Abstract
ABSTRACTWe have applied the formalism of classical density functional theory to study the shape and the orientation of the density profiles formed by aspherical, ultrasoft particles. For simplicity we have considered particles with an elliptic shape, characterised by an aspect ratio λ. The 's are obtained via the minimisation of the grand-potential functional , for which we have used a mean-field format. The optimisation of is numerically realised in a free (i.e. unbiased) manner minimising the functional with respect to the density profile, which we have discretised in the unit cell of the lattice on 803 grid points. Keeping the temperature fixed and varying the chemical potential and λ, we have investigated the impact of these parameters on the density profile.
Highlights
It has become common knowledge that anisotropy is a relevant driving force in establishing and triggering self-assembly of colloidal particles.In the past decade, the effect of particle shape on the symmetry of high-density phases has been studied in considerable detail, especially in hard ellipsoids [1] and hard polyhedra where a range of liquid-crystalline, quasicrystalline, plastic-crystalline, and crystalline structures were reported. [2,3,4,5,6]
Email: gerhard.kahl@tuwien.ac.at and thermodynamic properties of condensed-matter systems [13,14,15]. In this contribution we demonstrate that density functional theory (DFT) allows to calculate non-trivial single particle density profiles ρ(r), as they obviously arise in ordered structures formed by aspherical particles
As discussed in [16], optimization with respect to the lattice vectors is of paramount importance in order to prevent the occurrence of local minima of the grand-potential functional such as defective configurations, which would otherwise be those most frequently observed as a consequence of the intrinsic periodicity of the density profile being incommensurate with the size of the box where it is sampled
Summary
It has become common knowledge that anisotropy is a relevant driving force in establishing and triggering self-assembly of colloidal particles. In a recent contribution by Pini et al [16] it was shown that present day computational power in combination with highly efficient and reliable numerical optimization techniques enable to perform the minimization of Ω with respect to ρ(r) in an unbiased manner This could be achieved by representing ρ(r) in a finite volume (e.g., in a lattice cell), discretized on a sufficiently fine grid (with typically 803 to 1003, or even more, grid points) in r-space, avoiding thereby an a priori bias on the shape of the density profile. During the past decade, (colloidal) particles that interact via ultrasoft potentials have often been viewed as “effective particles”, representing considerably more complex macromolecules with an intricate internal structure, consisting of hundreds or thousands of atomistic entities.
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