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Domain Memory of Mixed Polymer Brushes Svetlana Santer,*,† Alexey Kopyshev, Jo¨rn Donges, Hyun-Kwan Yang, and Ju¨rgen Ru¨he Department of Microsystems Engineering (IMTEK), UniVersity of Freiburg, Georges-Koehler-Allee 103, D-79110 Freiburg, Germany ReceiVed January 13, 2006. In Final Form: March 7, 2006 The nano-phase-separation in mixed polymer brushes consisting of polystyrene and poly(methyl methacrylate) (PS-PMMA) chains attached to a silicon surface is studied. The topographies of the mixed brushes are examined after they have been exposed to solvents which induce or erase nano-phase-separation. It is discussed whether the brush locally forms the same pattern every time the transition from the smooth and featureless to the nanopatterned state occurs (“domain memory”) or if the local assembly of the domains emerges in a different arrangement after each cycle of topography switching. A memory measure parameter is introduced, which characterizes quantitatively the domain memory effect in the nanopattern. It is shown that at constant grafting density but with increasing molecular weight of the brush chains the memory measure parameter decreases. In contrast to this, brushes with constant molecular weight, but differing in grafting density, all have a similar domain memory. We discuss a possible origin of the domain memory effect in the mixed brush systems studied and point out its impact on the motion of nanoparticles adsorbed on top of such systems.
Introduction Diblock copolymer and mixed brushes are both systems in which monomolecular layers consisting of two polymeric components are attached to the surface of a solid substrate. If two incompatible polymers are used for the construction of such a system, the components in the monolayer tend to microphase separate. However, as all the chains are covalently bound to the surface, stable nanopattern are obtained, which respond to some extent to external stimuli and thus induce unique surface properties of the material. Such an interesting behavior has stimulated research on the creation of functional surfaces, where the surface properties can be switched reversibly.1-15 Recently, we have demonstrated that it is possible to move nanospheres adsorbed on top of diblock-copolymer brushes due to switching their topography between a flat and a nanopatterned state provided that nanospheres and nanopattern have roughly * To whom correspondence
[email protected]. † Born Prokhorova.
should
be
addressed.
E-mail:
(1) Matyjaszewski, K.; Patten, T. E.; Xia, J. H. J. Am. Chem. Soc. 1997, 119, 674. (2) Zhao, B.; Brittain, W. J. J. Am. Chem. Soc. 1999, 121, 3557. (3) Lemieux, M.; Usov, D.; Minko, S.; Stamm, M.; Shulha, H.; Tsukruk, V. V. Macromolecules 2003, 36, 7244. (4) Motornov, M.; Minko, S.; Eichhorn, K.-J.; Nitschke, M.; Simon, F.; Stamm, M. Langmuir 2003, 19, 8077. (5) Tokarev, I.; Minko, S.; Fendler, J. H.; Hutter, E. J. Am. Chem. Soc. 2004, 126, 15950. (6) Tokarev, I.; Krenek, R.; Burkov, Y.; Schmeisser, D.; Sidorenko, A.; Minko, S.; Stamm, M. Macromolecules 2005, 38, 507. (7) Luzinov, I.; Minko, S.; Tsukruk, V. V. Prog. Polym. Sci. 2004, 29, 635. (8) Minko, S.; Mu¨ller, M.; Usov, D.; Scholl, A.; Froeck, C.; Stamm, M. Phys. ReV. Lett. 2002, 88, 035502. (9) Boyes, S. G.; Brittain, W. J.; Weng, X.; Cheng, S. Z. D. Macromolecules 2002, 35, 4960. (10) Draper, J.; Luzinov, I.; Minko, S.; Tokarev, I.; Stamm, M. Langmuir 2004, 20, 4064. (11) Bhat, R. B.; Chaney, B. N.; Rowley, J.; Liebmann-Vinson, A.; Genzer, J. AdV. Mater. 2005, 17, 2802. (12) Zhao, B. Langmuir 2004, 20, 11748. (13) LeMieux, M. C.; Julthongpiput, D.; Bergman, K. N.; Cuong, P. D.; Ahn, H.-S.; Lin, Y.-H.; Tsukruk, V. V. Langmuir 2004, 20, 10046. (14) Feng, J.; Haasch, R. T.; Dyer, D. J. Macromolecules 2004, 37, 9525. (15) Lin, Y.-H.; Teng, J.; Zubarev, E. R.; Shulha, H.; Tsukruk, V. V. Nano Lett. 2005, 5, 491. (16) Prokhorova, S. A.; Kopyshev, A.; Ramakrishnan, A.; Zhang, H.; Ru¨he, J. Nanotechnology 2003, 14, 1098.
the same size.16 Such a motion is induced by periodically treating the brush with vapors of either a good or a selective solvent (i.e., a solvent which is good for one and poor for the other block). Passing many of such cycles leads to fluctuations of the brush morphology,17 which results in corresponding fluctuations of surface forces acting on the particle. Under some conditions, this can initiate motion of the particles on the surface. We have proposed a mechanism of how motion is induced based on the picture of a dynamically fluctuating force field:17 the topography switching is accompanied by changes in the local surface energy. If these fluctuations are on the same length scale as the size of the particle, they can induce movement of the particle on the surface. It was found that some brushes are less efficient to move nanospheres than others. It is thus necessary to understand the local morphology of the brushes and how it recovers during each cycle of topography switching after being erased by exposure to good solvent. For a certain type of mixed brushes consisting of poly(methyl methacrylate) and polyglycidyl methacrylate chains (PMMA-PGMA) (total thickness 100 nm), we have found that the pattern within the brush retains a strong memory concerning the position and shape of individual domains between successive cycles of topography switching. We call this pattern persistence “domain memory effect”.17 In contrast, the topography pattern of diblock-copolymer brushes of poly(methyl methacrylate-b-glycidyl methacrylate) (p(MMA-b-GMA)) appear with only a weak correlation in shape and position; the film seems to “forget” about a previous domain structure.17 In this paper, we follow up on earlier work and investigate this domain memory effect of polystyrene-poly(methyl methacrylate) (PS-PMMA) mixed brushes. We introduce a general measure describing the pattern memory of the system. Materials and Methods PS-PMMA Mixed Brushes. PS-PMMA mixed brushes were synthesized using surface initiated radical polymerization as described elsewhere.18-22 Here we report without details the main steps of the (17) Santer (Prokhorova), S. A.; Ru¨he, J. Polymer 2004, 45, 8279. (18) Santer, S.; Kopyshev, A.; Yang, H.-K.; Ru¨he, J. Local Composition of Nanophase Separated Mixed Polymer Brushes. Macromolecules submitted. (19) Prucker, O.; Ru¨he, J. Macromolecules 1998, 31, 592. (20) Prucker, O.; Ru¨he, J. Langmuir 1998, 14, 6893.
10.1021/la060134b CCC: $33.50 © 2006 American Chemical Society Published on Web 04/06/2006
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Table 1. Molecular Parameters of PS-PMMA Mixed Brushes a MPS n ,
I II III IV V VI
g/mol
Γ (t), µmol/m2
σPS, nm-2
hPS,b nm
MPMMA ,a n g/mol
Γtotal(t), µmol/m2
σtotal, nm-2
htotal,b nm
hPMMA,c nm
3 × 105 3 × 105 3 × 105 3 × 105 3 × 105 3 × 105
0.071 0.071 0.071 0.071 0.071 0.071
0.042 0.042 0.042 0.042 0.042 0.042
20 20 20 20 20 20
0.3 × 106 0.5 × 106 1 × 106 1 × 106 1 × 106 1 × 106
0.100 0.100 0.100 0.093 0.115 0.124
0.060 0.060 0.060 0.056 0.069 0.075
25 30 34 30 40 50
5 10 14 10 20 30
PS
a The number average molecular weight of the free PS and PMMA polymers were measured using an Agilent GPC setup. b The thickness of the brushes were measured in dry state using ELX-1 ellipsometer (Riss, Germany) operating with a 632.8 nm He/Ne laser at an incident angle of 70°. The refractive index of PMMA was assumed to be 1.49. The refractive index of the mixed layer (PMMA and PS) was calculated from a linear combination of the two refractive indices. c hPMMA was calculated from the difference in total dry thickness and the thickness of the PS brushes: hPMMA ) htotal - hPS.
synthesis. The dimethylchlorosilylpropyl 4-isobutyronitrile-4-cyano pentanoate (AMCS) initiator was prepared as described in ref 19. The azo initiator was immobilized on the surface of a silicon crystal in the presence of triethylamine (TEA) in dry toluene solution under nitrogen atmosphere. An excess of initiator was used to perform a condensation reaction between the chlorosilane groups and the silanol groups on the surface.18-22 This reaction results in a well-defined monolayer, covalently attached to the silicon surface. The grafting density of the initiator molecules is typically around 1.8 µmol/m2, which corresponds to 1.08 nm-2.18-22 The surface initiated radical polymerization of styrene and (methyl methacrylate) was carried out through thermal initiation at 60 °C. In the first step, the PS homopolymer was grown from the initiator surface. For all brushes discussed here, the polymerization time for the PS chains was 3 h, and the concentration of the styrene monomer in toluene was 1:1 (v/v). These reaction conditions yield a molecular weight of the PS chains of Mn ) 3 × 105 g/mol (number average molecular weight of the free polymers measured using an Agilent GPC setup).18-22 The grafting density of Γ(t) ) 0.071 µmol/m2, i.e., σ ) 0.042 nm-2 (Table 1) was calculated according to general kinetics of free radical polymerization: Γ(t) ) Γ0f exp(-kt), where Γ0 is the initial graft density of the initiator, f is the radical efficiency, k is the decomposition constant, and t is the polymerization time.20 As it was found in ref 20, Γ0 ) 1.8 µmol/m2, f ≈ 0.4, and k ) 9.6 × 10-6s-1. For this kind of synthesis, the grafting density depends on the polymerization time, whereas the molecular weight of the attached chains is controlled by the monomer concentration. After polymerization of the PS homopolymer, the samples were extracted with cold toluene in an externally cooled Soxhlet apparatus for at least 10 h. This allows all polymer chains formed in solution that not covalently attached to be removed.18-22 The dry thickness of the brush was 20 ( 1 nm as determined from ellipsometry, XRR, and AFM measurements. After polymerization, the silicon wafer containing the PS brush was cut into several pieces, which were used for growing a second homopolymer. Thus, a series of mixed brushes was synthesized having identical molecular characteristics (molecular weight and grafting density) of the PS chains and different characteristics of the second homopolymer (PMMA). The growth of the second polymer was initiated from the initiator, which was not activated during the first reaction.22 By varying the polymerization time at constant MMA/toluene concentration (in this paper 1:1 v/v), mixed brushes of varying PMMA grafting density were synthesized. When the polymerization time of PMMA is increased from 1 to 2 h and finally to 2.5 h, the overall grafting density of the brushes (Table 1) increases from Γ(t) ) 0.093 µmol/m2 (σ ) 0.056 nm-2) to Γ(t) ) 0.115 µmol/m2 (σ ) 0.069 nm-2), and Γ(t) ) 0.124 µmol/ m2 (σ ) 0.075 nm-2), respectively. When the polymerization time of the PMMA homopolymer is kept constant (Γ(t) ) 0.1 µmol/m2, σ ) 0.06 nm-2), the molecular mass of the PMMA homopolymer is changed by varying the MMA/toluene concentration (Table (21) Prucker, O.; Ru¨he, J. Macromolecules 1998, 31, 602. (22) Schimmel, M. Ph.D. Dissertation, MPI for polymer research; Mainz: Germany, 1998. (23) Press, W. H.; Vetterling, W. T.; Teukolsky, S. A.; Flannery B. P. Numerical Recipes in C, 2nd ed.; Cambridge University Press: New York, 1988.
Scheme 1. Chemical Structure of a PS-PMMA Mixed Brush
1).18-22After synthesis of the second polymer, the samples were again extracted with toluene to remove unbound PMMA chains. Two sets of brushes have been investigated. In the first series, three PS-PMMA mixed brushes with a fixed grafting density of σ ) 0.06 nm-2 and a molecular weight of the PS chains of MPS n ) 3 × 105 g/mol were studied, differing in molecular weight of the PMMA chains, which range from 3 × 105 to 1 × 106 g/mol (Table 1). In the second series, the brushes had the same molecular weight ) 1 × 106 g/mol of the PMMA and the PS chains, namely, MPMMA n 5 g/mol, while the grafting density of the brushes and MPS ) 3 × 10 n changed from σ ) 0.056 to 0.075 nm-2 (Table 1). Instrumentation. An atomic force microscope (AFM) (MultiMode, Veeco Metrology Group) was used to characterize the morphology of the layers. Tapping mode images were acquired using silicon cantilevers (Olympus) with a resonance frequency of ∼300 kHz, a spring constant of ∼50 N/m, and a tip radius of ∼10 nm. For pumping of the vapors, we designed a system with a mechanical pump that connects two reservoirs one filled with acetone the other with toluene and had an inlet for dry, clean air. With an appropriate switch, it was possible to control the flow of solvents or vapors through the liquid cell. After solvent exposure over 10 s, the samples were dried in air for typically 2 min. The AFM images were recorded in air at a relative humidity of 40-45% and at room temperature (∼25 °C). During solvent pumping, image acquisition was stopped without withdrawing the tip, allowing us to obtain an image of the very same area on the brush while switching the solvent and thus the topography. For the calculation of the cross-correlation function describing the similarity of the two images, an image processing software was developed based on the commercial PV-Wave software. Details about the cross correlation function will be explained below. The computation time for calculating the covariance of two functions f(i,j) and g(i,j) is reduced by employing a fast Fourier transform (FFT).23 Here, f represents the distribution of brightness corresponding to the bit-encoded linear gray scale of a pixel (i,j) of a micrograph (24) Prokhorova, S. A.; Kopyshev, A.; Ramakrishnan, A.; Zhang, H.; Ru¨he, J. Proc. SPIE, Nanotechnol. 2003, 5118, 30.
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Figure 1. AFM micrographs of the brush II acquired after the first cycle (a) and the second cycle (b) of exposition to acetone/toluene/acetone solvents. On the micrographs, two areas marked as 1 and 2 are selected. Magnifications of selected areas of the micrographs are shown in a1, a2 and b1, b2 on the right. and g is the same function of the subsequent micrograph. In the frequency domain, the covariance becomes a point-wise product of the transforms of each of the functions FFT(Covar(i,j)) ) FFT(f(i,j)) FFT(g(i,j)) The covariance function in real space is then recovered by applying an inverse FFT. To calculate the covariance of a certain brush, areas of (1.5 µm)2 from at least 10 different spots on the brush were examined, and the covariances averaged over switching cycles at the same spot and between different spots of the brush. This way, the covariance reflects the characteristics of the whole sample.
Results and Discussion To switch the topography of the mixed brushes between different morphologies, vapors of good and poor solvents for the polymers were pumped through the liquid cell.24 This allows scanning of the same area on the brush surface during topography switching. Figure 1 shows the topography of brush II (grafting density σ ) 0.06 nm-2, φ ) MPMMA /MPS n n ) 1.7) after treatment with acetone/toluene/acetone, i.e., after a complete first cycle (Figure 1a), and a second cycle of topography switching (Figure 1b). When referring to one cycle of topography switching, we mean that the brush is exposed to a certain solvent, for example, acetone, followed by treatment with another solvent (e.g., toluene), and then again back to the first solvent (acetone). That indeed the same area of the brush is viewed can be seen, when the position of a characteristic defect (marked by an arrow in the lower right corner of the micrographs) is viewed. The topography of the brush can be described as dimple-like, with an rms roughness of 8.5 nm. The height of the pattern is 25 ( 3 nm, and the distance between two neighboring pattern is ∼120 nm. As we have shown in a previous publication,18 after exposure to acetone, the surface of the brush II consists mostly of PMMA chains. This conclusion was drawn from an analysis of AFM phase images and on a macroscopic level, from measuring the advancing contact angle of water on the sample (θa ) 73 ( 1°). The main goal of this paper is to understand what the fate of a single domain is during its erasure and re-formation due to treatment with the phase separation inducing solvent. To examine whether a single domain appears at the same position and in the same shape after topography switching, two areas (marked by a dashed square on the image) were selected: area 1 from the middle of the micrograph (Figure 1a,b) and area 2 from the upper right corner (Figure 1a,b). The magnified images of area 1 (Figure 1, panels a1 and b1), taken before and after a switching cycle, show that all domains appear at the same position and with almost similar shape. In contrast, in area 2 of the micrograph (Figure 1, panels a2 and b2) domains can be seen that appear at a location and with a (25) Santer, S.; Donges, J. in preparation.
Figure 2. Schematic representation of the domain memory effect in mixed brushes. The dashed line in panel c shows the initial profile of the brush topography. The scheme only represents the topography of the system, no implication about the local distribution of A and B polymers is made.
shape not correlated with that of the domains before topography switching. It should be noted that the images shown in Figure 1 are representative for this sample: in many areas the pattern possesses a strong domain memory, whereas in other areas no or only a weak correlation between the position and shape of the formed domains can be observed. This behavior is very different from that of other, structurally similar systems. When a p(MMAb-GMA) diblock copolymer brush system is subjected to the same cyclic solvent exposure process, the features before and after solvent exposure are totally uncorrelated.17 In contrast to this, PMMA-PGMA mixed brushes exhibit a very strong memory, and all domains reemerge at the same location after structure erasure.17 The topography of the mixed brush system is schematically depicted in Figure 2. After treating the sample with a selective solvent for one of the polymers, the brush shows nanophase separation into “dimple-like” structures. Additionally, one observes a lateral variation of areas rich in polymer A and areas rich in B (as information only about the surface composition is available, we do not differentiate between A and B in the scheme shown in Figure 2).8 Upon exposure to a nonselective good solvent for both blocks, the brush adopts a flat, featureless topography, and the lateral distribution of A and B chains is determined by the attachment points of the homopolymer chains to the surface. When the sample is reexposed to a selective solvent, nanophase separation into a patterned topography occurs (Figure 2c). When the domains are formed at the same position and their shape is similar to the domains before switching the topography, we term this a strong domain memory effect, whereas in the case of uncorrelated appearance of domains, as it is shown in the Figure 2c, the brush has no or only a weak domain memory effect. Another important question is how long, i.e., over how many switching cycles, the domain memory is kept. When the topography of the brush is switched over many cycles (acetone/ toluene/acetone), and the same area on the brush is recorded after each cycle, one obtains a movie sequence showing
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Figure 3. Topography of the brush III acquired after treatment with acetone: (a) is the first cycle and (b) is the second cycle of topography switching. The 6 cycles of the magnified area marked by the white dashed square reveal the details of appearance of the single domains. The area selected by the black dashed square in a and b shows the part of the brush with weak restoring of a position and a shape of the domains after topography switching.
Figure 4. Illustration of the meaning of f(i,j), g(i,j) (a), and the covariance function (b). The gray scale representing the height is given in (a).
fluctuations of the pattern during topography switching. Figure 3 shows the surface of brush III after two subsequent cycles of topography switching (Figure 3, panels a and b). A complete set of 6 cycles is shown to the right by a magnification of a selected area (dashed white square in Figure 3, panels a and b). In total, the topography of brush III was switched 11 times by cyclic exposure to acetone and toluene and recorded after each cycle. From this series of the micrographs, it is evident that the central semi-spherical domain persists in position and shape, whereas the position and shape of the surrounding domains fluctuate from cycle to cycle in a random fashion (Figure 3, panels 1-6). To characterize quantitatively to which degree a certain initial pattern is recovered after a number of switching cycles, we use the covariance of the brightness distribution of AFM micrographs taken at two subsequent switching cycles. We represent the distribution of brightness by a function f(i,j) corresponding to the bit-encoded linear gray scale of a pixel (i,j) of a micrograph. The value of f is set to -1 if the pixel (i,j) is completely black and +1 if it is white. g(i,j) denotes the function of the subsequent cycle (Figure 4). We then calculate the cross correlation function from the distributions f and g defined as corr(m,n) ) (f(i,j) - 〈f(i,j)〉)(g(m + i,n + j) - 〈g(m + i,n + j)〉)
∑ i,j
(
∑(f(i,j) - 〈f(i,j)〉) ‚∑(g(m + i,n + j) - 〈g(m + i,n + j)〉) ) 2
i,j
2 1/2
i,j
〈f(i,j)〉 and 〈g(m+i,n+j)〉 are the mean value of the brightness calculated over all ensembles of pixels i and j ranging from 1 to 512 and m and n are the cross-variables (relative differences between pixel coordinates). If we could ensure that the two pictures are taken at exactly the same location, with no offset of the AFM micrographs, corr(0,0) would just directly give the covariance of the two data sets f and g. During an experiment, however, slight shifts of the order of a few pixels may occur, e.g., caused by thermal drift of the instrument. This is especially problematic as the time required for an experiment is quite long because the sample must be exposed to several different vapors. If these shifts are described by a pair (m,n) for the x and y coordinate, respectively, one expects the maximum(minimum) for corr to shift from (0,0) to a nearby point (m,n), not influencing its value. This value is found by plotting the cross-correlation function as a 2D graph for all possible shifts (m,n) (Figure 4). Thus, even if the two pictures are slightly shifted against each other, the extremal (i.e., minimum or maximum) value of corr gives the covariance (covar) and thus measures their similarity: covar ) 1 would correspond to identical, covar ) -1 to inverted images. The measure of correlation between two images may thus be characterized by the absolute value of covar, and termed the “memory measure” (mm). Taking the example of brush IV, Figure 5 illustrates the covariance function (Figure 5c) calculated from the whole micrographs (Figure 5, panels a and b) and those obtained from the selected areas 1 and 2. The memory measure parameter of brush IV over an area 2.5 × 2.5 µm is 0.64. This value describes the relatively high similarity between two subsequent images.
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Figure 5. AFM micrographs of the brush IV recorded after treatment with toluene (a). The image was acquired with 512 × 512 pixels. (b) shows the same area after one cycle of topography switching, divided into 64 regions consisting of 64 pixels. (1a, 1b) and (2a, 2b) show the selected area marked in panels a and b after first and second cycle of topography switching, respectively, and their covariance functions.
When subdividing the whole micrograph into 64 smaller areas each of size 312 × 312 nm, and comparing some of these areas between subsequent cycles, it is observed that the memory measure varies significantly. For instance, for the area 1 selected in Figure 5, panels a and b, the pattern looks very similar before and after switching and a memory measure of 0.89 is obtained. In contrast to this, the area 2 selected in Figure 5, panels a and b, exhibits no apparent correlation between the two states (Figure 5, panels 2a and 2b), and the corresponding memory measure is only 0.23, indicating weak correlation. Not only in this specific case but in all PS-PMMA mixed brushes discussed here, in some areas of the brush, the domains appear uncorrelated, whereas in other areas, the position and shape of domains reappear at the same place and in the same shape during each of the cycles of topography switching. We refer to such a domain as possessing “partial domain memory”. The memory measure parameter does vary for brushes of different composition (Tables 3 and 4), but it is independent from the solvent with which the nano-phase-separation was induced. Thus, Figure 6 shows the covariance functions and the memory measure of brush V calculated for two subsequent cycles from the micrographs acquired after treatment with acetone solvent. mm over the whole area is 0.64 (Figure 6c), whereas the smaller
areas 1 and 2 selected in Figure 6, panels a and b, have mm values of 0.8 and 0.5, respectively (Figure 6, panels c1 and c2). It should be noted that the peak of the covariance function of the brush section shown in Figure 6c is sharper than that of the brush depicted in Figure 6, panels c1 and c2. This is a natural consequence of zooming into the picture, leading to an increasing number of pixels per structure element; the memory measure is well defined only in the limit where the picture size is much larger than the length scale of the structure elements. If scanning areas are chosen much larger than the domain sizes, the memory measure no longer depends on the peculiarities of the image but reflects a material property of the brush. It has been found that this size dependence persists up to image sizes of roughly 10 times a domain size. If images larger than that are evaluated, the memory measure stays constant. For example, when the average distance between the pattern of the mixed brushes is 120 nm, the mm value calculated from an area of size 10 × 120 nm ) 1.2 µm and larger stays constant, whereas mm for areas smaller than 1.2 µm fluctuates strongly.25 In the following, only scanning areas of sufficient size are employed to compare different brushes with each other. (26) Wenning, L.; Mu¨ller, M.; Binder, K. Europhys. Lett. 2005, 71, 639.
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Figure 6. AFM micrographs of brush V after the first cycle (a), and the second cycle (b) of topography switching, acquired after treatment with acetone. On both micrographs the areas 1 and 2 are selected and their magnifications are presented in the a1, b1, and a2, b2 images. (c) Shows the covariance function of panels a and b. c1 and c2 are the corresponding functions of the selected areas 1 and 2.
The mm parameter of a brush undergoing repeated topography switching stays constant over many cycles (Figure 7). For example, brush II was treated with acetone and toluene over 18 cycles, and an image of the same area was acquired after each exposure to acetone. The images show fluctuations of the domains within the brush topography. Figure 7 shows the first 4 cycles and then the 8th, 12th, 15th, and 18th cycles of the process. The series of the magnified areas marked by a white dashed square reveals the details of domain recovery after topography switching (see the Supporting Information). The memory measure parameter, calculated for two subsequent images, of 0.65 ( 0.04 stays constant over all 18 cycles of topography switching. The memory measure parameter of mixed brushes with a constant grafting density and a fixed molecular weight of the PS chains decreases with increasing molecular weight of the PMMA chains (Table 2). Brush I which has the smallest molecular weight ) 3 × 105 g/mol) has the highest of the PMMA chains (MPMMA n mm parameter, mm ) 0.73 ( 0.05. An increase of the PMMA molecular weight by roughly a factor of 2 results in a decrease of mm to 0.65 ( 0.04 (brush II). The mm of brush III with the ) 1 × 106 g/mol) is highest PMMA molecular weight (MPMMA n only 0.53 ( 0.04 (Figure 8). To establish a relation between φ and mm in a quantitative way, additional measurements are required. In the case of brushes with a constant molecular weight of both, PS and PMMA chains and a composition of φ ) 3.33 but varying grafting density, the memory measure does not change. For example, for brushes with grafting densities between σ ) 0.075 and σ ) 0.045, mm is constant (∼0.64). The latter sample is not included in Table 3 as it originated from a different synthetic procedure and has the correct composition but a different absolute molecular weight in both chains. Thus, in the case of the mixed brushes studied here, the mm parameter is quite high and ranges above mm ) 0.5 for all samples
studied. The reason for such a strong local domain memory might be (i) an inhomogeneous distribution of the grafting points for A and B chains on the surface, resulting in a formation of “nucleation centers” rich in one of the polymers, (ii) external nucleation originating from nano dust particles, or (iii) fluctuations in the segment density within the brush induced by the polydispersity of the chains. However, in the latter case, the connection to the pinning of domains is not so straightforward. We exclude nanodust as an origin of pattern formation, because dust particles are polydisperse and at least the largest ones should have been visible in the micrographs, but this is not the case. We favor the explanation that a high value of mm is caused by an inhomogeneous distribution of grafting points of the PS and PMMA polymer chains giving rise to nucleation centers determining the formation of domains during nano-phaseseparation. The decrease of the mm parameter with increasing PMMA molecular weight should then result from a “screening” of the fluctuations in the grafting points with increasing length of the PMMA chains. It is characteristic for growth processes for the generation of brushes such as described here that the anchor points of all polymer chains are randomly placed on the amorphous surface. In such mixed brush systems, two effects are superimposed. One is local fluctuations of the grafting density caused by (a) the noncrystalline two-dimensional lattice of the anchor points of the initiator and (b) the statistical nature of a free radical initiation process, described by the radical efficiency factor and the total initiator conversion. These fluctuations exist in all polymer brush systems, regardless of whether it is a homopolymer or a mixed brush system. The second deals with the local chemical nature of the polymer chains. As the average grafting density of the two polymers is roughly the same and the chance to find either one or the other of two polymers in a given location is the same, it
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Figure 8. Dependence of the domain memory measure, mm, parameter of PS-PMMA mixed brushes on the ratio φ between the molecular weight of the PMMA to those of the PS chains. Table 3. Domain Memory Measure Parameter, mm, of PS-PMMA Mixed Brushes Having Similar Molecular Weight of Both PS and PMMA Chains, but Varying Grafting Densities
IV V VI
Figure 7. AFM micrographs of brush II recorded at the same location after each of the 8 cycles of topography switching. The size of the micrographs is 2.5 × 2.5 µm. The memory measure parameters vs number of cycles is presented together with the magnifications of the selected area. The same area on the brush can be identified according to the eminence in the lower right edge of the images. Table 2. Domain Memory Measure Parameter (mm) of PS-PMMA Mixed Brushes of Differing Molecular Weight of the PMMA Chains hPS - hPMMA, nm I II III a
20-5 20-10 20-14
σtotal, nm-2
MPMMA , n g/mol
φa
mm
0.060 0.060 0.060
0.3 × 0.5 × 106 1 × 106
1 1.7 3.3
0.73 ( 0.05 0.65 ( 0.04 0.53 ( 0.04
106
φ ) MPMMA /MPS n n .
is evident that some locations on the surface have a higher local grafting density of the A polymer, whereas others have a higher local B polymer grafting density. Thus, local fluctuations in the chemical composition of the two polymers result. The influence of the distribution of the grafting points on the morphology of the brushes has been recently discussed from a theoretical perspective by Mu¨ller et al.26 It was shown using Monte Carlo simulations that a random arrangement of grafting points pins significantly the lateral structure of the homopolymer and mixed brushes imposing formation of larger patterns than those in the case of a homogeneous distribution of the grafting points.19
Conclusions In this paper, the domain memory effect of mixed brushes has been studied experimentally. The domain memory effect is defined as the ability of single patterns of the brush topography to recover after erasure and regeneration of the nanopattern by exposure to selective and nonselective solvents, respectively. A quantitative
hPS - hPMMA, nm
σtotal, nm-2
MPMMA , n g/mol
φ
mm
20-10 20-20 20-30
0.056 0.069 0.075
1 × 106 1 × 106 1 × 106
3.33 3.33 3.33
0.64 ( 0.04 0.64 ( 0.04 0.64 ( 0.04
description of the degree of domain recovery, the memory measure parameter (mm), was introduced. It was defined as the maximum of the cross-correlation function calculated from two AFM micrographs acquired from the same area on the brush surface after two subsequent cycles of the topography switching. It was found that PS-PMMA brushes possess a partial domain memory effect. This means that locations on the brush surface exist that recover completely, i.e., the patterns on the brush appear at the same place and with the same shape and size after each cycle of topography switching. On the other hand, there is a certain part of the film in which the domain shapes and positions are completely uncorrelated to the position of the previous cycle; that is, they show no or only a very weak domain memory effect. The mm parameter was found to decrease with increasing molecular weight of the brush chains, when the grafting density of the brush is kept constant. In the case of a constant molecular weight of the chains and varying grafting density, the mm parameter stays constant for all brushes studied. The extent to which such surfaces keep a memory of the nanopattern during topography switching determines whether these topographical changes can be used for applications such as the movement of nanoparticles adsorbed on its top. As the movement of nano-objects on such a “magic carpet” depends on fluctuations of the force field which the nano-objects experience, it is evident that systems where the domains have a strong memory and thus a very similar structure before and after switching are not able to move particles through externally induced morphology changes. Experimentally, we have found that only brushes with a small domain memory effect possess the ability to move nanoobjects.16,17 Returning to these investigations16,17 and calculating the mm parameter from these images, we find that the samples where nano-objects were successfully moved had mm parameters ranging from 0.3 to 0.5. In a forthcoming paper, we show that
Domain Memory of Mixed Polymer Brushes
mixed brushes with a small domain memory effect, i.e., a mm parameter of 0.53, allow one to move nanospheres, but only in places where strong fluctuations of the brush topography are observed. Acknowledgment. We thank Prof. M. Mu¨ller for fruitful discussions. This work was supported by the Deutsche Fors-
Langmuir, Vol. 22, No. 10, 2006 4667
chungsgemeinschaft and the Landesstiftung Baden-Wu¨rttemberg, Germany. Supporting Information Available: Image of domain recovery after topography switching. This material is available free of charge via the Internet at http://pubs.acs.org. LA060134B
