Heat capacity study of the first monolayer of adsorbed methane on grafoil

Heat capacity study of the first monolayer of adsorbed methane on grafoil

0038-1098/81/460959-03$02.00/O Solid State Communications, Vol. 40, pp. 959-961. Pergamon Press Ltd. 1981. Printed in Great Britain. HEAT CAPACITY S...

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0038-1098/81/460959-03$02.00/O

Solid State Communications, Vol. 40, pp. 959-961. Pergamon Press Ltd. 1981. Printed in Great Britain.

HEAT CAPACITY STUDY OF THE FIRST MONOLAYER OF ADSORBED METHANE ON GRAFOIL R. Marx and E.F. Wassermann Labor fur Tieftemperaturphysik

der Universitlt

Duisburg, 4100 Duisburg, Germany

(Received 3 August 198 1 by B. Miihlschlegel)

The heat capacity of CH4 adsorbed on Grafoil below monolayer completion has been determined experimentally for the first time. The specific heat at constant density shows two characteristic features, very broad, weak anomalies at 47.6 K (around one third of a monolayer) and (for occupation numbers below two thirds of a monolayer) very narrow, strong peaks at 56.35 K. The anomalies at 47.6 K are interpreted as being due to a registry - out-of-registry transition of the two dimensional (2D) solid CH, adsorbate into an incommensurate expanded structure. The anomalies at 56.35 K define the 2D triple point of adsorbed CH* For higher occupation numbers the liquid-solid phase boundary shifts to higher temperatures. The present data make partial redefinition of the 2D-CH4 phase diagram necessary. AMONG THE LARGE VARIETY of 2D adsorbed systems studied in the last years with increasing intensity, CH,, - the simplest hydrocarbon - adsorbed on Grafoil is especially interesting because of its quasi 2D-phases and phase transitions. Based on early measurements of adsorption isotherms [ 11, quasi-elastic neutron scattering and neutron diffraction studies [2,3] revealed two kinds of fluids in the first monolayer: a 2D hypercritical fluid with high compressibility, occupying the total surface available, characterized by a strongly coverage dependent diffusion coefficient and a 2D liquid, where the mobility is an intensive property for changing coverages, analog to a conventional 2D liquid [4]. Moreover, there is experimental evidence [3] that at lower coverages adsorbed CH4 shortly before melting into a fluid is subjected to a registry-outof-registry transition, which does not seem to have ever been observed before in such systems. In this letter we present the first heat capacity measurements of CH4 submonolayers on Grafoil with specific emphasis concerning this registry-out-ofregistry transition, and the 2D triple point. Heat capacity measurements as a function of temperature along constant density lines are most sensitive to phase boundaries, and therefore are especially suitable to set up and/or complete phase diagrams. The experimental arrangement used for the present investigation has been recently described in connection with the specific heat measurement of adsorbed O2 submonolayers [5,7]. The adsorption cell has a CH4 monolayer capacity (coverage n = 1) of approximately 33.6 cm3 STP, corresponding to a molecular density of 0.073 A-2 [2]. Figures 1 and 2 show typical results of the specific

heat per particle in units of kb vs temperature for a coverage of n = 0.33 and n = 0.47, respectively. We We observe a very broad, weak anomaly at a critical temperature T, = 47.6 + 0.5 K (Fig. 1) and a very narrow, strong peak at Tc = 56.35 f 0.5 K (Fig. 2). We think that the anomalies at T, = 47.6 K correspond to the registry-out-of-registry transition (refer to Fig. 3) and are therefore of continuous order. This will be discussed in detail elsewhere [8]. We checked several times that this bumps are only observed for occupation numbers around one third of a monolayer. The reason for this is not known to us. The agreement with the coverage of the ordering transition of He is very likely fortituous and we do not claim that there is any similarity between the two systems. The anomalies at 56.35 K start at a coverage of about n = 0.25 and - with increasing coverage - rapidly develop into a near “delta-function”. They indicate a clear-cut melting transition of first order and define the 2D triple point of the layer. From a theoretical point of view a triple point peak should be of infinite height. Note, however, that the specific heat of a finite system willl never reach infinity as thermal fluctuations set an upper limit to the observable values. Since the temperature difference between two measuring points is about 60 mK, we do not think that the top of the peak is fully resolved. As a measure of the sharpness of the peak we take the width at half maximum (WHM). Because of the finite temperature resolution this should be an upper limit. From the data of Fig. 1 a WHM results which is smaller than 6 x low3 and is of the same order of magnitude as observed for other 2D systems (e.g. Neon [9,

101). There is some uncertainty 959

with regard to the falling

960

LII

Jo

45

T.

K

Fig. 1. Heat capacity per particle in units of kt, corresponding to the registry-out-of-registry transition of CH4 adsorbed on Grafoil (n = 0.33). The smooth curve is thought as a guide for the eye. The error bars correspond to our measuring accuracy off 0.25%.

I

55

55 5

I 56 T,

I

I

56 5

57

I

80 T,

I 100

I 2’

K

Figure 3. Phase diagram of the first monolayer of CH4 adsorbed on Grafoil. The dots correspond to the present work. For explanation of the several phase regions refer to text.

575

K

Fig. 2. Heat capacity per particle in units of k, corresponding to the triple-point transition of CH4 adsorbed on Grafoil (n = 0.47). off below and above T,, because at maximum the specific heat of the adsorbate is only about 2% and 13% of the background (copper can and Grafoil disks) for the 47.6 and 56.35 K anomaly, respectively. The experimental heights of the anomalies corresponding to the triple point increase approximately linearly as a function of coverage up to n = 0.6. The mean position varies by no more than about f 0.05 K for these coverages. Then the anomalies start to fade away, at the same time the critical temperature T, shifts to higher values. This is similar to what has been observed in other 2D systems investigated so far (e.g. O2 [5-71, neon [9, lo], xenon [Ill). Based on these experimental results we are able to complete and correct in certain sections the 2D phase diagram of CH4 [l-4]. Figure 3 shows this diagram in the coverage vs temperature plane. The data of the

X

Fig. 4. Plot of theoretical and experimental normalized peak heights C &ZFez as a function of occupation number x = a- p”[C(T = T,) = C&J. The smooth line corresponds to the theoretical dependence; 0: 02, l : xenon, x: neon, A: CH4 experimental results. Note that the slopes in the text are given for Cpeak vs x. Inset: pressure @) - specific area (a) diagram in analogy to a p-v diagram of a 3D system. Horizontal line between a0 and a2: triple line. present investigations are given by the dots. Only the phase boundaries Sr-Sn and Sn-Lr have been detected in specific heat. We have no specific heat evidence for the phase boundary L,-L,, possibly due to lack of sensitivity. The diagram shows a variety of phases of the first monolayer, starting at low temperatures with a registered d3 solid structure (region Sr). At 47.6 K this solid expands into an incommensurate solid phase (region Sn) by a transition which is - as mentioned -

Vol. 40, No. 10

FIRST MONOLAYER OF ADSORBED METHANE ON GRAFOIL

very likely continuous. Although earlier data suggested that the Sr-Sn phase boundary extends at constant temperatures up to n = 0.85, the present experimental results make this extension doubtful (see dashed line and question marks in Fig. 3) because the corresponding heat anomalies could, as explained above, only be observed around one third of a monolayer. The triple line is located at 56.35 K, representing the broader between the solid and fluid phases (regions Sr, SII and Lr, L,, respectively). At coverages around n = 0.85 it originally ended vertically in a two phase liquid + solid region (see dashed line in Fig. 3). Due to the results of our investigations the location of the phase line between the liquid + solid region and the fluid regions does not end horizontally at the triple point line, but has a smooth curvature as shown in Fig. 3 (dasheddotted line). Comparing CH4 with the other gases investigated so far, showing a triple line, one can see that for all these gases the specific heat anomalies start at an occupation number of about one fifth of a monolayer, and this independently whether the molecules form commensurate or incommensurate layers. The succeeding higher coverage peaks lie up to about two thirds of a monolayer on a constant temperature line. At first sight it might seem that O2 is an exception to the rule, but it goes with the other gases if the completion of the epitaxial 43 monolayer is considered as relevant (refer to [7] and [ 121). Figure 4 shows that a plot of the normalized peaks heights Cpeak/Cn~~ vs occupations lying between the limiting values mentioned, results in a linear dependence for CH4, xenon, and neon. For 02, on the other hand, it varies with a higher power (see open circles in Fig. 4). Moreover, for CH4 and xenon the slopes are nearly equal, 300k,,/monolayer for xenon, 325kr,/monolayer for CH4. In the case of neon the slope is just about half, 130kt,/monolayer. The differential slope for O2 varies between 30k,/monolayer at an occupation number of 0.3 and 100kb/monolayer at 0.55. Krypton and Nz are not comparable in this context because they very likely do not show a triple line [ 13, 141. Based on the lever rule, one can try to understand the experimental results given in Fig. 4 on the physical background of a pressure @) vs area (a) constitutional diagram, analogous to a p(v)-diagram of a real 3D gas. The inset of Fig. 4 shows this p(a)-diagram, where the horizontal line between the specific areas a0 and a2 represents the triple line. We neglect the influence of the Grafoil substrate (which is of course a rather crude approximation), and assume that the lower limit of appearance of the anornalies at x2 (one fifth of a monolayer) can be identified with the specific area a2 and the upper limit x1 (two thirds of a monolayer) with

al (a = x-l). The normalized

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peak height is then given by

This dependence is plotted in Fig. 4 (smooth line). One can see that this curve describes the experimental results quite well. Note that for experimental reasons there is a large scattering in the peak heights C’nz of different systems. Therefore, all to be hoped is agreement in tendency of experimental points with the smooth curve of the model. Because this proves true, the above assumption to associate the specific area a2 of the phase boundary, corresponding to gas and liquid-gas coexistence, with the first occurence of the anomalies is reasonable. However, difficulties arise, when one tries to identify the coverage corresponding to maximum peak height C’ns with the specific area a1 at which the systems pass from solid-gas coexistence to the pure liquid state, because in all systems investigated so far the experimental results show that the mean position of peaks at higher occupation numbers shifts to higher temperatures. This contradicts the P(a)-phase diagram, where the triple line terminates not at al but a, and implies that obviously at high coverages the systems move along their melting line. This could be either due to an influence of the substrate or the triple point concept is at least questionable. Acknowledgements - One of the authors (R.M.) wants to thank B. Croset, J.H. Lauter and C. Marti of the ILL for a fruitful and stimulating discussion. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 12.

A. Thorny & X. Duval, J. Chim. Phys. 67,llOl (1970). J.P. Coulomb, M. Bienfait & P. Thorel, Phys. Rev. Lett. 42,733 (1979). P. Vora, S.K. Sinha & R.K. Crawford, Phys. Rev. Lett. 43,704 (1979). J.P. Coulomb, M. Bienfait & P. Thorel, J. Phys. 42,293 (1981). R. Marx & R. Braun, Solid State Commun. 33, 229 (1980). J. Stoltenberg & O.E. Vilches, Phys. Rev. B22, 2920 (1980). R. Marx & R. Braun, Proc. Ecoss 3, Supplement a la Revue “Le Vide, les Chouches Minces” No. 201, 1, 100 (1980). R. Marx (to be published). G.B. Huff & J.G. Dash, Low Temp. Phys. Lt 23, Vol. 2. Plenum Press, New York-London (1974). G.B. Huff & J.G. Dash, J. Low Temp. Phys. 24, 155 (1976). J.A. Litzinger & G.A. Stewart (preprint). J.P. McTaque & M. Nielsen,Phys. Rev. Lett. 37, 596 (1976). D.M. Butler, J.A. Litzinger, G.A. Stewart & R.B. Griffiths, Phys. Rev. Lett. 42,1289 (1979). T.T. Chung & J.G. Dash,&& Sci. 66,559 (1977).