Recent Advances in the Theory and Simulation of Model Colloidal Microphase Formers

Abstract

This mini-review synthesizes our understanding of the equilibrium behavior of particle-based models with short-range attractive and long-range repulsive (SALR) interactions. These models, which can form stable periodic microphases, aim to reproduce the essence of colloidal suspensions with competing interparticle interactions. Ordered structures, however, have yet to be obtained in experiments. In order to better understand the hurdles to periodic microphase assembly, marked theoretical and simulation advances have been made over the past few years. Here, we present recent progress in the study of microphases in models with SALR interactions using liquid-state theory and density-functional theory as well as numerical simulations. Combining these various approaches provides a description of periodic microphases, and gives insights into the rich phenomenology of the surrounding disordered regime. Ongoing research directions in the thermodynamics of models with SALR interactions are also presented.

Communication: Microphase equilibrium and assembly dynamics

“…Regime (II) sees the emergence of void clustering, which in a sense complements the formation of particle clusters as density increases. This clustering is, however, seemingly distinct from that observed in SALR systems at even higher densities 3,23,24 Upon further lowering temperature, the void clusters become wormlike and eventually percolate, thus giving rise to an amorphous, bicontinuous microphase structure (III). The formation of these structures is again complementary to the particle clusters becoming wormlike and eventually percolating upon increasing the particle density.…”

“…Introduction -Microphases replace liquid-gas coexistence in systems for which interparticle (short-range) attraction is frustrated by (long-range) repulsion, i.e., for SALR interactions [1][2][3] . Beyond their mere aesthetic value, some of the resulting ordered and disordered structures of diblock copolymers have found uses as nanoscale templates and filters 4,5 .…”

“…Colloidal analogues, however, have thus far only given rise to disordered microphases, such as clusters and gels [6][7][8] . Recent advances describing the equilibrium behavior of model colloidal microphaseformers 9,10 confirm that such ordering should be thermodynamically possible 2,3 , but whether it is dynamically accessible remains an open question.…”

Spatially localized quasicrystalline structures

“…QCs are formed when the ratio of the two length scales is near particular values specified below. Two length scales can arise in other pattern forming soft matter systems due to the interaction of particles with short-range attraction and long-range repulsion [20,21] or other forms of frustration in the interactions [22]. Just as in the QC-forming systems of interest here, the liquid state static structure factor S(k) in the above systems has two distinct peaks, corresponding to the two different length scales, but their ratio is different from the values required for QC formation.…”

Effects of non-pairwise repulsion on nanoparticle assembly

“…For starters, the long-ranged van der Waals attraction becomes less important than shortranged interactions like H-bonds and the hydrophobic effect. This has inspired numerous studies of the competition between short-range attraction and long-range repulsion, where the repulsion is modeled using a repulsive Yukawa potential [7][8][9][10][11][12][13] . This qualitatively captures the effects of Coulomb repulsion screened by salt because the Yukawa potential emerges from the small potential limit of the Poisson-Boltzmann (PB) equation.…”