Kryptori atoms adsorbed in submonolayer quantities onto the basal graphite surface may be represented by a triangular lattice gas with nearest-neighbor exclusion and further-neighbor attraction decreasing with separation. %'e view this as a three-state Potts model with thermodynamic vacancies which are controlled by a chemical potential. A position-space renormalization-group treatment is performed by adapting Migdal's approximate recursion to the triangular lattice, and results are compared with experimental data. Our temperature versus density phase diagram for krypton submonolayers has an in-registry solid phase separated from a liquid phase by a line of continuous {Potts tricritical) transitions at higher temperatures. At lower temperatures, the solid phase is separated from a gas phase by first-order transitions. The Potts tricritical line meets the coexistence region of the f&rst-order transitions at an isolated fourth-order transition point. This point may be related to the transition of the triplet Ising model, solved exactly by Baxter and %'u. Our "Potts lattice gas" global phase diagram is in a three-parameter space of pair-interaction constants and chemical potential. It contains solid, liquid, and gas phases, variously separated by first-order, Ising critical, threeand four-state Potts, and fourth-order transitions. The Lennard-Jones potential between krypton adatoms determines the planar subspace applicable to krypton subrnonolayers. Other planes, similarly determined, are applicable to adsorbed nitrogen, methane, and ethane, for which we estir»ate the temperatures of the foUrth-order points. Our treatment also predicts a tricfitical end-point topology, instead of the fourth-order point topology, when second-neighbor adatom pair attraction is not much stronger than thirdand fourth-neighbor attractions.

Adsorption isotherms, adsorption heats, and spreading pressures are presented for the krypton-graphitized carbon black system from 0.002 to 4.5 statistical adsorbed layers, in the 95-105 K temperature range. The existence of a second-order fluid-solid phase transition in the submonolayer film is confirmed, and evidence is presented for an in-registry to out-of-registry transition. The sample surface is shown to be composed of 0.5% high-energy sites and 99.5% lower energy sites with adsorption energy tga/k = 1466 ± 6 K. From spreading pressure calculations, the dispersion force contribution to the surface free energy of (0001) graphite is estimated to be = 151 mN/m.

Physical adsorption data for krypton adsorbed on graphitized carbon black (gcb) is analyzed by the virial coefficient (VC) theory of adsorption. Both high and low temperature adsorption data are included, and heterogeneity is determined. Strong site heterogeneity of Sterling FT gcb is found to be 0.5 ± 0.1% of the surface, a considerably higher value than previous estimates. Adsorption data taken over a wide temperature range is found to be capable of determining three attributes of the gas-solid potential energy function: capacity, depth, and anharmonicity. The best-fit Lennard-Jones (LJ) Kr-(OOOl) graphite potential is a 12-3 potential with depth tgJk = 1461 ± 6 K and distance parameter z0 = 0.23 ± 0.01 nm. A LJ 12-6 potential with distance parameter am = 0.36 nm is used to represent the pair interaction between adsorbed Kr atoms, and the depth of this effective potential is found to be egg/fe = 145 ± 3 K, in excellent agreement with previous high temperature VC studies. This potential is considerably shallower than the gas phase Kr LJ 12-6 potential, which cannot be reconciled with the present data.The terms "homogeneous", "uniform", and "heterogeneous" are now defined. A "homogeneous" surface has only one type of adsorption site (for example, any low index crystal plane). A "uniform" surface is a homogeneous surface which presents negligibly small barriers to translation across the surface. No real surface is perfectly uniform, though some homogeneous surfaces may be regarded as uniform, especially at high temperatures. "Heterogeneity" denotes the presence of more than one type of adsorption site on a surface.B. Surface Area. A puzzling result of the Halsey study was that the surface area determined by the VC method, ß = 8.38 m2/g, using crystallographic radii to determine the gas-solid distance,2 was considerably smaller than that determined by various methods which used the monolayer capacity to determine the surface area. The BET nitrogen área of the Halsey sample was 12.5 m2/g,9 and "step height" and "surface titration" areas determined with Ar, Kr, and Xe were 12.30-12.45 m2/g.10 Pierotti and Thomas7

Experimental vapor pressure data for krypton adsorption on graphitized carbon black are analyzed thermodynamically such that the shapes of the thermodynamic singularities near phase transitions are preserved. The thermodynamic potential and all of its derivatives are calculated in the transition region. The analysis assumes a classical Ehrenfest type second-order transition for the "fluid-solid" monolayer transition. Singularities for this lower-density transition are much more pronounced in the compressibility and heat capacity at constant spreading pressure than in the isosteric heat or heat capacity at constant density. The higher-density phase transition region was investigated by careful differentiation of the experimental isotherms, which revealed a pronounced compressibility minimum at amount adsorbed = 124 ± 2 µ /g, and compressibility peaks at higher densities. The higher and lower-density peaks appear to all lie on a line of continuous order-disorder transitions, as in helium and nitrogen monolayers on graphite, and certain theoretical models.

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