The patterns that form upon molecular self-assembly are a direct consequence of interaction forces among the entities constituting the structure. Thus, the study of different intermolecular forces and the resulting self-assembled pattern is of extreme importance. Corresponding mathematical modeling has its roots in statistical mechanics. The usual practice is to modify the interparticle interaction and simulate the resulting self-assembly. A recent study led by Thomas Truskett and co-workers at The University of Texas at Austin asks an inverse question: “Can one know what sort of intermolecular forces are required to produce a desired structure upon self-assembly?” The findings were published recently in the Journal of Chemical Physics.

The simulations begin with an initial estimate of the interaction potential and a target structure. Other inputs such as number of particles (N), volume of the ensemble (V), and temperature (T) are specified and kept constant (for an NVT ensemble). First, molecular dynamics simulations are used to compute the equilibrium structure from the initial guess for intermolecular forces. Then based upon the difference between the current and target structures, optimization calculations are used to iteratively improve the interaction potentials (“difference of two self-assembled structures” is defined by the Kullback–Leibler measure in the present calculations). At every iteration, the researchers find a new equilibrium structure based on the most recent estimate for interaction potential. Calculations are terminated once a prescribed accuracy is achieved; in other words, when the structure based on the force field is close to the target structure.

The research team also demonstrated the applicability of the formulation by applying it to three distinct system types: cluster fluids (fluid-like particle aggregates that are roughly spherical in shape and monodisperse in size); porous mesophases (self-assembly of the conjugate inverse cluster phase); and crystals, with multiple examples of each.

The beauty of the procedure lies in its generality. It can be easily extended to study systems with more complex molecules such as polymer chains having additional rotational and stretching degrees of freedom. Similarly, additional effects such as solvent interaction, boundary and interfacial contributions, and field effects can be straightforwardly integrated into the system’s total energy potential.

Salvatore Torquato from Princeton University, a theoretician in the field of heterogeneous materials and microstructures, says, “The authors have made novel contributions to this field by applying inverse design methods to optimize for interparticle interactions that self-assemble particles into a variety of complex microstructures, including cluster fluids, porous mesophases, and crystalline lattices, by isotropic interactions. This work represents a significant advancement in inverse design of materials.”

While discussing future directions, Truskett mentions “to start extending the work to more experimentally realistic systems including particles with patchy interactions, shape anisotropy, and more complicated ‘many-body’ interactions due to the presence of other particles (e.g., salt, small polymers, etc.).” He emphasizes the importance of these further extensions as they will make the approach more useful for experimental design, and provide information regarding the parameters that are to be tuned in a laboratory setting.

Originally published in the July 2017 issue of MRS Bulletin.