Physical adsorption on patchwise heterogeneous surfaces. 2. Virial coefficient theory analysis of krypton adsorption on graphitized carbon black

Abstract

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

The interaction of rare gas atoms with graphitized carbon black

“…Indeed, Putnam and a somewhat better fit to the data than the (4-10), and that variations in m from 9 to 16 with = 3 give a marginally best fit at me* 12. The preference for a (3-m) potential is surprising at first because the theoretical justification for this model is weak; however, one of the most interesting features of Figure 3 is the indication that the deviations of In SAS* vs. 1/T* from linearity are nearly the same for the £(4-10) models as for the (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) potential, at least for 1/T* > 4.5. Thus, one concludes that the £(4-10) potentials should fit the Kr-gcb data at least as well as the (3)(4)(5)(6)(7)(8)(9)(10)(11)(12).…”

“…The preference for a (3-m) potential is surprising at first because the theoretical justification for this model is weak; however, one of the most interesting features of Figure 3 is the indication that the deviations of In SAS* vs. 1/T* from linearity are nearly the same for the £(4-10) models as for the (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) potential, at least for 1/T* > 4.5. Thus, one concludes that the £(4-10) potentials should fit the Kr-gcb data at least as well as the (3)(4)(5)(6)(7)(8)(9)(10)(11)(12). It is also clear that the task of refitting the data for Ar, Kr, and Xe on gcb to the £(4-10) model will be greatly facilitated by this similarity in shape.…”

“…If one replaced the sums in eq 1.5 by integrals over the volume of the solid, a (3-9) power law in z results; if one replaces the sums by an integral over the surface plane and neglects the interactions with more distant planes of atoms in the solid, a (4-10) potential is obtained. Sams et al7 compared their data with virial coefficients calculated for both of these functions as well as the (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and the rather unrealistic (3-") law, which…”

“…Of the various power laws considered for w0(z), they concluded that a (3-m) potential gave the best fit to the Kr data, with m = 12 being marginally better than m = 9. Oddly, they did not consider the averaged potential obtained from the model of additive energies and a (6)(7)(8)(9)(10)(11)(12) pairwise interaction. This function can be written where ac is the area per carbon atom in the basal plane (2.62 Á2).…”

“…It is also clear that the task of refitting the data for Ar, Kr, and Xe on gcb to the £(4-10) model will be greatly facilitated by this similarity in shape. The An iterative technique was used to calculate constants for the £(4-10) potential from the published values for ela (3)(4)(5)(6)(7)(8)(9)(10)(11)(12) and s0 (3)(4)(5)(6)(7)(8)(9)(10)(11)(12). Trial values of a{£(4-10)( and 6{£(4-10)} were selected using a reasonable guess for d* = djcgB.…”