Mark Ferraro

Density Functional Theory for Directed Self-Assembly

Currently, nanopatterning is often carried out using various lithography techniques. Despite their successes in many applications, one of the challenges facing such lithographic methods is their inability to generate patterns smaller than 20nm in a way that is reliable, cost-effective and rapid enough for industrial-scale manufacturing processes. Understanding how to overcome these engineering hurdles is the reason for my interest in “self-assembly” as a chemical engineering graduate student. In short I am interested in developing strategies to induce nanometer scale particles to arrange themselves into specific patterns required for the aforementioned technological applications.


Figure 1: For a typical hard-sphere system in two dimensions, one would expect the crystalline phase to be a hexagonal close-packed lattice (a). Our research hopes to broaden the set of attainable lattice structures by topologically patterning a substrate with posts (b), chemical patterns, etc. to force the particles to form different structures. This project will determine the maximum length between the posts (or chemical patterning) that would be required to form a desired, defect-free lattice.

Templated self-assembly has already been demonstrated for systems of block copolymers on a pre-patterned substrate.  While nanoparticle systems will not generally exhibit the same type of phase behaviors as the block copolymers, they show promise for self-assembly due to their highly tunable interactions and their ability to order in the presence of an external field.  Even for simple hard particle suspensions, the effects of volume exclusion produce a wide variety of entropy-driven, ordered equilibrium phases.  A topologically (or chemically) patterned substrate can expand the set of possible ordered structures that these systems can attain. The question is what is the relationship between the substrate pattern and the resulting self-assembled structure? Moreover, can the substrate pattern be rationally designed in order to target specified nanostructures?  Finally, what control parameters govern the type and level of defects in the self-assembly?

To date, this project has focused mainly on systems of hard-sphere nanoparticles.  As stated in the previously, hard sphere fluids exhibit a local ordering near a wall, which can lead to long-range order with the correct topological pattern.  This phenomenon can be examined through density functional theory (DFT), since it is well-formulated for hard sphere systems (specifically Rosenfeld’s Fundamental Measure Theory, which has been updated for two-dimensional systems by Roth et al).  As this theory determines the equilibrium density profile for a given, imposed external field, it can be a useful tool in the analysis of directed self-assembly.  Similarly, DFT can provide the ideal external field for a desired lattice structure.  Using templates suggested by DFT, I will also perform molecular dynamics simulations in order to visualize and verify the self-assembly process.  The aim will be to find the limiting topological spacing required for the assembly of a desired nanoparticle lattice.  Since the use of nanoparticles for self-assembly is motivated by the ability to tune interparticle interactions, this process will be repeated for particles with more complicated interactions than simple hard spheres.


Figure 2: Energy minimizing external potentials for the (a) square and (b) honeycomb lattices of hard-spheres. A goal of this project will be to smooth out these potentials in order to create a more experimentally realizable field.

If this project is successful, it could result in a methodology for creating patterned substrates with details on nanometer length scales (comparable to the size of the particles that form the lattice). With the proper framework for determining the appropriate, tunable particle interactions, materials could be created with desired macroscopic properties from the bottom up.  In addition, the use of a limited scaffold for directing self-assembly results in a relatively cheap manufacturing process.  Surprisingly, the area of nanomanufacturing lacks a universally accepted set of production strategies.  As a result, any advances that allow for reliable, cost-efficient manufacturing strategies could have a profound effect on the fields of nanotechnology and material science.