# Difference between revisions of "Microscopic Structure and Elasticity of Weakly Aggregated Colloidal Gels"

Original entry: Warren Lloyd Ung, APPHY 225, Fall 2009

"Microscopic Structure and Elasticity of Weakly Aggregated Colloidal Gels"
A. D. Dinsmore, V. Prasad, I.Y. Wong, & D.A. Weitz, (2006).
Physical Review Letters.

## Soft Matter Keywords

colloids, colloidal gel, confocal microscopy

Figure 1: Reconstruction of confocal images of a colloidal gel to obtain a 3D model. Blue spheres donate the shortest path between two spheres (red and blue stripes), while red spheres indicate the second shortest path between the same two spheres. The inset shows a single section of the confocal stack taken of this colloidal gel.
Figure 2: (a) Pair Distribution Function (b) Probability of finding a secondary path between particles based on the length of the shortest path between the particles.
Figure 3: (a) Spring constant of colloidal gel (b) N dependence of spring constant.
Figure 4: Scaling of spring constant for colloidal gel with short range interaction.

## Summary

The authors examine colloidal gels using confocal microscopy to determine details about the structure of the gels and their elasticity. Colloidal gels are formed by creating an attractive force between large colloidal particles and allowing them to aggregate into a gel, which is essentially an elastic solid with a finite yield stress. By labeling the colloid particles with a fluorophore, it is possible to visualize the microstructure of a colloidal gel (see Figure 1). In addition to making observations about the gel's structure, Dinsmore et al. examine the dynamic behaviour - in particular, the elastic modulus - of the chains that make up the gel and compare their results with the established theory, with a number of noteworthy results.

## Soft Matter Discussion

In this experiment, the colloidal particles are sterically-stabilized poly(methyl methacrylate) (PMMA) spheres. Gels are formed by adding molecules of polystyrene with a known radius in solution. These polystyrene molecules induce a depletion attraction due to the osmotic pressure between PMMA spheres in regions, from which the polymer molecules have been excluded.

Colloidal gels are interesting materials in that they can provide some resistance to shear stress similar to an elastic solid, but once they yield, they flow easily, much like a liquid. The formalism used to describe colloidal gels is very similar to that used to describe polymers, and qualitatively has many similar features. Below their correlation length, $\xi$, these colloidal gels are fractal, while at larger length scales they are mostly homogeneous.

The PMMA spheres are labeled with a fluorescent rhodamine dye to allow them to be imaged using a confocal microscope. The 3D reconstructions of the image, which are generated, can be analyzed to obtain models of the gel's structure. This analysis yields a measurement of the fractal dimension of the colloidal gels, which agrees with the specific mechanism of irreversible cluster-cluster aggregation for formation of these gels (see Figure 2 for the radial distribution of particles, g, which relates to the fractal dimension). Qualitatively, the structure is shown to be a network of chains, which intersect at various points.

By observing a particular region over time, it is possible to observe the fluctuations in distance between particles of the colloidal gel due to thermal energy. Averaging over these fluctuations yields a probability density, whose local curvature (small deviations from a particular length) corresponds to the spring constant of the chains connecting the observed particles (Figure 3a). For long range interactions, the spring constant depends on the number of colloidal particles between two particles at the cross-links in the network. This is contrary to the theoretical expectation that the spring constant should go as the inverse of the square of the perpendicular distance between these particles. On the other hand, for systems with short range interactions, the expected scaling is produced (Figure 4). Note, the range of these interactions is determined by the radius of the soluble polymers added to the system. This quantitative distinction between short and long range interactions is unexpected, and seems to be indicative of a model, in which short-range interactions create bonds, which are prevented from bending.

## Applications

The techniques laid out in this paper are generally applicable to a large range of interesting problems in soft matter. The ability to visualize networks of soft materials gives insight into the behaviour of such materials, which can be compared with theoretical predictions of structure. It also motivates models, which explain the results obtained with other methods, such as rheological techniques.

Using microscopy to observe the dynamics of the particles within the network can be applied to a range of other interesting systems in soft matter as well. For instance, studies are being undertaken on networks of biopolymers, such as actin and microtubule networks used by cells, to elucidate their material properties in ways that are impossible with other methods.