Order to disorder at the atomic scale opens possibilities for next-generation electronic devices

Two decades ago, scientists peeled away layers from graphite, the soft carbon in pencil tips, to isolate a single atomic sheet known as graphene—the first human-synthesized two-dimensional (2D) material. Its discovery heralded new technologies: flexible displays, faster computer chips, and high-capacity batteries.

But graphene is made entirely of carbon, which limits scientists’ ability to fine-tune its properties for new functions. A “gold rush-like” search for other alternatives ensued, producing boron nitride, dichalcogenides like molybdenum sulfide, and the largest family of all, MXenes, says Aleksandra Vojvodic, professor in the Department of Chemical and Biomolecular Engineering in Penn’s School of Engineering and Applied Science.

The 2D MXenes consist of sheets of carbon or nitrogen sandwiched between sheets of transition metals like titanium, vanadium, and molybdenum, resulting in thin materials that are typically three, five, or seven atomic layers. So far, MXenes uses have generally been limited to just one or two transition metal types—owing to inherent chemical and thermodynamic constraints related to combining many more metals.

“While these 2D materials hold a great promise for next-generation applications, for example, consumer electronics, medical devices, energy storage and conversion, the exact material synthesis recipes on where and how to position the atoms within the sheets are extremely limited and mostly unknown,” Vojvodic says.

Now, Vojvodic, along with Penn’s Zahra Fakhraai, and collaborators at the MXenes Synthesis, Tunability and Reactivity (M-STAR) Center for Chemical Innovation (CCI, supported by National Science Foundation), have found a way add up to nine metals into the mix. Their findings speak to a longstanding issue multi-metal materials: does atomic order (enthalpy) or disorder (entropy) ultimately dictate the synthesis and behavior of these materials? Put another way, they showed that in the world of MXenes, chaos can be constructive. Sometimes adding more elements, makes it is easier to manipulate the system for greater versatility.

“This discovery shows how chemistry and geometry interplay to dictate order or disorder, offering new pathways for designing MXenes with precisely controlled properties for diverse applications,” says Fakhraai, a professor in the Department of Chemistry. “Now you can choose anywhere from one up to nine metals to be incorporated into unique 2D MXene materials with different degrees of structural ordering offering potentially new properties.”

Their findings are published in Science.

MAX to MXenes

The M-STAR team synthesized and characterized about 40 MAX-phase ceramics, the parent materials for MXenes, and found a critical transition. Once more than seven metals are present, entropy dominates, leading to fully disordered atomic arrangements in both the MAX precursors and their MXene offspring.

The MXenes are made by chemically treating a library of 3D parent MAX materials, synthesized by Babak Anasori’s group at Purdue University, with harsh solvents like hydrofluoric acid or hydrochloric acid, leaving behind atomically thin sheets of carbon and metal layers capped with surface functional groups, such as oxygen, hydroxyl, or fluorine.

“These functional groups,“ Vojvodic says, “are critical, contributing to the material’s properties and stability beyond that provided by layering of the metals and carbon.“

For the MXene with few metals (up to six), the team found that some metals tended to segregate into distinct layers. For instance, Group 6 atoms like molybdenum occupy the surface while Group 4 atoms like titanium settle in the middle, Vojvodic explains.

This “natural” preference of different metals to be in different layers was initially seen to be a design limitation. “It’s sort of like attending a cocktail party where every guest sits only with familiar faces,” Vojvodic says, “you just end up with predictable cliques and no unexpected chemistry.“

However, the team found that the exact preference is driven by chemical interactions and enthalpy, and that once the number of metals is large enough—seven or more different types the entropy wins and takes over—the location of the different metals becomes completely mixed and disordered. “Essentially, the number of guests becomes so large, you can’t find your besties anymore, and you are forced to mingle and make new acquaintances.”

Probing and calculating

The composition of each layer of the MAX and MXenes was experimentally determined by studies using time of flight secondary ion mass spectroscopy performed by collaborator Paweł Michałowski at Łukasiewicz Research Network.

Meanwhile, Yury Gogotsi’s group at Drexel delaminated MXene sheets, confirming that even in disordered form they retained structural integrity and robustness.

The Fakhraai Group mapped structure of these materials using atomic force microscopy and probed their optical and electronic properties using spectroscopic ellipsometry, finding that resistivity and emissivity shifted as disorder increased. Their work identified key insights into how the specific mix of metals in MXenes can reshape their behavior in fundamental ways.

On the computational side, the Vojvodic Lab ran density functional theory simulations to calculate formation energies and stability of MXenes across different combinations and surface terminations. Working together with computational MAX data from De-en Jiang at Vanderbilt, they pinpointed the crossover: fewer than six metals, enthalpy drives order; at six or seven, entropy tips the balance.

“The beauty of simulations,” says Vojvodic, “is that we can test conditions difficult to realize experimentally. By combining computational and experimental data, we could identify exactly where order gives way to disorder.”

Next steps

Looking ahead, both labs at Penn are exploring new possibilities for creating the materials that could someday advance energy storage technology and speed up the reactions that generate clean energy. Vojvodic’s group is expanding predictions with machine learning to scan vast combinations of metals; and Fakhraai’s lab is probing stability and conductivity in disordered MXenes, looking especially at how surface chemistry shapes performance.

“What’s on the surface matters far more than you might think,” Fakhraai says. “When surface atoms are a random mix, they create diverse reactive sites, which can be really powerful for catalysis.”

“What’s on the surface matters far more than you might think,” Fakhraai says. “When surface atoms are a random mix, they create diverse reactive sites, which can be really powerful for catalysis.”

“This is ultimately a story about control,” Vojvodic adds. “By understanding how entropy and enthalpy compete in the 2D material landscape, we gain a better handle on how to design the materials of the future.”

The project, supported by the NSF’s M-STAR Center, relied on close collaboration among graduate students and postdocs across multiple institutions for several years.

“It’s very exciting to report that our team has made major inroads in not only addressing a long-standing debate in materials science but also in educating the next generation innovators, scientists, and engineers” says Fakhraai.

Aleksandra Vojvodic is a professor in the Department of Chemical and Biomolecular Engineering at the School of Engineering and Applied Science and director of the Penn Institute for Computational Science at the University of Pennsylvania.

Zahra Fakhraai is a professor in the Department of Chemistry at the School of Arts & Sciences at Penn.

Authors include Sanguk Han, Yamilée Morency, and Aleksandra Vojvodic of Penn Engineering; Zahra Fakhraai, Hui Fang, Givi Kadagishvili, and Manushree Tanwar of Penn Arts & Sciences; Brian C. Wyatt, Srinivasa K. Nemani, Annabelle Bedford, Babak Anasori, Rebecca Disko, Junwoo Jang, Neil Ghosh, Krutarth Kamath, Anupma Thakur, Bethany G. Wright, and Xianfan Xu of Purdue University; Yinan Yang and De-en Jiang of Vanderbilt University; Paweł P. Michałowski of Łukasiewicz Research Network; Yury Gogotsi, Tetiana Parker, and Francesca Urban of Drexel University; and Zachary D. Hood and Sixbert P. Muhoza of Argonne National Laboratory.

This work received support from the National Science Foundation (Grants 2318105, 2419026, CBET-2051525; Awards 1229514 and 1429241), the National Science Centre of Poland (SONATA BIS 14 2024/54/E/ST11/00171; LIDER XII LIDER/8/0055/L-12/20/NCBR/2021 projects), Department of Energy (Contracts DE-AC02-06CH11357, BES-ERCAP0023161 and DE-AC02-05CH11231). Further support came from the Vagelos Institute for Energy Science and Technology University of Pennsylvania, the Korea Institute for Advancement of Technology (Grant P0028332)