The picture below is taken by Tony Dinsmore with our confocal microscope, which he uses to study the relationship between microstructure and bulk viscoelasticity of weakly aggregating systems.

Introduction to Weakly Aggregating Systems Weakly aggregating systems are systems where the energy of interaction between the colloidal particles are of the order of thermal fluctuations, kT. We first begin with hard sphere particles made up os Polymethylmethacrylate (PMMA) suspended in a mixture of organic solvents, decalin and cycloheptyl bromide. This index and density matches the suspension which enables visualization and prevents sedimentation of the constituent colloidal particles. We then add non-adsorbing polystyrene polymer (PS) to the suspension, which induces attraction between the particles through the well-known depletion interaction. Both the depth and range of the interaction potential can be tuned at will by changing the polymer concentration and size. For deep quenches of polymer, we see amorphous aggregates of particles, and these aggregates show no crystalline order. These aggregates seem to fall into classes : fluid clusters (where the aggregates are still free to diffuse around) and solid clusters (where the aggregates themselves are joined together to form a space spanning gel. The two pictures below demonstrate the two classes very nicely.

Bulk viscoelasticity

The two pictures above were taken at the same energy of interaction, but different colloidal volume fractions. The solid cluster phase must show a bulk elastic modulus, as it is essentially a space spanning gel. We have performed bulk viscoelastic measurements on these depletion gels, and find some striking results.

The figure above shows the elastic plateau modulus as a function of the reduced volume fraction (phi-phi_c). In the above curve, both the depth and range of interaction have been varied. There are two classes of power law exponents we see, that is solely a function of the range of the interaction potential. For the short range potential, nu=3.3, while for the long range potential, nu = 2.1. The observed exponents are consistent with there being two mechanisms for bearing stress in these gels, which are: bond stretching and bond bending . We postulate that long range potentials interact by bond stretching while short range potentials interact by bond bending. This hypothesis can be checked by looking at the microscopic dynamics of single particles, which brings us to :

Microscopic dynamics

The stress in the weakly aggregating gels is borne by chains comprising of the colloidal particles. Thermal fluctuations cause the particles in the chains to move about their mean positions. With the confocal microscope, we can observe the fluctuations in the interparticle separations, and this gives us information about how strong the chains are. We find different behavior, depending on the range of interaction, as shown below.

Long-range potential

Short-range potential

The graphs show that the spring constant of a chain has a spatial dependence that is a function of the range of the interaction potential. We are at present attemting to relate the spatial information present in the confocal measurements with the bulk measurements through simple scaling arguments.

Some Useful References

Publications in this group on weakly aggregating systems:

• "Scaling of the viscoelasticity of weakly attractive particles"
  V. Trappe and D. A. Weitz, Phys. Rev. Lett. 85, 449 (2000).

• "Glass-like kinetic arrest at the colloidal gelation transition"
  P. N. Segre, V. Prasad, A. B. Schofield, and D. A. Weitz, Phys. Rev. Lett. 86, 6042-6045 (2001). .

• "Jamming phase diagram for attractive particles"
  V. Trappe, V. Prasad, Luca Cipelletti, P.N. Segre and D. A. Weitz, Nature 411, 772-775 (2001).

• Witten, Thomas A., Structured Fluids. Physics Today. 21-28 (July 1990).
• W. B. Russel, D. A. Saville, and W. R. Schowalter, Colloidal Dispersions, Cambridge University Press, Cambridge (1989).

Rheology:

• Ronald G. Larsen, The Structure and Rheology of Complex Fluids, Oxford University Press, New York (1999).
• Christopher W. Macosko, Rheology: Principles, Measurements and Applications, Wiley-VCH, Inc. , (1994).

Weitz group links:

Contact info:

Vikram Prasad
prasad@deas.harvard.edu
Department of Physics
Harvard University
Engineering Sciences Laboratory
40 Oxford Street
Cambridge, MA 02138