MITRE's R&D in Multi-Scale Modeling

A fundamental challenge in the field of nanotechnology is to model and design bulk properties of matter accurately from the "bottom up" - that is, based on the quantum properties and the arrangement of trillions upon trillions of individual component atoms and molecules. This capability would enable rapid, economical design of materials with pre-specified unique properties, using much less of the expensive physical experimentation that presently is required. This challenge, however, is quite formidable, as it implicitly involves multi-scale materials modeling—i.e., modeling matter on multiple length scales that range over 10 to 12 orders of magnitude. Rapid, seamless modeling on all these scales is made particularly difficult because the quantum laws of physics that prevail on the smallest, atomic and molecular scales are seen to differ from the classical laws that govern matter on macroscopic scales.

The quantum capacitances of atoms and molecules scale with the effective radius in a manner analogous to the classical capacitances of macroscopic spherical capacitors. Parts (a) and (b) depict the storage of positive charges in a macroscopic spherical capacitor, as well as how the capacitance of a sphere scales with its radius with a slope proportional to the dielectric constant. Part (c) shows that the capacitance of atoms also scales linearly, suggesting that atoms have atomic dielectric constants. However, the capacitances for sets of atoms extrapolate to a nonzero capacitance at effective radius zero, which is—a counterintuitive finding.

Over the past several years, however, research in the MITRE Nanosystems Group has yielded new insights into the electronic properties of materials across multiple scales. These investigations revealed new regularities or laws of physics that govern the ability of matter to hold charge on all scales. These laws are expressed by the same, simple linear equations from the pico-scale to the macro-scale. These scale-invariant linear relations governing charges in matter are particularly significant for multi-scale modeling because it is charge that holds matter together on all these scales and dictates all its properties. The unique effort going forward involves learning how to extend and apply these new, multi-scale laws of physics to the modeling of matter on all scales.

The atoms along each of the colored capacitance scaling lines (left) correspond to atoms in different parts of the periodic table (right). This suggests that all of the periodic properties of the elements correlate with their capacitance scaling properties or parameters. Similar principles have been shown to apply for molecules.

This research has led to the publication of several papers on this and related topics that can be found on our publications page.

This research is conducted by MITRE senior scientists and student researchers through the Nanosystems Group Student Program.