ON PHYSICAL ADSORPTION

IX. Sub-critical and Supracritical Adsorption Isotherms for Krypton Monolayers on Graphitized Carbon Black 1

Sydney Ross and Wemer Winkler

Departments of Chemistry and Chemical Engineering, Rensselaer Polytechnic Institute, Troy, New York

Received May I~, 1955

ABSTRACT

The critical temperature of condensation for an adsorbed monolayer of krypton on graphitized carbon black, P-33, is shown to be approximately 82°K. Adsorption isotherms for temperatures (77.1°K. and 90.1°K.) close to this critical temperature offer experimental evidence that two-dimensional condensation may be described by a two-dimensional analogue of van der Waals' equation.

INTRODUCTION

Hadden Clark (1) reports tha t k ryp ton adsorbed on graphitized carbon black, P-33, at 70°K. shows evidence of a two-dimensional phase transi- tion. Amberg, Spencer, and Beebe (2) have determined calorimetric heats of adsorption of k ryp ton on the same adsorbent. F rom da ta in the latter paper, the two-dimensional critical t empera ture of condensation for the adsorbed monolayer can be estimated as approximately 85°K.

This paper reports and discusses adsorption isotherms for k ryp ton on graphitized carbon black, P-33, a t temperatures (77.8°K. and 90.1°K.) lying slightly above and slightly below the est imated critical tempera ture of condensation for the adsorbed monolayer.

MATERIALS, APPARATUS, AND METHODS

A sample of carbon black, P-33, which was graphitized a t 2700°K., was supplied by the courtesy of Dr. Wal ter R. Smith of Godfrey L. Cabot , Inc. A spectroscopically pure grade of k ryp ton was obtained f rom the Mathe- son Company.

The determinations of the adsorption isotherms were made with the volu-

1 Based on a Thesis presented by W. Winkler, in partial fulfillment of the require- ments for the degree of Doctor of Philosophy, to the Department of Chemical Engi- neering, Rensselaer Polytechnic Institute, June, 1955. The experimental observa- tions are reported in full in the original Thesis, copies of which may be obtained from University Microfilms, .Ann Arbor, Mich.

33O

ON PHYSICAL ADSORPTION. IX 331

metric adsorption system and McLeod gauge previously described (3) ; and the corrections for thermal transpiration obtained from Liang's formula (4). A few points at high coverage on the 90.1°K. isotherm had to be deter- mined with a higher pressure adsorption apparatus, using an oil manome- ter. The time required for adsorption equilibrium varied at different por- tions of the isotherm, and was markedly longer at 77.8°K., and particularly in the range of the isotherm during and following the vertical discontinuity. It was found also that the time required depended on the sample weight and could be greatly reduced with small quantities of adsorbent. In the

P (mm H9) o )

2.0

V

LO

0(~ A 6 40

Px I0 s (ram HV)

FIG. l . Adsorpt ion i so therm of k r yp t on at 90.1°K. on graphi t ized carbon black, P-33, a f te r correct ion of the values at lower pressures for the rmal t ransp i ra t ion . The low-pressure pa r t of the i so therm is shown on an expanded scale by the lower curve.

2.4

t.e

V

0.!

0.8 1.6 2.4 1t2 4.0

P xlO s (ram Hg)

FIG. 2. Adsorpt ion i so therm of k r yp t on a t 77.8°K. on graphi t ized carbon black, P-33, a f te r correct ion of the values for the rmal t r ansp i ra t ion .

332 SYDNEY ROSS AND WERNER WINKLER

present experiments the weight of sample was 175 mg., and the time re- quired was from 20 minutes to a few hours.

EXPERIMENTAL RESULTS

The adsorption isotherm of krypton at 90.1°K. on graphitized carbon black, after correction of the values at lower pressures for thermal trans, piration, is reported in Fig. 1. The adsorption isotherm of the same system at 77.8°K., after correction for thermal transpiration, is reported in Fig. 2.

The equations that are used to describe the experimental findings are listed below, and the equation constants and other physical constants derived from them are reported in Table I.

]~quations Approx. Range 0 p = ~ o - o . l o [1] 0 [ 0 2a~] p = ka ~ exp 1 - ~ b2RT o 0.10-0 .50 [2]

V = V,,,19p/(1 --[- ~p) 0.60--0.90 [3]

To ffi 8a2/27 Rb2 [4] Equations

AH (low #) RT~ T_..__...~ In k..£ ffi T ~ - T l kl [5]

RT~ ~1 In B_.I AH (high 0) ffi T2 - & [6]

zE ffi A H ( h i g h O) - - AH (low 0) [7]

Equations [5], [6], and [7] are derived and the symbols used are defined in the previous paper of the series (3).

T A B L E I

Equation Constants and Estimated Physical Constants of Krypton Adsorbed on Graphi- tized Carbon

Definition Unit 0-Range to which 77.8OK. 90.1OK. Constant by eq. no. eq. applies

k 1 m m . 04). 1 0.0162 0.28 kb 2 m m . 0 .1 -0 .5 - - 0.25

2a~ 2 ra t io 0 .1 -0 .5 - - 6.16

b2RT V,~ 3 cc a t S T P 0.50-0,89 4 .85 \ V,, 3 cc a t S T P 0 .89-0 .95 3.23J 2.94

3 m m . - ' 0 .89-0 ,95 1820 68.0 Tc 4 °K. - - 82.1 AH (low 0) 5 ca l . /mo le - - 3240 AH (high 0) 6 ca l . /mo le - - 3740 zE 7 ca l . /mo le 500

ON PHYSICAL ADSORPTION. IX 333

DISCUSSION

I. The Adsorption Isotherm8

The adsorption of krypton on graphitized P-33 at 90.1°K., reported in Fig. 1, follows a similar pattern to that shown by adsorbed argon or nitro- gen on the same adsorbent: the adsorbed molecules behave first as an ideal two-dimensional gas, as is evident from the initial linear portion of the adsorption isotherm, conforming to Eq. [1]; at higher pressures the adsorption isotherm can be described by Eq. [2], which is based on a two- dimensional van der Waals equation; and at still higher pressures, when more than half the available surface is covered with adsorbate molecules, the adsorption isotherm has the form of a Langmuir equation, Eq. [3]. The precision of the description of the experimental results by Eq. [2] is

0 0 shown in Fig. 3, in which the function W = In ~ + 1 ~ In p

is plotted vs. O, for the range 0.1 < 0 < 0.5. Mter half the surface is occu- pied the description of the isotherm is continued by Eq. [3], and the pre- cision of this description is shown in Fig. 4. The value of V~ derived from the plot of Fig. 4 is the basis for the calculation of 0 in Eq. [2], and hence for the construction of the plot given in Fig. 3. An estimate of the two- dimensional critical temperature of condensation of the adsorbed mono-

-4 W

I - | ~ Z 0.4 0,6

0

FI~. 3. Test of the adsorption isotherm of krypton on graphlti~ed carbon black, P-33, at 90.1°K., to show the description of the adsorbed monolayer by a two-dimen- sional van der Waals equation, at coverage below 50%.

334 SYDNEY ROSS AND WERNER WINKLER

O.a

0.4

P

0. |

P (ram Hg) 0.4 O.Q | .2 1.6 2,0

.BeK" ~x|011,.

2

f PxlOU (ram Hg)

FIo. 4. Test of the adsorption isotherms of krypton on graphitized carbon black, P-33, at 90°K. and 77.8°K., to show their description by the Langmuir equation, at coverage above 50%. The lines AB and BC represent two Langmuir equations for the description of the 77.8 ° isotherm.

layer can be obtained from the slope of the straight-line portion of Fig. 3, which equals 2a2/b~RT, yielding (Eq. [4]) Tc = 82.1°K.

The adsorption isotherm at 77.8°K. is reported in Fig. 2. At the lowest pressures measured the isotherm is linear; at higher pressures a vertical discontinuity appears in the range of monolayer coverage (0.1 < 8 < 0.5), which is the same portion of the isotherm described at 90.1°K. by a two- dimensional van der Waals equation. This finding offers a complete analogy to the behavior of a gas below its critical temperature; it also substantiates the van der Waals equation applied to the description of an adsorbed monolayer. This is the first experimental evidence that the two-dimensional van der Waals constants have an exactly analogous significance with respect to the critical point of an adsorbed monolayer, as their three- dimensional originals have for the critical point of a gas.

Above 50 % coverage the isotherm would be expected to have the form of a Langmuir equation, if it were to behave in the same way as the supra- critical isotherm at 90.1°K. The Langmuir plot is shown in Fig. 4, from which it can be seen that the experimental data are described by two Langmuir equations, with a transition at 8 = 0.89. The determination of this portion of the isotherm was confirmed by duplication of the measure- ments. The two Langmuir equations give values of Vm that are, respec- tively, for the AB and the BC portions of the Fig. 4 plot, 4.85 and 3.23 c.c. at S.T.P. per gram. The monolayer capacity of this sample of graphitized carbon per gram is 2.65 c.c. in terms of nitrogen at S.T.P., which corre- sponds closely to 3.23 c.c. in terms of krypton, based on normally used molecular areas of nitrogen and krypton. The calculation of 0 is based,

ON PHYSICAL ADSORPTION. IX 335

therefore, on V~ = 3.23 c.c./g. The lower pressure Langmuir equation has a value of V~ corresponding to 1.50 8. A tentative model that describes this phenomenon is suggested in Fig. 5, where the order in which krypton molecules adsorb on an energetically uniform solid substrate is designated by the numbers; equivalent positions being given the same number. The suggested arrangement is cubic, with O - 0.50 corresponding to the com- pletion of the adsorption of the No. 4 atoms. Second-layer adsorption occurring at that point, on sites indicated by shaded circles, would show, by virtue of the number and nature of these sites, localized adsorption with an available Vm = 1.50 O. If the observed transition at higher pres- sures is caused by a shifting of the second-layer adsorption to the filling

FIG. 5. F i r s t and second adsorbed layers of k r yp ton in cubic array. I t is sug- gested t h a t adsorp t ion on the second layer (shaded circles) begins before the sites on the first layer occupied by the No. 5 a toms are occupied.

in of the No. 5 sites on the first layer, the isotherm would also shift, to display localized adsorption with Vm = 1.00 O. The adsorption of nitrogen on Graphon has been similarly characterized by Graham (5) : " . . . a delayed equilibration involving the necessity for some shifting of adsorbed mole- cules to permit occupancy of the last portion of the adsorbent surface."

2. Heats of Adsorption

The initial linear isotherms define a constant isosteric heat of adsorp- tion, which can be calculated from the slopes kl and k2 at temperatures TI and T2 by means of the Clausius-Clapeyron equation; the equation that is developed is Eq. [5]. The value of 3240 cals./mole (Table I) is significantly lower than the heat of adsorption for the same system deter- mined calorimetrically (2), which, for low values of 8, is about 4000 cals./ mole. Isosteric heats of adsorption, particularly when based on constant

rather than constant amount adsorbed, V, have been found to be less

3 3 6 SYDNEY ROSS AND W E R N E R WINKLER

than their calorimetrically determined counterparts (6), although the difference does not account fully for the present discrepancy. I t is also possible tha t there are differences in the adsorbent, which is prepared by batch process and so is not necessarily always equally free of high-energy adsorption sites on the surface.

A method of calculating the nonpolar van der Waal's forces (dispersion forces) between an argon atom and the basal-plane surface of graphite, and evaluating the resulting energy of adsorption, has been employed by de Boer (7). A similar calculation can be made for krypton, using the following numerical data:

Operating radius of krypton atom, from equation of state = 2.03 A. Operating radius of carbon atom in van der Waals inter-

action, from interlayer spacing of graphite = 1.70 A.

a s = 1 X 10 -s' cm) axr = 2.46 X 10 -2` cm. s I, = 258 kcal./mole Is, = 321 kcal./mole r0 = 3.45A. N, == 1.13 X I0 sa

The symbols used are defined by de Boer (7). The distance of an adsorbed krypton atom to the 6 nearest carbon atoms of the basal plane of graphite will be 3.73 A.; the distance to the next 6 is 4.52 A.; and the distance to the next 12 is 5.21 A. Summations over the 24 nearest carbon atoms and integration over the rest leads to an adsorption energy of 2.8 kcal./mole; this is as close to our present reported value of 3.2 kcal./mole as a calcula- tion of this type can be expected to come.

A test of the internal consistency of the reported isosteric heats of argon and krypton at low coverage is the ratio of the heat of evaporation to the heat of adsorption of each gas on the same adsorbent: at corresponding temperatures this ratio would be expected to be constant for all the noble gases. The numerical values are:

Argon Krypton AH evaporation 1570 2170 AH adsorption (78°-90°K.) 2270 3200 Ratio 0.69 0.68

Although the calorimetric heats of adsorption of krypton on graphitized P-33 at 90°K. (2) are higher at all values of O than the isosteric heats reported here, both methods agree in their determination of the variation of AH with O. On the calorimetric curve the initial constant AH at low coverage corresponds to the ideal linear adsorption isotherm; the rising calorimetric heat from 0.2 < O < 0.6 corresponds approximately to the central portion of the isotherm that is described by Eq. 2, for it can be

( 0 ~ H ) = 262//52; and the final shown tha t this isotherm equation leads to \ , ~

constant AH at high monolayer coverage corresponds to the portion of

ON PHYSICAL ADSORPTION. IX 337

the adsorption isotherm that has the form of a Langmuir equation. It is indeed possible to find more than this qualitative similarity: the slope of the rising portion of the calorimetric heat curve yields a value of 2a~/b2, from which the critical temperature is estimated (Eq. 4) at about 85°K; the adsorption isotherm in the same range of coverage can be used for the same purpose (Table I), yielding a critical temperature of 82°K.

ACKNOWLEDGMENT

The authors gratefully acknowledge grants (G353 and G754) from the National Science Foundation for the support of the present series of researches.

REFERENCES

1. CLARK, H., J. Phys. Chem., in the press. 2. AMBERG, C. H., SPSNCER, W. B., AND BEESE, R. A., Can. J . Chem. 33,305 (1955). 3. Ross, S., AND WINXLER, W., J. Colloid Sci. 10, 319 (1955). 4. LIANG, C. S., J. Phys. Chem. 57, 910 (1953). 5. GRAHAM, D., J . Phys. Chem. 58, 869 (1954). 6. JOYNER, L. G., AND E~IMETT, P. H., J. Am. Chem. Soc. 70, 2353 (1948). 7. DE BOER, J. I-I., "Advances in Colloid Science," Vol. III , p. 26. Interscience

Publishers, Inc., New York, 1950.