The solvent-mediated interaction, or equivalently the depletion force, play a pivotal role in the processes, by which two objects in solution such as lock and key particles, antibody and antigen, macromolecule and substrate, are attracted to each other. The quantification of this interaction is important yet challenging since it depends on the microscopic solvent structure in the surrounding. Here, we report an efficient molecular approach for predicting the solvent-mediated interaction by combining the classical density functional theory with a reversible solvation thermodynamic circle. For demonstration, the solvent-mediated interactions between two nanoparticles and between a nanoparticle and a rough wall are examined, and good agreements compared with the simulation results are illustrated. This approach is thereafter employed to interpret the reported self-assembly phenomena of lock and key colloidal particles. We show that the binding probability between the lock and key colloids can be successfully characterized at different depletant concentrations and system temperatures. This approach provides a potential route for identifying the coarse-graining interaction between two objects in fluid systems.

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It is promising yet challenging to develop efficient methods to separate nanoparticles (NPs) with nanochannel devices. Herein, in order to guide and develop the separation method, the thermodynamic mechanism of NP penetration into solvent-filled nanotubes is investigated by using classical density functional theory. The potential of mean force (PMF) is calculated to evaluate the thermodynamic energy barrier for NP penetration into nanotubes. The accuracy of the theory is validated by comparing it with parallel molecular dynamics simulation. By examining the effects of nanotube size, solvent density, and substrate wettability on the PMF, we find that a large tube, a low bulk solvent density, and a solvophilic substrate can boost the NP penetration into nanotubes. In addition, it is found that an hourglass-shaped entrance can effectively improve the NP penetration efficiency compared with a square-shaped entrance. Furthermore, the minimum separation density of NPs in solution is identified, below which the NP penetration into nanotubes requires an additional driving force. Our findings provide fundamental insights into the thermodynamic barrier for NP penetration into nanotubes, which may provide theoretical guidance for separating two components using microfluidics.