# Inverse optimization techniques for targeted self-assembly

@article{Torquato2008InverseOT, title={Inverse optimization techniques for targeted self-assembly}, author={Salvatore Torquato}, journal={Soft Matter}, year={2008}, volume={5}, pages={1157-1173} }

This article reviews recent inverse statistical-mechanical methodologies that we have devised to optimize interaction potentials in soft matter systems that correspond to stable “target” structures. We are interested in finding the interaction potential, not necessarily pairwise additive or spherically symmetric, that stabilizes a targeted many-body system by generally incorporating complete configurational information. Unlike previous work, our primary interest is in the possible many-body… Expand

#### 137 Citations

The role of pressure in inverse design for assembly.

- Computer Science, Physics
- The Journal of chemical physics
- 2019

It is demonstrated that relative entropy optimization can be used to discover potentials that self-assemble into targeted cluster morphologies with a prescribed pressure when the iterative simulations are performed in the isothermal-isobaric ensemble. Expand

Inverse design of multicomponent assemblies.

- Physics, Medicine
- The Journal of chemical physics
- 2018

This work extends an inverse design methodology to determine isotropic interactions that promote assembly of targeted multicomponent phases, and applies this extension to design interactions for a variety of binary crystals ranging from compact triangular and square architectures to highly open structures with dodecagonal and octadecagonal motifs. Expand

Inverse design of simple pair potentials for the self-assembly of complex structures.

- Computer Science, Physics
- The Journal of chemical physics
- 2018

This approach maximizes the relative information of a target pair distribution function with respect to an ansatz distribution function via an iterative update process, resulting in interaction potentials that are smoother and simpler in real space and therefore likely easier to make. Expand

Probabilistic inverse design for self-assembling materials

- Materials Science, Computer Science
- 2017

Using the method, isotropic pair interactions are discovered that lead to the 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. Expand

Inverse Design for Self Assembly via On-the-Fly Optimization

- Physics, Computer Science
- 2016

This work introduces a molecular dynamics simulation-based, optimization design strategy that iteratively and systematically refines the pair interaction according to the fluid and crystalline structural ensembles encountered during the assembly process and successfully applies this probabilistic, machine-learning approach to the design of repulsive, isotropic pair potentials. Expand

Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis.

- Materials Science, Medicine
- Soft matter
- 2017

This work presents a geometrical analysis that generates connectivity landscapes for target superstructures, greatly reducing the space over which subsequent experimental trials must search, and validate and extend the analytical constraint approach with direct MD simulations of superstructure nucleation and growth. Expand

Breadth versus depth: Interactions that stabilize particle assemblies to changes in density or temperature.

- Chemistry, Physics
- The Journal of chemical physics
- 2016

We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature.… Expand

Non-additive simple potentials for pre-programmed self-assembly.

- Physics, Medicine
- Soft matter
- 2015

The model is designed in such a way that it may be implemented using discotic particles or, alternatively, using exclusively spherical particles interacting isotropically, and represents a promising strategy for bottom-up nano-fabrication. Expand

Equilibrium cluster fluids: pair interactions via inverse design.

- Physics, Medicine
- Soft matter
- 2015

Inverse methods of statistical mechanics are becoming productive tools in the design of materials with specific microstructures or properties. While initial studies have focused on solid-state design… Expand

Inverse methods for design of soft materials.

- Physics, Computer Science
- The Journal of chemical physics
- 2020

This work discusses recent advances in inverse methods for design of soft materials that address two challenges: methodological limitations that prevent such approaches from satisfying design constraints and computational challenges that limit the size and complexity of systems that can be addressed. Expand

#### References

SHOWING 1-10 OF 206 REFERENCES

Designed interaction potentials via inverse methods for self-assembly.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2006

This work proposes and discusses two computational algorithms that search for optimal potentials for self- assembly of a given target configuration and demonstrates that the algorithms do indeed cause self-assembly of the target lattice. Expand

Self-assembly of the simple cubic lattice with an isotropic potential.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2006

An isotropic pair potential V(r) is presented for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic lattice and it is shown that standard approximate integral-equation theories of the liquid state cannot be used in the reverse mode to predict the correct simple cubic potential. Expand

Optimized interactions for targeted self-assembly: application to a honeycomb lattice.

- Materials Science, Medicine
- Physical review letters
- 2005

An inverse statistical-mechanical methodology to find optimized interaction potentials that lead spontaneously to a target many-particle configuration, extending the traditional idea of self-assembly to incorporate both amorphous and crystalline structures as well as quasicrystals. Expand

Controlling the Short-Range Order and Packing Densities of Many-Particle Systems†

- Physics, Mathematics
- 2002

Questions surrounding the spatial disposition of particles in various condensed-matter systems continue to pose many theoretical challenges. This paper explores the geometric availability of… Expand

Reversible self-assembly of patchy particles into monodisperse icosahedral clusters.

- Materials Science, Medicine
- The Journal of chemical physics
- 2007

This work systematically study the design of simple patchy sphere models that reversibly self-assemble into monodisperse icosahedral clusters and finds that the optimal patch width is a compromise between structural specificity and kinetic accessibility. Expand

Erratum: Optimized Interactions for Targeted Self-Assembly: Application to a Honeycomb Lattice [Phys. Rev. Lett.95, 228301 (2005)]

- Physics
- 2006

The phonon spectrum shown in Fig. 3 of the Letter contained some minor errors; it should be replaced with Fig. 1 below. The changes do not qualitatively alter the conclusions that the phonon spectra… Expand

Electrostatic self-assembly of macroscopic crystals using contact electrification

- Materials Science, Medicine
- Nature materials
- 2003

Electrostatic self-assembly of two types of macroscopic components of identical dimensions using interactions that are generated by contact electrification is described, suggesting that the stability of these unusual structures can be explained by accounting for the interactions between electric dipoles that the particles in the aggregates induce in their neighbours. Expand

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions.

- Medicine, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is demonstrated that a pair potential cannot simultaneously reproduce the two- and three-body correlations in a system with many-body interactions, and is used to discuss how the coarse-grained free energy converges when expanded to arbitrary order in the many- body potentials. Expand

Self-Assembly of Patchy Particles.

- Materials Science, Medicine
- Nano letters
- 2004

The results show how precise arrangements of patches combined with patch "recognition" or selectivity may be used to control the relative position of particles and the overall structure of particle assemblies. Expand

Coarse Graining of Nonbonded Inter-Particle Potentials Using Automatic Simplex Optimization to Fit Structural Properties

- Chemistry, Physics
- 2000

We implemented a coarse-graining procedure to construct mesoscopic models of complex molecules. The final aim is to obtain better results on properties depending on slow modes of the molecules.… Expand