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Submitted on 1 Jan 1977
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MOBILITY OF THE 2 D ADSORBED
PHASESSTUDY OF THE MOBILITY OF AN
HYPERCRITICAL TWO-DIMENSIONAL FLUID BY
QUASI-ELASTIC NEUTRON SCATTERING
J. Coulomb, M. Bienfait, P. Thorel
To cite this version:
MOBILITY OF THE 2 D ADSORBED PHASES.
STUDY OF THE MOBILITY Ol? AN HYPERCRITICAL TWO-DIMENSIONAL
FLUID BY QUASI-ELASTIC NEUTRON SCATTERING
J. P. COULOMB, M. BIENFAIT
Laboratoire des Mkcanismes de la Croissance Cristalline, Centre Universitaire de Luminy, 13288 Marseille Cedex 2, France
and P. THOREL
DRF. CENG and I.L.L., 156 X, 38042 Grenoble Cedex, France
R6sum6. - L'adsorption de mCthane sur une forme comprimee de graphite exfoliC (papyex) est caractCris6e du point de vue physicochimique en mesurant des isothermes d'adsorption. On montre que 1'6chantillon posskde des surfaces (0001) homogknes et qu'il est apte
B
6tre utilis6 pour des Ctudes de diffusion neutronique. A partir de 1'6largissement des pics de diffusion incohkente, on dktermine le coefficient de diffusion du fluide hypercritique bidimensionnel, ainsi que sa variation en fonction du degrC de recouvrement 6. On trouve que la variation du coefficient de diffusion est importante, de 13 B 2,2 x lo-' cmZ s-', en passant de 6 = 0,45B
8 = 0,9 BT = 90 K, et qu'elle s'explique bien par un modkle de mobilit6 due
B
des trous.Abstract. - The adsorption of methane on a compressed form of exfoliated graphite (papyex) is characterized from a thermodynamical point of view by measuring a few adsorption isotherms. It is shown that the sample offers homogeneous (0001) surfaces and is well suited for neutron scattering studies. From the broadening of the incoherent neutron quasi-elastic peak, we are able to determine the diffusion coefficient of the two-dimensional hypercritical fluid of methane adsorbed on the graphite basal plane. We also measure its variation as a function of the coverage. The change in the diffusion coefficient is important, from 13 to 2.2 x 10 - cm2 s -
'
in the 0.45-0.9 coverage range and for T = 90 K, and consistent with a hole mobility model.The incoherent quasi-elastic neutron scattering is a well-known method to study the mobility of the three-dimensional (3 D) fluids [I, 2, 31. It seems natural to adapt this technics to measure the dynamical properties of the two-dimensional (2 D) adsorbed fluids pointed out a few years ago by Thorny and Duval [4]. The major handicap is the low surface to bulk ratio of the usual samples ; thus the surface effects are overwhemed by a very important bulk noise. This difficulty can be removed by using powders with very large specific surfaces. This has been done on charcoal or on metallic substrates [S-
101 which, unfortunately, are rather poorly defined. Yet there are powders with well homogeneous surfaces, like, for instance, exfoliated graphite [1 l] showing practically nothing but well-defined (0001) faces. Exfoliated graphite can be compressed up to a density close to the unity. Then, it has a texture along the six-fold axis and a specific surface of about 20 m2/g. Its trade name is grafoil [I21 in U.S.A. and papyex [I31 in France. We use papyex here. Its texture offers an appreciable advantage : it allows us to measure the mobility in a plane parallel to (0001) by choosing an experimental set-up in such
a way that the wave vectors of the incident and scattered neutrons lie in (0001). This is done here in the case of methane adsorbed on papyex. Methane has a large incoherent cross section. Furthermore, the physical chemistry of its adsorption on graphite (0001) is fairly well known. The adsorption isotherms have been drawn above the 2 D critical temperature, that is to say, in the region where the hypercritical phase of the first adsorbed monolayer is stable [4]. We have previously shown in a preliminary study [14] that the mobility of the molecules of this phase manifests itself by a broadening of the elastic graphite scattering peak. This effect was also observed recently in Argonne National Laboratory (I). We carry out here
a
more detailed study and determine the variation of the broadening as a function of coverage and temperature. A related work is published in these proceedings [15] for NH, adsorbed on graphon. This later study differs from ours in two points. First, the adsorption of NH, does not occur in a layer-by-layer mode but in a three-dimensional island growth.(') S. Sinha, private communication.
C4-32 J. P. COULOMB, M. BIENFAIT,'P. THOREL
Secondly, graphon is a graphite powder with a very large specific surface (86 m2/g) but with no texture ; this involves a measurement of an average (upon all directions) diffusion coefficient.
Before starting a neutron scattering study, one has to characterize the sample from the physical chemistry point of view. This is done in part 1. Then we describe the experimental conditions in 2 and report the results in 3. Finally, part 4 is devoted to a discussion of these results.
1. Papyex adsorbing properties.
-
The density and the thickness of the papyex used are respectively 1.1 and 0.15 mm. Papyex is first outgassed under vacuum at 250 OC during 24 h in the measurement cell which contains 55 g of it. An outgassing at 950 OC for 24 h does not change the adsorption results. The experimental set-up described in 2 is used to perform, before (or after) the neutron scattering experiments, some adsorption isotherm measurements. A typical isotherm obtained by volumetry at 90 K is drawn in figure 1.FIG. 1.
-
Adsorption isotherm a t 90 K of CH, on papyex (thickness : 0.15 mm ; diameter : 26 mm ; weight : 55 g). The experiment has been carried out with the set-up sketched in figure 4 and which is also used for the neutron scattering measurements. (A adsorption o desorption). The solid line serves a s a guide t o the eye. The arrows indicate the neutron scatteringoperating points.
Finally, it is possible, from this isotherm, to determine the specific surface of the sample since we know the epitaxial structure of the CH, first
monolayer [15]. One finds 19 m2/g.
It seems important to emphasize t h e adsorbing qualities of papyex. One knows that the isotherm shape near the transition points is very sensitive to the quality of the adsorbent. It is why we have performed a detailed study of the 2 D hypercritical fluid-2 D solid transition of methane and also of the 2 D localized-2 D delocalized transition in the first monolayer of krypton [4, 161. This later transition is very sensitive to the inhomogeneities of the substrate [17].
First, let us consider the methane adsorption in the region where the coverage approaches the unity. For this, we use an adsorption dynamical method [18] ; it consists in introducing continuously the adsorbate. The pressure is measured with a baratron gauge ; it is not corrected for the thermal transpiration. The adsorption isotherm obtained at 77.3 K is given in figure 2b. We observe a well marked hypercritical fluid-solid transition. We have also given in figure 2a, for comparison, the isotherm
For every pressure, equilibrium is fairly quickly reached (about 1/2 h); One finds the classical shape already obtained by Thomy and Duval [4]. In comparison with these previous results one recognizes at low pressure the hypercritical fluid characteristic part-(up to
N =
160 cm3 STP), then the hypercritical fluid-solid transition and at last the completion of the first solid monolayer, and the beginning of the adsorption of CH, in the second layer. In this figure, the operating points of the neutron scattering experiments are also drawn.I
20 40FIG. 2. - Transition 2 D hypercritical fluid-2 D solid. a ) CH,/exfoliated graphite (recording time
-
4 h).b ) CHs/papyex (recording time
-
8 h).STUDY OF THE MOBILITY OF AN HYPERCRITICAL C4-33
respectively. This isotherm is normalized to the same adsorbate quan$ity as in figure 2b. It shows a hypercritical fluid-solid transition better marked than in figure 2a ; it is comparable to the one published by Thomy and Duval [4].
Another 2 D transition is still more sensitive to the adsorbent quality[17]. We mean the localized-delocalized transition of krypton. The method used here to measure the isotherm at 87.5 K is the adsorption gravimetry [19], which is also a dynarnical method. The measurement has been achieved in the Centre ,de Microcalorim6trie of Marseille. We have noticed that the time necessary to reach equilibrium was significantly longer for krypton than for methane. We see in figure 3b that the expected transition actually occurs ; it is less marked than the transition obtained on the Carbone-Lorraine exfoliated graphite (Fig. 3 a ).
2. Experimental conditions.
-
The experiment is carried out with a metallic set-up made up of a calibrated volume for CH, introduction, a baratron pressure gauge, a diffusion pump system, and a liquid helium cooled cryostat containing the aluminium can filled up with papyex disks(0
2.6 cm) (Fig. 4). The temperature regulation is better than 0.02 K. VALVE CALIBRATED VOLUME CRYOSTAT S A M P L E (PAPYEX) L. . . PUMPSFIG. 4. -Sketch of the experimental set-up.
b) performed with the multichopper time of flight The neutron scattering measurements are spectrometer IN5 of the high flux reactor at ILL-Grenoble. We have chosen a wavelength of 6.0
A
( E , = 2.27 meV) larger than the cut-of f--
5P Kr wavelength of the hk.0 diffracted graphite beams. I + There is still the 0002 peak left for disoriented 2 4 crystals. It occurs for an angle of 127". No counter is
set in this direction. The instrumental resolution is
--
5.5 80 peV. Let us recall that the papyex disks are stacked in such a way that the (0001) surfaces are parallel to the scattering plane. We record the quasi-elastic incoherent spectra for various values of the wave vector Q(E,) ranging from 0.24 to 1.93A-'.
These spectra are converted into the scattering cross section S ( Q , E ) without correcting for instrumental p K~ resolution and self shielding. Thus we obtain raw I + scattering cross section and have to keep it in mind2 4 for the interpretation of the results when the FIG. 3. - Transition 2 D out of registered-2 D in registered solid broadening of the quasi-elastic peak is close to the (recording time
-
16 h). a ) Krlexfoliated graphite. instrumental resolution.b ) Krlpapyex.
Thus, we see that, on papyex, the second order transition Kr localized-Kr delocalized occurs. It is a favorable test for the quality of the product. We have shown in the introduction that owing to its texture papyex seems to be well adapted for neutron scattering, and it still keeps relatively good adsorption qualities. One has, however, to notice that papyex is not so good an adsorbent as exfoliated graphite ; it appears that the compression favors intergranular condensation, thus smoothing the discontinuities due to the transitions.
3. Experimental results. - 3.1. COVERAGE EFFECT. - We have measured the broadening of the incoherent quasi-elastic peak at T = 90 K for different coverages (8 = 0.45 ; 0.7 ; 0.9 ; 1 ; 1.2 , see figure 1). The first three coverages correspond to the 2 D hypercritical phase ; the two others to the solid monolayer and to the beginning of the formation of the second layer respectively.
C4-34 J. P. COULOMB, M. BIENFAIT, P. THOREL
FIG. 5.
-
Difference of the CH4 covered and bare papyexspectra. These incoherent quasi-elastic peaks have been obtained
at T = 90 K, for Q = 0.70
k'
and for three coverages (0.45 ;0.7 ; 0.9). The absence of self shielding corrections yields a drop in the spectra near E = Eo. The broadening decreases when the
coverage increases.
I
I
i
i
.
.
. 8 = 1 ' , 8=1,2 INSTRUMENTAL
I I
I
I
FIG. 6.
-
Ibid. figure 5 for 0 = 1 and 8 = 1.2. By comparison with the instrumental resolution, the broadening disappears.methane only. A few difference spectra for a given scattering angle are drawn on figures 5 and 6. Two important facts can be emphasized. First, the peak for 0 = 0.45 ; 0.7 and 0.9 is broader than the instrumental resolution ; this broadening, due to molecular mobility, decreases when 0 increases. Secondly, we notice that for 0 = 1 and 0 = 1.2 the width of the peak is equal to the instrumental resolution. This lack of broadening means that the monolayer is solidified.
In order to interpret these results, we use a simple model [1, 241 yielding a scattering cross section proportional to a Lorentzian function
where E is the neutron energy and D the translational diffusion coefficient. From the Lorentzian width
one can determine this diffusion coefficient. Our first task js to show that this model fits the experimental results very well. We have to be cautious in using our neutron spectra ; as a matter of fact, the intensity I ( Q , E) is the convolution of the scattering cross section S ( Q , E) with the instrumental resolution which can be approximated
l , , , , l , , , , , , * , I ! t , , 3 1 1 0 3 %
I 3 2 E mev
FIG. 7. - Ibid. figure 5 for T = 90 K , 8 = 0.45 and three values of the scattering vector Qo. The solid curves represent best fits to
STUDY OF THE MOBILITY OF AN HYPERCRITICAL
I 3 i c EmeO
FIG. 8. - Ibid. figure 7 for T = 90 K, 13 = 0.9.
by a triangular function. Then the convolution can be made analytically [20]. All our fits are carried out in this way.
As we can see in figures 7 and 8, there is a good agreement for 8 = 0.45 and 0 = 0.9 between the experiment and the theory. The agreement for 8 = 0.7 is very good too as shown previously [21]. As for 8 = 1 and 8 = 1.2, we have seen in figure 6 that the peak width shows the instrumental resolution, as a solid usually behaves. However, a careful examination of the lower part of the spectra shows a slight broadening. In amplifying this part, this effect is confirmed and can be interpreted in two ways : (i) a translational mobility for a small number of atoms in the gas phase of the second layer, (ii) a rotational mobility of all the atoms in the solid monolayer. It is ,also interesting to notice that the subtraction of these two spectra (8 = 1.2 and 8 = 1) gives a narrow peak mainly due to a solid phase (beginning of the second layer or intergranular condensation). The intergranular condensation is likely considering the isotherm shape (Fig. 1, 2b, 3b ) after the formation of the first layer.
Let us come back to the submonolayer coverage range for which the broadening is important. One can determine the diffusion coefficient D by drawing a diogram A E (Q@ (Fig. 9). The slope of the straight line, obtained for every coverage, gives D whose different values are kept in the table I. The
FIG. 9.
-
Full width half maximum as a function of Q; (equation(2)) fox 0 = 0.45 ; 0.7 and 0.9. The slope of the straight lines yields
the diffusion coefficient.
uncertainty can be estimated to 10-20 %. We ,43serve a very strong dependence of D on 8 which w~ll be interpreted in 4.
3.2. TEMPERATURE EFFECT. - Only one preliminary experiment to measure the temperature effect on the time of flight spectrometer of E L 3 reactor located at CEN, Saclay, has been achieved, so far (A, = 4.2
A
; E, = 4.65 meV). The neutron flux is weaker in Saclay than at the ILL of Grenoble, and the resolution is poorer, too (240 peV instead of 80 peV). In every run, the measurement is carried out for a given scattering angle whereas in Grenoble we use a multicounter spectrometer. However a few interesting results have been obtained.If we look at the raw spectra (without subtracting. the bare graphite peaks) drawn in figure 10 and recorded for 8 = 0.7 and T = 55, 60 and 85 K, we observe two salient facts.
C4-36 J. P. COULOMB, M. BIENFAIT, P. THOREL
FIG. 10. - Time of flight scattering spectra of CH, covered papyex at 85,60 and 55 K. The broadening disappears between 60
and 55 K.
(ii) The broadening decreases when one goes from the hypercritical fluid (85 K ) to the 2 D liquid (60 K). Thus it seems that the diffusion coefficient lowers when passing from one phase to the other, which is worth studying thoroughly.
4. Discussion and conclusion. -The main result of this paper is the observation of a strong variation of the 2 D hypercritical fluid mobility as a function of the coverage. We can interpret it with a very simple model. According to Eyring [23], holes are necessary for a fluid to flow. Then, the fluidity 1/77 can be assumed to be proportional to the number of holes. In the case of a submonolayer, this number is proportional to the free surface that is to say, for a molecule
1 S S
---
rl
"
n sS
where - is the mean surface experienced by a n
S
molecule on a surface S and
-
is the hard core n ssurface of the molecule. n and n , are respectively the number of molecules when the surface S is covered with a diluted phase or with a 2 D solid. Hence
The diffusion coefficient can be expressed by the relation [23]
where k is the Boltzmann constant and A the mean distance between the molecules.
S
From the fact that h
'
= - = and from (3),n n , 0
equation (4) can be rewritten
This relation is approximately checked as can be seen in figure 11 where D is represented versus ( 1 - 0 ) / 8 ' / ' for three 0 values (6 = 0.45 ; 0.7 ; 0.9). One can conclude that, at first approximation, the diffusion coefficient of the 2 D hypercritical fluid is proportional to the free space between the molecules.
FIG. 11. -The diffusion coefficient obeys a hole mobility model.
Other results on the mobility of CH, adsorbed on
graphite have already been published [22]. They have been obtained with another technics. By measuring the NMR relaxation time, one can reach the residence time 7 of the molecules (the waiting
time between jumps). It has been shown on graphitized carbon black that at low coverage and for the 70-100 K temperature range, one can measure the mobility of a 2 D CH, fluid. Unfortunately, it is impossible to compare this result with ours for we do not know the r.m.s. distance
-
X = (2 07)"' between two jumps.
STUDY OF THE MOBILITY OF AN HYPERCRITICAL C4-37
the scattering graphite peak. This method can be used to analyse more closely the mobility of the CH, hypercritical fluid and, in particular, to determine the activation energy of diffusion for various coverages. Furthermore, it can be used to measure the mobility of the 2 D liquid in paying special attention to the molecular dynamics near the critical temperature. It will also be interesting to study the rotations of the molecules which can be pointed out for large scattering vectors. Finally, this method will enable to study the mobility of other 2 D fluids on conditions that they have high incoherent neutron cross sections.
For every experiment to be performed, it seems to us, absolutely necessary to characterize the adsorbent-adsorbate system from the thermo-
dynamical point of view by measuring for instance the adsorption isotherms or the variation of the specific heat by calorimetry. This is the best way to rely on the interpretation of the neutron spectra.
Acknowledgments.
-
We are deeply indebted to J. and F. Rouquerol for giving us the opportunity for measuring adsorption isotherms in the Centre de Microcalorim6trie of Marseille. We are especially grateful to R. Kahn for his pieces of advice during the preliminary neutron experiments in CEN, Saclay, J. Rkgnier for building up an adsorption measurement device, A. J. Dianoux and the IN5 staff for helping us in the neutron measurements in Grenoble and C. Marti and B. Croset for numerous fruitful discussions.References
[I] VINEYARD, G. H., Phys. Rev. 110 (1958) 999. [IS] MARLOW, I., THOMAS, R. K., TREVERN, T. D., WHITE, J .
121 DASANNACHARYA, B. A., VENKATARAMAN, C., USHA DENIZ, W . , J . Physique Colloq. 38 (1977) C4-19.
.
K . , Inelastic scattering o f neutrons in solids and liquids [16] FAIN, S. C., CHINN, M. D., J. Physique Colloq. 38 (1977)
I1 ((I.A.E.A.) Bombay), 1964, p. 157. C4-99.
[3] MARSHALL, W. and LOVESEY, S. W., Theory of thermal [17] RECNIER, J . , Thesis, Nancy University (1976).
neutron scattering (Clarendon Press, Oxford) 1971. 1181 CRILLET, Y ., ROUQUEROL, F., ROUQUEROL, J . , J. Chim.
141 THOMY, A., DUVAL, X., J. Chim. Phys. 67 (1970) 1101. Phys. 2 (1977) 179.
[5] TODIREANU, S., HAUTECLER, S., Phys. Lett. 43A (1973) 189. [I91 ROUQUEROL, J., PARTYKA, S., ROUQUEROL, F., J. Ckem.
[6] TODIREANU, S., NUOVO Cimento Suppl. V (1967) 543. Soc. Faraday Trans I 73 (1977) 306.
[7] TODIREANU, S., Phys., Lett. 30A (1969) 367. [20] VOLINO, F., DIANOUX, A. J . , LECHNER, R. E., HERVET, H., [8] VERDAN, G., Phys. Lett. 25A (1967) 435. J. Physique Colloq. 36 (1975) C1-83.
[9] ASADA, H., TOYA, T., MOTOHASHI, H., SAKAMOTO, M., [211 COULOMB, J . P., BIENFAIT, M., THOREL, P., Proc. 7th HAMACUCHI, Y., J. Chem. Phys. 63 (1975) 4078. Intern. Vac. Congr. and 3rd Intern. Conf. Solid [I01 RENOUPREZ, A., ILL Annual Report (1976) 357-358. Surfaces (Vienna 1977).
[ I l l THOMY, A., DUVAL, X., J. Chim. Phys. 66 (1969) 1966 ; 67 [221 RIEHL, J. W., KOCH, K., J. Chem. Phys. 57 (1972) 2199. (1970) 286. [231 GLASSTONE, S., LAIDLER, K. J., EYRINC, H., The theory of [I21 Crafoil is a product of Union Carbide Corp. Carbon rate processes (Mc Craw-Hill Book Company, N.Y.)
Products Div. 270 Park Ave. New York. 1941, p. 486.
[I31 Papyex is a product of Le Carbone Lorraine, 45 rue des [241 SCHOFIELD, P., Inelastic scattering o f neutron in solids and Acacias, 75821 Paris Cedex 17. liquids (I.A.E.A. Vienna), 1961, p. 39.
[I41 COULOMB, J. P., KAHN, R., BIENFAIT, M., Surf. Sci. 61
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DISCUSSION
R. K. THOMAS. -The plots of A E against Q 2 are linear up to a Q of about 1
A,
but you have measured spectra up to a higher value of Q. ~ d e s the broadening remain linear at these higher values ofQ ?
M. BIENFAIT.
-
No, the slope of the curves decreases for higher Q2.W. STEELE.
-
There are theoretical arguments indicating that the quasi-elastic line shapes should be non-Lorentzian ; i-e., that ( SrZ ) should not be strictly proportional to time. Is there any sign of this in these experiments ?K. CARNEIRO.
-
(Comment to W. Steele's question.) Strictly speaking, the Lorentzian lineshape is unphysical ; but I think that the experience from bulk liquids has shown us that if one uses measurement,s obtained at small enough wavevectors, one gets reliable results .for thediffusion constant. On the other hand, I find it rather dangerous to use deviations from this simplest model (that FWHM = 2 DQ ') at larger Q 's to promote more detailed models.
J. P. MCTAGUE.
-
(Comment on question by W. Steele concerning deviations from a Lorentzian shape fit diffusion in 2-dimensions.) These deviations, like the 2 D mean-square displacements discussed earlier, are only logarithmic in the sample size and only set in at very long times. Before they would have any effect, I assume that interactions with defects or edges or hopping into a second layer would dominate. Neutrons are sensitive mainly to relatively short-time dynamics ( t 5hLl
,A E (Resolution)I
).J. FRIPIAT.
