In A Show Of Entropy's Benefits, Scientists Find "Fuzzy" Molecules Can Assemble Precisely Into Distinct Lattices

The finding, in which researchers led by Penn physicist Randall D. Kamien examined the effects of a halo of polymer limbs on otherwise spherical molecules suspended in liquid, is the cover story in today’s issue of the Journal of Physical Chemistry B.

Kamien’s work adds new evidence that entropy is far richer than the gloomy drive toward universal disorder it was once thought to be and suggests it could become a player in the world of self-assembling molecules. Entropy’s knack for driving fuzzy molecules into distinct lattices offers scientists the promise of new materials designed rationally rather than through trial and error.

"Predicting the symmetry of the lattice formed by an organic compound is one of the oldest dreams of synthetic chemists," said Kamien, an associate professor of physics and astronomy at Penn. "By providing an empirical connection between molecular structure and macroscopic organization, our result will allow chemists to design new materials from the top down."

Kamien’s theoretical work focused on colloids, which feature particles suspended in liquid. Colloids are all around us, from milk to microreactors, from pie filling to paint. Crystals formed from colloids form the basis for a new class of functional materials for use in optical switches, chemical microreactors and molecular sieves; the new finding suggests the possibility of creating "designer molecules" to speed this process along.

"Because both the size of the colloidal particles and interparticle interactions are tunable," Kamien said, "this provides the basis for the manufacture of ordered structures with desired lattice spacings as well as mechanical, thermal and electrical properties."

Ever since Sir Walter Raleigh pondered the most efficient means of stacking cannonballs some 400 years ago, scientists have suspected that free energy, and therefore entropy, is maximized by packing particles as tightly as possible. Only in 1998 was it shown that what’s called a face-centered cubic lattice maximizes the entropy of an array of perfect spheres – but the mathematical mystery of the myriad lattices formed by certain fuzzy molecules remained. Kamien’s work solves that puzzle, showing that things become more complicated when a little fuzz enters the picture.

"The old view was that the densest packing wins," Kamien said. "Our work shows it’s not that simple, especially as molecules grow less dense."

The molecules in the colloids Kamien studied were characterized by a relatively dense core surrounded by a corona of hundreds of spindly chemical arms. When virtually none of the fuzz was present, the particles did indeed organize themselves into a face-centered cubic array.

But as the fuzz grows in length, to the point that the molecules were almost all fluff with a very small core, they would form different arrays of lattices that could be mapped with precise phase diagrams. At stages where the fuzz was of an intermediate length, Kamien’s theoretical work predicts a mixture of face-centered cubic and other lattices corresponding to the length of the fuzz, a prediction consistent with experimental findings by Penn chemist Virgil Percec and others.

Kamien’s co-author on the Journal of Physical Chemistry B paper is Primoz Ziherl, on leave from the Institut Jozef Stefan in Ljubljana, Slovenia. Kamien and Ziherl’s work was supported by the National Science Foundation, the American Chemical Society’s Petroleum Research Fund, the Alfred P. Sloan Foundation and Penn alumnus Larry Bernstein.