Probabilistic inverse design for self-assembling materials

Abstract

One emerging approach for the fabrication of complex architectures on the nanoscale is to utilize particles customized to intrinsically self-assemble into a desired structure. Inverse methods of statistical mechanics have proven particularly effective for the discovery of interparticle interactions suitable for this aim. Here we evaluate the generality and robustness of a recently introduced inverse design strategy [Lindquist et al., J. Chem. Phys. 145, 111101 (2016)] by applying this simulated-based, machine learning method to optimize for interparticle interactions that self-assemble particles into a variety of complex microstructures: cluster fluids, porous mesophases, and crystalline lattices. Using the method, we discover isotropic pair interactions that lead to self-assembly of each of the desired morphologies, including several types of potentials that were not previously understood to be capable of stabilizing such systems. One such pair potential led to assembly of the highly asymmetric truncated trihexagonal lattice and another produced a fluid containing spherical voids, or pores, of designed size via purely repulsive interactions. Through these examples, we demonstrate several advantages inherent to this particular design approach including the use of a parametrized functional form for the optimized interparticle interactions, the ability to constrain the range of said parameters, and compatibility of the inverse design strategy with a variety of simulation protocols (e.g., positional restraints).

Assembly of multi-flavored two-dimensional colloidal crystals

“…However, this additional complexity may be acceptable especially when compared to difficulties involved in the latter case. 70 …”

Realizable hyperuniform and nonhyperuniform particle configurations with targeted spectral functions via effective pair interactions

“…A 3D configuration is shown in Fig. 14 (62). Here it turns out that our usual reciprocal-space cutoff of K = 15 is not large enough, and so we use K = 25 instead.…”

Design of two-dimensional particle assemblies using isotropic pair interactions with an attractive well

“…Detailed derivation of this update procedure is available in previous work. 29,30 In this paper, we use u(r|θ) consisting of Akima splines whose knots are the parameters. We constrain the splines to display the features of a single attractive well with a minimum located at r min .…”

“…An alternative, simulation-based design method focused on relative-entropy (RE) maximization was recently shown 29,30 capable of discovering interactions that promote spontaneous assembly of a target lattice from the disordered fluid upon cooling. Notably, the RE optimization computes interactions "on-the-fly" based on structures accessed in a simulation and thus avoids the need to explicitly identify possible competing structures in advance.…”

“…Notably, the RE optimization computes interactions "on-the-fly" based on structures accessed in a simulation and thus avoids the need to explicitly identify possible competing structures in advance. As a result, the RE approach has been able to help design isotropic interactions that favor unusually open ordered phases (e.g., truncated hexagonal 29 and truncated tri-hexagonal 30 lattices, which naturally compete with a variety of stripe-phase structures that are difficult to identify a priori) as well as disordered hierarchical structures (e.g., porous mesophases 30,31 and cluster fluids, 30,32 which are not easily designable with GS-based optimization strategies). However, because RE maximization does not require identification of competing structures, it cannot provide direct insights into how the optimized interactions stabilize the target relative to its competitors.…”