2024 David Turnbull Lectureship

Sharon C. Glotzer, University of Michigan

Entropic Bonds in Colloidal Crystals

Written by Vineeth Venugopal

At the 2024 MRS Fall Meeting & Exhibit, Sharon C. Glotzer of the University of Michigan was honored with the prestigious David Turnbull Lectureship Award. Recognizing her career-long contributions to theoretical materials science, Glotzer delivered a captivating talk titled “A Theory of Entropic Bonds in Colloidal Crystals.” Her presentation explored the transformative role of entropy in the assembly of colloidal crystals, challenging traditional notions of order and disorder.

The Mystery of Colloidal Crystals

Colloidal crystals are structures formed by nanoparticles suspended in a solution. These ordered lattices arise from a combination of intrinsic forces, such as van der Waals forces, hydrogen bonding, and electrostatic interactions, alongside interactions with the solvent. However, Glotzer invited the audience to consider what happens when all these forces are excluded, leaving only entropy to drive assembly.

In such a system, nanoparticles behave like hard spheres undergoing Brownian motion. This phenomenon is described by the hard sphere model, which predicts a phase transition from a liquid state to a face-centered cubic (FCC) phase. Although theorized by John Kirkwood in 1941 and simulated using density functional theory (DFT) in 1958, it wasn’t experimentally confirmed until 1997 when the STS-73 Space Shuttle crew observed colloidal crystals forming in a microgravity environment.

Glotzer highlighted a counterintuitive aspect of entropy in these systems: despite their apparent order, FCC crystals have more entropy than disordered fluids. This paradox arises because ordered phases possess more microstates and therefore higher entropy, a principle that has been central to her research.

Entropy as a Driving Force

The concept of entropy as a driving force in phase transitions dates back to Lars Onsager’s 1949 work on isotropic-nematic transitions in hard rods. Building on this foundation, Glotzer’s research group explored how entropy alone can drive the self-assembly of complex structures, including quasicrystals. In 2009, her team demonstrated the assembly of a three-dimensional (3D) quasicrystal from tetrahedral shapes—an achievement celebrated globally, including as a BBC “Image of the Day.” This year, Xingchen Ye of Indiana University experimentally realized a 12-fold quasicrystal from gold tetrahedra, underscoring the practical implications of her theoretical insights.

Glotzer emphasized that virtually any atomic crystal structure can be replicated by hard particles, provided the system is ergodic. “Statistical thermodynamics does not care about the origin of forces,” she said, underscoring the universality of entropy-driven assembly.

Entropic Bonds: A New Paradigm

While entropy is often considered a global quantity, Glotzer’s work reveals that it can also manifest locally, generating directional forces akin to chemical bonds. These “entropic bonds” emerge from particle shape and packing constraints, enabling the self-assembly of complex colloidal crystals. By engineering the strength of entropic bonds through particle design, her team successfully created twinned crystal structures, including cubic and hexagonal diamond lattices.

One striking example was the assembly of an entropically self-organized clathrate colloidal crystal using hard spheres. This process mimicked the fluid-fluid phase separation pathway observed in molecular clathrates, further bridging the gap between molecular and colloidal systems.

Glotzer posed a fundamental question: which atomic crystal structures cannot be achieved through shape and entropy alone, and why? Answering this could unlock a deeper understanding of structural complexity and guide the design of novel materials.

Toward a First-Principles Theory of Entropic Bonding

Inspired by the rigorous theoretical frameworks of chemical bonding, Glotzer and her team are developing a first-principles theory of entropic bonding. Drawing parallels to Kohn-Sham density functional theory, her approach treats particles as fixed nuclei surrounded by a “fictitious glue” of pseudo-particles. This framework enables the prediction of preferred arrangements of particles by minimizing entropy, akin to minimizing energy in electron density theories.

The proposed classical density functional theory of hard particle systems reinterprets classical theories through the lens of entropy. Glotzer’s findings suggest that entropy can act as a bonding force, fundamentally altering our understanding of materials assembly.

Transforming Perspectives on Materials Science

Glotzer’s lecture left the audience with a profound takeaway: entropy, often associated with disorder, plays a critical and directional role in creating order at the nanoscale. Her work not only expands the boundaries of materials science but also offers a new lens through which to view classical theories.

In honoring Sharon Glotzer, the MRS recognized a pioneer whose groundbreaking contributions exemplify the spirit of David Turnbull. Her innovative research continues to shape the future of materials science, bridging theory and experiment in the quest to uncover the fundamental principles of materials assembly.

The David Turnbull Lectureship recognizes the career contribution of a scientist to fundamental understanding of the science of materials through experimental and/or theoretical research. In the spirit of the life work of David Turnbull, writing and lecturing also can be factors in the selection process.