LS Instruments

Microrheology is a rheological method that uses colloidal tracer particles, dispersed within a sample, as probes. As discussed in the previous sections, tracer particles may be naturally present in the system, as in suspensions and emulsions, or added to the medium under interest. The motion of the tracer particles reflects the rheological properties of their local environment.

Most microrheology methods are said to be "passive", i.e., they exclusively rely on thermal energy (i.e. Brownian motion) to displace the tracer particles within the sample. Some specialized methods (e.g. optical tweezers, magnetic microrheology) are instead said to be "active". In the case of active microrheology, an external force (optical, electric, or magnetic) moves the tracer particles with energies that are stronger than the thermal energy  . The advantage of active methods is that the amplitude of the particle displacements can be controlled, which allows performing of both linear and non-linear rheology. On the other hand, passive microrheology is ideal for measurements in the linear viscoelastic region (LVR) because the weak thermal energy,  , ensures small amplitudes in the displacement of the tracer particles.

Microrheology can be further differentiated by the method used to measure the MSD of the tracer particles. The most common techniques are particle tracking, and DWS microrheology.

Many materials probed through DWS microrheology are complex fluids that exhibit both viscous and elastic behaviors. For this reason, they are called viscoelastic materials. Their response typically depends on the length and time scale probed in the measurements. A natural way to describe viscoelastic behavior is to use the Generalized Stokes-Einstein relation:

This equation allows calculation of the frequency-dependent storage G′(ω) and loss G″(ω) moduli from the measured MSD. The values obtained for G′(ω) and G″(ω) from microrheology performed on a gelation solution containing tracer particles are shown in the following figure.

Fig. 7: MSD from freely diffusing (red) and trapped (blue) particles in a gelatin sample, at high or low temperatures (respectively). b) Storage G′(ω) and loss G″(ω) moduli from freely diffusing (red) and trapped particles (blue). c) Kelvin-Voigt model consisting of a spring and a dashpot connected in parallel.

At high temperatures (e.g. 50 °C, red line), the MSD is linear as in a pure liquid, and G″(ω) is proportional to the frequency ω, whereas G′(ω) is very small and out of plotting range. However, at low temperatures (blue lines, 15 °C), the MSD shifts to a non-linear behavior, and G′(ω) dominates G″(ω) over an extended frequency range; only at very high frequency, a cross-over to a domain where G″(ω) is larger than G′(ω) is observed. Such behavior may be approximately described by the Kelvin-Voigt model (Fig. 2c), which consists of a spring and dashpot connected in parallel. The spring describes the elasticity of the gelatin network, whereas the dashpot represents a viscous damper that describes the dissipative effect of water around the gelatin network.

The microstructure of the sample can be studied by DWS in a perfectly analogous way as in mechanical rheology – with the usual advantages of DWS in terms of speed, sample volume, and frequency range.

Reference: E. M. Furst, T. M. Squires, Microrheology, Oxford University Press, (2017)