Adsorption Isotherms. Critical Conditions

Abstract

1. In a recent note I showed that Langmuir's adsorption isothermwhere θ is the fraction of the surface covered by adsorbed gas, p the gas pressure in equilibrium with it, and A (T) a specified function of the temperature, can be derived as a theorem in statistical mechanics without any appeal to the mechanism of deposition and re-evaporation. Necessary and sufficient assumptions for the truth of (1) are that the atoms (or molecules) of the gas are adsorbed as wholes on to definite points of attachment on the surface of the adsorber, that each point of attachment can accommodate one and only one adsorbed atom, and that the energies of the states of any adsorbed atom are independent of the presence or absence of other adsorbed atoms on neighbouring points of attachment. Under these assumptions the explicit form of (1) iswhere m is the mass of the adsorbed atom or molecule, bg(T) the partition function for its internal states in the gas phase, and vs(T) the partition function for its set of adsorbed states. These sets of states are to be so specified that the energy zero is assigned tot the lowest state of each set in constructing bg(T) and vs(T), and then X is the energy required to transfer a molecule from the lowest adsorbed state tot the lowest gas state. Quite another adsorption isotherm was shown to hold when adsorption of a molecule takes place as atoms and requires two or more points of attachment.

Effects of the Electronic Band Shape of Palladium Metal on the Proton Model for Hydrogen Absorption

“…A necessary postulate of the proton model is that nearest-neighbor protons interact attractively via their coillpensating atillospheres of electrons. This postulate was made, by analogy with Fowler's treatment of critical adsorption on surfaces (9), in order to account for the observed critical phenomenon in the Pd-H system; the P-C-T relationship exhibits a critical point below which two solid phases, a and P, coexist over a range of coinpositions and above which only a single phase exists. The nature of the attractive interaction between protons was unspecified by Lacher but has recently been discussed somewhat more specifically by Makrides (10).…”

The influence of surfaces on vapor pressures

“…When surface effects are negligible, Gtvb = kT in X 0 vb' and Eq. (9) becomes 8 where G 0 is the standard free energy of the bulk solid.…”

Thermochemistry and kinetics of oxygen interaction with microporous chars. Technical report 12. [199 references]

“…The original derivation of equation 2.1 and the assumption used for it are presented elsewhere (30,31). The rate of adsorption is given by…”