pubs.acs.org/Langmuir © 2009 American Chemical Society
Polymer Loop Formation on a Functionalized Hard Surface: Quantitative Insight by Comparison of Experimental and Monte Carlo Simulation Results Zhenyu Haung, Haining Ji, Jimmy Mays, and Mark Dadmun* Chemistry Department, University of Tennessee, Knoxville, Tennessee 37996
Grant Smith, Dmitry Bedrov, and Ye Zhang Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112 Received June 4, 2009. Revised Manuscript Received July 22, 2009 Polystyrene terminated with carboxylic acid end groups (telechelic polymer) was grafted from the melt onto a silicon wafer that contained a monolayer of epoxy groups. Ellipsometry and fluorimetry were employed to monitor the kinetics of the grafting and loop formation, respectively. These results are quantitatively correlated with bond fluctuation Monte Carlo (BFMC) simulations that model the grafting and loop formation process. The quantitative correlation found between experiment and simulation provides unique insight into the process of polymer loop formation. Specifically, this correlation provides a calibration of the fluorescence intensity to the amount of singly bound chains present on the surface, revealing that about 80% of the bound chains form loops on the surface at the longest reaction time studied, and provides the time evolution of singly and doubly bound chains during the reaction. Moreover, this correlation is broadly applicable and can be used to readily monitor the impact of a broad range of reaction conditions (e.g., temperature, telechelic concentration, surface density of functional groups) on the loop formation process. This correlation, therefore, provides a method to access fundamental information that is not accessible by experiment alone and yet is required to tailor surface properties through adjusting the coverage and fraction of loops in the grafted layer and to correlate surface-sensitive properties to specific grafted layer structure.
Introduction Anchoring polymer chains to a solid surface is an effective and often-utilized technique to modify surface properties, such as adhesion,1-4 friction,5-9 and wettability.10-18 This anchoring often occurs via a “grafting to” mechanism, where a reaction between functional groups on the polymer chain and the substrate is exploited. The surface properties can be tailored for a given polymer-surface pair by controlling the chemical structure, grafted amount, and molecular weight of the grafted polymers. Thus far, most work in this arena has focused on singly tethered *To whom correspondence should be addressed. (1) Smith, J. W.; Kramer, E. J.; Xiao, F.; Hui, J.; Reichharts, W.; Brown, H. J. Mater. Sci. 1993, 28, 4234. (2) Smith, J. W.; Kramer, E. J.; Mills, P. J. J. Polym. Sci., Polym. Phys. 1994, 32, 1731. (3) Derulle, M.; Tirrell, M.; Marciano, Y.; Hervet, H.; Leger, L. Faraday Discuss. 1994, 98, 55. (4) Norton, L. J.; Smiglova, V.; Pralle, M. U.; Hubenko, A.; Dai, K. H.; Kramer, E. J.; Hahn, S.; Begrlund, C.; DeKoven, B. Macromolecules 1995, 28, 1999. (5) Klein, J.; Kumacheva, E.; Mahalu, D.; Perahia, D.; Fetters, L. J. Nature 1994, 370, 634. (6) Klein, J. J. Annu. Rev. Mater. Sci. 1996, 26, 581. (7) Brown, H. R. Faraday Discuss. 1994, 98, 47. (8) Tomita, N.; Tamai, S.; Okajima, E.; Hirao, Y.; Ikeuch, K.; Ikada, Y. J Appl. Biomater. 1994, 5, 175. (9) Kilbey, S. M.; Watanabe, H.; Tirrell, M. Macromolecules 2001, 34, 5249. (10) Shull, K. R. Faraday Discuss. 1994, 98, 203. (11) Yerushalmi-Rozen, R.; Klein, J.; Fetters, L. J. Science 1994, 263, 793. (12) Luzinov, I.; Minko, S.; Senkovsky, V.; Voronov, A.; Hild, S.; Marti, O.; Wilke, W. Macromolecules 1998, 31, 3945. (13) Reiter, G.; Auroy, P.; Auvray, L. Macromolecules 1996, 29, 2150. (14) Ge, S. R.; Guo, L. T.; Rafailovich, M. H.; Sokolov, J. Langmuir 2001, 17, 1687. (15) Reiter, G.; Khanna, R. Phys. Rev. Lett. 2000, 85, 2753. (16) Reiter, G.; Khanna, R. Langmuir 2000, 16, 6351. (17) Kerle, T.; Yerushalmi-Rozen, R.; Klein, J. Macromolecules 1998, 31, 422. (18) M€uller, M.; MacDowell, L. G. Europhys. Lett. 2001, 55(2), 221.
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chains, i.e., polymer chains attached only at one end to the substrate, while recent studies indicate that polymer loops, created by tethering both chain ends to the substrate, provide different and potentially improved interfacial properties relative to singly tethered chains. For example, Shull notes that, in contrast to the tail configurations formed by singly bound chains, multiply bound chains, or loops, are more autophobic in their wetting behaviors.10 Additionally, recent work in our group19-23 has demonstrated that the adhesion at a polymer-polymer interface is most robust with polymer loops present at the interface. This result is interpreted to indicate that the entanglement of free chains with the loops creates a molecular level “Velcro” that is more robust than the entanglement of two singly bound chains. Unfortunately, the mechanism and kinetics of loop formation by reacting both ends of a polymer chain with a hard surface are not well understood. When a telechelic polymer chain, which has reactive functional groups on both chain ends, comes into contact with a surface decorated with moieties that covalently bond with the chain ends, both singly and doubly bound chains will be generated during the grafting process. In order to control and optimize the polymer loop formation and structure at the interface, it is important that the competition between the formation of singly bound and doubly bound chains be understood. In our previous study,24 the grafting kinetics of a series of telechelic polystyrene with carboxylic acid groups at both chain ends onto (19) Dadmun, M. D. Macromolecules 1996, 29, 3868. (20) Dadmun, M. D. Computational Studies, Nanotechnology, and Solution Thermodynamics of Polymer Systems; Kluwer Academic: New York, 2000; p 69. (21) Eastwood, E.; Dadmun, M. D. Macromolecules 2002, 35, 5069. (22) Eastwood, E.; Dadmun, M. D. Polymer 2002, 43, 6707. (23) O0 Brien, C.; Rice, J. K.; Dadmun, M. D. Eur. Polym. J. 2004, 40, 115. (24) Huang, Z. Y.; Ji, H. N.; Mays, J. W.; Dadmun, M. D. Macromolecules 2008, 41, 1009–1018.
Published on Web 08/12/2009
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an epoxy-functionalized silica substrate was investigated. The results of this study, which document the dependence of the grafting kinetics on molecular weight, annealing temperature, and surface functionality, point toward the rate of brush growth (grafting) being controlled by the rate of reaction of the telechelic chains with the substrate, rather than being limited by the diffusion of the telechelics to the surface. Specifically, the time evolution of the singly bound chains during grafting was monitored by labeling the free carboxylic acid chain ends of singly bound polymers with a fluorescence probe 1-pyrenyldiazomethane (PDAM). These results provided important insight into the kinetics of loop formation, indicating that the telechelics bind to the surface at one end early in the reaction to form singly bound chains. This is followed by a period of nearly constant concentration of singly bound chains that is the result of more singly bound chains forming at the functionalized surface balanced by the loss of singly bound chains when the second end of a bound chain reacts with the surface to create a loop. At longer times, the number of singly bound chains decreases as loop formation dominates the reactions at the surface. However, since we are not able to correlate the fluorescence intensity with the amount of fluorescence probes present in the polymer thin film, a quantitative description of the kinetics of loop formation, including the competition between singly and doubly bound chain formation, is still absent. With this in mind, a quantitative comparison between Monte Carlo simulation results and experimental results was attempted, with the goal of establishing a unique mapping of both data sets that can be utilized to correlate experimentally determined fluorescence intensity to unbound chain ends. This, in turn, creates a correlation that can be used to monitor the formation of singly and doubly bound chains experimentally for a range of reaction conditions and telechelic polymers. The bond-fluctuation Monte Carlo (BFMC) simulation method has been used extensively in simulations of the structure and dynamics of polymer solutions,25 polymer melts,26 and polymers at solid substrates,27 including polymeric brushes.28-39 Two of the latter studies38,39 involve investigation of equilibrium conformations and dynamics of double-tethered polymers at an impenetrable interface but did not address issues of the kinetics of brush formation. We recently applied the BFMC method to the problem of the time evolution of brush formation due to irreversible adsorption/reaction of telechelic polymers from solution and melt onto a solid substrate.40 An important advantage of simulations of the brush formation process is that the attachment of the first chain end to the substrate (resulting in the formation of a singly bound chain) and attachment of the second chain end to the substrate (to form loops) can (25) Paul, W.; Binder, K.; Heermann, D. W.; Kremer, K. J. Non-Cryst. Solids 1991, 131-133 (Pt. 2), 650. (26) Lobe, B.; Baschnagel, J.; Binder, K. J. Non-Cryst. Solids 1994, 172-174 (Pt. 1), 384. (27) Baschnagel, J.; Binder, K. Macromol. Theory Simul. 1996, 5, 417. (28) Lai, P.-Y.; Binder, K. J. Chem. Phys. 1991, 95, 9288. (29) Lai, P.-Y.; Binder, K. J. Chem. Phys. 1993, 98, 586. (30) Lai, P.-Y.; Binder, K. J. Chem. Phys. 1993, 98, 2366. (31) Lai, P.-Y. J. Chem. Phys. 1993, 98, 669. (32) Wittmer, J.; Johner, A.; Joanny, J.-F.; Binder, K. J. Chem. Phys. 1994, 101, 4379. (33) Binder, K.; Lai, P.-Y.; Wittmer, J. Faraday Discuss. Chem. Soc. 1994, 98, 97. (34) Wittmer, J.; Johner, A.; Joanny, J.-F. Colloids Surf., A 1994, 1, 37. (35) Binder Kopf, A.; Baschnagel, J.; Wittmer, J.; Binder, K. Macromolecules 1996, 29, 1433. (36) Huh, J.; Balazs, A. C. J. Chem. Phys. 2000, 113, 2025. (37) Chen, C.-M.; Fwu, Y.-A. Phys. Rev. E 2000, 63, 011506–1. (38) Gulati, H. S.; Hall, C. K.; Jones, R. L.; Spontak, R. J. J. Chem. Phys. 1996, 105, 7712. (39) Jones, R. L.; Spontak, R. J. J. Chem. Phys. 1995, 103, 5137. (40) Smith, G. D.; Zhang, Y.; Yin, F.; Bedrov, D.; Dadmun, M. D.; Huang, Z. Y. Langmuir 2006, 22, 664.
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be distinguished and their absolute rates can be monitored simultaneously. In this simulation model, a polymer chain end is grafted to the surface once it comes into contact with the surface, and thus initial growth of the brush is diffusion controlled. This diffusion-controlled regime is followed by a penetration-limited regime once the grafted layer became sufficiently dense. As our experimental results indicate that the initial brush growth is reaction-controlled, the Monte Carlo simulation methodology has been expanded in the current study to allow for a reactioncontrolled process as described below. BFMC simulation results have been compared and correlated to the experimental fluorimetry and ellipsometry results. We find excellent agreement between the BFMC simulation results and experimental, which in turn offers additional quantitative insight into the grafting process and provides a method to calibrate fluorescence measurements to unbound chains. This last result is particularly beneficial, as it means that the same mapping of experiment and simulation can be applied to a variety of telechelic systems, and enables the experimental quantification of the competition between singly and doubly bound chains as a function of a variety of parameters, such as telechelic molecular weight, reaction temperature, solvent, and functionality density on the surface, Thus, this is an enabling process that can be used to provide crucial fundamental understanding of the loop formation process by grafting telechelics to hard surfaces.
Experimental Section Materials. Telechelic polystyrene with carboxylic acid group at both chain ends was synthesized anionically. The details of synthesis and characterization of these polymers can be found elsewhere.41 The molecular weight used in these studies is 3500 g/ mol with a polydispersity (Mw/Mn) of 1.14. The polymer samples were dissolved in HPLC grade toluene (Fisher Scientific), which had been filtered using a 0.02 μm filter before use. The sulfuric acid (95%), 30% w/w hydrogen peroxide, and absolute ethanol used in this study were all certified ACS grade (Fisher Scientific) and used as received. The nanopure water used in this study was purified using a Milli-Pore water treatment apparatus. The epoxysilane (3-glycidyloxypropyl)trimethoxysilane (GPS, structure shown below) was obtained from Gelest, Inc., and stored in a nitrogen-filled glovebox.
The fluorescence probe, 1-pyrenyldiazomethane (PDAM), was purchased from Molecular Probes, Inc. (Eugene, OR), and dissolved in ethyl acetate and stored at -20 C. To keep it fresh, a new solution was made every 2 weeks. The one-side polished single-crystal silicon wafers of {110} orientation were purchased from Wafer World, Inc. (West Palm Beach, FL). Before treatment, they were cut into pieces of ca. 12 cm2. Sample Preparation. The preparation of the epoxysilane monolayer is based on the procedure introduced by Luzinov et al.42-45 In this procedure, the silicon wafers were first precleaned in a bath of fuming H2SO4/30% H2O2 (3:1) piranha solution (41) Ji, H. N.; Nonidez, W. K.; Advincula, R. C.; Smith, G. D.; Kilbey, S. M., II; Dadmun, M. D.; Mays, J. W. Macromolecules 2005, 38, 9950. (42) Tsukruk, V. V.; Luzinov, I.; Julthongpiput, D. Langmuir 1999, 15, 3029. (43) Luzinov, I.; Julthongpiput, D.; Liebmann-Vinson, A.; Creeger, T.; Foster, M. D.; Tsukruk, V. V. Langmuir 2000, 16, 504. (44) Luzinov, I.; Julthongpiput, D.; Malz, H.; Pionteck, J.; Tsukruk, V. V. Macromolecules 2000, 33, 1043. (45) Luzinov, I.; Julthongpiput, D.; Tsukruk, V. V. Macromolecules 2000, 33, 7629.
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Article followed by rinsing with nanopure water and drying with a dry nitrogen stream. After cleaning, the silicon wafers were immediately moved into a nitrogen-filled glovebox and immersed in a 1% solution of epoxysilane in toluene. After 24 h, the wafers were removed from solution and rinsed alternatively with ethanol and toluene three times, sonicated in ethanol for 30 min, rinsed again with ethanol, and finally dried under a stream of dry nitrogen. The resultant epoxysilane layer was then characterized using ellipsometry and water contact angle. The telechelic polymer was spin-coated from a toluene solution onto a functionalized wafer with spin rate 2500 rpm. The thickness of the polymer thin film was mainly controlled by the concentration of the solution. The coated wafers were annealed in a vacuum oven at 150 C (>Tg), allowing the grafting of polymers onto the substrate through the reaction between the carboxylic chain ends and surface bound epoxy groups. The unreacted polymers were then removed by multiple washings with toluene and sonication in toluene for 20 h. The thickness of the grafted layer was measured by ellipsometry. No further change in thickness was observed after 20 h sonication. Sample Characterization. Measurements of dry layer thickness for epoxysilane monolayer and polymer thin films were made on an EL X-02C ellipsometer at an angle of 70. Prior to the preparation of the silane layer and polymer film, the thickness of the silicon oxide layer was measured and found to be in the range of 1.5-2 nm. The refractive indices of SiO2, epoxysilane, and PS were assumed to be equal to the bulk values 1.46, 1.429, and 1.59, respectively. At least five measurements from different locations on the wafers were averaged to give the reported thickness values. The measured thicknesses of polymer thin films were also used to estimate the surface density of chains (σ), which is defined as the number of chains per unit area. Contact angle measurements were performed on a model 10000 contact angle goniometer (Rame-hart, Inc.). Water advancing contact angles were recorded while a water droplet was placed on the surface with a syringe. To monitor the amount of singly grafted chains during the grafting process, the fluorescent probe 1-pyrenyldiazomethane (PDAM) was employed to label the free carboxylic acid groups on the singly bound chains. PDAM reacts with carboxylic acid at room temperature without catalyst, and the products are intensely fluorescent esters.46 Both PDAM and products are stable. In addition, it has been shown that PDAM is highly specific for carboxylic acid groups.47 Because of these advantages, PDAM has been used as a fluorescence labeling reagent for chromatographic analysis46,48 and also in the solid-phase reaction system.47 The reaction between PDAM and a carboxylic acid is
During the labeling process, the substrate coated with the telechelic polymers was immersed in a 0.01% (w/v) ethyl acetate solution. Kinetics studies showed that 6 h reaction time is sufficient to complete the PDAM labeling reaction, as no further increase in fluorescence intensity was observed with reaction times longer than 6 h. The substrate was then removed from the PDAM solution, washed several times, and sonicated in ethyl acetate to remove unreacted PDAM. After drying with a dry nitrogen stream, the fluorescence spectra were recorded immediately. (46) Nimura, N.; Kinoshita, T.; Yoshida, T.; Uetake, A.; Nakai, C. Anal. Chem. 1988, 60, 2067. (47) Yan, B.; Liu, L.; Astor, C. A.; Tang, Q. Anal. Chem. 1999, 71, 4564. (48) (a) Iwamura, M.; Ishikawa, T.; Koyama, Y.; Sakuma, K.; Iwamura, H. Tetrahedron Lett. 1987, 28, 679. (b) Yoshida, T.; Uetake, A.; Nakai, C.; Nimura, N.; Kinoshita, T. J. Chromatogr. 1988, 456, 421. (c) Iohan, F.; Monder, C.; Cohen, S. J. Chromatogr. 1991, 564, 27. (d) Scneede, J.; Ueland, P. M. Anal. Chem. 1992, 64, 315.
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Haung et al. Blank tests were also performed to calibrate physically adsorbed PDAM on the epoxysilane monolayer and unfunctionalized polystyrene. To check the interaction between the bound polystyrene and PDAM, a monofunctionalized polystyrene was used to generate a grafted layer of singly bound chains. It was found that the fluorescence intensity measured for wafers coated with an epoxysilane monolayer or grafted polystyrene without carboxylic acid end groups are negligible relative to the fluorescence of the grafted telechelic polymers in this present study. All fluorescence spectra were collected on an Aminco-Bowman series 2 luminescence spectrometer. A continuous high-power xenon lamp was utilized as a light source, and the spectra were recorded in the front-face mode. The incident angle was set at 20 to avoid overlapping of the fluorescence and reflection peaks. To achieve sufficient intensity and resolution, the excitation and emission wavelength were carefully selected and set at 330 and 410 nm, respectively. Excitation and emission band-passes were set to 4 and 16 nm for excitation spectra and 16 and 4 nm for emission spectra, respectively.
Simulation Methodology The details of the BFMC methodology employed can be found in our previous paper.40 Briefly, each polymer bead occupies eight sites in a cubic lattice, which for the present study was 48 48 58 sites in dimension. In the first two dimensions (x and y) the system are periodic, whereas in the z-direction the system is bounded on both sides by a solid substrate comprised of “reactive” sites. In our previous study40 an irreversible reaction between the substrate and a chain end was considered to occur every time a chain end came into contact with a substrate due to the BFMC moves that are described in our previous paper. In this present study, this has been modified so that on every MC step (MCS) there is a finite probability that each chain end in contact with a solid substrate will irreversibly react. Note that a MCS consists of a set of 1193 7 trial local displacements, i.e., one (on average) trial displacement for each polymer bead in the system (see below). This probability is referred to as the “reaction probability” in discussions below. At the beginning of each MCS, the possibility of an irreversible reaction is considered for every chain end in contact with the substrate. A reaction probability of unity results in the same behavior studied in our previous work, i.e., diffusion limited brush growth followed by a penetration limited regime.40 In this work we found that a sufficiently low reaction probability results in elimination of the diffusion limited regime, as discussed below. A total of 1193 chains each comprised of seven beads was employed in the current study. This results in a BFMC lattice which is half filled with polymer beads (i.e., [8 1193 7]/[48 48 58] = 0.5). This occupancy corresponds to melt densities within the BFMC framework26 which is appropriate for comparison with the experimental system where rapid solvent evaporation rapidly leads to meltlike densities in the deposited polymer layer. A chain length of seven was obtained by matching the number of statistical segments in the BFMC chain with that in the 3.5 kDa polystyrene chain. This was accomplished by mapping both chains to equivalent freely jointed chains described as ÆRg 2 æ ¼ Neq leq 2 =6
ð1aÞ
Lc ¼ Neq leq
ð1bÞ
where the radius of gyration and the contour length are given as a function of the number of statistical segments and the length of the statistical segment. For the 3.5 kDa polystyrene, Rg =17 A˚. Langmuir 2010, 26(1), 202–209
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Equating the contour length with the sum of all backbone bonds (Lc=109 A˚) yields 7 statistical segments using eq 1. However, if we take into account the fixed backbone bond angles in polystryrene, we obtain a smaller contour length of Lc = 74 A˚ and only 3.1 statistical segments. We have chosen to utilize an intermediate value around 5 statistical segments, yielding a statistical segment length of 18-19 A˚ (eq 1a) and a contour length Lc=93 A˚ (eq 1b). Assuming that the contour of the BFMC is given by the sum of bond lengths, which average 2.6λ, where λ is the lattice spacing, the radius of gyration and contour length for the BFMC chain are well represented by 2
ÆRg æ ¼ 1:3ðNBFMC -1Þð2:6λÞ =6
ð2aÞ
Lc ¼ 2:6λðNBFMC -1Þ
ð2bÞ
2
Figure 1. Surface density of the grafted layer as a function of annealing time for H3.5K. The reaction temperature is 150 C.
Using values for 3.5 kDa polystyrene allows us to obtain NBFMC ≈ 7.4 and λ ≈ 5.5 A˚. Consequently, we utilized chains of length NBFMC =7 in our simulations. Results for each reaction rate investigated (see below) were obtained by averaging over five BFMC runs that began from uncorrelated initial configurations. The initial systems for these simulations were obtained by running independent systems ∼107 MCS without polymer-surface reaction. After this equilibration, reaction was allowed to occur, but only for chain ends that were not in contact with the surface at the end of the equilibration period. This limitation removes the instantaneous reaction that can occur for chain ends in contact with the substrate at the beginning of the simulation.
Results and Discussion Ellipsometry and Fluorimetry Results. The thin films of the telechelic polystyrene (H3.5K) were prepared by spin-coating from 1 wt % (w/v) solution onto an epoxy-functionalized silicon wafer. The thickness of the epoxysilane monolayer was determined to be ca. 0.8 nm with a water contact angle of 53, indicating the formation of a monolayer.43,44 The initial film thickness of the spin-coated telechelic polymer determined by ellipsometer was 36 nm, which is much higher than 2Rg (ca. 3.3 nm), the size of a polymer chain in its unperturbed state. Our previous work has demonstrated that the amount of grafted polymer after 4 days of reaction is independent of initial film thickness if the initial film thickness exceeds 2Rg. To examine the kinetics of the grafting process, the ellipsometric thickness (H) of the grafted layer was measured as a function of reaction time. The surface density (σ), which is the number of grafted chains per unit area, was calculated from H using eq 3: σ ¼
HNav FPS MW
ð3Þ
In this equation, Nav is Avogadro’s number, FPS is the density for bulk PS, and MW is the grafted polymer molecular weight. Note that the surface density determined from the ellipsometry measurements includes the contribution from both singly and doubly bound chains. Figure 1 displays the surface density σ as a function of reaction time at 150 C up to 4 days. As can be seen from this plot, only slight changes are observed after 2 days of reaction, indicating that the grafting in this time regime is apparently saturating on the laboratory time scale (days). Fluorescence was used to monitor the presence of singly bound chains on the surface as the grafting reaction progresses. The emission and excitation fluorescence spectra were recorded for the Langmuir 2010, 26(1), 202–209
Figure 2. (a) Fluorescence emission spectrum and (b) excitation spectrum recorded for the polymer layer labeled by PDAM. The excitation and emission wavelength for emission spectrum and excitation spectrum are 330 and 410 nm, respectively.
PDAM labeled surfaces, as displayed in parts a and b of Figure 2, respectively. It was found that the intensity increases uniformly over the entire spectrum with reaction time; therefore, the change in intensity of any peak can be used to monitor the bound fluorescent PDAM. In the present work, the peak located at 397 nm in the emission spectrum was chosen. In our system, the concentration of free carboxylic acid groups in the polymer thin film are sufficiently low that the distance between two neighboring fluorophores is large enough to mitigate self-quenching contributions of these fluorophores to the fluorescence curves. Thus, we equate the fluorescence intensity to the amount of PDAM attached to the surface, which in turn directly correlates to the amount of singly bound chains. The fluorescence intensity, and therefore the amount of singly bound chains, as a function of reaction time at 150 C is shown in Figure 3. An increase in fluorescence is observed at early reaction times (100 min). The early rise in fluorescence is interpreted to indicate an increase in the amount of singly bound chain at early reaction times, when the formation of singly bound chain dominates. As the reaction proceeds, the free carboxylic acid groups of the singly bound chains begin to explore space, reach the surface, and react there to form doubly bound loops. This is balanced by the incoming chains that continue to form singly bound chains in the plateau regime (∼10-100 min). DOI: 10.1021/la902012z
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Figure 3. Fluorescent intensity for the 397 nm emission peak as a function of annealing time for H3.5K.
At later times, however, the rate of addition of singly bound chains decreases with reaction time, as the attachment of the second end of singly bound chains outpaces the attachment of new singly bound chains, presumably due to the crowding near the surface that occurs at these later times. Clearly, the free functional ends on singly bound chains are able to react with the surface more readily than new chains, as the access of the free chains that reside away from the surface is limited by the need to penetrate the increasingly dense brush formed at the surface. These results and interpretation provides a qualitative understanding of the evolution of the amount of singly bound chains with reaction time. But other questions remain. For example, how does the amount of singly bound chain compare to that of the loops? The present fluorimetry results only provide insight into the evolution of the singly bound chains, but not loops. Similarly, we have been unable to develop a quantitative correlation between the fluorescence intensity and the amount of singly bound chain. Thus, we turn to Monte Carlo simulation to provide additional insight into these promising results. Bond Fluctuation Monte Carlo Simulation Results. As mentioned above, the current BFMC simulation studies involve an important modification to our previous studies in that the reaction rate of the chain end with substrate is variable. Figure 4a shows σ, the total density of grafted telechelic chains, given as the number of singly and doubly bound chains per substrate divided by the substrate area in lattice units squared, as a function of reaction time (number of MCS) for three reaction rates (reactivities). From Figure 4a it can be seen that systems with reactivity values of 1 10-5 and 1 10-6 do not exhibit the shorttime, diffusion-controlled regime seen for the case with unity reaction probability. Figures 4b,c provide a picture of the density of the singly bound and doubly bound grafted polymers on the surface for the two systems with finite reaction rates. Clearly, the formation of singly bound chains dominates the early times, where a maximum is observed in the amount of singly bound chain with reaction time. At early times, there exist few doubly bound chains, but as the maximum in the amount of singly bound chains is reached, the amount of doubly bound loops begins to increase, concomitant with a decrease in the amount of singly bound. The behavior, qualitatively, follows that of the experimental measurements of the amount of singly bound chains. For completeness, the progress of singly bound and doubly chains with time for the infinite reaction rate (reactivity = 1) system is also shown in Figure 4d. This system differs from the reaction limited systems, as the singly bound chains do not show a maximum, but rather a plateau with reaction time. The clear differences between the diffusion-limited simulation results and the experimental fluorescence data combined with the similarity of the reaction limited simulation and experimental results further 206 DOI: 10.1021/la902012z
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bolsters our interpretation24 that the grafting of the telechelics in these systems is not diffusion limited. Quantitative Correlation between the Simulation and Experimental Results. In order to develop a more quantitative correlation between the simulation and experimental results, the time and length scales of the simulation must be correlated to that of the experiment. For the time scale, it is clear from Figures 4b,c that the data for the two reactivities (110-5 and 110-6) are merely shifted on the time axis by 1 order of magnitude from each other for both the singly bound or overall bound chain data. This is clearly demonstrated in Figures 5a,b where the curves readily overlap when shifted on the x-axis. This is a natural result of assuming that the grafting is reaction controlled and the grafting rate is proportional to the reactivity. Since the simulation results with reactivity=110-5 cover a wider time scale, this set of data are adopted for the following comparison. To map the experimental data to the simulation results, the conversion factors for time and surface density were chosen as 1 min= 70 000 MCS and 1 nm-2 = 0.102 lattice-2. The fluorescence intensity is also scaled to meet the simulation data. It can be seen from Figure 6a that the simulation for the total grafted amount fits the experimental data very well for times greater than 10 min. Simultaneously, with the same time scaling, good agreement between the simulation and fluorescence data for the singly bound chain is also observed in Figure 6b. Therefore, the simulation results simultaneously fit the experimental data for both singly and total bound chains, indicating that the time scale is self-consistent. In both comparisons, however, the fitting at early times is poor. Upon reflection, this is not surprising, given that the initial configuration of the simulation and the highly nonequilibrium spin-coated samples are not expected to coincide. The consistency of the relationship between the real length scale and lattice spacing (λ) can also be quantitatively examined. The conversion factor 1 nm-2 =0.102λ-2 corresponds to λ=3.2 A˚. This is somewhat below the value obtained based upon matching contour length and radius of gyration of λ = 5.5 A˚. However, matching the volumetric mass density of the BFMC chains to that of polystyrene at 150 C (around 1 g/cm3)49 yields a lattice spacing of about 3.8 A˚. The agreement between the simulation and experimental results indicates that the simulation accurately captures the physics of the grafting kinetics and can be used to further quantify the experimental results. The BFMC simulation, therefore, provides a method to estimate the fraction of loops in the grafted layer. For example, at the longest experimental time investigated (4 days), the amount of loops is ∼3.5 times that of the singly bound chain; i.e., ca. 80% of bound chains have formed loops at that time, where the fraction of the loops in the grafted layer as a function of time is shown in Figure 7. Therefore, the correlation of the simulation and experimental data provides crucial information that is not available by any other method. This information is required to create loops on a solid interface with a targeted fraction of loops, such that this process can be utilized to tailor the surface properties of a functionalized surface. Moreover, as the correlation between experimental and simulation length scales is based on the size of the polymer, this mapping can be expanded to other telechelic systems, providing a straightforward method to experimentally monitor the formation and mechanism of loop formation for a variety of reaction conditions. For instance, the impact of reaction temperature or telechelic molecular weight on the evolution of singly bound and doubly bound chains can now be experimentally (49) Wu, S. J. Phys. Chem. 1970, 74, 632.
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Figure 4. Bond fluctuation Monte Carlo simulation results for (a) total surface density (σs-total) as a function of Monte Carlo step (MCS) for reactivity = 1, 1 10-5, and 1 10-6. Surface density σs for singly bound and doubly bound chain at reactivity (b) 1 10-5, (c) 1 10-6, and (d) 1 (diffusion-controlled), respectively.
Figure 5. Illustration that the kinetics of telechelics attachment for reactivity = 1 10-5 and 1 10-6 are 1 order of magnitude apart in both (a) total grafted chains and (b) singly bound chains.
determined, a result that is not possible without the insight provided by the calibration of fluorescence intensity to extent of singly bound chains formed that is elucidated by the correlation between experimental and simulation data. In fact, if the calibration between fluorescence intensity and number of singly bound polymer chains reported here can be verified to be valid for all reaction conditions, these results can be used to quantify the amount of singly bound chains by monitoring the fluorescence intensity for a wide range of systems, without the need to complete further simulations. Comparison of Experimental Results to Kramer’s Model. Kramer50 has proposed a kinetic model for both the diffusioncontrolled and reaction-controlled grafting processes. To provide further insight into the grafting reaction of this loop formation (50) Kramer, E. J. Isr. J. Chem. 1995, 35, 49.
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Figure 6. (a) Mapping of the evolution of total surface density of H3.5K obtained from ellipsometry experiments to that from bond fluctuation Monte Carlo simulation for reactivity=110-5. (b) Mapping of the evolution of singly bound chains from fluorescence experiments to the evolution of surface density for singly bound chain from BFMC simulation for reactivity=1 10-5.
process and the utility of this theory to model the behavior of this system, the kinetics of the grafting of H3.5K were estimated using Kramer’s model and compared with the experimental kinetics curve. In Kramer’s model, a chemical potential barrier must be overcome for the functional chain end to reach and react with the reactive interface. This potential barrier (μ*) is given by Rg μ μ ¼ þ 1:1 ln kB T kB T a DOI: 10.1021/la902012z
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Figure 7. Fraction of loops as a function of time in the BFMC simulation with reactivity=1 10-5.
The first term on the right side of this equation is the chemical potential of the chain in the grafted layer due to stretching and is a function of z*/Rg as shown by Shull,51 where z* is the interfacial excess and equal to the grafted layer thickness in the present case. The chemical potential μh has been calculated by Shull51 as a function of z*/Rg. The second term corresponds to the entropy penalty due to confining one chain end within an interface with thickness a, where a is the statistic segment length. The reaction between the functional end groups and those on the surface will further reduce the chemical potential by Δf/kBT, where Δf is the free energy of the reaction. The number density (number per unit volume) of end functional groups within this thin layer n* can be calculated using eq 5: μ n ¼ n¥ exp kB T
ð5Þ
Here, n¥ = 2F0/N is the number density of end-functional group in the bulk, F0 is the segment density of the reactive polymers and can be easily calculated from the density of the polymer and the molecular weight of the repeat unit, and N is the degree of polymerization. The number density of chain ends near the surface n* can be further correlated with the rate of grafting dσ/dt for both diffusion-controlled and reaction-controlled processes. The same equation describes the kinetics of grafting for both mechanisms50 Z
Z =Rg 0
! μðz=Rg Þ z t d ¼ exp Rg τ kB T
ð6Þ
Here τ is the characteristic time of the attachment process and has different forms in the two mechanisms. In the diffusion-limited process, τD = aRg/D, where D is the self-diffusion coefficient. In the case of reaction-controlled grafting, it is assumed that the reaction at the interface follows second-order kinetics. For our systems, the grafted rate depends on both the concentration of end-functional polymer and that of the epoxy group on the surface. It is also assumed that the product, the grafted PS, is very stable and will not desorb. In this case, τR takes a different expression, τR=Rg/(akf[ES]), where kf is the bimolecular forward rate constant and [ES] represents the concentration of epoxysilane on the surface. Equation 6 in both cases can be solved for our experimental system with no fitting parameters. In the calculation, the molecular weight of the repeat unit m0=112 g/mol was used to calculate the degree of polymerization n. The statistical segment length a = 0.67 nm was adopted. In the case of diffusion-controlled grafting, the diffusion coefficient D=2.557 105 cm2/s was used, which (51) Shull, K. R. J. Chem. Phys. 1991, 94, 5723.
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Figure 8. Comparison of the experimental kinetics curve for H3.5K and the kinetic curves determined using Kramer’s model for (a) diffusion-controlled and (a) reaction-controlled grafting.
was obtained from atomistic simulation results in the Rouse regime.52 As shown in Figure 8a, this model shows much faster kinetics than the experimental data, further verifying that the grafting process is not diffusion limited. The calculation for the reaction-controlled process was also completed using eq 6. The surface concentration of the epoxy group [ES] = 6/nm2, which was estimated assuming the formation of silane monolayer.42 The bimolecular rate constant kf = 9.9 10-3 kg s-1 mol-1 was adopted from the study by Guegan et al.53 for the homogeneous coupling between PS-COOH and PS-epoxy. As shown in Figure 8b, the calculated kinetics curve overlaps the experimental data at early times but deviates at longer times. The use of a reaction rate derived from the reaction of two mobile components to describe the kinetics of the reaction between a mobile chain end and an immobile surface bound functional group certainly contributes to this lack of correspondence across all times. Regardless, this analysis further exemplifies the importance of the reaction rate on the grafting process and that the reaction of the telechelics with a surface bound moiety is more accurately described as reaction controlled than diffusion controlled. Moreover, these analyses clearly show that the bond fluctuation Monte Carlo simulation more accurately describes the kinetics of the grafting process than Kramer’s model is able to. One reason for this may be that Kramer’s model does not consider the entropic penalty for diffusing through the previously grafted chains, which is inherently incorporated into the MC simulation model.
Conclusions Bond fluctuation Monte Carlo (BFMC) simulation was used to model the grafting and loop formation of telechelic polymer on a functionalized hard surface assuming a reaction-controlled process. These results were quantitatively compared to experimental results in which a telechelic polystyrene with carboxylic acid end (52) Sun, Q.; Faller, R. Macromolecules 2006, 39, 812. (53) Guegan, P.; Macosko, C. W.; Ishizone, T.; Hirao, A.; Nakahama, S. Macromolecules 1994, 27, 4993.
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groups was grafted on an epoxy-functionalized silicon wafer from the melt. The direct correlation of the simulation results to the experimental results provides quantitative insight into the grafting process, including the quantification of the amount of singly bound and doubly bound chains as the grafting reaction progresses. These two parameters are difficult to obtain experimentally, however are crucial in the correlation of grafted polymer structure to surface sensitive properties and in creating surfaces with targeted fraction and coverage of loops on the surface. Thus, the calibration of the fluorescence intensity to the amount of
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singly bound chains present, which is enabled by the quantitative correlation between the experimental and simulation results, provides a heretofore unavailable mechanism to monitor the effect of a broad range of reaction parameters, such as temperature, functional group density, or telechelic concentration, on the loop formation process. Acknowledgment. This work was financially supported by the National Science Foundation through its Collaborative Research in Chemistry Program (CRC-CHEM 0304807).
DOI: 10.1021/la902012z
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