MEAN FIELD THEORY OF PHASE TRANSITIONS IN KRYPTON MONOLAYERS ADSORBED ON GRAPHITE

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Submitted on 1 Jan 1977

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MEAN FIELD THEORY OF PHASE TRANSITIONS

IN KRYPTON MONOLAYERS ADSORBED ON

GRAPHITE

F. Putnam

To cite this version:

JOURNAL DE PHYSIQUE Colloque C4, suppl6ment au no 10, Tome 38, octobre 1977, page C4-115

MEAN FIELD THEORY OF PHASE TRANSITIONS

IN KRYPTON MONOLAYERS ADSORBED ON GRAPHITE

F. A. PUTNAM

Massachusetts Institute of Technology, USA

R6sum6.

-

La th6orie de Tsien et Halsey sur les transitions de phase dans les monocouches de gaz rares est appliqu6e au cas du krypton adsorb6 sur graphite. La phase mobile est d6crite par 1'6quation d'ktat de Henderson pour des disques rigides avec interaction attractive de champ moyen. La phase localiske est un gaz de rkseau de Bragg-Williani, comme dans le mod&le de Tsien et Halsey. La thkorie prkvoit deux transitions entre deux phases denses. La phase mobile est la plus stable

B

faible densit6. Pour des temperatures comprises entre 84,2 K et 122 K, il y a une transition vers la phase localis6e lorsqu'on augmente la densitk, Si l'on accroit davantage la densit6, une nouvelle transition vers la phase mobile a lieu. Ces transitions correspondent, selon la classification de Thomy et Duval, B A', + D: et

A:

+ B1. I1 existe une temp6rature maximum au-dessus de laquelle ces transitions n'ont plus lieu. Cette temperature est une fonction trks sensible des paramktres d'6nergie intermolkculaire de l'kquation d'6tat. Toutes les transitions que pr6voit le modkle sont du premier ordre, en dksaccord avec les exp6riences dans lesquelles des transitions continues ont kt6 observkes. On peut obtenir des transitions continues soit par un calcul de groupe de renormalisation pour certains modkles de gaz de rkseau, soit en introduisant des effets de taille finie dans le pr6sent modkle.

Abstract.

-

The theory of Tsien and Halsey [I] for phase transitions in rare gas monlayers is applied to the case of krypton on graphite. The mobile phase is described by Henderson's [2] equation of state for hard disks plus a mean field attractive interaction. The localized phase is a Bragg-Williams lattice gas, as in Tsien and Halsey's treatment. The theory predicts two high-density phase transitions. The mobile phase is most stable at low density. For temperature 84.2

<

T

<

122 K, as density is increased, there is a transition to the localized phase.

As

density is increased further, another transition, back to the mobile phase occurs. These transitions correspond to the A', to D: and

A':

to B, transitions as classified by Thomy and Duval [3]. There is a maximum temperature above which these transitions do not occur, which is a very sensitive function of the intermolecular energy parameters of the equations of state. All trahsitions produced by the model are first order, in disagreement with experiment, where continuous transitions have been observed [4]. Continuous transitions can be produced by renormalization group calculations for certain lattice gas models 151, or by introducing finite size effects [6] into the present model.

References

[I] TSIEN, F. and HALSEY, Jr. G. D., J. Phys. Chem. 71 (1%7) R. B., submitted to J. Phys. Chem.; FAIN, S . C. and

4012. CHINN, M . D . , J. Physique Colloq. 38 (1977) C4-99.

[2] HENDERSON, D., Mol. Phys. 30 (1975) 971. [5] SCHICK, M., WALKER, J. S. and WORTIS, M., J. Physique [3] THOMY A. and DUVAL, X., J. Chim. Phys. 67 (1970) 1101. Colloq. 38 (1977) C4-121.

[4] PUTNAM, F. A. and FORT, Jr.

T.,

J. Phys. Chem. 79 (1975) [6] HILL, T. L. u Thennodynamics of Small Systems >>, (Benja- 459; PUTNAM, F. A., FORT, Jr. T. and G R I F ~ S , min, New York), 1963.

DISCUSSION

S. C.

FAIN.

-

Extrapolation of the log P vs

T-'

curves shown in figure 1 of my paper suggests that

the second layer condensation becomes much closer

in P to the registry-deregistry transition at higher T.

This is one indication that a strictly monolayer

model will not be applicable to experiments for

T

>

100 K.

F. A. PUTNAM.

-

I

agree. Second layer

adsorption could easily be included in the model,

and I plan to do this.

W. STEELE.

-

The fact that this theory is

constrained to the monolayer only indicates that the

features observed at the highest densities will

probably not be observed because of the preferential

formation of multilayers. Although the high density

fluid phase is correctly predicted as a consequence

of its high compressibility relative to the lattice gas,

it seems unlikely to occur in real systems.

F.

A.

PUTNAM.

-

The second layer, if included in

the model, would indeed from at the higher

densities. The high density fluid phase may be

regarded as a model for the

dense unregistered

phases, which have been observed in nitrogen

monolayers by neutron diffraction.