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Heat Capacity Study of Monolayer Propane on Graphite M.-a. Lee, M. T. Alkhafaji, and A. D. Migone* Department of Physics, Southern Illinois University, Carbondale, Illinois 62901 Received November 18, 1996. In Final Form: February 24, 1997X
Heat capacity measurements have been conducted for monolayer propane films adsorbed on graphite in the vicinity of the melting transition. Films at ten coverages between 0.4 and 1.07 layers were studied. For coverages below n ) 1.0 a very weak heat capacity peak of height ∼2 C/NkB, is found at melting; the transition is centered about 67 K, in good agreement with the melting temperature found in structural studies. Above n ) 1.0 the melting peak moves to higher temperatures with increasing coverage. Data for propane are compared to those found for other hydrocarbon systems on graphite and to current theories of two-dimensional melting.
Introduction The Kosterlitz and Thouless1 prediction that the melting of a two-dimensional (2D) solid could be continuous, together with subsequent theoretical developments by Nelson and Halperin2 and by Young3 (i.e., the KTNHY theory), stimulated a great deal of study of 2D systems.4,5 However, in spite of an ever increasing body of work, controversy regarding the true nature of the melting of 2D solids continues, to date, in theory,2,3,6-9 experiment,10-12 and simulation.13 Recently, Kleinert6-8 proposed that the order of the 2D melting transition of an adsorbed film depends on the length scale of rotational stiffness of the film, a quantity which is roughly proportional to the molecular length of the adsorbate. 2D melting, in the Kleinert theory, evolves as a function of chain length from being strongly first order (for spherical adsorbates), to the full KTNHY scenario of a sequence of two continuous phase transitions (for elongated molecules). Hydrocarbon films were suggested as a suitable testing ground for these predictions.8 Hydrocarbon films provide sharp contrasts in 2D melting behavior: ethane14 and ethylene15,16 have broad and weak heat capacity peaks at melting, both are X
Abstract published in Advance ACS Abstracts, April 15, 1997.
(1) Kosterlitz, J. M.; Thouless, D. J. J. Phys. (Paris) 1979, C6, 1181. (2) Nelson, D. R.; Halperin, B. I. Phys. Rev. B 1979, 19, 2457. (3) Young, A. P. Phys. Rev. B 1979, 19, 1855. (4) Strandburg, K. J. Rev. Mod. Phys. 1988, 60, 161. (5) Chan, M. H. W. In Phase Transitions in Surface Films, 2 ed.; Taub, H., Torzo, G., Lauter, H. J., Fain, S. C., Eds.; NATO Advanced Study Institute; Plenum: New York, 1991; Ser. B, Vol. 267, p 1. (6) Janke, W.; Kleinert, H. Phys. Rev. Lett. 1988, 61, 2344. (7) Kleinert, H. Phys. Lett. A 1988, 130, 443. (8) Janke, W.; Kleinert, H. Phys. Rev. B 1990, 41, 6848. (9) Saito, Y. Phys. Rev. B 1982, 26, 6239; Phys. Rev. Lett. 1982, 48, 1114. (10) Migone, A. D.; Li, Z. R.; Chan, M. H. W. Phys. Rev. Lett. 1984, 53, 819. Zhang, Q. M.; Larese, J. Z. Phys. Rev. B 1991, 43, 938. Nielsen, M.; Als-Nielsen, J.; Bohr, J.; McTague, J. P.; Moncton, D. E.; Stephens, P. W. Phys. Rev. B 1987, 35, 1419. D’Amico, K. L.; Bohr, J.; Moncton, D. E.; Gibbs, D. Phys. Rev. B 1990, 41, 4368. (11) Jin, A. J.; Bjurstrom, M. R.; Chan, M. H. W. Phys. Rev. Lett. 1989, 62, 1372. (12) Colella, N. J.; Suter, R. M. Phys. Rev. B 1986, 34, 2052. Gangwar, R.; Colella, N. J.; Suter, R. M. Phys. Rev. B 1989, 39, 2459. Nuttall, W. J.; Noh, N. Y.; Wells, B. O.; Birgeneau, R. J. Surf. Sci. 1994, 307309, 768. Zerrouk, T. E. A.; Hamichi, M.; Pilkington, J. D. H.; Venables, J. A. Phys. Rev. B (Rapid Commun.) 1994, 50, 8946. (13) Weber, H.; Marx, D. Europhys. Lett. 1994, 27, 593. Weber, H.; Marx, D.; Binder, K. Phys. Rev. B 1995, 51, 14636. Bladon, P.; Frenkel, D. Phys. Rev. Lett. 1995, 74, 2519. Chen, K.; Kaplan, T.; Mostoller, M. Phys. Rev. Lett. 1995, 74, 4019. (14) Zhang, S.; Migone, A. D. Phys. Rev. B (Rapid Commun.) 1988, 38, 12039; Surf. Sci. 1989, 222, 31. (15) Kim, H. K.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. Lett. 1986, 56, 1579.
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identified as melting continuously; methane17 has some of the strongest first-order melting transitions observed in any physisorbed system; acetylene18 has first-order melting; butane19 has first-order melting at submonolayer coverages but melts continuously in the extended monolayer regime.19 Some bulk properties of the alkanes (e.g., the crystallographic structure and the triple point temperature), zigzag between two sequences, as a function of chain length: one for odd chains and another for even ones.20 It has been suggested that 2D alkanes might have a similar behavior.21 With the exception of methane, however, most studies have concentrated on even-numbered chains (ethane, ethylene, acetylene, butane, and hexane), leaving the suggestion largely untested. This report presents the results of a heat capacity study of propane adsorbed on graphite. Our aim is to determine the nature of 2D melting for this system. Since propane is a three-C chain, we can also use our results to determine, in a limited way, whether 2D alkane films exhibit the zigzagging behavior in the triple point temperature which is present in the bulk. Only preliminary reports on neutron scattering and X-ray studies21 of propane films on graphite are available; neither technique could determine the structure of the solid film. These studies established a melting temperature between 65 and 70 K for monolayer propane. A very gradual decrease in the amplitude of the scattering peaks was observed as the temperature increased through the melting point; it was concluded that the transition probably was continuous.21 Neutron scattering measurements, sensitive to the presence of orientational order in the film, found peaks indicative of the persistence of some degree of orientational and translational order in the liquid even at room temperature.21 Monolayer liquid propane is a highly ordered fluid.21 Experimental Section We studied propane films at ten coverages, between n ) 0.40 and n ) 1.07, for temperatures between 55 and 75 K. As in the (16) Larese, J. Z.; Passell, L.; Wicksted, J. P.; Heidemann, A. D.; Richter, A. D. Phys. Rev. Lett. 1988, 61, 432. (17) Kim, H. Q.; Zhang, Q. M.; Chan, M. H. W. Phys. Rev. B 1986, 34, 4699. (18) Alkhafaji, M. T.; Migone, A. D. Phys. Rev. B 1992, 45, 8767. (19) Alkhafaji, M. T.; Migone, A. D. Phys. Rev. B 1996, 53, 1152. (20) Noller, C. R. Chemistry of Organic Compounds, 3rd ed.; Saunders: Philadelphia, PA, 1966. (21) Matthies, B.; Herwig, K. W.; Taub, H. Bull. Am. Phys. Soc. 1994, 39, 455. Taub, H. Private communication.
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Figure 1. Background-subtracted heat capacity traces for three submonolayer coverages. From top to bottom, n ) 0.95, 0.75, and 0.40. The double-headed arrow corresponds to 1 C/NkB. The peaks for coverages below n ) 1.0 are centered about 67 ( 0.5 K.
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Figure 2. Background-subtracted traces for two coverages above layer completion: top, n ) 1.05; bottom, n ) 1.00. The melting temperature has shifted to 75 ( 1 K at these coverages. As in Figure 1, the arrow corresponds to 1 C/NkB.
In Figure 1 we display heat capacity traces for three coverages between n ) 0.4 and n ) 1.0. A smooth background has been subtracted from the data. The melting peaks are between 1.5 and 2.0 in reduced units (C/NkB). The most remarkable feature of the data is the weakness of the peaks. The melting peaks are symmetric: widths on the high and low temperature sides of the maximum are comparable. The full width at half maximum (fwhm) of the peaks is between 2.5 and 3 K (corresponding to a fractional half-width of 0.04). For all coverages shown in this figure the melting peak is centered at 67 ( 0.5 K, in good agreement with the melting temperature found in the structural studies.21 In order to verify that the weak signal for propane was not an experimental artifact (as would result, for example, if contaminants were present on the graphite and smeared a sharp first-order transition), at two instances in the sequence of measurements, after the second and sixth coverages, we extracted all the propane from the calorimeter and replaced it with n ) 0.55 layers of N2 and n ) 0.4 layers of CO, respectively. Reports for N2 and CO show sharp, first-order melting peaks for coverages near half a monolayer.5 The characteristics of the data for N2 and CO (i.e., peak height, peak width, and peak shape) measured by our calorimeter agreed very well with what is reported in the literature for these systems, thus,
confirming that our apparatus was functioning properly and that the weak nature of the melting signature was an intrinsic characteristic of the propane films. It is interesting to compare the melting peaks measured at submonolayer coverages for propane with those for ethane14 and ethylene15 on one hand and methane17 on the other. Methane17 has a submonolayer melting peak of at least 90 C/NkB, with a fractional fwhm smaller than 0.005. For methane, submonolayer melting is first order and takes place at a triple line. By contrast, ethane14 has heat capacity peaks between 2.5 and 3 C/NkB, with a fwhm of 2 K (0.032 fractional full-width) and ethylene15 has a melting peak of approximately 5 C/NkB, with a fwhm of about 3 K (0.044 fractional full width). The melting peaks for propane are weaker than those for either ethane or ethylene on graphite. In Figure 2 we display data measured for two of the highest coverages which we have studied: n ) 1.0 and n ) 1.05. In this region, the melting peak temperature moves up with increasing coverage. An analogous displacement of the melting peak to higher temperatures with increasing coverages has been reported for a number of other adsorbed systems (see, for example, ref 5). The entropy change at the transition can be obtained by integrating the heat capacity data. We get an entropy change at melting of 0.2 kB for propane. As a comparison, the melting entropies for ethylene15 and ethane14 are 0.4 and 0.1 kB, respectively, that for methane17 is 0.7 kB. Ethane melts to a very highly ordered liquid23 and has the smallest entropy change at melting. Since the neutron scattering study found the persistence of significant translational and orientational order in the 2D liquid for propane,21 an entropy change intermediate between those found for ethane and ethylene is entirely expected. (The highly ordered liquid phase present in ethane above melting was first called an “intermediate phase” because it had a degree of order intermediate between that of a solid and a liquid.23 This intermediate phase persists for approximately 30 K above melting. We note that the
(22) Yang, G.; Migone, A. D.; Johnson, K. W. Rev. Sci. Instrum. 1991, 62, 1836.
(23) Suzanne, J.; Seguin, J. L.; Taub, H.; Biberian, J. P. Surf. Sci. 1983, 125, 153.
structural studies,21 we defined n ) 1.00 at a density of 0.0347 molecule/Å2, the average between the densities of the S1 phase of ethane and that of monolayer butane. We used fully deuterated propane (produced by CDN Isotopes). The gas was admitted into the calorimeter above 200 K. The calorimeter’s surface area was determined from a Kr adsorption isotherm. We employed ac calorimetry in our measurements. Data were taken at intervals of between 0.3 and 0.5 K. Detailed descriptions of the setup and of the principle of operation of the ac calorimetry technique have been provided elsewhere.22
Results
Heat Capacity Study of Monolayer Propane on Graphite
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All the data presented for propane films are similar to those for monolayer and submonolayer ethylene and ethane on graphite. Both ethylene and ethane have been reported as undergoing continuous 2D melting. Following the same line of reasoning used for those two systems (i.e., by contrasting the weak, broad, features present at melting for them with the sharp melting signature of methane), we can also identify as continuous the melting transition of propane films adsorbed on graphite. It is important to note that while the identification of the melting of propane as a continuous transition is as valid as those for ethane or ethylene, a problem remains in all three cases: the difficulty in discerning experimentally between a very small, but finite, entropy difference in a weakly first-order phase transition and truly continuous melting. Experiments can only place upper bounds on the size of the first-order peaks which would be below the resolution limits of the measurements. In none of these three cases can a weakly first-order transition be ruled out completely.24 Is there a theoretical explanation that coherently encompasses the experimentally observed melting behavior of submonolayer and monolayer films of linear molecules studied so far? The best candidate is the Kleinert6-8 theory of 2D melting, which correlates the order of the 2D melting transition of an adsorbed film to the length of the adsorbate. In computer experiments, Janke and Kleinert6,8 found that the simulated specific heat peaks evolve from being strongly first order for spherical molecules, to a continuous transition for longer molecules, and, eventually, to the KTNHY sequence for even longer ones. If the Kleinert theory applies to submonolayer hydrocarbon films, it could explain the experimental results for methane, ethane, ethylene, and propane (and perhaps evey acetylene). However, the results for submonolayer butane19 are not in agreement with the expectations of the Kleinert theory, since butane is longer than any of the hydrocarbons discussed above but melts at a first-order transition. It should be noted that, aside from the problem presented by the submonolayer butane results, rather serious questions remain regarding the applicability of this theory to submonolayer hydrocarbon films: The Kleinert theory is strictly a 2D theory (that is, no motions perpendicular to the plane of the film are allowed). By contrast, simulations for specific hydrocarbon films (e.g., butane and hexane)25 find that motions perpendicular to the plane of the film play a crucial role at melting. These perpendicular motions are the mechanism by which vacancies are created in solid monolayer films. These motions involve either tilting of the molecule25,26 or, in the case of hexane, a conformational transformation of the molecule which results in a smaller “footprint” on the substrate.25 It is likely that perpendicular motions also play an important role at melting for other hydrocarbon films, as well.16,26 Very recently19 it has been suggested that the Kleinert theory should apply not to submonolayer systems but,
rather, to films in the extended monolayer regime. By extended monolayer regime we mean a first layer solid film which has additional film and/or bulk, on top of it. In the extended monolayer regime, motions perpendicular to the plane of the substrate would be quenched, resulting in a better realization of a truly 2D system. This suggestion appears to have been confirmed in those few adsorbed systems for which the first layer melting has been emplored in the extended monolayer: Xe,11 Ar,27 CH4,17,28 and butane.18 Of these systems, the first three are spherical (or effectively spherical at melting), and in all three cases melting in the extended monolayer regime is accompanied by very sharp, strong, heat capacity peaks.11,17,27,28 These results are in excellent agreement with the Kleinert theory, which predicts first-order melting for spherical adsorbates. Butane, an elongated molecule, melts at a continuous transition in the extended monolayer regime.18 This result is also in very good agreement with the prediction of the Kleinert theory that melting should be continuous for elongated adsorbates. We note, however, that the continuous melting for butane starts at a total surface coverage of three layers (i.e., the equivalent to two layers on top of the first layer), while the extended monolayer behavior for the three spherical systgems mentioned above (Ar, Xe, and CH4) starts soon after the first layer of the film has been completed (this suggests the possibility that different melting mechanisms might be at work for these two groups of systems). It thus appears that, so far, the Kleinert theory provides us with a consistent framework for explaining the behavior in the extended monolayer regime. By contrast, we do not understand why butane and propane have different melting behavior at submonolayer coverages; no theoretical explanation currently available accounts for the measured differences. In light of the present status of experiment and theory regarding the submonolayer melting transitions of hydrocarbon films, one could reasonably question whether a determination of the order of the melting transition for these systems would lead to a better understanding of their behavior. For instance, we note that by itself the vacancy creation mechanism does not appear to determine whether the transition is first order or continuous; essentially the same vacancy production mechanism (i.e., motion perpendicular to the substrate plane) is shared by systems which have first-order melting (e.g., butane) as well as by others (e.g., ethylene and ethane) which exhibit continuous melting. The information currently available for hydrocarbon films suggests that the principal ingredients which account for what occurs at the submonolayer melting transition are the value of the entropy change at melting, the degree of order present in the liquid phase above melting, and the nature of the vacancy-production mechanism at melting. We believe that a better theoretical understanding of these transitions could be reached using a theoretical or simulational approach which combined these factors meaningfully. We look, next, at the evolution of the submonolayer melting temperature as a function of chain length. Figure 3 displays the melting temperatures for the first six alkanes as a function of the number of C atoms in the
(24) Very recently Ma, and Kleinberg have reported on heat capacity results for Ar-CH4 mixtures which appear to evolve into continuous melting as the fraction of methane is increased. Ma, J.; Kleinberg, H. Am. Phys. Soc. 1996, 41, 192. (25) Hansen, F. Y.; Taub, H. Phys. Rev. Lett. 1992, 69, 652. (26) Moller, M. A.; Klein, M. L. Chem. Phys. 1989, 129, 235. Cheng, A.; Klein, M. L. Langmuir 1992, 8, 2798.
(27) Zhu, D. M.; Dash, J. G. Phys. Rev. B 1988, 38, 11673. Day, P.; Lysek, M.; LaMadrid, M. A.; Goodstein, D. L. Phys. Rev. B 1993, 47, 10716. (28) Lysek, M. J.; LaMadrid, M. A.; Day, P. K.; Goodstein, D. L. Phys. Rev. B 1993, 47, 7389. (29) Krim, J.; Suzanne, J.; Schechter, H.; Wang, R.; Taub, H. Surf. Sci. 1985, 162, 446.
degree of order in propane submonolayer films, while less marked than that of ethane in the immediate vicinity of melting, persists up to much higher temperatures.) Discussion
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between odd and even sequences, in a manner analogous to its behavior in the bulk. There is only a 5 K difference between the melting temperatures of ethane and propane films, while there is a 50 K difference between the melting temperatures for propane and butane. Finally, we should note that the present study has concentrated in a narrow temperature interval about the melting transition. This is not, however, the only region of interest for submonolayer propane films. The possibility exists that at some temperature below the melting transition there is a solid-solid transition from an orientationally ordered to a plastic phase, just as occurs for other molecular adsorbates. Such a possibility should be explored. Conclusions
Figure 3. Melting temperatures for bulk (filled squares connected by a short-dashed lines) and submonolayer (filled triangles, connected by long-dashed lines) alkane systems as a function of the number of carbon atoms present in the chain. The submonolayer melting temperature for methane is from ref 17, and that for ethane from ref 14. The submonolayer melting temperature for propane is from this work and from ref 21. For butane, we used ref 19, and for hexane we use the melting temperature from ref 29. The submonolayer melting temperature zigzags between odd and even chains in a manner analog to that for bulk.
chain. The results show that for 2D alkane films on graphite the submonolayer melting temperature zigzags
We have investigated the melting of monolayer propane on graphite. Our results are similar to those found for ethylene and ethane films: the melting heat capacity peaks are very weak, with no sharp features present in them. This indicates that the transition is, at best, no stronger than very weakly first order. The observed melting behavior is in good agreement with what was determined in structural studies of this system. Acknowledgment. We would like to acknowledge many useful discussions with H. Taub and K. W. Herwig, who shared with us their data prior to publication. We thank H. Taub for very carefully reading this manuscript and for his helpful suggestions on how to improve it. We have benefited from insightful comment by O. E. Vilches. LA962017U
