A highly collaborative research project on two-dimensional materials only a few atoms thick has resulted in an important advance that could lead to a new class of 2D materials for a range of critical applications in electronics, energy storage, and other areas.
In a paper published last week, “Order to disorder transition due to entropy in layered and 2D carbides,” in Science — the peer-reviewed journal of the American Association for the Advancement of Science —the limits for the construction of these ultra-thin materials were tested.

“This is a significant achievement for M-STAR,” a National Science Foundation Center for MXenes Synthesis, Tunability, and Reactivity, said De-en Jiang, H. Eugene McBrayer Professor of Chemical Engineering and professor of chemistry. Jiang, is an M-STAR co-principal investigator and a corresponding author of the paper. His graduate student Yinan Yang is second author of the paper.
Other M-STAR co-PI’s on the study include Babak Anasori, Purdue University; Yury Gogotsi, Drexel University; Aleksandra Vojvodic and Zahra Fakhraai, University of Pennsylvania. Other collaborators are from the Institute of Microelectronics and Photonics, Warsaw, Poland, and the Argonne National Laboratory in Illinois.
Vanderbilt researchers provided computational modeling, Purdue researchers synthesized nearly 40 known and novel structures, and the lab in Poland mapped out the elemental compositions of the samples atomic layer by atomic layer.
Computational modeling plays an important role in discovering new 2D materials because it allows researchers to understand and predict their properties, accelerate discovery, and guide synthesis in a way that is difficult or impossible with physical experiments alone. “The precise, atomic-level behavior of 2D materials makes them ideal for computational analysis,” said Jiang, who leads the Computational Chemical Sciences and Materials Laboratory at Vanderbilt. “I am grateful to my advisor and M-STAR for giving me the opportunity to collaborate with some of the most creative people in the field and to contribute my computational expertise,” Yang said.

The family of 2D materials the group studied are known as MXenes (pronounced “Max-eens”), which are 2D carbides/nitrides derived from MAX phases. Professor Yury Gogotsi at Drexel was one of the original discoverers in 2011of MXenes, and they have since become the largest known family of 2D materials.
An ultra-thin nanometer sheet (a few layers of atoms) of 2D MXenes is about 100,000 times thinner than a human hair. Construction of layered sheets offers a combination of properties—high electrical conductivity, readily soluble, compositional tunability, and novel functionality that makes them ideal building blocks for a variety of uses in technology.
The comprehensive study across different compositions spanning 2-9 transition metal elements demonstrates that enthalpy (the chemical preference for order) initially keeps metals in preferred positions until entropy (a measure of disorder or randomness) becomes strong enough to overcome this ordering when 7 or more different elements are present in a sample. The layered architecture—where metal atoms are sandwiched between carbon and aluminum layers—provides an exceptional platform for studying fundamental order-disorder transitions.
“Our computational modeling establishes a quantitative framework to explain the enthalpy vs entropy driving force in these fascinating 2D materials” Jiang said. “Next, we’d like to explore new properties and applications for high-entropy MXenes and to collaborate with a larger team as the M-STAR Center for Chemical Innovation pursues Phase II funding from the NSF.”