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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers
Photonics of template-mediated lattices of colloidal clusters Konstantin I. Morozov, and Alexander Leshansky Langmuir, Just Accepted Manuscript • Publication Date (Web): 15 Feb 2019 Downloaded from http://pubs.acs.org on February 15, 2019
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Langmuir
Photonics of template-mediated lattices of colloidal clusters Konstantin I. Morozov , Alexander M. Leshansky *
Department of Chemical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel KEYWORDS: colloidal photonic crystal, encapsulating technique, microfluidic assembly, photonic bandgap, colloidal molecules
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ABSTRACT The recent progress in microfluidic microfabrication enables mass production of “colloidal molecules” with preprogrammed geometry (e.g., dumbbells, tetrahedrons, etc.). Such colloids can be used as elementary building blocks in fabrication of colloidal crystal with unique optical properties. Anisotropic clusters, however, cannot be readily assembled into regular lattices. In this paper we study photonic properties of compact cubic templates of microdrops encapsulating complex “colloidal molecules”. Since monodisperse droplets can be easily packed into dense cubic lattices and encapsulation techniques (e.g., using microfluidics) are well developed, such material is experimentally feasible. The rationale behind such methodology is that for particular alignment of the encapsulated “colloidal molecules” (e.g., by applying an external magnetic or electric field) the resulting structures resemble a diamond lattice, which is known to exhibit a wide complete photonic band gap. The photonic properties of two cubic templates encapsulating dumbbells (symmetric and asymmetric) and tetrahedrons are investigated numerically. In particular, we show the emergence of the complete 3D bandgap (~8% wide for the dielectric contrast 𝜀 = 12.25) for symmetric dumbbells embedded within fcc template and oriented along the space diagonal of the elementary cubic cell.
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INTRODUCTION The monodisperse colloidal spheres hexagonally packed into two- or three-dimensional lattices form a colloidal crystal [1]. The colloidal crystals (CCs) exhibit unique optical properties, in particular, for some orientations of incident light, they may possess photonic band gaps [2-4]. The ability of CCs to dynamically modulate their optical properties in response to externally applied magnetic [5,6] or electric [7,8] fields makes them particularly attractive for technological (e.g. biomedical) applications [9]. The recently proposed method of patterning colloidal photonic crystals expands considerably their use for fabrication of novel display devices, sensors and anticounterfeiting devices [10]. The well-established approach to produce colloidal crystals relies on microfluidic techniques, including the formation of the double emulsion droplets [11, 12] with their subsequent photo- or evaporation-induced crystallization [9, 12, 13]. Using these techniques, the spherical particles (silica colloids, polymer latexes) which are typically 𝑑~100 − 500 nm in diameter [1, 9] are encapsulated within droplets of much larger diameter, 𝐷~100 µm. After droplet crystallization into, e.g., face-centered cubic (fcc) structure, it forms a photonic colloidal crystal with the characteristic peaks of the reflectance/transmittance spectra at the wavelength of order of 2𝑑-3𝑑, i.e. in the radiation wavelength range from ultraviolet to visible to near-IR (ca. 300 nm to 2000 nm) [14]. The modern search for smart materials with interesting optical properties was initiated by the concept of aggregates of small number of particles or “colloidal molecules” introduced by van Blaaderen [15], who proposed to use them as functional building blocks for fabrication of new photonic materials. This idea became basic for numerous subsequent investigations [16-19]. The main efforts nowadays are focused on fabrication of the diamond-like colloidal crystals using
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self-assembly of the elementary units. To accomplish such kind of anisotropic packing, these elementary units should be properly pre-programmed. Such pre-programming can be realized with the help of patchy, or surface-patterned particles with a controlled number of favored adhesion cites [20] or using DNA-coded nanoparticles [21]. These methods are, however, quite complex and technologically challenging. Thus, the development of the simpler alternative techniques of microfabrication of the colloidal crystals would be highly useful. Recently, Shen et al. [22] reported a novel microfluidic technique of flow-assisted assembly of liquid micron in size highly monodisperse microdroplets into clusters of pre-programmed configurations. Adjusting the relative strength of the adhesion-to-hydrodynamic forces allowed for fine-tuning of the morphology of such colloidal clusters. As example, Figure 1 shows the tetrahedrons assembled from monodisperse droplets using microfluidics. Fast production of a variety of anisotropic clusters (dumbbells, triangles, tetrahedrons etc.) at rates up to one million of identical “colloidal molecules” per hour with their subsequent solidification using UV light was readily demonstrated [22] and this technology is potentially attractive for fabrication of colloidal materials with interesting optical properties.
Figure 1. Tetrahedron clusters obtained via droplet self-assembly, as observed in the microscope. Picture is courtesy of Dr. Joshua Recouvier, for more details see Shen et al. [22].
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In the present paper we examine photonic properties of the materials that could potentially be fabricated from such “colloidal molecules”. The basic “building block” in colloidal assembly is a spherical particle. It is well known that identical dielectric spheres can be readily packed into fcc-lattice do not exhibit photonic band gap structure [23]. In order to approach the diamond-like structure, it was proposed to reduce symmetry by using “colloidal molecules” of more complex geometry – dumbbells, ellipsoids, tetrahedrons [24-28] and even very asymmetric mushroom cap-shaped polymer colloids [29]. Unfortunately, asymmetric particles cannot be easily packed into regular lattices [14]. Since monodisperse spherical particles (or droplets) can easily selfassemble into cubic lattices, in this paper we consider such lattices of spherical droplets with embedded “colloidal molecules” of more complex geometry. The encapsulating techniques are well developed in the microfluidics for production of double [11, 30, 31] or multiple [32] emulsions. In this work we focus on dumbbells and tetrahedrons, as such “colloidal molecules”, that can be produced, e.g., using microfluidics [22], encapsulated into larger spherical drops assembled into a cubic lattice, as illustrated in Figure 1.
Figure 2. Two examples of template-mediated lattices with encapsulated colloidal clusters. (a): the fcc-template lattice of dumbbells; (b): the simple cubic template lattice of tetrahedrons formed by the alternating empty and populated droplets.
We further assume that encapsulated clusters are co-oriented, while their orientation can be controlled by an external magnetic or electric field [22].
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Why the photonic properties of cubic templates with embedded colloidal clusters could be interesting? To understand this, let us consider the following hypothetical geometrical construct. We first take the dumbbells co-oriented along the main diagonal of cubic cell as in Figure 2a. Then we disregard the encapsulating drops and bring the neighboring spheres apart (along the line of centers) to a distance of ¼ of the space diagonal of cell shown in Figure 2a. In this case we would get the true diamond lattice [33] of spheres possessing the optimal bandgap [23]. The fcc-templated dumbbell lattice in Figure 2a, however, only partially imitates the ideal diamond lattice. The principle difference distinguishing both systems is the distance between neighboring spheres: for the dumbbells it is less than for the true diamond lattice. Therefore, we anticipate that the photonic band structure of the fcc-templated dumbbell system may resemble that of the diamond lattice. The encapsulated tetrahedrons in Figure 2b are assumed to be oriented along the main axis of the elementary cubic cell. Similarly to the mentioned case of dumbbells, the hypothetical inflation of the tetrahedrons at which the centers of the clusters turn out to be at the vertices of a simple cubic lattice, would transform the structure into the true diamond array. Thus, both systems illustrated in Figure 2 imitate, or approximate, the diamond structure. Notice that the structure in Figure 2a is practical feasible. Indeed, the encapsulating techniques are well developed, while droplets encapsulating the “colloidal molecules” can be easily packed into the fcc-lattice. Further, if the dumbbells are electrically or magnetically responsive, they can be oriented by the externally imposed electric/magnetic field. However, the structure depicted in Figure 2b is hypothetical, as it requires the NaCl-type of lattice with alternating empty and populated droplets. However, it is interesting to theoretically investigate the photonic properties of both systems.
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RESULTS AND DISCUSSION We first consider the photonic properties of the fcc-templated dumbbells (see Figure 2a). The dumbbells are composed of two touching spherical particles with the diameters 𝑑- and 𝑑. . The diameter of the encapsulating droplets is 𝐷 ≥ 𝑑- + 𝑑. . We assume that the dielectric contrast of the system is due to different dielectric constants of the dumbbells and the matrix (i.e., the fcc template of encapsulating drops is assumed to be filled with the same material). Photonic calculations were performed with the help of the MIT Photonic Bands (MPB) software [23]. We studied the band structure of the system as a function of: (i) orientation of the dumbbell relatively to the cubic cell; (ii) the dielectric contrast of the drop and surrounding media; (iii) size ratio of particles comprising the (asymmetric) dumbbell. We also studied the inverse systems of co-oriented dumbbell holes in dielectric matrix (iv). In the case (i) the symmetric dumbbells are formed by two equal spheres of the maximal possible diameter, 𝑑- = 𝑑. = 𝐷/2 (see Figure 2a). If we choose the period of the unit cubic cell 𝑎 = 1, then 𝑑- = 𝑑. = √2/4. We assume the dielectric contrast of the dumbbells and the composite to be 𝜀 = 12.25 corresponding to silicon-air system. The volume fraction of the dielectric is 𝜑 =
8√.
fcc-lattice is 𝛷 =
.9
= 0.185. The volume fraction of the encapsulating drops close-packed into
8√.
