we do not further consider results obtained with the FJC model. With the WLC model we obtained a persistence length of b ) 11 ( 5 Å and a contour length of L ) 490 ( 170 nm. The maximal stretching of the polymer chains reached just before detachment was 86 ( 2% of the contour length. The errors given are the errors of a single measurement not of the mean. This is to indicate typical fluctuations from force curve to force curve. The error of L is probably a consequence of the polydispersity and the fact that in stretching experiments we select long molecules. The magnitude of the persistence length agrees with values from the literature. Its accuracy is limited by the resolution with which the spring constant of the cantilever is known. In our case this could be a factor of 2. With the homemade heat stage we could adjust the temperature between room temperature and roughly 55 °C. The tip had to be withdrawn during an increase of the temperature. About 3 min after a temperature change, force curves or images could again be taken. In a typical experiment we started at room temperature, went up to high temperatures, and back to room temperature in steps of 5-10 °C. This cycle was usually repeated. When the temperature was increased, the decay lengths increased roughly linearly (Figure 4). At 52.5 °C the mean decay length was for instance 61 nm (and 8.5 nm for the short-range component). When an expansion coefficient as was defined as R ) λ(T)/λ(Θ), experimental values of dR/dT for the long decay-length were 0.03-0.04 K-1. This is three to four times larger than values measured by Webber et al. for adsorbed layers of poly(2-vinylpyridine)/ polystyrene diblock copolymers.51 The temperature-dependent swelling of surface-attached PS brushes has been studied by Bunjes using neutron reflectometry,52 by Domack et al. using quartz resonators,53 and by Habicht et al.38 using total internal reflectance ellipsometry (TIRE). In all cases it was found that the thickness of the PS brush in cyclohexane increases monotonically with increasing temperature between 10 and 70 °C. The behavior of the surface-attached chains differs strongly from the behavior of unattached PS chains in cyclohexane solution, which show a discontinuity of the radius of gyration at 34.5 °C, which is the Θ-temperature of PS in cyclohexane. This behavior has been explained by the fact that the polymer concentration perpendicular to the surface is not constant but that it decreases with increasing distance from the surface. Since the Θ-temperature depends strongly on the concentration, different layers in the brush have different “Θ-temperatures” and no discontinuous collapse occurs. A relevant quantity is the work required to penetrate the polymer layer. For the tip to penetrate the polymer (49) Fixman, M.; Kovac, J. J. Chem. Phys. 1973, 58, 1564-1568. (50) Smith, S. B.; Finzi, L.; Bustamante, C. Science 1992, 258, 11221126. (51) Webber, R. M.; van der Linden, C. C.; Anderson, J. L. Langmuir 1996, 12, 1040-1046. (52) Bunjes, N. Ph.D. Thesis, Mainz, 1998. (53) Domack, A.; Prucker, O.; Ru¨he, J.; Johannsmann, D. Phys. Rev. E 1997, 56, 680-689.

Figure 4. Temperature dependence of the two decay lengths measured on polystyrene grafted to silicon in cyclohexane. Usually only the long-range component was observed. Different symbols correspond to different experiments. Each point represents the average decay length of typically 20 force curves. In each experiment the temperature range was covered in both directions. The straight line is a linear fit to the dominating long-range component; the dashed line is a linear fit to the short-range component.

layer from an infinitely large distance to a distance D0, the work

W)

D D F(D) dD ) ∫D)∞A e-D/λ dD ) A λ e-D /λ ∫D)∞ 0

0

0

(10)

is required. Though the amplitude A varied by a factor 2-3 from experiment, to experiment no systematic change of A with temperature was observed. Hence, a possible temperature dependence is enclosed in the expression λ e-D0/λ. Assuming that the tip comes relatively close to the silicon surface (D0 , λ), we can write the exponential function in a series of D0/λ and neglect all terms higher than the linear term. The expression then becomes λ(1 D0/λ) ) λ - D0. Since λ increased roughly linearly with temperature, W does so too. This roughly linear increase of W with temperature indicates that the steric force caused by PS in cyclohexane is of entropic origin. Our experiments were done at constant temperature and pressure. Hence, the work done is equal to the change in Gibbs free energy: W ) ∆G ) G(D0) - G(∞). G(D0) is the Gibbs free energy of the compressed polymer brush when the tip is at a distance D0. G(∞) is the Gibbs free energy of the relaxed polymer brush when the tip is far away from the surface. Such a thermodynamic treatment with state functions is legitimated by the fact that in most cases completely reversible force curves were observed. The change in Gibbs energy can be expressed by the change in enthalpy and a change in entropy: ∆G ) ∆H - T∆S. ∆H ) H(D0) - H(∞) and ∆S ) S(D0) - S(∞) are the differences in enthalpy and entropy between the relaxed and the compressed polymer brush. As a first approximation we assume that ∆H and ∆S are independent of temperature. Then, since a strong linear dependence on T was observed, it follows that the entropic term dominates over the enthalpic contribution: |∆H| , |T∆S|. It should be kept in mind that this is only an indication, not proof. That the simplest thermodynamic model of constant ∆H and ∆S describes the results does not exclude

2564 Langmuir, Vol. 15, No. 7, 1999

Figure 5. Force curve between an aluminum oxide surface and a silicon nitride tip in aqueous medium with 50 mM KCl at 25 °C before and after adding 0.75 wt % of PEO/PMAA diblock copolymer (a). Often adhesion peaks were observed when the tip was retracted (b).

that other more complicated models also agree with the experimental results. PEO/PMAA Block Copolymers on Aluminum Oxide in Aqueous Medium. Force curves taken on a bare aluminum oxide sample showed an attractive force starting at distances of 4 nm (Figure 5). It is probably the van der Waals force. In the retracting force curve, a relatively strong adhesion force was observed. The adhesion force was so strong that the deflection signal was in the offset. To determine the adhesion force, we multiplied the jump-out distance with the spring constant of the cantilever. The adhesion force was typically 1-3 nN. After PEO/PMAA diblock copolymer was added, the force changed completely. Approaching force curves between a PEO polymer layer adsorbed via a PMAA block to aluminum oxide and a silicon nitride tip in aqueous medium showed a monotonically decaying repulsive force. This behavior was remarkably stable. It was observed even on aluminum oxide having been exposed to normal atmosphere and without cleaning for several weeks. After addition of PEO/PMAA, we always observed the repulsion. In contrast, the force observed on “bare” aluminum oxide varied drastically and depended on age and possible pretreatments such as plasma cleaning or rinsing. The repulsive force usually had to be described by two exponentially decaying components. At 25 °C the mean decay lengths were 3.4 and 11.2 nm for the short- and long-range component, respectively. The short-range component had a two to three times higher amplitude. Approaching parts of force curves were always smoothly and monotonically decaying with distance. We never observed discontinuous changes, which could have indicated an escape transition.31-33 As with PS in cyclohexane the repulsion could also be fitted with eqs 6 and 7. However, we again obtained unrealistically large offset distances of typically 7 and 4 nm, respectively.

Butt et al.

Figure 6. Temperature dependence of the two decay lengths measured between PEO adsorbed via a PMAA block to aluminum oxide and an AFM tip in aqueous medium containing 50 mM KCl. Different symbols correspond to different experiments. The continuous line represents the dominating shortrange decay length; dashed lines stand for the long-range decay length. Each point represents the average decay length of typically 20 force curves.

On retraction, the tip a hysteresis was observed. In some cases the hysteresis was small (Figure 5a), usually it was relatively strong (Figure 5b). Such a hysteresis was observed before with the AFM for PEO adsorbed to glass.25 The two main differences between the results obtained with PEO/PMAA and PS, namely, the fact that two rather than one exponential had to be used and the hysteresis between approach and retraction might be caused by the different attachment to the substrate. PS, being covalently bound to the silicon, was laterally immobile (solid brush). In contrast, the physisorbed PEO/PMAA diblock copolymers on aluminum oxide might diffuse on the surface (liquid brush). The amount adsorbed is constant, the individual molecules might, however, be shifted laterally under the influence of the tip. In this sense our results support the view of Subramanian et al. of an escape transition occurring in liquid brushes.18,33 Often adhesion peaks were visible in the retracting parts of force curves. These adhesion peaks were probably caused by the stretching and subsequent desorption of individual PEO chains. Hence, they represent a bridging of individual polymer chains. Good fits were obtained with the WLC model. Again the FJC model did not give good fits when keeping the contour length below the distance of detachment. A persistence length of 10 ( 4 Å and a contour length of 46 ( 15 nm were measured. Just before detachment, the polymer was stretched to 85 ( 5% of its contour length. The errors given are again the errors of a single measurement, not of the mean. The measured contour length is much higher than the contour length calculated from the mean number of monomers of the PEO chain. With 21 monomers we expected a contour length of 8.9 nm. However, 21 monomers is only the mean chain length. Due to the polydispersity of 1.3 there are also longer polymers. With the experiment, we select long molecules since the last molecules detaching when retracting the tip are the longest ones and only these events are recognized as single molecule stretching processes.

Steric Force Measurements

Langmuir, Vol. 15, No. 7, 1999 2565

We could observe no significant temperature dependence of the PEO/water system in the temperature range from 19 to 52.5 °C (Figure 6).This was expected. It is wellknown that free PEO in aqueous solution does not change its radius of gyration in the considered temperature range. Results obtained with the adsorbed block copolymers were significantly less reproducible than results obtained with grafted polymers. This can also be seen by the wide scattering of results obtained with the PEO/water system in comparison with the PS/cyclohexane experiments. In two experiments for instance we found a long-range decay length of ≈10 nm, in two other experiments the longrange component decayed with ≈20 nm, and in a fifth experiment no long-range component at all was found. The reason might be that the diblock copolymers can move laterally and assume a different position on the aluminum oxide surface under the influence of the tip. We also tried to measure the force with an AFM tip coated with aluminum oxide and adsorbed PEO/PMAA block copolymer. These experiments were, however, not reliable enough. Often we observed that the aluminum oxide coating had come off the cantilever and presumably the tip during the experiment. We have no explanation for this effect. Summary A schematic force curve of the interaction between the AFM tip and a polymer brush in a relatively good solvent is shown in Figure 7. The schematic summarizes the characteristic features observed. At large distances D the tip is not in contact with the brush. No force F acts between tip and sample, and the cantilever is not deflected (A). On approach the tip starts to compress the brush, which leads to a repulsive force (B). The repulsion can usually be described by an exponential function. At a certain point the tip is practically in contact (C). An additional increase of the force does not lead to a further decrease in distance. On retraction in some cases completely reversible force curves were observed. This was usually the case for PS covalently bound to silicon in cyclohexane. In other cases a more or less pronounced difference existed between

Figure 7. Schematic force curve which summarizes the features observed.

approach and retraction (D). Such a hysteresis was typical for PEO/PMAA diblock copolymers adsorbed to aluminum oxide. In some cases the stretching of individual polymer bridges was observed. In the schematic at point (E) two polymer chains are adsorbed to the tip. The force is dominated by the shorter one. After detachment of the shorter chain, the stretching of an individual polymer is observed (E). This stretching could be described by the WLC model. Acknowledgment. We acknowledge financial support of the Deutsche Forschungsgemeinschaft (H.M.) and the European Community (TMR for R.R.). LA981503+