Understanding and Controlling Directional Entropic Forces in Hard Particle Self-Assembly
[摘要] Particle shape plays a critical role in determining how systems of hard particles self-assemble into ordered structures. Under the hard particle model, the maximization of entropy dictates how systems minimize their free energy. The theory of directional entropic forces attempts to explain hard particle behavior through effective forces that particles exert on one another. These effective forces, which are statistical in nature, account for why particles enter specific relative configurations with one another in order to maximize the entropy of the system. This work examines the role of directional entropic forces in various systems. I show how the use of many small penetrable particles (the depletion interaction) can control the self-assembly of cuboctahedra into different structures based on the size of the depletant particles. Large depletants induce packing behavior in a fashion similar to increasing pressure in a depletant-free system, but sufficiently small depletants lead to a simple cubic crystal assembly by enhancing directional entropic forces at a shape;;s largest facets, in effect changing the valence for the entropic bonds a system forms. I compute free energies in these systems as a function of depletant size and concentration by using Free Volume Theory, a technique that accounts for entropic contributions from both the colloid and depletant phase. To examine specific effects of shape change, I compute directional entropic forces in shape families across changes in facet size. I show that rounding a chiral Voronoi particle can suppress the chiral nature of the directional entropic forces, and through depletion can re-strengthen them. I additionally show how the optimal shape for assembling a diamond crystal has larger facets than would be expected from packing arguments because these larger facets induce stronger directional entropic forces. I further study a group of shapes that form plastic crystals, wherein particles exhibit translational order but orientational disorder. To compare the behavior of particles, I develop new analysis methods to quantify global orientational order, relative angular separations between neighboring particles, and a rotational autocorrelation function. I show that, upon compression, these systems are capable of undergoing gradual ordering transitions, first-order transitions, and orientationally supercooled states that approach an orientational glass transition, and I identify how the valence set by the directional entropic forces connects to these different transition behaviors. Finally, I analyze systems of truncated dodecahedra that are capable of assembling the highly symmetric face-centered cubic crystal as well as the complex beta-Mn and gamma-brass phases with large unit cells and symmetrically distinct Wyckoff sites. In the complex phases, particles in certain Wyckoff sites experience stronger directional entropic forces and adopt an icosahedral coordination environment with less free volume. The other particles in these systems have a greater amount of free volume and are able to rotate more easily. I present the idea that the local free volume fluctuations that stabilize these complex phases is analogous to behavior seen in metallic and soft matter systems which undergo charge and mass transfer, respectively. The coordination for the sites with less free volume resembles a preferred local dense packing that directional entropic forces will favor. Overall, this work explores how the valence set by emergent directional entropic forces dictates phase behavior.
[发布日期] [发布机构] University of Michigan
[效力级别] Entropy [学科分类]
[关键词] Self-assembly;Entropy;Colloids;Monte Carlo simulations;Chemical Engineering;Engineering;Chemical Engineering [时效性]