Adsorption of mixtures of A and B with AA, AB and BB interactions

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Abstract
The theory of adsorption of mixtures of molecules A and B upon a set of homogeneous sites has been developed using order–disorder theory for the case when pairwise additive interactions arise for all of the pairs AA, AB and BB. The general isotherm equations are PA=P* AθA/θO(pOAθO/pOOθA)ν, PB=P* BθB/θO(pOBθO/pOOθB)ν where P* A, P* B are constants, PA and PB are the partial pressures of A and B, θA and θB are the fractions of sites occupied by A and B, θO=(1 –θA–θB) and ν is the coordination number of a site. pOA, pOB and pOO are the probabilities that on two nearest neighbour sites there are OA, OB and OO pairs, where O denotes an empty site. When only AA pairs give extra energy, the partial isotherm for A becomes the mixture analogue of the Fowler–Guggenheim isotherm equation for a single component, and the isotherm for B retains the form of the ideal Langmuir equation for mixtures. When only AB pairs give rise to extra energy different, explicit isotherm equations are obtained. When all three, or when two out of the three pairs AA, BB and AB give extra energy terms, the isotherms were calculated from appropriate groups of equations. The ways in which the relative values of the constants P* A and P* B, the value of ν, and the interplay between the extra energies influence the isotherms have been demonstrated by calculating the isotherms for the single components A and B and for their mixtures, starting with a 1:1 ratio of the components. Interaction energies can result in notable selectivities for one component.

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