  Clays control carbon, water and nutrient transport in the lithosphere,
promote cloud formation5 and lubricate fault slip through interactions among
hydrated mineral interfaces. Clay mineral properties are difficult to model
because their structures are disordered, curved and dynamic. Consequently,
interactions at the clay mineral-aqueous interface have been approximated using
electric double layer models based on single crystals of mica and atomistic
simulations. We discover that waves of complexation dipoles at dynamically
curving interfaces create an emergent long-range force that drives exfoliation
and restacking over time- and length-scales that are not captured in existing
models. Curvature delocalizes electrostatic interactions in ways that
fundamentally differ from planar surfaces, altering the ratio of ions bound to
the convex and concave sides of a layer. Multiple-scattering reconstruction of
low-dose energy-filtered cryo electron tomography enabled direct imaging of ion
complexes and electrolyte distributions at hydrated and curved mineral
interfaces with {\aa}ngstrom resolution over micron length scales. Layers
exfoliate and restack abruptly and repeatedly over timescales that depend
strongly on the counterion identity, demonstrating that the strong coupling
between elastic, electrostatic and hydration forces in clays promote collective
reorganization previously thought to be a feature only of active matter.
