Relating structure, entropy, and energy of solvation of nanoscale solutes: application to gold nanoparticle dispersions.

Structural estimators for the entropy are combined with an analysis of the different contributions to the energy of solvation to understand the molecular basis of the thermodynamics of solvation of passivated nanoparticles. Molecular dynamics simulations of thiolated gold clusters in ethane are performed over a wide range of densities close to the critical isotherm. The entropic changes associated with solvent reorganization around the passivated nanoparticle are estimated from the nanoparticle-solvent pair correlation function, while the entropy of the ligand shell is estimated from the covariance in the positional fluctuations of the ligand atoms. The ligand-shell entropy (S(L)) is shown to be fairly insensitive to variations in solvent density ranging from vacuum to twice the critical density (ρ(c)). In contrast, the entropy change due to solvent reorganization (ΔS(ns)(ord)) shows a minimum around the critical point where the solvent excess shows a maximum. Combining the entropic estimates with the nanoparticle-solvent interaction energies, the free energy of solvation is shown to decrease with density once the critical point is crossed in a manner qualitatively consistent with available experimental data. The results suggest that such an approach to obtain structural insights into the thermodynamics of solvation of passivated nanoparticles could be useful in understanding the stability of nanoparticle dispersions of widely varying chemistries. This study also demonstrates that the theoretical analysis of solvation and self-assembly developed in the context of biomolecular hydration can be very usefully extended to understand the behavior of inorganic nanoparticle dispersions.