# Optimizing Interacting Potentials to Form Targeted Materials Structures

## Abstract

Conventional applications of the principles of statistical mechanics (the "forward" problems), start with particle interaction potentials, and proceed to deduce local structure and macroscopic properties. Other applications (that may be classified as "inverse" problems), begin with targeted configurational information, such as low-order correlation functions that characterize local particle order, and attempt to back out full-system configurations and/or interaction potentials. To supplement these successful experimental and numerical "forward" approaches, we have focused on inverse approaches that make use of analytical and computational tools to optimize interactions for targeted self-assembly of nanosystems. The most original aspect of our work is its inherently inverse approach: instead of predicting structures that result from given interaction potentials among particles, we determine the optimal potential that most robustly stabilizes a given target structure subject to certain constraints. Our inverse approach could revolutionize the manner in which materials are designed and fabricated. There are a number of very tangible properties (e.g. zero thermal expansion behavior), elastic constants, optical properties for photonic applications, and transport properties.

- Authors:

- Princeton Univ., NJ (United States)

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1222771

- Report Number(s):
- DOE-PRINCETON-46108

- DOE Contract Number:
- FG02-04ER46108

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; Inverse statistical mechanics, optimization, materials design

### Citation Formats

```
Torquato, Salvatore.
```*Optimizing Interacting Potentials to Form Targeted Materials Structures*. United States: N. p., 2015.
Web. doi:10.2172/1222771.

```
Torquato, Salvatore.
```*Optimizing Interacting Potentials to Form Targeted Materials Structures*. United States. doi:10.2172/1222771.

```
Torquato, Salvatore. Mon .
"Optimizing Interacting Potentials to Form Targeted Materials Structures". United States. doi:10.2172/1222771. https://www.osti.gov/servlets/purl/1222771.
```

```
@article{osti_1222771,
```

title = {Optimizing Interacting Potentials to Form Targeted Materials Structures},

author = {Torquato, Salvatore},

abstractNote = {Conventional applications of the principles of statistical mechanics (the "forward" problems), start with particle interaction potentials, and proceed to deduce local structure and macroscopic properties. Other applications (that may be classified as "inverse" problems), begin with targeted configurational information, such as low-order correlation functions that characterize local particle order, and attempt to back out full-system configurations and/or interaction potentials. To supplement these successful experimental and numerical "forward" approaches, we have focused on inverse approaches that make use of analytical and computational tools to optimize interactions for targeted self-assembly of nanosystems. The most original aspect of our work is its inherently inverse approach: instead of predicting structures that result from given interaction potentials among particles, we determine the optimal potential that most robustly stabilizes a given target structure subject to certain constraints. Our inverse approach could revolutionize the manner in which materials are designed and fabricated. There are a number of very tangible properties (e.g. zero thermal expansion behavior), elastic constants, optical properties for photonic applications, and transport properties.},

doi = {10.2172/1222771},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {9}

}