Solvent Isotherms and Structural Transitions in Nanoparticle Superlattice Assembly.

We introduce a Molecular Theory for Compressible Fluids (MOLT-CF) that enables us to compute free energies and other thermodynamic functions for nanoparticle superlattices with any solvent content, including the dry limit. Quantitative agreement is observed between MOLT-CF and united-atom molecular dynamics simulations performed to assess the reliability and precision of the theory. Among other predictions, MOLT-CF shows that the amount of solvent within the superlattice decreases approximately linearly with its vapor pressure and that in the late stages of drying, solvent-filled voids form at lattice interstitials. Applied to single-component superlattices, MOLT-CF predicts fcc-to-bcc Bain transitions for decreasing vapor pressure and for increasing ligand length, both in agreement with experimental results. We explore the stability of other single-component phases and show that the C14 Frank-Kasper phase, which has been reported in experiments, is not a global free-energy minimum. Implications for precise assembly and prediction of multicomponent nanoparticle systems are discussed.