Thermodynamics of Decanethiol Adsorption on Au(111): Extension to

Organic SAMs can be “tailored” by systematic variations of (1) the group that binds to ... Using the Au(111) on mica system, we report here lower ...
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Langmuir 2002, 18, 2096-2102

Thermodynamics of Decanethiol Adsorption on Au(111): Extension to 0 °C W. P. Fitts† and J. M. White* Center for Materials Chemistry, Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712

G. E. Poirier‡ Chemical Science and Technology Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 Received May 23, 2001. In Final Form: December 12, 2001 The coverage-dependent phase behavior of the thiolate formed from decanethiol, CH3(CH2)9SH, on Au(111) was studied at 0 °C using variable-temperature scanning tunneling microscopy and compared to analogous results for temperatures between 25 and 65 °C. At 0 °C, the lowest density striped phase, β, converts to higher density striped phases, δ and χ, at exposures that are significantly less than those required at room temperature. The upright saturation phase, φ, is also obtained with a lower relative exposure. We discuss these results using an extrapolation of the schematic two-dimensional pressure (π) versus temperature phase diagram developed in previous work. The observed low-temperature phase behavior is rationalized on the basis of thermodynamic considerations. By use of a schematic plot of phase chemical potential versus lateral pressure, the range of exposures over which various phases are thermodynamically stable is assessed as a function of temperature between 0 and 65 °C.

1. Introduction Self-assembled monolayers (SAMs) are formed from a class of molecules that, upon exposure to a surface, form ordered two-dimensional arrays of adsorbates with the degree of ordering depending on molecular structure, substrate morphology, coverage, and temperature.1 Because substrate-chain and chain-chain interactions are limited to the surface, SAMs offer the opportunity to study complex interactions in two dimensions.2,3 SAMs adsorbed on well-defined substrates serve as model systems from which one can gain a fundamental understanding of two-dimensional self-organization, structural-chemical/thermal property relationships, and interfacial phenomena. Organic SAMs can be “tailored” by systematic variations of (1) the group that binds to the substrate (head), (2) the groups along the backbone, and (3) the terminal group (tail).4-10 In addition to their fundamental importance, SAM films have applications in * Corresponding author. Phone: 512-471-3704. Fax: 512-4719495. E-mail: [email protected]. † Present address: Intel Corp., 5200 N.E. Elam Young Parkway, MS AL3-66, Hillsboro, OR 97124. ‡ Deceased. (1) Ulman, A. An Introduction to Organic Films: From LangmuirBlodgett to Self-Assembly; Academic Press: San Diego, 1991. (2) (a) Ulman, A. Chem. Rev. 1996, 96, 1533. (b) Dubois, L. H.; Nuzzo, R. G. Annu. Rev. Phys. Chem. 1992, 43, 437. (c) Poirier, G. E. Chem. Rev. 1997, 97, 1117. (3) Sellers, H.; Ulman, A.; Shnidman, Y.; Eilers, J. E. J. Am. Chem. Soc. 1993, 115, 9389. (4) Dubois, L. H.; Zegarski, B. R.; Nuzzo, R. G. J. Chem. Phys. 1993, 98, 678. (5) Fenter, P.; Eisenberger, P.; Liang, K. S. Phys. Rev. Lett. 1993, 70, 2447. (6) Jung, C.; Dannenberger, O.; Xu, Y.; Buck, M.; Grunze, M. Langmuir 1998, 14, 1103. (7) Li, T.-W.; Chao, I.; Tao, Y.-T. J. Phys. Chem. B 1998, 102, 2935. (8) Camillone, N.; Chidsey, C. E. D.; Liu, G.-Y.; Scoles, G. Langmuir 1996, 12, 2737. (9) Poirier, G. E.; Pylant, E. D.; White, J. M. J. Chem. Phys. 1996, 105, 2089.

electrochemistry,11 biosensing,12,13 and studies of corrosion and wetting.14-16 A variety of ordered and disordered thiolate structures have been identified as the coverage is increased at 25 °C.17 Expanding the temperature range from 25 to 65 °C, we recently reported the first complete two-dimensional phase diagram of decanethiolate on Au(111).18 The work involved two Au(111) substrates, bulk Au(111) and thinfilm Au(111) on mica, and high-resolution scanning tunneling microscopy (STM) measurements in two laboratories. Both substrates gave the same results. Using the Au(111) on mica system, we report here lower temperature, 0 °C, results and present a qualitative thermodynamic analysis of the data from 0 to 65 °C. The chemical state reached upon adsorption is relevant. Recently, the question of dissociative versus nondissociative adsorption of thiols on Au(111) has been clarified in favor of S-H bond breaking below 0 °C.19 Electron energy loss spectroscopy shows evidence for Au-S bond(10) Wolf, H.; Ringsdorf, H.; Delamarche, E.; Takami, K.; Kang, H.; Michel, B.; Gerber, Ch.; Jaschke, M.; Butt, H.-J.; Bamberg, E. J. Phys. Chem. 1995, 99, 7102. (11) Gewirth, A. A.; Niece, B. K. Chem. Rev. 1997, 97, 1129. (12) Ferretti, S.; Paynter, S.; Russell, D. A.; Sapsford, K. E. TrAC, Trends Anal. Chem. 2000, 19, 530. (13) Gano, K. W.; Myles, D. C. Tetrahedron Lett. 2000, 41, 4247. (14) Zamborini, F. P.; Crooks, R. M. Langmuir 1998, 14, 3279. (15) Schmidt, E.; Schurig, W.; Sellschopp, W. Tech. Mech. Thermodyn. 1930, 1, 53. (16) Bigelow, W. C.; Pickett, D. L.; Ziseman, W. A. J. Colloid Interface Sci. 1946, 1, 513. (17) (a) Poirier, G. E. Langmuir 1999, 15, 1167. (b) Toerker, M.; Staub, R.; Fritz, T.; Schmitz-Hu¨bsch, T.; Sellam, F.; Leo, K. Surf. Sci. 2000, 445, 100. (c) Staub, R.; Toerker, M.; Fritz, T.; Schmitz-Hu¨bsch, T.; Sellam, F.; Leo, K. Langmuir 1998, 14, 6693. (d) Poirier, G. E.; Pylant, E. D. Science 1996, 272, 1145. (e) 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. (18) Poirier, G. E.; Fitts, W. P.; White, J. M. Langmuir 2001, 17, 1176. (19) Kodama, C.; Hayashi, T.; Nozoye, H. Appl. Surf. Sci. 2001, 264, 169.

10.1021/la010766s CCC: $22.00 © 2002 American Chemical Society Published on Web 02/02/2002

Thermodynamics of Decanethiol Adsorption

ing, and thermal desorption spectroscopy exhibits H2 and thiolate radical desorption. Thus, we present the discussion in terms of self-organization of decanethiolate, CH3(CH2)9S(a), where the subscript (a) indicates a chemical bond between Au and S. The question of the position of the sulfur atom with respect to the underlying gold atoms continues to be investigated.20,21 Comparing the vibrational spectra with density functional theory calculations for the shortest thiol, CH3SH, indicates that methylthiolate (CH3S-) does not adsorb in a 3-fold site; rather, for monolayer coverages, it is most stable in a bridge site with its S-C bond tilted by more than 45° from the surface normal.21 As the coverage drops, the calculations indicate that the 3-fold site, while not the most stable, becomes more favorable. Other work,20 at lower coverage, concludes that methylthiolate occupies a 3-fold site. For decanethiolate, the position, probably coverage-dependent, of the sulfur with respect to the surface gold atoms remains an open question. 2. Experimental Section As in our previous report,18 the experiments were carried out in a commercially designed ultrahigh vacuum (UHV)-STM (Omicron Vacuumphysik) operating at a base pressure of 2 × 10-10 Torr. The chamber is divided into two parts, one for dosing and performing STM measurements and the other for preparation and characterization by Auger electron spectroscopy (AES) and low-energy electron diffraction (LEED). Substrates were composed of thin-film gold (2000 Å) evaporated on mica. All Au samples were cleaned by Ar+ sputtering (1 keV, 1 µA, 20 min) and annealing from 400 to 500 °C to give a clean surface according to AES and, after transfer for STM, herringbone reconstructed areas on terraces ∼500 Å wide with occasional Au(111) atomic resolution. Decanethiol was stored in Viton-sealed glass vessels attached to the STM portion of the vacuum system via a variable aperture leak valve. The decanethiol was purified by repeated freeze-thaw cycles, and its purity was confirmed using in situ mass spectrometry. Reproducible doses were realized by opening the leak valve to give an ion gauge reading between 5 × 10-8 and 1 × 10-7 Torr (calibrated for N2) and dosing for times ranging between 10 s and 10 min. Decanethiol doses were repeated three times with reproducible STM results. Between experiments, the chamber was baked for 20 h at 140 °C to remove residual decanethiol. As outlined below, we determine coverages directly from the STM images. Operationally, we report relative doses in effective langmuir units, 1 langmuir ) 1 × 10-6 Torr s, where the effective pressure is the ion gauge output. For dosing and tunneling, the sample holder was mechanically fixed to the STM stage. A PID-controlled heater was mounted in a coldfinger that was attached to the STM stage by many fine Cu wires. Si diode temperature sensors were mounted on the STM stage and on the cryostat heat exchanger. Counter-heating of a liquid nitrogen continuous flow cryostat system maintained precise temperature control. The high-temperature limit using the heater block was ∼65 °C (with no cooling), and the lowtemperature limit was ca. -163 °C. The sample temperature was determined by measuring the temperature of the sample stage and calibrating it against a thermocouple attached to a reference gold-on-mica sample. Between 0 and 25 °C, the maximum deviation between the sample stage and the sample was 0.3 °C. STM data were acquired in constant tunneling current mode with a set point between 10 and 100 pA and tunneling bias between (0.2 and (1.2 V. While relative exposures are simple to measure, absolute exposures (molecules dosed cm-2) cannot be reliably determined in our system.18 This is not critical since coverage, not exposure, is the central parameter of interest and since, for ordered phases, local coverages (thiolates per unit area) are determined reliably and reproducibly by counting the number of molecules per unit (20) Groenbeck, H.; Curioni, A.; Andreoni, W. J. Am. Chem. Soc. 2000, 122, 3839. (21) Hayashi, T.; Morikawa, Y.; Nozoye, H. J. Chem. Phys. 2001, 114, 7615.

Langmuir, Vol. 18, No. 6, 2002 2097 area in an STM image. While this cannot be done for two disordered phases that we observe, sensible results have been obtained assuming that coverages in such phases lie between those of the ordered phases that appear at higher and lower relative exposures.

3. Results As a result of the complex interactions of decanethiolate with the surface and with itself, dosing decanethiol onto a clean surface leads to a sequence of two-dimensional phases appearing in the following order as coverage increases: lattice gas, R; three striped phases, β, χ, and δ; a two-dimensional liquid (melt) phase, ; and an upright (saturation) phase, φ.17 Typical STM images and schematic side views of these ordered decanethiolate phases are shown in Figure 1. As described in our previous paper,18 we examined the stability of coexisting decanethiolate phases by making measurements as a function of time and by approaching selected coverage and temperature conditions from both higher and lower values. Since the measurements were made in a pumped UHV system, equilibrium with the gas phase is not strictly realizable but the rate of loss by pumping is less than 0.2% per day. Thus, we suppose that the images are taken under conditions that are indistinguishable from equilibrium. STM at 25 °C. For comparison with the 0 °C data reported in this paper, we repeated the 25 °C work reported previously (Figure 2).18 Briefly, for the lowest coverage (Figure 2A), regions of R and β appear. As indicated in Figure 1, β is the lowest density ordered phase and appears in equilibrium with the lattice gas phase (R) in this coverage regime. The easily recognized striped β phase exhibits corrugated rows aligned along substrate 〈121〉 directions with a 5 Å periodicity, an inter-row spacing of 33 Å, and a molecular area of 82.8 Å2/thiolate. Increasing the coverage (not shown) saturates the β phase by lateral growth of β phase islands, elimination of the R phase, and coalescence of neighboring islands. Adding even more thiolate results in heterogeneous nucleation of the χ phase (not shown) that grows laterally at the expense of the β phase. In general, unambiguous separation of the χ and δ phases in STM topographs is difficult. χ involves rows of molecules lying down, as in the β phase, and molecules with interdigitated alkyl chains (as in the δ phase). The out-of-plane interdigitation of alternating rows of χ reduces the area per species to 65 Å2. While the stability of the χ phase is debatable,8,17 we include it in the final phase diagram for reasons outlined in our previous paper.18 Beyond saturation of χ, heterogeneous growth of δ phase domains commences (Figure 2B). This phase exhibits row segments that have a corrugation periodicity of 5 Å parallel to substrate 〈121〉 directions and a periodicity of 22 Å. The interdigitation retains the paired S-S rows, each decanethiolate occupying 54 Å2. For coverages exceeding saturation of the δ phase, a disordered metastable phase, , attributed to fluid decanethiolate forms by edgemediated melting of δ. Finally, relaxation of the  phase forms a saturation ordered monolayer phase, φ (Figure 2C). In this phase, the area per decanethiolate (21.6 Å2) is less than half that of the δ phase. IR and diffraction data show that, unlike the lower density phases, the alkyl chains in φ lie toward the surface normal (60° away from the surface plane).22 On the basis of STM observations, as coverage increases, the ordered phases appear in the (22) (a) Camillone, N.; Chidsey, C. E. D.; Liu, G.-Y.; Scoles, G. J. Chem. Phys. 1993, 98, 3503. (b) Nuzzo, R. G.; Korenic, E. M.; Dubois, L. H. J. Chem. Phys. 1990, 93, 767.

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Figure 1. STM images (left side) and schematic side views of the phases of decanethiolate. At the lowest coverage, the surface is composed of a weakly interacting, mobile lattice gas, R. As coverage and interadsorbate interactions increase, thiolate first condenses into a series of low density “striped” phases, β and δ, each with an increasing degree of out-of-plane interdigitation. Finally, the thiol stands up, 30° off normal, in a close-packed saturation phase, φ. A melt phase,  (not shown), is a slowly diffusing phase whose density lies somewhere between those of the δ and φ phases. From top to bottom, the length scales of the images are 140 × 140 nm, 18 × 18 nm, 12 × 12 nm, and 28 × 28 nm.

Figure 2. Thiolate monolayer growth at 25 °C. β phase domains nucleate from the lattice gas (A), convert to the next higher striped phase, δ, with increasing exposure (B), and ultimately form the upright saturation phase, φ (C).

following sequence at 25 °C: R f β f χ f δ f φ. At 40 °C, the χ and δ phases are unstable, the  phase is stable, and the growth sequence becomes R f β f  f φ.18 STM at 0 °C. Figure 3 summarizes an isothermal growth study done at 0 °C. Coupled with results at 25 and 40 °C, several aspects of the pressure-temperature (dπ/

dT) relationship of the two-dimensional solid-solid phase transitions can be assessed. Following a dose of 2 langmuir, the clean Au(111) herringbone reconstructed substrate (Figure 3A) promptly (within the 30 min required to begin imaging) exhibited small domains of β and δ phases in two-phase coexistence

Thermodynamics of Decanethiol Adsorption

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Figure 3. Thiolate monolayer growth at 0 °C. Prior to exposure, the surface exhibits the characteristic herringbone reconstruction (A). At 2 langmuir exposure, small domains of β and δ coexist (B). With increasing exposure, the δ phase saturates the surface (C,D). At significantly higher exposures (∼50 langmuir), saturation phase islands (φ) nucleate from the δ phase (E). Warming to 25 °C with no further dosing enlarged the φ phase islands and temporarily melted the remaining δ phase (F). Each image is 100 × 100 nm.

(Figure 3B), separated by herringbone-induced 60 Å bands of R phase (e.g., dashed line in Figure 3B). Upon increasing the exposure to 10 langmuir (Figure 3C), δ phase domains grew at the expense of β until the surface was completely covered with small domains of δ phase, still separated by narrow R phase domains (e.g., dashed line in Figure 3C). Narrow Au(111) herringbone-induced “bands” of lattice gas thiolates are commonly observed at low and intermediate coverage (eβ/δ coexistence). When the exposure was doubled (20 langmuir) the herringbone-induced bands of R phase disappeared and the image was saturated with the δ phase (Figure 3D). Evidently, the herringboneinduced properties are altered significantly as the coverage increases beyond some critical coverage. The relation of thiolate adsorption, phase structure, and the herringbone Au(111) reconstruction will be discussed in a separate paper.23 Upon increasing the effective dose to 50 langmuir, the φ phase nucleates within δ phase terraces (Figure 3E). Slowly warming from 0 to 25 °C led to nucleation of isolated φ phase regions and melting of the remaining δ domains to form  phase regions (Figure 3F). As expected from previous work,18 the  phase is metastable at 25 °C and evolves to the δ phase over time (not shown). Higher resolution images, Figure 4, are helpful. The geometry of a δ phase domain (Figure 4a) exhibits periodicity between rows of 22 Å, in agreement with literature values.19 More detailed analysis indicates the expected structural change (wavy appearance in Figures 2B and 4a) along the rows (〈121〉 direction) every 5-6 thiolates.24 The darker and structureless feature (along(23) Fitts, W. P.; Poirier, G. E.; White, J. M. Langmuir, in press.

side the dashed line) running parallel to the δ phase rows is an example of a herringbone-induced lattice gas band (R phase). Panel 4b is an image of the β and δ phases in coexistence at low exposure (∼5 langmuir). The small size of β phase domains (no more than 100 Å long) is unique to lowtemperature exposure; exposure at 25 °C and above leads to β phase domains that often propagate for hundreds of angstroms. This observation provides evidence that the complex intermolecular forces governing thiolate phase behaviors are closely linked, not surprisingly, with surface temperature as well as coverage. To summarize, at 0 °C, small β and δ phase domains formed and evolved into pure δ phase domains with an exposure of 10 langmuir. No β phase domains were observed for exposures above 10 langmuir. Islands of the saturation φ phase formed from δ at 50 langmuir and with warming grew at the expense of the metastable melt phase. 4. Discussion Our previous VT-STM study, from 25 to 65 °C, led to the development of a molecular area versus temperature phase diagram for thiolate on Au(111) that was compared to previous work17 and converted qualitatively to a more conventional relative lateral pressure (π) versus temperature diagram.18 Adding the 0 °C data provides an important extension to the π-T phase diagram and helps establish previously unavailable solid-solid phase relationships. (24) Fitts, W. P. Ph.D. Dissertation, University of Texas at Austin, Austin, TX, 2001.

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Figure 5. A lateral pressure (µ) vs T phase diagram of thiolate on Au(111) over the temperature range of 0-65 °C. A vertical gray line represents the monolayer growth experiment at 0 °C. A-E depict the frame sequence in Figure 3. T1-T4 represent the triple point temperatures determined in a previous study (ref 18).

two-dimensional Clapeyron equation:25

∆H dπ ∆S ) ) dT ∆A T∆A where ∆A is the area change. For sublimation, that is, along the β-R phase boundary (Figure 5), this becomes Figure 4. Two detailed views of the thiolate phase structure at 0 °C. (a) A 50 × 50 nm topograph of a large δ phase domain at 10 langmuir exposure. The stripe periodicity is 22 Å. The dark feature along the dashed line located on the right side of the domain parallel to the stripes is a herringbone-induced lattice gas domain. (b) A 102 × 102 nm image of several phases at low temperature. Very small β phase domains coexist with larger δ phase domains.

The extended π versus T diagram is shown in Figure 5. The five data points (A-E) extracted from Figure 3 are placed along the dashed vertical gray line. The previous data18 (gray region above 25 °C in Figure 5) are connected with smooth curves between 0 and 25 °C. Regions of twophase coexistence are depicted as solid lines separating the various thiolate phases. Consistent with the STM data, the sublimation curve separating the R and β region is drawn to reflect the lower π (dose) required for formation of the solid β phase at 0 °C. The solid-solid phase boundary between δ and χ is drawn as a dashed line to reflect the ambiguity regarding these two phases noted earlier. In the following, we denote this region as the δ/χ phase. The small π range (coverage range) over which β was observed at 0 °C (Figure 3B) is accounted for in the phase diagram by constructing the β-δ/χ coexistence curve so the gap between R-β and β-δ/χ shrinks as the temperature decreases from 25 to 0 °C. Compared to 25 °C, at 0 °C the δ/χ phase (Figure 3D) emerges at lower coverage and extends over a much broader π range (Figure 3E). Thus, the coexistence curve separating δ/χ and φ is drawn with a lower slope than that separating β and δ/χ. Since absolute lateral pressures are not available, the π versus T phase diagram is semiquantitative. However, we can gain insight based on the relative magnitudes and positive or negative slopes (dπ/dT) of the two-phase boundaries. For the solid-liquid, liquid-vapor, and solid-vapor phase transitions, we make use of the

∆Hsub dπβfR ∆Ssub ) ) dT ∆Asub T∆AβfR where the subscript sub indicates sublimation in two dimensions. The entropy of the ordered crystalline phase is lower than that of the lattice gas phase; therefore, SR - Sβ ) ∆Ssub > 0. The lattice gas, composed of a loose ensemble of weakly interacting thiolates, occupies a much greater molar area than that of the ordered β phase; therefore, ∆Asub > 0 and dπβfR/dT is small but positive. A similar argument holds for the liquid-vapor transition ( > R); that is, enthalpy, ∆Hvap, and entropy, ∆Svap, of vaporization are both positive. Further, ∆Avap < ∆Asub making dπfR/dT positive and larger than the corresponding slope for sublimation. For the solid-liquid transition (e.g., β > ), ∆H > 0. The area changes, ∆A, are assessed using the STM results. The striped phases (β, χ, and δ) all have a lower density than the fluid phase () while the close-packed phase (φ) has a higher density. This results in a negative slope, dπ/dT, in the case of a β (or χ/δ) f  transition (along the line segment from T4 to T1) but a positive slope for a φ f  phase transition (segment originating at T1 and extending upward as T increases). Compared to the other transitions to , that from φ to  does not involve as large a change in molar area. Consequently, |dπ/dT| characterizing the φ f  transition is larger. We turn to the solid-solid phase transitions, that is, β to δ/χ and δ/χ to φ. ∆A is straightforward and quantitative; the molecular area of each solid phase can be determined directly from STM images; the numerical values are -1.4 × 105 m2 mol-1 for the β to δ/χ transition and -2.2 × 105 m2 mol-1 for the δ/χ to φ transition. While neither ∆H nor ∆S is known, the 0 °C STM results indicate that the slope, (25) Atkins, P. Physical Chemistry; W. H. Freeman: New York, 1994.

Thermodynamics of Decanethiol Adsorption

dπ/dT, of the phase boundary separating β and δ/χ is positive and steeper than the β-R sublimation boundary since the π range over which pure β phase forms is very narrow compared to the range of the δ/χ phase. A similar argument applied to the boundary separating δ/χ and φ indicates a smaller positive slope than the boundary between β and δ/χ. In passing, we note that a constant coverage-variable temperature study might reveal the existence of additional triple points below 25 °C. For example, observation of β-R-χ three-phase coexistence would establish the lower temperature limit of β phase stability. Further, as the surface temperature is lowered, the lattice corrugation potential of gold, even though comparable or smaller than kT in our experiments, will alter the phase diagram. This remains an important issue for future study. Assuming Figure 5 represents the thiolate-on-gold system, certain aspects of the chemical potential can be assessed. Qualitatively, we can construct isothermal µ versus π curves for each phase. The intersections of these curves identify lateral pressures where two phases have the same chemical potential and will, therefore, coexist at equilibrium.26 Below and above these intersections, only the phase with the lowest chemical potential is thermodynamically stable. The qualitative construction proceeds by determining the slope of the chemical potential versus lateral pressure at constant T. For a pure substance in two dimensions, the desired relation is

(∂π∂µ)

T

)A

where A is the molar area that is available from the STM results. By use of results at one temperature as a reference, curves for other temperatures can be constructed using the two-dimensional temperature dependence of the chemical potential:

∂µ (∂T )

) -S

π

where S is the molar entropy.25 These entropies are not available, but we can reasonably assess how they vary from one phase to another using the arguments presented in conjunction with Figure 5. Combining the data reported here with that reported earlier,18 Figure 6 schematically shows five isothermal curves constructed in this way where diamonds identify the crossing points. Beginning with the 0 °C results, five segments are shown representing the observed phases. Each segment has a slope determined by the molar area (always positive), and because the molar area decreases from phase to phase as π increases, the slopes monotonically decrease in passing from R to φ. While the ranges of π are unknown, we do know that relative ranges, that is, R and β, are both quite narrow compared to δ/χ, and there is no well-defined upper limit on π. Thus, along the 0 °C curve, we begin with R and place the segments to mimic this experimental observation. The dashed segments extending R and β represent thermodynamically unstable extrapolations associated with each phase. Using the 0 °C curve as a reference, we estimate where the isothermal (25 °C) curve should be placed. First, increasing the temperature shifts all the segments downward by an amount equal to the entropy change associated with that phase, the largest shift for R and the (26) Sandler, S. I. Chemical and Engineering Thermodynamics; Wiley: New York, 1989.

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Figure 6. A schematic plot of chemical potential (µ) vs π for several temperatures. The phase sequence with increasing exposure is shown as a series of lines. The intersection points, diamonds, are regions of two-phase coexistence. With increasing temperature, the phases with the lowest relative entropy shift downward the least and thus “drop out” of thermodynamic stability at high T. The melt phase, , has a high degree of entropy and is stable over a large pressure range at T g 40 °C. At 65 °C, the only equilibrium phases are those with the highest entropy (R, ).

smallest shift for φ. The mathematical consequence of asserting that R shifts the most (highest entropy) is that its width increases, that is, the R segment intersects the β segment at a higher pressure. Similarly, asserting that φ shifts the least is that the δ/χ segment intersects the φ segment at higher π. To locate the intersection of the β and δ/χ segments at 25 °C, we assert, sensibly, that while SR . Sβ > Sδ/χ, the latter two are not very different. The result, depicted in Figure 6, is a wider β region and a slightly narrower δ/χ region, as observed experimentally. Between 25 and 40 °C, the situation changes because a new phase, , enters the picture between the φ and δ/χ phases with entropy exceeding both and with a molar area lying between those of the φ and δ/χ phases. The corresponding curve in Figure 6 is shown as a set of narrow lines, labeled T. The phase  is placed as a dashed line segment with a slope that is, by arguments made above, only slightly steeper than the φ phase. However, the entropy of , like R, is high compared to the entropy of φ and δ/χ. From the curve at T to that at 40 °C, it is clear that the construction places  as the lowest chemical potential over a very broad range of π that excludes the δ/χ and will at even higher T exclude the β and φ phases, that is, there will be no lateral pressure where the chemical potential of β, δ/χ, or φ lies below that of R or . In accord, at 65 °C only the phases with the highest entropy (R, ) “survive” and result in a phase sequence of R f , with no intermediate low-density solid phases.18 5. Summary The phase behavior of a well-known self-assembled monolayer system, decanethiolate on Au(111), was studied with VT-STM at 0 °C and compared to previous results for temperatures between 25 and 65 °C.18 At 0 °C, the lowest density striped phase, β, is only stable over a small exposure range, and for exposures in effective langmuirs, >2 langmuir converts into the higher density δ phase (taken to include a χ phase that may be metastable) and denoted δ/χ. Domains of the saturation phase, φ, grow at the expense of the δ phase at an exposure of ∼50 langmuir.

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The 0 °C behavior was used to extend a lateral pressure (π) versus temperature phase diagram developed for the region of 25-65 °C in an earlier study.18 By relating the pressure-temperature relationship of the solid-vapor, solid-melt, vapor-melt, and solid-solid phase boundaries, we construct a qualitative phase diagram. The thermodynamic relation requiring phases in equilibrium to have the same chemical potential was used to qualitatively account for the phases that disappear from images taken as π increases while holding the temperature constant.

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Acknowledgment. The authors gratefully acknowledge financial support by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Services, Office of Science, U.S. Department of Energy, through Grant DE-FG03-93ER14334. J.M.W. acknowledges the support by the Robert A. Welch Foundation (Welch Chair of Chemistry). LA010766S