Two variables must be considered when calculating exchange free energies (ΔG°ex) for 2:1 clays: (1) anionic field strength, as expressed by equivalent anionic radius (ra), and (2) interlayer water content, as expressed by interlayer molality. For smectites that are in a state of high hydration, interlayer molality is determined by the cations undergoing exchange. Thus ΔG°ex for an exchanging cation pair can be calculated solely from measurements of ra. ra is related to layer charge per half unit cell (C) and ab unit cell area (A) by: ra = (-A/8πC)1/2. The layer charge necessary for cation fixation can be predicted by calculating the ra at which cation exchange with an illite structure expresses a AG°ex equal to that of exchange with a smectite structure. The theory can also be applied qualitatively to understand the high selectivity of illite for Cs+, the fixation of K+ rather than Na+ in shales during diagenesis, the stability of illite over muscovite in the weathering environment, and cation segregation in smectite.
