The self-assembly of particles with isotropic interactions

Abstract

A generic field-theoretic model for the self-assembly of particles with isotropic interactions, mo tivated by ideas in DNA-mediated colloidal assembly, is presented. A simplest possible system of colloids in explicit solvent is examined to determine the ability of non-connected particles to form complex nanometre or micron scale equilibrium structures in the absence of confounding ki netic effects. It is found that non-trivial morphologies are possible and that, for this effectively one component system, these parallel the phases of diblock copolymer melts for certain parameter choices, despite the absence of connectivity or packing frustration in the model. An explanation for the morphological similarity between these architecturally disparate systems is given. For other parameter choices, it is found that meta-stable and defected phases become more common, and that similarity with block copolymer morphologies decreases.

An unconstrained DFT approach to microphase formation and application to binary Gaussian mixtures

“…Here, we will not try to elucidate the reason of such an interesting behavior, aside of the obvious remark that this system differs from block copolymers in three respects: First, there is no connectivity; second, its compressibility is non-vanishing; and third, particles of different species are more compatible (or less incompatible) with each other than those of the same species. The above observation that the same sequence of phases displayed by block copolymers has been reported also in fluids of unconnected particles with competing interactions 8,10 indicates that lack of connectivity alone is not sufficient to explain the behavior found here. We leave this point to future investigation.…”

“…As one moves out of this region by either decreasing or increasing the concentration, one meets first a gyroid phase, then a triangular phase of cylindrical rods, then a cubic bcc phase, and finally the homogeneous fluid. 25,26 It should also be remarked that recently effective DFT and SCFT approaches have predicted essentially the same sequence of phases in fluids with competing short-range attractive and longer-range repulsive interactions, [8][9][10] in which the inverse temperature and the density play the roles of the variables χN and c in block copolymer melts (in Ref. 9, a Fddd phase was found instead of the gyroid, but that was traced back in the same paper to the approximations inherent to the effective DFT).…”

“…The phase diagram of this model fluid has already been thoroughly studied in two dimensions. 6,7 In three dimensions, some general features of the phase diagram were obtained by combining numerical simulation and integral-equation theories, 70 and a detailed investigation of the structure of microphases was subsequently carried out by means of effective free-energy functionals, [8][9][10] which uncovered essentially the same sequence of microphases (bcc-triangular-gyroidlamellae) previously found in block copolymer models. 25,26,38 It would be interesting to see whether application of the present DFT will also predict the same scenario.…”

“…The feasibility of a purely numerical minimization in three dimensions was in fact already shown in the application of the self-consistent field theory (SCFT) originally developed for block copolymers 2,25 to amphiphilic molecules 30 and particles with competing attractive and repulsive interactions. 10 In those studies, the frequent occurrence of defective structures was also remarked.…”

“…When the competition between attraction and repulsion is strong enough, the gas-liquid phase transition is suppressed, and the phase diagram of the fluid has been shown to present microphases in both two [5][6][7] and three dimensions. [8][9][10] Irrespective of its specific nature, the attitude of a onecomponent system to form microphases ultimately rests upon a property of the effective interaction between its constituents: if the Fourier transform of the interaction has a negative minimum at some non-vanishing wave vector k, then density modulations with characteristic length d ∼ 2π/k will be strongly favored over the other Fourier components of the density profile and can lead to inhomogeneous phases under suitable thermodynamic conditions. 1 Another instance of this rather general scenario which has gained considerable attention in recent times is cluster formation in particles interacting via isotropic, bounded repulsive potentials of ultrasoft type such that not only are the overlaps between particles allowed but also the resulting energy penalty is very low.…”