JOURNAL OF COLLOID AND INTERFACE SCIENCE 200, 273–290 (1998) ARTICLE NO. CS975398 Analysis of Adsorption Isotherms: Lattice Theory Predictions, Classification of Isotherms for Gas–Solid Equilibria, and Similarities in Gas and Liquid Adsorption Behavior Grigoriy Aranovich and Marc Donohue 1 Department of Chemical Engineering, Johns Hopkins University, Baltimore, Maryland 21218 Received September 8, 1997; accepted December 30, 1997 sorption isotherms, (1) which is illustrated in Fig. 1. Type Adsorption at fluid–solid interfaces is considered in the frame- I isotherms are characteristic of microporous adsorbents. work of a lattice with boundaries. Using ideas proposed by S. Types II and III describe adsorption on macroporous adsor- Ono and S. Kondo ( in ‘‘Molecular Theory of Surface Tension in bents with strong and weak adsorbate – adsorbent interac- Liquids’’ (S. Flu ¨gge, Ed.), Encyclopedia of Physics, Vol. 10, p. tions respectively. Types IV and V represent adsorption iso- 134. Springer-Verlag, Berlin, 1960), a lattice model is derived, therms with hysteresis. In addition to the five types of iso- both rigorously and phenomenologically, and applied to macro-, therms identified by BDDT, the IUPAC classification meso-, and microporous adsorbents by imposing different bound- includes a sixth isotherm (Type VI) which has steps. All of ary conditions. It is shown that this lattice theory can predict the entire spectrum of behavior observed when gases, liquids, or these types of isotherms have been observed in numerous supercritical fluids adsorb on solid surfaces. In particular, it is able experiments (3) and have been analyzed theoretically (see, to predict steps in the isotherms, scaling behavior near saturation for example, (4, 5)). conditions, supercritical behavior, and adsorption hysteresis. It is However, the IUPAC classification has two deficiencies: shown that there is a profound analogy in the adsorption behavior it is incomplete and it gives the incorrect impression that of a one-component gas to that of a binary liquid mixture. This adsorption isotherms are always monotonic functions of analysis leads to a new classification of physisorption isotherms pressure. To illustrate these points, consider the following for fluid/solid equilibria.  1998 Academic Press experimental isotherms. Key Words: theory of adsorption; lattice model; supercritical Figure 2 gives examples of adsorption for several super- behavior; hysteresis; analogy between gas and liquid; new classifi- critical adsorbates on macroporous alumina (data from (6)) cation of adsorption isotherms. and on zeolite, a microporous adsorbent (data from (7)). As shown in Fig. 2, all these adsorption isotherms have INTRODUCTION maxima and exhibit nonmonotonic behavior. Figure 2 shows that similar behavior occurs for supercritical adsorbates on There usually are density and / or concentration gradients both microporous and macroporous adsorbents. The only at fluid surfaces or interfaces. This process of density change differences are in the pressure at the maximum and the near a surface is called adsorption and the excess density is amount of adsorption at the maximum. Thus, this behavior the Gibbs adsorption. The Gibbs adsorption is a function of is general but fundamentally different from the IUPAC clas- temperature, pressure ( or density ) , and composition, but this sification (1). Figure 2c shows adsorption as a function of functionality is complex. density for nitrogen on activated carbon at T Å 298 K in Adsorption data usually are presented as isotherms, and the pressure range from 0 to 650 Mpa (data from (8)). As the process of interpreting the isotherms begins by compari- shown in Fig. 2c, not only is the slope negative, but the son to standard isotherms (1). Several classifications have adsorption is negative at high densities. Similar behavior has been developed to characterize the shape of adsorption iso- been observed for supercritical methane, ethane, argon, therms. The first systematic attempt to interpret adsorption neon, krypton, nitrogen, carbon oxide, carbon dioxide, and isotherms for gas / solid equilibria was by Brunauer, Deming, nitrogen oxide on different adsorbents (6–13). Deming, and Teller (BDDT) in 1940 (2). These authors The characterization of different types of adsorption iso- classified isotherms into five types. The BDDT classification therms has been extremely valuable. Not only does it provide became the core of the modern IUPAC classification of ad- guidance as to which mathematical models may be most appropriate in correlating experimental data, it also provides 1 To whom correspondence should be addressed. a link between the macroscopic behavior reflected in the 273 0021-9797/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.