Researchers found empty spaces in matter at different scales using powerful microscopes and mathematical theory.

This advancement will improve the performance of materials used in the chemical, energy, medical, and home industries, especially in filtration.

Household filters look solid, but they are actually made up of many small voids that allow small particles to pass through.

Thin membranes made of paper are used in industry to separate fluids and particles, like water and solvents.

Falon Kalutantirige, a graduate student at the University of Illinois at Urbana-Champaign, stated that the materials science community has been aware of randomly oriented nanoscale voids within filter membranes for a long time.

The problem was that they couldn't see the empty areas clearly because the structure of the membrane was complex, like tiny mountains. The inability to observe them prevented the researchers from completely comprehending how they impacted the filtration properties. The researchers knew that by being able to see the filter membranes, they could understand how they work and improve their effectiveness.

Researchers from the University of Illinois and the University of Wisconsin-Madison have utilized graph theory to visualize and chart the placement of voids in filtration materials. This study is the first to combine materials science and graph theory in this way.

The results have been released in the Nature Communications journal.

The new study builds on a previous one using lab models and focuses on complex membranes used in industry.