Emergent Rate Laws for Collective Lying-Standing Transitions

Abstract

Lying-standing transitions in the first molecular monolayer at organic-inorganic interfaces strongly influence interface dipoles, energy-level alignment, and growth modes, yet their collective kinetics remain difficult to predict. Here, we establish a quantitative adsorbate-to-kinetics relationship using first-principles-based kinetic Monte Carlo simulations combined with a mean-field coarse-graining strategy. Focusing on tetracyanoethylene on Cu(111), we show that the collective transition rate cannot be inferred from any single elementary step but emerges from coupled microscopic processes, including reorientation, adsorption, and diffusion. A local two-step reorientation mechanism captures the diffusion-limited regime, while diffusion of lying molecules accelerates the transition in diffusion-enhanced regimes by suppressing back-reorientation via vacancy-molecule decoupling. This effect is described by a regime-dependent geometric factor accounting for deviations between single-molecule and collective rate constants. By varying molecular size and footprint ratio, we demonstrate that geometry is an intrinsic control parameter. While the collective rate scales approximately with molecular area, increasing the footprint ratio between lying and standing configurations yields order-of-magnitude accelerations due to enhanced vacancy creation and diffusion-assisted stabilization. Finally, we derive an analytical expression for the collective reorientation rate constant linking temperature- and pressure-dependent microscopic rate constants to geometric parameters. The formulation reproduces the simulations across kinetic regimes and provides transferable design principles for engineering lying-standing transition timescales at organic-inorganic interfaces.