Understanding shape entropy through local dense packing

TL;DR

This paper quantitatively defines and analyzes directional entropic forces (DEFs) in anisotropic particle systems, revealing their significant role in shape-driven phase behavior and self-assembly, and unifying entropy-driven phenomena across various shapes.

Contribution

It introduces a rigorous definition and computation of DEFs, demonstrating their comparable strength to other interactions and their fundamental role in entropy-driven self-assembly and packing.

Findings

DEFs are on the order of a few kT at ordering onset.

Entropic effects of shape significantly influence self-assembly.

The mechanism of DEFs is maximizing local packing entropy.

Abstract

Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals has been demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directional entropic forces (DEFs) that align neighboring particles, but these forces have been neither rigorously defined nor quantified in generic systems. Here, we show quantitatively that shape drives the phase behavior of systems of anisotropic particles upon crowding through DEFs. We define DEFs in generic systems, and compute them for several hard particle systems. We show that they are on the order of a few kT at the onset of ordering, placing DEFs on par with traditional depletion, van der Waals, and other intrinsic interactions. In experimental systems with these other interactions, we provide direct quantitative evidence that entropic effects of shape also contribute to self-assembly. We use DEFs to draw a distinction between self-assembly and packing behavior. We show that the mechanism that generates directional entropic forces is the maximization of entropy by optimizing local particle packing. We show that this mechanism occurs in a wide class of systems, and we treat, in a unified way, the entropy-driven phase behavior of arbitrary shapes incorporating the well-known works of Kirkwood, Onsager, and Asakura and Oosawa.