Controlling Chirality of Entropic Crystals

Abstract

Colloidal crystal structures with complexity and diversity rivaling atomic and molecular crystals have been predicted and obtained for hard particles by entropy maximization. However, so far homochiral colloidal crystals, which are candidates for photonic metamaterials, are absent. Using Monte Carlo simulations we show that chiral polyhedra exhibiting weak directional entropic forces self-assemble either an achiral crystal or a chiral crystal with limited control over the crystal handedness. Building blocks with stronger faceting exhibit higher selectivity and assemble a chiral crystal with handedness uniquely determined by the particle chirality. Tuning the strength of directional entropic forces by means of particle rounding or the use of depletants allows for reconfiguration between achiral and homochiral crystals. We rationalize our findings by quantifying the chirality strength of each particle, both from particle geometry and potential of mean force and torque diagrams.Controlling -and understanding the origins of-chirality is a major goal in the physical and chemical sciences. It has longstanding implications that range from the design of effective pharmaceuticals to explaining biological homochirality and the beginnings of life [1]. In recent years the expectation that chiral materials can provide a route for photonic metamaterials [2] has renewed the interest in chirality, now from a materials design perspective. A key remaining challenge for the development of metamaterials [3] is the ability to use scalable techniques to create crystals with unique chirality. Of particular importance are enantioselective processes, which select a pre-defined handedness of the crystal, thereby maximizing optical activity. [17][18][19][20], the final chiral structures have, so far, been restricted to liquid crystalline and low-dimensional arrangements. Growth of three-dimensional homochiral colloidal crystals has yet to be demonstrated. In fact, the only examples of chiral crystals with realized applications as polarization sensitive devices [21,22] were fabricated via non-scalable processes such as direct laser writing, hampering large scale production.Recent work has shown that hard polyhedra can selfassemble into a great diversity of crystals, liquid crystals, and quasicrystals via entropy maximization [23][24][25][26][27][28], a mechanism that can be understood as resulting from emergent directional entropic forces (DEFs) between neighboring particles due to crowding [25,29,30]. Even chiral crystals have been assembled. The β-Mn crystal structure with chiral space group P4 1 32 [ Fig. 1a], earlier reported in spheres interacting via an isotropic oscillatory pair potential [31], self-assembles from achiral dodecahedra shapes [27]. However, as expected, the handedness of the crystal could not be controlled and both left-and right-handed crystals were observed with equal probability. Given the ability of entropic interactions to imitate the plethora of complex structures achievable from atomistic interactions, the abs...

Molecular model for chirality phenomena

“…In addition to the above examples in pharmacology, chirality plays a key role in advanced photonics applications, 8,9 in low-power electronic display technologies, 10,11 and in the processing of amorphous pharmaceuticals. 12 A specific a) fhs@princeton.edu b) pdebene@princeton.edu example relevant to processing concerns the area of pressureinduced crystallization.…”

Entropy-driven formation of chiral nematic phases by computer simulations

“…As soon as we move away from spherical particles a bewildering variety of thermodynamically stable structures with increasing complexity arises 4 6 . As a result, a concurrent increase of simulation studies on hard particles show that entropy can be the sole driving force in the formation of crystals featuring different symmetries, plastic crystals, liquid crystals and even quasi-crystals 4 6 7 8 9 10 11 12 13 14 .…”

Theory and Simulation Studies of Self‐Assembly of Helical Particles

“…One interesting issue hinges on the possible presence of columnar phases in a system of monosized hard helices, which are exhibited for instance by fd -viruses [80]. Equally deserving a dedicated study is a detailed analysis of the high-densities ordered phases, as they might provide some surprising features in view of the non-convex nature of the helices [5]. Other important, still unexplored, issues concern the behavior of mixtures of helices, differing in length and morphology, mixtures of enantiomers, as well as the dynamics of the onset of screw-like phases.…”

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While it is possible to control the enantioselective process by using depletion interactions and faceting of the bulding blocks [5], helices are among the natural objects to focus on when dealing with chirality. New functional materials [9] [10] can be produced by exploiting the intrinsic chirality of the helical structures, which are useful in catalysis and demixing of enantiomers [11] [12].

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