Colloidal Aggregation

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This image shows an aggregate of carbon black in oil.

Temperature dependent structure of carbon black aggregates in oil:

Carbon black dispersed in oil (with dispersant present) is a model system for the study of the rheological properties of colloidal aggregates. We study such carbon black dispersions using oscillatory and steady shear rheology and video microscopy. The morphology of the aggregates changes with increasing temperature from a compact to a more tenuous structure. Since the low-temperature, compact aggregates do not span the sample, a fluid-like rheology is observed. However, the high-temperature, tenuous structure forms a gel network which spans the sample, resulting in a solid-like rheology. Therefore, a sol-gel transition is observed as a result of simply changing the temperature. This behaviour can also be seen by staying at a fixed temperature and varying the volume fraction of the constituent carbon black particles, where at a critical volume fraction, we see a transition from fluid to solid like behaviour. The structural differences can be explained by means of the 'sticky' hard sphere or Baxter model for the interactions between the constituent carbon black particles. This model has an infinitely deep potential with zero width, with a single free parameter, defined as the stickiness of the potential.

The above graph we like to call the Trappe master curve and is a master curve for the frequency dependent modulii (both loss and storage) of carbon black dispersions in oil. The surprising result here is that the frequency dependent moduli at different volume fractions of carbon black can be scaled onto a single curve, where a is the frequency scale factor and b is the amplitude scale factor.

Approaching the critical point from the left, we see that the viscosity diverges as we near the transition. One could draw an analogy with the glass transition where similar behaviour is seen, although with differing exponents. Also, the modulus (or susceptibility) of the solid-like dispersions diverges as the inverse of the reduced volume fraction, not unlike second order phase transitions, where the divergence is a function of the reduced temperature.

The elastic modulus shows a strong power law dependence on volume fraction, and the power law of 4.1 is not inconsistent with those observed on irreversible aggregate where the DLCA model holds (DLCA = diffusion limited colloidal agggregation). However, unlike the DLCA model, the power laws here are obtained relative to a critical point.

This work was started by Veronique Trappe during her post-doc at with the Weitz Group at UPenn. Vikram Prasad is currently extending her work to other interesting systems. Check out the more current work here.