by Luca Cipelletti and Suliana Manley
Download paper (PDF) (Phys. Rev. Lett. 84, 2275 (2000)).
 
 

Aging is a quite general phenomenon which occurs in a wide variety of off-equilibrium materials, such as glasses. Aging affects the properties (mechanical, rheological, magnetic...) of materials. The most direct way to assess aging is to measure the change in the sample dynamics. For polymers and colloidal systems, this can be nicely done by measuring the dynamic structure factor f(q,t) by means of dynamic light scattering (DLS).

There are several tricky issues involved in using DLS techniques for measuring the aging. This explains why, to date, theory and simulation works abound, while experiments are scarce. To address these issues, we use a novel, CCD-based low angle dynamic light scattering apparatus to take "snapshots" of the dynamics, thereby probing directly the aging. Read this page to discover our fascinating findings (scaling behavior, analogies with glassy systems...).
 
 

 
 

The system we study is a gel composed of interconnected fractal aggregates, formed by aggregating buoyancy-matched polystyrene colloids.

 
 
 

For a typical Diffusion Limited Cluster Aggregation, the clusters grow nearly monodisperse in size. This results in a (broad) peak in the static light scatterng (SLS), as can be seen in the figure to the left. Note that, after a couple of hours (blue curves), the SLS curves bearly change in the next 24 h. The system has gelled and the clusters form an interconnected network.   However, the gel slowly evolves. Aging leads to a compaction of the structure (see the increase ofthe fractal dimension in the inset) and to the formation of large-scale inhomogeneities (see the 10-fold increase of I(q) at very low q in thelast two data sets).   Note the unusually low q that our apparatus probes. This corresponds to length scales up to tens of microns.

 
 

After several days, inhomogeneities can be so big to be seen by naked eye! The cell to the left is about 20x40x2 mm. It contains a 23-days-old gel. No lumps were visibleat the beginning, and the gel looked nicely uniform.

 
 

How does the aging affect the gel dynamics? The plot to the left shows the evolution of f(q=6000cm-1,t) with gel age. The relaxation time increases by more than 2 orders of magnitude! The slowing down of the dynamics is typical of aging phenomena. It has been observed in simulations of structural and spin glasses.  Note that the relaxation time of the correlation functions is as large as many hours. Such long delays are not accessible to a traditional DLS setup. In our apparatus, we take advantage of the "multispeckle" technique to overcome this limitation.

 
 

All data can be scaledonto a master curve, by scaling time with respect to the relaxation time tf (see inset). Asymptotically,tf grows nearly linearly with sample age tw.  These results are similar to what is found in simulation works on glasses. This analogy is very intriguing, since people are uncovering many similarities between the glass transition and gelation.

 
 

What is the physical mechanism leading to the aging of the colloidal gels? We get a clue from the very peculiar shape of the correlation functions.   The graph to the left shows the correlation functions measured simulataneously for different q vectors. Note the scaling on a straight line when plotting ln[f(q,t)] vs (qt)3/2 (inset). This indicates  f(q,t) = exp[-(t/tf)3/2], with tf(q) ~ q-1.  Robin Ball came up with a nice model to explain the data. The model is based on the (local) shrinking of the gel. This is somehow similar to the shrinking of polymer gels.

 
 

You can read about the details of the model in our preprint.   Here are some images to demonstrate how the gels shrink macroscopically, when detached from the cell walls. (To detach the gel without breaking it, we spun the cell).  Undisturbed gel can not shrink macroscopically, due to the adhesion to the cell walls.  However, they can shrink locally, since on small length scales they are inhomogeneous. It is this local shrinking that causes the decay of the dynamic structure factor.    We believe that the shrinking is driven by particle sintering, due to the strong Van der Waals attractive forces acting on the relatively soft polystyrene particles.

 
 

To test the uneversality of the aging behavior in colloidal gels, we plan to use colloids of different materials.   Most colloids can not be buoyancy matched, and the tenuous gels that we study would collapse under their own weight.  Therefore, we plan to do experiments under micro-gravity conditions, on the Internatonal Space Station. This is part of the NASA-sponsored Physics of Colloids in Space (PCS) project.

 

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