A colorized electron microscope image shows lipid nanoparticles containing a cancer drug. The amount of drug contained depends on the size of each nanoparticle. NIST researchers have developed a new analysis to better understand how the useful properties of nanoparticles depend on their size — in this example, to optimize drug delivery to cancer patients. The new analysis can also find use in other products that use nanoparticles and other nanomaterials, including electronics, ceramics and coatings.
Credit: Dr. Pierre-Alain Burnouf/Shutterstock, Natasha Hanacek/NIST
Nanoscience, which studies small objects, has a big problem. According to a team of scientists at the National Institute of Standards and Technology (NIST), the field confronts a pervasive error of data analysis that can give misleading insights into how these tiny objects’ properties depend on their size. The team also offers a practical solution — a mathematical correction that can reveal how these materials truly behave.
Reported in ACS Nano, the team’s discovery has many implications, from testing material properties to developing products that use nanotechnology, which takes advantage of the behavior of materials at very small sizes. Nanoscale objects range from a few to a few hundred nanometers across — the size range of many viruses. At the nanoscale, a material often shows properties that differ from what the same material would exhibit in larger bulk form. For example, nanoscale chunks of gold metal can appear to be ruby red in color.
Nanomaterials form the basis of a wide variety of products including electronics, ceramics, paints and plastics, and they have many applications in chemical catalysis and drug delivery. The global market for nanotech is more than $100 billion annually and growing. Making better products depends in part on measuring and analyzing how nanoscale materials perform, a part of the process that the NIST scientists say requires an update.
“Many studies begin by measuring the size of a nanomaterial,” said mathematical statistician Adam Pintar, a member of the NIST team. “But these measurements are imperfect, and sizing errors matter.”
When researchers develop nanotechnologies like particles that glow a certain color or deliver medical treatments, their fundamental goal is to determine how the size of a nanoparticle affects its performance — such as how brightly it glows or how much medicine it carries. To do so, they plot a measure of performance versus size on a graph to analyze the trend.
However, the team noticed a common mistake in the statistical analysis of such trends. Researchers often assume that their measurements of particle size are perfectly precise and accurate. In practice, though, size measurements of nanoscale objects have limited precision and accuracy — sometimes very limited.
“These overlooked sizing errors have the effect of jostling a light bulb’s dimmer switch,” said electrical engineer Andrew Madison, also of the NIST team. “The errors dim the apparent relationship between the size of a particle and its brightness.”
After noticing the issue in a few key publications, the team looked through several other studies that measured various nanomaterials and found similar issues.
“The dimming effect can turn out the lights for understanding the properties of a nanomaterial,” said physical scientist Samuel Stavis, also of the team. “If a nanoparticle carries drugs for a medical treatment, for example, analysis of the dose could be mistaken. Or if a nanoscale wire was measured imperfectly, understanding of how much current flows through it could be off.”
After identifying the broader problem, the team developed a solution by deriving and testing mathematical corrections for the apparent trends. By quantifying the limited precision and accuracy of particle size measurements, the correction reverses the dimming effect, revealing the true relationship between particle property and size.
To use the correction, researchers must estimate their measurement errors, Pintar said. The best way to do so is to obtain a reliable reference material for the particles and measure its size with their own instruments and methods. The difference between the measurement results and the reference values gives an estimate of the errors. (NIST sells a wide selection of reference materials, as do other organizations.) If there is no reference material for a particular nanomaterial, researchers can still use the mathematical correction by carefully calculating the uncertainty of their sizing measurements.
In keeping with NIST’s mission to advance measurement science, the team members have identified a fundamental problem, Stavis said, and their solution will help nanoscience and nanotechnology to fulfill its potential for enhancing economic security and improving quality of life.
“It is a big ask to confront an overlooked problem at the foundation of a field of research,” he said. “But other fields of research have done so, and we offer a practical solution.”
A.L. Pintar, A.C. Madison, C.R. Copeland, N. Farkas and S.M. Stavis. Measurement Error Models Enable Accurate Correlation of Nanoscale Properties and Structures. ACS Nano. Published online Aug. 6, 2026. DOI: 10.1021/acsnano.5c12141
