Rheology is concerned with understanding how materials flow. A traditional mechanical rotational rheometer measures the rheological properties by applying a stress to the sample and detecting the response to that applied perturbation in various geometries (for example ‘cup and bob’, or ‘cone and plate’). More recently, microfluidics allow access to the ultra-high shear rate regime with the added benefit of low sample volume requirement to still obtain information on the bulk sample properties.

An entirely different approach is microrheology by light scattering. Here, the diffusion of tracer particles is observed to deduct the viscoeleastic properties for the rheological characterization of low viscosity and weakly-structured complex fluids. Technically this involves calculation of the mean square displacement (MSD) of the tracers as a function of time. The MSD can be converted into a complex viscosity η*, the storage modulus G’ and the loss modulus G’’.

In an ideal Newtonian liquid the mean square displacement is given by simple Brownian diffusion, i.e. linearly in time proportional to the Diffusion coefficient D

$<\Delta r^2(t)>=6Dt$

Once the mean square displacement is determined from the correlation function, it can then be turned into the complex modulus in Fourier space

$G^*(i \omega) = \frac{k_B T}{\pi a i \omega <\Delta r^{2}(i \omega)> }$

The details of the mathematics are described in a white paper and an advanced technical note. For practical tips on how to perform these measurements, see the special chapter on this topic in the Zetasizer Accessories Manual which by default is installed on your computer at

 Start - All Programs - Malvern Instruments - Zetasizer Software - Manuals
      - Man0487-1.1 (Zetasizer Nano Accessories Guide).pdf

Performing a microrheology experiment involves measuring the tracer particles in buffer/dispersant, and then in the sample of interest. Optionally, a zeta potential measurement of the tracer particles in buffer and in the sample helps to confirm whether interactions between the sample material and the tracer particles take place (and would thus lead to an incorrect interpretation of the microrheology data). For a variety of samples, Latex Nanosphere Size standards are suitable, other materials (like biomolecules or proteins) may require alternative surface chemistries.  As an example, for bovine serum albumin (BSA) carboxylated melamine particles such as MEL0665 and MEL1180 have been found to be viable tracers. As a potential universal tracer PEGylated polystyrene which is sterically stabilized may be suitable so long as the PEG coating is pretty dense and sufficiently thick.

### Does the tracer particle size matter?

Yes, it is very possible that tracer size will have an influence on the observed behavior, especially when testing a gel-like network. The probe size must be larger than the pore size of the underlying microstructure, and results obtained using probe sizes larger than the typical  pore dimension should all overlay.

### How to try out the micro rheology features

If you already have a Zetasizer Nano ZS or ZSP, the feature can be evaluated (30-day free trial) in the current software under

Tools – Options – Feature Keys – Microrheology Features – Install license key

If the “install license key” is greyed out, then either a functional key is already installed, or the trial license for that computer has expired.

To see and try out the software features, open the “Example Results.dts” data file and select a microrheology record (select the ‘Summary’ workspace, for example record #88), then go to Tools – Utilities – Microrheology Utilities to open a new window displaying taps for mean square displacement, viscoelastic moduli, complex viscosity – and various fitting model tools (context sensitive, generalized Newtonian. Complex viscosity: power law, Cross model, Sisko model; viscoelastic moduli: G” one element Maxwell, G” two element Maxwell, power law; mean square displacement: power law). To the left is an example screen shot showing the fit of microrheology data to the G” two element Maxwell model, the fit range can be adjusted by dragging the upper and lower range indicators (red triangles on the x-axis).

### How to check for feature keys

There are several feature keys and here are two possibilities to list a summary of the state of all keys that are currently installed on your computer:

• In the Zetasizer software go to Tools – Options – Feature Keys – Feature Keys Summary    or
• Double-click on the “Features” symbol in the bottom right corner of the Zetasizer software

This will open a window with a summary of the currently installed feature licenses. It may for example list Microrheology Features: None when the special micro rheology features are not present in the software.

Further Resources

Previously