# Non-equilibrium cluster states in colloids with competing interactions

*Entry by Max Darnell, AP 225, Fall 2011*

Reference:

**Title:** Non-equilibrium cluster states in colloids with competing interactions

**Authors:** Tian Hui Zhang, Jan Klok, R. Hans Tromp, Jan Groenewold and Willem K. Kegel

**Journal:** Soft Matter DOI: 10.1039/c1sm06570j (2011)

**Keywords:** colloid, gel, nucleation, self-assembly

## Summary

The authors examined a colloidal system in which there were competing short-range and long-range interactions. It has recently been found that such systems exhibit a stable cluster phase if low volume fractions of the particles are present. In this paper, the effects of varying attractive and repulsive strength were observed. In addition, at high volume fractions of particles, gelation is observed, which, like the clustering, is also dependent on attraction strength. By changing the strengths of attraction, the nucleation and rearrangement process can be controlled, leading to controlled gel formation.

## Methods/Results

The authors used fluorescently-labeled PMMA spheres in a mixture of cyclohexyl bromide (CHB) and cis-decalin as the colloid mixture. Here, the spheres, become slightly positively charged, which results in a long-range repulsion. Then, by adding polystyrene, the authors are able to introduce an attractive force as well, now resulting in competing interactions. Microscopy was performed on the colloid, as different volume fractions of the spheres were introduced. The figure below shows increasing volume fractions as one moves down the figure. It can be seen that at low-volume fractions, the spheres form clusters, but at higher volume fractions, the structures are more linear. The right half of the figure shows radius of gyration versus cluster size. One can see that indeed, as the volume fraction increases, the growth is more linear and even leads to branching of the structures.

The authors then used a model to predict the relationship between energy required for nucleation and cluster size. The first part of the figure below shows that there exists an ideal size at which these energies are minimized and that this energy increases with increasing strength of attraction. The second plot shows that the nucleation energy barrier decreases with increasing cluster size.

Finally, the authors showed that these colloids can form gel structures by tuning their attractions. Similar to the first plot, one can see that at low volume fractions(on the left), the aggregates are clustered, while at high volume fractions, the aggregates are more linear.

## Connection to Soft Matter

Colloids are an important aspect of soft matter physics, in part due to their ability to self-assemble into higher-order structures. This paper is relevant in that it examines different parameters that can be fine-tuned to achieve various self-assembled structures. By understanding these interactions, the prospect of building materials starting with particles and tweaking environmental conditions to control self-assembly becomes possible. Especially with the recent focus on gels for biomaterial applications, it also seems possible that biomolecules could be incorporated early in this gelation process, providing a new method of encapsulation for drug delivery.