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40.Other choices for the definition of size parameter are possible, with the condition that it, together with the shape parameter, fixes the dimensions of the particle. For example, a possibility would be to define the size parameter as the diameter of the particle's circumscribed sphere. Qualitatively, this new definition does not cause any change to our results; quantitatively, we observe that the minima for rods shift to l/L ≈ 0.47 and those for platelets to L/l ≈ 0.32, while there is no change for bowls and dumbbells (since the size parameter remains σ and σ + L, respectively).
41.The reason why a lower lattice constant lowers L* or l* is two-fold: a lower lattice constant means that atoms interact more and hence will have a higher Δf; at the same time it also means that the atom density is higher and thus smaller dimensions are needed to achieve a certain number of atoms.

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Self-assembly 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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