A MICROSCOPIC THEORY OF ENTROPIC BONDING
Abstract
Entropy is arguably one of the most confounding and counterintuitive concepts in science. For example, although usually associated with disorder, entropy maximization can actually lead to order. When crowded in solution, nanoparticles interacting only via excluded volume will selforganize from a disordered fluid phase into a colloidal crystal to maximize entropy. In colloidal crystals of non-spherical particles, entropic forces are directional and mimic the chemical bonds that hold molecules together and create solids from atoms. Indeed, while the extraordinary complexity and diversity of atomic and molecular crystals arises due to chemical bonds, it is “entropic bonds” that produce colloidal crystals of similar complexity and diversity from simple particle shapes. To demonstrate this, we propose to develop the first ever microscopic theory of entropic bonding. In analogy with chemical bonding and Schrodinger’s equation for electronic wave functions, we will derive – beginning from fundamental statistical mechanical principles – an eigenvalue equation whose solution via the introduction of “shape orbitals” allows for a priori prediction of entropically preferred colloidal crystal structures from nothing more than particle shape. Although it is well known that entropic forces can produce colloidal crystals, the idea that these entropic forces can be quantified as bonds in direct analogy with chemical bonds is a new and heretical idea that, once demonstrated here from first principles, will result in a fundamental conceptual shift in our understanding of matter and in our ability to predict and design materials. The microscopic theory we aim to develop will provide specific, quantitative predictions that can be tested immediately in experimental labs when they reopen.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 25, 2021
- Source ID
- HQ00342010030
Entities
People
- Sharon Glotzer
Organizations
- Office of the Secretary of Defense
- University of Michigan
- Washington Headquarters Services