Unexpected Dependence of Photonic Band Gap Size on Randomness in Self-Assembled Colloidal Crystals

Wan, Duanduan; Glotzer, Sharon C.

doi:10.1103/physrevlett.126.208002

Cited by 13 publications

(12 citation statements)

References 57 publications

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“…2). We choose ǫ = 20 to be consistent with the previous study [37]. We see that the four lines are basically divided into two groups: The upper two lines represent the perfect situation and the random orientation situation, while the lower two lines represent the random position situation and the thermal situation.…”

Section: Resultsmentioning

confidence: 97%

“…See Refs. [13,37] for more simulation details. We used the supercell method implemented in the open source code MIT PHOTONIC BANDS [40] to obtain the photonic band structure of equilibrated snapshots.…”

Section: Methodsmentioning

confidence: 99%

“…An inevitable question about self-assembly approaches is how "randomness" arising from thermal noise in a self-assembled colloidal structure affects its PBGs. A recent study explores two-dimensional self-assembled structures, i.e., parallel dielectric rods of infinitely long length with circular or square cross section, and finds that in general, the randomness in the self-assembled (i.e., thermal) structure decreases the PBGs, compared to the system of rods arranged in its corresponding perfect lattice [37]. However, for rods with square cross sections at intermediate packing densities, interestingly, the transverse magnetic (TM) band gap of the self-assembled system can be larger than that of rods arranged in a perfect square lattice.…”

Section: Introductionmentioning

confidence: 99%

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Effects of orientational and positional randomness of particles on photonic band gap

Qin¹,

Liu²,

Wan³

2023

Preprint

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A recent work [PRL, 126, 208002 (2021)] has explored how thermal noise-induced randomness in a self-assembled photonic crystal affects photonic band gaps (PBGs). For the system of a twodimensional photonic crystal composed of a self-assembled array of rods with square cross sections, it was found that its PBGs can exist over an extensive range of packing densities. Counterintuitively, at intermediate packing densities, the transverse magnetic (TM) band gap of the self-assembled system can be larger than that of its corresponding perfect system (rods arranged in a perfect square lattice and having identical orientations). Due to shape anisotropicity, the randomness in the selfassembled system contains two kinds of randomness, i.e., positional and orientational randomness of the particles. In this work, we further investigate how PBGs are influenced solely by positional or orientational randomness. We find that compared to the perfect situation, the introduction of only orientational randomness decreases the transverse electric (TE) band gap while having no obvious effects on the transverse magnetic (TM) band gap. In contrast, the introduction of only positional randomness decreases the TE band gap significantly, while it can widen or narrow the TM band gap, depending on the parameter range. We also discuss the thermal (i.e., self-assembled) system where two kinds of randomness are present. Our study contributes to a better understanding of the role orientational randomness and positional randomness play on PBGs, and may benefit the PBG engineering of photonic crystals through self-assembly approaches.

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Section: Resultsmentioning

confidence: 97%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Effects of orientational and positional randomness of particles on photonic band gap

Qin¹,

Liu²,

Wan³

2023

Preprint

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“…a few hundred to a few thousand particles, and use periodic boundary conditions that mimic the presence of an infinite bulk surrounding the studied system (e.g., Refs. [7][8][9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

The configurational entropy of colloidal particles in a confined space

Wan

2022

Preprint

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We calculate the configurational entropy of colloidal particles in a confined geometry interacting as hard disks using Monte Carlo integration method. In particular, we consider systems with three kinds of boundary conditions: hard, periodic and spherical. For small to moderate packing fraction φ values, we find the entropies per particle for systems with the periodic and spherical boundary conditions tend to reach a same value with the increase of the particle number N , while that for the system with the hard boundary conditions still has obvious differences compared to them within the studied N range. Surprisingly, despite the small system sizes, the estimated entropies per particle at infinite system size from extrapolations in the periodic and spherical systems are in reasonable agreement with that calculated using thermodynamic integration method. Besides, as N increases we find the pair correlation function begins to exhibit similar features as that of a large selfassembled system at the same packing fraction. Our findings may contribute to a better understanding of how the configurational entropy changes with the system size and the influence of boundary conditions, and provide insights relevant to engineering particles in confined spaces.

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“…Crystallization and melting are among the most studied phenomena from both fundamental and technological points of view. In particular, colloidal crystals are of great interest for developing new novel materials such as optical fibers , and photonic band gap materials. − The volume fraction is one of the most important factors in determining the phase behaviors of all the colloidal suspensions. For hard-sphere colloids, the volume fraction is the only controlling parameter that determines whether the suspension is in a fluid state or in a solid state.…”

Section: Introductionmentioning

confidence: 99%

Depletion Induced Demixing and Crystallization in Binary Colloids Subjected to an External Potential Barrier

Mustakim¹,

Kumar

2021

J. Phys. Chem. B

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Depletion interaction plays an important role in determining the structural and dynamical properties of binary colloidal mixtures. We have investigated the effect of the attractive depletion interaction between an external potential barrier and larger species in the binary mixture on the phase behavior of a binary colloidal mixture using canonical–isokinetic ensemble molecular dynamics simulations. The demixing of the binary mixture due to this depletion interaction increases as the volume fraction increases, and a pure phase of larger particles forms in the region of the potential barrier. The local density of this pure phase is high enough that a face centered cubic crystalline domain is formed at this region. This crystalline phase diffuses perpendicular to the external potential barrier, indicating that moving crystals can be obtained in an equilibrium system. The temperature dependence of diffusivity of larger particles is non-Arrhenius and changes from sub-Arrhenius to super-Arrhenius as the volume fraction increases. This crossover from sub-Arrhenius to super-Arrhenius diffusion coincides with the crystalline formation near the potential barrier.

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Unexpected Dependence of Photonic Band Gap Size on Randomness in Self-Assembled Colloidal Crystals

Cited by 13 publications

References 57 publications

Effects of orientational and positional randomness of particles on photonic band gap

Effects of orientational and positional randomness of particles on photonic band gap

The configurational entropy of colloidal particles in a confined space

Depletion Induced Demixing and Crystallization in Binary Colloids Subjected to an External Potential Barrier

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