Two-Dimensional Phase Diagram of Decanethiol on Au(111

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Two-Dimensional Phase Diagram of Decanethiol on Au(111) G. E. Poirier† Chemical Science and Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899

W. P. Fitts and J. M. White* Center for Nano- and Molecular Science and Technology, Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712 Received September 6, 2000. In Final Form: October 30, 2000 On the basis of variable-temperature ultrahigh vacuum scanning tunneling microscopy data, we propose a two-dimensional phase diagram of monolayer decanethiol on Au(111). Four triple-point temperatures were determined: T1 at ≈27 °C, T2 at ≈33 °C, T3 at ≈35 °C, and T4 at ≈56 °C. T1 defines the lowest temperature melting point, and T4 defines the temperature above which striped phases are metastable. These data provide a fundamental framework to understand and control mesoscale monolayer structure; moreover, they provide fundamental insight into the two-dimensional phase behavior of molecules with many degrees-of-freedom.

Introduction Amphiphile monolayers are intriguing because they provide a window into a world of lower dimensionality.1,2 The “headgroup” of certain amphiphiles binds strongly to surfaces, resulting in adhesion, but the chain-chain and chain-headgroup interactions are weak enough to preclude multilayer formation under ambient conditions. These properties result in spontaneous monolayer formation, and these monolayers are likely candidates for any application requiring precise control of the physical, chemical, and electron-transfer properties of metal surfaces. One hundred twenty-five years ago the pioneering work of J. W. Gibbs led to the phase rule and our current understanding of phase equilibria.3 Since that time, scientists have endeavored to construct and compile phase diagrams of technologically relevant material systems.4,5 Seventy years ago metal-supported amphiphile monolayers were studied as a means to control the wetting properties of metal condenser plates in steam engines.6,7 More recently, alkanethiols on Au surfaces were identified as a generic system for surface customization.7,8 This system has advantages of a degree of stability in air,9,10 amenability to controlled dosing in vacuo,11,12 and extensive study by the scientific community.13,14,15 In recent times, scientists have explored methods of constructing * Corresponding author. E-mail: [email protected]. † Deceased. (1) Abbott, E. A. Flatland; Oneworld: Rockport, 1884. (2) Dash, J. G. Phys. Today 1985, 38, 26. (3) Gibbs, J. W. Trans. Connect. Acad. 1876, 3, 108. (4) Levin, E. M.; Robbins, C. R.; McMurdie, H. F. Phase Diagrams for Ceramists; The American Ceramic Society: Columbus, 1974. (5) Massalski, T. B.; Murray, J. L.; Bennet, L. H.; Baker, H. Binary Alloy Phase Diagrams; American Society for Metals: Metals Park, 1986. (6) Emmons, H. Trans. Am. Inst. Chem. Eng. 1939, 35, 109. (7) Blackman, L. C. F.; Dewar, M. J. S. J. Chem. Soc. 1957, 162. (8) Nuzzo, R. G.; Fusco, F. A.; Allara, D. L. J. Am. Chem. Soc. 1987, 109, 2358. (9) Schoenfisch, M. H.; Pemberton, J. E. J. Am. Chem. Soc. 1998, 120, 4502. (10) Poirier, G. E.; Herne, T. M.; Miller, C. C.; Tarlov, M. J. J. Am. Chem. Soc. 1999, 121, 9703.

patterned amphiphile monolayers with the goal of making novel bioactive surfaces.16,17 Fabrication of well-characterized and thermodynamically stable surface monolayers depends on an understanding of the coverage and temperature dependence of two-dimensional phase behavior. Two-dimensional phase diagrams have been determined for various atoms and small molecules on crystalline substrates,18-21 and aspects of monolayer melting have been characterized for alkanethiol monolayers.22,23 Currently, however, there are no reports of a complete phase diagram of an amphiphile monolayer on a crystalline substrate. The goal of this study was to determine the regions of two-dimensional phase stability for decanethiol on Au(111) for coverages ranging from zero to saturation monolayer and temperatures ranging from 20 °C to 60 °C. Variable-temperature scanning tunneling microscopy (STM) was used because it provides molecule-resolved, real-space characterization of phase coexistence. Experiment Experiments were done in parallel on a custom ultrahigh vacuum (UHV) STM system at National Institute of Standards and Technology in Gaithersburg, MD (NIST), and a commercial (11) Camillone, N.; Leung, T. Y. B.; Schwartz, P.; Eisenberger, P.; Scoles, G. Langmuir 1996, 12, 2737. (12) Poirier, G. E.; Pylant, E. D. Science 1996, 272, 1145. (13) Dubois, L. H.; Nuzzo, R. G. Annu. Rev. Phys. Chem. 1992, 43, 437. (14) Ulman, A. Chem. Rev. 1996, 96, 1533. (15) Poirier, G. E. Chem. Rev. 1997, 97, 1117. (16) Xia, Y. N.; Whitesides, G. M. Annu. Rev. Mater. Sci. 1998, 28, 153. (17) Gasson, S. S.; et al. Nature Biotechnol. 1999, 17, 974. (18) Butler, D. M.; Litzinger, J. A.; Stewart, G. A. Phys. Rev. Lett. 1980, 44, 466. (19) Zhang, Q. M.; Kim, H. K.; Chan, M. H. W. Phys. Rev. B 1986, 34, 8050. (20) Kim, H. K.; Feng, Y. P.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. B 1988, 37, 3511. (21) Gangwar, R.; Suter, R. M. Phys. Rev. B 1990, 42, 2711. (22) Fenter, P.; Eisenberger, P.; Liang, K. S. Phys. Rev. Lett. 1993, 70, 2447. (23) Schreiber, F.; et al. Phys. Rev. B 1998, 57, 12476.

10.1021/la0012788 CCC: $20.00 © 2001 American Chemical Society Published on Web 01/17/2001

Phase Diagram of Decanethiol on Au(111) UHV STM system at the University of Texas at Austin (UT). Both the NIST system and the UT system have a base pressure of 3 × 10-8 Pa (2 × 10-10 Torr) and are equipped with a rapidentry load-lock. Studies conducted at NIST used single-crystal Au(111); those at UT used thin film Au on cleaved mica. All Au samples were cleaned by sequential Ar ion sputtering and annealing from 400 to 600 °C for 5 to 10 min, after which they exhibited herringbone reconstructed (111) terraces. Surface purity was confirmed using Auger electron spectroscopy, X-ray photoelectron spectroscopy, or STM. Decanethiol was stored in Teflon-sealed or viton-sealed glass vessels attached to the vacuum system by variable aperture leak valves. The decanethiol was purified using either vacuum distillation or repeated freezepump-thaw cycles or both. The purity of the decanethiol was confirmed using in-situ quadrupole mass spectroscopy. The surface coverage of decanethiol molecules was increased in a controlled manner by leaking decanethiol vapor into the pumped chamber to a pressure of between 7 × 10-6 and 13 × 10-6 Pa (5 × 10-8 and 10 × 10-8 Torr). Typical dosing times were 10 s to 10 min. The chamber interior surfaces were contaminated with decanethiol as a result of these exposures. Between experiments, the NIST chamber was cleaned by filling to 10 mTorr of oxygen and igniting a 10 W RF plasma for 15 min; the UT system was cleaned by baking at 140 °C for 20 h. Scanning tunneling microscopy (STM) data were acquired in constant tunneling current mode with a setpoint between 10 and 100 pA and tunneling bias between (0.2 and (1.2 V. On the NIST system, a boron nitride element mounted on the inner STM stage heated the entire stage to roughly uniform temperature. Two thermocouples were mounted on the stage, one near the heater element and one on the sample block ≈2 cm from the sample. A calibration test in which a thermocouple was fixed directly to the sample mount showed that the maximum temperature deviation between sample block and sample was 0.3 °C. On the UT system, the heater was mounted in a coldfinger attached to the sample holder by many fine Cu wires. Two thermocouples were mounted in this system, one on the heater element and one on the block that clamps onto the sample holder. Isothermal growth studies were conducted at both NIST and UT; each was repeated at least five times and as many as thirteen times. All data shown in this paper were acquired on the NIST system; however, data from both systems were in full agreement.

Results and Discussion Decanethiol adopts six discrete structural phases with increasing surface coverage. These are a two-dimensional gas, R; three striped phases, β, χ, and δ; a two-dimensional liquid, ; and the upright phase, φ.24,25 The two-dimensional gas comprises a low density of weakly interacting, highly mobile, surface-bound molecules. The β-phase (Figure 1β) has a molecular packing area of 82.8 Å2/molecule, and the alkyl chains in adjacent rows are antiparallel and strictly confined to the surface plane.24,26 The χ-phase (Figure 1χ) has a molecular packing area of 64.8 Å2/molecule and comprises alternating β-like and δ-like row-segments.24,25 Previously, we reported the χ-phase packing area as 68.4 Å2/molecule;24 however, refined measurements indicate the slightly higher density. The δ-phase (Figure 1δ) has a molecular packing area of 54.0 Å2/molecule, and the alkyl chains in adjacent rows are antiparallel and with an out-of-plane interdigitated configuration.24 The -phase is a two-dimensional liquid; it has the same symmetry properties as the R-phase but is a condensed phase with molecular area intermediate between δ and φ. The φ-phase (Figure 1φ) has a molecular packing area of 21.6 Å2/ molecule, and the alkyl chains are oriented upright and tilted 30° from the surface normal.13,27,28 (24) Poirier, G. E. Langmuir 1999, 15, 1167. (25) Toerker, M.; et al. Surf. Sci. 2000, 445, 100. (26) Staub, R.; et al. Langmuir 1998, 14, 6693. (27) Camillone, N.; Chidsey, C. E. D.; Liu, G.-y.; Scoles, G. J. Chem. Phys. 1993, 98, 3503. (28) Poirier, G. E.; Tarlov, M. J. Langmuir 1994, 10, 2853.

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Figure 1. Schematics of the crystalline phases of decanethiol on Au(111). (β) Schematic packing arrangement of the β-phase. The unit cell is oblique with long dimension ≈ 11.5a and short dimension exactly x3a, where a is the Au lattice constant. The alkyl chains in adjacent rows are counter-oriented and strictly confined in the surface plane. (χ) χ-phase unit cell is rectangular with dimensions of 19a by x3a and comprises alternating row segments of β and δ. (δ) δ-phase unit cell is oblique with long dimension ≈ 7.5a and short dimension exactly x3a. Alkyl chains in adjacent rows are counter-oriented; chains indicated by bold are lifted out of the surface plane and lie atop and between counter-oriented chains. (φ) φ-phase unit cell is rectangular with dimensions 3a by 2x3a; top view (left) shows unit cell comprising two inequivalent molecules; side view (right) indicates alkyl chains oriented upright and tilted ≈30° offnormal.

Figure 2 shows the isothermal variation in surface structure with increasing coverage at the laboratory ambient temperature, 22 °C. Figure 2A shows the herringbone reconstruction that is characteristic of clean Au(111).29 Figure 2B, obtained after exposing the surface to decanethiol flux, shows coexistence of R and β. The herringbone reconstruction was retained in the R-covered regions and influenced the β-phase island shape. Exposing the surface to additional decanethiol flux increased the coverage and resulted in growth of β, at the expense of R, until the surface was saturated with the β-phase. With increasing coverage, the χ-phase nucleated heterogeneously at the β-phase domain boundaries and grew in equilibrium with β until saturation.24 Figure 2C shows β-χ coexistence. Above saturation of χ, the δ-phase nucleated heterogeneously and grew in equilibrium with χ (Figure 2D) until saturation. Dark features in Figure 2D (pits) are islands of surface Au vacancies that arose from self-assembly induced rearrangement of surface Au atoms.30 Above saturation of δ, the -phase nucleated heterogeneously and grew at the expense of δ. Figure 2E shows δ- coexistence. At 22 °C, the -phase never reached saturation; instead, the φ-phase nucleated spontaneously in the -phase domains and grew laterally at the expense (29) Chambliss, D. D.; Wilson, R. J.; Chiang, S. J. Vac. Sci. Technol. B 1991, 9, 933. (30) Poirier, G. E. Langmuir 1997, 13, 2019.

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Figure 2. 22 °C isothermal growth of decanethiol on Au(111) in an ultrahigh vacuum scanning tunneling microscope. (A) Herringbone reconstruction characteristic of clean Au(111). (B) Surface exposed to decanethiol flux shows the β-phase in coexistence with two-dimensional gas R. Au reconstruction influences β-phase island shapes. (C) At higher surface coverage, β and χ coexist. (D) At higher surface coverage, χ and δ coexist. Dark features (pits) are Au vacancy islands. (E) At higher surface coverage, δ and  coexist.  is metastable at 22 °C. (F) At higher surface coverage, δ and φ coexist. With increasing coverage, the φ-phase saturates the surface.

of . At 22 °C, the -phase became a metastable twodimensional liquid, transiently interceding δ and φ.24 A system in δ--φ coexistence at 22 °C will spontaneously evolve by growth of δ and φ until  is eliminated, as shown in Figure 2F.24 With increasing coverage, the φ-phase grew to saturation, at which point growth terminated. 12 Neither in this nor in higher temperature growth studies was there evidence for second-layer growth. Considering only those phases that appeared to be stable, as evidenced by saturation coverage, isothermal growth at 22 °C exhibited the following sequence of phases: R f β f χ f δ f φ.31,32 A prior study employed helium and X-ray diffraction to characterize room-temperature growth of this same system.23 Converted to the terminology used in this study, (31) Repeated imaging at positive sample bias appeared to have the same effect as dosing decanethiol; that is, the scanned region stepped through phases of increasing density. If the imaging area was shifted several microns, images in the new area had a coverage that was consistent with what existed in the former location prior to repeated scanning. Our interpretation is that the surface dipole associated with the thiolate bond is attracted to the DC field of the tip-sample junction, thereby pulling thiolates in from surrounding regions. This interpretation is consistent with our observation that scanning at negative sample bias had a less pronounced effect. A similar phenomenon was observed for Cs adatoms on GaAs (Whitman, L. J.; et al. Science 1991, 251, 1206). (32) On some occasions we observed another phase interceding β and χ. This was reported as β′ in a prior publication; the data suggest that the β′ structure is similar to that of β but with periodic antiphase boundaries and a slightly higher density (Poirier, G. E. Langmuir 1999, 15, 1167). β′ may also be a stable phase, but for the sake of simplicity it has been left out of the discussion of this paper.

the sequence reported from the prior study was β f  f φ, though the intermediate phase  was not explicitly identified as a liquid.23 Another prior study employed STM to characterize the phase sequence with decreasing coverage, wherein this decrease was achieved by sequential thermal desorption cycles.25 This study reported the sequence (with decreasing coverage) φ f δ f χ/χ* f β f R, where χ* is a χ-phase variant.25 This is consistent with our current and previous results.24 Isothermal growth studies were also conducted at (30 ( 2) °C (see Figure 3). At coverages below that for saturation δ-phase, the growth sequence matched that shown in Figure 2. To conserve space, for this and the higher temperature growth data that follow, we show only those topographs where the growth sequence deviated from that shown in Figure 2. Figure 3A shows that, above δ-phase saturation, -phase nucleated heterogeneously and grew in equilibrium with δ. The Au vacancy islands (pits) shown in this topograph have a noticeable triangular geometry due to anisotropy of the step-edge energy. In contrast to growth at 22 °C, growth at 30 °C proceeded with saturation of the surface by the -phase (Figure 3B). The -saturated surface persisted for at least tens of hours, suggesting that  may be stable above 30 °C. With increasing coverage, φ-phase islands nucleated and grew in equilibrium with  (Figure 3C). Because φ-phase islands nucleated from the  fluid, the nucleation was presumed homogeneous. Curiously, in this experiment, φ-phase

Phase Diagram of Decanethiol on Au(111)

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Figure 3. 30 °C isothermal growth of decanethiol on Au(111) in an ultrahigh vacuum scanning tunneling microscope. The clean surface exposed to decanethiol flux shows a phase sequence comparable to that of Figure 2A-2E; only topographs depicting a change in phase sequence relative to Figure 2 are displayed. (A) Au surface exposed to sufficient decanethiol flux achieves δ- coexistence. Au vacancy islands (pits) exhibit triangular geometry. To enhance molecular contrast, the topography of the Au step-edge was removed using height-sensitive plane subtraction. (B) At higher surface coverage,  reaches saturation and vacancy islands grow.  is stable at 30 °C and above. (C) At higher surface coverage,  and φ coexist. Inset shows corrugation of the φ-phase, which nucleates preferentially in pits. As a landmark, the arrow indicates the pit corresponding to that indicated in frame B. Increasing coverage results in saturation of the φ-phase.

Figure 4. 35 °C isothermal growth of decanethiol on Au(111) in an ultrahigh vacuum scanning tunneling microscope. The clean surface exposed to a decanethiol flux shows a phase sequence comparable to that of Figure 2A-C; only topographs depicting a change in phase sequence relative to Figure 2 are displayed. (A) Au surface exposed to sufficient decanethiol flux achieves χ- coexistence. To enhance molecular contrast, the topography of the Au step-edges was removed using height-sensitive plane subtraction. The -phase saturates the surface with increasing coverage. (B) At higher surface coverage,  and φ coexist. φ-phase islands exist on terraces and in pits and, with increasing coverage, saturate the surface.

nucleation occurred preferentially in pits. For isothermal growth at (30 ( 2) °C the sequence of phases that appeared to be stable was R f β f χ f δ f  f φ. Isothermal growth at (35 ( 1) °C (see Figure 4) matched growth at 22 °C for coverages up to saturation χ-phase. Above χ-phase saturation, the -phase, rather than δ, nucleated heterogeneously and grew in equilibrium with χ (Figure 4A) until saturation. This observation of a saturation-coverage -phase at 35 °C confirms -phase stability above 30 °C. With increasing coverage, φ-phase islands nucleated homogeneously and grew in equilibrium with  (Figure 4B) until saturation. For isothermal growth at (35 ( 1) °C, the δ-phase was not observed and the sequence of phases that appeared to be stable was R f β f χ f  f φ.33 (33) We found that repeatedly scanning a χ-phase-dominated surface tended to convert the χ-phase domains into the δ-phase, even at temperatures in excess of that determined for the -δ-χ triple point. We assume that this represents nonequilibrium behavior.

Isothermal growth at (40 ( 1) °C (see Figure 5) matched growth at 22 °C up until saturation β-phase. Above β-phase saturation, the -phase, rather than χ, nucleated heterogeneously and grew in equilibrium with β (Figure 5A) until saturation. Above saturation , φ-phase islands nucleated homogeneously and grew in equilibrium with  (Figure 5B) until saturation. For isothermal growth at (40 ( 1) °C, neither χ nor δ was observed and the sequence of phases that appeared to be stable was R f β f  f φ. For isothermal growth studies at (59 ( 2) °C, the -phase nucleated directly from R and grew in equilibrium with R (Figure 6A). With increasing coverage,  grew until saturation. With further coverage, φ-phase islands nucleated homogeneously and grew in equilibrium with  (Figure 6B) until saturation. The sequence of phases observed for growth at (59 ( 2) °C was R f  f φ.34 Figures 2-6 show that isothermal growth studies conducted at incrementally increasing surface temperatures result first in the appearance of a stable liquid phase

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Figure 5. 40 °C isothermal growth of decanethiol on Au(111) in an ultrahigh vacuum scanning tunneling microscope. The clean surface exposed to a decanethiol flux shows a phase sequence comparable to that of Figure 2A and B; only topographs depicting a change in phase sequence relative to Figure 2 are displayed. (A) Au surface exposed to sufficient decanethiol flux achieves β- coexistence. To enhance molecular contrast, the topography of the Au step-edges was removed using height-sensitive plane subtraction. The -phase saturates the surface with increasing coverage. (B) At higher surface coverage,  and φ coexist. To enhance monolayer contrast, the topograph is presented as a summation of height and height-gradient. The dark furrow in the central φ-phase island is a monolayer grain boundary. φ-phase islands saturate the surface with increasing coverage.

Figure 6. 59 °C isothermal growth of decanethiol on Au(111) in an ultrahigh vacuum scanning tunneling microscope. (A) Clean surface exposed to decanethiol flux shows the -phase in coexistence with R. To enhance molecular contrast, topography of Au step-edge was removed using height-sensitive plane subtraction. Au surface in R-covered regions retains herringbone reconstruction. (B) At higher surface coverage,  and φ coexist. With increasing coverage, φ-phase islands would saturate the surface.

and subsequent sequential disappearance of the striped phases in order of decreasing density. These studies provide a rough idea of the stability region of each phase. They indicate, for example, that the upper limit of χ-phase thermodynamic stability lies somewhere between 35 °C and 40 °C. The regions of phase stability were refined by determining the surface structure while varying the surface temperature at fixed coverage. In the experiment (34) On two occasions β was observed during growth at (59 ( 2) °C. On those occasions β converted to  over the course of several hours at that temperature in UHV. We consider three possible mechanisms to explain this behavior. First, high-temperature condensation of R into β may be associated with loss of thiol hydrogen; this activated process results in temperature hysteresis. Second, the admolecules condense onto a metastable extension of the β-phase condensation curve that projects into the R- coexistence region. Third, formation of a stable -phase is hindered by restructuring of the substrate lattice. The density of the -phase is sufficient to completely lift the herringbone reconstruction, whereas that of the β-phase is not (Poirier, G. E. Langmuir 1997, 13, 2019; 1999, 15, 1167; 1999, 15, 3018). One or a combination of these may give rise to high-temperature β-phase persistence.

shown in Figure 7, a monolayer was grown to R-β coexistence at 40 °C (Figure 7A). The surface molecular area was then decreased by increasing the surface coverage to form  coexisting with β (Figure 7B). The surface temperature was then decreased under conditions of constant surface area and adsorbate number (Figure 7CE), thereby changing the surface pressure, π. Equation 1 is a two-dimensional version of the Clapyron equation for the case of freezing:

∆Hf dπ ) dT ∆AfTf

(1)

The enthalpy of freezing, ∆Hf, is negative, and the area change of freezing, ∆Af, is positive because the molecular area of the β-phase is greater than that of . dπ/dT is therefore negative, and lowering the surface temperature increases π at constant area. This increase of π occurs by growth of β at the expense of . The system arrives at the

Phase Diagram of Decanethiol on Au(111)

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Figure 7. Variable-temperature ultrahigh vacuum scanning tunneling microscopy of decanethiol on Au(111) near the β-χ- triple point. (A) Clean surface exposed to 16 Langmuirs (L) (1 L ) 10-6 Torr s) at 39.9 °C. β-phase in coexistence with R; melting is apparent at β-phase island edges. (B) After exposure to an additional 12 L at 38.9 °C. β-phase in coexistence with nascent  domains. To enhance molecular contrast, the topography of the Au step-edge was removed using height-sensitive plane subtraction. (C) Temperature is lowered to 36.5 °C; β and  coexist with the nascent χ-phase island. Herringbone ridges apparent under β-phase domains. (D) Temperature is lowered to 33.1 °C; χ-phase islands grow laterally and in number. As a landmark, the χ-phase island in frame C corresponds to that in the lower left corner of part D. (E) Surface after 15 h and cooling to 32 °C; β and χ coexist with a negligible fraction of . (F) Surface after reheating to 37.6 °C showing coexistence of β and ; χ-phase has melted. Locations corresponding to frames A-F are plotted on the phase diagram in Figure 8.

β-χ- triple point with decreasing temperature, as π has increased and caused the denser χ to form at the expense of β. Figure 7C shows the structure of the surface after the temperature dropped to 36.5 °C. An isolated nucleus of χ-phase formed within an -phase domain and coexisted with β-phase islands. The system is now at the β-χ- triple point. To our knowledge, this is the first direct space picture of three-phase coexistence near equilibrium in a two-dimensional system. The χ-phase islands grew laterally upon further cooling, as shown in Figure 7D. Gibbs’ phase rule dictates that a single-component system in three-phase equilibrium has no degrees of freedom; that is, the temperature and pressure are fixed. This contradicts Figure 7C and D, where the temperature appeared to drop during three-phase coexistence, suggesting the presence of thermal gradients or imperfect equilibrium. Figure 7E shows the surface after it evolved for 15 h; β and χ coexisted with a negligible fraction of -phase. Here, at the β-χ (solid-solid) phase boundary, the sign of the pressure change with further cooling depends on the enthalpy change. Figure 7F shows the surface after it was heated to 37.6 °C. At this temperature, the χ-phase melted, and the β-phase coexisted with  as in Figure 7B. This melt-freeze cycle was repeated several times;

however, after several days the monolayer began to show signs of contamination. Upon cooling, the temperature of first appearance of a solid nucleus from a bulk melt tends to occur below the bulk freezing point due to supercooling; this is the result of the finite time required for stochastic formation of critical nuclei.35 Thus, the temperature of first appearance of solid nuclei provides a lower bound on the bulk freezing point. Upon heating, the temperature of last appearance of the solid will typically occur above, but close to, the bulk melting point. Superheating of the solid is less common than supercooling of the liquid because melting tends to nucleate heterogeneously at solid grain boundaries, whereas freezing tends to nucleate homogeneously from a fluid. On heating, then, the temperature of last appearance of the solid phase provides an upper bound on the bulk melting point. To determine the temperatures of three-phase coexistence, heating-cooling cycles such as that shown in Figure 7 were conducted by monitoring for first appearance of the relevant solid (on cooling) and first disappearance of the relevant solid (on heating). The results are listed in Table 1 with the number of repeat trials for each three-phase temperature, the mean of the (35) Zinke-Allmang, M.; Feldman, L. C.; Grabow, M. H. Surf. Sci. Rep. 1992, 16, 378.

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Table 1. Temperatures of Three-Phase Coexistence for Monolayer Decanethiol on Au(111) name

identity

trials

avg temp (°C)

2σ (°C)

T1 T2 T3 T4

φ--δ -δ-χ -χ-β -β-R

5 2 5 5

27 33 35 55

1 2 2 4

trials, and an uncertainty that is calculated as twice the standard deviation from the mean. It is conventional to plot regions of phase stability on a pressure versus temperature phase diagram. However, because measuring π on solid surfaces is problematic,36 we plot a molecular area versus temperature phase diagram in Figure 8A. Boundaries of the pure crystalline phases β, χ, δ, and φ are indicated by thin solid line segments oriented horizontally; their locations along the ordinate are based on previous measurements.24 In a molecular area versus temperature phase diagram, the features demarcating three-phase coexistence extend over a line segment; we refer to these as triple-point lines. The temperatures of these triple-point lines, from Table 1, are labeled T1 through T4 in Figure 8. The open squares labeled A through F in Figure 8A represent the locations of the corresponding frames in Figure 7. This phase diagram is consistent with the growth sequences shown in Figures 2-6. Determining the density of fluid phases is problematic because individual molecules cannot be resolved and counted, as they can for crystalline phases. Nevertheless, we calculated the densities of the fluid phases, R and , by using measured fractional areas of coexisting phases in heating-cooling experiments at constant coverage. As an example, consider Figure 7E and F. The number of molecules in the χ-phase in frame E is given by the product of the area of the χ-phase in frame E (Aχ,E) and the density of the χ-phase (Fχ). The number of molecules in frame E is the sum of the molecules in phases χ and β. Assuming that the areal phase fraction in each image is representative of the whole surface, and invoking conservation of mass, the number of molecules in frame F is equal to that in frame E:

Aχ,EFχ + Aβ,EFβ ) A,FF + Aβ,FFβ

(2)

Solving for Fβ and taking the reciprocal provides the molecular area of the -phase in coexistence with β at 37.6 °C. The values obtained along with those from similar measurements of the -phase in coexistence with striped phases were plotted as filled circles in Figure 8A. Similar calculations were made for the -phase in coexistence with φ (filled diamonds) and for the -phase in coexistence with R (filled squares) with the further assumption that the density of the R-phase is negligible. These data points were used as a rough guide to sketch (as solid heavy lines) the freezing curves for β, χ, and δ, the low-temperature segment of the φ-phase freezing curve, and the initial -phase segment of the R- coexistence curve. Due to the imprecision of the calculation of -phase densities, -phase endpoints of T2, T3, and T4 and the -phase intersection with T1 are not accurately known. We have no measurement of the high-density φ-phase freezing curve, the remainder of the R- coexistence curve, and the R f β condensation curve. These three features were arbitrarily sketched using dashed lines to complete the diagram. The R- coexistence curve encompasses the (36) Dash, J. G.; Suzanne, J.; Shechter, H.; Peierls, R. E. Surf. Sci. 1976, 60, 411.

Figure 8. (A) Proposed two-dimensional phase diagram in temperature versus molecular area for monolayer decanethiol on Au(111). Triple-point lines are labeled as T1-T4. Singlephase regions for β, χ, and δ are encompassed by thin horizontal lines. Filled symbols represent -phase density in two-phase coexistence; circles are for equilibrium with striped phase; filled diamonds are for equilibrium with φ; filled squares are for equilibrium with R. Filled symbols were used as a rough guide to draw freezing curves (solid curves). Labeled open squares indicate locations of corresponding frames in Figure 7. sf indicates hypothetical region of two-dimensional supercritical fluid. Speculative aspects of the diagram are drawn as dashed curves. (B) Pressure-temperature phase diagram. Surface pressure π was not measured; the π-axis is merely schematic, neither calibrated nor linear. Two-phase regions in frame A collapse to phase boundary lines in frame B; triple-point lines in frame A collapse to triple points in frame B. Labeled open squares indicate locations corresponding to frames in Figure 7.

region at temperatures above the R-β- triple-point line where gas and liquid coexist as separate phases in thermodynamic equilibrium; its maximum is the critical point. For temperatures above the critical point the growing monolayer would exist as a supercritical fluid transforming continuously from gaslike to liquidlike with

Phase Diagram of Decanethiol on Au(111)

increasing coverage. Abrupt boundaries separate R and  at 59 °C (see Figure 6A and B); therefore, the critical point temperature must be greater than 59 °C. This study did not explore sample temperatures greater than 63 °C because of instrumental limitations; the critical temperature value depicted in Figure 8 was chosen arbitrarily. Moreover, R may condense into β at significantly higher molecular areas than depicted in Figure 8, as is seen for insoluble monolayers at the air-water interface.37 Though we have no measure of the lateral pressure π, we can schematically diagram a π-T phase diagram using the data in Figure 8A and assuming π is greater for higher density phases (see Figure 8B). The triple-point lines collapse into triple points, and the regions of two-phase coexistence collapse into phase boundary lines when Figure 8A is projected onto Figure 8B. The slopes of the boundaries separating commensurate solid phases are assumed positive; we have no measure of the enthalpy or entropy of the transitions. The positions corresponding to frames A-F in Figure 7 are again plotted as open squares. Figure 8B exhibits similarities to the phase diagram of water, which has a voluminous solid, relative to the melt, at low pressures, and dense solids at higher pressures.38 In this study, we assumed that observed phase changes were simple changes in molecular packing arrangement, without concomitant chemistry. At some point during monolayer self-assembly, however, the thiol hydrogen is lost.39,40 Recent experiments that correlate STM topographs with thermal desorption data indicate that thiol hydrogen scission and desorption is complete by saturation coverage of the β-phase.39,40 This is corroborated in the present study; reversible transitions between  and the striped phases (e.g., Figure 7) suggest that these transitions are simple phase changes, without concomitant thiol hydrogen scission. The transition from R to β exhibits some irreversibility,34 suggesting that the two-dimensional gas may comprise thiols and the transition to the β-phase may involve loss of hydrogen. We have no direct evidence for this, however, and there are other explanations for the observed irreversibility.34 The transition from  to φ was not checked for reversibility. Except where noted, we assume that the system is in thermodynamic equilibrium and that the diagrammed phases are stable. Because our measurements were made in a pumped UHV system, this is not strictly true. Surface thiolates have a finite desorption probability, and those that desorb are lost to the pump. Stable surface phases can be realized, at least in a thought experiment, by establishing equilibrium with a bulk gas in a sealed system. Imagine a 1 cm3 box with one gold wall and five inert walls at room temperature into which we place 1014 thiol molecules. Depending on the partitioning between bulk and surface phases, an equilibrium would be (37) Knobler, C. M. J. Phys.: Condens. Matter 1991, 3, S17. (38) Atkins, P. W. Physical Chemistry; W. H. Freeman: New York, 1986. (39) Kondoh, H.; Kodama, C.; Nozoye, H. J. Phys. Chem. 1998, 102, 2310. (40) Kondoh, H.; Kodama, C.; Sumida, H.; Nozoye, H. J. Chem. Phys. 1999, 111, 1175.

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established between a bulk gas and R/β or β/χ on the gold wall. This could be called an “equilibrium across dimensionality”.2 In our case, with measurements made over 40 days in UHV, the rate of molecule desorption or disruption was less than 0.2% per day. Consequently, we believe that our system is reasonably close to thermodynamic equilibrium. In previous work metastability was assigned to the χ-phase at room temperature. This was based on the observation that, over several days, the χ-phase spontaneously converted into phases termed β′ and δ′.24 In the present study we observed the same temporal instability of the χ-phase. Two other observations, however, suggest that the χ-phase may be stable. In this study, the χ-phase nucleated both from β with increasing coverage (Figure 2) and from  with decreasing temperature (Figure 7). In a separate study, a χ-phase variant nucleated from the δ-phase with decreasing coverage.25 In drawing the phase diagram, we assume that χ is stable; however, based on conflicting reports, its stability is indeterminate. In addition to the phases diagrammed in Figure 8, there exist phases that are subtle variations on β, χ, and δ.11,24-26,41 These variations may have different packing densities and belong to different plane groups. They may also be stable phases with boundaries in the twodimensional equilibrium phase diagram. For simplicity we do not explicitly consider them in this paper. We caution the reader, however, that the equilibrium phase diagram may be more complicated than the model depicted in Figure 8. Conclusions We measured isothermal growth of decanethiol on Au(111) at fixed temperatures between 20 °C and 60 °C. The temperatures of three-phase coexistence were determined using constant-coverage heating-cooling cycles, and some values of the temperature-dependent -phase density were determined by analyzing these data with the constraint of conservation-of-mass. This study establishes a working model for the phase diagram of a solid-supported monolayer of amphiphilic molecules. The derived phase diagram is subject to further refinement by measuring the -φ freezing curve, the R- coexistence curve, and the R-phase density at β-phase condensation. The work described here highlights the complexity of phase behavior for long-chain amphiphile monolayers and paves the way for studies of the effect of chain-length and end-groups on the phase diagrams of amphiphile monolayers. Acknowledgment. G.E.P. is grateful for helpful discussions with W. J. Boettinger, P. Cook, J. W. Cahn, G. Scoles, J. M. H. Levelt-Sengers, and M. R. Moldover. J.M.W. acknowledges support by the U.S. Department of Energy, Office of Basic Energy Sciences. LA0012788 (41) Gerlach, R.; Polanski, G.; Rubahn, H.-G. Appl. Phys. A 1997, 65, 375.