Enthalpy and entropy of nanoparticle association from temperature-dependent cryo-TEM.

Quantum dots form equilibrium structures in liquid dispersions, due to thermodynamic forces that are often hard to quantify. Analysis of these structures, visualized using cryogenic electron microscopy, yields their formation free energy. Here we show that the nanoparticle interaction free energy can be further separated into the enthalpic and entropic contributions, using the temperature dependence of the assembled structures. Monodisperse oleic acid-capped PbSe nanoparticles dispersed in decalin were used as a model system, and the temperature-dependent equilibrium structures were imaged by cryo-TEM, after quenching from different initial temperatures. The interaction enthalpy and entropy follow from van 't Hoff's exact equation for the temperature dependence of thermodynamic equilibria, now applied to associating nanoparticles. The enthalpic component gives the magnitude of the contact interaction, which is crucial information in understanding the energetics of the self-assembly of nanoparticles into ordered structures.