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Abstract
Selfassembly and alignment of anisotropiccolloidal particles are important processes that can be influenced by external electric fields. However, dielectric nanoparticles are generally hard to align this way because of their small size and low polarizability. In this work, we employ the coupled dipole method to show that the minimum size parameter for which a particle may be aligned using an external electric field depends on the dimension ratio that defines the exact shape of the particle. We show, for rods, platelets, bowls, and dumbbells, that the optimal dimension ratio (the dimension ratio for which the size parameter that first allows alignment is minimal) depends on a nontrivial competition between particle bulkiness and anisotropy because more bulkiness implies more polarizable substance and thus higher polarizability, while more anisotropy implies a larger (relative) difference in polarizability.
This work is part of the research programme of FOM, which is financially supported by NWO. Financial support by an NWOVICI grant is acknowledged.
Key Topics
 Anisotropy
 17.0
 Polarizability
 16.0
 Electric fields
 12.0
 Cold dark matter
 9.0
 Nanoparticles
 5.0
B01J13/00
B82B1/00
B82B3/00
Figures
The angular distribution function ψ(θ) (a), and the order parameter S (b), of an anisotropic particle with orientational energy V _{ E }(θ) = −Δcos ^{2}θ in an external electric field E _{0}. Here, θ is the angle between the particle's rotational symmetry axis and E _{0} and Δ is the energy difference of turning the particle from its least to its most favorable orientation.
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The angular distribution function ψ(θ) (a), and the order parameter S (b), of an anisotropic particle with orientational energy V _{ E }(θ) = −Δcos ^{2}θ in an external electric field E _{0}. Here, θ is the angle between the particle's rotational symmetry axis and E _{0} and Δ is the energy difference of turning the particle from its least to its most favorable orientation.
The length aL* (a) and the width al* (b) for which l × l × L cuboidal rods and platelets, respectively, first become alignable by an electric field , as a function of their shape (l/L and L/l, respectively), for several different lattice constants , 2, 2.5 and 3. The temperature is , and the atomic polarizability is . The dots denote the minima in the graphs.
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The length aL* (a) and the width al* (b) for which l × l × L cuboidal rods and platelets, respectively, first become alignable by an electric field , as a function of their shape (l/L and L/l, respectively), for several different lattice constants , 2, 2.5 and 3. The temperature is , and the atomic polarizability is . The dots denote the minima in the graphs.
To get the bowl shape, we revolve a crescent around its symmetry axis.^{4} This crescent is the result of the settheoretic subtraction of a disk with diameter σ^{′} > σ from a disk with diameter σ. The relative position of the two disks and the diameter σ^{′} have to be chosen such that the center of the small disk lies on the line connecting the two points where the edges of the disks intersect, and such that in its middle, the thickness of the crescent is d. In this work, we also allow d > σ/2, which we associate with the settheoretic intersection of the two disks (the green area with thickness d ^{′}).
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To get the bowl shape, we revolve a crescent around its symmetry axis.^{4} This crescent is the result of the settheoretic subtraction of a disk with diameter σ^{′} > σ from a disk with diameter σ. The relative position of the two disks and the diameter σ^{′} have to be chosen such that the center of the small disk lies on the line connecting the two points where the edges of the disks intersect, and such that in its middle, the thickness of the crescent is d. In this work, we also allow d > σ/2, which we associate with the settheoretic intersection of the two disks (the green area with thickness d ^{′}).
The size parameter σ* (a) and σ* + L* (b) for which colloidal bowls and dumbbells, respectively, first become alignable by an electric field , as a function of their shape parameters d/σ and L/σ, respectively. Here, d is the thickness of a bowl and L is the separation of the two composing spheres of a dumbbell. The bowls and dumbbells are built up of atoms on a simple cubic lattice with dimensionless lattice spacings , 2, 2.5, and 3. The temperature is , and the atomic polarizability is . The dots denote the minima in the graphs.
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The size parameter σ* (a) and σ* + L* (b) for which colloidal bowls and dumbbells, respectively, first become alignable by an electric field , as a function of their shape parameters d/σ and L/σ, respectively. Here, d is the thickness of a bowl and L is the separation of the two composing spheres of a dumbbell. The bowls and dumbbells are built up of atoms on a simple cubic lattice with dimensionless lattice spacings , 2, 2.5, and 3. The temperature is , and the atomic polarizability is . The dots denote the minima in the graphs.
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Abstract
Selfassembly and alignment of anisotropiccolloidal particles are important processes that can be influenced by external electric fields. However, dielectric nanoparticles are generally hard to align this way because of their small size and low polarizability. In this work, we employ the coupled dipole method to show that the minimum size parameter for which a particle may be aligned using an external electric field depends on the dimension ratio that defines the exact shape of the particle. We show, for rods, platelets, bowls, and dumbbells, that the optimal dimension ratio (the dimension ratio for which the size parameter that first allows alignment is minimal) depends on a nontrivial competition between particle bulkiness and anisotropy because more bulkiness implies more polarizable substance and thus higher polarizability, while more anisotropy implies a larger (relative) difference in polarizability.
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