# Difference between revisions of "Gelation as arrested phase separation in short-ranged attractive colloid-polymer mixtures"

Original entry: Naveen Sinha, APPHY 226, Spring 2009

## Gelation as arrested phase separation in short-ranged attractive colloid-polymer mixtures

Emanuela Zaccarelli, Peter J Lu, Fabio Ciulla, David A. Weitz, and Francesco Sciortino

J. Phys.: Condens. Matter 20, 494242 (2008).

Soft matter keywords: gelation, phase separation, colloid, polymer, spinodal decomposition

### Summary

Gels are a ubiquitous presence in the world of soft matter. Understanding the gelation process has wide-ranging industrial applications, such as food and cosmetics, where the stability of the product is crucial. The authors used a colloid-polymer mixture as a model for these systems. The micron-sized particles are in the ideal size range, in which they are large enough to view under an optical microscope, yet small enough to be affected by fluctuations with energy comparable to kBT. The process of gelation occurs when networks of particles span the entire fluid. When these networks become arrested, they retain their form and are able to support shear stress. The present study uses a combination of confocal microscopy and numerical simulations to verify a new theory for how phase separation can lead to gelation. This process is independent of the specific interaction potential between the colloid particles, making it more widely applicable.

### What does this have to do with soft matter?

• What is the experimental system? The authors studied a solution of PMMA beads (wth dye) in a solution of polymers. The size of the particles was 560 nm +/- 10 nm. The dye enabled confocal microscopy to track the positions of every single one of the particles. The polymers produced the attraction between these particles through a depletion force. In the reconstruction below, the monomers are translucent, the small clusters are red, and the spanning network is blue.

• How was this system modeled? The colloid particles were simply modeled as hard spheres with radius a. These long-chained molecules were modeled in two different ways: (1) with other polymers they behaved as interpenetrating particles in an ideal gas and (2) with colloid particles they behaved as hard spheres with radius ra.
• What is the phase space of the state space of the system? The three controllable parameters that determined the behavior of the system were: (1) $\phi$, the volume fraction of particles, (2) $\eta$, the ratio of equivalent polymer diameter (ra) to the colloid particle radius (a), and (3) U, the strength of the interaction potential.
• At small volume fractions, the gelation is driven by Diffusion Limited Aggregation of clusters.
• At large volume fractions, the system behaves as a colloidal glass.
• What causes the gel to form? The authors propose the following mechanism: (1) the system undergoes spinodal formation into a gas-like region (low colloid density) and a liquid-like region (high colloid density), (2) the denser region is unstable and undergoes large fluctuations, and (3) one or more of the large scale fluctuations spans the system and becomes arrested, leading to a gel. Normally, monomers and small clusters are continually in flux, but these arrested fluctuations are stable.

My take-home message from this paper is that gel-formation is a heterogeneous process, in which different "phases" can separate and lead to large-scale, qualitative changes. I would be interested in finding out how these results relate to colloids used in industry.

written by Naveen N. Sinha