Directed self-assembly of nanoparticles (DSA-n) over a templated surface has extensive applications in semiconducting, plasmonic, and photovoltaic devices. The pre-designed templated surface is able to selectively capture nanoparticles, induce interaction-based orientation and even organize them into a complex structure using a bottom-up fabrication process. In DSA-n, a thin film of suspension of nanoparticles slides over a templated surface, which allows high yield of nanoparticle deposition with specific ordering or alignment. In DSA-n with sub-10 nm particles, it is thought that the thin liquid film facilitates the positioning of nanoparticle. Although the fabrication strategy of template-assisted DSA-n is able to achieve ordered arrays of nanoparticles over large areas of the templated surface, the yield of self-assembly is sensitive to the nanoparticle density among other parameters. This variation of yield at different nanoparticle density indicates that the density is one of the structural determinants of the efficiency of DSA-n, and plays a key role in the energetics of the complex self-assembly process. In this process, computational modeling has come illustrative to aid with explaining the contributions to the associated free energy.<br/> <br/>Most of free energy calculation approaches such as thermodynamic integration, or probability ratio method, are equilibrium methods that require the simulation environment to be at equilibrium during the transition of tracked molecule. As such, aforementioned techniques seem not suitable for measuring free energy contributions to the DSA-n, considering that the process is continuously out of equilibrium.<br/> <br/>The purpose of this work is to utilize Jarzynski’s equality to calculate the free energy contributions to the DSA-n into templated surfaces from Steered Molecular Dynamics (SMD) simulations. For SMD simulations, we use many-body dissipative particle dynamics. We focus on DSA of a spherical nanoparticle into a circular nanocavity. The self-assembly is observed in two cases: from (1) a stagnant bulk thin liquid film, and (2) a thin liquid film with flow field and a receding interface, to the nanocavity. Our results suggest that overall the free energy contribution to DSA-n decreases with the nanoparticle density until a critical density after which the free energy increases. Moreover, we find that the free energy is minimum at this critical density whether the liquid film is stagnant or moving.

Free energy contributions to template-assisted self-assembly of sub-10 nm particles from steered molecular dynamics simulations

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