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Transition from Mushroom to Brush during Formation of a Tethered Layer Heqing Huang, Stephen E. Rankin, and Lynn S. Penn* Department of Chemical and Materials Engineering, University of Kentucky, Lexington, Kentucky 40506-0046
Roderic P. Quirk and Tae Hee Cheong Department of Polymer Science, University of Akron, Akron, Ohio 44325-3909 Received November 19, 2003. In Final Form: April 20, 2004 Tethering of monodisperse, chain-end-functionalized polymer from dilute solution to a solid surface shows three regimes of kinetics. This paper presents support for the hypothesis that the experimentally observed third regime is indeed the transition from mushroom to brush and that it occurs in a spatially nonuniform manner. Both time-step snapshots generated by a Monte Carlo simulation of the tethering process and atomic force microscopy images of actual surfaces during the process show that the third regime is characterized by nonuniform surface texture, while the surface texture is uniform prior to and after the third regime.
I. Introduction Recently, work in our laboratory has been focused on the kinetics of tethering of monodisperse, end-functionalized polymer chains from dilute solution to the surface of an impenetrable solid to form polymer brushes.1-4 In this work, the tethering was accomplished by formation of a chemical bond between the amine end-functional group of each chain and an epoxide reactive site previously introduced to the surface of the solid. Figure 1 shows the reaction between chain and surface, which proceeds readily and irreversibly. The experimental systems that have been the focus of our attention, that is, those in which the polymer chains are monodisperse, the tethering mechanism is irreversible, and segmental adsorption to the substrate does not take place, all have exhibited three distinct regimes of kinetics. These three regimes have been observed for numerous molecular weights, in diverse solvents, at several (dilute) concentrations, and at different temperatures. The observation of three regimes is notable because only two regimes had been predicted previously by theory. According to previous theory, the tethering process in good solvent would exhibit only two stages.5-7 The first stage, or regime, would be one of fast tethering, in which the rate would be controlled by center-of-mass diffusion of the polymer chains through the solvent to the bare * To whom correspondence should be addressed. Address: Prof. L. S. Penn, Department of Chemical and Materials Engineering, 177 Anderson Hall, University of Kentucky, Lexington, KY 40506-0046. Phone: 859-257-7897. Fax: 859-323-1929. E-mail:
[email protected]. (1) Penn, L. S.; Hunter, T. F.; Lee, Y.; Quirk, R. P. Macromolecules 2000, 33, 1105-1107. (2) Penn, L. S.; Hunter, T. F.; Quirk, R. P.; Lee, Y. Macromolecules 2002, 35, 2859-2860. (3) Penn, L. S.; Huang, H.; Sindkhedkar, M.; Rankin, S. E.; Chittenden, K.; Quirk, R. P.; Mathers, R. T.; Lee, Y. Macromolecules 2002, 35, 7054-7066. (4) Huang, H.; Penn, L. S.; Quirk, R. P.; Cheong, T. H. Macromolecules 2004, 37, 516-523. (5) Ligoure, C.; Leibler, L. J. Phys. France 1990, 51, 1313-1328. (6) Hasegawa, R.; Doi, M. Macromolecules 1997, 30, 5490-5493. (7) Zajac, R.; Chakrabarti, A. Phys. Rev. E 1994, 49, 3069-3078.
Figure 1. Chemical reaction between chain-end-functionalized polystyrene (PS-NH2) and an active site on the surface of the substrate.
surface. The second stage, or regime, would be one of slow tethering, in which the rate would be controlled by diffusion of free chains through the already tethered layer to reach the surface. Tethering in the second regime would proceed at a progressively slower and slower rate, that is, proportional to ln(time), because of the progressive increase in the energy barrier with increase in number of tethered chains per unit area of substrate. This slow tethering would be expected to continue to saturation, that is, a natural stopping point at which the energy benefit of chemical reaction of chain ends with the surface would be offset by the entropy cost of chain stretching.5,8 According to theory, the first regime above corresponds to formation of a mushroom layer, that is, a layer of nonoverlapping, relaxed polymer coils of the same dimensions as free chains in solution with spaces between them not large enough to accept another chain without overlap.5 Theory describes the second regime as corresponding to the gradual formation of a brush as the increasing surface attachment forces the tethered chains gradually to stretch away from the underlying surface to avoid overlap.5 The tethering process observed experimentally in our laboratory at first followed the scenario described above and then diverged from it. Typical examples of the threeregime kinetics displayed by the systems studied in our laboratory are shown in Figure 2a,b. The first regime, in which chains were being tethered to the bare surface, (8) Milner, S. T. Europhys. Lett. 1988, 7, 695-699.
10.1021/la030422x CCC: $27.50 © 2004 American Chemical Society Published on Web 05/29/2004
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in the second. This observed diminution of the rate of increase in the energy barrier suggests a change from the uniform process of the second regime, associated with addition of chains to the surface in a spatially random fashion, to a nonuniform process in the third regime, associated with the addition of chains to the surface at preferred locations, where the energy barrier to diffusion through the layer is lower than it would be in a random process. This line of reasoning, coupled with the experimental observation that the surface attachment density increased only a small amount in the second regime but nearly doubled in the third regime, led us to make the hypothesis that the transition from mushroom to brush takes place mainly in the third regime and that it occurs in a spatially nonuniform manner. The purpose of the present paper is to explore that hypothesis in greater detail. To do this, we used a previously developed simulation method to focus on the events of the third regime and to generate images of the evolving surface texture during this regime. We also obtained atomic force microscopy images of the surfaces of the actual tethered layers in the third regime. II. Experimental Methods
Figure 2. Typical profile for the kinetics of tethering of monodisperse, chain-end-functionalized polymers. Surface attachment density is plotted versus time for tethering of monodisperse, amine-ended polystyrene, (a) Mn ) 15 000 g/mol and (b) Mn ) 44 000 g/mol, from toluene to epoxide-derivatized silicate glass. The x-axis for the first regime is linear, while for the remainder it is logarithmic. For each molecular weight, twin reactions were conducted side by side to check for reproducibility; the squares are for one twin, and the circles are for the other.
corresponded to the fast, first regime predicted by theory. After the formation of the mushroom layer, there was an abrupt slowdown in rate, and tethering in the second regime proceeded proportionally to log(time), also as predicted by theory. (Note the change in the x-axis from linear to logarithmic at about 60 min in Figure 2.) Divergence of experiment from theory came in the second regime, which, instead of continuing smoothly to saturation as predicted by theory, was interrupted by a relative acceleration in tethering rate. This “accelerated” tethering was also proportional to log(time), but with a steeper slope; the distinct change in slope established the accelerated tethering as a third regime, different from the second. In Figure 2, it can be seen that it was the third regime rather than the second that led to saturation. The final result for the experimental systems was a brush, as evaluated by the commonly used criterion that the average distance between chain attachment points is less than twice the radius of gyration of the relaxed chain.1,3,4 We interpret the third regime by examining the implications of the relative increase in slope observed from the second to the third regime. The increase in slope means that the incremental increases in the energy barrier to diffusion are not as large in the third regime as they were
Monodisperse, primary-amine-end-functionalized polystyrene of Mn ) 15 000 g/ mol and Mn ) 44 000 g/mol for use in tethering reactions was synthesized by means of living anionic polymerization methods9-12 described in detail in a previous publication.3 The kinetics data for tethering of these two molecular weights were generated from full-scale tethering reactions conducted on epoxidederivatized silicate glass beads. These data were already shown in Figure 2 in the Introduction. The details of tethering reactions and the real-time, quantitative analysis procedure used to monitor the kinetics of tethering were described previously.1,3,4 For atomic force microscopy (AFM), it was necessary to form tethered layers on flat substrates instead of beads. Flat, silicate glass substrates were available in the form of 15-mm-diameter silicate glass disks (Ted Pella, Inc., Redding, CA) manufactured especially for AFM applications. Prior to their use in tethering reactions, the disks had to be chemically derivatized with epoxide groups in the same way the beads were derivatized with epoxide groups.3 To circumvent their tendency to stick face-toface to each other in the reaction vessel, the disks were derivatized individually in 18-mm-diameter test tubes. Each tube was topped with a rubber septum and was connected to a line of inert gas, so derivatization could be conducted under the same anhydrous conditions as were used for the beads. Derivatization was effected by exposure of each disk to a toluene solution of glycidyl propyl trimethoxy silane, after which any nonchemically bonded silane was removed from the surface of each disk by extraction with toluene in a Soxhlet apparatus. The smoothness and uniformity of the derivatized disks were verified by means of AFM. Next, the epoxide-derivatized disks were subjected to tethering reactions, again in their own individual test tubes. Six disks were reacted with amine-ended polystyrene of Mn ) 15 000 g/mol, and six disks were reacted (9) Quirk, R. P.; Chen, W.-C. Makromol. Chem. 1982, 183, 20712076. (10) Morton, M.; Fetters, L. J. Rubber Chem. Technol. 1975, 48, 359365. (11) Quirk, R. P. In Comprehensive Polymer Science; Agarwal, S. L., Russo, S., Eds.; Pergamon Press: Oxford, 1992; First Supplement, pp 83-106. (12) Quirk, R. P.; Lee, Y. Macromol. Symp. 2000, 157, 161-169.
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with amine-ended polystyrene of Mn ) 44 000 g/mol. In all cases, the amine-ended polystyrene was present as 3 mL of toluene solution (0.255 mg/mL), and reactions were conducted under argon at room temperature. The use of six disks for each molecular weight allowed us to interrupt the tethering process and capture the tethered layer at different points in the process. Immediately upon removal from its test tube, each disk was subjected to extraction with toluene in a Soxhlet apparatus to remove any nontethered polymer chains left on the surface by draining. Because the small scale of the tethering reactions in the test tubes precluded direct monitoring of the kinetics by quantitative analysis, we had to use the detailed kinetics profiles obtained previously on larger scale tethering reactions as guides for the timing of removal of each of the six disks from the tethering reaction. Atomic force microscopy of surfaces containing tethered chains was conducted with a Nanoscope IIIa (Veeco Instruments, Inc., Santa Barbara, CA). The surfaces of the disks were imaged in air in tapping mode with Olympus Tapping Mode etched silicon probes (Veeco). The single-beam cantilever on the probe was 160 µm long with a nominal spring constant of 42 N/m. The resonant frequency of the cantilever on the probe ranged from 200 to 400 kHz. The surface area included in each AFM image was 1 µm × 1 µm. Scan rates were between 0.5 and 1.0 Hz. Four images were obtained from separate locations on each glass disk to evaluate the reproducibility. III. The Simulation The Monte Carlo simulation method used was based on a random sequential deposition model13-17 in which hemispheres, all of equal radii, represented the monodisperse population of polymer chains to be tethered. As described in a previous publication,3 the hemispheres were allowed to deposit at random, flat side down, on the smooth, horizontal surface of a substrate. Mutual interactions between an incoming hemisphere and already deposited hemispheres were included in the model as deformation to eliminate overlap. These interactions were not important in the beginning of the process, when no overlap occurred, but became important later in the process, when incoming hemispheres always overlapped the hemispheres on the crowded surface to some extent. Following a precedent set by others,18 we stipulated conservation of volume for the hemispheres, so that those forced to contract laterally to eliminate overlap would also extend vertically,18,19 becoming cylinders topped by hemispherical caps. A Monte Carlo simulation of this sequential deposition model was conducted, with the overall probability of depositing an additional hemisphere within a Monte Carlo time-step being dependent on two particular probabilities. One probability was related to, and diminished with, the area of overlap between an incoming hemisphere and the hemispheres already deposited on the surface below it. The other probability was related to the energy required to accomplish the deformation described above that (13) Hinrichsen, E. L.; Feder, J.; Jossang, T. Geometry of Random Sequential Adsorption; Report No. 85-22; Institute of Physics, University of Oslo: Oslo, Norway, 1985. (14) Evans, J. W. Rev. Mod. Phys. 1993, 65, 1281-1329. (15) Zhdanov, V. P.; Kasemo, B. J. Chem. Phys. 1998, 109, 64976501. (16) Talbot, J.; Tarjus, G.; Van Tassel, P. R.; Viot, P. Colloids Surf., A 2000 165, 287-324. (17) Kopf, A.; Baschnagel, J.; Wittmer, J.; Binder, K. Macromolecules 1996, 29, 1433-1441. (18) Douglas, J. F.; Schneider, H. M.; Frantz, P.; Lipman, R.; Granick, S. J. Phys.: Condens. Matter 1997, 9, 7699-7718. (19) Tonelli, A. E. Comput. Polym. Sci. 1991, 1, 22-29.
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eliminated overlap between incoming and already deposited hemispheres. Each Monte Carlo step was an attempted addition of a hemisphere to the surface of the substrate. The addition of the incoming hemisphere to the surface was accepted according to the Metropolis criterion for Monte Carlo simulations.20 IV. Results and Discussion In the Introduction, we presented our hypothesis that the transition from mushroom to brush occurs mainly in the third regime and that the transition should be spatially nonuniform. Here we present two kinds of supporting data for this hypothesis: first, time-step snapshots produced by the computer simulation, and second, AFM images of the surface texture of experimental tethered layers. The Monte Carlo simulation, like the experiments, showed three regimes of kinetics rather than two.3 The results of the simulation were described in detail in ref 3 but are briefly recapitulated here for convenience. The first regime was one in which hemispheres deposited randomly and without overlap on the bare surface. Thus the first regime corresponded to the construction of the mushroom layer, for which the surface coverage is high enough so that none of the open spaces between hemispheres are large enough to accommodate an additional hemisphere without overlap. The first regime was followed by the second regime in which deposition was accompanied by small mutual deformations to eliminate the small overlap between incoming and already deposited hemispheres. In the second regime, as in the first, hemispheres continued to be deposited at random locations. However, the increase in the surface density of the hemispheres in the second regime was only a small fraction of the total amount. Then, suddenly, the third regime appeared, in which hemispheres began to deposit more frequently than in the second regime and preferentially at sites of slightly higher density, creating clusters of laterally contracted, vertically extended hemispheres that had the appearance of spikelike islands rising from the sea. Subsequent deposition of hemispheres took place at the periphery of these islands, causing them to broaden and merge into each other until the whole substrate was covered with vertically extended (strongly stretched) hemispheres. In the present work, we used the Monte Carlo simulation again to generate additional images of the surface at several preselected points in the tethering process. The new images, in the form of time-step snapshots, are shown in Figure 3a-e. These images show the evolution of surface texture of the tethered layer before, during, and after the transition from mushroom to brush. Snapshot a typifies the surface texture of the fully formed mushroom layer. The surface texture shown for the completed mushroom layer persists and is stable throughout the second regime. This stability of texture is perhaps not surprising, because the surface density of hemispheres increases so little during the second regime; even by the end of second regime, the layer is only a slightly more crowded mushroom layer. Snapshots b-d depict the evolution of surface texture during the third regime, where the hemispheres deposit rapidly and the nonuniform texture emerges. In snapshot b, the beginning of the third regime, spikes of vertically extended hemispheres have started to appear. In snapshot c, the middle of the third regime, the spikelike islands are increasing in number and in size. In snapshot d, late in the third regime, the islands of vertically extended hemispheres have broadened, so that they are nearly (20) Metropolis, N.; Rosenbluth, N. A.; Rosenbluth, M. N.; Teller, A. H.; Teller, E. J. Chem. Phys. 1953, 21, 1087-1092.
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Figure 4. Typical AFM image of the surface of the epoxidederivatized silicate glass substrate before any polymer chains have been tethered to it.
Figure 3. Time-step snapshots from the Monte Carlo simulation of the deposition process. These snapshots show the surface texture (a) in the mushroom stage, (b) early in the third regime, (c) in the middle of the third regime, (d) late in the third regime, and (e) in the brush stage. Rg in the snapshots is the radius of the undeformed hemisphere.
merged. Finally, snapshot e typifies the surface texture when saturation has been reached. At saturation, the islands of vertically extended hemispheres have com-
pletely merged, making the surface texture again uniformly rough but now farther from the underlying substrate. To sum up, the simulation depicts the first regime as the mushroom layer being formed, depicts the second regime as the fully formed mushroom layer, depicts the third regime as the transition from mushroom to brush, and depicts saturation as the brush. The AFM images obtained of tethered layers at various points in the tethering process show striking similarities to the simulation snapshots. First, we show for reference a typical AFM image of the surface of the epoxidederivatized silicate glass before any polymer chains have been tethered to it (Figure 4). The smooth and featureless quality of this surface is to be contrasted with the AFM images that follow. AFM images of surfaces to which monodisperse polystyrene of Mn ) 15 000 g/mol has been tethered are shown in Figure 5A-D. Like the simulation images, these AFM images show the evolution of surface texture of the layer before, during, and after the transition from mushroom to brush. Image A is from the interruption of tethering right after the end of the first regime and depicts a typical mushroom layer. The surface texture appears rough but uniform overall. Images B and C are from interruption of tethering early and late in the third regime, respectively. They depict early and late times in the transition from mushroom to brush, showing a nonuniform texture having large “bumps” emerging from the surface. Finally, image D is from tethering allowed to proceed, uninterrupted, to saturation. It can be seen that the surface texture has returned to a uniform roughness. Images of only four disks are presented here; the remaining two disks in the series were removed at redundant times and gave no new information. AFM images of surfaces to which monodisperse polystyrene of Mn ) 44 000 g/mol has been tethered are shown in Figure 6A-D. Like those of Figure 5, these images show the evolution of surface texture before, during, and after the transition from mushroom to brush. Image A typifies the mushroom stage, images B and C depict early and late times in the transition, and image D depicts the brush stage. The nonuniformity of the surface texture in images B and C compared with the relative uniformity in images A and D is striking.
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Figure 5. AFM images of surfaces containing tethered polystyrene of Mn ) 15 000 g/mol. These images show the surface texture (A) in the mushroom stage, (B) early in the third regime, (C) late in the third regime, and (D) in the brush stage.
We emphasize that the comparison between simulation images and AFM images is qualitative only. Qualitatively speaking, our hypothesis associates the large bumps in the surface texture during the third regime with local areas of much higher surface attachment density. We suggest that these bumps correspond to the areas where preferential tethering is taking place, forcing the tethered chains to make the transition from mushroom to brush. In good solvent, the chains in the most crowded areas would be stretched away from the surface in mutual
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Figure 6. AFM images of surfaces containing tethered polystyrene of Mn ) 44 000 g/mol. These images show the surface texture (A) in the mushroom stage, (B) early in the third regime, (C) late in the third regime, and (D) in the brush stage.
avoidance. Unfortunately, a stable image of a tethered layer cannot be obtained in good solvent, because the solvated layer is perturbed by the AFM tip, destroying the conformation one is trying to evaluate.21 Thus, the images had to be obtained in a nonsolvent, such as air. (21) O’Shea, S. J.; Welland, M. E.; Rayment, T. Langmuir 1993, 9, 1826-1835.
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Images obtained in air are highly relevant in the case of permanently tethered chains, because each chain is fixed at one end and confined to an area within its own contour length during the evaporation of solvent and resultant collapse of the chains onto the surface beneath. This limitation on mobility is severe enough to prevent any significant evening out of the texture by migration of chains from areas of high density to areas of lower density. Thus, areas of high surface attachment density would appear as bumps (higher concentrations of incompressible mass) on a field of low level, background roughness. The background roughness is of a lower amplitude and higher frequency than the third-regime bumps and may originate in the occurrence of simple clustering during evaporation of the good solvent and its replacement by the nonsolvent, air.22 The Monte Carlo simulation offers some additional insight into the transition from mushroom to brush, so we now return the discussion to it. In the simulation, the third regime begins with the appearance of sharp spikes, that is, a small cluster of severely deformed hemispheres. These spikes emerge at only the most crowded locations in the mushroom layer, suggesting that a critical overlap is necessary to initiate strong lateral contraction and vertical extension of the interacting hemispheres. Spike formation starts as a random and rare event, but once it begins in a particular location on the surface, it becomes autoaccelerating. The acceleration in the simulation arises from a feature built into the model: axisymmetric lateral contraction. Because of this feature, a strong lateral contraction on the part of an already deposited hemisphere exposes bare surface on the side opposite that of the incoming hemisphere. This newly exposed bare surface then makes it easier for an additional incoming hemisphere to be accepted. The result is the preferential deposition of incoming hemispheres at the periphery of a cluster in which the deposited hemispheres have been severely contracted into cylinders. As additional hemispheres are deposited on the periphery of an existing cluster, it spreads outward in the surface plane until it impinges on other spreading clusters. Finally, when the simulation area is covered with vertically stretched cylinders, the surface texture becomes uniform again. Obviously, the real physical situation is more complex than the situation depicted in the simulation. It would be desirable to identify a molecular level behavior that would be analogous to the axisymmetric lateral contraction of the deposited hemispheres that opens a space on the side opposite the incoming hemisphere and starts the autoacceleration and the simultaneous spatially nonuniform transition from mushroom to brush. Existing descriptions (22) Yeung, C.; Balasz, A. C.; Jasnow, D. Macromolecules 1993, 26, 1914-1921.
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of lateral contraction and vertical extension of chains caused by excluded volume effects23-26 do not describe any processes that could be the source of either an autoacceleration or a spatially nonuniform transition. We suggest that the autoacceleration observed in the real tethering systems might originate in the detailed nature of concentration fluctuations within the layer during the lateral contraction and vertical extension of a tethered chain. A distinct lateral concentration fluctuation was found recently for an analogous situation studied by means of a self-consistent field analysis; a tethered chain was subjected to vertical compression and was found at high compression to undergo a lateral displacement in one direction, opening a space on the opposite side.27 Some aspects of this analysis might be applicable to the present problem. We are hopeful that computer simulations will be conducted soon to probe the concentration fluctuations within the layer caused by lateral contraction and simultaneous vertical extension and that these studies will shed light on the mechanism that causes the observed autoacceleration and spatial nonuniformity of tethering. V. Conclusions Tethering of monodisperse, chain-end-functionalized polymer from dilute solution to a solid surface shows three regimes of kinetics. This paper presents supporting data for, but does not prove, the hypothesis that the transition from mushroom to brush takes place in the third regime and that it occurs in a spatially nonuniform manner. Timestep snapshots generated by a Monte Carlo simulation of the tethering process and AFM images of actual surfaces at different times during the process were compared. The AFM images echo the time-step snapshots, showing that the texture is fairly uniform in the mushroom stage (from the end of the first regime to the end of the second regime), is nonuniform during the third regime when the surface attachment density is increasing strongly, and returns to uniformity in the brush stage when no further tethering occurs. Acknowledgment. This work was supported in part by Grant CTS 0218977 from the National Science Foundation. LA030422X (23) Fleer, G. J.; Cohen Stuart, M. A.; Scheutjens, J. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman & Hall: London, 1993; Chapter 8. (24) Netz, R. R.; Schick, M. Macromolecules 1998, 31, 5105-5122. (25) Sidel, C.; Netz, R. R. Macromolecules 2000, 33, 634-640. (26) Livadaru, L.; Netz, R. R.; Kreuzer, H. J. J. Chem. Phys. 2003, 118, 1404-1416. (27) Steels, B. M.; Leermakers, F. A.; Haynes, C. A. J. Chromatogr., B: Biomed. Sci. Appl. 2000, 743, 31-40.
