The charged surfaces of micaceous minerals, especially illite, regulate the mobility of the major radioisotopes of Cs (Cs-134, Cs-135, Cs-137) in the geosphere. Despite the long history of Cs adsorption studies, the nature of the illite surface sites remains incompletely understood. To address this problem, we present atomistic simulations of Cs competition with Na for three candidate illite adsorption sites-edge, basal plane, and interlayer. Our simulation results are broadly consistent with affinities and selectivities that have been inferred from surface complexation models. Cation exchange on the basal planes is thermodynamically ideal, but exchange on edge surfaces and within interlayers shows complex, thermodynamically non-ideal behavior. The basal planes are weakly Cs-selective, while edges and interlayers have much higher affinity for Cs. The dynamics of No Cs exchange are rapid for both cations on the basal planes, but considerably slower for Cs localized on edge surfaces. In addition to new insights into Cs adsorption and exchange with Na on illite, we report the development of a methodology capable of simulating fully-flexible clay mineral nanoparticles with stable edge surfaces using a well-tested interatomic potential model. (C) 2016 Elsevier Inc. All rights reserved.