Potential of Mean Force for Face–Face Interactions between Pairs of 2:1 Clay Mineral Platelets

Bottom-up modeling of clay behavior from the molecular scale requires a detailed understanding of the free energy between pairs of clay platelets. We investigate the potential of mean force (PMF) for hydrated clays in face-to-face interactions with free energy perturbation (FEP) methods through molecular dynamics simulations using simple overlap sampling (SOS). We show that PMF results for open systems with one finite in-plane dimension are affected by migration of counterions from within the interlayer space compared with fully confined closed system conditions. We compare PMFs for two common 2:1 clay sheet minerals Illite (IMt-1) and Na-smectite. The PMFs for the open illite systems exhibit a strong attractive energy well at a basal layer separation, d = 11 Å and interlayer water content, w IL = ∼0.4% while the attractive minimum for the closed system occurs at d = 12 Å, w IL = 3.5%. In contrast, net repulsion occurs between pairs of Na-smectite platelets for both open and closed systems (for d < 15–16 Å). The free energy is closely related to the distribution of counterions; while K+ ions are bound closely to the surfaces of the illite platelets, Na+ ions are more spatially disperse. This PMF results contradict prior findings for Na-smectite and prompted further comparisons with other published results. We find that most of the published results do not represent accurately the free energy for face–face interactions between pairs of clay platelets that are effectively infinite (with width/thickness O­[104]). The PMF results presented in this paper form a reliable basis for mesoscale, coarse-grained modeling of illite and smectite particle assemblies. We show that the Gay–Berne potential provides a reasonable first-order model for upscaling, while the solvation potential proposed by Masoumi enables a more accurate representation of the computed PMFs.