Kinetic Landscape Framework for Persistent Luminescence: a disorder-based state space for decay kinetics and materials design

Persistent luminescence is commonly described in terms of discrete traps, defect chemistries, or empirical decay laws, thereby limiting direct comparison across materials and obscuring the underlying kinetic structure. Here, a kinetic landscape framework that represents afterglow as relaxation within a disordered ensemble of trapping states is introduced. Within this description, the decay dynamics are governed by two dimensionless coordinates: an effective trap-depth parameter (η) that controls the overall timescale, and a disorder parameter (ξ) that shapes the distribution of escape pathways. Starting from a Markovian master equation with a distributed energy landscape, persistent luminescence decays collapse onto a reduced two-parameter manifold, with a global kinetic coordinate Φ = ηξ governing the long-time relaxation regime. These coordinates are extracted directly from experimental decay curves using a consistent analysis protocol, enabling different phosphor families to be mapped into a common kinetic space. Application to sulfide, aluminate, and silicate-based persistent phosphors reveals that chemically distinct systems occupy a constrained region of this landscape, despite differences in composition and synthesis history. Compositional tuning and processing routes primarily redistribute the balance between depth and disorder, while preserving the global relaxation regime. Covariance-resolved analysis further indicates that the scalar coordinate Φ provides a more robust descriptor of the asymptotic kinetics than either parameter alone. This kinetic landscape representation provides a compact framework for organizing persistent luminescence behavior and offers a route toward interpreting composition and synthesis effects in terms of underlying relaxation dynamics.