Langmuir 2000, 16, 5955-5959
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Experimental and Modeling Study of the Adsorption of Supercritical Methane on a High Surface Activated Carbon† Li Zhou,*,‡ Yaping Zhou,§ Ming Li,‡ Ping Chen,‡ and Yu Wang‡ Hydrogen Energy Research Center and Department of Chemistry, Tianjin University, Tianjin 300072, China Received August 27, 1999. In Final Form: April 7, 2000
The adsorption of methane on an activated carbon of high surface was measured in the range of 233-333 K and 0-10 MPa. The isotherms showed a considerably different feature than that measured on low surface carbon. A maximum appeared on isotherms at relatively low temperatures. All the experimental isotherms were well modeled by the Langmuir-Freundlich equation. The difference between the measured and the so-called absolute adsorption was properly accounted for in modeling. An assumption of monolayer adsorbate adsorbed was included in the model. The layer volume evaluated was consistent with the pore volume of adsorbent reported by CO2 adsorption. The intermolecular distance in the adsorbed phase was evaluated from a model parameter. This intermolecular distance was compared with that in the free sate, which revealed a basic picture of the physical state of the adsorbed phase at above-critical temperatures.
Introduction Studies on the adsorption of supercritical methane on high surface activated carbon (so-called superactivated carbon) have been stimulated by potential industrial applications in the past decade. It is of interest for the adsorptive storage of natural gas and for the separation or purification of gas mixtures. Methane is the major component of natural gas, coal bed gas, and some exhaust gases of petrochemical or chemical units. The application of superactivated carbons in industry will enhance the performance of many processes. Therefore, a fundamental study on the adsorption was encouraged by engineering concerns. Another stimulation for studying the adsorption comes from theoretical interests on supercritical adsorption. As pointed out by Aranovich and Donohue,1 there are very few papers that contributed to physical adsorption of supercritical gases. The Gibbs thermodynamic approach in studying adsorption assumes a phase equilibrium mechanism.2 The adsorbed molecules constitute a thermodynamically distinct phase. Chemical potential theory was applied to describe the equilibrium between ambient gas and the adsorbed phase. A reference state has to be assigned to the adsorbed phase for defining the chemical potential. Because the adsorbed phase is much the same as liquid for low-pressure vapor adsorption, the reference state is usually taken as the saturated liquid of the adsorbate. However, this reference state cannot be real when the equilibrium temperatures are much above critical. It was argued that critical temperature would increase because of molecular interaction between ad† This work was accomplished in the High-Pressure Adsorption Laboratory, Hydrogen Energy Research Center, Tianjin University, Tianjin 300072, People’s Republic of China. * To whom correspondence may be addressed: Phone: 86 22 27406163. Fax: 86 22 27404757. E-mail:
[email protected]. ‡ Hydrogen Energy Research Center. § Department of Chemistry.
(1) Aranovich, G. L.; Donohue, M. D. J. Colloid Interface Sci. 1996, 180, 537-541. (2) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984; Chapter 3.
sorbate and adsorbent.3 Therefore, quasi- or overheated liquid states4,5 were assumed for the adsorbed phase. However, how much the critical temperature has shifted up is a problem waiting for answers. Nevertheless, efforts have been made to establish an empirical correlation for saturated pressure at supercritical temperatures6 aiming at expanding the applicability of the vapor adsorption theory to supercritical adsorption. It is clear that understanding the physical nature of the adsorbed phase is very important for developing supercritical adsorption theories. Modeling adsorption isotherms may help to gain an insight into the nature of supercritical adsorption. Actually, it is a fundamental task in adsorption studies because much important information can be drawn from a pertinent model. Although the isotherms of vapor adsorption show different types,7 the isotherms of supercritical adsorption largely belong to type I. However, isotherms will show a maximum if the amount adsorbed becomes fairly high. The adsorption will decrease with the increasing pressure after the maximum, as shown by some isotherms in Figure 1. All the well-known isotherm equations7 are monotonically increasing functions of pressure and, therefore, cannot represent the isotherms of maximum. Some efforts have been contributed to explain the adsorption equilibrium between activated carbon and supercritical gases.1,8-10 The simplified local density (SLD) model11 does work successfully for the adsorption iso(3) Bering, B P.; Dubinin, M M.; Serpinsky, V. V. J. Colloid Interface Sci. 1966, 21, 378-393. (4) Ozawa, S.; Kusumi S.; Ogino, Y. J. ColloidInterface Sci. 1976, 56, 83-91. (5) Kaneko, K.; Shimizu, K.; Suzuki, T. J. Chem. Phys. 1992, 97, 8705-8711. (6) Amankwah, K. A. G.; Schwarz, J. A. Carbon 1995, 33, 13131319. (7) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity, 2nd ed.; Academic Press: London, 1982. (8) Malbrunot, P.; Vidal, D.; Vermesse, J. Langmuir 1992, 8, 577580. (9) Staudt, R.; Saller, G.; Tomalla, M.; Keller, J. U. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 98-105. (10) Be´nard, P.; Chahine, R. Langmuir 1997, 13, 808-813. (11) Subramanian, R.; Pyada H.; Lira, C. T. Ind. Eng. Chem. Res. 1995, 34, 3830-3837.
10.1021/la991159w CCC: $19.00 © 2000 American Chemical Society Published on Web 06/17/2000
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Figure 1. Adsorption isotherms of methane: points, experimental; curves, predicted by the Langmuir-Freundlich equation.
therms with maximum and explained the clustering phenomenon near critical state. However, it looks not as pertinent as the model presented in present paper. Chemical potential constitutes a basic physicochemical quantity of the SLD model, which is not well defined for supercritical adsorbate. This might be the cause of impertinence of the model over a wide range of temperatures and pressures. Compared with the recently published works on methane adsorption,6,12,13 the present work covered a wider range of experiments. The work of Be´nard and Chahine10 covered almost the same range of temperatures and pressures, yet the CNS-201 carbon used in their experiment has much less specific surface area than the carbon used in the present work. Less specific surface yields less amount adsorbed for the same equilibrium condition. As a result, methane isotherms measured on CNS-201 did not show maximum remarkably. The appearance of maximum on isotherms calls for a different strategy of modeling. A strategy presented in the paper allowed for the difference between the measured and the so-called absolute adsorption. The LangmuirFreundlich equation was used in modeling because it does not assume any unreal physical quantity such as “saturated pressure” in the Dubinin-Astakhov equation. Monolayer adsorbate was also assumed in modeling. Compared to the models assuming a multilayer1 or volumefilling14 mechanism, this model predicted the experimental isotherms very well. The intermolecular distances of adsorbate were calculated from the model parameter, which suggested the existence of a distinct interface between the two phases in equilibrium and showed a variation pattern of the physical state of the adsorbate adsorbed at above-critical temperatures. Experimental Section A standard volumetric method was used to measure adsorption and desorption isotherms. The experimental setup and procedure (12) Jagiello, J.; Sanghani, P.; Bandosz, T. J.; et al. Carbon 1992, 30, 507-512. (13) Kaneko, K.; Murata, K. Adsorption 1997, 3, 197-208. (14) Dubinin, M. M.; Astakhov, V. A. Izvest. Akad. Nauk SSSR, Ser. Khim. 1971, No.1, 5-11.
Zhou et al. are much the same as used in studying hydrogen adsorption.15 Both expansion and adsorption cells have volumes of 61 mL. The expansion cell was maintained with a thermostat of 30 °C, while the adsorption cell was maintained in another thermostat, whose temperature is adjustable in the range of -50 to 60 °C. The temperature in both thermostats was kept constant to (0.1 °C. The pressure in the expansion cell was measured by a pressure transducer manufactured by the ABB Company with a precision of 0.1%. The virial equation of three orders was used to calculate the compressibility factor of methane. The activated carbon used was manufactured from coconut shell by KOH activation. The activation technology has been popular in the literature. The well-known activated carbon AX-21 was manufactured by similar processing; therefore, the structure property of this kind of carbon looks quite similar. The surface area and micropore volume reported for CO2 adsorption at 273 K was 3106 m2/g and 1.29 mL/g, respectively. The carbon sample was dried to constant weight under vacuum at 110-120 °C before adsorption. Methane of purity 99.995% was used as adsorptive without pretreatment. Helium of purity of 99.999% was used to measure the “dead volume” of the adsorbent. Equilibrium pressure was controlled to vary in the range of 0-10 MPa. Six isotherms were measured, which uniformly distributed in the range of 233-333 K with 20 K intervals. The measured adsorption data are presented in the Appendix, and the isotherms are shown in Figure 1, where points represent the experimental adsorption and the curves the predicted values of model. Equilibrium temperatures are noted near each isotherm.
Description of the Adsorption Equilibrium System A group of adsorption phenomena have attracted special research interest because they assumed unusual behavior. There is a maximum on the isotherm if the amount adsorbed becomes fairly high. The amount adsorbed decreases with the increasing pressure after the maximum, as shown in Figure 1 at 273 K and lower temperatures. There are several explanations1,8-10 for this behavior in the literature. However, to our understanding, it can attributed to the effect of volume of the adsorbate in the adsorbed phase, at least for the adsorption conditions tested in the present work. It is known from the Gibbs definition of adsorption that not all the molecules in the adsorbed phase should be included in the amount adsorbed. The adsorptive molecules spread in adsorbate space according to the density of ambient gas are irrelevant with the molecular interaction between gas and solid. Therefore, the amount adsorbed is an excess quantity of the adsorbate over the gas-phase density. The relation between the measured or excess adsorption and the socalled absolute adsorption is defined by the following equation
n′ ) n + vaFg
(1)
where n′ is the total amount of adsorptive molecules in the adsorbed phase, which is named as absolute adsorption, mol/g; n is the measured amount adsorbed or the excess adsorption, mol/g; va is the volume of adsorbate in the adsorbed phase, m3/g; and Fg is the density of the bulk gas, mol/m3. When the amount adsorbed is not much, the value of va is neglectable and n and n′ are actually the same. However, when the amount adsorbed becomes high and the adsorbate volume vs can no longer be neglected, the difference between n and n′ becomes larger and larger. It is known from eq 1 that n′ is a unimodal increasing function of pressure as a sum of two positive terms. However, as a difference of n′ and vaFg, n might have (15) Zhou, Y.; Zhou, L. Sci. China (Ser. B) 1996, 39, 598-607.
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negative rate of increment if vaFg increases faster than n′ at higher pressures and/or at lower temperatures. It is shown presently that this kind of isotherm can be explained by the available adsorption knowledge if the effect of adsorbate volume can be reasonably accounted. All the conventional isotherm equations were originally derived for absolute adsorption and, therefore, are monotonically increasing functions of pressure. They work well for the excess adsorption too if it differs little from the absolute values. However, these equations cannot represent the excess adsorption isotherms if the amount adsorbed is high, for example, when isotherm showed a maximum. Presently, instead of measured isotherms, the absolute adsorption isotherms were assigned the Langmuir-Freundlich equation. This equation was usually applied to the adsorption of ideal monocomponent adsorptive on a heterogeneous surface
(
n′ ) nm′
)
bPq ) n + vaFg 1 + bPq
(
)
bPq - vaFg 1 + bPq
(
(3)
)
bPq Aσsg 1 + bPq
(4)
A)
(5)
( )
1/2
(
(7)
)(
)
(8)
Pressure should be replaced by fugacity to describe the thermodynamic state of fluid at high pressure and/or low temperatures. Therefore, eq 8 is modified to
n)
( )(
)
A3/2 bfq nm′ Fg q 1 + bf (nm′Av)1/2
(8a)
A* B* f ) z - 1 - ln(z - B*) ln 1 + P B* z
(
A* ) 0.4278R
B* ) 0.0867
P/Pc
where A is a measured property of adsorbent and is 3106 m2/g as mentioned before, and Av is the Avogadro (16) Findenegg, G H. Fundamentals of adsorption. Proceedings of the Engineering Foundation Conference, Germany 1983; 1983; pp 207218.
(9)
(9-1)
(T/Tc)2 P/Pc T/Tc
(9-2)
R0.5 ) 1 + m(1 - Tr0.5)
(9-3)
m ) 0.480 + 1.574ω - 0.176ω2
(9-4)
Compressibility factor z is obtained by solving the following equation:
z3 - z2 + z(A* - B* - B*2) - A*B* ) 0
(9-5)
The relevant property of methane is
Pc ) 4.54 MPa;
ω ) 0.00817
It yields from eq 9-4) that
m ) 0.4926 By substitution of m and Tc into eq 9-3, one obtains
T ) ]} [ (190.6
R ) 1 + 0.4926 1 (6)
)
where
{
Therefore
A σsg ) nm′Av
)
bPq A3/2 nm′ Fg q 1 + bP (nm′Av)1/2
Tc ) 190.6 K;
The quantity σsg is an “average reach” of an adsorbed molecule, it relates, therefore, to nm′ by the relation that follows.
nm′Avσsg2
n)
ln
where θ is the percent coverage of the surface when the adsorbed amount is n; A is the specific surface area of adsorbent, m2/g; and σsg is the depth of the adsorbed layer, m. The subscript “sg” denotes the interaction between solid and gas. Since θ ) n′/nm′, it holds from eqs 1 and 2 that
va )
(
bPq A3/2 1 + bPq (nm′Av)1/2
By substituting eq 7 into eq 2, we obtain
(2)
where P is the equilibrium pressure, MPa; nm′ is a parameter that corresponds to full coverage of solid surface; and b and q are parameters of the LangmuirFreundlich equation. Considering the isotherm behavior crossing the critical temperature reported by Finndenegg16 and the potential profile in a slit pore,13 an assumption of monolayer arrangement of adsorbate molecules adsorbed at above-critical temperatures was applied in modeling. Then the following relation holds
va ) θAσsg
va )
Pressure P was transformed to fugacity f by the fugacity coefficient, which was determined by a state equation of real gases. The Soave-Redlich-Kwong equation that follows is possibly the best tradeoff between precision and tediousness of computation for methane.17
or
n ) nm′
number. Equation 7 is obtained by substituting eq 6 into eq 4
0.5
2
(9-6)
The values of A* and B* in eq 9-5 can thus be determined. Equation 9-5 was solved by an iteration method. The convergence criterion was set equal to 10-6. The values of A*, B*, and z were substituted to eq 9, from which the fugacity coefficient f/P was determined. (17) Guo, T.; et al. Multicomponent Vapor-Liquid Equilibrium and Distillation (in Chinese); Chemical Industry Press: Beijing, 1983.
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Zhou et al.
Table 1. Coefficient of Equation 10 (f in MPa, Gg in mmol/mL) T, K
c0
c1
233.15 0.03956 253.15 -0.0015653 273.15 0.034342 293.15 0.011651 313.15 0.00130868 333.15 -0.0021004
c2
0.4032 0.49245 0.381142 0.389376 0.38027 0.3632
c3
0.1147 -0.017493 0.013257 0.0060443 0.0391973 0 0.0220492 0 0.012952 0 0.0079888 0
Table 2. Depths and Volumes of the Adsorbed Layer Determined by L-F Model
c4
T, K
σsg × 1010, m
σgg × 1010, m
layer volume, mL g-1
0.003426 0 0 0 0 0
233 253 273 293 313 333 111.7
4.36 4.38 4.47 4.59 4.69 4.75 3.69
5.32 5.36 5.54 5.78 5.98 6.10 3.97
1.35 1.36 1.39 1.43 1.46 1.48
To facilitate nonlinear regression analysis, the bulk gas density of methane was presented as a function of fugacity for the experimental condition
Fg ) c0 + c1 f + c2 f 2 + c3 f 3 + c4 f 4
(10)
The coefficients of eq 10 are listed in Table 1. Instead of mol/g, mmol/g was used for the amount adsorbed in measurements. Besides, the unit of Fg is in mmol/mL in Table 1. However, it should be in mmol/m3 in eq 8. Therefore, eq 8a was modified to
n)
(
)(
)
7.053Fg bf q nm′ q 1 + bf nm′ 1/2
(8b)
There are three independent parameters, b, nm′, and q, that can be determined by fitting eq 8b to the experimental data. Commercial scientific software accomplished the procedure of curve fitting. The evaluated parameters at different temperatures can be correlated with temperature:
nm′ ) 164.29 - (1.3016 × 105)/T + (3.8770 × 107)/T2 - (3.7017 × 109)/T3 (mmol/g) (11a) b ) 0.77147 - 634.19/T + (1.4601 × 105)/T2
(11b)
q ) exp(-2.0168 + (2.1347 × 103)/T (7.4125 × 105)/T2 + (7.7682 × 107)/T3) (11c) The fitness of the model is shown by curves in Figure 1. More strictly, the standard deviation of the model is calculated18
(∑
1/2
N
d)
i)1
si2/(N - ψ)
)
(12)
where si is the difference between the ith measurement and that predicted by the model, N is the number of measurements at a given temperature, and ψ is the number of parameters in the model equation. The average standard deviation in the whole range is 1% if the first measurement at the lower end of pressure was skipped. Information Provided by the Model
Figure 2. A comparison of intermolecular distances: O, in free state; b, in the adsorbed state.
also identified, which were designated as σgg and are shown in the third column of Table 2. The interaction between adsorbate molecules and carbon atoms makes the intermolecular distances of adsorbate different from that without the interaction. The relation between σgg and σsg was governed by the Lorentz-Berthlot combining rule:19
σsg )
1 (σ + σss) 2 gg
(13)
where σss ) 3.40 Å is the distance between carbon atoms in graphite crystals. Because the adsorbed state is basically the same as the saturated liquid below critical temperature, the intermolecular distance of methane at normal boiling point was also presented. The density of liquid methane at the normal boiling point (111.7 K) is 0.425 g/mL,17 from which the intermolecular distance was evaluated
σllfree )
(
)
1/3 1 ) 23 0.425/(16 × 10 ) × (6.023 × 10 ) 3.97 × 10-10 m (14) 6
Interesting information of the adsorption system can be extracted from the model. The layer depth σsg was regarded as an average reach of an adsorbed molecule. Therefore, it is a kind of index of the physical state of adsorbate. The σsg values shown in the second column of Table 2 were calculated by eq 6 from the evaluated nm′. To clarify the change in state due to adsorption, the average intermolecular distances in bulk gas phase were
where σllfree is the average intermolecular distance in liquid methane without adsorption on carbon. The corresponding intermolecular distance in the adsorbed state is smaller (3.69 nm) as reported by eq 13. If we present the two sets of intermolecular distance with temperature, two distinct linear plots were obtained as shown in Figure 2. Since the
(18) Snedecor, G. W.; Cochran, W. G. Statistical Methods, 7th ed.; The Iowa State University Press: Ames, IA, 1980; p 409.
(19) Matranga, K. R.; Myers, A. L.; Glandt, E. D. Chem. Eng. Sci. 1992, 47, 1569-1579.
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Table 3. The Measured Adsorption Data (P in MPa, n in mmol of CH4/g of carbon) T ) 333.15 K
T ) 313.15 K
T ) 293.15 K
T ) 273.15 K
T ) 253.15 K
T ) 233.15 K
P
n
P
n
P
n
P
n
P
n
P
n
0.1775 0.4625 0.7800 1.2000 1.6350 2.0900 2.5475 3.0400 3.5600 4.1925 4.8075 5.3475 6.0175 6.7400 7.3525 7.9250 8.4625 8.9825 9.3800
0.9022 2.0864 3.1435 4.2401 5.1369 5.9403 6.6073 7.2043 7.7697 8.2985 8.7241 9.0577 9.3709 9.6607 9.8621 10.0081 10.1378 10.2267 10.2770
0.1225 0.4000 0.8400 1.3325 1.8225 2.3125 2.7975 3.3050 3.8325 4.3450 4.8775 5.3925 5.9250 6.4400 6.9550 7.4850 7.9875 8.4625 8.9975 9.3950
0.9508 2.5298 4.3246 5.6973 6.7807 7.6196 8.2825 8.8595 9.3659 9.7554 10.1002 10.3598 10.5898 10.7692 10.9329 11.0177 11.1125 11.1769 11.2162 11.2609
0.1475 0.4100 0.7875 1.2775 1.8025 2.3200 2.8200 3.3000 3.7875 4.2550 4.6800 5.1000 5.5125 5.9625 6.4475 6.9475 7.4250 8.0300 8.5075 8.9900 9.3775
1.6151 3.5750 5.4421 7.0653 8.3099 9.2257 10.0211 10.5370 10.9660 11.2934 11.6780 11.8586 12.0137 12.1341 12.2575 12.3262 12.4407 12.4248 12.3765 12.3403 12.4705
0.1250 0.3750 0.7425 1.2125 1.6900 2.1475 2.5750 3.0325 3.4775 3.8950 4.3525 4.7650 5.1975 5.6075 6.0575 6.5200 6.9550 7.4350 7.9150 8.4300 8.9300 9.3275
2.0934 4.5881 6.8710 8.6892 9.9717 10.8769 11.5503 12.0878 12.5296 12.8654 13.1784 13.3564 13.5264 13.6527 13.7419 13.8028 13.8402 13.8459 13.7810 13.7063 13.6091 13.5036
0.0900 0.3150 0.7100 1.3075 2.0025 2.7050 3.3800 4.0200 4.6150 5.1825 5.7375 6.2600 6.7775 7.2875 7.6875 8.1250 8.5175 8.8800 9.2750
2.4695 5.6635 8.6701 11.0280 12.7160 13.8168 14.5613 14.9681 15.2934 15.4158 15.4553 15.4515 15.3742 15.2465 15.1271 14.9751 14.7591 14.5261 14.2899
0.375 0.1500 0.3825 0.7700 1.2700 1.8050 2.3975 2.9575 3.5375 4.0900 4.6425 5.1425 5.6625 6.1675 6.5775 6.9175 7.4025 7.8775 8.3000 8.6975 9.1400
2.0556 4.9020 8.1294 10.9361 12.9208 14.3374 15.4189 16.0899 16.4976 16.7479 16.8883 16.8887 16.6835 16.5061 15.9597 15.9921 15.6230 15.1578 14.9071 14.5377 13.6218
at different temperatures are quite reasonable in comparison with the pore volume reported. Finally, the values of q of the model provided information about the adsorbent geometry. It was pointed20 that the exponent of the Langmuir-Freundlich (L-F) equation reflects the fractal dimension of activated carbon. As shown in Figure 3, the fractal dimension of the space occupied by the adsorbed molecules increased slowly with temperature. The fractal dimension for monolayer adsorbates on zeolites and activated carbon normally ranges in 2-3. However, all the q values are less than 1. It seems more efforts need to be paid to clarifying the relation between the exponent of the L-F equation and the adsorbent geometry.
Figure 3. Variation of q with temperature.
difference between the intermolecular distance in the free state and in the adsorbed state is considerable, the existence of a distinct interface between the two equilibrium phases could be concluded. The intermolecular distance at the intersection of the two plots is 3.40 × 10-10 m, which is the distance between carbon atoms in graphite crystals. Apparently, it is the limit value of intermolecular distance of any adsorbed molecules. It is thus concluded that the state of the adsorbed methane is not the same as liquid at above-critical temperature; however, the liquid state seems to be a target state of the supercritical adsorbate following the temperature-decreasing direction. The volumes of the adsorbed layer are presented in the fourth column of Table 2. They were calculated from the σsg values by eq 3. The micropore volume reported for the carbon is 1.29 mL/g, which is less than the layer volumes listed in Table 2. However, micropore volume itself is not a precise value. It depends on how to interpret the CO2 adsorption data. Therefore, the layer volumes calculated
Conclusions 1. The adsorption isotherms of supercritical methane on a high surface carbon were measured in the range of 233-333 K and 0-10 MPa. A remarkable difference from that observed on lower surface carbon (CNS-201) was acknowledged. A maximum was observed on isotherms at relatively low temperatures. 2. The isotherms with maximum were well modeled by using the Langmuir-Freundlich equation on the basis of the Gibbs definition of adsorption. A monolayer adsorption mechanism was assumed in the modeling. The average standard deviation of the model is less than 1%. Therefore, monolayer assumption seems reasonable. Intermolecular distances of the adsorbed methane were evaluated from the model parameter. Those data implied the existence of a distinct interface between the bulk gas and the adsorbed phase. A plot of the data versus temperature showed the variation pattern of the physical state of the supercritical adsorbate. Acknowledgment. The authors thank the National Natural Science Foundation of China for the financial support (Project 29936100). The stimulating discussion with and valuable suggestion of Professor J. U. Keller, University of Siegen, Germany, are gratefully appreciated. Appendix The measured adsorption data are given in Table 3. LA991159W (20) Keller, J. U. Physica A 1990, 166, 180-192.
