Mathematics points the way to new, advanced materials

Work conducted by Christopher Rinderspacher, a theoretical chemist with the US Army Research Laboratory (ARL), could lead to a future in which materials scientists specify the properties they desire in a material to advanced software, which will then deliver a choice of optimized chemical compounds. He recently published a paper in the Journal of Mathematical Chemistry that describes a process for using mathematics to design chemical compounds by reducing complexity and taking advantage of machine learning.

"What this does is actually open up the potential number of compounds," Rinderspacher said.

The search for materials with particularly useful properties is like finding a needle in a haystack. In the past, chemists would search based on an established framework and often find new combinations in a hit-or-miss fashion.

"The problem with that is you never find anything that's truly new or surprising because what we want is something that breaks the norm," Rinderspacher explained. "If we stay within our own thought patterns – conventional thought patterns – we're never going to find breakout materials."

For the US Army, ground-breaking advances in materials science could result in stronger, lighter armor or equipment for soldiers of the future. This aligns with US Army modernization priorities that seek long-range precision fires, next generation combat vehicles, future vertical lift platforms and advanced soldier lethality. Materials science will play a huge role in realizing the army of the future, officials said.

"Science usually works by walking up to the frontier of what we know and poking around," Rinderspacher said. "Where do we find something new and interesting?"

By introducing a new path to discovery, Rinderspacher hopes to point chemists in the right direction with a mathematical approach. Using what's known as nuclear charge distributions, he developed a general theoretical framework for finding desired chemical compounds.

The conventional path for discovering new chemical compounds is "long and tedious," he said. "If we were to go wherever we wanted, in terms of all the possible chemicals without any restrictions that aren't inherent to your problem, you would be able to access everything."

The key, he said, is coming up with a way to optimize what's known as "probability density functions in chemical space".

In the next three to five years, Rinderspacher said he hopes to incorporate machine learning into his algorithms to deliver a solution and narrow the search parameters for new chemical compounds.

Rinderspacher has been pursuing this line of research since January 2009, when he came to the ARL as a post-doctoral fellow after earning his doctorate at the University of Georgia. A self-proclaimed puzzle solver, he is driven by finding efficient solutions.

"I know that some people are really driven by the application that will be at the end, but to me getting it to work is fascinating enough," he said. "I like to look at the problem and then figure out 'How many other problems are like that and can be solved the same way?'"

According to Rinderspacher, the activity of math involves thinking about generalizing stuff, organizing ideas and showing what does and doesn't work. "The right math will get you there," he said. "It's mathematical thinking – outside of the box – that I'm trying to enable."

This story is adapted from material from the US Army Research Laboratory, with editorial changes made by Materials Today. The views expressed in this article do not necessarily represent those of Elsevier. Link to original source.