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Mechanism of Reactive Wetting and Direct Visual Determination of the Kinetics of Self-Assembled Monolayer Formation Christopher J. Campbell, Marcin Fialkowski, Kyle J. M. Bishop, and Bartosz A. Grzybowski* Department of Chemical & Biological Engineering and Department of Chemistry, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208 ReceiVed March 7, 2008 Reactive wetting (RW) of alkane thiols and disulfides on gold is studied experimentally using the wet stamping technique. Theoretical description based on Langevin dynamics is developed to explain the experimental results and to clarify the physical processes underlying RW. In this description, thermal fluctuations of the three-phase contact line combine with the surface reaction to gradually build a low-energy self-assembled monolayer (SAM) onto which the front propagates. The results of the model match the experiments and allow determination of the kinetic rate constants of SAM formation.
Reactive wetting (RW) is a process in which the area of contact between two phases increases as a result of a reaction occurring at the interface that separates them. Over the last several decades, RW has been studied both for its fundamental interest1 as well as its practical relevance to metal bonding and metallurgy,2 heterogeneous catalysis,3 droplet actuation/manipulation,4 and formation of self-assembled monolayers (SAMs).5,6 In the context of SAMs, RW has usually been considered an untoward effect accompanying micro- (e.g., microcontact printing (µCP7)) and nanopatterning techniques (e.g., dip-pen lithography8), where spreading of the patterned molecules (thiols, disulfides,6 proteins, etc.) from the features of a printing stamp or from a writing pen decreases spatial resolution. Although there has recently been significant experimental progress in using RW more controllably (e.g., to prepare unique types of nanoring patterns9 or phaseseparated double-thiol SAMs10), the fundamental aspects of the underlying wetting phenomena are still incompletely understood and often attributed to simple surface-diffusion or even gastransport mechanisms.11,12 In this paper, we attempt to gain a more detailed mechanistic understanding of RW in a model system of various SAM-forming, ω-functionalized alkane thiols and disulfides on gold. Using the wet stamping technique,13 we collect data of the extent of wetting as a function of time and of the thiol/disulfide concentration. The results of these experiments rule out the diffusive, interfacial, or gas-transport mechanisms of RW and substantiate a description based on Langevin dynamics, * Corresponding author. E-mail:
[email protected]. Phone: 847491-3024. (1) Degennes, P. G. ReV. Mod. Phys. 1985, 57, 827–863. (2) Saiz, E.; Tomsia, A. P. Nat. Mater. 2004, 3, 903–909. (3) Feibelman, P. J. Science 2002, 295, 99–102. (4) Thiele, U.; John, K.; Bar, M. Phys. ReV. Lett. 2004, 93, n/a. (5) Schwartz, D. K. Annu. ReV. Phys. Chem. 2001, 52, 107–137. (6) Witt, D.; Klajn, R.; Barski, P.; Grzybowski, B. A. Curr. Org. Chem. 2004, 8, 1763–1797. (7) Xia, Y. N.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 551–575. (8) Piner, R. D.; Zhu, J.; Xu, F.; Hong, S. H.; Mirkin, C. A. Science 1999, 283, 661–663. (9) McLellan, J. M.; Geissler, M.; Xia, Y. N. J. Am. Chem. Soc. 2004, 126, 10830–10831. (10) Geissler, M.; McLellan, J. M.; Chen, J. Y.; Xia, Y. N. Angew. Chem., Int. Ed. 2005, 44, 3596–3600. (11) Sheehan, P. E.; Whitman, L. J. Phys. ReV. Lett. 2002, 88, n/a. (12) Xia, Y. N.; Mrksich, M.; Kim, E.; Whitesides, G. M. J. Am. Chem. Soc. 1995, 117, 9576–9577. (13) Campbell, C. J.; Smoukov, S. K.; Bishop, K. J. M.; Grzybowski, B. A. Langmuir 2005, 21, 2637–2640.
in which wetting is promoted by thermal fluctuations of the spreading layer and by SAM formation. Remarkably, the wetting equations this formalism yields allow for the determination of the rate constants of SAM formation directly from the time dependence of the position of the spreading front. Ethanolic solutions of ω-functionalized alkane thiols and disulfides [HS-C11-X and (-S-C11-X)2, respectively] were delivered onto e-beam evaporated gold surfaces from agarose stamps (1-2 cm × 1-2 cm × 2-5 mm) micropatterned in bas-relief with arrays of parallel lines separated by D ) 300 µm, L ) 150 µm wide, and H ) 50 µm high (Figure 1a). Prior to stamping, the stamps were soaked overnight in large excess (50 mL of solution per stamp) of 0.01-5.0 mM solutions of thiols/ disulfides in reagent-grade ethanol (VWR Chemicals).14 They were then blotted dry on filter paper for 5 min (to remove any excess surface liquid), and allowed to rest on a clean glass slide for 5 min to equilibrate any hydration gradients that might have developed during blotting. The stamps were then applied onto nitrogen-dried gold slides for times ranging from 1 s to 17 h. To minimize stamp drying during the spreading experiments, the stamp/substrate was housed in a sealed Petri dish (i.e., covered and wrapped in parafilm) containing a few droplets of liquid ethanol. After stamping, gold surfaces were washed with ethanol and dried under nitrogen stream immediately prior to microscopic analysis (for further experimental details, see Supporting Information). This so-called wet stamping method13 allowed for a localized delivery of molecules terminated in either hydrophobic (X ) CH3) or hydrophilic groups [X ) OH, COOH, (OCH2CH2)3OH] and in concentrations varying from C ) 0.01 to 5.0 mM. When the tops of the stamp’s features came into contact with the gold surface, the thiol/disulfide molecules transferred onto the metal to form a SAM. Importantly, the SAM formed not only beneath the patterned features, but also around them via RW (Figure 1b). For each thiol (or disulfide) used and for different values of C, the positions of the spreading front, x0(t), at different times were visualized by three independent methods (Figure (14) Overnight soaking (∼12 hrs) ensured a homogeneous distribution of thiols/ disulfides within the stamp. To see this, note that the characteristic time of diffusive equilibration is less than the soaking time: τdiff ) L2/D ∼ 7 h, where L ∼ 5 mm is the smallest dimension of the stamp, and D ∼ 10-5 cm2/s is the typical diffusion coefficient of the thiols/disulfides in agarose gels.
10.1021/la800726p CCC: $40.75 2009 American Chemical Society Published on Web 12/10/2008
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Figure 1. (a) The scheme of wet stamping. Menisci from the sidewalls of the agarose stamp spread reactively onto the metal surrounding the features (right). (b) Examples of spreading patterns originating from an array of stamped squares (marked by dotted white lines) visualized by condensation figures (left), etching of unprotected gold (middle), and marking with an alkyl disulfide terminated in a fluorescent group (see reference 15).
1b): imaging of the condensation figures, etching of unprotected gold, and by fluorescence marking. In the first method, the shapes and sizes of the condensation droplets varied between bare gold and gold covered with a SAM; in the second, the unprotected areas of the metal surface were chemically etched away;15 in the third, a solution of a fluorescent alkyl disulfide or thiol (cf. Supporting Information) was applied onto gold to form a fluorescent SAM at locations not previously covered by reactive spreading. All three methods gave similar results [within 5% of x0(t)]. In addition, the stability of gold behind the front to prolonged etching (for up to 12 h) and the lack of fluorescence from these regions indicated that the SAM formed therein was densely packed (albeit not necessarily crystalline); this was the case irrespective of when the dynamic process of wetting was interrupted. The dependencies of x0(t) on t shown in Figure 2 reveal that (1) both thiols and disulfides spread on gold only to certain equilibrium (i.e., maximum) distances, xEq; (2) the values of xEq depend on the chemical nature of the terminal group X but not on the thiol/disulfide concentration, C; (3) For a given X, the rate of wetting increases with C; and (4) the hydrophilicity of the SAMs is related to the degree of wetting. SAMs presenting terminal hydrophilic groups (X ) OH, COOH, (OCH2CH2)3OH) enhance wetting compared to pure ethanol [i.e., xEq > xEq(C2H5OH) ) 8.6 µm], while those terminated in hydrophobic groups (X ) CH3) diminish it [i.e., xEq < xEq(C2H5OH)] due to autophobic pinning, in which monolayer formation increases the surface free energy. Observations (1) and (2) directly rule out the possibility of a diffusive mechanism11 of RW since, if diffusion were the driving force, the x0(t) curves would not plateau. Also, stalagmometric measurements of the dependence of the liquid-gas surface tension on the concentration, C, revealed that the liquid-gas surface tension, σGL, is roughly the same for ethanolic solutions of thiols/ disulfides as it is for pure ethanol, indicating that the thiol/disulfide molecules are not surface-active and, as such, do not exhibit a tendency to accumulate at the liquid-gas interface. This result rules out a surfactant-enhanced wetting/spreading mechanism,16 in which the molecules are transferred on the substrate directly (15) Grzybowski, B. A.; Haag, R.; Bowden, N.; Whitesides, G. M. Anal. Chem. 1998, 70, 4645–4652. (16) Tiberg, F.; Zhmud, B.; Hallstensson, K.; von Bahr, M. Phys. Chem. Chem. Phys. 2000, 2, 5189–5196.
Figure 2. Dynamics of RW of different alkyl thiols and disulfides on gold. (a-e) Experimental (symbols) and theoretical (lines) spreading curves for compounds shown in the insets. For clarity, the horizontal axis is logarithmic, and only data for the lowest and highest thiol concentrations studied are shown here; comprehensive data sets may be found in the Supporting Information. Error bars represent one standard deviation above and below the average distances, which were based on at least 20 independent experiments. The spreading distance of pure ethanol was 8.6 µm.
from a dense-packed layer formed at the liquid-gas interface. Finally, we verified that no SAM-forming molecules were transported through a gas phase. This was done by placing a stamp soaked in either a fluorescent disulfide or a fluorescent thiol close to (∼50 µm) but not in contact with an edge of a gold-coated plate. Even after long times (days), no fluorescence was detected on the gold surface.
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Langmuir, Vol. 25, No. 1, 2009 11
∆x located on the bare gold. Au ∆W ∼ (σLS + σGL cos R - σS)∆x
Figure 3. (a) Qualitative scheme illustrating the LD description of RW from the stamp’s feature. The uneven shape of the liquid-gas interface emphasizes the stochastic, microscale fluctuations of all layers and the minimal a priori assumptions used to model this interface. (b) Extent of the lowest layer determines the position of the spreading front, x0(t). A SAM forms continuously behind this front, and the surface fraction, ϑ, of the thiol/disulfide molecules (red curves) changes in time proportionally to the free surface area available at a given location. Note: surface concentration gradients are not drawn to scale and serve only to illustrate the phenomenon.
On the basis of these observations, the following mechanism of reactive spreading can be proposed that uses only minimal physical assumptions (notably, the presence of thermal noise) to account for the experimentally observed trends. Initially, it is driven by capillarity, and the wetting front advances rapidly (within ∼1 s) by a small distance corresponding roughly to the equilibrium position of pure ethanol, xEq(C2H5OH) and contact angle R(C2H5OH).17 Subsequently, the front advances slowly (∼hours) as a result of reactive spreading until it reaches an equilibrium distance, xEq, determined by the wetting angle, RSAM, characterizing the three-phase contact line (TPL) between the air, thiol/disulfide solution, and the gold substrate completely covered with the monolayer. Importantly, the second stage of the process is controlled by the rate of SAM formation (cf. Supporting Information) and is enabled by thermal fluctuations of the spreading front (Figure 3), which, at every instant of time, oscillates stochastically back and forth. To see why these oscillations are necessary to explain RW, we first note that capillarity by itself cannot advance the TPL beyond xEq(C2H5OH). This is because, for x > xEq(C2H5OH), the contact angle, R, becomes smaller than R(C2H5OH), and the gas-solid (i.e., gas/ Au + σ Au Au) surface energy, σGS, is lower than σLS GL cos R (σLS and σGL are the surface energies of the solid-liquid and gas-liquid interfaces, respectively, and the Au superscript indicates that the gold is not yet covered with the SAM; Figure 3a). Consequently, work, ∆W, against the capillary forces must be done to advance the TPL forward from position x0(t) located on the substrate already covered with the liquid/SAM to a new position x0(t) + (17) Capillary wetting of ethanolic thiol/disulfide solutions onto bare gold should be similar to that of pure ethanol, because (i) the gas-liquid surface energy σGL is roughly equal to that of pure ethanol, as confirmed by stalagmometric Au at the advancing TPL measurements; and (ii) the solid-liquid surface energy σLS should not be effected by the presence of thiols/disulfides, which modify the surface only behind the advancing front.
(1)
Thermal fluctuations of the TPL help to overcome the “forward” energy barrier, ∆W. Once the front moves to a new location (Figure 3b), it is less likely to retract because new SAM is gradually (at the rate of thiol deposition, dϑ(x,t)/dt) being formed behind it (i.e., between x0(t) and x0(t) + ∆x). This process continues until the contact angle at the TPL reaches the value of RSAM, at which further forward motion is energetically unfavorable, and the position of the TPL oscillates around xEq. Quantitatively, the outlined scenario can be described within the framework of Langevin dynamics (LD). This approach has previously proved to be very successful in modeling the kinetics of spreading in both the complete- and partial-wetting regimes18,19 and requires only minimal assumptions about the shape of the propagating liquid/air interface. For the experimental geometry of long, parallel lines, the model is two-dimensional, and the spreading fluid is divided into N horizontal, discrete layers of equal thickness h ) H/N, where H is the height of the stamp’s feature (Figure 3a). The lateral displacement, xi(t), of the ith layer follows the Langevin-type dynamics18,19 and is given by the following stochastic equation:
dxi ∂F({xi}) + ηi(t) ) -Γ dt ∂xi
(2)
where η(t) is an external random force. Here, this force is the white Gaussian thermal noise with zero mean, 〈η〉 ) 0, and satisfying the fluctuation-dissipation relation 〈ηi(t)ηj(t′)〉 ) 2ΓkBTδijδ(t - t′), with Γ being a dissipation coefficient, T being the temperature, and kB being the Boltzmann constant. The free energy, F({xi}), of the entire spreading fluid is then given by the following functional: N-1
F({xi}) ) σLG
∑ √h2 + (xi+1 - xi)2 - ∫0
x0
[σGS(x, t) -
i)0
σLS(x, t)]dx (3) in which the first term represents the energy of the liquid-gas interface (σLG is the liquid-gas surface energy), and the second one gives the energy difference, ∆σ t σGS(x,t) - σLS(x,t), associated with the change from the solid-gas to the solid-liquid interface. The integral is taken from the sidewall of the feature (x ) 0) to the current position of the precursor, x ) x0(t), at time t. The decrease in surface energy, -∆σ, associated with the formation of the solid-liquid interface, is assumed to change linearly with the fraction of the surface covered with thiol/ disulfide, ϑ(x,t), from a value ∆σAu (pure surface) to ∆σSAM (surface fully covered with a monolayer). It is thus given by
∆σ(x, t) ) ∆σAu + (∆σSAM - ∆σAu)ϑ(x, t)
(4)
which follows from Cassie’s law applied to a chemically heterogeneous planar surface. Finally, we assume that the molecules bind to the surface irreversibly (see Supporting Information for discussion) and that the surface fraction at a given location, x, changes in time proportionally to the free surface area therein:
dϑ(x, t) ⁄ dt ) keff(1 - ϑ(x, t))
(5)
where keff is the apparent kinetic rate constant of the surface (18) Abraham, D. B.; Collet, P.; Deconinck, J.; Dunlop, F. Phys. ReV. Lett. 1990, 65, 195–198. (19) Heinio, J.; Kaski, K.; Abraham, D. B. Phys. ReV. B 1992, 45, 4409–4416.
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Figure 4. Log-log plot of the rate constants of SAM formation for different thiols and disulfides as a function of their concentrations. Colored lines correspond to the least-squares fits to data. Open symbols illustrate the relatively wide spread of the rate-constant values measured by others for straight-chain, nonfunctionalized alkane thiols; the dashed line is the average of these measurements (3 - Dannenberger, 1999; 4 - Karpovich, 1994; 0 - DeBono, 1996; O - Bain, 1989; ] - Schessler, 1996; see reference 5 for details). The red “x” marked by the vertical red arrow corresponds to the rate constant of HS-(CH2)15-COOH SAM formation reported in reference 20.
reaction (i.e., SAM formation), which has a dimension of s-1 and can, in principle, be a function of the thiol/disulfide concentration, C (cf. Figure 4). We note that, in the absence of a surface reaction, the second term in the free-energy formula reduces to the product ∆σAux0 and leads to simple capillary spreading, as expected. With these preliminaries, the set of N-1 coupled Langevin equations governing the motion of the “layered,” spreading fluid can be written in terms of mathematically convenient, nondimensional variables ˜t ) t/τ (τ ) h/ΓσLG is the scaling time factor) and x˜i ) xi/h as follows:
∂x˜0 )∂t˜
x˜0 - x˜1
√1 + (x˜0 - x˜1)
2
+ ∆σ˜ Au + (∆σ˜ SAM - ∆σ˜ Au)ϑ(x˜0, ˜t) + η˜ 0(t˜), and
∂x˜i )∂t˜
x˜i - x˜i+1
√1 + (x˜i - x˜i+1)2
+
x˜i-1 - x˜i
+ η˜ i(t˜) 2 1 + (x ˜ x ˜ ) √ i-1 i for i ) 1, ..., N - 2 (6)
with the surface fraction given by the formula ϑ(x˜0,t˜) ) 1 exp(-k˜eff χ(x˜0,t˜)t˜), in which χ(x˜0, ˜t) denotes the fraction of the elapsed time for which a surface element at location x˜0 has been covered by the liquid such that a SAM could form at this location. In the above formulas, all “tilde” quantities are appropriately rescaled, ∆σ˜ Au ) ∆σAu/σLG, ∆σ˜ SAM ) ∆σSAM/σLG, k˜eff ) keffτ,
and η˜ i(t˜) is the rescaled noise obeying the relation 〈η˜ i(t˜)ηj(t˜′)〉 ) εδijδ(t˜ - ˜t′) with ε ) 2kBT/hσLG. When the governing LD equations (eq 6) are solved numerically (cf. Supporting Information), the theoretical x0(t) versus t dependencies can be fitted (cf. Figure 2) to the experimental spreading curves, thus allowing determination of kinetic rate constants, keff, of SAM formation (in the fitting procedure, k˜eff and τ are the only free parameters, and the rate constants are determined unambiguously from keff ) k˜eff/τ). Figure 4 shows the values of keff for the different types of thiols/disulfides studied here and plotted on a log-log scale against concentrations, C. The data fits well to linear log(keff) versus log(C) dependencies with an overall correlation coefficient of 0.75 and correlation coefficients for individual compounds of 0.87 (EG3-terminated thiol), 0.82 (OH thiol), 0.47 (OH disulfide), 0.91 (COOH thiol), and 0.82 (COOH disulfide). Similar linear trends for thiol-ongold SAMs were previously observed by other groups using ellipsometry, quartz crystal microbalance, surface plasmon resonance, atomic force microscopy, second harmonic generation, and vibrational spectroscopy (see ref 5 and references therein). The average values from these studies (dotted line in Figure 4) are close to those we obtained for structurally related thiols/ disulfides, and the spreads of our rate-constant estimates are comparable to individual data sets reported by other groups (open symbols in Figure 4). In the case of one thiol where a direct comparison of the functional group is possible, HS(CH2)15-COOH, our results are within a factor of 2 from those of Nuzzo and co-workers.20 In summary, we have formulated and tested experimentally a mesoscopic, theoretical model that explains RW in terms of an interplay between thermal fluctuations and chemical kinetics. The “master” equation derived from this model enables determination of rate constants of SAM formation directly from the dynamics of the spreading front. While here we studied the formation of SAMs of alkane thiols and disulfides on gold, this approach should be extendable to other surfaces, surface-reactive compounds, and types of solutions (including those incompatible with commercially available analytical instruments). Acknowledgment. B.A.G. gratefully acknowledges financial support from the Pew Scholars Program in Biomedical Sciences and from the NIH/NCI Center for Cancer Nanotechnology Excellence. C.J.C. was supported by a Northwestern Presidential Fellowship. and K.J.M.B. was supported by an NSF graduate fellowship. Supporting Information Available: Experimental details, description of the numerical fitting procedures, and brief discussions of reaction kinetics and reaction-vs-diffusion estimates. This material is available free of charge via the Internet at http://pubs.acs.org. LA800726P (20) Bain, C. D.; Troughton, E. B.; Tao, Y. T.; Evall, J.; Whitesides, G. M.; Nuzzo, R. G. J. Am. Chem. Soc. 1989, 111, 321–335.
