The sorption of radionuclides onto mineral-water interfaces is an important mechanism of radionuclide retardation in subsurface environments. Although a large body of data on metal sorption has been accumulated, the interaction of radionuclides at the mineral-water interface is still not well quantified. In this paper, we establish a linear free energy relationship that can correlate intrinsic metal sorption constants to the known thermodynamic properties of metal cations and mineral phases. This relationship can be used to predict the intrinsic sorption constants of metal cations adsorption on various mineral-water interfaces. Based on a surface complexation model, an adsorption constant of a cation Mn+ onto a mineral surface can be represented by the sum of “intrinsic” and coulombic terms, that is logKads, Mn+ = logKint, Mn+ - (nF/2.303RT)0. To construct our linear free energy relationship, we further decompose an intrinsic sorption constant into the solvation contribution, which characterizes the work to be done to move a cation from one dielectric medium (solution) to another (interface), and the chemical contribution, which characterizes the chemical bonding abilities of cations to mineral surface sites. The overall intrinsic sorption constant can be calculated by the equation of:
2.303RTlogKint, Mn+ = -ΩMn+ (1/εk) - a* δG0n, Mn+ - b* - β*rMn+ + δG0f, Mn+, or
2.303 RT logKint, Mn+ = -ΩMn+ (1/εk) + a* δG0s, Mn+ + (1 - a*)δG0f, Mn+ - b* - β* rMn+,
where, ΩMn+ is interfacial Born solvation coefficient of cation M, εk is the dielectric constant of a mineral; δG0n, Mn+, δG0s, Mn+ and δG0f, Mn+ are the non-solvation energy, solvation energy and the Gibbs free energy formation of a cation, respectively; rMn+ is the ionic radius of a cation; and a*, β*, and b* are constants, which can be determined by fitting the equation to the existing experimental data. We have applied the equation to the sorption of divalent cations on oxide, hydroxide, and silicate minerals. In particular, based on additivity of molecular polarizabilities, we have used the equation to calculate the intrinsic sorption constants of divalent metals and radionuclides on interstratified clay minerals that are commonly found in the nature or are proposed as backfills for nuclear waste geologic repositories. The discrepancies between calculated and measured values are generally within 0.8 log unit.