Structural rearrangements that govern flow in colloidal glasses

Peter Schall, David A. Weitz, Frans Spaepen Science 318, 1895 (2007)

Colloid, Glass

Experiment

The authors created a glass out of silica spheres $1.5 \mu m$ radius spheres. The spheres were collected on a coverslip by centrifrugation at a packing faction of 0.61, which is higher than needed to created a glass and at a height of $42 \mu m$. A water-dimethylsulfoxide-fluorescein mixture was used to index match the spheres and then to contrast the spheres against the solvent. Then with the top stabilized, the coverslip at the bottom is sheared at rates about $10^{-5}s^{-1}$. The authors then recorded 3 Dimensional stacks using confocal microscopy.

Diagram of experimental setup.

The stacks revealed how the colloidal glass rearranged over the course of 20 minutes. The authors find that the strain is oscillatory, which they attribute to brownian motion. To confirm this, the authors analyze the glass in small cubic sections and measure the elastic energies. From this, they find that the distribution is exponential as indicated by the linearity of the semi-log graph in Figure 2.

Graph of relative frequency vs energy.

The use what appears to be a Maxwell-Boltzmann distribution to associate the frequency to the energy, temperature and shear modulus ($\mu$,) $ln(f(E)=\mu \frac{E}{\mu k_B T}$. Using this, the shear modulus is calculated to be one half of a value previously measured in a colloidal glass. The authors interpret this as confirmation that the oscillations in strain are thermally induced.

A key point is that the thermally oscillations aren't reversible and create rearrangements in the glass. The cumulative strain after twenty minutes was graphed for a vertical section of the glass. From, it is seen that localized regions of large strain persist and that these regions do not lead to macroscopic strain.

Cumulative Strain.

The authors also applied positive shear strain which indicated that average displacement in y increased nearly linearly in z.

Graph of strain in z versus y.

The macroscopic shear strain was found to be $\gamma = 0.03$ or $10^{-5}\frac{1}{s}$. The externally applied shear strain also produced localized regions of strain. Also there are regions where shear strain is opposite to the applied strain (blue).

They find a "shear transformation zone", a local region where opposite strain accumulates. Since high local shear is associated with the creation of this zone, the authors conclude that its thermally induced. Simultaneously, four zones of negative shear surround a region of high shear. The authors find that "the shear strain is constant at small r, decays as $r^{-3}$. The energy cost associated with the zone is found to be $E_f=20.5k_BT$ and the activation volume is $7.5\mu m ^3$, which is four times the volume of a single particle.