Diffusion NMR for Measuring Dynamic Ligand Exchange on Colloidal Nanocrystals

Ligand exchange is fundamentally related to the surface chemistry of nanoparticles in solution and is also an essential procedure for their synthesis and solution processing. The solution of ligand-bearing nanoparticles can be regarded as a dynamic equilibrium of bound and free ligands depending on the concentration and temperature. The direct experimental calibration of the ligand exchange dynamics relies on the in situ and real-time quantification of bound and free ligands. However, existing analytical strategies are often with limited applicability considering the requirement of special functional groups or the indirect detection of photoluminescence or reaction heat. In this work, we explore diffusion-based methods of solution-state nuclear magnetic resonance (NMR) as a general strategy to probe ligand exchange. Using comprehensive numerical simulations, we show that diffusion NMR with designable time sequences can effectively distinguish bound and free ligands and measure the exchange rate constants from 0.5 to 200 s^-1 under typical instrumental settings. These methods are demonstrated experimentally on colloidal CdSe nanocrystal systems with carboxylate or amine ligands whose exchange rates were previously undetectable. The kinetic rate constants, activation energies, and thermodynamic parameters of ligand exchange have been obtained under variable temperature conditions. We expect the diffusion NMR strategies to be generally applicable for calibrating the exchange of organic ligands on various nanoparticle systems.