Langmuir 2004, 20, 1199-1206
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Diffusion-Limited Thiol Adsorption on the Gold(111) Surface Nicholas Camillone III* Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973 Received March 24, 2003. In Final Form: October 8, 2003
An optical second harmonic generation measurement of the kinetics of self-assembly of a monolayer of thiols on the Au(111) surface reveals a marked dependence of the adsorption rate upon the solution flow rate. The nature of this dependence indicates that at low concentration and low flow rate the monolayer growth is limited by the existence of a Nernst diffusion layer, not by surface reaction rate kinetics.
Introduction Thiol monolayers on gold are the canonical self-assembly system and rank among the most extensively studied monolayers. The list of techniques applied to their characterization is long, and the list of their applications in science and technology is growing, particularly with the burgeoning of nanoscience driving the need for rational design of interfacial structure and chemistry.1-4 Increasingly detailed studies have revealed a rich complexity in what was initially conceptualized as a simple model system. The existence of a c(4x3 × 2x3)R30° “superlattice” periodicity, the formation and ripening of etch pits, and growth modes involving so-called “striped” phases exemplify the richness of these systems. Despite the level of detail to which these systems have been characterized, debate continues regarding certain details of their exact structure and chemical dynamics, even for the simplest n-alkanethiol monolayers. For example, the self-assembly kinetics has been studied in situ (in solution), in vacuo, and ex situ by a number of techniques including SPM (scanning probe microscopy),5-8 SPR (surface plasmon resonance) spectroscopy,9-11 SHG (second harmonic generation),12,13 SFG (sum frequency generation),14,15 QCM (quartz crystal microbalance) gravim* E-mail:
[email protected]. Voice: (631) 344-4412. Fax: (631) 344-5815. (1) Hata, K.; Fujita, M.; Yoshida, S.; Yasuda, S.; Makimura, T.; Murakami, K.; Shigekawa, H.; Mizutani, W.; Tokumoto, H. Appl. Phys. Lett. 2001, 79, 692. (2) Geyer, W.; Stadler, V.; Eck, W.; Golzhauser, A.; Grunze, M.; Sauer, M.; Weimann, T.; Hinze, P. J. Vac. Sci. Technol., B. 2001, 19, 2732. (3) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Science 2001, 294, 571. (4) Liu, G.-Y.; Xu, S.; Qian, Y. Acc. Chem. Res. 2000, 33, 457. (5) Poirier, G. E.; Pylant, E. D. Science 1996, 272, 1145. (6) Xu, S.; Cruchon-Dupeyrat, S. J. N.; Garno, J. C.; Liu, G.-Y.; Jennings, G. K.; Yong, T.-H.; Laibinis, P. E. J. Chem. Phys. 1998, 108, 5002. (7) Kawasaki, M.; Sato, T.; Tanaka, T.; Takao, K. Langmuir 2000, 16, 1719. (8) Yamada, R.; Uosaki, K. Langmuir 1997, 13, 5218; 1998, 14, 855. (9) Peterlinz, K. A.; Georgiadis, R. Langmuir 1996, 12, 4731. (10) Jung, L. S.; Campbell, C. T. J. Phys. Chem. B 2000, 104, 11168. (11) DeBono, R. F.; Loucks, G. D.; DellaManna, D.; Krull, U. J. Can. J. Chem. 1996, 74, 677. (12) Dannenberger, O.; Buck, M.; Grunze, M. J. Phys. Chem. B 1999, 103, 2202. (13) Jung, Ch.; Dannenberger, O.; Xu, Y.; Buck, M.; Grunze, M. Langmuir 1998, 14, 1103. (14) Himmelhaus, M.; Eisert, F.; Buck, M.; Grunze, M. J. Phys. Chem. B 2000, 104, 576. (15) Yang, C. S.-C.; Richter, L. J.; Stephenson, J. C.; Briggman, K. A. Langmuir 2002, 18, 7549.
etry,16,17 XPS (X-ray photoelectron spectroscopy),18 FTIR (Fourier transform infrared) spectroscopy,19-21 surface stress measurements,22 and X-ray and He diffraction measurements.23-25 Helpful overviews of the results of recent in situ studies can be found in many places, including papers by Jung and Campbell,10 Dannenberger et al.,12 Bensebaa et al.,21 Schreiber,26 and Schwartz.26 Whereas a well-developed consensus exists concerning in vacuo adsorption, despite numerous studies quantitative agreement on the detailed mechanisms and kinetics of growth from solution has yet to be achieved. Regarding the qualitative understanding of the mechanism, it is agreed that the growth process is complex and follows a multiple-step process. The precise nature of these steps likely depends on the length of the hydrocarbon chain and concentration of the thiol solute, which may be one reason that a universal consensus on the details of the various stages of growth is lacking. Nevertheless, a synthesis of the available data indicates the following sequence of growth stages which are reviewed here to place the current work in context. Stage 1 of the growth is described as a 2-D lattice-gas. Molecules in this phase are highly mobile and not fully imaged by scanning probe microscopies.5,6 During in situ AFM (atomic force microscopy) experiments, spikelike features evidenced weakly bound species that move with the probe tip.6 Stage 2 of the growth begins with nucleation of islands comprised of molecules oriented with their molecular axes parallel to the plane of the surface; thus this phase has been termed the “lying-down” phase. In situ AFM6 and STM (scanning tunneling microscopy)5,8 measurements (16) Karpovich, D. S.; Blanchard, G. J. Langmuir 1994, 10, 3315. (17) Kim, D. H.; Noh, J.; Hara, M.; Lee, H. Bull. Korean Chem. Soc. 2001, 22, 276. (18) Buck, M.; Grunze, M.; Eisert, F.; Fischer, J.; Trager, F. J. Vac. Sci. Technol., A 1992, 10, 926. (19) Truong, K. D.; Rowntree, P. A. Prog. Surf. Sci. 1995, 50, 207. (20) Truong, K. D.; Rowntree, P. A. J. Phys. Chem. 1996, 100, 19917. (21) Bensebaa, F.; Voicu, R.; Huron, L.; Ellis, T. H.; Kruus, E. Langmuir 1997, 13, 5335. (22) Berger, R.; Delemarche, E.; Lang, H. P.; Gerber, C.; Gimzewski, J. K.; Meyer, E.; Guntherodt, H.-J. Science 1997, 276, 2021. (23) Schreiber, F.; Eberhardt, A.; Leung, T. Y. B.; Schwartz, P.; Wetterer, S. M.; Lavrich, D. J.; Berman, L.; Fenter, P.; Eisenberger, P.; Scoles, G. Phys. Rev. B 1998, 57, 12476. (24) Lavrich, D. J.; Wetterer, S. M.; Bernasek, S. L.; Scoles, G. J. Phys. Chem. B 1998, 102, 3456. (25) Schwartz, P.; Schreiber, F.; Eisenberger, P.; Scoles, G. Surf. Sci. 1999, 423, 208. (26) Schrieber, F. Prog. Surf. Sci. 2000, 65, 151. Schwartz, D. K. Annu. Rev. Phys. Chem. 2001, 52, 107.
10.1021/la030121n CCC: $27.50 © 2004 American Chemical Society Published on Web 01/17/2004
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show direct evidence of this initial condensation step. In vacuo STM indicates the formation of a 2-D solid that is described as a “pinstripe” structure. The most detailed information available for these structures is from the in vacuo work which indicates that the periodicity of the stripes is equal to roughly twice the length of the adsorbate.5,27,28 However, other periodicities have been observed.5 A link between in vacuo observations of pinstripe phases at low coverage and the surface-parallel molecules observed in solution was suggested by Yamada and Uosaki, who observed the transformation from stripes to (x3 × x3)R30° islands in real time.8 There is evidence that shorter chain homologues (viz., for CH3(CH2)n-1SH, n e 6-10, the chain length of demarcation may depend on the presence and nature of the solvent) exhibit a 2-D liquid phase at this stage.8,29 The nature of the bonding of the molecules comprising the surface-parallel-oriented molecules in solution growth has been labeled as physisorption.6,8 However, both in situ8 and in vacuo5 STM measurements indicate the formation of vacancy islands (vis., monatomic-deep pits) during stage 2, suggesting a chemical interaction between the adsorbate and the surface. Furthermore, combined thermodynamic and structural studies in UHV (ultrahigh vacuum) indicate that, at least in the absence of solvent, molecules comprising the pinstripe phases are chemisorbed.23 Ex situ combined STM and FTIR studies indicate that over time the thiolates in the lying-down phase reorient toward the surface normal,20,30 and there are indications that the periodicity of the stripes decreases as the coverage increases.27 Thus structures characterized by a tilt angle and coverage intermediate between that for the lyingdown phase and the completed SAM (self-assembled monolayer) have been observed. Also, arrangements involving pseudobilayers of surface-parallel-oriented molecules have been proposed to explain STM images.31 However, these structures are observed after exposures less than that required to form a completed SAM and the time scale of the formation of these structures exceeds that of the formation of a completed SAM; thus, their existence as an ordered phase that can be distinguished as a stage or transition state in the growth of the SAM in solution remains unclear. Stage 3 of the growth begins at a critical coverage after complete coverage of the surface by surface-paralleloriented molecules and entails reorientation of the molecules such that their molecular axes move toward the surface normal, achieving a characteristic tilt of ∼30° with reference to the surface normal. Ex situ FTIR and ex situ and in situ SFG spectroscopic studies of short-chain (n ) 4) and long-chain (n ) 22) thiols have shown a decrease (increase) in band intensities associated with the methylene (methyl) groups, indicating reorientation of the molecules toward the surface normal.14,15,20 One SFG study found this reorientation step to proceed 3-4 times more slowly than stage 2 adsorption.14 In vacuo studies indicate that with increasing coverage, the striped phase disorders and that the coverage must exceed that corresponding to completion of the striped phase by ∼70% for n ) 10 before (27) Camillone, N., III; Leung, T. Y. B.; Schwartz, P.; Eisenberger, P.; Scoles, G. Langmuir 1996, 12, 2737. Camillone, N., III; Eisenberger, P.; Leung, T. Y. B.; Schwartz, P.; Scoles, G.; Poirier, G. E.; Tarlov, M. J. J. Chem. Phys. 1994, 101, 11031. Camillone, N., III; Leung, T. Y. B.; Scoles, G. SPIE OE/LASE 1994 Proc. 1994, 2125, paper 29. (28) Staub, R.; Toerker, M.; Fritz, T.; Schmitz-Hu¨bsch, T.; Sellam, F.; Leo, K. Langmuir 1998, 14, 6693. (29) Poirier, G. E.; Tarlov, M. J.; Rushmeier, H. E. Langmuir 1994, 10, 3383. (30) Kang, J.; Rowntree, P. A. Langmuir 1996, 12, 2813. (31) Poirier, G. E. Langmuir 1999, 15, 1167.
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nucleation of the “standing-up” phase.23 In solution, analysis of AFM images indicates that nucleation of the standing-up phase occurs as the coverage approaches saturation of the lying-down phase, and the kinetics is described best by a second-order process.6 In vacuo, the phase transition has been shown to be driven by adsorption into a physisorbed precursor state.25,32 The existence of such a state has also been suggested to explain the observed concentration independence of the rate constant in the 10-5-10-3 M regime and a distinct decrease in rate constant at 10-6 M9 and to explain deviations from simple Langmuir adsorption kinetics observed in SHG studies12 during growth in solution. Stage 4 involves a “healing” of defects in the SAM and occurs on a much longer time scale. This healing involves filling molecular vacancy sites in the monolayer and organization of the hydrocarbon chains. For shorter chains, n ) 10, in vacuo completion of the film is not thought of as a molecular organization process (e.g., healing of gauche defects along the hydrocarbon chains) as diffraction measurements show no evidence for such an intrinsic reorganization process.23,33 For longer chains, n ) 22, there is vibrational mode-specific evidence for reorganization involving “straightening” of the hydrocarbon chains into the all-trans configuration showing that the time required for full ordering of the methyl moiety is 100-300 times longer than the initial fast adsorption step.14 At micromolar thiol concentrations, the ordering of the chain termini occurs on a time scale of ∼1 h and may be driven by the adsorption of the last few percent of thiol molecules as the monolayer approaches saturation coverage. A coverage increase associated with the filling of monolayer vacancies has been estimated to be 10-20% of a monolayer by ellipsometry34 and NEXAFS (near-edge X-ray absorption fine structure)35 studies; however, some SPR experiments associate a final slow step with a 50% increase in film thickness,9 though later SPR work found much more rapid kinetics, suggesting that adsorbed impurities interfered with the earlier measurements.10 Molecularly resolved in situ AFM shows that the SAM continues to evolve over a period of days, during which “scars”, presumably surface-parallel molecules or uncovered strips of gold, are healed by the adsorption of the last 10-20% of the monolayer.6 The most detailed thiol monolayer growth information is available from the in vacuo studies as the vacuum provides the more convenient ambient for reproducible preparation of clean, well-ordered surfaces and wellcontrolled conditions where molecular impingement rates are simply understood. The UHV ambient also allows for a wide range of surface spectroscopies to be employed. The use of in situ probes in solution, however, is required to measure the temporal evolution of adsorbate order during SAM growth by conventional solution deposition. Comparison of the results of in situ studies with those from the in vacuo measurements is important to understanding the role of the solvent. For example, the presence of the solvent at the surface may interfere with the ordering of the surface-parallel-oriented molecules during solution growth and will likely have a marked effect on the 2-D pressure within the monolayer, thus affecting the relative time scales of stage 2 and stage 3. In this connection, we (32) Lavrich, D. J.; Wetterer, S. M.; Bernasek, S. L.; Scoles, G. J. Phys. Chem. B 1998, 102, 3456. (33) Eberhardt, A.; Fenter, P.; Eisenberger, P. Surf. Sci. 1998, 397, L285. (34) Bain, C. D.; Troughton, E. B.; Tao, Y. T.; Evall, J.; Whitesides, G.; Nuzzo, R. G. J. Am. Chem. Soc. 1989, 111, 321. (35) Ha¨hner, G.; Wo¨ll, Ch.; Buck, M.; Grunze, M. Langmuir 1993, 9, 1955.
Diffusion-Limited Thiol Adsorption on Gold
note that whereas in vacuo the rate constant for stage 3 is 500 times smaller than that for stage 2,23 in solution the per molecule rates of the two stages are within a factor of 5.6 We have chosen to follow the growth using the optical second harmonic technique, which affords submonolayer sensitivity while the surface is submersed in the growth solution. STM and AFM are obviously preferred for their ability to image individual molecules during adsorption; however, SHG and other “macroscopic” probes provide areal averaged information with significantly higher time resolution than the local probe techniques and thus provide a complementary approach. This paper describes in situ SHG measurements of the initial, more rapid stages of the growth, involving stages 1-3 only. For the case of thiol adsorption on gold surfaces, the intensity of second harmonic (SH) radiation generated is believed to be specifically sensitive to the formation of the sulfur-gold bond at the solid-liquid interface.12,13,15 It is our interpretation that the S-Au bond does in fact bind the molecule to the surface already during stage 2. Furthermore, in the micromolar concentration regime the molecular flux is sufficient to provide the requisite 2-D pressure to nucleate the striped phase within a few seconds. Thus the SH measurements discussed here are insensitive to stage 1, and the response we observe is attributed to the onset of stage 2. A possible SH signature for the onset of stage 3 growth will also be considered. This report is focused on experiments which show a marked dependence of the rate of stage 2 growth upon the rate at which the thiol solution is flowed past the surface. To complement the information currently available, experiments have been performed on freshly flame annealed thin films in a spectrochemical cell wherein the rate of introduction of fresh solution can be varied. Thus the surface is clean and well-ordered and a new control parameter (solution flow rate) has been explored. Examination of the relevant parameters indicates that the simplest explanation for our results is that at lower flow rates, the growth is limited by diffusion of the solute across a Nernst diffusion layer.36 At higher flow rates, the kinetics is expected to approach the surface reaction rate limit, though we do not find clear evidence for this in 2 µM solutions.
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Figure 1. Schematic of the experimental optical configuration. The pulsed 780 nm radiation is supplied by a doubled-Nd:YVO4pumped mode-locked Ti:Sapphire laser. Safety interlock is achieved by use of an external shutter (SH). Prior to introduction into the spectrochemical cell, the pulses are compressed by means of a two-prism group velocity dispersion compensator (GVDC). The pulse width and spectral line shape are measured, respectively, by interferometric autocorrelation and a fiber optic spectrometer (SP). The laser is chopped by a low-duty-cycle chopper (CH) to eliminate heating effects at high peak powers. The polarization orientation and pulse intensity are controlled by a half waveplate (HWP) and a polarizer (P1). Incident light is focused onto the sample (S) by a simple lens (L1), and stray second harmonic generated along the optical path prior to impingement on the sample is filtered out (F1). A second filter (F2) efficiently blocks radiation at the fundamental wavelength but allows second harmonic generated at the sample surface to pass. The SH is collimated by a lens (L2), analyzed by a second polarizer (P2), isolated from residual 780 nm and stray background light by a single-grating (G) monochromator, and sent to a photomultiplier tube (PMT). Photons are counted by pulse counting electronics, and the resultant signals are stored in a computer.
Experimental Section A schematic of the optical setup is shown in Figure 1. A solidstate-pumped, mode-locked Ti:Sapphire laser (Spectra Physics, Tsunami) operating at 780 nm is focused on the Au(111) surface which is suspended in the liquid phase in a custom-built spectrochemical cell (Figure 2, described in the following paragraph). The laser pulses are precompensated by a prism pair, and the pulse width prior to entry into the spectrochemical cell is Fourier transform limited at ∼60 fs. The optical configuration is typical of that used for interface SHG measurements.37 A zero-order 1/2-λ waveplate is used in tandem with a polarizer to control the incident laser intensity and polarization orientation. Just prior to the spectrochemical cell, a red filter (Schott Glass RG-610) is positioned in the path of the laser to block any second harmonic light generated in the optics leading up to the cell. The light is focused by a 125 mm focal length lens through the fused quartz cell window which is oriented parallel to the Au(111) surface. Measurements were made at incident powers of 100500 mW chopped at a 1.8% duty cycle, corresponding to an incident power of 2-9 mW at the sample. The estimated spot diameter on the sample is 70 µm. The large majority of the (36) Castellan, G. W. Physical Chemistry, 3rd ed.; Addison-Wesley: Reading, MA, 1983; Chapter 34. (37) Dadap, J. I.; Heinz, T. F. Nonlinear Optical Spectroscopy of Surfaces and Interfaces. In Encyclopedia of Chemical Physics and Physical Chemistry; Moore, J. H., Spencer, N. D., Eds.; Institute of Physics: London, 2001; Chapter B1.5.
Figure 2. Schematic of the spectrochemical cell. The Teflon cell body (CB) is mounted on a base plate (BP) which houses a fused silica window (FS). The sample is clamped to a Kel-F rod (KR) which is suspended from a kinematic mirror mount (KM) which is in turn mounted on a rotational stage (RS). The entire assembly is supported on a 1.5 in. optical post (OP). Liquid is introduced to (LI) and removed from (LO) the cell through Teflon tubing. The plane of laser access (LA) is perpendicular to the plane of the figure, and the distance between the sample surface (SS) and the window is ∼2 mm. reflected light at the fundamental wavelength is blocked by a second filter (Schott Glass BG-39) positioned just after the spectrochemical cell. The second harmonic light is directed into a light-tight enclosure containing a single-grating monochromator which effectively separates the desired 390 nm light from the ambient and any residual 780 nm light. The second harmonic light is detected by a low-dark-count photomultiplier tube (Hammamatsu), and the signal is processed by a photon counter (Stanford Research Systems, SRS400). All measurements were made with p-polarized incident light and detection of p-polarized second harmonic.
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The apparatus used to grow the organic monolayer films consisted of a sample mounting assembly, a spectrochemical cell, a solution reservoir bottle, and two peristaltic liquid pumps. A schematic of the sample holder and spectrochemical cell is provided in Figure 2. The crystal mounting rod, spectrochemical cell, cell window, reservoir bottle, and connecting tubing materials are Kel-F, Teflon, fused silica, low-density polyethylene, and Teflon, respectively. The window was sealed with a silicone O-ring. Solvent is circulated through the system by the peristaltic pumps. The reservoir bottle allows for nitrogen bubbling, mixing, filtering, and the introduction of solutions into the system, while maintaining a low level of turbulence in the cell. Given the maximum flow rate of the peristaltic pumps (∼1 mL s-1) and the volume of the cell (∼2 mL when filled just enough to immerse the surface), reasonably abrupt (∼5 s) concentration changes from pure solvent to desired adsorbate concentration are achieved. The Au(111) surfaces used in this study were ∼250 nm thick gold thin films evaporated onto borosilicate glass (Metallhandel Schroer). Immediately prior to immersion in pure ethanol in the spectrochemical cell, the gold film was cleaned by annealing in a propane flame according to a procedure recommended by the film manufacturer.38 Gold films thus prepared were found to give a stable (∼tens of minutes) SH signal at the highest laser powers used in this study (500 mW measured before a chopper operating with a ∼1.8% duty cycle). The sample could be recycled following monolayer deposition and emersion by the same flame annealing procedure. However, after the second or third cycle, the SH signal from the bare surface appeared stable only after reducing the laser power by a factor of ∼2 or more, with the degradation of the SH signal showing a clear correlation to the laser power. The reason for this laser-induced “damage” has not been fully explored but may be related to increased roughening of the surface or the concentration of adsorbed contaminants with repeated use. Thus far, it has been noted that while the laser-induced damage affected the initial and final signal levels, it did not alter the slope of the SH signal due to thiol adsorption within experimental uncertainty. Nevertheless, to avoid ambiguity, a new substrate was used after two to four adsorption runs. Decanethiol was obtained from Aldrich and used without further purification. The sample cell and associated tubing were rinsed multiple times with 190 proof ethanol (Aaper Alcohol and Chemical Co.), Millipore water (18 MΩ/cm), and 200 proof ethanol (Aaper Alcohol and Chemical Co.) between runs. The stability of the SH signal, particularly at low laser fluence, and the lack of any significant “induction” period such as reported in the literature6 indicated the absence of the influence of any significant amount of solution-borne contaminants over the time scale of the measurements. The kinetics experiments were carried out as follows. The gold thin film was flame annealed, mounted to the Kel-F sample stage (see Figure 2), and immersed in pure ethanol within ∼2 min. During laser alignment, the sample was exposed to pure ethanol for ∼10 min. The large majority of the ethanol was then pumped out of the cell. The separation between the sample surface and the cell window was small enough (∼2 mm) that a small volume of ethanol remained supported between them by surface tension. The decanethiol solution was then introduced at maximum circulation speed (∼1 mL s-1) so as to minimize uncertainty in determining starting time for the reaction. For measurement of the dependence of the growth kinetics on solution flow rate, the flow rate was decreased to the level desired for the particular experiment within ∼5 s of introduction of the solution to the cell.
Results An example of raw SH kinetics measurements is shown in Figure 3a. The clean surface gives a large, readily detectable SH signal of approximately 8500 counts per second at 500 mW incident power (as measured before the chopper). Upon introduction of the thiol solution, the SH signal is observed to drop. The onset of this drop is instantaneous within the 2-5 s uncertainty associated (38) See http://www.arrandee.com.
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Figure 3. (a) Raw SH signal measured at 390 nm for 780 nm light incident with a pulse energy of ∼6 nJ and an average power of 500 mW (before being chopped at 1.8% duty cycle). The solution flow rate was 1 mL s-1. (b) Signal converted to relative coverage using eq 4. The straight line is a guide to the eye, and the curved line demonstrates a failed attempt to fit a Langmuir uptake curve to the early time data. (c) The derivative of the coverage data from panel b with a line to guide the eye.
with measuring the time required for the thiol solution to be pumped from the reservoir bottle to the spectrochemical cell. The SH signal decreases, reaches a minimum in ∼80 s, and then rises slightly with a rate of increase that is about one-fifth of the maximum rate of the initial signal decrease. These data were collected at a solution flow rate of 1 mL s-1. Similar measurements made at flow rates ranging from 0.1 to 1 mL s-1 showed similar qualitative features aside from an obvious difference in the rate of change of the SH signal as described in detail below. Interpretation of the data is complicated by the fact that the SH signal depends on the second-order nonlinear susceptibility of the solid-liquid interface, which in general is a complicated function of adsorbate density, orientation, and the nature of the adsorbate-surface interaction. For example, changes in phase of the SH can result in a complicated coverage dependence of the SH signal.39 To further quantify the data, more detailed systematic studies aimed at determination of the susceptibility tensor must be performed. Currently data exist for the thiol/Au(111) SAMs only for wavelengths between 610 and 660 nm and at 1064 nm. In a follow-up study, we plan to extend these measurements over the range of the Ti:Sapphire laser (∼750-1000 nm). We proceed with the analysis of the current data under the provision that the absolute rates will need to be corrected after these further (39) Buck, M.; Eisert, F.; Grunze, M.; Tra¨ger, F. Appl. Phys. A 1995, 60, 1.
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measurements are made. However, the qualitative conclusions reached below are robust with respect to further refinements in the quantitative interpretation. First, given that the intensity of SH radiation generated is sensitive to the formation of the sulfur-gold bond at the solid-liquid interface,12,13 the observed instantaneous onset of change in the SH signal indicates that formation of any physisorbed initial phase is very rapid and that the onset of chemisorption, within an experimental uncertainty of ∼5 s, begins immediately upon introduction of the thiol solution to the surface. The initial drop in signal, therefore, must correspond to adsorption of molecules with their molecular axes parallel to the surface, or stage 2 of the growth sequence described in the Introduction. Extraction of a relative rate parameter is made under the following assumptions. As will become clear, these assumptions preclude the determination of absolute growth rates; however, they enable a comparison of relative growth rates as a function of the rate of the flow of the solution through the cell. The intensity of the SH generated by a material system is given by 2 I2ω ∝ |χ(2) eff |
(1)
where χ(2) eff represents an effective second-order nonlinear susceptibility of the overall system and is a function of the adsorbate coverage, θ. This effective susceptibility can be decomposed as12,40 (2) (2) (2) (2) χ(2) eff (θ) ) ∆χsurf(θ) + χsurf(0) + χbulk + χads(θ)
(2)
(2) where χ(2) surf(0) and χbulk are the interfacial and bulk contributions, respectively, for the adsorbate-free surface, ∆χ(2) surf(θ) is the adsorption-induced change in the surface susceptibility, and χ(2) ads(θ) is the contribution from the susceptibility of the adsorbed molecules themselves. Following Dannenberger et al., we provisionally assume (2) that χ(2) ads(θ) is negligible and that ∆χsurf(θ) is shifted in (2) (2) . Thus, the phase by π with respect to χsurf(0) + χbulk 12 measured SH signal can be written as
2 (2) I2ω(θ) ∝ |χ(2) sub - ∆χsurf(θ)|
(3)
where we have collapsed the two adsorbate-free terms into the single term χ(2) sub. To extract the adsorbate coverage from the SH data, we assume a linear dependence (2) (2) of ∆χ(2) surf(θ) on coverage, such that ∆χsurf(θ) ) ∆χsurf(1)θ. The validity of this assumption will be examined below. Employing the above-described formulation, the time dependence of the adsorbate coverage becomes
( x )( x )
θ) 1-
I2ω(1) I2ω(0)
-1
1-
I2ω
I2ω(0)
(4)
where I2ω(1) is chosen as the observed minimum in the SH signal. Figure 3b shows the result of the application of eq 4 to the data. As expected from the shape of the raw data and the simplifying assumptions inherent in the above analysis, the data peak at “full” coverage and then show a decay to approximately 0.8 ML (monolayer). This nonmonotonic behavior is attributed not to a real fluctuation in the coverage but rather to a change in the phase of ∆χ(2) surf(θ) with coverage.39 In our analysis, we have arbitrarily (40) Zhu, X. D.; Daum, W.; Xiao, X.-D.; Chin, R.; Shen, Y. R. Phys. Rev. B 1991, 43, 11571.
Figure 4. Thiol uptake curves measured at (a) 1.0, (b) 0.22, and (c) 0.1 mL s-1, showing a distinct dependence of the growth rate upon flow rate.
assumed a constant phase shift of π; the resulting nonmonotonic trend shown in Figure 3b indicates that the phase shift either differs from π or depends on coverage, or both. Thus, phase-sensitive measurements39 are necessary for a full quantification of the data. In the absence of such measurements, our analysis is somewhat restricted; we may make relative comparisons among the measurements presented in this paper but cannot attempt an absolute determination of the growth rates. More careful measurements addressing absolute rates have previously been made by others.10,12,39 Note that normalization of the data to the minimum of the SH signal means that here coverage is specified relative to the value at the signal minimum. The coverage at this stage of the growth could be as low as 0.27 ML (assuming it signifies the onset of the phase transition from lying down to standing up, i.e., completion of stage 2 growth6) or as high as ∼80-90% (assuming it signifies completion of stage 3 growth14). Note the nearly linear time dependence of θ from 0 to ∼0.75 ML. A nearly identical behavior has been noted by Dannenberger et al., and the deviation from Langmuir adsorption kinetics [i.e., θ ) 1 - exp(-kLct)] has been attributed to involvement of an “island precursor state” wherein the presence of adsorbed thiolates promotes further adsorption.12 This agreement between the time dependence of the results of Dannenberger et al. and the measurements reported here suggests that in the lowcoverage regime, a linear relation between ∆χ(2) surf(θ) and θ is a reasonable approximation. However, as shown in the Discussion, our flow rate dependence indicates that in the micromolar regime the deviation from Langmuir kinetics is due to the existence of a diffusion layer. Figure 4 shows the data from three measurements made at three different flow rates and processed using eq 4. The data reveal a marked dependence of the growth rate on the flow rate. The final step in data analysis is to quantify this dependence by extracting a rate constant or rate parameter. This has been done by two methods. The simpler method was to determine the time elapsed, ∆t, between the onset of the initial SH signal decay and the minimum in the SH signal (Figure 3a) and take ∆t-1 as proportional to the rate parameter. The second method was to compute the time derivative of the coverage. An example of this approach is depicted in Figure 3c, wherein the first derivative of the data in Figure 3b is plotted. The time dependence of the derivative shows that after a brief (
