Ordered structures formed by ultrasoft, aspherical particles

Abstract

We have applied the formalism of classical density functional theory to study the shape and the orientation of the density profiles ρ(r) formed by aspherical, ultrasoft particles. For simplicity we have considered particles with an elliptic shape, characterised by an aspect ratio λ. The ρ(r)'s are obtained via the minimisation of the grand-potential functional [ρ], for which we have used a mean-field format. The optimisation of [ρ] 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 80 3 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.

On the degeneracy of ordered ground state configurations of the aspherical Gaussian core model

“…However, it is possible that in this respect the specific form of the interaction may play some role, as seems to be the case, for instance, for the aspherical GEM-4 particles of Ref. [16]. We plan to come back to this issue in the near future.…”

“…Moreover, it is not peculiar to the Gaussian potential, and could be equally well applied to different soft-core interactions, including the cluster-forming potentials of the so-called Q ± class [19] such as the generalized exponential model of order four (GEM-4) considered in Ref. [16], even though the resulting phase diagram will of course be different from that described in this contribution.…”

“…The study by PS [5] and a subsequent contribution by Nikoubashman and Likos (NL) [12] on the very same system have revealed important features which apparently have not been sufficiently noticed within the community, so far: PS reported about the emergence of "topologically different degenerate structures", whereas NL observed that, for each value of λ, the system undergoes a phase transition at a density which is related to that of the fcc-bcc transition expected in the spherical system with λ = 1 by a simple scaling law. Motivated by our own recent investigations of the ordered structures formed by yet another ultra-soft system [16] (based on classical density functional theory [13][14][15]) where we have encountered -similar as PS [5] -unexpected degeneracy issues, we have re-considered the problem from scratch. Eventually we provide in this contribution a formally exact evidence for the two following facts: (i) the energy of the aspherical system can be mapped exactly on the energy of the related spherically symmetric system; (ii) further, we rigorously show that an infinite number of ordered ground state structures must exist for the aspherical system.…”

Unraveling the Conformations of Backbone and Side Chains in Thermosensitive Bottlebrush Polymers

“…The asphericity for the entire BBP, the backbone, and side chains are listed in parentheses next to the snapshot. The asphericity values of 0 and 1 represent the sphere and rod geometry, respectively. ,, The asphericity for the overall BBP and side chains decreases when grafting density is increased from ∼16 to ∼50% at 290 K (below the LCST). This suggests that the shape of BBP is more spherical at 50% grafting density as compared to ∼16%.…”

Deformable hard particles particles confined in a disordered porous matrix

“…However the situation is different for the mobile, fluid particles: in particular in the realm of soft matter physics these particles are usually viewed as coarse-grained, "effective" models whose shape can in principle vary as a consequence of the internal dynamics of the constituent entities of such molecules. In the vast majority of scientific investigations such "effective" particles are considered as spherical; still, in a few contributions the non-spherical shape of these molecules has been taken into account, for instance, in polymers [37][38][39][40], dendrimers [41,42], or patchy particles [43]. Within the framework of "effective" particles it is therefore not surprising that the shape of such "effective" particles adopt their shape to their immediate surrounding -be it another mobile particle or the rigid matrix.…”