pubs.acs.org/Langmuir © 2010 American Chemical Society
Investigation of the Behavior of Ethylene Molecular Films Using High Resolution Adsorption Isotherms and Neutron Scattering Andi M. Barbour,† Mark T. F. Telling,‡ and J. Z. Larese*,†,§ †
Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, ‡ISIS, Rutherford Appleton Laboratory, Chilton, Didcot, U.K., and §Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 Received November 23, 2009. Revised Manuscript Received January 28, 2010
The wetting behavior of ethylene adsorbed on MgO(100) was investigated from 83-135 K using high resolution volumetric adsorption isotherms. The results are compared to ethylene adsorption on graphite, a prototype adsorption system, in an effort to gain further insight into the forces that drive the observed film growth. Layering transitions for ethylene on MgO(100) are observed below the bulk triple point of ethylene (T = 104.0 K). The formation of three discrete adlayers is observed on the MgO(100) surface; onset of the second and third layers occurs at 79.2 ( 1.3 K and 98.3 ( 0.9 K, respectively. Thermodynamic quantities such as differential enthalpy and entropy, heat of adsorption, and isosteric heat of adsorption are determined and compared to the previously published values for ethylene on graphite. The average area occupied by a ethylene molecule on MgO(100) is 22.6 ( 1.1 A˚2 molecule-1. The locations of two phase transitions are identified (i.e., layer critical temperatures at T(n=1) at 108.6 ( 1.7 K and T(n=2) at 116.5 ( 1.2 K) and a c2 c2 phase diagram is proposed. Preliminary neutron diffraction measurements reveal evidence of a monolayer solid with a lattice constant of ∼4.2 A˚. High resolution INS measurements show that the onset to dynamical motion and monolayer melting take place at ∼35 K and ∼65 K, respectively. The data reported here exhibit a striking similarity to ethylene on graphite which suggests that molecule-molecule interactions play an important role in determining the physical properties and growth of molecularly thin ethylene films.
Introduction The competition between molecule-substrate (M-S) and molecule-molecule (M-M) interactions and the role these interactions play in determining the wetting of interfaces has been described in recent monographs and detailed reviews.1-4 Understanding how these forces influence the adsorption/wetting behavior is an active area of research covering a wide variety of topics ranging from the study of multilayer formation of lung surfactant5,6 to molecular electronics.7-10 Although an extensive set of theoretical models and predictions have been proposed, limitations on the number and variety of substrate/adlayer combinations have precluded a systematic experimental investigation of the full range of M-S and M-M interactions. One classic study of wetting is the adsorption of ethylene on graphite in which Menaucourt, Thomy, and Duval, using volumetric adsorption *Corresponding author. E-mail:
[email protected]. (1) Dietrich, S. In Phase Transitions and Critical Phenomena; Domb, C., Lebowitz, J. L., Eds.; Academic Press: San Diego, CA, 1988; Vol. 12, Chapter 1, Wetting Phenomena, pp 1-218. (2) Schick, M. In Les Houches Session XLVIII: Liquides Aux Interfaces; Charvoline, J., Joanny, J. F., Zinn-Justin, J., Eds.; Elsevier Science Publications: San Diego, CA, 1990; Vol. 12, Chapter 9, Wetting Phenomena, pp 417-497. (3) Bruch, L. W.; Cole, M. W.; Zaremba, E. Physical Adsorption Forces and Phenomena; Dover Publications, Inc.: Mineola, NY, 2007. (4) Bruch, L. W.; Diehl, R. D.; Venables, J. A. Rev. Mod. Phys. 2007, 79, 1381– 1454. (5) Wang, L.; Cai, P.; Galla, H.-J.; He, H.; Flach, C. R.; Mendelsohn, R. Eur. Biophys. J. 2005, 34, 243–254. (6) Follows, D.; Tiberg, F.; Thomas, R.; Larsson, M. Biochim. Biophys. Acta (BBA);Biomembr. 2007, 1768, 228–235. (7) Zheng, Y.; Qi, D.; Chandrasekhar, N.; Gao, X.; Troadec, C.; Wee, A. T. S. Langmuir 2007, 23, 8336–8342. (8) Oehzelt, M.; Grill, L.; Berkebile, S.; Koller, G.; Netzer, F. P.; Ramsey, M. G. ChemPhysChem 2007, 8, 1707–1712. (9) Oncel, N.; Bernasek, S. L. Appl. Phys. Lett. 2008, 92, 133305–133307. (10) Liu, R.; Ke, S.-H.; Baranger, H. U.; Yang, W. J. Chem. Phys. 2005, 122, 044703–044706.
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techniques, observed a series of temperature dependent layering transitions (i.e., formation of an increasing number of discrete adlayers with increasing temperature).11,12 Interestingly, the C2H4/ graphite system also exhibits evidence for a continuous melting of an incommensurate monolayer solid13-15 and the onset of uniaxial rotation well below the monolayer melting point16,17 (i.e., rotational order-disorder transition). Other studies of ethylene adsorption on substrates similar to graphite have been performed using the isostructural equivalent, boron nitride, and the layered dihalide, PbI2; however, the literature is less complete for these systems.18,19 Most importantly, no neutron scattering (i.e., microscopic) results exist for these other ethylene systems making it more difficult to establish the microscopic driving force(s) behind the observed behavior. By selecting a substrate significantly different from graphite and one amenable to examination using neutron scattering techniques, it is possible to compare the physical properties of the two systems and explore the effects introduced by changes in surface corrugation, potential energy landscape, and substrate symmetry and lattice parameters. With that said, one begins to understand the motivation behind an investigation of the adsorption properties of ethylene on MgO(100) surfaces, the results of which are of both (11) Menaucourt, J.; Thomy, A.; Duval, X. J. Phys. Colloq. 1977, 38, C4-195– C4-200. (12) Drir, M.; Nham, H. S.; Hess, G. B. Phys. Rev. B 1986, 33, 5145–5148. (13) Kim, H. K.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. Lett. 1986, 56, 1579– 1582. (14) Larese, J. Z.; Passell, L.; Heidemann, A. D.; Richter, D.; Wicksted, J. P. Phys. Rev. Lett. 1988, 61, 432–435. (15) Larese, J.; Rollefson, R. Surf. Sci. 1983, 127, L172–L178. (16) Larese, J. Z.; Rollefson, R. J. Phys. Rev. B 1985, 31, 3048–3050. (17) Larese, J. Z.; Passell, L.; Ravel, B. Can. J. Chem. 1988, 66, 633–636. (18) Bockel, C.; Menaucourt, J.; Thomy, A. J. Phys. (Paris) 1984, 45, 1391– 1399. (19) Bassignana, I. C.; Larher, Y. Surf. Sci. 1984, 147, 48–64.
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fundamental and industrial interest. Ethylene is the most widely produced hydrocarbon in the world (∼107 million metric tones in 2005), and it is also a potent modulator in plant growth and development (i.e., a plant hormone). Metal oxides, which are used as paint pigments, optoelectronic devices, and catalytic supports, are ideal candidates for use as substrates for ethylene adsorption. In particular, the MgO(100) surface is a good choice because it has a simple rock salt structure, and the (100) is the predominant equilibrium surface.20 Employing MgO(100) also provides a solid framework to build and test theory because this surface is prototypical of many metal oxides. Furthermore, the insulating MgO differs from the semiconducting graphite because the MgO(100) surface exhibits a square lattice (versus hexagonal lattice of the graphite basal plane) and is more corrugated due to the size difference between Mg2þ and O2- ions. The results and discussion below detail the effects and consequences of the changes in substrate, highlight the competition between M-S and M-M interactions, and lay the foundation for future neutron experiments involving phase transitions, dynamics, and structure.
Methods The MgO powder used in this study was synthesized from magnesium vapors using a patented process that yields chemically pure, single faceted nanocubes.21 The rock salt structured cubes have an average edge length of ∼250 nm and a surface area ca. 10 m2 g-1. It has been previously shown that heating the MgO above 900 C reduces the number of surface defects.20,22 Therefore, the powders were annealed under vacuum (10-7 Torr) at 950 C, typically for 36 h, to ensure exposure of the homogeneous (100) face. After heat treatment, the MgO sample is handled in an argon atmosphere to avoid hydroxylation by atmospheric water. Approximately 0.3 g of MgO is needed to fill the two piece sample cell fabricated from oxygen free high conductivity copper (OFHC), which is sealed with an indium gasket. The temperature of the cell was measured and controlled (within 2 mK) using a calibrated platinum resistance thermometer in conjunction with a Neocera LTC-10 temperature controller. The dead space volume of the sample cell was determined using helium gas expansions, and a “calibration” methane isotherm was performed at 77 K to verify the quality and surface area of each sample prior to the ethylene experiments.22 Five different MgO samples from the same batch were used to complete the study over the full temperature range presented here. The total sorption area and area occupied per molecule (APM) for the ethylene monolayer were calculated for every isotherm. The ethylene gas (Matheson, 99.99%) used for the adsorption studies was further purified by using multiple freezepump-thaw cycles. After each adsorption isotherm was completed, the sample cell was warmed to 300 K and evacuated (10-8 Torr) for a minimum of 12 h. Data reduction was aided by using KaleidaGraph, a commercial software package. MgO used in the neutron experiments were prepared in a manner similar to the one described above; however, ∼7 g of MgO is typically loaded into an aluminum sample cell described elsewhere.23 The neutron diffraction work was performed using the time-of-flight (TOF) instrument, OSIRIS, at the ISIS Spallation Neutron Source at Rutherford Appleton Laboratory, U.K. in the diffraction mode. The structural measurement was accomplished by first recording a background diffraction pattern of pristine MgO at 4.2 K. A calibrated amount of deuterated ethylene gas was then added in order to obtain a nominal surface coverage of 0.9 monolayer, which is based on the monolayer capacity of the neutron sample. After annealing and slowly cooling the (20) Cox, P. A.; Henrich, V. E. The Surface Science of Metal Oxides; Cambridge University Press: Cambridge, U.K.,1994. (21) Kunnman, W.; Larese, J. Z. US Patent 6,179,897 2001. (22) Freitag, A.; Larese, J. Z. Phys. Rev. B 2000, 62, 8360–8365. (23) Koehler, C. F.; Larese, J. Z. Rev. Sci. Instrum. 2000, 71, 324–325.
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Figure 1. (a) Three isotherms of C2H4/MgO below the bulk Ttriple at 98.50 K (filled diamond), 92.25 K (filled square), and 83.00 K (filled circle). The moles adsorbed is plotted as a function of reduced pressure (p/p0), where p0 is the saturated vapor pressure at a given temperature. Half of the data points collected are included for clarity. (b) Numerical derivative of isotherms at 98.50 K (filled diamond) and 92.25 K (filled square) in the second and third adlayer region, which clearly shows the presence of three adsorption steps at 98.50 K.
sample (∼1 K min-1) from 140 K, a second diffraction pattern was collected at 4.2 K. Hence, the diffraction pattern used for analysis has the MgO background subtracted. Similar procedures have been successfully used for earlier adsorbed film studies.24-26 Additionally, neutron studies of the elastic incoherent structure factor (EISF) at several C2H4 coverages were performed using the high flux backscattering spectrometer (HFBS) at the NIST Center for Neutron Research (NCNR), Gaithersburg, MD. Temperature scans were made between 5-180 K using a warming rate of 0.3 K min-1. The elastic window scan data were collected at several values of momentum transfer within the range of 0.47 e Q (A˚-1) e 1.75 using an incident neutron energy of 2.08 meV, which results in a 0.6 μeV energy resolution (at the elastic position). We hereafter refer to these measurements as modified (24) Larese, J. Z.; Arnold, T.; Frazier, L.; Hinde, R. J.; Ramirez-Cuesta, A. J. Phys. Rev. Lett. 2008, 101, 165302. (25) Arnold, T.; Cook, R. E.; Larese, J. Z. J. Phys. Chem. B 2005, 109, 8799– 8805. (26) Arnold, T.; Chanaa, S.; Clarke, S. M.; Cook, R. E.; Larese, J. Z. Phys. Rev. B 2006, 74, 085421.
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Figure 2. Four C2H4/MgO isotherms above the bulk Ttriple at 110.00 K (filled circle), 125.00 K (filled square), 130.00 K (filled diamond), and 135.00 K (filled triangle). Half of the data points are shown for clarity. EISF since only a fixed window elastic intensity over a limited range of Q was recorded. Additionally, HFBS is sensitive to dynamic fluctuations on the nanosecond time scale. The software package DAVE was employed to calculate the mean square atomic displacement (MDS) at the lowest coverage (nominally 0.4 monolayer).27
Results Adsorption Isotherms. Figure 1 and Figure 2 display two representative sets of adsorption isotherms for ethylene on MgO(100) or C2H4/MgO. The traces (Figure 1a) start ∼20 K below ethylene’s bulk triple point (Ttriple = 104.0 K), while the set in Figure 2 are above Ttriple and rise to 135 K. Figure 1b clearly shows that as the temperature approaches the Ttriple, the number of adsorption steps increases with temperature (i.e., clear evidence of layering transitions). Figure 2 shows that the number and the sharpness of the adsorption steps decrease as temperature rises above Ttriple. The monolayer capacity for each C2H4 isotherm can be used to calculate the APM for a given temperature because the APM of CH4/MgO is known from neutron diffraction.22 The APM between 100 and 120 K is found to be 23 ( 1 A˚2 molecule-1 (as compared to 17.73 A˚2 molecule-1 for the low density solid phase of C2H4 on graphite).17 We can investigate the thermodynamic behavior of the films as a function of temperature more thoroughly by using the numerical derivative of the moles adsorbed (N) as a function of the equilibrium pressure, p, (e.g., Figure 1b). After identifying p, where the peak position of the numerical derivative appears, a graph of p versus inverse temperature (T-1) can be used to generate a Clausius-Clapeyron (CC) plot of the form AðnÞ lnðpÞ ¼ BðnÞ T
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Table 1. CC Analysis Results for C2H4/MgO System
A(n) B(n) ΔT (K)
n=1
n=2
n=3
n = ¥(s)
n = ¥(l)
1972.7 14.677 85-135
1845.7 17.271 85-130
1851.8 17.810 98-127
2040.3 19.728 85-103.5
1833.0 17.819 105-135
differentiate between the bulk solid (s) and bulk liquid (l) phases. The same convention is employed by others.11,18 The coefficients of determination (R2) for the linear fits are greater than 0.998, except for the n = 1 and the bulk solid linear regressions (both with R2=0.993), which is attributed to the error associated with the pressure resolution at lower temperatures (p ∼1 mTorr). The CC results, along with the temperature ranges studied, are reported in Table 1. The differential enthalpy (ΔH), differential entropy (ΔS), and heat of adsorption (Qads) can be calculated using the following equations. ΔH ¼ -RðAðnÞ - Að¥Þ Þ
ð2Þ
ΔS ¼ -RðBðnÞ - Bð¥Þ Þ
ð3Þ
ð1Þ
where B(n) and A(n) are the y-intercept and slope of the nth layer.28 Linear fits to the CC plots for C2H4/MgO are displayed in Figure 3. The saturated vapor pressure (SVP, p0, or n = ¥) portion of the plot is broken into two regions at 104 K (9.6 10-3 K-1) to (27) http://www.ncnr.nist.gov/dave. (28) Larher, Y. J. Chim. Phys. Physico-Chim. Biol. 1968, 65, 974–976.
Figure 3. CC plot for C2H4/MgO of the first (filled triangle, left axis), second (inverted triangle, right axis), third (circle, right axis) adlayers as well as the bulk solid (filled square, right axis) and bulk liquid (square, right axis) phases, which are in equilibrium with the adfilm. The line through each data set is the linear fit.
ðnÞ
Qads ¼ RAðnÞ
ð4Þ
Equations 2 and 3 are the difference between the nth layer quantity and the bulk value listed in Table 1. Table 2 contains the average thermodynamic values ΔH, ΔS, and Q(n) ads for C2H4/MgO DOI: 10.1021/la9044368
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Barbour et al. Table 2. Comparison of C2H4/Graphite18 and C2H4/MgO Adsorption Thermodynamics Calculated from the CC Analysis (Bulk Heat of Sublimation is 18.3 kJ mol-1 for 79-104 K and Bulk Heat of Vaporization is 15.5 kJ at 104 K mol-1)30,31
substrate
layer
ΔH(n), H(¥)/(s) (kJ mol-1)
ΔH(n)H(¥)/(l) (kJ mol-1)
ΔS(n)S(¥)(s) (kJ mol-1)
ΔS(n), S(¥) (l) (J mol-1 K-1)
Q(n) ads (kJ mol-1)
graphite32
1 2 3 1 2 3
-2.950 2.630 3.800 0.52 ( 0.17 1.62 ( 0.17 1.52 ( 0.22
-6.950 -1.370 -0.200 -1.14 ( 0.23 -0.04 ( 0.16 -0.14 ( 0.14
42.5 32.9 38.7 41.6 ( 1.5 20.4 ( 1.8 15.5 ( 2.2
4.0 -5.6 0.2 26.3 ( 2.0 5.1 ( 1.5 0.02 ( 1.2
22.69 17.11 15.94 16.40 ( 0.20 15.31 ( 0.12 15.40 ( 0.12
MgO
determined from the present study along with the same values determined from the experiments of C2H4/graphite performed by Menaucourt et al. Both ΔH and ΔS approach zero with increasing film thickness, n, because the film behaves more bulk-like as the film grows (i.e., as n approaches infinity). In the bulk solid regime (T < 104 K), ΔH increases from near zero (0.52 kJ mol-1) because the bulk enthalpy of fusion (ΔHfus) is significantly greater than the bulk enthalpy of vaporization (ΔHvap). As eq 2 shows, ΔH is the difference of the enthalpy between the nth layer adsorption and the SVP (bulk). The magnitude of the enthalpy of adsorption for the nth layer is given by eq 4. Above the melting -1 at 169.40 K29 point, Q(n) ads should approach ΔHvap (13.544 kJ mol -1 30 and 15.5 kJ mol at 112 K ). Using the slope of the linear fit to the SVP data shown in Figure 3, as a check, we find a value nearly (¥) -1 and equal to bulk C2H4. Q(¥) ads(s) and Qads(l) are 16.93 kJ mol (¥) (n) -1 15.27 kJ mol , respectively. Normally Qads(s) > Qads > Q(¥) ads(l) if the adsorbed film is not in the solid phase. The monolayer melting point for C2H4/graphite is found to be less than 80 K; hence, it is reasonable to expect that the adsorption isotherm study presented here is conducted in the liquid phase since the monolayer melting point is typically 0.75 of the bulk value. The Q(n) ads for the mono-, bi-, and trilayer ethylene films on MgO are listed in Table 2. The CC analysis can also be used to locate Tn, the temperature at which the nth layer appears (i.e., onset of layer formation), by using the point where the CC fits intersect the bulk SVP data (Figure 3). We find that T2 and T3 for C2H4/MgO are 79.2 ( 1.3 K and 98.3 ( 0.9 K, respectively. The thermodynamic values calculated using the CC analysis are based on a linear fit over the entire temperature range investigated; hence, the reported thermodynamic results represent the average values. It is possible to calculate the heat of adsorption at a specific (fixed) coverage and temperature (i.e., the isosteric heat of adsorption or qst) using: Δðln pÞ 2 δðln pÞ qst ¼ RT ð5Þ ≈ RT 2 δT ΔT θ
The partial derivative in eq 5 can be numerically approximated by taking the difference between two isotherms narrowly separated in temperature (i.e., ΔT of ∼1 K). The values quoted in this study for qst determined using eq 5 are at the mean temperature, and hence, Figure 4 displays the qst for T = 103.35 K using isotherms recorded at 103.00 and 103.70 K. Factors that influence the accuracy to which qst can be determined are: temperature stability of the experimental apparatus and accuracy of the interpolation performed to obtain adsorption data at constant coverage. One gauge of the reliability of the numerical derivative can be obtained by examining the values of qst in Figure 4 at high coverage. At ∼7 equiv layers, qst is roughly 15 kJ mol-1, which correlates favorably with the ΔHvap of 15.5 kJ mol-1 at 112 K. Additional (29) Egan, C. J.; Kemp, J. D. J. Am. Chem. Soc. 1937, 59, 1264–1268. (30) Inaba, A.; Morrison, J. A. Phys. Rev. B 1986, 34, 3238–3242.
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Figure 4. Isosteric heat of adsorption for C2H4/MgO at 103.35 K. Note the two maxima in qst below monolayer completion. The inset depicts the isotherms used to calculate qst at 103.00 (solid line) and 103.70 K (dashed line) with the long dashed lines representing the nominal coverage of the qst features below a monolayer.
thermodynamic information can be extracted from the low coverage isosteric heat data which exhibit two features in the submonolayer region (in the neighborhood of =21 and =22 kJ mol-1) and a third feature in the bilayer region (i.e., near =16.2 kJ mol-1). The inset of Figure 4 can be used to determine the nominal coverage where each feature appears. These nominal coverages can be converted to molecular densities using the methane calibration data for each sample. The peaks at 21 and 22 kJ mol-1 in Figure 4 correspond to densities of 0.018 and 0.036 molecules A˚-2, respectively. Larher has shown that adsorption data can be used to identify the locations where phase transitions take place by monitoring the changes in the slope of the vertical riser as a function of temperature.33 We note that the same information may be obtained by tracking the changes in the two-dimensional compressibility (K2D) with temperature. K2D is given by: K 2D ¼
Ap dN N A k B TN 2 dp
ð6Þ
where the substrate surface area is represented by A, which in the present study was determined using a methane isotherm at 77 K. NA, kB, and N are Avogadro’s number, the Boltzmann constant, (31) Stephenson, R.; Malanowski, S. Handbook of the Thermodynamics of Organic Compounds; Elsevier: Amsterdam, 1987. (32) Q(n) ads was calculated from the slope values provided. The remaining thermodynamic values were directly transcribed. No error was provided. The ranges utilized for n = 1, 2, and 3 are 105.7-128 K, 85-114.3 K, and 98-114.3 K, respectively.11,18 (33) Larher, Y.; Angerand, F. Europhys. Lett. 1988, 7, 447–451.
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Figure 5. The isothermal compressibility, K2D versus reduced chemical potential for 106.00 (solid gray line) and 130.00 K (black dashed line). The drastic change of the adlayer compressibility indicates there is a phase change.
Figure 6. Fwhm (full width half-maximum) evaluation of the K2D for the first (filled triangles) and second (filled diamonds) adlayer over a series of isotherms for C2H4/MgO. Lorentzian fits to the K2D peaks are the source of the fwhm data. Linear fits for the first (black) and second (gray) layers over low and high temperature ranges are used to identify the temperature of the phase transition.
and the moles adsorbed, respectively.22 Upon examination of eq 6, it is clear that K2D can be used to apply Larher’s logic since the slope of the amount adsorbed versus p (ΔN/Δp) is the main contributor to the behavior of K2D.33 When the adsorption step is nearly vertical, K2D is a prominent, sharply peaked function that becomes less pronounced and broader when the adsorption step is more rounded. In Figure 5 the behavior of K2D in the neighborhood of adsorption steps at 106 and 130 K is shown. These traces illustrate that dramatic changes occur as a function of temperature in the C2H4/MgO system. Therefore, we calculated the width of K2D as a function of temperature to identify regions of the phase diagram where transitions may appear (as Larher has suggested; see Figure 6). Thus, we have self-consistently determined the width of K2D as a function of temperature by fitting a Lorentzian to the K2D data versus chemical potential (a typical fit is displayed in Figure 7) in the neighborhood of both the first and second steps in the isotherms as shown in Figure 6. We observed that there were two regions where the width of K2D Langmuir 2010, 26(11), 8113–8121
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Figure 7. Lorentzian fit to the K2D of the second layer at 106.00 K resulting in a fwhm of 1.21 ( 0.139 with an R2 = 0.92.
Figure 8. Proposed phase diagram for C2H4/MgO developed from a series of isotherms using various coverage points (filled circles). Possible phase transition temperatures, as determined by the fwhm evaluation, are included for the first (108.6 ( 1.7 K) and second (116.5 ( 1.2 K) layers (filled diamonds with error bars). The phase labels are discussed within the text. The shape of the coexistence regions are similar to those for the C2H4/graphite.34
varied linearly over an extended range in T for each layer. We locate the temperature where the potential phase transition may occur by using the point where the linear regions intersect by making a separate linear fit to the full width at half-maximum (fwhm) K2D data. The intersection of the applied linear fits was then used to identify the location of the phase transitions associated with each layer. For the fits shown in Figure 6, the lines cross at 108.2 ( 1.7 K and 116.4 ( 0.8 K for the first and second layer plots, respectively. As a check, the same procedure is performed using Gaussian fits to the K2D data which identify potential phase transitions for the mono and bi layers at 109.0 ( 1.4 K and 116.6 ( 1.6 K, respectively. For the third layer, it was unreliable to apply this method because the difference in chemical potential between the third layer and asymptotic rise toward the SVP is so small that the K2D features are discernible over only a narrow temperature range. By combining the results of the compressibility analysis, the CC analysis and the set of adsorption DOI: 10.1021/la9044368
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Figure 10. Normalized, background subtracted modified EISF Figure 9. Partial diffraction pattern of C2D4, nominally 0.9 layers, adsorbed on MgO(100) at 4.2 K. A small background was subtracted. The peak at 1.49 A˚-1 is in a similar position of the (11) peak of the rectangular centered unit cell in the low density (LD) phase at 0.6 and 0.75 layers for C2D4/graphite 20 and 9 K.17,36 We note that the width of the diffraction is instrumentally limited (i.e., ∼0.01 A˚-1).
isotherms, it was possible to construct the phase diagram shown in Figure 8, which is further explained in the Discussion. Neutron Scattering. While adsorption isotherms are extremly useful in producing a macroscopic description of the adsorbed film phase diagram, they are unable to produce model independent information that identify the precise nature of phase transitions or probe the microscopic changes in the system. It has been shown that neutron scattering techniques are an extremely valuable method to address the microscopic status of the structure and dynamics of the adsorbed system. For example, neutron diffraction allows one to identify both the atomistic structure and range of spatial correlation and inelastic techniques enable measurement and characterization of the atomistic dynamics of the system. The solid monolayer phase of C2H4/MgO has an extremely low partial vapor pressure (p < 10-4 Torr) making it nearly impossible to probe using vapor pressure techniques; however, neutron diffraction (coherent, elastic scattering) is well suited to the study of the solid phase(s) as mentioned in the methods section above. A portion of the difference diffraction pattern for 0.9 layers of C2D4 on MgO at 4.2 K, recorded using OSIRIS, is shown in Figure 9. The sawtooth shape of the Bragg peak is due to the twodimensional (2D) nature of the film and powdered status of the substrate (i.e., Warren line shape).35 The 2D Bragg peak is located at 1.49 A˚-1 (d-spacing of 4.22 A˚ where the real space distance, d, is 2π/Q). We note that, as illustrated by the results of C2D4/graphite, it is a challenge to record more than a couple Bragg peaks. The dominant Bragg peak for C2D4/graphite is at 1.54 A˚-1.17,36 Inelastic neutron scattering (INS) methods provide a suitable avenue to directly probe the microscopic dynamics of the adsorbed film as temperature and coverage change. In this study, we have used the modified elastic incoherent structure factor (EISF) to identify the onset of the film dynamics. Using HFBS, we were (34) Kim, H. K.; Feng, Y. P.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. B 1988, 37, 3511–3523. (35) Warren, B. E. Phys. Rev. 1941, 59, 693–698. (36) Satija, S. K.; Passell, L.; Eckert, J.; Ellenson, W.; Patterson, H. Phys. Rev. Lett. 1983, 51, 411–414.
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scans of five various coverages of C2H4/MgO summed over 0.47 e Q e 1.75 A˚-1. Occurrences of a sudden change in intensity (normalized to the incident radiation) as the adfilm warms are marked with labeled arrows A and B. The elastic response for the lower two coverages was not recorded below 20 K, and data above 120 K is not shown because the elastic response is small and equal for all coverages.
able to track the total elastic scattering intensity (Iel) as a function of temperature in order to identify temperature regions where the film’s microscopic dynamics change. The types of dynamical changes we are generally interested in locating and characterizing are the onset of rotational and translational diffusion, librations and vibrations as well as phonon modes. The details of the dynamical changes cannot be identified unambiguously using this modified EISF technique because a full determination of the quasi-elastic and inelastic response as a function of Q is not recorded. What we record is the change in the Iel as a function of temperature and film thickness. Figure 10 shows the normalized, background subtracted Iel as a function of temperature for 0.42, 0.75, 1.18, 1.56, and 1.81 nominal layers of C2H4 on MgO. Some general comments are appropriate. First, we are confident in our in situ film deposition procedure because there is an increase in the initial Iel at low temperatures that is directly proportional to the increase in coverage. Second, we know that there is some component of the adsorbed film dynamics that are in the nanosecond time scale because there is a (monotonic) decrease in Iel with increasing temperature for all coverages shown. This loss of Iel results from the onset of dynamical motion causing some neutrons to be scattering inelastically from the sample (i.e., neutron signals are now present in the quasi-elastic and inelastic regions) and therefore not observed in this window. Third, while there are readily observed changes in Iel that take place as a function of T (e.g., A at ∼40 K and B at ∼100 K) there are also important changes in Iel that are more subtle. In order to accentuate the more subtle changes, we examined the numerical derivative of Iel with respect to temperature (ΔIel/ΔT). In order for any dynamical changes to be observable in our neutron measurements, the motion must be fast enough to no longer appear “elastic” on the time scale of the instrument response (a few ns for HFBS). Figure 11 displays the modified EISF summed over two detectors that correspond to Q’s at approximately 1.42 and 1.51 A˚ for the 0.42 and 0.75 monolayer films. These Q values were chosen because they are in the neighborhood of the Bragg peak shown in Figure 9. To improve the quality of the numerical derivative (ΔIel/ΔT), we first fit the data with an eighth order polynomial Langmuir 2010, 26(11), 8113–8121
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Figure 11. Modified EISF (circles) for submonolayer coverages at nominally 0.42 monolayer (a) and 0.75 (b) summed over Q equal to 1.42 and 1.51 A˚-1. Note that these plots are the full traces shown in Figure 10 data. The dark line is an eighth order polynomial fit to the data (to guide the eye) and the gray dashed line is ΔIel/ΔT (using the polynomial fit). The vertical dashed line marks the possible monolayer melting point.
and then calculated ΔIel/ΔT from it. The change near 40 K (A in Figure 10) is apparent. However, closer inspection of the temperature dependence of ΔIel reveals a distinct change in the rate of decay in Iel between =55 and =75 K, centered around 65 K (see black dashed line in Figure 11). We will examine this behavior more thoroughly below to see if it might correspond to a change in dynamics associated with a phase transition. We note that other fits (weighted, moving average, and sixth and seventh order polynomials) of the data generated the same result. The temperatures reported here may be an offset from the actual cell temperature because the sample was warmed at a constant rate of 0.3 K min-1. Finally, the modified EISF data can be used to calculate the MSD (Æμ2æ) from the Debye-Waller factor because 1 I el exp - Q2 Æμ2 æ 3
ð7Þ
by plotting ln(Iel) at each temperature versus Q2 to find the MSD. For weakly interacting particles (i.e., low density regime) the average MSD is equivalent to single particle motion (Debye-Waller description). This is a reasonable assumption at all coverages where the monolayer solid is not highly compressed. However, if the monolayer solid is more dense, this assumption is less reasonable. Figure 12 shows the MSD versus T for 0.42 layers C2H4/MgO is essentially zero below 35 K where it begins to steadily increase until T reaches =65 K where the MSD levels off to a value near 0.8 A˚2.
Discussion Adsorption Isotherms. Having presented the experimental data above, we would like to summarize the main results and discuss their implications. Figure 1a clearly illustrates that multiple layering transitions occur for C2H4/MgO, as is the case for equivalent adsorbed films of C2H4/graphite.11,18 Thus, we use a quantitative comparison of the thermodynamics of C2H4 on MgO and graphite to demonstrate the similarities in film growth on Langmuir 2010, 26(11), 8113–8121
Figure 12. Mean square atomic displacement of C2H4/MgO at
0.42 layers. The MSD approaches ∼0.8 A˚2. The line is drawn to guide the eye.
these two dissimilar substrates. An examination of Table 2 make it clear that the thermodynamic values of ΔH, ΔS, Q(n) ads follow similar trends for both substrates (e.g., approach the expected values as noted in the Results section above). Closer examination of Q(1) ads reveals that the C2H4 monolayer film is more strongly -1 bound to the graphite basal plane (Q(1) ads =22.69 kJ mol ) than to (1) -1 MgO(100) surface (Qads = 16.40 kJ mol ). The same trend is observed for the second and third layers; however, the magnitude of the differences diminish with increasing coverage because of the direct response to the decrease in the relative strength of M-S interaction as molecules in the second and third layers are located further from the surface. We pointed out above that the onset of layering for C2H4/MgO is T2 = 79.2 ( 1.3 K and T3 = 98.3 ( 0.9 K. Menaucourt et al. report T2 =79.9 K and T3 =98.3 K11,18 for C2H4/graphite. The results of Menaucourt et al. are within the range of our experimental error for C2H4/MgO, also suggesting that, after monolayer formation, film growth is very similar on both substrates. The isosteric heat of adsorption can be used to gain additional insight into the interaction potentials because it is related to the energy required to bring a molecule from infinity to the surface and how that energy changes with coverage. Figure 4 shows a typical example of qst and how it reaches a maximum value of ∼22 kJ mol-1 near monolayer completion, followed by a smaller peak near two layers (16.2 kJ mol-1). We noted above that evidence exists for discrete formation of a third layer at 103.35 K, but the associated change in energy is too small to be resolved as a peak on this plot. This behavior of qst as a function of coverage is also consistent with a decrease in M-S interaction as molecules in the growing film move further from the MgO substrate. For comparison, qst at 105 K for C2H4/graphite monolayer is 3 kJ mol-1 greater. Unfortunately, the value for the second layer of C2H4 on graphite was not reported.30 Another notable feature in Figure 4 is the peak at ∼0.4 layer. This submonolayer peak appears to be associated with a phase change as the film density increases. Support for this suggestion comes from the change in shape of the isotherms shown in the inset of Figure 4. The shape change in the submonolayer region is obvious at 83 K (Figure 1a). Future neutron diffraction and dynamical measurements are planned to shed light on the submonolayer phase in order to clarify whether it differs from the one that forms near monolayer completion at higher temperatures (85-110 K). DOI: 10.1021/la9044368
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Table 3. Summary of Confirmed and Likely Tc2 (K) for C2H4 Adfilms substrate
T(n=1) c2
T(n=2) c2
graphite11,18 graphite34 MgO(100)38
114 110 108.6 ( 1.7
118 115.3 116.5 ( 1.2
Additional comments regarding the phase diagram can be made using the fwhm analysis of K2Ds from a set of C2H4/MgO adsorption isotherms. In the analysis of K2D presented above, we note that a phase transition for the mono and bilayers occurs at 109.0 ( 1.4 K and 116.6 ( 1.6 K, respectively. Comparison of these values to the two-dimensional critical temperatures (Tc2) for the case of C2H4 on graphite (Table 3) will aid our assignments of C2H4 on MgO phase transitions. Specifically, the assigned phase transition for C2H4/graphite are the monolayer liquid-vapor critical point is at 110 K and the second layer critical point is at 115.3 K for C2H4/graphite.13,34 These values are within the experimental error of our reported values for C2H4/MgO. Additional confidence for assigning the two phase transitions as layer critical temperatures comes from examining the proposed phase diagram in Figure 8. We expect to confirm the layer critical temperatures in the future using neutron scattering techniques. Nonetheless, assigning these transitions as critical points reinforces the striking similarity in the film growth on graphite and MgO. Examination of the phase diagram makes it clear that film growth proceeds with increasing density from a monolayer vapor phase (1 V) to a monolayer liquid (1 L) by passing through a region of two phase coexistence (1 V and 1 L). In the bilayer regime, the second layer liquid (2 L) coexists with 1 L upon increasing thickness until only a bilayer liquid is present. At higher temperatures, (i.e., beyond the 1 V-1 L coexistence) only the fluid < T(n=2) . In phase (F) exists. Figure 8 also illustrates that T(n=1) c2 c2 this region one might imagine a scenario where a space filling dense monolayer fluid phase is decorated by a second layer of isolated liquid puddles (of lower density) “floating” on top of it. It is known from the earlier C2H4/graphite studies that there are significant changes and differences in the interlayer mobility and the translational-rotational coupling in the submonolayer and near layer completion regime.37 However, detailed knowledge of the microscopic behavior in this regime will require an extensive set of microscopic measurements and companion computer modeling before completion of the phase diagram and an attendant description of the molecular structure/dynamics can be achieved. Neutron Scattering. Although the neutron scattering studies reported here are in their initial stages, several important comments can be made based upon these preliminary microscopic measurements. First, earlier diffraction studies of monolayer C2D4 films on graphite found that at low temperatures an incommensurate, low-density (LD) solid phase formed which had a centered rectangular unit cell where the (11) Bragg peak appeared at 1.54 A˚-1.17,36 We direct the readers’ attention to Figure 9, which displays a Bragg peak for the C2D4/MgO at Q = 1.49 A˚-1. If the solid C2D4 monolayer structure on MgO(100) is similar to that on graphite(0001), a peak at this Q represents a d spacing that is ∼3% larger than the lattice constant recorded for the C2D4/graphite solid monolayer. Hence, the solid monolayer that forms on MgO is probably more like the low temperature centered rectangular solid that forms on graphite (or perhaps a commensurate c(2 2) solid) where one lattice constants in the (37) Grier, B. H.; Passell, L.; Eckert, J.; Patterson, H.; Richter, D.; Rollefson, R. J. Phys. Rev. Lett. 1984, 53, 814–817. (38) Result obtained by combining Gaussian and Lorentzian fwhm analyses.
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unit cell is ∼4.2 A˚. Unfortunately, solving crystal structures with only one diffraction peak is not a prudent practice; we simply note what at this point in time appears to be a striking similarity to the diffraction data recorded for C2D4/graphite. Confirming the structure of the C2D4 monolayer solid(s) on MgO(100) requires additional measurements that include collecting diffraction patterns at various surface coverages of sufficient quality to enable us to make a higher quality structural determination (e.g., like those performed for n-butane/MgO26). Next, our preliminary microscopic dynamical results also provide some key information for understanding the C2H4/ MgO behavior. As noted above, the scattering data can be used to identify the temperature regions where changes the ethylene film dynamics occur (see Figure 10). Here, the most dramatic change in dynamics is signaled by the initial drop in Iel at
