(3ah) Density-Functional Theories for Solvent-Free Nanoparticle-Organic Hybrid Materials

Nanoparticle-organic hybrid materials (NOHMs) consist of 10 nm diameter spherical inorganic core particles surface-functionalized with oligomeric organic molecules. Although these systems contain no added solvent, they exhibit fluid behavior with the fluidity provided by the attached oligomers, which in turn mediate the interparticle forces and affect the equilibrium properties and dynamic behavior of the bulk system. The absence of a solvent, the small size of the nanocores and oligomers, and the incompressibility of the tethered oligomeric fluid make the oligomer-mediated interactions non-pairwise-additive. Oligomers from many neighboring cores compete to uniformly fill the interstitial space.

In my PhD research, I developed a classical density-functional approach for model hard spheres with tethered bead-spring oligomers to predict the equilibrium properties and the transport properties of solventless, pure NOHMs. The simple coarse-grained model allows one to have a direct description of the system free energy as a functional of the probability densities of cores and oligomers without assuming pairwise additivity. Under a weak oligomeric-field approximation valid when the oligomer radius of gyration is much greater than the core radius, the equilibrium distribution function of the cores and the concentration field of oligomers are determined semi-analytically. Using the resultant, I obtained the static structure factor of NOHMs that can be utilized to characterize experimental systems as well as the solvent capacity of the suspension as the solute releases the entropic penalty of the space-filling oligomers. This thermodynamic driving force for solute uptake makes NOHMs a candidate for carbon capture showing good CO­₂ selectivity over N­₂ and CH­₄ as the lower affinity of CO­₂ for oligomers make the chains retract and reduce more of the free energy. Meanwhile, since many neighboring particles cooperate in filling the space, it is found that NOHMs can remain disordered even if the core volume fraction is above the freezing transition point of hard-sphere suspensions. Finally, transport properties such as the long-time self-diffusivity and linear viscoelastic behavior are determined by solving for the non-equilibrium probability density function for pairs of particles subjected to a weak applied flow and many-body intercore potential of mean force without hydrodynamic interactions.