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Transition in heterogeneous dynamics across the morphological hierarchy in two-dimensional aggregates

Two-dimensional (2D) particulate aggregates formed due to competing interactions exhibit a range of non-equilibrium steady state morphologies from finite-size compact crystalline structures to non-compact string-like conformations. We report a transition in heterogeneous microscopic dynamics across this morphological hierarchy as a function of decreasing long-range repulsion relative to short-range attraction at a constant {\it low} density and temperature. Following a very slow cooling protocol to form steady state aggregates, we show that geometric frustration inherent to competing interactions assures non-ergodicity of the system, which in turn results in long-time sub diffusive relaxation of the same. Analysing individual particle trajectories generated by molecular dynamics, we identify {\it caging} dynamics of particles in compact clusters in contrast to the {\it bonding} scenario for non-compact ones. Finally, by monitoring temperature dependence, we present a generic relation between diffusivity and structural randomness of the aggregates, irrespective of their thermodynamic equilibrium.